33. Calista earns $300 per week for a 40 hour work week plus $12.32 per hour for each hour of
overtime after 40 hours. Write an equation that would be used to determine her weekly wages
where w is her wages, and v is the number of overtime hours worked.

Answer: The slope of BC is -2.

Step-by-step explanation:

We know that a rectangle has all opposite sides equal and parallel.

Each interior angle is a right angle.

Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to  BC.   [ ∵ Angle between AB and BC is 90° .]   (1)

Also , slope of line passing through (a,b) and (c,d) :  [tex]\dfrac{d-b}{c-a}[/tex]

If A is located at (3, 4) and B is located at (7,6) .

Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Also, the product of slopes of two perpendicular lines is -1.

Then , (Slope of AB) x  (Slope of BC) = -1     [From (1)]

[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]

Hence, the slope of BC is -2.

Answer:

Distance = 63 km

Step-by-step explanation:

Speed = 90 km/h

Time = 42 mins

Time = 42 / 60 = 0.7 hrs

Distance = Speed × time

Distance = 90 km/h × 0.7 hr

Distance = 63 km

Answer:

adolescence

Step-by-step explanation:

Answer:

5a²+22a+8

Step-by-step explanation:

(5a+2)(a+4)

5a² + 20a + 2a + 8

5a² + 22a + 8

Answer:

⅓ remaining

Step-by-step explanation:

½ of 24 = 12

12 + 4 = 16 done

24 - 16 = 8

8/24 = 1/3

Answer:

1/3

Step-by-step explanation:

1) we have 24 problems

2) we finish half of them

What is half of 24?

It’s 12

So far, we have 12 problems to do

Then we finished 4 more problems so we can subtract 4 from 12

12-4=8

8 more problems left out of the 24 we had

8/24=1/3

1/3 of the 24 problems remain

Hope this helps!

Answer: c

Step-by-step explanation:

Answer:

C y = −4.6 and y = 4.6

Step-by-step explanation:

Edge 2023

Answer:

C. As the air is heated, it becomes less dense and the balloon rises.

Step-by-step explanation:

A is wrong. The denser cold air would cause the balloon to drop.

B is wrong. As the air is cooled, it becomes less dense.

The discount is $43.50, making the price of the discounted TV $246.50.

15% = .15

.15 x 290 = 43.5

$290 - $43.50 = $246.50

Answer:

Cos 2x = Cos (5x-3x)

Cos(5x)Cos(3x) + Sin(5x)Sin(3x)

Cos 8x = Cos (5x + 3x)

Cos(5x)Cos(3x) - Sin(5x)Sin(3x)

Cos 2x - Cos 8x

= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -

[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]

= 2Sin(5x)Sin(3x)

Cos 2x + Cos 8x

= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +

[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]

= 2Cos(5x)Cos(3x)

= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)

2 gets cancelled out

Sin(5x)/Cos(5x) is Tan(5x)

Sin(3x)/Cos(3x) is Tan(3x)

Hence the fraction is identical to

Tan(5x)Tan(3x)

Answer:

Teo's rectangle has the greater area.

Step-by-step explanation:

Since a rectangle has the same opposite sides of parallel sides, you need to add or multiply 9 times 9 or 9 + 9 and 5 times 5 or 5 + 5. 9 x 9 or 9 + 9 equals 18, and 5 + 5 or 5 x 5 equals 10. Then, 18 and 10 is to be added. 18 + 10 is 28. So, that means Teo's rectangle has the greater area because, 28 is less than 36.

To compare the areas of the rectangles, calculate the area of each rectangle. Ryan's rectangle has a greater area of 45 square feet compared to Teo's rectangle which has an area of 36 square feet.

To compare the areas of the two rectangles, we need to calculate the area of each rectangle. The area of a rectangle is found by multiplying its length by its width. For Ryan's rectangle, the length is 9 feet and the width is 5 feet, so the area is 9 feet × 5 feet = 45 square feet. For Teo's rectangle, we are given that the area is 36 square feet. Since 45 is greater than 36, Ryan's rectangle has the greater area.

