A service center charges a fee of x dollars for an oil change plus y dollars per quart of oil used. A sample of its sales record is shown.
A table shows the oil tank size in quarts and total cost for two customers. Customer A: Oil tank size, 5 quarts. Total cost, 22.45 dollars. Customer B: Oil tank size, 7 quarts. Total cost, 25.45 dollars.
Write a system of linear equations that represents this situation.
Equation for customer A:
____=22.45$
Equation for customer B:
___=25.45$
Question 2
Find the fee and cost per quart of oil.
$ fee?
$ per quart of oil?
Answers
Answer:
Fee - $14.95, and $1.5 per quart of oilStep-by-step explanation:
Equation for customer A:
x + 5y =22.45$Equation for customer B:
x + 7y=25.45$Subtract the first equation from the second and solve for y:
x + 7y - x - 5y = 25.45 - 22.452y = 3y = 3/2y = 1.5Find x by substituting the value of y:
x + 5*1.5 = 22.45x = 22.45 - 7.5x = 14.95Related Questions
Compute (4803) • 95. *
Answers
Answer:
456,285
zzzzzzzzzzzzzzzzzzzzz
Use the given x and y values to write a direct variation
equation.
x = 2, y = 30
Answers
Answer:
y = 15x
Step-by-step explanation:
Given x and y are in direct variation then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 2, y = 30, then
30 = 2k ( divide both sides by 2 )
15 = k
y = 15x ← equation of variation
What is 5 divided by 3/4?
Answers
20/3 was the answer
Answer:
20/3 or 6 2/3
Step-by-step explanation:
to divide fractions, you flip the second fraction then multiply across.
5=5/1
5/1divided by 3/4
change to 5/1 x 4/3
multiply across
answer is 20/3 or 6 and 2/3
Help plz
(1,-4)
(4,1))
(-1,-4)
(1,4)
Answers
Answer:
(1, -4)
Step-by-step explanation:
1d - 2) = 6
4
What is the value of d + 3?
Answers
Step-by-step explanation:
6 c. 2 d. 6 e. a2 + 2a + 3 f. (x + h)2 + 2(x + h) + 3 9. a. 2 b. 0 c. 65/4 d. x2 + 1/x e. (s + h)2 + 1/(s +
Hannah takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the length of the cut is 12inches and the paper is 8 inches long, what is the width of the sheet of paper (nearest tenth)?
Answers
Distribute 3x ( -x + 4).
Answers
Convert: 1000 g = __ kg
Answers
Answer: 1000 G= 1kg
Step-by-step explanation:
Answer:
1000 g=1 kg
5000 mm = 5 m
Step-by-step explanation:
NEED HELP ASAP ILL GIVE BRAINLIST RN
For ΔABC, the measure in degrees of angles A, B, and C are 36, 3x, and 48 respectively. What is the value of x?
A
2
B
32
C
93
D
96
Answers
Answer:
B. 32
Step-by-step explanation:
[tex]\angle A + \angle B + \angle C = 180\\36 + 3x + 48 = 180 => 3x = 96 => x = 32[/tex]
Answer:
bgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbg
Step-by-step explanation:
HELP PLEASE!!
Helen rolls a dice and flips a coin.
Calculate the probability that she gets a 4 and a tail.
Answers
Answer:
Step-by-step explanation:
The probability of getting a 4 is 1/6, the probability of getting a tails is 1/2. Add the two together 8/12. I don't know if its right but hopefully it helped.
How you Can find the area of a composite figure?
Answers
Answer:
Here are the steps to find the area of a composite figure.
1. Split the composite figure into simpler shapes.
2. Find the area of each of the simpler shapes.
3. Add the area of all the simpler shapes together.
4. You'll have the area of the composite figure.
Let me know if this helps!
−214=r−45
Help
Asp
Plz
Answers
Answer:
-169
Step-by-step explanation: add 45 on both sides
Answer:
r=-169
Step-by-step explanation:
I hope it helped bro
HELP PLEASE
The value of h, to the nearest hundredth, is ...
Answers
Answer:
50.19
Step-by-step explanation:
quick mafs hun <3
Suppose Jordan buys five notebooks with a unit rate of $3 and five packages of pens with a unit rate of $1. Which of the expressions below represent Jordan's purchases?
Answers
Answer:
Jordan's purchase was $20
Step-by-step explanation:
3x5=15 5x1=5 5+15=20
What is the slope of the graphed line?
Answers
Answer:
3/9
Step-by-step explanation:
3/9 because it goes up 3 right 9
If you answer both of these i will give
Brainliest ( if thats how you spell it )
Answers
Answer:
first one:4/10
second one: 8/24
Step-by-step explanation:
i think this works but a hundred 100% sure though.
here you go hope its correct.
Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical. At a point d = 37 meters from the tree, the angle of elevation to the top of the trees
is a = 29° (see figure). Find the height h of the tree. (Round your answer to one decimal place.)
h =
m
d m
Additional Materials
eBook
Answers
Answer:
Height of the tree is 40.0 meters.
Step-by-step explanation:
From ΔABC,
m∠ABC = 90°
Since, m∠ABC = m∠CBD + m∠ABD
90° = 6° + m∠ABD
m∠ABD = 90°- 6° = 84°
By triangle sum theorem in ΔABD,
m∠ABD + m∠BDA + m∠DAB = 180°
84° + 29° + m∠BDA = 180°
m∠BDA = 180° - 113°
= 67°
By sine rule in ΔABD,
[tex]\frac{\text{sin}(\angle BDA)}{d}= \frac{\text{sin}(\angle ABD)}{h}[/tex]
[tex]\frac{\text{sin}(67)}{37}= \frac{\text{sin}(84)}{h}[/tex]
h = [tex]\frac{\text{sin}(84)\times 37}{\text{sin}(67)}[/tex]
h = 39.98
h ≈ 40.0 meters
Therefore, height of the tree is 40.0 meters.
