To find the constant 'a' in the function g(x) = 5x + a, you can substitute the known values into the function. Here, it leads us to the equation 5*4 + a = 31. Solving this equation gives 'a' = 11.
Explanation:The question gives us the value of g(4) and asks us to find the constant 'a' in the function g(x) = 5x + a.
To solve for 'a', we can substitute the known values into the equation. We know that g(4) = 31, and the function g(x) is defined as 5x + a. Therefore, we replace 'x' with 4 in the function. This gives us 5*4 + a = 31.
Solving this equation, we find that 20 + a = 31. By subtracting 20 from both sides of the equation, we can solve for 'a', giving us 'a' = 31 - 20 = 11.
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Determine the volume of a rectangle box with a link of 5 inches height of 7 inches and the width of 9 inches
PLZ HELP ASAP
The system of equations is graphed on the coordinate plane.
y=−12x−1y=14x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answer-
The coordinates of the solution to the system of equations is (4, -3)
Solution-
According to the graph the equations are,
[tex]y=-\frac{1}{2}x-1\\\\y=\frac{1}{4}x-4[/tex]
We can get the coordinates of the solution to the system of equations, by substitution.
[tex]\Rightarrow y=\frac{1}{4}x-4[/tex]
Putting the value of y in first equation,
[tex]\Rightarrow \frac{1}{4}x-4=-\frac{1}{2}x-1[/tex]
[tex]\Rightarrow \frac{1}{4}x+\frac{1}{2}x=-1+4[/tex]
[tex]\Rightarrow \frac{3}{4}x=3[/tex]
[tex]\Rightarrow x=3\times \frac{4}{3}[/tex]
[tex]\Rightarrow x=4[/tex]
Putting the value of x in the first equation,
[tex]y=-\frac{1}{2}\times 4-1=-2-1=-3[/tex]
Therefore, the coordinates of the solution to the system of equations is (4, -3)
The volume of a spherical tank is 790.272 pie cubic feet what is the
We are given the volume of a spherical tank = 790.272 π cubic feet.
We need to find the diameter of the container .
We know formula for volume of a sphere.
[tex]V=\frac{3}{4}(r^{3}\pi)[/tex]
Where r is the radius.
Plugging V= 790.272 π in the above formula, we get
[tex]790.272\pi =\frac{3}{4}(r^{3}\pi)[/tex]
Dividing both sides by π, we get
790.272 =[tex]\frac{4}{3}(r^{3})[/tex]
Multiplying both sides by 3, we get
2370.816 = [tex]4r^3[/tex]
Dividing both sides by 4, we get
592.704 = [tex]r^3[/tex]
Taking cube root on both sides, we get
r=8.4.
Diamater is 2 times of radius, that is 2 × 8.4 = 16.8
Therefore, the diameter of the container = 16.8 feet.
8 more than 5 times a number is -27
8 + 5n = -27
5n = -35
n = -7
The ratio of the prices of Emma's phone to Sophie's phone is 7:8. If Sophie's phone costs $640, how much should the prices of their phones decrease in order to have a ratio of 9:11 ?
Let cost of Emma's phone = x
Given that cost of Sophie's phone = 640
Then ratio of their phones cost will be x:640 or x/640
Given that ratio of their phones cost is 7:8 or 7/8
So both ratios will be equal.
[tex]\frac{x}{640}=\frac{7}{8}[/tex]
[tex]x=\frac{7}{8}*640[/tex]
x=560
So the new ratio of the cost of their phones will be 560:640
Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.
So let that decreased amount is k then we will get equation :
[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]
11(560-k)=9(640-k)
6160-11k=5760-9k
6160-5760=11k-9k
400=2k
200=k
Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.
Answer:
For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364
Step-by-step explanation:
To answer this question, call x on Emma's phone and z on Sophie's phone.