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Answer:

pentagon

Step-by-step explanation:

In this problem we have a pentagonal prism

so

The solid has two pentagonal bases and five lateral rectangular faces

we know that

A plane parallel to the base of a pentagonal prism will intersect a cross section that is the same shape as its bases

so

The shape of the horizontal cross section of the given prism, is a pentagon

Answer: Pentagon

Step-by-step explanation:

Answer:   -√6 + 1

Step-by-step explanation:

[tex]\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}[/tex]

Answer:

264.06

Step-by-step explanation:

Answer:

264.06

Step-by-step explanation:

54% of 489

0.54 x 489=264.06

Answer:

The length of the radius of the circle is 7 mm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If HK is tangent to circle O at point K

then

The radius OK is perpendicular to segment HK and triangle OKH is a right triangle

Applying the Pythagorean Theorem

[tex]OH^2=OK^2+HK^2[/tex]

we have

[tex]OH=(r+18)\ mm\\OK=r\ mm\\HK=24\ mm[/tex]

substitute

[tex](r+18)^2=r^2+24^2[/tex]

solve for r

[tex]r^2+36r+324=r^2+576[/tex]

[tex]36r=576-324\\36r=252\\r=7\ mm[/tex]

therefore

The length of the radius of the circle is 7 mm

Final answer:

Yes, there is a constant of variation in the given equation y = 26.2x. The constant of variation represents the rate at which the number of miles y increases for every marathon x completed by Conrad.

Explanation:

Yes, there is a constant of variation in the given equation y = 26.2x. A constant of variation is represented by the coefficient or the number multiplied by x in the equation, which in this case is 26.2. It represents the rate at which the number of miles y increases for every marathon x completed by Conrad. So, for every marathon Conrad runs, the number of miles he runs increases by 26.2.

Answer:

8p + 25b

Step-by-step explanation:

The expression of the word problem above can be written thus:

[tex]8p + 25b[/tex]

The product of a rational number multiplied by itself is called as a perfect square.,we can easily find out the square root for a number which is a imperfect square

Step-by-step explanation:

using the following formula we can find a square root for a number which is a imperfect square

X = Non perfect square

√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )

[tex]√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )[/tex]Example

√38

the nearest perfect root is 36

36 (√36=6)

so √38 = √36 + (38-36)/2√36

= 6 + 2/12

=6 + 1/6 = 6.166 (answer)

[tex]√38 the nearest perfect root is 36 36 (√36=6)so √38 = √36 + (38-36)/2√36 = 6 + 2/12=6 + 1/6 = 6.166 (answer)[/tex]

To find the square root of a non-perfect square, use estimation techniques or the quadratic formula if in relation to an equation. Use the imaginary unit i for square roots of negative numbers, and simplify by removing perfect squares when adding or subtracting radicals.

Finding the square root of a number that is not a perfect square can be done using a few different methods. One simple non-calculator method is to use estimation and refinement; start with an approximate guess and improve it. When dealing with negative numbers, remember that we use the imaginary unit i to denote the square roots of negative numbers. For example, a₂ can be written as 2i. Adding and subtracting radicals involves simplifying each radical by removing perfect squares and combining like terms.

For equations where the square root is part of a quadratic equation, ax²+bx+c = 0, if a, b, and c are non-zero, we should use the quadratic formula to find solutions. Estimation also applies when dealing with cube roots or higher, where we can start with an initial guess and use methods like calculus to refine it.

To estimate a surd like a₃ without a calculator, consider its place on the number line between two integers, knowing that a₃ is about 1.732. This helps get an approximate value which is often sufficient for many applications.

Answer:

y = -2x - 2

Plug the x- and y-values into the appropriate spaces in the slope-intercept form and see which value for b would make the equation true:

4 = -2(-3) +/- ?

4 = 6 - 2

4 = 4

I don't know if this makes sense, I'm sorry if it doesn't but the answer is correct because it goes through the point (-3,4)

The answer is y = -2x - 2

You have to first plug the x- and y-values into the correct spots in the slope-intercept form and see which value for b would make the equation true.

4 = -2(-3) +/- ?

4 = 6 - 2

4 = 4

Hope to help.

Complete Question:

Option 1: $30 an hour plus a non-refundable deposit of $50.

Option 2: $20 an hour plus a non-refundable deposit of $75.

Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1?

Answer:

Kyle must rent the jetski for three hours for option 2 to be a better deal than option 1

Solution:

Let "x" be the number of hours

Therefore,

Charge for option 1: 50 + 30x

For 1 hour,

Charge = 50 + 30(1) = 80

For 2 hours,

Charge = 30(2) + 50 = 110

For 3 hours,

Charge = 30(3) + 50 = 140

For 4 hours,

Charge =  30(4) + 50 = 160

Charge for option 2 : 75 + 20x

For 1 hour,

Charge = 20(1) + 75 = 95

For 2 hours ,

Charge = 20(2) + 75 = 115

For 3 hours,

Charge =  20(3) + 75 = 135

For 4 hours,

Charge =  20(4) + 75 = 155

For the first two hours , the charge of option 2 is more than the rent of option 1

