Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
Complete Question: What is the equation of line that is parallel to the line [tex]y=\frac{1}{5}+4[/tex] and passes through [tex](-2,2).[/tex]
[tex]Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}[/tex]
To find the equation of a line parallel to a given line and passing through a given point, use the point-slope form of a line.
Explanation:To find the equation of a line parallel to the given line, we need to remember that parallel lines have the same slope. The given line has a slope of 1/5. So, the parallel line will also have a slope of 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get:
y - 2 = 1/5(x + 2)
To simplify the equation, we can multiply through by 5 to get rid of the fraction:
5y - 10 = x + 2
Finally, we can rearrange the equation to the standard form:
x - 5y = -12
Learn more about Equation of a line here:https://brainly.com/question/21511618
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Given the system of equations, what is the solution?
3x - 2y + 10 = 0
5y = 4x + 8
{(-34/7, -16/7)}
{(-34/7, 16/7)}
{(34/7, -16/7)}
Answer:
{(-34/7, -16/7)}
Step-by-step explanation:
Rearrange values, multiply to solve for x.
(5) 2y = 3x + 10
(-2) 5y = 4x + 8
Solve for x.
10y = 15x + 50 ↓
-10y = -8x -16
Combine and evaluate.
0 = 7x + 34
Subtract 34 from both sides.
7x = -34
Divide both sides by 7.
x = [tex]\frac{-34}{7}[/tex]
Plugin x value into either equation to solve for y.
2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10
2y = [tex]\frac{-102}{7}[/tex] + 10
2y = [tex]\frac{-32}{7}[/tex]
y = [tex]\frac{-16}{7}[/tex]
16 divided by a number minus four is 40
Answer:
16/x - 4 = 40
16/x = 44
16 = 44x
16/44 = 44x
Hope this helps! pls rate me!
Step-by-step explanation:
Della Ahkta has a whole life policy for $50,000. She pays an annual premium rate of $13.47 per
$1,000. When she signed her insurance contract she chose to use the annual dividend to reduce the
annual premium. When she gets a notice that her insurance premium is due, she is notified that her
policy has paid an annual dividend of $27.94. What amount will Della need to send the insurance
company to pay the balance due on the annual premium?
Answer:
645.56
Step-by-step explanation:
50000/1000 13.37=673.50
673.50
-27.94
Evaluate the function. F(x)=3/x-1/. F(-3)
Simplify the expression 6s + 9c - 2s
Answer:
4s+9c
Step-by-step explanation:
6s+9c-2s
-2s. -2s
4s+9
The sum of four and three multiplied by the quotient of four and two
Answer:
14
Step-by-step explanation:
4+3=7
4/2=2
7•2=14
A curtain measuring 6ft wide was bought for a window. However, when it hung, the curtain covered only 2/3 of the window. How wide was the window?
Answer:
9ft wide
Step-by-step explanation:
First we convert it to ratios
[tex]\frac{6}{x} \frac{2}{3}[/tex]
Then we cross-multiply
6*3=2x
Multiply 6 and 3
18=2x
Solve for x
x=18/2
x=9
-4/3x-3=1/3x+3/4 solve for X
Answer:
-9/4
Step-by-step explanation:
-4/3x-3=1/3x+3/4
-4/3x-1/3x-3=3/4
-5/3x=3/4+3
-5/3x=3/4+12/4
-5/3x=15/4
x=(15/4)/(-5/3)
x=(15/4)(-3/5)
x=-45/20
simplify
x=-9/4
Can you divide a number with a fraction
Answer:
yes
Step-by-step explanation:
yesAnswer:
yes you can
Step-by-step explanation:
if its a number put it as a fraction put a one number the number your divining and divide and if it's a improper fraction turn in into a mixed number :)
perimeter of a triangle formula
Side 1 + side 2 + side 3 = perimeter
Step-by-step explanation:
You add all three side lengths
Twenty-four hundredth in decimal notation
Answer:
0.24
Step-by-step explanation:
Twenty-four hundredths = 24/100 = 24×(1/100) = 24×0.01 = 0.24
_____
Both 24/100 and 0.24 are pronounced "twenty-four hundredths."
Answer:
0.24
Step-by-step explanation:
If you say hundredths with ths it means that the number is at the right side the decimal point. so that means twenty four hundredths is at the right side of the decimal point so the answer will be 0.24 hundredths.
HELPPP....PLEASE...........
Answer:
9 1/3, 12 1/2, 14 3/4
Step-by-step explanation:
I assume the formula you’re working with is A=b*h since nothing says otherwise...
((Patio 1))
So you have your area (147) and your base (15 3/4), now you need to plug them in, which should look like this:
147= 15 3/4*h
You need to isolate your h in order to get the missing number, so you should divide both sides by 15 3/4 OR 63/4 ((15*3—>60+3=63))
Dividing by a fraction is the equivalent of multiplying by its reciprocal... so
147 * 4/63 = 588/63 which can be simplified to 84/9 once both the numerator and denominator are divided by 7
In mixed number for it is 9 3/9 which simplified becomes 9 1/3
You solve the other similarly
Jaqueline buys 4 bracelets and 2 necklaces each bracelet cost $8 and jaqueline’s total is $70
Answer:
1 necklace is $19!
