Lionel uses two functions to model the costs of having a problem diagnosed and repaired by two appliance repair companies. He models the cost, in dollars, of having Phil’s Appliances handle the repair job, requiring x hours of labor, with function p: p(x) = 68x + 81. He models the cost of having Quality Electric handle the same repair with function q: q(x) = 51x + 90. The function_______ represents the amount, in dollars, Lionel will save by having Quality Electric handle an x-hour repair instead of Phil’s Appliances. Lionel will save_____ $ if he uses Quality Electric for a repair needing 2 hours of labor.
Answers
The function (119x + 171) represents the amount, in dollars. Lionel will save 409 $ if he uses Quality Electric for a repair needing 2 hours of labor.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The system of equations are;
p(x) = 68x + 81.
q(x) = 51x + 90.
So,
p(x) + q(x) = 68x + 81 + 51x + 90
p(x) + q(x) = 119x + 171
The function (119x + 171) represents the amount, in dollars, Lionel will save by having Quality Electric handle an x-hour repair instead of Phil’s Appliances.
p(x) + q(x) = 119x + 171
x= 2 hours
p(x) + q(x) = 119 (2) + 171
p(x) + q(x) = 409
Lionel will save 409 $ if he uses Quality Electric for a repair needing 2 hours of labor.
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Related Questions
use spherical coordinates. evaluate x2 dv, e where e is bounded by the xz-plane and the hemispheres y = 1 − x2 − z2 and y = 16 − x2 − z2
Answers
To evaluate x² dV over the region E bounded by the xz-plane and the hemispheres y = √16 − x² − z² and y = √25 − x² − z² using spherical coordinates, set up the triple integral as ∫∫∫ (r sin θ cos φ)² r² sin θ dr dθ dφ, with the limits of integration as 0 ≤ r ≤ √(16 - z²), 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ 2π.
To evaluate the integral x² dV using spherical coordinates, we first need to express the integral in terms of the spherical coordinate system. The differential volume element in spherical coordinates is given by dV = r² sin θ dr dθ dφ.
Since we want to find the integral over the region E, which is bounded by the xz-plane and the two hemispheres, we need to determine the limits of integration for the spherical coordinates.
The bounds for the other two spherical coordinates, r and φ, can be determined by considering the equations of the two hemispheres.
For the upper hemisphere, we have:
y = √(16 - x² - z²)
Setting y = 0, we can solve for r and z:
0 = √(16 - x² - z²)
Squaring both sides, we get:
0 = 16 - x² - z²
Rearranging the equation, we have:
x² + z² = 16
This represents the boundary of the upper hemisphere, so the limits for r and φ will be determined by this equation.
For the lower hemisphere, we have:
y = √(25 - x² - z²)
Setting y = 0, we can solve for r and z:
0 = √(25 - x² - z²)
Squaring both sides, we get:
0 = 25 - x² - z²
Rearranging the equation, we have:
x² + z² = 25
This represents the boundary of the lower hemisphere, so the limits for r and φ will be determined by this equation.
Using the spherical coordinate system, we can rewrite x² dV as (r sin θ cos φ)² r² sin θ dr dθ dφ.
Now, we can set up the integral:
∫∫∫ (r sin θ cos φ)² r² sin θ dr dθ dφ
The limits of integration are as follows:
0 ≤ r ≤ √(16 - z²)
0 ≤ θ ≤ π/2
0 ≤ φ ≤ 2π
By evaluating this triple integral, we can find the value of x² dV over the region E.
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Complete Question:
Use spherical coordinates. Evaluate x² dV, E where E is bounded by the xz-plane and the hemispheres y =√16 − x² − z² and y = √25 − x² − z² .
Edward buys 6 yards of fabric for $15. How much money does it cost per
yard?
Answers
Answer:
$2.5
Step-by-step explanation:
15 divided by 6 because its asking to split into groups equally
Answer:2.5
Step-by-step explanation:
please help i have no clue how to this any tips appreciated:))
Answers
Answer:
\( \displaystyle PW = \underline{ \quad18 \quad}\)
Step-by-step explanation:
by tangent property we acquire:
\( \displaystyle 3x - 6 = x + 10\)
add 6 to both sides:
\( \displaystyle 3x= x + 16\)
cancel x from both sides:
\( \displaystyle 2x= 16\)
divide both sides by 2:
\( \displaystyle x= 8\)
so,
\( \displaystyle PW = 3x - 6\)
plug in the got value of x:
\( \displaystyle PW = 3.8 - 6\)
simplify multiplication:
\( \displaystyle PW = 24- 6\)
simplify Substraction:
\( \displaystyle PW =18\)
hence, The measure of PW is 18 unit
please help :) im giving brainlyyyy
Answers
Answer:
a. 3
b. 9
Step-by-step explanation:
6 / 2 = 3
It takes each person 3 hours.
a. 3
b. 3*3 = 9
I NEED HELP!!!
solve x^3 - 6x^2 - 7x + 60 by factoring. show all work
(using the method in the picture below)
Answers
Answer: x = -3, 5, 4
Step-by-step explanation:
Don't have time for it
Which expression is equivalent to 4(3 + b)?