From 3 hours, option 2 will be better deal than option 1

Answer:

I got 3591.36 cubic inches

Step-by-step explanation:

Its wrong its wrong

Answer:

q=4

Step-by-step explanation:

brainlest would be epic owo

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6*q-11-(13)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  6q - 24  =   6 • (q - 4)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    6   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    q-4 = 0

Add  4  to both sides of the equation :

                     q = 4

Answer:

q=4

Step-by-step explanation:

6q-11=13    first you have to get all the like terms together so add 11 to both sides

6q=24             Now divide both sides by 6 so you just have q on one side

q=4

Answer:

292 in^2

Step-by-step explanation:

Area of the top and bottom combined is 2(14 inches)(5 inches)), or 140 in^2.

Area of the two ends, combined, is 2(4 inches)(5 inches)) = 40 in^2.

Are of the two sides, combined, is 2(14 inches)(4 inches)) = 112 in^2.

Summing up these three subtotals, we get the total area 292 in^2.

Answer:

$339.25

Step-by-step explanation:

Since the credit card customer owes $523.85 and is only able to make a payment of $184.50

Amount still owed

= $523.85 - $184.60

= $339.25

The customer still owes $339.25

Answer:

39.69 degrees

Step-by-step explanation:

Let

x ----> the measure of the angle

we have that

[tex]tan(X)=0.83[/tex]

using a calculator

[tex]m\angle X=tan^{-1}(0.83)=39.69^o[/tex]

Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.

Solution:

Given data represents the length of the insects.

Length of the walking stick = 4 in

Length of the bumble bee = [tex]\frac{5}{8}[/tex] in

Difference between their length

                                        [tex]$=4-\frac{5}{8}[/tex]

                                        [tex]$=\frac{4}{1} -\frac{5}{8}[/tex]

To make the denominator same, multiply and divide the first term by 8.

                                        [tex]$=\frac{32}{8} -\frac{5}{8}[/tex]

                                        [tex]$=\frac{32-5}{8}[/tex]

                                        [tex]$=\frac{27}{8}[/tex]

Now, change improper fraction into mixed fraction, we get

                                         [tex]$=3\frac{4}{8}[/tex]

Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.

Answer:

[tex]y = \frac{32}{4} = 8[/tex]

Answer 13-6=7

Step-by-step explanation:

The given expression indicates a difference of six and an unknown number equals to seven. To solve, we isolate the unknown number by adding six to both sides of the equation. Thus, the unknown number is 13.

The question states that 'The difference of a number and six is seven.' To find out the number, we can set up the following equation where x represents our unknown number:

x - 6 = 7

To solve for x, we can add 6 to both sides of the equation, which balances it rendering the final result:

x = 7 + 6

Finally, adding 7 and 6, we find that x = 13. The number we are seeking is 13.

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Answer:

Option A, Trapezoid

Step-by-step explanation:

Since there is two parallel sides and two nonparallel, that means it is a trapezoid.

Answer:  Option A, Trapezoid

The length of the minor axis is 4

Step-by-step explanation:

Step 1 :

The given equation  is  [tex]\frac{(x-3)^{2}}{64} + \frac{(y-7)^{2}}{4} = 1[/tex]

Here we see the denominator below the variable x is greater than below y. Hence the ellipse's major axis and the minor axis are parallel to x-axis  and  y-axis respectively

Step 2 :

The square of the semi minor axis will be the denominator of the y variable. So in the given ellipse ,

the square of the semi minor axis = 4

Hence the length of the semi minor axis  = [tex]\sqrt{4}[/tex]  = 2

Step 3 :

The length of the minor axis = 2 times the length of the semi minor axis

                                               = 2 × 2 = 4

Answer :

The length of the minor axis is 4

Final answer:

The length of the minor axis of the given ellipse is 4 units, as the semi-minor axis length is derived from the square root of the denominator of the y-term in the ellipse equation. The correct option is B.

Explanation:

The minor axis of an ellipse is the shortest diameter of the ellipse, and it runs perpendicular to the major axis. In the given equation of the ellipse, (x+3)²/64 + (y-7)²/4=1, the denominators of the fractions correspond to the squares of the semi-axes lengths. Therefore, the length of the semi-minor axis 'b' is the square root of 4, which is 2. Since the minor axis is twice the length of the semi-minor axis, we must multiply 2 by 2 to get the length of the minor axis, which is 4.

So the correct answer for the length of the minor axis for the given ellipse is 4 units, which corresponds to option B.