Step-by-step explanation:
4•$8=$32
$70-$32=$38
$38/2=$19
A skating rink sold 66 tickets. Of these, 2/3 were children’s tickets, and the rest were adult tickets. What total number of adult tickets were sold
Answer:22
Step-by-step explanation:
66/3=22 so each part is 22 1 part for adults is 22
Sam invests $6000 in an account that pays interest of 4.5% per year.
a) How much interest would he earn each year?
b) How much would he have in his account at the end of the first year?
He would earn an interest of $270 each year and at the end of the first year he would have $6270 in his account.
Step-by-step explanation:
Step 1: Given details are Principal Amount (P) = $6000, Rate of Interest (R) = 4.5% and time (T) = 1 yearStep 2: Calculate simple interest by using the formula SI = PRT/100⇒ SI = 6000 × 4.5 × 1/100
⇒ SI = 60 × 4.5 = $270
Step 3: Calculate the amount he would receive at the end of an year by using the formula, A = P + SI⇒ A = 6000 + 270
⇒ A = $6270
If you have 470 apples and the price is 67 apples how much is each apple
Answer:
Each apples cost about $0.14
Step-by-step explanation:
cost / amount = price per piece
67 / 470 = 0.14
So every apple costs about $0.14
You are on your way to work. You drive 3.9 miles to a gas station and buy gas. Your workplace is 1.39 miles from the gas station. What is the distance of your commute to work?
Your commute is
( ?????) Miles.
Answer:
Approx. 5.3 miles
Step-by-step explanation:
find the area of the shape shown below
Answer: 42 units squared
Step-by-step explanation:
3x7=21
3x7=21 divided by 2 = 10.5 + 10.5 = 21 so,
21+21=42
Hope it helps
Answer:
34.5 units^2
Step-by-step explanation:
The square is A = bh.
A = 7 * 3 = 24.
The triangle is A = 0.5bh.
A = 0.5 * 7 * 3 = 0.5 * 21 = 10.5.
24 + 10.5 = 34.5 units^2.
The ratio of faculty members to students at a college is 1:15. If there are 675 students, then how many faculty members are there?
Answer:
The number of faculty member is 45.
Step-by-step explanation:
Ratio of faculty members to students = 1 : 15
Number of students = 675
Total = Number students + faculty members
Let the total be t
Let the faculty member be f
Representing the ratio, we have:
[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]
Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:
Total = Number students + faculty members
[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]
The number of faculty member is 45.
1) What percent of 29 is 3?
Answer: It's about 10.34%
Step-by-step explanation:
There are 180 calories in 3 scoops of vanilla ice cream. How many calories are in 7 scoops.
Answer:
420 calories
Step-by-step explanation:
180 / 3 = 60 calories
60 x 7 =420 calories
i really need help i cant fail this
Answer:
[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex] [tex]or\ 0.42x^2[/tex]
Step-by-step explanation:
Given:
Height of the triangle [tex]h = x[/tex]
Base of the triangle [tex]b=\frac{5}{6}x[/tex]
We need to find the area of the triangle.
Solution:
Using given Formula:
[tex]Area\ of\ a\ trinagle = \frac{1}{2}bh[/tex]
Where:
b = Base of the triangle.
h = Height of the triangle.
Substitute [tex]h = x[/tex] and [tex]b=\frac{5}{6}x[/tex] in equation in given formula.
[tex]Area\ of\ a\ trinagle = \frac{1}{2}(\frac{5}{6})x\times x[/tex]
[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex]
[tex]Area\ of\ a\ trinagle =0.42x^2[/tex]
Therefore, Area of the triangle is [tex]\frac{5}{12}x^2[/tex] or [tex]0.42x^2[/tex].
Ava’s aquarium is 95% filled with water. The tank holds 1,120 gallons of water. Which is the remaining number of gallons of water needed to fill the aquarium to the top?
Answer:
The aquarium needs 56 more gallons to be completely filled.
Step-by-step explanation:
To get the amount remaining you have to first divide 1120 by 100
1120/100=11.2
Then multiply it by 95
11.2*95=1064
You take the maximum amount (1120) and subtract the amount in the tank (1064) to get the amount left.
1120-1064= 56
With 56 gallons as your final answer.
a woman making$25 an hour gets a 30% raise how much is her new salery
Answer:
32.5
Step-by-step explanation:
Take 30% of $25, and get 7.5, then add $7.50 to $25. Now she's making $32.50 an hour.
A cylindrical jar's lid has a radius of 4 inches. If the volume is 351.68 in , approximately what is the height of the jar?
