Answer:
Use the quadratic formula
Step-by-step explanation:
Use the quadratic formula
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex]
Where a, b and c are the real coefficients of the polynomial
Then, for
[tex]2x^2+4x-7=0\\a = 2\\b = 4\\c = -7[/tex]
The solutions are:
[tex]x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_2 = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x_1 = \frac{-4+\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_2 = \frac{-4-\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_1 = \frac{-2+3\sqrt{2}}{2}\\\\x_2 = \frac{-2-3\sqrt{2}}{2}[/tex]
Kaitlin spent 2/3 of an hour on homework. Her sister Judy spent 1 1/2 times that amount. Explain why Judy’s homework time is between 2/3 of an hour and 1/2 of an hour?
[tex]\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Judy spent time}}{\stackrel{\textit{Kaitlin's time}}{\cfrac{2}{3}}\cdot \cfrac{3}{2}}\implies \cfrac{2}{2}\cdot \cfrac{3}{3}\implies 1~\hfill \boxed{\cfrac{1}{2}}\rule[0.35em]{3em}{0.25pt}\stackrel{\stackrel{Judy's}{\downarrow }}{1}\rule[0.35em]{5em}{0.25pt}\stackrel{1\frac{2}{3}}{\boxed{\cfrac{2}{3}}}[/tex]
so, Judy's time is really 1 hour exactly.
and on the number line, we could place that 1 in between the first half and the two thirds of the of the next number, as you see above.
There is a mistake in the question as Judy's homework time cannot be between 2/3 and 1/2 of an hour if she spent 1 1/2 times as much time as Kaitlin who spent 2/3 of an hour. Judy's homework time would be 1 hour.
The question seems to have a typo or a logical error, as it is not possible for Judy's homework time, which is 1 1/2 times Kaitlin's time, to be between 2/3 of an hour and 1/2 of an hour. Instead, if Kaitlin spent 2/3 of an hour on homework, Judy would have spent (2/3) * (3/2) = 1 hour on homework, which is more than both 2/3 and 1/2 of an hour. It appears that Judy's actual homework time would be exactly one hour, not between the two given times.
ABC HAS A VERTICES. A(-2,10), B(4,8),C(2,4). determine the coordinates of A',B',AND C' HAS UNDERGONE THE DESCRIBED TRANSFORMATION. A DILATION WITH THE SCALE FACTOR OF3 AND A CENTER OF DILATION AT THE ORIGIN.
Answer:
A'(-6,30)
B'(12,24)
C'(6,12)
Step-by-step explanation:
By definition, dilation is a tranformation in which the the image and the pre-image have the same shapes but differente sizes.
You know that:
- The vertices of ABC are: A(-2,10), B(4,8),C(2,4).
- The scale factor is 3.
- The center of dilation is at the origin.
By definition, if the scale factor is greater than 1, then the image is an enlargement.
Therefore, you must multiply each original vertex by 3:
(x,y)→(3x,3y)
Then the coordinates A',B' and C' are:
A'→ [tex](-2(3), 10(3))=(-6,30)[/tex]
B'→ [tex](4(3), 8(3))=(12,24)[/tex]
C'→ [tex](2(3), 4(3))=(6,12)[/tex]
Hello people of AMERICA!!! :)
Captain Tellez plans to reach a cruising altitude in his passenger plane and then maintain a cruising speed of 570 miles per hour for approximately 400 miles. Which is closest to the length of time, in minutes, that his plane will maintain cruising speed?
A. 0.70
B. 1.43
C. 42
D. 86
Answer:
option (c)
42 minutes
Step-by-step explanation:
Given in the question:
cruising speed of passenger plane = 570 miles/hour
distance passenger plane travelled = 400 miles
Formula to usedistance = speed x time
time = distance / speed
time = 400 / 570
= 0.7018 hours
1 hour = 60 minutes
228000 hours = 60 x 0.7018 minutes
= 42.1052 minutes
≈ 42 minutes
Closest to the length of time, in minutes, that Captain Tellez's plane will maintain cruising speed is 42 minutes.
How do you figure out 3.72 times 10.?
Answer:
Every time you multiply by 10, you move all the digits one place to the left. You could also think about so that the decimal point moves one place to the right.
Step-by-step explanation:
Answer: The answer to the problem is 37.2
Step-by-step explanation: When you are multiplying a number by 10 you need to move the decimal point one place to the right. 3.72 x 10 = 37.2.
