Which TWO linear equations represent perpendicular lines?

y = ½x + 4

x - 3y = -8

y = -2x - 3

y = 2x - 4

Answer: 20x + 15k

Step-by-step explanation:

Lose the parentheses and add the like terms. Add 18x and 2x, then add 9k and 6k. That's all there is to it.

The equivalent expression of (18x + 9k) + (2x + 6k) is 20x + 15k.

The correct option is A.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

We have an expression,

(18x + 9k) + (2x + 6k).

To find the equivalent expressions:

Simplifying,

(18x + 9k) + (2x + 6k),

= 20x + 15k

This is the equivalent expression.

Therefore,  20x + 15k is the equivalent expression.

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Probability of randomly rolling a 3 is 1/4

Step-by-step explanation:

Step 1:

It is given that a tetrahedron has 4 sides with 1,2,3 and 4 and is randomly rolled. We need to compute the probability of randomly rolling a 3.

Step 2:

Probability of an event = (Favorable outcomes) / (Total outcomes).

There are 4 total outcomes when the tetrahedron is rolled, these are the values 1 to 4.

The only favorable outcome is getting a 3

Probability of getting a 3 when the tetrahedron is randomly rolled = 1/4

Step 3:

Answer:

Probability of randomly rolling a 3 is 1/4

Answer:

3/4

Step-by-step explanation:

The total cost of a cake that serves 20 people is $35.

Step-by-step explanation:

The equation can be formed as:

Therefore, the total cost of a cake that serves 20 people is $35.

The stock purchased for $77 grew by 17.9%, which equals an increase of $13.78. Therefore, the current stock price is $90.78.

To solve this problem, we need to calculate the percent increase of the stock's price. A percent increase of 17.9% means that the stock price has increased by 17.9% of the original price. To calculate the amount of the increase, we multiply the original price ($77) by the percent increase (17.9%), remembering to convert the percentage to a decimal (0.179).

So, $77 times 0.179 equals ~$13.78. This is the amount by which the stock price has increased. To find the new price of the stock, we add this increase to the original price, which gives us $77 (Original price) + $13.78 (Increase) = $90.78, so the stock is worth $90.78 now.

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Option A: [tex]y=-\frac{1}{2} x+5[/tex] is the equation of the line.

Explanation:

It is given that the equation has a slope is [tex]m=-\frac{1}{2}[/tex]

It also contains the point [tex](8,1)[/tex]

We need to find the equation of line in slope - intercept form.

First, we shall determine the value of y - intercept(b).

Let us substitute the slope [tex]m=-\frac{1}{2}[/tex] and the point [tex](8,1)[/tex] in the slope - intercept form [tex]y=mx+b[/tex] , we get,

[tex]1=-\frac{1}{2} (8)+b[/tex]

Simplifying, we have,

[tex]1=-4+b[/tex]

Adding both sides of the equation by 4, we have,

[tex]1+4=b[/tex]

     [tex]5=b[/tex]

Thus, the y - intercept is [tex]b=5[/tex]

Now, substituting the slope [tex]m=-\frac{1}{2}[/tex] and the y - intercept [tex]b=5[/tex] in the slope - intercept form [tex]y=mx+b[/tex] , we get,

[tex]y=-\frac{1}{2} x+5[/tex]

Thus, the equation of the line is [tex]y=-\frac{1}{2} x+5[/tex]

Hence, Option A is the correct answer.

Answer:

Step-by-step explanation:

∠ M + ∠N = 180 {supplementary}

5x+18 + 3x + 2 = 180    {Now add the like terms}

8x + 20 = 180

        8x = 180 - 20

        8x = 160

          x = 160/8

         x = 20

∠M = 5x + 18 = 5*20 + 18 = 100 + 18 = 118

∠N = 3x + 2 = 3*20 + 2 = 60 + 2 = 62

Answer:

The answer is 15 units!!

Step-by-step explanation:

[tex]17^{2} -8^{2} = 225\\\sqrt{225} =15[/tex]

The length of ZY to be a tangent is 15.

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is pir^2.

We have,

XY = Radius

And,

Radius = 8

Applying the Pythagorean theorem,

XZ² = XY² + ZY²

8² = (8 + 9)² + ZY²

64 = 289 + ZY²

ZY² = 289 - 64

ZY² = 225

ZY = 15

Thus,

The length of ZY is 15.

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Answer:

0.4 U.S dollars-4 I guess

Answer:

Step-by-step explanation:

Information: 1 ton = 2000 lb

Step one:

Do problem:

6000lb divides by 2000lb.

The answer is 3 tons.

Answer:

The number is 20

Step-by-step explanation:

Step 1:  Convert words into an expression

5 less than a number is 15

5 less than a number is n - 5

n - 5 = 15

Step 2:  Add 5 to both sides to get the number

n - 5 + 5 = 15 + 5

n = 20

Answer:  The number is 20

Answer:

$3.40

Step-by-step explanation:

Final answer:

To determine the cost Geraldo will pay for 4 pounds of apples, we find the cost per pound from his previous purchase and multiply by the desired weight. At $0.85 per pound, Geraldo will pay $3.40 for 4 pounds of apples.

