Answer: rotation
Step-by-step explanation:
Rotation is required to map DEF onto D'EF'
What is Rotation?Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Rotation exists as the operation or act of turning or circling something.
Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.
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PLEASE HELP ASAP
30 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
d. 3x³ and 2x³
Step-by-step explanation:
In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.
Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.
Please help me out please!! :)
Starting from the Pythagorean identity, we deduce
[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]
If we plug in the value 7/10 for sin(x), we have
[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]
The ratio of men to women working for a company is 5 to 7. If there are 156 employees total, how many women work for the company?
I hope it’s correct
Answer:
65 men
91 women
Step-by-step explanation:
the ratio is 5 to 7 and there are 156 total
5+7 is 12
so this gives us
5/12*156=65 men
7/12*156=91 women
65 + 91 = 156
One day at lunch, the cafeteria sold thirty-four 1-pint containers of milk. The cafeteria also sold forty-eight 12-fl-oz bottles of water. Did the cafeteria sell more fluid ounces or milk? How many more?
Fluid ounces, 47 more
(14x^(2)-21x)/(2x-3)
need answer now please! show work
Answer:
7x
Step-by-step explanation:
Sorry this is the best way I could show the work as the equation maker on this site does not support doing something in this format
To divide the expression (14x^2 - 21x) by (2x - 3), you can use long division to get the answer 7x.
Explanation:To divide the expression (14x^2 - 21x) by (2x - 3), we can use long division. Here are the steps:
Divide (14x^2) by (2x) to get 7x.Multiply (2x - 3) by 7x to get 14x^2 - 21x.Subtract (14x^2 - 21x) - (14x^2 - 21x) to get 0.Therefore, the answer is 7x.
The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.
Answer:
6√2.
Step-by-step explanation:
The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90. Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.
Celia and Jake bought 4 pizzas that cost $7 each and bread sticks that cost $3 they spilt the cost between them. Which equations could be used to find how much each paid? Let T stand for the total coat and E stand for the amount each paid.
Answer:
E = (3b+28)/2
T=3b+28
E= t/2
Step-by-step explanation:
The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.
Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.
T=3b+28
E= t/2
The scores of a psychology exam were normally distributed with a mean of 70 and a standard deviation of 5 a failing grade on the exam was anything two or more standard deviations below the mean what was the cutoff for a failing score
Answer:
The Answer is likely 60.
Step-by-step explanation:
Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.
Answer:
60
Step-by-step explanation:
Two standard deviations below the mean is:
70 - 2(5) = 60
The graphs of f(x) and g(x) are shown below: graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals 3.4 times x minus 6.6 What are the solutions to the equation f(x) = g(x)?
a) x = −1, 5.4
b)x = −3, 4
c)x = −1, 2
d)x = −10, 12
Answer:
Option a) x = −1, 5.4
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -x-12[/tex]
[tex]g(x)=3.4x-6.6[/tex]
equate f(x) and g(x)
[tex]x^{2} -x-12=3.4x-6.6[/tex]
Solve the quadratic equation by graphing
The solutions are x=-1 and x=5.4
see the attached figure
Answer:
x= -1, 5.4
Step-by-step explanation:
[tex]f(x)= x^2-x-12[/tex]
[tex]g(x)= 3.4x -6.6[/tex]
f(x) is a quadratic equation and g(x) is a linear equation
To find f(x)= g(x) we need to find the point where the graph of f(x) and g(x) intersects.
The quadratic equation f(x) and linear equation g(X) intersects at two points
from the graph f(x)= g(x) at x= -1 and x=5.4
Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2).
Answer:
https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Given the roots are x = 6 and x = 10, then
the factors are (x - 6) and (x - 10)
The quadratic is then the product of the roots
y = a(x - 6)(x - 10) ← a is a multiplier
To find a substitute (8, 2) into the equation
2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
a = - [tex]\frac{1}{2}[/tex]
Hence
y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors
y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute
y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30
Use the domain and range of each of the following relations to determine which is a function.
Answer:
a) Function
b) Not a function
c) Function
d) Not a function
Step-by-step explanation:
a) Domain = { 7,-6,2}
Range = {5,0,3}
It is a function as every value in domain has some and unique value mapped to it in Range
b)
Domain = { 7,-6,2}
Range = {5,0,-2,3}
It is not a function as -6 value in domain has two values mapped to it in Range
c)
Domain = { 7,2}
Range = {-6,-7}
It is a function as every value in domain has some and unique value mapped to it in Range
d)
Domain = { 7,-6}
Range = {5,0,3}
It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range
A certain city has a population of 10000 and increases by 4% per year. What will the population be 5 years later? (The answer has been simplified.)
53782
12167
12000
30000
Answer:
Option B is correct.