7 + b
12b
12 + b
12 + 4b
Pls help!!
Answers
You leave a 20% tip of $4.50. How much was the bill?
Answers
Answer:
Rm5.40
Step-by-step explanation:
First, 20/100 × Rm4.50 = Rm0.90. Second, Rm4.50 + Rm 0.90 = Rm5.40
Please give me brainliest hehe.
Answer: 0.90 BUT IF YOU ROUND UP TO HOLE DOLLARS THEN YOUR TIP WOULD BE 1 DOLLAR
Step-by-step explanation: THAT IS YOUR ANSWER HOPE I HELPED :D
What is the measure of angle 1?
920
2.
86
88°
90°
92°
Answers
Answer:
m∠1 = 88°
m∠2 = 92°
Step-by-step explanation:
From the given figure lines 'k' and 'm' are the parallel lines and line 'L' is the transversal line,
m∠1 + 92° = 180° [Sum of consecutive exterior angles is 180°]
m∠1 = 180 - 92
m∠1 = 88°
m∠1 + m∠2 = 180° [Linear pair of angles are supplementary angles]
88° + m∠2 = 180°
m∠2 = 180 - 88
m∠2 = 92°
Solve 270=3e^2.4K to the nearest hundredth
If you can solve this for me could you please give steps so I can understand, please and thank you so much!
Answers
Given:
The equation is:
\(270=3e^{2.4K}\)
To find:
The solution for the given equation to the nearest hundredth.
Solution:
We have,
\(270=3e^{2.4K}\)
Divide both sides by 3.
\(\dfrac{270}{3}=e^{2.4K}\)
\(90=e^{2.4K}\)
Taking ln on both sides, we get
\(\ln (90)=\ln e^{2.4K}\)
\(\ln (90)=2.4K\) \([\because \ln e^x=x]\)
Divide both sides by 2.4.
\(\dfrac{\ln (90)}{2.4}=K\)
\(\dfrac{4.4998}{2.4}=K\) \([\because \ln (90)\approx 4.4998]\)
\(1.874916667=K\)
Round the value to the nearest hundredth (two decimal place)
\(K\approx 1.87\)
Therefore, the value of K is 1.87.
6. One of the transformations above was a dilation by a scale factor of k. The scale factor is the multiplicative amount that the picture has been enlarged. To calculate it, divide any length on B by the corresponding length on A. Use your ruler to make these measurements and then calculate the scale factor of the dilation. Round to the nearest tenth.
Answers
Answer:
well it is b
Step-by-step explanation:
well I tried my best
When a figure or a shape is dilated, the size of its image will either be enlarged or compressed.
The scale of dilation from A to B is 1.5
See attachment for the image that completes the question.
Using a ruler, we have the following measurements
\(\mathbf{A = 1\ inch}\)
\(\mathbf{B = 1.5\ inches}\)
The scale factor (k) from A to B is:
\(\mathbf{k = \frac BA}\)
This gives
\(\mathbf{k = \frac {1.5\ inches}{1\ inch}}\)
\(\mathbf{k = \frac {1.5}{1}}\)
\(\mathbf{k = 1.5}\)
Hence, the scale factor (k) from A to B is 1.5
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Is -1 1/6 rational? HURRY
Answers
Answer:
yes
Step-by-step explanation:
since it can be expressed as a fraction, it is rational
a $12$-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. only six slices have pepperoni, and exactly ten slices have mushrooms. how many slices have both pepperoni and mushrooms?
Answers
The terms with "x" cancel out, and we're left with:
0 = 12
6 + 10 + x + (12 - (6 + 10 + x)) = 12
Simplifying the equation, we have:
16 + x - (16 + x) = 12
The terms with "x" cancel out, and we're left with:
0 = 12
Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.
Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:
Slices with only pepperoni: 6 slices
Slices with only mushrooms: 10 slices
Slices with both pepperoni and mushrooms: $x$ slices
Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices
We know that the total number of slices is 12, so we can write an equation:
6 + 10 + x + (12 - (6 + 10 + x)) = 12
Simplifying the equation, we have:
16 + x - (16 + x) = 12
The terms with "x" cancel out, and we're left with:
0 = 12
This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.
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the geometric shape of a smooth up-and-down motion that represents a periodic oscillation like tides is a
Answers
The geometric shape that represents a smooth up-and-down motion of a periodic oscillation like tides is a sine wave. A sine wave is a smooth, continuous curve that repeats itself in a regular and periodic manner.
