Write the equation of the line passing
through the point (2, -1) with a slope of -3.

Given:

The line passing through (-2,5) and (2,p) has a gradient of [tex]-\dfrac{1}{2}[/tex].

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The line passing through (-2,5) and (2,p). So, the slope of the line is:

[tex]m=\dfrac{p-5}{2-(-2)}[/tex]

[tex]m=\dfrac{p-5}{2+2}[/tex]

[tex]m=\dfrac{p-5}{4}[/tex]

It is given that the gradient or slope of the line is [tex]-\dfrac{1}{2}[/tex].

[tex]\dfrac{p-5}{4}=-\dfrac{1}{2}[/tex]

On cross multiplication, we get

[tex]2(p-5)=-4(1)[/tex]

[tex]2p-10=-4[/tex]

[tex]2p=-4+10[/tex]

[tex]2p=6[/tex]

Divide both sides by 2.

[tex]p=3[/tex]

Therefore, the value of p is 3.

Answer:

See Explanation

Step-by-step explanation:

Given

Base Dimension

[tex]Length = 4\frac{1}{4}yd[/tex]

[tex]Width = 1\frac{2}{3}yd[/tex]

Required

The base area of all containers

First, calculate the base area of 1 container.

This is calculated as:

[tex]Area = Length * Width[/tex]

[tex]Area = 4\frac{1}{4}yd * 1\frac{2}{3}yd[/tex]

Express as improper fraction

[tex]Area = \frac{17}{4}yd * \frac{5}{3}yd[/tex]

So, we have:

[tex]Area = \frac{17*5}{4*3}yd^2[/tex]

[tex]Area = \frac{85}{12}yd^2[/tex]

The number of containers is not given. So, I will use 'n' as the number of containers.

So, we have:

[tex]Total = n * Area[/tex]

[tex]Total= n * \frac{85}{12}yd^2[/tex]

--------------------------------------------------------------------------------------------

Assume n is 3 (i.e. 3 containers)

The total area is:

[tex]Total= 3 * \frac{85}{12}yd^2[/tex]

[tex]Total= \frac{85}{4}yd^2[/tex]

[tex]Total= 21\frac{1}{4}yd^2[/tex]

--------------------------------------------------------------------------------------------

Answer:

FV= 24,000*(1.07^-10)

Step-by-step explanation:

Giving the following information:

Present Value (PV)= $24,000

Decrease rate (d)= 7%

Number of periods (n)= 10 years

To calculate the value of the car after 10 years, we need to use the following formula:

FV= PV*(1+d)^-n

FV= 24,000*(1.07^-10)

FV= $12,200.38

Answer:

2

Explanation:

Degree 4 is the term with the exponent that is 4. The 2 in front of the x is the coefficient.

Answer: Paul

Step-by-step explanation: Paul is correct because Joe isn’t.

0.052= 5.2% not 52%

Jo is correct in saying that that number is less than 52%.

Answer:

Step-by-step explanation:

 D

Answer:

a

Step-by-step explanation:

unshaded circle is for more than or less than

Focus on the values in red outside the table (on the left and right sides). As the output increases by 4, the input increases by 1. This leads to the slope being rise/run = 4/1 = 4. The slope is the number just to the left of the x variable. So that's how they ended up with the equation y = 4x.

You can think of it as y = 4x+0, and note how it's in the form y = mx+b

m = 4 = slope

b = 0 = y intercept

The y intercept is the value of y when x = 0.

--------

Now because x = 0 and y = 0 pair up together, we can find the slope a different way: Pick any row other than the first row. Divide the y value over its paired x value. So let's say we pick on row two and we'd get a slope of y/x = 4/1 = 4.

Or we could pick on row three and get y/x = 8/2 = 4.

Picking on the fourth row gets us the slope to be y/x = 12/3 = 4. We end up with the same slope value each time. Again, this trick only works if (x,y) = (0,0) is on the line. Otherwise, you'll need to use the first method or use the slope formula.

For equations like this, we consider them a direct proportion. As x increases, so does y. As x increases by 1, y increases by 4. This is the same throughout the table.

----------

A real world example of this could be that x represents the number of sodas you buy, and if each soda is $4, then y = 4x represents the total cost of buying x number of sodas.

For instance, if you bought x = 10 sodas, then y = 4*x = 4*10 = 40 dollars is what you spend overall.

Answer: No

Step-by-step explanation:

Points inserted are

[tex](1\ \frac{1}{2},4), (2,4), (5,4)\\[/tex]

As all the points have the same y-coordinate, therefore, they must lie on the same horizontal line of [tex]y=4[/tex]

So, the ingested points are not correct.

