Answers
Answer:
m = -3x = 6Step-by-step explanation:
1)
[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]
____
2)
[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]
Related Questions
Mrs. Pender shows her students 2 sticks measuring 6 inches and 2 sticks measuring 8 inches. She asks the students to arrange the sticks to make a two-dimensional figure with the greatest possible area. The ways in which Anna and Reggie organize the sticks are shown. Which statement comparing the areas of the figures is true? The areas are the same because . Reggie’s shape has greater area because . Reggie’s shape has greater area because . Anna’s shape has greater area because .
Answers
Answer:
its d
Step-by-step explanation:
if im wrong then sorry :(
Answer:
A
100% Correct ANSWER. Pls, give me brainliest. Thank You!
The points (1, r) and (4, -13) lie on a line with slope – 3. Find the missing coordinate r.
Answers
The value of missing coordinate "r" is -4
Solution:
Given that,
The points (1, r) and (4, -13) lie on a line with slope – 3
To find: missing coordinate r
The slope of a line is given by formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Where, "m" is the slope of line
Here in this sum,
m = -3
[tex](x_1, y_1) = (1, r)\\\\(x_2, y_2) = (4, -13)[/tex]
Substituting the values in formula,
[tex]-3 = \frac{-13-r}{4-1}\\\\-3=\frac{-13-r}{3}\\\\-9 = -13 - r\\\\r = -13+9\\\\r = -4[/tex]
Thus the value of missing coordinate "r" is -4
A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the pentagon greater than 26 centimeters?(1) The area of the circle is 16π square centimeters.
(2) The length of each diagonal of the pentagon is less than 8 centimeters.
Answers
Answer:
Step-by-step explanation:
Check the attachment for solution
Every day a new frog is born weight grams and grows at a rate of 10 grams/day, maxing out at 100grams in 10 days. On day n, what is the total weight of the frog community?
Answers
10n * f where f is the number of frogs in that community.
Step-by-step explanation:
The growth rate is given as 10g /day
For 10 days, the weight in grams will be 10*10 =100 grams
This means that for n days, the weight gained by a new frog will be; n*10 g
=10n grams
Lets assume the frog community has a population of f frogs, then total weight of the frog community will be;
10n * f where f is the number of frogs in that community.
Learn More
Multiplication in equations :https://brainly.com/question/11171579
Keywords : frog, born, weight, grams, rate, grows, total weight, community
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In year 1, nominal GDP for the United States was $2,250 billion and in year 2 it was $2,508 billion. The GDP deflator was 72 in year 1 and 79 in year 2. Between year 1 and year 2, real GDP rose by:
Answers
Answer:
1.6%
Step-by-step explanation:
The real GDP is given by the nominal GDP divided by the GDP deflator, the real GDP for year 1 and year 2, respectively, were:
[tex]GDP_1=\frac{2250}{0.72}\\GDP_1=\$3,125\ billion\\\\GDP_2=\frac{2,508}{0.79}\\GDP_2=\$3,174.68\ billion[/tex]
The percentage change in GDP is:
[tex]P=\frac{3,174.68-3,125}{3,125}\\ P=0.016=1.6\%[/tex]
Between year 1 and year 2, real GDP rose by 1.6%.
Using a metric line, convert the following metric measurement. (Remember to use the same number of significant figures as in the original measurement.) 505 kL expressed in La. 50,500 Lb. 505,000 Lc. 5,050 Ld. 50.5 L
Answers
Answer:
B
Step-by-step explanation:
This question is asking to make a conversion from kilolitres to liters.
There is a total of 1000L in 1kL.
Hence to make the conversion from KL to L , we have to multiply the KL by 1000. Hence, for 505KL, its equivalent measurement in L would be 505 * 1000 = 505,000
Hence, 505kL expressed in L is 505,000
Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping side AB to side DC. What is sin(angle ABC)?
Answers
Final answer:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder.
Explanation:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Since the volume of the cylinder is given as 6, we can use the formula V = πr^2h to find the height of the cylinder. Plugging in the values, we get 6 = πr^2h. Since the radius of the cylinder is half the length of side AB, which is 3, we can solve for h to find that h = 4/π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder. Plugging in the values, we get θ = 6π/3 = 2π.
line passes through the points (3 comma 19 )and (7 comma 23 ). Write a linear function rule in terms of x and y for this line.