The sine rule is the ratio of the side length to the sine of the opposite angles. Then the height of the tree is 40 meters.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a triangle.
Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical.
At a point d = 37 meters from the tree, the angle of elevation to the top of the trees is a = 29° (see figure).
∠ABC = 90
We have
In ΔABC
∠ABC = ∠CBD + ∠ABD
∠ABD = 90 - 6
∠ABD = 84
By triangle sum in ΔABD, we have
∠ABD + ∠BDA + ∠DAB = 180
∠BDA = 180 - 84 - 29
∠BDA = 67
Then by the sine rule, we have
[tex]\begin{aligned} \dfrac{\sin \angle BDA}{d} &= \dfrac{ \sin \angle ABD }{h}\\\\\dfrac{\sin 67}{37} &= \dfrac{\sin 84}{h}\\\\h &= \dfrac{\sin 84} \times 37{\sin 67}\\\\h &= 39.98 \approx 40 \end{aligned}[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Which equation represents the line that passes through
the points (2, 3) and (4, 7)?
Answers
Answer:
Step-by-step explanation:
(7 - 3)/(4 - 2) = 4/2 = 2
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 1
x-3y=7
2х-6у=12
Solve the following systems
Answers
Answer:
Step-by-step explanation:
this system doesnt have any solutions
if you multiply the first equation by 2 you will get
2x-6y=14
second equation is
2x-6y=12
the result will -12=14
no solutions
what is the slope of 2y + 8x = 20
Answers
Answer:
y=4x+10
Step-by-step explanation:
2y-8x-20=0
2y-8x=0+20
2y-8x=20
2y=8x+20
y=4x+10
Hope this will help!!:)
The side lengths of a triangle are 5,√3,√28. Is the triangle a right triangle? How would I solve this?
Answers
Answer:
it is a right triangle.
Step-by-step explanation:
you would solve by using pythagorean theorem. Firstly you would find the square roots. Then write the pythagorean theorem out replacing the variables with the corresponding numbers. All you do for this is find the greatest number and that is c. Lastly you would add the square roots of a and b, if this equals 28 then they are equal. Ask more questions if I did not explain this clearly.
A light bulb is designed by revolving the graph of:
[tex]y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}[/tex]
Over the interval 0 ≤ x ≤ 1/3 about the x-axis, where x and y are measured in feet. Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. (Glass is 0.015 inch thick).
Answers
Answer:
[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringCalculus
Differentiation
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]Step 3: Integrate Pt. 1
Substitute [Surface Area]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property: [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]Step 4: Integrate Pt. 2
[Integral] Define: [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply: [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]Step 5: Integrate Pt. 3
[Integral] Substitute/Integral - FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply: [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]It is in ft² because it is given that our axis are in ft.
Step 6: Find Amount of Glass
Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.
Convert ft² to in²: [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply: [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]And we have our final answer! Hope this helped on your Calc BC journey!
Share £160 in the ratio 1:9
Answers
Answer:
let ratio be x and9x
x +9 x=£160
x=£160/10
x=£16
9x=£16×9=£144
Answer:
16 and 144
Step-by-step explanation:
Breaking 160 into 1+9 = 10 parts
1 part would be 16
the rest would be 9 parts = 160 - 16 =144
The floor of a rectangular shed is 12 ft by 14 ft.
What is the area of the floor in square feet?
Answers
Answer:
Step-by-step explanation:
S=a*b=12*14=168feet²
Can someone please help me with this!! ASAP
Answers
Answer:
The bbn vxcndzx Decide which item would best check the reliability of each statement.
Bvdfiuxjgiodfjcgkfmctgihnrdtjfk,m viufihjmgjkhyntfuvibjkhmgutjfyh,jmtifg
This book was written by a prominent banker in England.
check author's background
check copyright date
check another referenceb
Step-by-step explanation:
is this correct??
ONLY ANSWER IF YOU ARE FOR SURE RIGHT!
the question: “which trig. ratio woild you use to find the missing side?”
Answers
Answer:
Step-by-step explanation:
It's not the tangent. The tangent relates two sides neither of which is the hypotenuse, which you are given.
The trig ratio you would use is the one that relates the angle to the side opposite the angle and the hypotenuse.
That is the definition for the Sine.
BRAINLIEST N 15 POINTS
Table to Linear Equation
Answers
Answer:
Y=-5X+1
Step-by-step explanation:
Answer:
y = -5x + 1
Step-by-step explanation:
y = mx + b
m = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1}}[/tex] = [tex]\frac{-9-(-4)}{2-1} = -5[/tex]
y = -5x + b: then plug in a point to find b
-19 = -5(4) + b
-19 = -20 + b
b = 1
Plug in all the values to get: y = -5x + 1
The triangles are similar.
What is the value of x?
Enter your answer in the box
x=
Answers
Answer:
Since the corresponding sides of similar triangles are proportional,
[tex]\frac{x}{7} =\frac{75}{25} \\or, x = \frac{75(7)}{25}\\or, x = 21[/tex]
the store offers a 40% discount the regular price of a t-shirt is 22 what is the discount price?
Answers
Answer:
$8.80
Step-by-step explanation:
So because [tex]40\% = .4[/tex], then the equation is [tex].4 \times 22[/tex] which equals [tex]8.8[/tex], or $8.80.
Bobby had a box of berry flavored hard candies. Fifteen candies were strawberry flavored, twelve candies were blueberry flavored, and thirteen candies were raspberry flavored. Bobby picked one candy from the box without looking. What is the probability, written as a percent, that the candy he picked was not raspberry flavored?
Answers
15 strawberry
12 blueberry
13 raspberry
27/40