The geometric shape of a smooth up-and-down motion that represents a periodic oscillation like tides is a sinusoidal curve or a wave. More specifically, it can be described as a sine wave.
A sine wave is a smooth, continuous curve that repeats itself in a regular and periodic manner. It is characterized by its oscillating pattern, where it alternates between positive and negative values as it moves along the x-axis. The shape of the sine wave resembles the rising and falling motion of tides, making it an appropriate geometric representation.
In the context of tides, the sine wave represents the periodic variations in the water level caused by the gravitational pull of the Moon and the Sun. As the tide rises and falls, the water level follows a smooth, up-and-down motion similar to the shape of a sine wave.
By using mathematical functions and trigonometry, the behavior of tides and other periodic oscillations can be accurately modeled and represented by sinusoidal curves, allowing us to study and predict their patterns and behaviors.
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Kirigami is the Japanese art of making paper designs by folding and cutting paper. A student sells small and large greeting cards decorated with kirigami at a craft fair. The small cards cost $3 per card, and the large cards cost $5 per card. The student collects $95 for selling a total of 25 cards. How many of each type of card did the student sell?
Answers
Let x be the number of small cards sold, and y be the number of large cards sold.
From the problem, we know that:
x + y = 25 (the total number of cards sold is 25)
3x + 5y = 95 (the total amount collected is $95)
We can use the first equation to solve for x in terms of y:
x = 25 - y
Substituting this into the second equation, we get:
3(25 - y) + 5y = 95
Simplifying and solving for y, we get:
75 - 3y + 5y = 95
2y = 20
y = 10
So the student sold 10 large cards.
Substituting this into x + y = 25, we get:
x + 10 = 25
x = 15
So the student sold 15 small cards.
Therefore, the student sold 15 small cards and 10 large cards.
Did I get this right? If I did t could someone explain it to me
Answers
Answer:
Yes, you are correct.
Step-by-step explanation:
Angle three and angle for our sample Mary angle three equals five times +15 and angle four equals 10 X
Answers
We can't say much about the relationship between angles three and four, or about their exact measurements.
Based on the information provided, we know that:
- Angle three is equal to 5 times +15, which can be simplified as 5(15) = 75.
- Angle four is equal to 10 X in 150, which means that 10 X = 150 - angle four.
- We don't have enough information to solve for X or to determine the exact measures of angles three and four.
However, we can make some observations:
- Angle three is a multiple of 15, which suggests that it may be a special angle in some way (e.g. a multiple of 30 or 45 degrees).
- Angle four is complementary to some other angle (since 150 degrees is the complement of 30 degrees). This means that if we knew the measure of the other angle, we could solve for X and then find the measure of angle four.
Overall, without more information, we can't say much about the relationship between angles three and four, or about their exact measurements.
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If AC bisects ∠BAD, is ABC ≅ ADC? Explain.
The?image?consists?of?a?regular?triangle?ABD?with?base?AD.?A?segment?joins?vertex?A?to?side?BD?at?point?C?making?an?angle?of?90?degrees?with?it.
A. Yes; then ∠BAC is congruent to ∠DAC, and the triangles are congruent by ASA.
B. Yes; then ∠BAC is congruent to ∠CAD, and the triangles are congruent by AAS.
C. No; in that case, only two pairs of corresponding congruent angles would be known.
D. No; in that case, only one pair of corresponding congruent angles and one pair of corresponding congruent sides would be known.
Answers
Answer: I think it’s a or c
Step-by-step explanation:
for the table below, what is the range?
Answers
Answer:
second option
Step-by-step explanation:
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A couple plans to save for their child’s college education. What principle must be deposited by the parents when their child is born to have $43,000 when their child reaches the age of 18 assume the money earned 8% interest compounded quarterly round your answer to the nearest decimal
Answers
SOLUTION
We will apply the amount formula
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where } \\ A\text{ = amount = }43,000\text{ dollars } \\ P=pri\text{ncipal money deposited }=\text{ ?} \\ r=\text{interest rate = 8}\%=0.08 \\ n\text{ = number of times compounded = quarterly = 4} \\ t=\text{ time in years = 18years } \end{gathered}\)Substituting each into the equation, we have
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 43,000=P(1+\frac{0.08}{4})^{4\times18} \\ 43,000=P(1.02)^{72} \\ 43,000=4.161140375P \\ P=\frac{43,000}{4.161140375} \\ P=10,333.7056972 \end{gathered}\)Hence the answer is $10,333.71 to two decimal places
solve -6x-2-8x=-1-14x-3
Which solution
Answers
Answer:
No solution
Step-by-step explanation:
1. Combine like terms: -14x -2 = -14x -4
2. Add 2 on both sides to isolate x: -14x = -14x -2
3. Add 14x on both sides: 0 = -2
There is no solution because 0 does not equal to -2.