Answers
Answer:
[tex]y=1x+16[/tex]
Step-by-step explanation:
Two given points are (3,19) and (7,23)
f(x)=mx+b
slope is m and b is the y intercept
[tex]slope m =\frac{y_2-y_1}{x_2-x_1} =\frac{23-19}{7-3} =1[/tex]
slope m= 1 (3,19) is (x1,y1)
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-19=1(x-3)[/tex]
[tex]y-19=1x-3[/tex]
Add 19 on both sides
[tex]y=1x+16[/tex]
Final answer:
The linear function rule for the line passing through the points (3, 19) and (7, 23) is found by calculating the slope (which is 1) and using the point-slope form to derive the slope-intercept form y = x + 16.
Explanation:
To write a linear function rule for a line that passes through the points (3, 19) and (7, 23), we need to calculate the slope of the line and use the point-slope form to write the equation.
Finding the Slope (m)
Using the formula for the slope m = (y2 - y1) / (x2 - x1):
m = (23 - 19) / (7 - 3) = 4 / 4 = 1
We can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is a point on the line:
y - 19 = 1(x - 3)
Simplifying this equation to the slope-intercept form (y = mx + b), we get:
y = 1x + 16
Therefore, the linear function rule in terms of x and y for this line is y = x + 16.
A national polling organization wants to estimate the percentage of all teenagers who believe social security will 'be there' for them. The organization surveys a random sample of 1500 teenagers, and 37% of this sample says that they believe social security will 'be there' for them. In this survey, what is the population of interest?
A) The people in the sample who believe social security will 'be there' for them.B) All teenagers.C) The 1500 teenagers who were surveyed.D) Teenagers who believe social security will 'be there' for them.
Answers
Answer: B) All teenagers.
Step-by-step explanation:
In statistical survey , a population is a large group of individuals that share some similar characteristics according to the researchers's point of view or the demand of the study.
When the population very large , then he take a sample of population that represents the whole population.
For example : If a researcher wants know the average weight of women in the university , he will need the data of all women in university which is the population for this study.
As per given : A national polling organization wants to estimate the percentage of all teenagers who believe social security will 'be there' for them.
Here , the population of interest : All teenagers.
Sample : 1500 teenagers
37% : sample proportion of teenagers says that they believe social security will 'be there' for them.
Hence, the correct answer is : B) All teenagers.
Colorblindness is an X-linked recessive condition. If a woman with normal vision whose father was colorblind has a son with a man with normal vision, what is the probability that he will be colorblind?
Answers
Answer: 0.25 or 25%
Step-by-step explanation:Women have two chromosomes XX and men have two also XY.
From the question, it can be seen that colorblindness is an X-linked recessive condition.
Let the X-linked recessive gene be specified as [tex]X^{-}[/tex] and the dominant gene which is not colorblind linked as [tex]X^{+}[/tex].
The question says the woman has a father who is colourblind which means her father possesses the X-linked recessive gene [tex]X^{-}[/tex] which means he has chromosomes [tex]X^{-}Y[/tex] and therefore must have given his daughter the recessive gene
For her husband who has normal vision his chromosomes will be [tex]X^{+} Y[/tex].
So, the probability that their son will be colourblind will be;
Chromosomes [tex]X^{+}[/tex] Y
[tex]X^{+}[/tex] [tex]X^{+} X^{+}[/tex] [tex]X^{+}Y[/tex].
[tex]X^{-}[/tex] [tex]X^{-} X^{+}[/tex]. [tex]X^{-}Y[/tex].
Therefore, the probability that their son will be color blind = ¼ or 0.25 or 25%
Manuel's grade on a science quiz was 80%. He got 20 problems correct on the quiz. How many problems were on the science quiz?
Answers
Answer:
There were 25 problems on the science quiz
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Grade Manuel got on the science quiz = 80% or 80/100
Number of correct answers = 20
2. How many problems were on the science quiz?
Let's use the Rule of Three Simple, this way:
Problems on the science quiz Percentage
20 80
x 100
x * 80 = 20 * 100
80x = 2,000
x = 2,000/80
x = 25
There were 25 problems on the science quiz
Answer:
25
Step-by-step explanation:
20 x 100/80 = 25
or 20/80 = x/100
The account balance on April 1st is $102.33. On April 15th a payment of $25.00 is made. On April 25th a purchase of $11.27 is made. What is the finance charge if the annual rate is 22%? What is the new account balance?
