A repair service charges $45 for a house call and an additional $50 per hour of work. The formula T=45+50Hrepresents the total charge T for H hours of work. If the total bill for a customer was $270, how many hours of actual labor were there?There were____ hours of actual labor.

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function f(x) = -5(x + 7)

When x = -2; f(-2) = -5(-2 + 7) = -25

When x = -1; f(-1) = -5(-1 + 7) = -30

When x = 0; f(0) = -5(0 + 7) = -35

When x = 1; f(1) = -5(1 + 7) = -40

When x = 2; f(2) = -5(2 + 7) = -45

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

5

Step-by-step explanation:

All you would have to do is read the question. Because if it is like a block than it couldn't be any closer to the bottom than five inches.

Answer:

beeebooobeeeeeboooooobeeeeebooooooo

Step-by-step explanation:

option a

Answer:

Option A: \(\{0,\frac{\pi}{2},\frac{3\pi}{2}\}\)

Step-by-step explanation:

\(sin^2(\theta)=2sin^2(\frac{\theta}{2}), [0,2\pi)\)

\(sin^2(\theta)=2sin^2(\frac{\theta}{2})\)

\(sin^2(\theta)=2sin(\frac{\theta}{2})sin(\frac{\theta}{2})\)

\(sin^2(\theta)=2(\sqrt{\frac{1-cos(\theta)}{2}})(\sqrt{\frac{1-cos(\theta)}{2}})\)

\(sin^2(\theta)=2(\frac{1-cos(\theta)}{2})\)

\(sin^2(\theta)=\frac{2-2cos(\theta)}{2}\)

\(sin^2(\theta)=1-cos(\theta)\)

\(1-cos^2(\theta)=1-cos(\theta)\)

\(-cos^2(\theta)=-cos(\theta)\)

\(cos^2(\theta)=cos(\theta)\)

\(cos^2(\theta)-cos(\theta)=0\)

\(cos(\theta)[cos(\theta)-1]=0\)

\(cos(\theta)=0\)

\(\theta=\frac{\pi}{2},\frac{3\pi}{2}\)

\(cos(\theta)-1=0\)

\(cos(\theta)=1\)

\(\theta=0\)

Therefore, the solutions contained within the interval are \(\{0,\frac{\pi}{2},\frac{3\pi}{2}\}\)

Helpful Tips:

Half-Angle Formula: \(sin(\frac{\theta}{2})=\pm\sqrt{\frac{1-cos(\theta)}{2}}\)

Pythagorean Identity: \(sin^2(\theta)+cos^2(\theta)=1,sin^2(\theta)=1-cos^2(\theta),cos^2(\theta)=1-sin^2(\theta)\)

\(\sin^2 \theta = 2 \sin^2 \left(\dfrac{\theta}2 \right)\\\\\implies \sin^2 \theta = 1- \cos 2 \cdot \dfrac{\theta}2\\\\\implies \sin^2 \theta = 1- \cos \theta \\\\\implies 1-\cos^2 \theta = 1 - \cos \theta \\\\\implies -\cos^2 \theta - \cos \theta = 0\\\\\implies \cos^2 \theta - \cos \theta = 0\\\\\implies \cos \theta( \cos \theta -1) = 0\\\\\\\text{Now,}\\\\\cos \theta = 0\\\\\implies \theta = n\pi + \dfrac{\pi}2\\\\\text{For n = 0,1 and}~ [0.2\pi)\\\\\)

\(\theta = \dfrac{\pi}2, \dfrac{3\pi}2\)

\(\text{Again,} \\\\\cos \theta -1= 0\\\\\implies \cos \theta = 1\\\\\implies \theta = 2n\pi\\\\\text{For n= 0 and}~ [0,2\pi)\\\\\theta = 0\\\\\text{Combine solutions,}\\\\\theta = 0, \dfrac{\pi}2, \dfrac{3\pi}2\)

Domain of the function represented by the graph of a quadratic function y = \(x^2\) – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = \(x^2\) - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  \(x^2\) - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

For more such information on: quadratic function

https://brainly.com/question/29293854

#SPJ8

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

Learn more about standard deviation here :

brainly.com/question/29991053

#SPJ4

Answer: You can turn 7/6 into a mix number as you can see for a    example 6/6 is a whole number so 7/6 is 1 extra number in the numerator so 6/6 makes 1 and 1 extra so the answer is

1  1/6  

Answer:

8%

Step-by-step explanation:

Solving our equation

r = 2800 / ( 7000 × 5 ) = 0.08

r = 0.08

converting r decimal to a percentage

R = 0.08 * 100 = 8%/year

The interest rate required to

accumulate simple interest of $ 2,800.00

from a principal of $ 7,000.00

over 5 years is 8% per year.

Answer:

$609

Step-by-step explanation:

Answer:

\(\frac{20}{9}\) or \(2 \frac{2}{9}\)

Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

Answer:

C

Step-by-step explanation:

There are all types of radio signals traveling around us, just not the extra-terrestrial type!

Answer:  The first one (-3,6)

Step-by-step explanation:

Both linear functions meet at (-3,6).

You can graph both linear functions on the Desmos graphing calculator website to verify your answer.

Answer:

3.704 and

Step-by-step explanation:

Place a decimal number as the denominator of a fraction with 1 as the numerator, then divide to calculate the reciprocal of a decimal

1/0.27=3.704

1/3.6=0.2778

Check the picture below.

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

Answer:

Step-by-step explanation:

-11°

The value of y is 48.

To find the value of y in this scenario, we need to use the fact that the angle bisector of ∠JSL splits it into two congruent angles.

