A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road, (x2 + 3) miles downhill, and (x − 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?
A spherical fish bowl is half-filled with water. The center of the bowl is C, and the length of segment AB is 20 inches, as shown below. Use for pi. Which of the following can be used to calculate the volume of water inside the fish bowl?
complete the point slope equation of line through (1,-1) and (5,2) use exact numbers
y-(-1)=
The point - slope equation of line passing through points (1, -1) and (5, 2) is (y + 1) = (3/4)(x - 1).
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line.[c] → is the y - intercept.Other possible equations of lines are -
Point - slope form → (y - y₁) = m(x - x₁) Two point - slope form → (y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) Intercept form → x/a + y/b = 1 Normal form → x cos(β) + y sin(β) = LGiven is a line passing through points (1, -1) and (5, 2).
The point slope form of the line is -
(y - y₁) = m(x - x₁)
y - (- 1) = {(2 + 1)/(5 - 1)}(x - 1)
y + 1 = (3/4)(x - 1)
Therefore, the point - slope equation of line passing through points (1, -1) and (5, 2) is -
(y + 1) = (3/4)(x - 1)
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At the movie theatre, you pay a different price depending on your age. Children 5 and under get in for free. Children ages 6 to 18 pay $5. Everyone else pays $8. Write a piecewise function for this situation
Which table shows a proportional relationship between miles traveled and gas used?
Answer:
last fourth table given in the figure shows the proportional relationship .
Step-by-step explanation:
Definition of proportional relationship
The relationship in which two quantities are varies proportional to each other .
[tex]a = kb[/tex]
Where k is called the proportional constant .
Let us assume that the number of miles travelled be y .
let us assume that the gas used be x .
[tex]y\propto x[/tex]
y = ca
Where c is the proportional constant .
In first table
Miles travelled = 27.3 mi
Gas used =1.5 gal
Putting in the formula
y = ca
27.3 = 1.5c
[tex]\frac{27.3}{1.5}=c[/tex]
c = 18.2
Miles travelled = 49.16 mi
Gas used = 3.8 gal
Putting in the formula
y = ca
49.16 = 3.8c
[tex]\frac{49.16}{3.8}=c[/tex]
c = 12.94 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Second Part
Miles travelled = 135 mi
Gas used = 7.4 gal
Putting in the formula
y = ca
135 = 7.4c
[tex]\frac{135}{7.4}=c[/tex]
c = 18.2
Miles travelled = 135.5 mi
Gas used = 7.9 gal
Putting in the formula
y = ca
135.5 = 7.9c
[tex]\frac{135.5}{7.9}=c[/tex]
c = 17.2 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Third table
Miles travelled = 120 mi
Gas used = 6.2 gal
Putting in the formula
y = ca
120 = 6.2c
[tex]\frac{120}{6.2}=c[/tex]
c = 19.4 (Approx)
Miles travelled = 180 mi
Gas used = 12.2 gal
Putting in the formula
y = ca
180 = 12.2c
[tex]\frac{180}{12.2}=c[/tex]
c = 14.8 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Fourth table
Miles travelled = 270 mi
Gas used = 15gal
Putting in the formula
y = ca
270 = 15c
[tex]\frac{270}{15}=c[/tex]
c = 18
Miles travelled = 135 mi
Gas used = 7.5 gal
Putting in the formula
y = ca
135= 7.5c
[tex]\frac{135}{7.5}=c[/tex]
c = 18
Thus the miles travelled is vary with the gas used .
Therefore table shows the proportional relationship .
The last fourth table given in the figure shows the proportional relationship .
Janet's Junk Shop is having its annual sale. Matt wants to buy a mixer that originally sold for $28.62 and is now on sale for off. Matt also has a coupon for an additional 15% off the discounted price.
How much will Matt pay for the mixer?
How do you find the LCM???
I know that I asked how to find the LCM of 8 and 9 but I don't know what to multiply by to get it.
9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.
A 6
B 15.7
C 3
D 9.42
Answer:
A. 6
Step-by-step explanation:
Write the formula c = 2πr. Substitute the value 18.84 feet for c. Solve the equation for c. Since the radius always measures one-half the length of the diameter, multiply the value of c by 2.
Sales of a new tablet grow by 10% every month. Sales for this month are at 5 thousand. Write an equation to represent this situation and then approximate the sales 6 months from now.
Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0
modal of 9
10
11
14
19
22
27
29
21
18
11
6
Solve the equation ax + 1 = bx for 'x'. Please be sure to include all steps.
How does changing the function from f(x) = −4 cos 3x to g(x) = −4 cos 3x − 6 affect the range of the function?
The function shifts down 4 units, so the range changes from −4 to 4 in f(x) to −8 to 0 in g(x).
The function shifts down 4 units, so the range changes from −1 to 1 in f(x) to −5 to −3 in g(x).
The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).
The function shifts down 6 units, so the range changes from −1 to 1 in f(x) to −7 to −5 in g(x).
Answer:
The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).
Step-by-step explanation:
Given : f(x) = −4 cos 3x and g(x) = −4 cos 3x − 6.