Answers
Answer:
Finance Charge = $1.42
New Account Balance = $90.02
Step-by-step explanation:
APR (Annual Percentage Rate) = 22%
Periodic Rate = 1.83% (APR/12)
Beginning Balance = $102.33
Payment made on 15th day = $25.00
Purchase made on 25th day = $11.27
Finance Charge = (Beginning Balance - Payment made on 15th day) x Periodic Rate
Finance Charge = ($102.33 - $25.00) x 0.0183
Finance Charge = $77.33 x 0.0183
Finance Charge = $1.42
New Account Balance = Beginning Balance - Payment made on 15th day + Purchase made on 25th day + Finance Charge
New Account Balance = $102.33 - $25.00 + $11.27 + $1.42
New Account Balance = $90.02
The finance charge is approximately $1.67, and the new account balance after accounting for the payment and purchase is $90.27.
We start with the account balance on April 1st, which is $102.33. On April 15th, a payment of $25.00 is made, and on April 25th, a purchase of $11.27 is made.
1: Calculate the Average Daily Balance
From April 1st to April 14th (14 days): $102.33From April 15th to April 24th (10 days): $102.33 - $25.00 = $77.33From April 25th to April 30th (6 days): $77.33 + $11.27 = $88.60Average Daily Balance = ( (14 * 102.33) + (10 * 77.33) + (6 * 88.60) ) / 30 = $91.22
2: Calculate the Finance Charge
Given the annual interest rate of 22%, we first find the monthly rate: 22% / 12 = 1.833%.
Then we calculate the finance charge:
Finance Charge = Average Daily Balance * Monthly Rate
Finance Charge = $91.22 * 0.01833 ≈ $1.67
3: Calculate New Account Balance
New Balance = Previous Balance - Payment + Purchase + Finance Charge
New Balance = $102.33 - $25.00 + $11.27 + $1.67 = $90.27
The new account balance is $90.27.
For the graph above, what is the rate in miles per hour?
Answers
Answer:
26 2/3
Step-by-step explanation:
The easiest way to find the answer is to look at the graph value for 1 hour. It is slightly more than 25, but the graph isn't detailed enough to let us read a precise value.
The next best way is to find a grid intersection that the line goes through. We observe that (1.5 hours, 40 miles) is on the plotted line, so the proportion is ...
(40 mi)/(1.5 h) = 26 2/3 mi/h
Paisley was organizing her shoe collection. She counted 24 pairs of sandals. This represents 32% of the total number of shoes she owns. How many shoes does Paisley own?
Answers
Answer:
The number of shoes Paisley own is 75.
Step-by-step explanation:
Given:
Paisley was organizing her shoe collection.
She counted 24 pairs of sandals.
This represents 32% of the total number of shoes she owns.
Now, to find the number of shoes Paisley own.
Let the number of shoes Paisley own be [tex]x.[/tex]
According to question:
32% of [tex]x[/tex] = 24.
[tex]\frac{32}{100} \times x=24[/tex]
[tex]0.32x=24[/tex]
Dividing both sides by 0.32 we get:
[tex]x=75.[/tex]
Therefore, the number of shoes Paisley own is 75.
Answer:
The total number of shoes Paisley owns = 75
Step-by-step explanation:
Given:
24 pairs of sandals represent 32% of the shoes Paisley owns.
To find the total number of shoes Paisley owns.
Solution:
Let the total number of pairs of shoes be = [tex]x[/tex]
Thus, number of sandals can be represented as:
⇒ 32% of [tex]x[/tex]
⇒ [tex]0.32\times x[/tex]
⇒ [tex]0.32x[/tex]
Number of sandals = 24
So, we can write the equation as:
⇒ [tex]0.32x=24[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 0.32.
⇒ [tex]\frac{0.32x}{0.32}=\frac{24}{0.32}[/tex]
⇒ [tex]x=75[/tex]
Thus, the total number of shoes Paisley owns = 75
A company wants to decrease their energy use by 13%. If their electric bill is currently $1,800 a month, what will their bill be if they are successful?
Answers
Step-by-step explanation:
what is the midpoint of the segment shown below?