Do any of you know the answer to this
Answer: n< -4 , or Interval notation as ( -∞, -4 )
Step-by-step explanation:
* Hopefully the work below helps:) Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
n < -4 is equivalent to -n > 4Step-by-step explanation:
-n > 4 change the signs
n < -4
Going to the movies costs $9.50 per person. What is the slope of the line that models this situation, if x represents the number of people and y represents the total cost?
Answer:
The slope is 9.5
The equation is y = 9.5x
Step-by-step explanation:
The equation is in the form of y = mx + b, where m represents the slope.
In the case of our situation, y = 9.5x , b = 0 and m = 9.5
9.5 is the slope because that is the rate of change as x increases per ticket sale
The slope of the line that models this situation will be 9.5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Heading out to the films costs $9.50 per individual.
Let 'x' be the number of people and 'y' be the total cost. Then the equation is given as,
y = 9.5x
The slope of the line that models this situation will be 9.5.
More about the linear equation link is given below.
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A bank teller notices that an account was overdrawn and had a balance that can be represented by –$324. The account holder then deposited 3 checks for $150 each and made 4 withdrawals of $20 each. The teller used the steps below to find the new balance for the account. Step 1 Start: –$324 Deposits: $150 each Withdrawals: –$20 each Step 2 –324 + 3(150) + 4(–20) Step 3 –324 + 450 – 80 = 46 Step 4 The account is overdrawn by $46.
The problem is a basic mathematical exercise involving negative and positive numbers related to bank transactions. The original balance is overdrawn and represented as a negative number, and then deposits and withdrawals are added and subtracted respectively to find the new balance which still ends up overdrawn.
Explanation:The problem given is about mathematical operations and bank transactions. The subject here is a subtraction and addition problem involving negative and positive numbers. The initial account balance represented as '––$324' shows an overdrawn account and is a negative number. Then, the account holder deposited checks, which is a positive value represented by '3(150)', and each deposit is $150 making it a total deposit of $450. Then, the account holder made withdrawals represented by '4(–20)', each withdrawal of $20 thereby making a total withdrawal of $80. Therefore, to find the new balance of the account, the calculation should be as follows: '–324 + 3(150) – 4(20) -> –324 + 450 – 80', which equals 46, indicating that the account is overdrawn by $46.
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If arc AD = 130° and arc AB = arc CD = 80°, what is the measure of ∠APD?
Answer:
the answer is 25
Step-by-step explanation:
1/2(130-80)
Answer:
(B)
Step-by-step explanation:
Given: It is given that arc AD=130° and arc AB=arc CD=80°.
To find: The measure of ∠APD.
Solution: It is given that arc AD=130°⇒m∠AOD=130° (The measure of the central angel is equal to the intercepted arc)
Also, arc AB=arc CD=80°⇒m∠AOB=m∠DOC=80° (The measure of the central angel is equal to the intercepted arc)
We know that the sum of the central angles is equal to 360°, thus
m∠AOD+m∠AOB+m∠BOC+m∠COD=360°
⇒130°+80°+m∠BOC+80°=360°
⇒290°+m∠BOC=360°
⇒m∠BOC=360°-290°
⇒m∠BOC=70°
Now, since (The measure of the central angel is equal to the intercepted arc), therefore arcBC=70°.
Also, we know that Angle Formed by Two Secants is half of the DIFFERENCE of Intercepted Arcs, therefore
[tex]m{\angle}APD=\frac{1}{2} (arcAD-arBC)[/tex]
Substituting the values, we get
[tex]m{\angle}APD=\frac{1}{2} (130-70)[/tex]
⇒[tex]m{\angle}APD=\frac{60}{2}[/tex]
⇒[tex]m{\angle}APD=30^{\circ}[/tex]
Thus, the measure of ∠APD is 30°.
Hence, option B is correct.
A room contains 55 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the number of rows.
Answer:
i believe its 27
Step-by-step explanation:25 times two= 50 27 times two= 54 +one more is 55. so it is 27
Answer:
11 rows.Step-by-step explanation:
Givens
The room contains 55 chairs arranged in rows.The number of rows is one more than twice the number of chairs.We know that the total number of chairs must be the product between the number of chairs per row and the total number of rows, which can be expressed as
[tex]c \times r = 55[/tex]
Where [tex]c[/tex] represents the number of chairs per row and [tex]r[/tex] representes the number of rows.