When one increases the confidence level (1-α), say from 0.90 to 0.95, what happens to the width of the confidence interval? a. It stays the same b. It becomes wider c. It becomes narrower
Answers
Step-by-step explanation:
A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.
in a well-shuffled, standard 52 card deck, what is the probability that a card is a two, given that it is not a face card? answer choices are in a percentage format, rounded to the nearest whole number. a.) 4% b.) 8% c.) 10% d.) 29%
Answers
ahmed is 4 years old than sara, 5 years ago the sum of their age was 48, write a algebric equation to represent the situation and find saras age
Answers
Answer:
bjbhj
Step-by-step explanation:
Callan knows that the area of a square piece of artwork he owns is 289 square inches. Which shows the correct step he should take if he wants to find out the side lengths of the piece of artwork?.
Answers
Answer:
One side length is 17. Because you square root 289 to figure out the side length.
Step-by-step explanation:
The area of a square is a side length * a side length
or l^2 = 289
sqrt or 289 = 17
What is the answer to this equation -3+-5=?
Answers
Answer:
-8
Step-by-step explanation:
-3 + -5 = -8
Answer:
The answer to this equation is:
-8(-) + (-) = (-)
=> -3 + -5 = -8
Hope this helps you...
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Toothy the crocodile wants to eat a delicious chicken. His mouth is open to an angle of 30 degrees.
He needs to open his mouth to an angle of 55 degrees for the chicken to fit.
What is the measure of the additional angle Toothy's mouth needs to open so he can eat the chicken?
Answers
Answer: 25°
Step-by-step explanation:
From the question, Toothy the crocodile wants to eat a delicious chicken and his mouth is open to an angle of 30 degrees but he needs to open his mouth to the angle of 55 degrees for the chicken to fit.
The additional angle that Toothy's mouth needs to be open so he can eat the chicken will be:
= 55° - 30°
= 25°
Answer:
25
Step-by-step explanation:
did it on khan academy
What is the solution set to the following equation?
x4+2x−48=0
Select one:
a. { ±2i2–√,±6–√ }
b. { ±i6–√,±2–√ }
c. { ±2i2–√,±3 }
d. { ±i3–√,±22–√ }
Answers
The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
How to determine the solution set of the equation?The equation is given as:
x^2 + 2x - 48 = 0
A quadratic equation is represented as:
ax^2 + bx + c = 0
By comparing both equations, we have
a = 1, b = 2 and c = -48
The solution of the quadratic equation is then calculated using
x = (-b ± √(b^2 - 4ac))/2a
Substitute values for a, b and c in the above equation
x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1
This gives
x = (-2 ± √196)/2
Evaluate the square root of 196
x = (-2 ± 14)/2
Divide through by 2
x = -1 ± 7
Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
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The sides of One World Trade Center in New York City form
eight isosceles triangles, four of which are 200 ft long at their base BC. The
length AC of each sloping side is approximately 1185 ft.
Answers
The value of ∠BAC in the isosceles triangle is 9.7°
Cosine rule
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
a² = b² + c² - 2bc*cos(A)
where a, b, c are the sides of the triangle and A, B, C are the angles opposite the sides.
AB = AC = 1185 (isosceles), BC = 200, let ∠BAC = x°, hence:
200² = 1185² + 1185² - 2(1185)(1185)cos(x)
2(1185)(1185)cos(x) = 2808450
cos(x) = 0.9857
x = 9.7°
The value of ∠BAC in the isosceles triangle is 9.7°
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mina's explanation: i counted up from 15.75 to 176.3 to find the difference. i underlined each number i added on each line.
Answers
160.55 is the difference. i underlined each number i added on each line.
What is an linear equation in math?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The two numbers are 15.75 and 176.3
First we will compare the numbers.
1. A=176.3
2. B=15.75
one's place of A is greater than once place of B.
tens place of A is greater than tens place of B.
Hundred place of A is greater than hundred place of B.
So, A>B
So we will subtract 15.75 from 176.3.
176.30 -15.75=
176.30 ----A
- 1 5.75 ----B
Hundreths place of A - Hundreths place of B = 0-5=10-5=5
Tenth place of A - Tenth place of B =12-7=5
ones place of A - ones place of B=5-5=0
Tens place of A - Tens place of B =7-1=6
So the solution is 160.55
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factorise 9a^2-b^2??
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
3² * a² - b²
▹ Step-by-Step Explanation
9a² - b²
Break down each coefficient and variable:
9 = 3²
a² = a²
b² = b²
Combine everything together:
3² * a² - b²
Hope this helps!
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━━━━━━━☆☆━━━━━━━
Answer:
Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=[a+b][a-b] where a=3a and b=b