Answers
The answer is D
Cory bought some baseball equipment. He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75. Write and evaluate a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each
Answers
Answer:
Step-by-step explanation:
He used a coupon for 1/2 off the price of the bat which is $69. With the coupon applied, the cost of the bat would be 69 × 1/2 = $34.5
He also used a coupon for 1/2 off the price of the glove which is $75. With the coupon applied, the cost of the bat would be 75 × 1/2 = $37.5
Therefore, a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each would be
34.5 + 37.5 + 3 × 5.5 = $88.5
The total cost of the bat, the glove, and the baseballs is $88.5 and this can be determined by using the given data and arithmetic operations.
Given :
He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75.
The following steps can be used to evaluate the total cost:
Step 1 - Find the cost of the bat after the discount.
[tex]= \dfrac{1}{2}\times 69[/tex]
= $34.5
Step 2 - Find the cost of the glove after the discount.
[tex]=\dfrac{1}{2}\times 75[/tex]
= $37.5
Step 3 - Now, evaluate the cost of the baseballs.
[tex]=3\times 5.5[/tex]
= $16.5
Step 4 - Add all the costs to determine the total cost.
= 16.5 + 37.5 + 34.5
= $88.5
For more information, refer to the link given below:
https://brainly.com/question/20595275
Triangle P has a base of 12 inches and a corresponding height of 8 inches triangle Q has a base of 15 inches and a corresponding height of 6.5 inches which triangle has a greater area?
Answers
Answer:
Triangle Q has the greatest area
Step-by-step explanation:
Answer:
Triangle Q is the greatest
Step-by-step explanation:
The value for P is 48
The value for Q is 48.75
*Remember once we get the area of a triangle we must divided by 2*
Therefore, Q has a greater value then P
Pls mark me brainliest!!!
)Which polynomial functions have only the roots 1 and 6? Check all that apply.
f(x) = (x – 1)(x – 6)
f(x) = 3(x + 1)(x + 6)
f(x) =(3x – 1)(x – 6)
f(x) = 3(x – 1)(x – 6)
f(x) = 6(x – 1)(x – 6)
the answer is:
f(x) = (x – 1)(x – 6)
f(x) = 3(x – 1)(x – 6)
f(x) = 6(x – 1)(x – 6)
so all you little snow flakes sayin aaahhh no its this aahh no its that sfu cause i just took the evaluation.
Answers
Answer:
a,d,e
Step-by-step explanation:
x=1,x-1=0
x=6
x-6=0
if 1,6 are roots then (x-1) and (x-6) are factors of f(x)
Answer:a,d,e
Step-by-step explanation:
In a study commuting patterns of people in a large metropolitan area, respondents were asked to report the time they took to travel to their work on a specific day of the week. What is the individual?a. travel timeb. a personc. day of the weekd. city in which they lived
Answers
Answer:
b. a person
Step-by-step explanation:
The conducted study demonstrates the commuting patterns of people. Here, the information is collected from a person about amount of time consumes in travel to their work on a certain day of the week. Thus, here the individual is "a person" because the information is collected from a person about their time travel.
In the diagram below triangle abc ~ triangle dec . What is the value of x
Answers
Answer:
the answer is D
Step-by-step explanation
the ratio of the triangles is 3:1 (you find that out because 21:7 is simplified to 3:1.
when you plug in 6 as x then you get 18:6 which simplifies to 3:1 also
What happens to principal and interest of the monthly payment on a loan over time?
A. They go up
B. They go down
C the principal goes down and interest goes up
D. The principal goes up and the interest goes down
Answers
Answer:
The answer is C because the principal goes down and interest goes up. The part of your payment goes to....
Step-by-step explanation:
The points (4, -11) and (8, r) lie on a line with slope 2. Find the missing coordinate r.
Answers
Following steps and calculations, the missing coordinate r is -3. This point lies on line with slope of 2 along with other given point (4, -11).
Step-by-Step Calculation:
1. Identify the slope formula:
The slope (m) of a line passing through points (x1, y1) and (x2, y2) is calculated as:
m = (y2 - y1) / (x2 - x1)
2. Plug in known values:
We know the slope (m) is 2, points (x1, y1) are (4, -11), and points (x2, y2) are (8, r). Substitute these values:
2 = (r - (-11)) / (8 - 4)
3. Simplify the equation:
2 = (r + 11) / 4
2 × 4 = r + 11
8 = r + 11
4. Isolate r:
8 - 11 = r
r = -3
Cathy is looking for a job as a bookkeeper. One online job site lists a job in a stereo store that pays 34.6K. Another job, in a clothing store, has a weekly salary of $620. A. Which job is the higher-paying job? B. What is the difference in the weekly salaries of these two jobs? Round to the nearest dollar.