The second given statment defined a second equation
[tex]r=2c+1[/tex]
Now, we can substitute the second equation into the first one, and solve
[tex]c \times r = 55\\c (2c+1)=55\\2c^{2}+c-55=0[/tex]
Which can be factored by multiplying the expression by 2, and solve has a perfect trinomial
[tex]2(2c^{2}+c-55)=0\\2^{2}c^{2}+2c- 110=0\\(2c)^{2}+2c-110=0[/tex]
So, we need to find two number which product is 110 and is 1. If you think this through, those numbers are 11 and 10, because 11*10=110 and 11-10=1.
The factors are
[tex]\frac{(2c+11)(2c-10)}{2} =0[/tex], we have to divide by the number we multiplied before, then we simplify this number with the second factor
[tex](2c+11)(c-5)=0[/tex]
Where the positive solution is the only one that can be part of the answer because it doesn't make sense if we say -3 chairs. So,
[tex]c-5=0\\c=5[/tex]
This means there are 5 chairs per row.
Then, we use this value to find the other one.
[tex]c \times r=55\\5 \times r=55\\r=\frac{55}{5}\\ r=11[/tex]
Therefore, there are 11 rows and 5 chairs per row.
Eddie had a favorable simple annual interest rate on a used car loan, but he can’t remember what it was. His paperwork shows that he originally borrowed S4000 and paid a total of $1280 in interest on the 4-year loan. What was Eddie’s annual interest rate?
Answer: 8%
Step-by-step explanation:
Answer:
8%
Step-by-step explanation:
1/8x=1/4 what is the value x that makes the equation true
Answer:
x = 2
How?:
1/4 ÷ 1/8 = 0,25
0.25 as a fraction is 1/4
1/8 × 2 = 1/4
Which equations represent functions?
2x + 3y = 10
4x = 16
2x − 3 = 14
3y = 18
14.6 = 2x
Answer:
2x + 3y = 10, 3y = 18 (in both cases, for each input x, there is exactly one output y.
Step-by-step explanation:
3y = 10 - 2x, or y = (1/3)(10 - 2x) Yes, this is a function.
4x = 16 → x = 4 NOT a Function, because for x = 4 there are an infinite number of possible y -values
2x - 3 = 14 → 2x = 17 → x = 17/2 Not a function. See reason given above.
3y = 18 → y = 6 Function
2x = 14.6 → x = 7.3 Not a function. See reason given above
Answer:
it's a i got it right
Step-by-step explanation:
Here is the question: Alicia wrote numbers:2,9,15,21 what of the numbers is not a composite number?
the answer is 2 because you can't divided 2 by anything else other then itself
one letter tile is drawn from the bag and replaced 300 times. Predict how many times a consonant will not be picked
The predicted number of times a consonant will not be could be picked is 58 times.
The total number English alphabets = 26
Number of non consonant letters = 5
The probability of choosing a non-consonant letter at random from a single pick :
Number of non- consonant letters / total number of alphabets = 5 /26
To predict the number of times a non-consonant letter could be selected from 300 selections :
(Number of selections × probability per pick)
(300 × 5/26)
= 57.69
= 58 times
A non- consonant could be selected approximately 58 times.
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PLEASE HELP ME
When keeping records, expenses should be
A. added
B. subtracted
C. multiplied
D. divided
she has saved $30 which is three fifths of the total cost, how much is the total cost
Answer:
$50
Step-by-step explanation:
3/5=30/x
x= The total cost
You can see that 3×10 multiplies to 30, so the total cost would be 5×10.
Total cost= 50
Based on a sample survey, a company claims that 75% of their costumers are satisfied with their products. Out of 1,176 customers, how many would you predict to be satisfied?
Answer:
I got 882
Step-by-step explanation:
I did what is 75% of 1,176
An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.
Answer:
[tex]p = -10x + 200[/tex]
[tex]m = -10x^2 +200x[/tex]
Step-by-step explanation:
We know that at a price of $ 150, 5 televisions are sold and at a price of $ 100, 10 televisions are sold.
We must write a linear equation for this situation.
The equation of the line will have the following form
[tex]p = mx + b[/tex]
Where m is the slope of the line and b is the intercept with the p axis
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{100-150}{10-5}=-10[/tex]
[tex]b=p_1-mx_1\\\\b=150-(-10)(5)\\\\b=200[/tex]
The equation is:
[tex]p = -10x + 200[/tex]
Now we know that the revenue m is the product of the price p for the quantity sold x.
