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
Plz help me with this math problem
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
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?
A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 41. What is the number
kasabihan sa bibliya
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).
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 .
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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What number should the fraction 15/3 be multiplied by in order to equal one ?
The next three terms in the pattern 1, 10, 19, 28, 37 are
modal of 9
10
11
14
19
22
27
29
21
18
11
6
Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0
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.
divide
27,092÷45=
a.646 r22
b.624 r12
c.620 r2
d.602 r2
45.5 meters in 13 seconds
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?
Maric mailed 9 letters at the post office . each letter weighed 3.5 ounces. What was the total weightof the letters?
A company designs a logo using a kite figure around the letter t.
The logo is 12 centimeters wide and 16 centimeters tall. What is the area of the logo ?
Answer:
it is indeed B.96
Step-by-step explanation:
Solve the equation ax + 1 = bx for 'x'. Please be sure to include all steps.
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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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?
Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth.
Crystal rollerbladed 150 feet in 15 seconds, while Gavin rollerbladed 150 feet in 10 seconds. Without doing any calculations, who was faster? Why?
Ur answer is d have a nice day
Which shows the expressions in the order they would appear on a number line from least to greatest?
2 to the power of 3, square root of 5, square root of 20, square root of 11 11 over 9
2 to the power of 3, square root of 11, 11 over 9, square root of 20, square root of 11
11 over 9, square root of 5, square root of 11, square root of 20, 2 to the power of 3
11 over 9, 2 to the power of 3, square root of 5, square root of 20, square root of 11
The expressions in the order they would appear on a number line from least to greatest is 11/9, √5, √11, √20, 2³
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given are the statements expressing expressions,
2³ = 8
11/9 = 1.22
sqrt 5 = 2.24
sqrt 20 = 4.47
sqrt 11 = 3.32
Hence, the expressions in the order they would appear on a number line from least to greatest is 11/9, √5, √11, √20, 2³
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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.
1/2x =20
Pls help
I need answer in like a minute
Replace ? with a whole number to make the statements true. a. 20 ÷ 4 ? means ? × 4 = 20 b. 2,725 ÷ 5 ? means ? × 5 = 2,725 c. ? ÷ 5 = 0 ABC Preschool spent $1,475 on diapers this year. If the diapers cost $25 per box, how many boxes did they use? Grace, a hairdresser, charges $18 for a haircut and $70 for a perm. She did 36 perms this month. The total amount of money Grace took in was $4,608. How many haircuts did Grace do this month? Mr. and Mrs. Wilson hosted their daughter’s wedding. They paid $575 to rent a banquet hall and $13 per person for a catered dinner. In all, there were 118 people at the wedding. How much did the Wilsons pay for the hall and the food? Use inverse operations to check your answer. Carmel can drive 320 miles on one tank of gas, and one tankful costs $39. How many tanks of gas will she need to drive 2,240 miles, and how much will it cost? Use inverse operations to check your answer.
Why would experimental probability differ from theoretical probability?
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?