Explanation:

Last week, Geraldo bought 7 pounds of apples for $5.95. To find out how much he will pay for 4 pounds of apples this week at the same price, we first need to calculate the cost per pound of the apples. We do this by dividing the total cost by the total weight in pounds from the previous purchase.

The cost per pound is $5.95 divided by 7 pounds, which equates to approximately $0.85 per pound (rounding to two decimal places).

So, for 4 pounds of apples, Geraldo will pay 4 times $0.85, which results in a total of $3.40.

Therefore, Geraldo will pay $3.40 for 4 pounds of apples.

Answer:

  8/12 yard or 2/3 yard

Step-by-step explanation:

The sum of the two lengths is ...

  5/12 yd + 3/12 yd = (5+3)/12 yd = 8/12 yd

This fraction can be reduced by removing a factor of 4 from numerator and denominator.

  8/12 yd = 2/3 yd

If the arm portions are end-to-end, the total length is 2/3 yard.

Answer: x =750

Step-by-step explanation:

Well you just make 3 and 400 a fraction 3/400 and 100,000 and the unknown number a fraction x/100,000. Now you do :

3/400=x/100,000

and figure that out :

3/400=x/100,000

3/400=x/100,000

(3)*(100000)=x*(400)

300000=400x

400x=300000

400x/400=300000/400

x=750 is your answer.

3/400=750/100,000.

Hoped I helped!

Answer:

The first point should be plotted at -4, then there should be a line that goes up 8 units and gives us a final destination of 4.

Answer:

w

Step-by-step explanation:

In y = f(x), for every x value, there can be at most one y value. All the other tables have duplicate x values.

Answer:

1904 units^3

Step-by-step explanation:

multiply all of the sides by each other. 17 X 14 X 8 =

Answer:

the answer is 317

Step-by-step explanation:

I did the test

Answer:

A. 7(3v-7)(v-1)

Step-by-step explanation:

21v2 - 70v +49

Factor out 7

7(3v2 - 10v +7)

write -10v as a difference

7(3v2 - 3v -7v +7)

Factor out 3v

7(3v × (v-1) - 7 × (v-1))

Factor out (v-1)

7(3v-7)(v-1)

Answer:

1

Step-by-step explanation:

The cone is sliced by a plane, which produces a smaller cone on top.  This cone is similar to the original cone.  Therefore:

R / H = r / h

2 / 8 = r / 4

r = 1

The radius of the circle at the intersection of the plane and the cone is 1.

To find the radius of the circle at the intersection of the plane and the cone, we start by understanding the geometry of the cone and the slicing plane.

Given:

- Cone height ( h = 8 )

- Cone radius ( r = 2 )

- The plane slices the cone halfway along its height, so the distance from the vertex to the plane is  [tex]\( \frac{8}{2} = 4 \)[/tex].

Let's denote:

- ( R ): Radius of the circle at the intersection of the plane and the cone.

At height ( h ) from the vertex of the cone, the radius ( R ) of the circle formed by the intersection with the plane is related to the similar triangles formed by the cone and the slice plane.

The ratio of corresponding sides of similar triangles gives us:

[tex]\[ \frac{R}{r} = \frac{h - 4}{h} \][/tex]

Substitute the given values:

[tex]\[ \frac{R}{2} = \frac{8 - 4}{8} = \frac{4}{8} = \frac{1}{2} \][/tex]

Now, solve for ( R ):

[tex]\[ R = 2 \cdot \frac{1}{2} = 1 \][/tex]

Therefore, the radius of the circle at the intersection of the plane and the cone is [tex]\( \boxed{1} \).[/tex]

Answer:

it has 5 sides and she walks a total of 12.5

Step-by-step explanation:

The Garden have 5 congruent side.

The Perimeter of Pentagon is 12.5 m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We have, a pentagon having congruent sides as 2.5 cm

So, the Garden have 5 congruent side.

Now, the Perimeter of Pentagon

= 2.5 x 5

= 12.5 m

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Answer: 2

Step-by-step explanation:

So first combine like terms, -4x-6x= -10x. Then to isolate x by itself, divide both sides by -10 and get 2=x.

Answer:

x=2

Step-by-step explanation:

-20=-4x-6x

In this kind of question, ensure that you collect like terms especially when they are scattered that is not well arranged...

But the question given is straight forward so there is no need to collect like terms...but to solve directly,

-20=-4x-6x

-20=-10x

Divide both sides by -10

x=2

Answer:

18

Step-by-step explanation:

Step 1:  Combine

16 + 8 - 3 + 6 - 9

24 - 3 + 6 - 9

21 + 6 - 9

27 - 9

18

Answer:  18

Answer: 1

Step-by-step explanation:

16+8

23 - 3

2 + 6

8 - 9

1

Answer: I would say imaginary numbers...

Step-by-step explanation:

It follows the format of imaginary numbers: bi, where i = [tex]\sqrt{-1}[/tex] and b = -91.

Final answer:

The number -91i is an imaginary number, which is a subset of complex numbers with a real part of 0 and an imaginary part of -91.

Explanation:

The number -91i is a complex number.