[tex]m = p * x[/tex]
[tex]m=(-10x + 200)*x[/tex]
[tex]m = -10x^2 +200x[/tex]
Answer:
[tex]p=-10x+200[/tex]
[tex]m = -10x^2+200x[/tex]
Step-by-step explanation:
Given : An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day.
To Find: Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.
Solution:
Let p be the price and x be the no. of television sold
We are given that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. i.e(5,150) and (10,100)
Now to find the linear equation to compare the price of a television, p, to the number sold, x.
We will use two point slope form
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(5,150)[/tex]
[tex](x_2,y_2)=(10,100)[/tex]
Substitute the values in the formula
[tex]y-150=\frac{100-150}{10-5}(x-5)[/tex]
[tex]y-150=\frac{-50}{5}(x-5)[/tex]
[tex]y-150=-10(x-5)[/tex]
[tex]y-150=-10x+50[/tex]
[tex]y=-10x+50+150[/tex]
[tex]y=-10x+200[/tex]
x is the no. of television sold
y is the price
Since p denotes the price
So, [tex]p=-10x+200[/tex]
Thus a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex]
Now [tex]Revenue = Cost \times quantity[/tex]
Since price of x telivisons = [tex]p=-10x+200[/tex]
So, [tex]Revenue = (-10x+200) \times x[/tex]
[tex]Revenue = -10x^2+200x[/tex]
m denotes revenue
So,[tex]m = -10x^2+200x[/tex]
Thus a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]
Hence a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex] and a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]
Write an expression the represents the sum of any number plus 3
Answer: x + 3
Step-by-step explanation: In this question you need to know that a sum is the answer when you add numbers. In this case x = any number. The expression is x + 3
Answer:
Step-by-step explanation:
Hello
Being X represented on any number, the expression will be:
X+3
Best regards
please please help 1-5
Answer:
1. 12 bags for total cost of 119.88
2. Yes. You'll make $180.12 for your labor.
3. Other tools, transportation, weather delay etc.
4. $28.02
5. Yes
Step-by-step explanation:
Begin by finding the area of the field. The field is a rectangle and measures 360 by 160. The area is A = l*w = 360*160 = 57,600 square feet. One bag of fertilizer will cover 5000 square feet. Divide 57,600 by 5000 to find the number of bags needed. You'll need 11.52 bags or rounded 12 bags.
Since each bag costs $9.99, multiply 12 by $9.99 to get the total cost for the fertilizer. The cost is $119.88. If the athletic department pays you $300. You'll make 300 - 119.88 = 180.12 for your labor. This is a good profit.
If you have to purchase another tool for $40, then the cost increases to 159.88. This decreases your profit to 180.12 - 40 = 140.12. Divide your profit 140.12 by the 5 hours you work to find how much you earn per hour. You earn $28.02 per hour.
Yes, I would take the job, since $28.02 is well above minimum wage.
What is the distance between the points (−7, 1) and (−7, −5) on the coordinate plane, in units?
Answer:
6 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (- 7, - 5)
d = [tex]\sqrt{(-7+7)^2+(-5-1)^2}[/tex]
= [tex]\sqrt{0+(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 units
Final answer:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane is 6 units, calculated by the absolute difference in their y-coordinates.
Explanation:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane can be found by calculating the difference in their y-coordinates. Since the x-coordinates are the same, the points lie on a vertical line, and the distance is simply the absolute difference in the y-coordinates.
The calculation would be: distance = |y2 - y1| = |-5 - 1| = | -6 | = 6 units
Therefore, the distance between the two points is 6 units.
Solve by Elimination. (10 Points)
Show all work. Clearly identify the solution.
y=2x+3
x+y=6
Make y the subject:
y = 6 - x
Now, use Elimination.
0 = 3x - 3
Divide both sides by 3:
0 = x - 1
So x = 1.
Substitute back into the equation:
y = 6 - (1)
So y = 5.
Hence, the answers are x = 1, y = 5.
PLEASE HELP ASAP!!!!
1. Give an example of a compound event. Why is it a compound event? How do you calculate the probability of a compound event?
2.Explain how you would create and use a spinner to simulate the probability of an event.
3.Max has a bag of plain and cat’s eye marbles. There are 30 plain marbles and 7 cat’s eyes. He picks one marble and sets it aside. Then he picks
another. What is the probability that he picked 2 cat’s eye marbles?