Answers
Answer:
A. Stereo Store Job is highest paying Job.
B. The Difference between the weekly salaries of these two jobs is $45.
Step-by-step explanation:
Given:
Annual Pay of job in stereo store = 34.6K
Now K here means (1000).
So we can say that;
Annual Pay of job in stereo store = [tex]\$34.6\times 1000= \$34600[/tex]
Also Given:
Weekly salary of Job at clothing store = $620
We need to find which job is the higher-paying job.
Also We need to find the difference in the weekly salaries of these two jobs
Solution:
First we will find the weekly salary of job in stereo store.
Now we know that there are 52 weeks in a year.
So weekly salary of job in stereo store can be calculated by Annual Pay of job in stereo store divided by total number of weeks.
framing in equation form we get;
weekly salary of job in stereo store = [tex]\frac{34600}{52}=\$665.38[/tex]
Now we see that weekly salary of job in stereo store is greater than Weekly salary of Job at clothing store.
Hence Stereo Store Job is highest paying Job.
Now we need to find the difference in the weekly salaries of these two jobs.
difference in the weekly salaries can be calculated by weekly salary of job in stereo store minus weekly salary of job in clothing store.
framing in equation form we get;
Difference = [tex]\$665.38-\$620 =\$45.38[/tex]
Rounding to nearest dollar we get;
Difference = $45
Hence the Difference between the weekly salaries of these two jobs is $45.
A. The job in the clothing store is the higher-paying job. B. The difference in the weekly salaries of these two jobs is $45.
To determine which job is higher-paying, we need to compare the annual salaries of both jobs and convert them to weekly salaries for a fair comparison, assuming a standard work year of 52 weeks.
A. Comparing the annual salaries:
1. The job at the stereo store pays $34,600 per year. To find the weekly salary, we divide this amount by 52 weeks:
[tex]\[ \frac{34,600}{52} = 665.38 \][/tex]
So, the weekly salary for the job at the stereo store is approximately $665.38.
2. The job at the clothing store pays a weekly salary of $620.
Now, comparing the weekly salaries:
Stereo store: $665.38 per week
Clothing store: $620 per week
The job at the clothing store pays more per week than the job at the stereo store.
B. Calculating the difference in weekly salaries:
To find the difference between the weekly salaries of the two jobs, we subtract the weekly salary of the stereo store job from the weekly salary of the clothing store job:
[tex]\[ 665.38 - 620 = 45.38 \][/tex]
Rounding to the nearest dollar, the difference in the weekly salaries is approximately $45.
However, the question asks for the difference in the weekly salaries of these two jobs, not the difference in the weekly salary of the stereo store job from the clothing store job. Since the clothing store job pays more, we should actually subtract the weekly salary of the clothing store job from the weekly salary of the stereo store job to find the additional amount the clothing store job pays per week:
[tex]\[ 620 - 665.38 = -45.38 \][/tex]
Since we are looking for a positive difference, we take the absolute value:
[tex]\[ |-45.38| = 45.38 \][/tex]
Rounding to the nearest dollar, the difference in the weekly salaries of these two jobs is approximately $45. However, it seems there was a mistake in the initial answer provided for part B. Let's correct this:
The correct calculation for the difference in weekly salaries is:
[tex]\[ 665.38 - 620 = 45.38 \][/tex]
Rounding to the nearest dollar, the difference is $45.
In order to study whether IQ level is related to birth order, data were collected from a sample of 540 students on their birth order (Oldest/In Between/Youngest) and their score on an IQ test.
Which of the following would be a meaningful display of the data from this study?
a. A pie chart
b. A histogram
c. A scatterplot
d. A two-way table
e. Side-by-side boxplots
Answers
Answer:
correct answer is e. Side-by-side boxplots
Step-by-step explanation:
given data
IQ test
sample = 540 students
solution
here Side-by-side boxplots that is apply it to the data set with 1 quantitative and 1 categorical variable
Side-by-side boxplots is also very useful in the comparing fundamental information for 2 data set
eg median value and range of value they cover from data
and
Side-by-side boxplots also provide target summary and it analysis the data
so here correct answer is e. Side-by-side boxplots
The relation between the two dataset can be shown by placing the
dataset side-by-side, to give a meaningful display.