We know that the price relationship between x and z is 7: 8
This means that:
[tex]\frac{7}{8} =\frac{x}{z}[/tex]
We know that the price of Sophie's phone is $ 640
Entoces z = 640
Now we clear x
[tex]\frac{7}{8} =\frac{x}{640}\\ x =640}\frac{7}{8}=560\\ x = 560[/tex]
Then, if the new relationship is 9:11 then:
[tex]\frac{9}{11} =\frac{x}{640}[/tex]
x = $523,636
For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364
A 275 inch pipe is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.
Since one piece is four time the length x, we can represent that as 4x.
Thus making the equation:
4x+x=275
5x=275
x=55
4(55)=220
220+55=275
So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.
In order to find the length of the shorter piece of pipe, we can set up and solve the equation x + 4x = 275. When simplified, we get 5x = 275, and by dividing both sides of the equation by 5, we find that x = 55. This tells us that the length of the shorter piece is 55 inches.
Explanation:To solve this problem, let's denote the shorter piece as x. Because the other piece is four times the length of the shorter one, it can be denoted as 4x. We know that these two pieces put together make the total length of the initial pipe, which is 275 inches. Therefore, we can set up the equation: x + 4x = 275.
Simplifying this equation, we get 5x = 275. To get the value of x, we need to divide both sides of this equation by 5, resulting in x = 55. Hence, the length of the shorter piece is 55 inches.
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There arre a total of 82 students in robotics club and the science club the science club has 6 fewer students than the robotics club. How many students are in the science club?
Answer:
88
Step-by-step explanation:
You are just adding 82+6=88
2 11/32 divide by 1 1/2
2 11/32 / 1 1/2 = 25/16 hope this helps you
Antoine and Angela both like to walk for exercise. Today they are walking together. Antoine walks every 3 days and Angela walks every 5 days. Circle all the days on which they will walk together again. Choices are 8, 12, 15, 25, 45.
15 and 45 becuase bith 3 and 8 can go into them.
Solve for x over the complex numbers. x^2+8x+20=0
X= or X=
Steps:
[tex]x=\frac{-8+\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1}: -4+2i[/tex]
[tex]x=\frac{-8-\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1} -4-2i[/tex]
=\frac{-8-\sqrt{16}i}{2\cdot \:1}[tex]=-8-\sqrt{16}i[/tex]
[tex]=\frac{-8-\sqrt{16}i}{2}[/tex]
[tex]=\frac{-8-4i}{2}[/tex]
[tex]=-2\left(2+i\right)[/tex]
[tex]=-4-2i[/tex]
[tex]x=-4+2i,\:x=-4-2i[/tex]
Answer:you can use the quadratic formula but if you have to factor do the following:
x^2+8x+20=0
add -4 to both sides of the equation to complete the square
x^2+8x+20+(-4)=0+(-4)
x^2+8x+16=-4
(x+4)^2=-4
take the square root of both sides
x+4=+sqrt(-4)
x+4=+sqrt[(4)(-1)]
x+4=+2sqrt(-1) where sqrt(-1)=i, a complex number
x+4=+2i
x=-4+2i
x=-4+2i and x=-4-2i
you would get the same answer using the quadratic formula
Step-by-step explanation:
Today only, a table is being sold at a 27% discount. The sale price is $438 . What was the price yesterday?
It is $600. Hope i helped
Find the equation of the line that is perpendicular to y=3y-x=7 and contains the point (2,-1).
Chen rode his stake board 3 3/4 miles of an hour. What was his average speed in miles per hour?
3 3/4 miles as a decimal is 3.75 miles. He rode for one hour. Average speed within an interval is (distance made) / (interval duration). So the average speed = 3.75 miles / 1 hour, or 3.75 mph.
Francis heard that a car stereo system was on sale for 30% off. If the sale price was 57.75, what was the original price of the stereo?
Answer:
$82.5
Step-by-step explanation:
We can calculate it with a direct rule of 3. As it has a 30% off, the remaining price is the 70% and we want to know how much is the 100%
[tex]70\% -\!\!\!-\!\!\!- \$57.75\\ 100\% -\!\!\!-\!\!\!- \$ x[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {100/100*57.75}{70/100} \\ \\ x = \frac {57.75}{70/100}\\ x = 57.75 * 100/70[/tex]
x = 82.5
The original price of the stereo was $82.5
The original price of the stereo is 82.5
Since the car stereo system was on sale for 30% off, this means that it was sold for 100% - 30% = 70% of the original price.