Answer: a compound event is when only 2 things can happemn
you divide the first number by the second number
you would creat a spinner with several collers then each coler would be a event you spin and that coler is the event
7/37
please give me brainly
Step-by-step explanation:
An example of a compound event is tossing a coin and drawing a card; it involves multiple independent events. A spinner for probability should represent outcomes fairly. The probability that Max picks 2 cat's eye marbles consecutively is calculated by multiplying the probability of each selection.
Explanation:Understanding Compound Events and Probability
An example of a compound event is tossing a coin and drawing a card from a poker deck simultaneously. It is classified as a compound event because it consists of two independent events that result in a combined outcome. The probability of a compound event is calculated using the product rule when the events are independent. This is done by multiplying the probabilities of each independent event occurring on its own.
To create a spinner that simulates the probability of an event, identify all the possible outcomes and ensure they are represented on the spinner fairly, with areas proportional to the probabilities of the outcomes. Spin the spinner a large number of times, documenting the outcomes to estimate the probability based on relative frequency.
Calculating the probability that Max picks 2 cat’s eye marbles in a row involves dependent events since the outcome of the first draw influences the outcome of the second. Initially, there is a 7/37 chance of picking a cat’s eye marble. Once one is picked, there are 6 cat’s eye marbles left and 36 marbles in total, so the probability of the second pick being a cat’s eye marble is 6/36. The combined probability is (7/37)*(6/36).
Of the choices below, which unit of measurement would be most appropriate for measuring the mass of a train?
comment the choices and I can tell you the answer. from a guess I would say kilogram
Kilograms kg is the unit of measurement would be most appropriate for measuring the mass of a train.
What is mass?Mass is defined as the matter that is present in the given object. Following are the most commonly used units for the measurement of mass:
GramKilogramSI Unit of Mass;
The standard SI unit of mass is as; kilogram (kg)
Other units that are accepted for use in SI are gram (g) and its multiples and submultiples, a tonne (t) (or “metric ton”), electronvolt (eV), the atomic mass unit (u) which is most convenient for expressing the masses of atoms and molecules.
Hence, Kilograms kg is the unit of measurement would be most appropriate for measuring the mass of a train.
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Explain how you would use mental math to express 16/25 as a percent???
16/25 (× 4 -up & down)
=64/100 (devide)
=0.64%
Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the total length
One centimenter is 0.01 meters. So, you can write the measures as
[tex] 152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}[/tex]
Once this rewriting is done, getting the total length [tex]T[/tex] is quite trivial, since all measurements are in the same unit, and we can simply sum everything:
[tex]T = 152.40+205.10+310.39 = 667.89[/tex]
Which equation or inequality shows the relationship between the values |7| and |-7|? A. |7| > |-7| B. |7| < |-7| C. |7| = |-7| D. |7| ≠ |-7|
Answer:
C.)
| 7 | = | -7|
Step-by-step explanation:
because absolute values are always positive....so, absolute values of | -7 | and | 7 | are both 7
Answer:
Step-by-step explanation:
7 I guess
what is the range for 2,8,15,4,11,6,2,6
Answer:
The range is 13. Hope this helps.
Answer:
13
Step-by-step explanation:
Range = Highest value - lowest value
Range = 15-2
Range = 13
Hope This Helps:)
Which of the following are point-slope equations of the line going through (-5,6) and (1,1)?
Answer:
[tex]A.\ y-6=-\dfrac{5}{6}(x+5)\\\\B.\ y-1=-\dfrac{5}{6}(x-1)[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-5, 6) and (1, 1). Substitute:
[tex]m=\dfrac{1-6}{1-(-5)}=\dfrac{-5}{6}\\\\\text{For point (-5, 6):}\\\\y-6=-\dfrac{5}{6}(x-(-5))\\\\y-6=-\dfrac{5}{6}(x+5)[/tex]
[tex]\text{For point (1, 1):}\\\\y-1=-\dfrac{5}{6}(x-1)[/tex]
On a map, 1 inch equals 20 miles. Two cities are 8 inches apart on the map. What is the actual distance between the cities?
If 1 inch equals 20miles then 8 inches equals 20 x 8 = 160 miles.
So you want to find out the distance for both the cities. Since there are 8 inches to both cities, then the answer would be 160 miles since every inch would equal to 20 miles, which is the actual distance.
Hope this helped!
Nate