Correct response:
The correct option is; e. Side-by-side boxplotsMethod used to make the above selectionThe number of student in the study = 540
The categories of the data = Oldest/In Between/Youngest
The category of the other data collected = Their score on IQ test
Required:
To choose the option that would be a meaningful display of the data
from the study.
Solution:
The number of categories of the order of birth = 3
Therefore, a meaningful display of the order of birth is possible using a boxplot.
The IQ test scores can be categorized as follows;
Maximum test score;75th percentile = Third quartile = Q₃50th percentile = Second quartile = Q₂25th percentile = first quartile = Q₁Minimum test scoreTherefore, the dataset for the order of birth and the dataset for the IQ
test score can be presented side-by-side, thereby providing a
meaningful display.
The correct option is therefore;
e. Side-by-side boxplotsLearn more about side-by-side boxplots here:
https://brainly.com/question/13504155
The general equation for a circle is a(x2+y2)+bx+cy+d=0. There is exactly one circle passing through the points (1,2),(3,−1), and (0,0). Find an equation for this circle.
Answers
Answer:
Step-by-step explanation:
let the eq. of circle be a(x²+y²)+bx+cy+d=0
x²+y²+b/a x+c/a y+d/a=0
if it passes through (0,0)
0²+0²+b/a*0+c/a*0+d/a=0
so d=0
Hence x²+y²+b/a x+c/a y=0
if it passes through (1,2) and (3,-1)
1²+2²+b/a×1+c/a×2=0
5+b/a+2c/a=0 ...(1)
and 3²+(-1)²+b/a*3+c/a*(-1)=0
10+3b/a-c/a=0 ...(2)
(1)+2(2) gives
5+b/a+2 c/a+20+6 b/a -2 c/a=0
7 b/a+25=0
b/a=-25/7
from (1)
5-25/7+2 c/a=0
2 c/a+10/7=0
2 c/a=-10/7
c/a=-5/7
so eq. of circle is x²+y²-25/7 x-5/7 y=0
7(x²+y²)-25 x-5 y=0
I don't understand how to solve these problems, someone please explain.
Answers
Answer:
Step-by-step explanation:
When two triangles are similar, it means that the ratio of their corresponding sides is equal.
Therefore
96/(6x + 28) = 24/25
Crossmultiplying,
1) 96 × 25 = 24(6x + 28)
2400 = 144x + 672
144x = 2400 - 672 = 1728
x = 1728/144
x = 12
2) angle A and angle D is equal because they are alternate angles.
(2x + 6)/(x + 6) = 10/8
Crossmultiplying
8(2x + 6) = 10(x + 6)
16x + 48 = 10x + 60
16x - 10x = 60 - 48
6x = 12
x = 12/6 = 2
3) both triangles are right angle triangles. All angles are similar in both triangles. It also means that all the sides are similar. Therefore
45/30 = 40/x
Crossmultiplying
45 × x = 30 × 40
45x = 120
x = 120/45 = 26.7
A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is fi ve feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?
Answers
Answer:
46 jumps
Step-by-step explanation:
Since the grasshopper is two inches long, and can jump a distance of 40 inches, then its jump ratio is 2:40 = 1:20.
The athlete's body-length is 5 feet 9 inches. We convert this to inches which is 5 × 12 = 60 inches. We then add the remaining 9 inches to make it 60 + 9 = 69 inches. Since our jump ratio for the grasshopper equals that for the athlete, 1:20 = 69: 20 × 69= 69 : 1380. Thus the athlete's jump ratio is 69 inches to 1380 inches.
The athlete wants to cover one mile and we know that 1 mile = 63360 inches. So, we divide the distance the athlete wants to cover(1 mile = 63360 inches) by his jump-length(1380 inches) to get the number of jumps it takes to cover a mile. Number of jumps × jump-length of athlete = one mile, so Number of jumps = one mile/jump-length of athlete = 63360 inches/ 1380 inches= 45.9 jumps ≈ 46 jumps.
It would take the athlete approximately 46 jumps to cover one mile.