Let's denote one of these congruent angles as ∠HSL and the other as ∠LSJ. Since ∠JSL is bisected, we have:

m∠JSL = m∠HSL + m∠LSJ

Given that m∠JSL = (4y - 10)° and m∠HSL = m∠LSJ = ∠HSJ = (y + 43)°, we can substitute these values into the equation:

4y - 10 = (y + 43) + (y + 43)

Simplifying the equation:

4y - 10 = 2y + 86

Subtracting 2y from both sides:

2y - 10 = 86

Adding 10 to both sides:

2y = 96

Dividing both sides by 2:

y = 48

Therefore, the value of y is 48.

For more questions on value of y

https://brainly.com/question/28896476

#SPJ8

The accrued value of Staci's investment in the account in the year 2029 is $26933.59

The statements in the question can be sumarrized as

The formula to calculate amount on investment is

Amount = P * (1 + r)ⁿ

Where

When the values are substituted in the amount equation, we have

Amount = 14500 * (1 + 3.5%)¹⁸

Evaluate

Amount = 26933.59

Hence, the amount after the investment is $26933.59

Read more about compound interest at

brainly.com/question/28020457

#SPJ1

The height of the mountain estimated by two students is 2,467.98 meters.

The height of the mountain is calculated as follows;

tanα = h/( a + b + x)

where;

tan37 = h/(1850 + 740 + x)

tan37 = h/(2590 + x)

h = tan37(2590 + x)

h =1,951.82 +  0.7536x  ---- (1)

tanβ = h/(b + x)

tan60 = h/(740 + x)

h = tan60(740 + x)

h = 1,281.68 + 1.732x ---- (2)

Solve (1) and (2) together

1,951.82 +  0.7536x = 1,281.68 + 1.732x

1,951.82  -  1,281.68 = 1.732x  -  0.7536x

670.14 = 0.9784x

x = 684.93 m

h = 1,281.68 + 1.732x

h = 1,281.68 + 1.732(684.93)

h = 2,467.98 m

Thus, the height of the mountain estimated by two students is 2,467.98 meters.

Learn more about angle of elevation here: https://brainly.com/question/88158

#SPJ1

if the question is 2y+3y=a and z+6z=b

then i could solve it otherwise sry

Answer: x+2, 2x=10, and x-1=4

Step-by-step explanation:

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

11

Step-by-step explanation:

3 x 4 ÷ 6 + 3²

multiply 3 and 4 to get 12

\(\frac{12}{6}\)+3²

divide 12 by 6 to get 2

2+3²

find 3 to the power of 2 to get 9

2+9

Add 2 and 9 to get 11

11

hope this helps!

Marina could use for the third side of the triangular sandbox the option: C - 7.25 ft.

In mathematic, there is a rule for triangle side lengths. This rule says that the sum of the lengths of any two sides of a triangle is greater than the length of the one side (third side).  Therefore,

                                       \(L_1+L_2 > L_3\, (1)\\ \\ L1+L_3 > L_2\, (2)\\ \\ L_2+L_3 > L_1\, (3)\)

The question gives two sides: 3 ft (L1) and 7.25 ft (L2), applying the equation (1) of rule for triangle side lengths, you have:

                                          \(L_1+L_2 > L_3\\ \\ 3+7.25 > L_3\\ \\ 10.25 > L_3\\ \\ L_3 < 10.25\)

The options for answer are: 4.25ft, 10.25ft,  7.25ft and 3ft. According to triangle inequality \(L_3 < 10.25\), hence, the letter B is not the answer.

After that, you can apply equations (2) or (3) for testing the options. For solution below, it was used the equation (2).

                                 \(L_1+L_3 > L_2\\ \\ 3+4.25 > L_2\\ \\ 7.25 > L_2\\ \\ L_2 < 7.25\)

The second side is exactly equal to 7.25, according to the rule this side should be less than 7.25. Therefore, the option 4.25 ft is not the answer.

                                 \(L_1+L_3 > L_2\\ \\ 3+7.25 > L_2\\ \\ 10.25 > L_2\\ \\ L_2 < 10.25\)

The question informs that the second side is 7.25 ft. Then 7.25 < 10.25, so the option 7.25 ft is the answer.

You can continue to test the last option, but it is not necessary since you have already found the corrected answer.

                                 \(L_1+L_3 > L_2\\ \\ 3+3 > L_2\\ \\ 6 > L_2\\ \\ L_2 < 6\)

The second side is equal to 7.25, hence, the option 3 ft is not the answer.

Read more about the triangle inequality theorem here:

https://brainly.com/question/2403556

Answer:

Step 3: Add those deviations together.

Step-by-step explanation:

The approximate percentage difference of the best and worst rose deals according to their unit costs is; 25%

Percent difference formula is obtained by dividing the absolute value of change by the average of the values and then multiplying it with 100. Thus;

Percentage difference = (x2 - x1)/x1

where;

x2 is final value

x1 is initial value

3 roses cost $4.80. Thus;

Unit cost of this is; 4.8/3 = $1.60 each

6 roses cost $9.. Thus;

Unit cost = 9/6 = $1.50

12 roses cost $14.40. Thus;

Unit Cost = 14.40/12 = $1.2

36 roses cost $45. Thus;

Unit cost = 45/36 = $1.25

Best deal = $1.6 and worse deal = $1.2

Percentage difference = (1.6 - 1.2)/1.6 * 100% = 25%

Read more about percentage difference at; https://brainly.com/question/11360390

#SPJ1