Step-by-step explanation:
A city has population = 10000
Population increase each year = 4%
So, Population increase after 1 year = 10000 * 4%
= 10000*4/100
= 400
Adding in the current population:
10000+400 = 10,400
Population increase after 2 year = 10,400*4%
= 10400*4/100
= 416
Adding in the current population:
10400+416 = 10816
Population increase after 3 year = 10,816*4%
= 10816*4/100
= 433
Adding in the current population:
10816+433 = 11,249
Population increase after 4 year = 11,249*4%
= 11249*4/100
= 450
Adding in the current population:
11249+450 = 11,699
Population increase after 5 year = 11,699*4%
= 11699*4/100
= 468
Adding in the current population:
11699+468 = 12167
So, the population after 5 yeras will be 12167.
Option B is correct.
The population of the city will be approximately 12,167 people after 5 years, calculated by using the formula for exponential growth with a 4% annual increase from the initial population of 10,000.
The question involves calculating the future population of a city that is experiencing exponential growth over a period of time. To find the population of a city 5 years later when the population increases by 4% per year, we use the formula for exponential growth, which is:
P = [tex]P0 * (1 + r)^t[/tex]
Where:
P is the future population
P0 is the initial population (which is 10,000)
r is the annual growth rate (which is 4% or 0.04)
t is the number of years (which is 5)
Using the formula, we calculate:
P = 10,000 × (1 + 0.04)⁵
P = 10,000 × (1.04)⁵
P = 10,000 × 1.2166529
P = 12,166.529
So, the population will be approximately 12,167 people 5 years later.
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.
Step-by-step answer:
Given:
Geometric sequence with
second term, T2 = 6
third term, T3 = 12
Wants to have the explicit and recursive rules.
Solution:
common ratio, r = 12/6 = 2
Therefore the first term, T1
= second term /r
= 6/2
=3
Thus the absolute rule is
Tn = T1 *r^(n-1) where T1 = 3, r=2. Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good
The recursive rule (depending on the previous term)
Tn = Tn-1*r = 2*Tn-1
The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.
Explanation:In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.
So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).
The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.
To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.
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Mary Beth and her family ate a meal in a restaurant the cost of the meal was $34.50 the sales tax was 8% of the cost of the meal
What is the value of x? Enter your answer in the box x=
Answer: 45°
Step-by-step explanation:
There are 180 degrees in a triangle so
180-80=100-55=45°
Simplify 3ab + 4ab + 5
12ab
7ab + 5
not possible
Answer:
7ab+5
Step-by-step explanation:
add like terms (3ab+4ab=7ab)
5 doesn't have a like term so it stays by itself
Hey there! :)
3ab + 4ab + 5
In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.
Since both "3ab" & "4ab" contain "ab," you are able to combine them together!
When combining like terms, you only add the numerical value, not the letters.
This leaves us with : 7ab + 5
Therefore, your answer is 7ab + 5
~Hope I helped!~
In the figure, AB ||CD and m3=130. What is
m<6 = 180° - m<3
m<6 = 180° - 130°
m<6 = 50°
Answer: m6 equals 50 degrees
Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 Determine the solutions of the equation. What solution makes sense for the situation? x = What are the dimensions of the rectangle? width = inches length = inches
Answer:
Step-by-step explanation:
x² + 5x – 104 = 0
Factor using the AC method. Here, a = 1 and c = -104. Multiplied together, ac = -104. Factors of -104 that add up to +5 are +13 and -8.
(x + 13) (x - 8) = 0
x = -13, 8
A negative width doesn't make sense, so x = 8. Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.
Answer:
width = 8
length = 13
Step-by-step explanation:
All that is left to do is factor the results that you have
x^2 + 5x - 104 = 0
You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.
The two numbers are 8 and 13
More formally stated, the quadratic can be factored to
(x + 13)(x - 8) = 0
x - 8 =0
x - 8 + 8 = 8 + 0
x = 8
x + 13 = 0 has no meaning.
That means that the width ( a positive number ) = 8
The length is 5 more = 13
A totem pole casts a 20 meter shadow when the angle of elevation of the sum is 45what is the distance from the top of the totem pole to the end of the shadow
Answer:
20√2 meters (approximately 28.28 m)
Step-by-step explanation:
It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.
Final answer:
The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.
Explanation:
The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.
Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.
What is the solution to the equation below?
Please show work.
Answer:
x = -9
Step-by-step explanation:
Multiply both sides by √(x - 6) to eliminate the fraction:
√(3x) = 3√(x - 6)
Now square both sides:
3x = 9(x - 6), or 3x = 9x - 54.
Combining the x terms results in -6x = -54, and thus x = 9.