To solve this problem, we'll start by establishing the jumping ratio of the grasshopper and then applying that ratio to the athlete to determine how many jumps it would take for the athlete to cover one mile.
First, let's calculate the jump ratio for the grasshopper:
- Grasshopper's length: 2 inches
- Grasshopper's jump length: 40 inches
The ratio of the grasshopper's jump length to its body length is:
[tex]\[ \text{Jump ratio} = \frac{40 \text{ inches}}{2 \text{ inches}} = 20 \][/tex]
Next, let's find the athlete's height in inches:
- Athlete's height: 5 feet 9 inches
- 1 foot = 12 inches
Thus, the athlete's height in inches is:
[tex]\[ 5 \text{ feet} \times 12 \text{ inches/foot} + 9 \text{ inches} = 60 \text{ inches} + 9 \text{ inches} = 69 \text{ inches} \][/tex]
Using the grasshopper's jump ratio, we can determine the distance the athlete could jump:
[tex]\[ \text{Athlete's jump length} = 69 \text{ inches} \times 20 = 1380 \text{ inches} \][/tex]
Now, we need to determine the total number of jumps the athlete would need to cover one mile. First, convert one mile to inches:
- 1 mile = 5280 feet
- 1 foot = 12 inches
Therefore, the distance of one mile in inches is:
[tex]\[ 5280 \text{ feet} \times 12 \text{ inches/foot} = 63360 \text{ inches} \][/tex]
Finally, the number of jumps required for the athlete to cover this distance is:
[tex]\[ \text{Number of jumps} = \frac{63360 \text{ inches}}{1380 \text{ inches/jump}} \][/tex]
Calculating this value:
[tex]\[ \text{Number of jumps} \approx \frac{63360}{1380} \approx 45.92 \][/tex]
Since the number of jumps must be a whole number, we round 45.92 to the nearest whole number:
[tex]\[ \text{Number of jumps} \approx 46 \][/tex]
Therefore, it would take the athlete approximately 46 jumps to cover one mile.
A chef uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors 16 ounces/1 pound and 28.4 grams/1 ounce
Answers
Answer:
The chef uses 5452.8 grams of butter each day.
Step-by-step explanation:
Given:
Chef use 12 pounds of butter each day.
To find the amount of butter in grams used by chef each day.
Conversion units:
1 pound = 16 ounces
1 ounce = 28.4 grams
Solution:
We need to convert 12 pounds of butter in grams of butter.
We will apply unitary method to carry out the conversion.
If 1 pound = 16 ounces
Then, 12 pounds = [tex]12\ pounds\times\frac{16\ ounces}{1\ pound}= 192\ ounces[/tex]
If 1 ounce = 28.4 grams
Then, 192 ounces = [tex]192\ ounces \times \frac{28.4\ grams}{1\ ounce} = 5452.8\ grams[/tex]
Thus, the chef uses 5452.8 grams of butter each day.
Final answer:
convert 12 pounds to ounces (192 ounces) and then multiply by 28.4 to convert ounces to grams, resulting in 5452.8 grams of butter used per day.
Explanation:
To find out how many grams of butter the chef uses each day, we need to convert pounds to ounces and then ounces to grams.
First, we use the conversion factor that there are 16 ounces in a pound. So, for 12 pounds of butter:
12 pounds × 16 ounces/pound = 192 ounces.
Next, we use the conversion factor that there are 28.4 grams in an ounce. So, for 192 ounces of butter:
192 ounces × 28.4 grams/ounce = 5452.8 grams.
Therefore, the chef uses approximately 5452.8 grams of butter each day.
y varies jointly as x and z z. If y = 6 when x = 3 and z = 9, find y when x = 4 and z = 3.6.
but z is in square root, just the symbol doesn't show.
Answers
Answer:
y = (8/5)√10
Step-by-step explanation:
You seem to have ...
[tex]y=kx\sqrt{z}[/tex]
We can find k from the given values ...
[tex]\dfrac{y}{x\sqrt{z}}=k=\dfrac{6}{3\sqrt{9}}=\dfrac{6}{3\cdot 3}=\dfrac{2}{3}[/tex]
Then for the new values, ...
[tex]y=\dfrac{2}{3}\cdot 4\sqrt{3.6}=\dfrac{8\sqrt{90}}{3\cdot 5}=\dfrac{8\sqrt{10}}{5}[/tex]