Write the equation of the line that passes through the points (0, -6) and (-4, 0).
Show how you arrived at your answer.
What would be the EQUATION? I’m confused. Please help.

Step-by-step explanation:

(f+g)(x) means f(x) + g(x).

(f−g)(x) means f(x) − g(x).

So all you have to do is add them and subtract them.

1. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (3x − 7) + (2x − 4)

(f+g)(x) = 5x − 11

2. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (3x − 7) − (2x − 4)

(f−g)(x) = 3x − 7 − 2x + 4

(f−g)(x) = x − 3

3. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (2x + 3) + (x² + ½ x − 7)

(f+g)(x) = x² + 2½ x − 4

4. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (2x + 3) − (x² + ½ x − 7)

(f−g)(x) = 2x + 3 − x² − ½ x + 7

(f−g)(x) = -x² + 1½ x + 10

Answer:

x=9

Step-by-step explanation:

90-30= 60

now set 60 = 5x + 15

solve for x

45= 5x

divide by 5

x = 5

[tex]\bf \cfrac{p^{-4}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^{-7}}{p^{-2}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^{-2}}\implies \cfrac{1}{p^{4}p^{-2}p^{-2}r^7}\implies \cfrac{1}{p^{4-2-2}r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}[/tex]

Answer:

[tex]\large\boxed{r^{-7}=\dfrac{1}{r^7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{p^{-4}q^3r^{-7}}{p^{-2}q^3p^{-2}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=p^{-4-(-2)-(-2)}q^{3-3}r^{-7}\\\\=p^{-4+2+2}q^0r^{-7}\\\\=p^0q^0r^{-7}\\\\=r^{-7}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{r^7}[/tex]

Answer:

[tex]\large\boxed{y+5=\dfrac{2}{3}(x-4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Parallel lines have the same slope.

We have the equation in the slope-intercept form (y = mx + b)

[tex]y=-\dfrac{2}{3}x+8\to m=\dfrac{2}{3}[/tex]

Put to the point-slope equation value of the slope and the coordinates of the point (4, -5):

[tex]y-(-5)=\dfrac{2}{3}(x-4)\\\\y+5=\dfrac{2}{3}(x-4)[/tex]

The equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
The equation of a line in point-slope form is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is a point on the line.

We are given that the line we want to find is parallel to y = (-2/3)x + 8, which means it has the same slope of -2/3.

We are also given that the line passes through the point (4, -5).

Substituting the values into the point-slope form equation, we get:

y - (-5) = (-2/3)(x - 4)

Therefore, the equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.

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Answer:

The correct answer for question A is x=2i or x= -2i

The correct answer for question B is (x+2i)(x-2i)

Step-by-step explanation:

Solution of question A:

x²+4=0

Subtract 4 from both sides.

x²+4-4=0-4

x²=-4

Take square root of both sides

√x²=+/-√-4

We know that i=√-1

So,

x=+/-(√4)(√-1)

x=+/-2i

Therefore x= 2i, x= -2i

Solution of question B:

x²+4

It cannot be factored using real number coefficient. You have to use complex numbers.

As we know -4 =(2i)², so we can write as:

x²+4=x² - (-4)= x²-(2i)²

Now factor using the difference of squares:

x²+4=(x+2i) (x-2i)....

Answer:

c on edge 2020

Step-by-step explanation:

i just did the assignment

The solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.

The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. It is denoted by ln x.

For the given situation,

The function is 5e^2x - 4 = 11

⇒ [tex]5e^{2x} - 4 = 11[/tex]

⇒ [tex]5e^{2x} = 11+4[/tex]

⇒ [tex]5e^{2x} = 15[/tex]

⇒ [tex]e^{2x} = \frac{15}{5}[/tex]

⇒ [tex]e^{2x} = 3[/tex]

Taking ln on both sides,

⇒ [tex]ln e^{2x} = ln3[/tex]                       [∵ ln e = 1 ]

⇒ [tex]{2x} = ln3[/tex]

⇒ [tex]x=\frac{ln3}{2}[/tex]

Hence we can conclude that the solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.