To find : How does changing the function affect the range of the function?
Solution : We have given that
Function change from f(x) = −4 cos 3x to g(x) = −4 cos 3x − 6.
By the transformation rule : f(x) →→→f(x) -k it mean function shifted down k unit .
Then Function would shift down 6 unit .
For f(x) = −4 cos 3x
Range: [ -4,4]
For g(x) = −4 cos 3x − 6.
Range : [-10 ,-2]
Therefore, The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).
The scores of several classmates on a language arts test are shown below: 86 points 87 points 87 points 94 points 95 points 82 points 78 points 89 points 80 points 84 points What is the median score for these students?
Answer:
78,80,82,84,86,87,87,89,94,95
86+87/2 = 86.5
Step-by-step explanation:
You decide to start saving up to buy your first home. You find an account that pays 8% interest compounded monthly. If you plan on purchasing your home in ten years, how much must you put into the account to have $50,000 for a down payment?
Each pack of hot dogs contains 10 hot dogs (no buns), but each pack of hot dog buns contains 8 buns. Phil buys a number of these packs for a barbecue. After the barbecue, Phil finds that he has 4 hot dogs left over. What is the SECOND smallest number of packs of hot dogs he could have bought?
The second smallest number of packs of hot dogs that Phil could have bought is three. This gives him 30 hot dogs, and after eating some, he would be left with 4. The number 30 ends with a 0 and when 4 is subtracted from it, it does result in a number ending in 4 (26 in this case).
Explanation:To solve this problem, we need to understand that Phil must have bought a number of hot dog packs where the total number of hot dogs (10 per pack) ends with a 4. This is because after eating some, he had 4 hot dogs leftover. If he bought 1 pack of hot dogs, he'd have 10. This does not work because it doesn't end with 4. However, if Phil bought 2 packs, this would give him 20 hot dogs, which does end with 0.
We need to continue on this pattern, using multiples of 10, until we find the second smallest number that, when 4 is subtracted from it, leaves a number ending in 4. That number is 30, which gives 30 hot dogs. After eating some, he would be left over with 4 dogs, hence he has eaten 26 dogs (30-4=26). This means, the second smallest number of hot dog packs Phil could have bought is three.
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jenny borrowed $500 for 5 years at 4% interest compounded annually. what is the total amount she will have paid when she pays off the loan?
The next three terms in the pattern 1, 10, 19, 28, 37 are
Write 0.8 repeating as a fraction
Answer: 8/9
Step-by-step explanation: I got the answer right
Plz help me with this math problem
45.5 meters in 13 seconds
1/2x =20
Pls help
I need answer in like a minute
Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?
y = 3x + 2
6x – 2y = 10
Ryan’s answer:
I solved by adding the equations. The solution is .
y = 3x + 2 → 3x + y = 2
6x – 2y = 10 → 3x – y = 5
6x = 7
x =
6x – 2y = 10 → 6 – 2y = 10
7 – 2y = 10
–2y = –3
y = -
Jesse’s answer:
I used matrices. The solution is .
Mark’s answer:
I graphed the equations. The lines are parallel and do not intersect, so there is no solution.
6x - 2y = 10
-2y = -6x + 10
reduce by dividing by -2
y = 3x - 5
slope = 3 and y int = -5
y = 3x + 2
slope = 3, y int = 2
These lines are parallel. Parallel lines will have the same slope, but different y integers. There is no solution to this because the lines never intersect.
Mark's answer is correct
A bag has 6 yellow marbles and 6 brown marbles. Half of the brown marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a brown, glass marble?
Write your answer as a fraction in simplest form.
A gift box is a rectangular prism14inches long,5inches wide,and 4inches high.If the box is to be covered in fabric ,how much fabric is needed if there is no overlap?
The total fabric needed would be 292 square inches.
To calculate how much fabric is needed to cover the gift box without overlap, we must find the surface area of the rectangular prism representing the box. The formula to find the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height.
Given the dimensions of the box are 14 inches (length), 5 inches (width), and 4 inches (height), we calculate the surface area as follows:
2 (14 × 5) = 2 × 70 = 140 square inches (for the top and bottom)2 (14 × 4) = 2 × 56 = 112 square inches (for the front and back)2 (5 × 4) = 2 × 20 = 40 square inches (for the left and right sides)The total surface area is 140 + 112 + 40 = 292 square inches of fabric needed to cover the entire box.
whats the property in equation 3(2x-6)=6x-18
A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 41. What is the number
Why would experimental probability differ from theoretical probability?
Sam bought 86 pounds of flour for his bakery. Every day he used the same amount of flour to make bakery items. After 10 days, Sam was left with 25.2 pounds of flour. On average, how many pounds of flour did Sam use each day?
86-25.2 = 60.8 pounds of flour used
60.8/10 = 6.08 pounds used per day
Answer:
6.08
Step-by-step explanation:
first, i subtracted 86 from 25.2 to get what he used in the 10 days, which was 60.8, then i would divide it by 10 bc of 10 days to get 6.08. Hope this helps!
kasabihan sa bibliya