Answer:
7 inches
Step-by-step explanation:
The volume of a cylinder is calculated using
[tex]V = \pi {r}^{2}h[/tex]
where r =4 inches is the radius and V=351.68 is the volume.
To find the height of the jar, we substitute these values and solve for h.
[tex]351.68 = 3.14 \times {4}^{2} \times h[/tex]
[tex]351.68 = 50.24h[/tex]
Divide both sides by 50.24 to get:
[tex]h = \frac{351.68}{50.24} [/tex]
h=7 inches
Therefore the height of the jar is 7 inches
Frankie and his family go out to dinner. Dinner cost $32.43 and she gave an 18% tip. Along with 7% tax, what is the final bill?
Answer:
40.54
Step-by-step explanation:
32.43×3%=2.27
32.43×18%=8.107.
2.27+5.84=8.11.
32.43+8.11=40.54 total paid.
If a polynomial function f(x) has roots 4 - 131 and 5, what must be a factor of f(x)?
Answer:
(x - 4), (x + 131), and (x - 5) must all be factors of f(x).
Step-by-step explanation:
A square coaster has a side length of 512 feet on each side.
What is the area of the coaster?
Answer:
do u mean 5/12
Step-by-step explanation:
What is the final amount if 943 is decreased by 13% followed by a further 6% decrease?
Give your answer rounded to 2 DP.
The final amount after a 13% decrease followed by a further 6% decrease from 943, rounded to two decimal places, is 771.19.
Explanation:To calculate the final amount after sequential percentage decreases, you first apply the initial percentage decrease to the original amount, then apply the second percentage decrease to the new, lower amount.
Here’s how you can do it step by step:
Calculate the first decrease of 13%: 943 × 0.13 = 122.59Subtract the first decrease from the original amount: 943 - 122.59 = 820.41Calculate the second decrease of 6% on the new amount: 820.41 × 0.06 = 49.2246Subtract the second decrease from the new amount: 820.41 - 49.2246 = 771.1854The calculator answer is 771.1854, but since we want the answer rounded to two decimal places, we must look at the third decimal place. Since the digit in the thousandths place (5) is greater than or equal to 5, we round up giving us a final answer of 771.19.
At the zoo, the Spencer family bought 3 adult tickets and 2 children's tickets for $23.50. The Yang family bought 2 adult tickets and 4 children's tickets for $25. How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?
Diaz family spend $ 20 if they bought 3 adults tickets and 1 children's ticket
Solution:
Let "a" be the cost of each adult ticket
Let "c" be the cost of each student ticket
The Spencer family bought 3 adult tickets and 2 children's tickets for $23.50
Therefore, we frame a equation as:
[tex]3 \times a + 2 \times c = 23.50[/tex]
3a + 2c = 23.50 --------- eqn 1
The Yang family bought 2 adult tickets and 4 children's tickets for $25
Therefore, we frame a equation as:
[tex]2 \times a + 4 \times c = 25[/tex]
2a + 4c = 25 ----------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
6a + 4c = 47 ---------- eqn 3
Subtract eqn 2 from eqn 3
6a + 4c = 47
2a + 4c = 25
( - ) --------------
4a = 47 - 25
4a = 22
Divide both sides of equation by 4
a = 5.5
Substitute a = 5.5 in eqn 1
3(5.5) + 2c = 23.50
16.5 + 2c = 23.50
2c = 23.50 - 16.5
2c = 7
Divide both sides of equation by 2
c = 3.5
Thus, cost of each adult ticket = $ 5.5
Cost of each student ticket = $ 3.5
How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?
Total cost = 3a + 1c
Total cost = 3(5.5) + 1(3.5) = 16.5 + 3.5
Total cost = 20
Thus Diaz family spend $ 20
Final answer:
The Diaz family would spend $20 for 3 adult tickets and 1 children's ticket at the zoo after solving the system of linear equations given by the Spencer and Yang families' purchases.
Explanation:
Let A be the price of an adult ticket and C be the price of a children's ticket. We are given:
3A + 2C = $23.50 (Spencer family)
2A + 4C = $25 (Yang family)
To solve this system, we can multiply the first equation by 2 and the second equation by 3:
6A + 4C = $47 (Spencer family doubled)
6A + 12C = $75 (Yang family tripled)
Subtracting the first equation from the second gives us:
8C = $28
Dividing both sides by 8 yields:
C = $3.50
Now that we know the price of a children's ticket, we can substitute this value back into one of the original equations to find the price of an adult ticket.
3A + 2(3.50) = $23.50
3A + $7 = $23.50
3A = $16.50
A = $5.50
With the price of both ticket types known, we can now calculate the cost for the Diaz family:
3A + 1C = 3($5.50) + 1($3.50)
3A + 1C = $16.50 + $3.50
3A + 1C = $20
Therefore, the Diaz family would spend $20 if they bought 3 adult tickets and 1 children's ticket.