Let the original price be represented by x
Therefore, 70% of x will be 57.75
70/100 × x = 57.75
0.7 × x = 57.75
0.7x = 57.75
Divide both side by 0.7
0.7x/0.7 = 57.75/0.7
x = 82.5
The original price of the stereo is 82.5
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Solve for t. −22t>66 Enter your answer, as an inequality, in the box.
t<-3 should be the answer. I hope this helps
At a chess tournament, the number of competitors in each round is 50% of the number of competitors in the previous round. What type of relationship most appropriately models this situation?
A. linear increase
B. exponential decay
C. exponential growth
D. linear decrease
Answer: Option B. exponential decay
Solution:
If initially the number of competitors is n
If the number of round is "r" and the number of competitors after "r" rounds is N(r)
1) After the first round (r=1), the number of competitors is:
N(r)=N(1) = n * 50% = n * 50/100 →N(r)=N(1)=n*0.5=n*0.5^1
2) After the second round (r=2), the number of competitors is:
N(r)=N(2) = N(1) * 50% = (0.5 n)*(50/100)=(0.5n)*(0.5)→N(r)=N(2)=n*0.5^2
3) After the third round (r=3), the number of competitors is:
N(r)=N(3)=N(2)*50%=(n*0.5^2)*(50/100)=(n*0.5^2)*(0.5)→N(r)=N(3)=n*0.5^3
Then:
For r=1→N(r)=N(1)=n*0.5^1
For r=2→N(r)=N(2)=n*0.5^2
For r=3→N(r)=N(3)=n*0.5^3
In general: N(r)=n*0.5^r
This is an exponential function because the independent variable "r" is in the exponent, and because the number of competitors (funcion N(r) )decrease with the number of rounds the type of relationship most appropiately models this situation is an exponential decay
The reduction by 50% of competitors each round in a chess tournament is modeled by an exponential decay relationship, not a linear decrease, as it depends on the current number of competitors.
The chess tournament with the number of competitors decreasing by 50% each round is best modeled by a exponential decay relationship. This is because with each round, the number of competitors is halved, which is a rate that depends on the current number of competitors. (A) linear decrease would imply a constant decrease irrespective of the current number of competitors, which is not the case here.
Exponential relationships can be represented by mathematical functions where the rate of change is proportional to the current value. In contrast to exponential growth, where the quantity increases at a rate proportional to its current value, exponential decay describes a situation where the quantity is reduced by a certain factor over equal successive periods.
using the distributive property method on 6x32 and 7x29
[tex]6\cdot32=6(30+2)=(6)(30)+(6)(2)=180+12=192\\\\7\cdot29=7(30-1)=(7)(30)-(7)(1)=210-7=203[/tex]
Answer:
Step-by-step explanation:
Students in Mr. Smith's class want to find out how far they can jump. Which of the following will help give a valid conclusion about the data?
1. Five students are chosen randomly to jump.
2. All 25 students are measured.
3. Students who want to jump are measured.
4. Students playing during recess are measured.
Answer:
2 student who want to jump are measured
the sum of a number 9 is multiplied by -2 and the answer is -8
find the number.
-2(x + 9) = -8
Distributive property.
-2x - 18 = -8
Add 18 to both sides.
-2x = 10
Divide both sides by -2.
x = -5
what is the solution of 7k+2=4k-10?
It rained on 3 out of every 5 days in the month of April. There are 30 days in April. On how many days did it rain that month?
3/5(30) = 18.
60% of the days in April it rained.
It rained 18 days in April.
Best of luck.
60% of it rained cause 3/5 is equaled to 60% so 18 Yeah.
What is the coefficient in the expression 3x13+4 ? Enter your answer in the box.
Answer:
3
Step-by-step explanation:
Its the number immediately before x
Answer:
What is the coefficient in the expression 3x13+4?