Points maybe [tex](1,2), (1, 3), (1,3\ \frac{1}{2})[/tex] as they line on the same vertical line.

Answer: 90 mm cubed

Step-by-step explanation:

Formula = (L*W*H) / 2

5 * 12 * 3 = 60 * 3 = 180

180 / 2 = 90

hyfhsudeh it heieheueheiheeiheehheehe 70m

Answer:

3 + 9 = 12 !

Step-by-step explanation:

Answer:

21.8

Step-by-step explanation:

The distance for the side of the house will the ladder reach now should be considered as the 21.8 ft.

Since first we have to determine BC i.e.

[tex]= \sqrt{50^2 - 30^2} \\\\= \sqrt{1600}[/tex]

=  40 ft

Now

In the case when Alonso grabs the ladder at its base and pulls it 5 feet farther from the house

So,

[tex]= \sqrt{(50)^2 - (45)^2} \\\\= \sqrt{475} \\\\= 5 \sqrt 19[/tex]

= 21.8 ft.

Learn more about base here: https://brainly.com/question/23854119

Answer:

1,296 FT2

Step-by-step explanation:

Answer:

i tried every way possible and none of the have the same answer as the solutions i made BUT, all of my answer were the closest to 216 so i would guess that one

Step-by-step explanation:

Sorry if i was wrong, i tried my best but i didnt get any of those answers

Answer:

Area = 12 square units

Step-by-step explanation:

Area = b x h x 1/2

Area = 8 x 3 x 1/2

Area = 24 x 1/2

Area = 12

Hope that helps! :)

Answer:

12 is the area . ihshssisjjss

Answer:

I believe that the answer is 'C. 9d+2c+3t'.

Step-by-step explanation:

I hope this was helpful, have a blessed day.

Answer:

3cm

Step-by-step explanation:

The length of a rectangle Is 9cm

The perimeter Is 24

Let the width be x

Therefore the width can be calculated as follows

Perimeter= 2(length+width)

24= 2(9+x)

24= 18+2x

24-18= 2x

6= 2x

x= 6/2

x= 3cm

Hence tbe width is 3cm

Answer:

Simple interest:

Compound interest:

Sum of the balances:

Answer:

8 + 0.25g

Step-by-step explanation:

(g is the variable for garnish)

Answer:

A. -1

Step-by-step explanation:

To find the slope, subtract the x-coordinates, subtract the y-coordinates, lastly, divide the differences.

(3,1) (4,0)

3 - 4 = -1

1 - 0 = 1

-1 ÷ 1 = -1

-1 is the slope.

Answer:

5. the given ordered pair is not a solution 6. the given ordered pair is a solution 7. the given ordered pair is a solution

Step-by-step explanation:

5. 8 = -4(-2) => 8 = 8 (true)

8 = 1/2(-2) + 7 => 8 ≠ 6 (false)

the given ordered pair is not a solution

6. 3 + 5(1) = 8 => 8 = 8 (true)

4(3) - 5(1) = 7 => 7 = 7 (true)

the given ordered pair is a solution

7. -5 = 4 - 9 => -5 = -5 (true)

4 + (-5) = -1 => -1 = -1 (true)

the given ordered pair is a solution

Answer:

Hello! Your answer would be B)B

Step-by-step explanation:

Hope I helped! Brainiest plz!♥ Have a nice morning! Hope you make a 100%! -Amelia

Answer:

1. A

2. C

3. A

Hope this helped!

The expression is equivalent to the 1/4 (12 -3x) is 3 - 3/4x.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

We have the Expression

1/4 (12 - 3x)

Now, using Distributive Property we get

a x (b+ c) = a x b + a x c

Then, 1/4 (12 - 3x)

= 1/4(12) - 1/4 (3x)

= 3 - 3/4x

Thus, the required expression is 3 - 3/4x.

Learn more about Expression here:

https://brainly.com/question/16804733

#SPJ3

Answer:

V = 400in.

Step-by-step explanation:

We are given the measurements of what can be assumed to be a rectangular prism, and we need to find the volume.

When finding volume of a rectangular prism, we need to multiply length by width by height.

So we know all of these,

L = 10in

W = 5in

H = 8in

V = LWH

Substitute :

V = (10)(5)(8)

Mutiply :

V = (50)(8)

Multiply :

V = 400in.

Answer:

the formula to find volume is length times width times height.

Step-by-step explanation:

10 times 5 = 50 then multiply 50 by 8 which equals 400. brainliest :0

Answer:

9

Step-by-step explanation:

0,1,2

0,2,1

1,2,0

1,0,2

2,0,1

2,1,0

2,2,2

1,1,1

0,0,0