Complex numbers consist of two parts: a real part and an imaginary part. In this case, the real part is 0 and the imaginary part is -91.

The 'i' represents the imaginary unit, which is defined as √(-1).

Therefore, -91i is an imaginary number because it exists only with the imaginary unit 'i', and does not have a real part.

The width of the rectangle, given its perimeter and length, is calculated using the formula for the perimeter of a rectangle. By reorganizing the terms and isolating the width, we find that the width is 4x + 3/2y, which is Answer Choice A.

The perimeter of a rectangle is given as 15x + 17y. The length is provided as 7/2x + 7y. To find the width, we need to remember that the perimeter of a rectangle is twice the sum of its length and width (P = 2l + 2w). Let's denote the width of the rectangle as 'w'.

So, the equation representing the perimeter is:

15x + 17y = 2(7/2x + 7y) + 2w

Now let's multiply out the factors on the right side:

15x + 17y = 2(7/2x) + 2(7y) + 2w

15x + 17y = 7x + 14y + 2w

To find 'w', we need to move all terms involving 'w' to one side of the equation and all other terms to the other side:

2w = 15x + 17y - (7x + 14y)

2w = 15x - 7x + 17y - 14y

2w = 8x + 3y

Divide throughout by 2 to find 'w':

w = 4x + 3/2y

The width of the rectangle is 4x + 3/2y, which corresponds to Answer Choice A.

Answer:

10 peaches and 5 bananas

Step-by-step explanation:

To solve the problem increase the cost by adding more peaches and less by adding more bananas

7 peaches = 3.50

8 bananas = 3.20 + 3.50 = 6.70

We need 30 more cents so add three more peaches

10 peaches = 5

5 x 0.4 = 2

2 + 5 = 7

Final answer:

To determine the number of bananas and peaches Samantha bought, we can set up a system of equations and solve for the variables. By using substitution, we find that Samantha bought 5 bananas and 10 peaches.

Explanation:

To determine the number of bananas and peaches that Samantha bought, we can set up a system of equations. Let x represent the number of bananas and y represent the number of peaches. From the given information, we know the cost of each banana is $0.40 and the cost of each peach is $0.50. We can write two equations to represent the total cost of the bananas and peaches:

$0.40x + $0.50y = $7 (equation 1)

x + y = 15 (equation 2)

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From equation 2, we know that x = 15 - y. We can substitute this value of x into equation 1:

$0.40(15 - y) + $0.50y = $7

Simplifying the equation, we get:

$6 - $0.40y + $0.50y = $7

Combining like terms, we have:

$0.10y = $1

Dividing both sides by $0.10, we get:

y = 10

So, Samantha bought 10 peaches. Substituting this value of y back into equation 2, we can solve for x:

x + 10 = 15

Subtracting 10 from both sides, we get:

x = 5

Therefore, Samantha bought 5 bananas and 10 peaches.

Quotient is 21

Step-by-step explanation:

Step 1:

Divide 85 by 4. Using long division method, find the quotient.   

  21

4|85

  8

-------

     5

  -  4

--------

      1

Answer:

This formula corresponds to find the area of a rectangle/square.  You multiply one side by the other to get the area.

Example:  The sides of a rectangle are 6 in and 14 in.  Find the area.

A = l * w

A = 6 * 14

A = 84

Answer:

Step-by-step explanation:

15Answer:

Step-by-step explanation:

Answer:

[tex]x\geq 0[/tex]  Domain

y = 40+1.5x  relationship

[tex]y \geq 40[/tex]  range

Step-by-step explanation:

The domain is the amount of carpet installed.  We can install zero carpeting or any positive amount of carpeting.

[tex]x\geq 0[/tex]

Now writing the equation for the cost

They charge 40 flat rate plus 1.50 per square foot

y = 40+1.5x

Let x = 0

y = 40+0

Even if they do not install anything, they still charge 40 dollars flat rate.  That is the minimum amount we have to pay.  As x increases, the cost will increase.

That is the range, or the values of y

[tex]y \geq 40[/tex]

We want to get the equation for the total cost and its domain and range.

The equation is:

c(x) = $40 + $1.50*x

domain: x > 0ft^2

range: y > $40.

First, let's get the equation.

We know that the carpet installer charges a flat rate of $40 plus $1.50 per square feet.

So if he/she works for x square feets, the cost is:

c(x) = $40 + $1.50*x

This is the cost equation.

Now we want to find the domain and range of this. The domain is given by the possible values of x that we can input in the function. Here we know that x must represent the number of square feet that are worked on, so it only must be a number larger than zero.

x > 0ft^2.

While the range is the set of the possible outputs.

The smallest possible output is the one we get when we evaluate the function in the smallest value of the domain, so we get:

y > $40.

These two define the domain and range.

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The number of fluid ounces equivalent to 12 1/4 cups is; 98 fl Oz.

It follows from the task content that it is required to determine the number of fluid ounces in 12 1/4 cups.

Since, 1 Cup contains 8 fluid ounces; it therefore follows that 12 1/4 cups will contain;

= 12 1/4 × 8

= 98 fl Oz.

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