3/13
Step-by-step explanation:
How to represent the number 8.2 using base 10 blocks. How much each size blocks is worth?
To represent 8.2 using base 10 blocks, you need 8 one blocks and 2 tenth blocks, where one blocks represent 1 and tenth blocks represent 0.1. This method is effective for visualizing numbers in base 10.
Explanation:To represent the number 8.2 using base 10 blocks, we use different sizes of blocks to represent different place values in base 10.
Each size block is worth a different value based on its place in the number.
A hundred block represents 100.A ten rod represents 10.A one block represents 1.A tenth block (also known as a flat or a piece of flat) represents 0.1.To represent 8.2, we would need:
8 one blocks (because 8 is in the ones place).2 tenth blocks (because 2 is in the tenths place, representing 0.2).This method of representation helps in visualizing and understanding the value of numbers in the base 10 system. It's particularly useful in educational settings for explaining the concept of place values and decimals.
PLEASE HELP!!!!!
Which linear equation is in slope-intercept form? A) y = mx + b B) Ax + By = C C) y - y1 = m(x - x1) D) x - x1 y - y1 = m
Answer:
A) y=mx+b
Step-by-step explanation:
The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form.
what is a reasonable estimate for the product 43x68
You would first try to round the numbers to the nearest 10 and then multiply for a reasonable estimate. In other words, 40x70=2800
need help asap im not good at math
g(x):
flip f(x) over x-axist and next translate 2 units down.
Look at the picture.
Therefore your answer is: B. g(x) = -x² - 2Translations
y = f (x) + m up m units
y = f (x) - m down m units
y = f (x + m) left m units
y = f (x - m) right m units
Stretches/Shrinks
y = n · f (x) stretch vertically by a factor of n
y = 1/n · f (x) shrink vertically by a factor of m (stretch by 1/n)
y = f (1/n x) stretch horizonally by a factor of n
y = f (nx) shrink horizontally by a factor of n (stretch by 1/n)
Reflections
y = - f (x) reflect over x-axis (over line y = 0)
y = f (- x) reflect over y-axis (over line x = 0)
x = f (y) reflect over line y = x
How to find X intercept and Y intercept from a slope intercept equation
To find the X and Y intercepts from a slope intercept equation, first understand the equation structure (y = mx + b). The 'm' signifies the slope, and the 'b' indicates the y-intercept. To find the x-intercept, set y to zero and solve for x. To find the y-intercept, look at the 'b' value.
Explanation:In a slope intercept equation written in the form y = mx + b, the x-intercept and y-intercept are determined by values of y and x when they equal zero respectively. The 'm' signifies the slope of the line, indicating the rise over run on the graph, and the 'b' indicates the y-intercept, which is the point at which the line intersects the y axis.
To find the y-intercept from a slope-intercept equation, you consider the 'b' in the equation. For instance, in the line graph, the y-intercept is 9, meaning the line crosses the y-axis at the point (0,9).
To find the x-intercept (the point where the line crosses the x-axis), you set y equal to zero and solve for x. If 'y' is equal to '0', then the equation becomes 0 = mx + b. Solving for 'x' in this equation will give the x-intercept.
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you have already saved $55. you earn $9 per hour at your job. you are saving for a bicycle that cists $199. what inequality represents the possible numbers of hours you need to work to buy the bicycle ?
Henrieta divided 0.80 by 20 as shown. Is her work correc? If not , explain why and give a correct response.
Henrieta's work is incorrect. The correct answer is 0.04.
Explanation:No, Henrieta's work is not correct. To divide 0.80 by 20, we need to divide the numerator (0.80) by the denominator (20).
Dividing 0.80 by 20, we get 0.04.
Therefore, the correct answer is 0.04.
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What is 20k+11=8k+1 find k
k=-5/6 would be your answer
The answer you are looking for is K = -5/6.
To find this, you must get K by itself. First, subtract 8k from both sides to get 12k + 11 = 1. Next, subtract 11 from both sides to get 12k = -10. Finally, divide both sides by 12 to get K = -10/12, which simplified, is -5/6. Thus making -5/6 the answer.
I hope this helps!