Answer:
The correct answer is option D. x = 9
Step-by-step explanation:
From the attached question we get an expression,
√3x/√(x - 6) = 3
To find the solution of given expression
√3x/√(x - 6) = 3
Squaring both side we get,
3x/(x - 6) = 9
3x = 9 * (x - 6)
3x = 9x - 54
9x - 3x = 54
6x = 54
x = 54/6 = 9
Therefore the correct option is D. x = 9
If $125 is invested at an interest rate of 18% per year and is compounded continuously, how much will the investment be worth in 2 years? Use the continuous compound interest formula A = Pert.
Answer:
$179.17
Step-by-step explanation:
You already know the formula but you have it typed incorrectly. The rt is raised as a power to the e. Just in case you didn't know that. Filling in our formula with what we have gives us:
[tex]A(t)=125e^{(.18)(2)[/tex]
Simplify that power to .36 and we have
[tex]A(t)=125e^{.36}[/tex]
Now raise e to the power of .36 on your calculator and get
A(t)= 125(1.433329415) and
A(t) = $179.17
Answer:
C 179 is the answer.
Step-by-step explanation:
You have a total of 45 dimes and quarters. You have 3 more quarters than dimes. Which system of equations can you use to find the number x of quarters and number y of dimes you have? Use the system to determine how much money you have in quarters and dimes.
Let's call dimes x and the quarters x+3 since we have 3 more of them.
x+x+3=45
2x=42
x=21
we have 21 dimes and 23 quarters
21*0.10=2.1
23*0,25=5.98
if we add those together it equals 8.08
Answer:
$8.10
Step-by-step explanation:
Let d and q represent the # of dimes and quarters, respectively. Then write equations reflecting this story:
q = d + 3, and d + q = 45. Substitute d + 3 for q in the second equation, obtaining:
d + d + 3 = 45, or 2d = 42, or d = 21. Then there are 21 dimes and 24 quarters. That comes to $2.10 + $6.00, or $8.10.
Photo Attached! Help with my algebra please!
Answer:
A
Step-by-step explanation:
(x−2) means the graph is shifted 2 units to the right.
+3 means the graph is shifted 3 units up.
So the graph of g(x) is shifted 2 units right and 3 units up.
Which graph shows a car traveling at 50 miles per hour?
Answer:
If you could insert a picture of the graphs that would help! thank you!
Step-by-step explanation:
in order to solve he following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them? 4x-2y=7, 3x-3y=15
Answer:
To eliminate x multiply the first equation by 3 and the second equation by 4
To eliminate y multiply the first equation by 3 and the second equation by 2
Step-by-step explanation:
We are given a system of linear equations;
4x-2y=7
3x-3y=15
solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;
Multiply the first equation by 3 and the second equation by 4.
To eliminate y;
Multiply the first equation by 3 and the second equation by 2.
Identify the volume and surface area of the sphere in terms of π. HELP PLEASE!!
Answer:
the third one.
Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]
Step-by-step explanation: Please see the image below!
NEED MATH HELP!!!!
( with the 2 problems I missed)
Answer:
[tex]t=7.4years[/tex]
Step-by-step explanation:
Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.
[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]
By using properties of the logarithm
[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]
We obtain:
[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]
Ordering using the logarithm property [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]
[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]
[tex]log_{10}N=log_{10}(16)+0.15t[/tex]
Clearing t
[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]
we obtain:
[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]
The number of Elm trees is N = 204
Solving
[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]
Round to the nearest tenths place [tex]t=7.4years[/tex]
The average age three people running for election is 42. A fourth person joins the race and the average drops to 40. What is the fourth person's age?
Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then
[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]
[tex]a_1+a_2+a_3+a_4=160[/tex]
[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]
The average age of the first 3 candidates is 42, so
[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]
[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]
Three friends buy one pack of 80 stickers. T hey divide the stickers equally and give the remainder to their teacher. How many will each friend get?
Answer:
26
Step-by-step explanation:
80 divided by three = 26.666666
26 times 3 = 78
2 leftover
The number sticker each student get is 26 and the number stickers teacher got is 2.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, three friends buy one pack of 80 stickers.
Now, number of stickers each friend = 80/3
3|80|26
78
_____
2
Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.
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A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. y – 5 = 3(x + 1); y = 3x + 8 y + 5 = –3(x – 1); y = –3x – 2
see picture attached.
i hope this helped !!
ANSWER
Point-slope form:
[tex]y + 5 = -3(x - 1)[/tex]
Slope-intercept form;
[tex]y = - 3x - 2[/tex]
EXPLANATION
The point-slope form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We need to find the slope using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let us substitute the point (1, –5) and (–3, 7).
This implies that,
[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]
[tex]m = \frac{12}{ - 4} = - 3[/tex]
The point slope form now becomes,
[tex]y - - 5 = - 3(x - 1)[/tex]
[tex]y + 5 = -3(x - 1)[/tex]
To find the slope intercept form, we expand to obtain;
[tex]y = - 3x + 3 - 5[/tex]
[tex]y = - 3x - 2[/tex]