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Answer:

The correct answer is option C. 75 m³

Step-by-step explanation:

Points to remember

Volume of rectangular prism = Base area * Height

To find the volume of given prism

Here Base area = 15 m² and

Height = 5 m

Volume = base area * height

 = 15 * 5

 = 75 m³

Volume of prism = 75 m³

Therefore the correct answer is option C. 75 m³

Answer:

Rectangular Prism Volume =  length x width x height

Rectangular Prism Volume =  15 x 5

Rectangular Prism Volume =  75 cubic meters

Step-by-step explanation:

Answer:

[tex]x=-\frac{6}{7}[/tex]

[tex]y=-17\frac{6}{7}[/tex]

Step-by-step explanation:

We are given the following system of equations that we are to solve:

[tex] y = 8 x - 1 1 [/tex] - (1)

[tex] y = x - 1 7 [/tex] - (2)

Since the left hand side of both the equations is the same so we will equate the right hand sides of both the equations to get:

[tex]8x-11=x-17[/tex]

[tex]8x-x=-17+11[/tex]

[tex]7x=-6[/tex]

[tex]x=-\frac{6}{7}[/tex]

Substituting this value of [tex]x[/tex] in (1) to find [tex]y[/tex]:

[tex]y=8(-\frac{6}{7})-11[/tex]

[tex]y=-17\frac{6}{7}[/tex]

Final answer:

The solution to the system of equations y = 8x - 11 and y = x - 17 is found by setting the equations equal to each other and solving for x, then substituting back to find y. The solution is x = -6/7 and y = -125/7.

Explanation:

To solve the system of equations, you want to find a single value for x and y that satisfies both equations simultaneously. The given equations are:

y = 8x - 11

y = x - 17

Since both equations are equal to y, we can set them equal to each other and solve for x:

8x - 11 = x - 17

Now, let's get all the x terms on one side and the numbers on the other:

8x - x = -17 + 11

7x = -6

Dividing both sides by 7 gives us:

x = -6/7

Now that we have x, we can substitute it back into one of the equations to find y:

y = 8(-6/7) - 11

y = -48/7 - 11

Convert -11 to a fraction,

y = -48/7 - 77/7

y = -125/7

The solution to the system of equations is x = -6/7 and y = -125/7.

Answer:

She has seven 3 cents stamps and six 8 cents stamps.

Step-by-step explanation:

7*3 = 21

6*8 = 48

48 + 21 = 69

Answer: She has SEVEN 3 cent stamps and SIX 8 cent stamps.

Step-by-step explanation:

Let be "x" the number of  8 cent stamps and "y" the number of  3 cent stamps.

Set up the following system of equations:

[tex]\left \{ {{x=y-1} \atop {8x+3y=69}} \right.[/tex]

Substitute the first equation into the second one and the solve for "y":

[tex]8(y-1)+3y=69\\\\8y-8+3y=69\\\\11y=77\\\\y=7[/tex]

Substitute the value of "y" into the first equation:

[tex]x=7-1\\\\x=6[/tex]

Answer:

Step-by-step explanation:

Graph the absolute value function y = |x|.  This is v-shaped and opens up.

Now translate the entire graph 2 units to the left.  You will then have the graph of y=|x+2|​.

Answer:

C

Step-by-step explanation:

c is the answer to your question

Answer:

C

Step-by-step explanation:

Answer:

Option C is correct.

Step-by-step explanation:

-10<3x-4<8

Solving the given equation,

we know that if a<b<c then a<b and b<c

s0, -10<3x-4 and 3x-4<8

Solving to find the value of x

-10<3x-4

Switching sides,

3x-4>-10

3x > -10 +4

3x > -6

x > -6/3

x > -2

3x-4 < 8

3x < 8+4

3x < 12

x < 12/3

x < 4

s0, x >-2 and x < 4

-2 < x <4

Option C is correct.

-10 < 3x-4 < 8

Isolate x

First add 4 to each side:

-6 < 3x < 12

Divide each side by 3:

-2 < x < 4

The inequality signs do not contain equal to, so you would have open circles on both -2 and positive 4.

This means x is greater than -2 and less than 4, which is shown as the 3rd choice.

Answer:

Step-by-step explanation:

Put the coordinates of the points to the each inequality, and check the inequality:

A. (1, -5)

y < -3x + 3

-5 < - 3(1) + 3

-5 < -3 + 3

-5 < 0     CORRECT

y < x + 2

-5 < 1 + 3

-5 < 3      CORRECT

B. (1, 5)

y < -3x + 3

5 < -3(1) + 3

5 < -3 + 3

5 < 0     FALSE

C. (5, 1)

y < -3x + 3

1 < -3(5) + 3

1 < -15 + 3

1 < -12     FALSE

D. (-1, 5)

y < -3x + 3

5 < -3(-1) + 3

5 < 3 + 3

5 < 6      CORRECT

y < x + 2

5 < -1 + 2

5 < 1      FALSE

Answer:

500.5

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers divided by the number of numbers.

The sum of all whole number form 1 to n is n(n + 1)/2.

The sum of all whole numbers from 1 to 1000 is

1000(1000 + 1)/2 = 1000(1001)/2 = 500,500

The average is the sum of the numbers divided by the number of numbers.

average = 500,500/1000 = 500.5

[tex]20-20\cdot0.15=\boxed{17}[/tex]

Comic book cost is reduced from 20 dollars to 17 dollars.

Hope this helps.

r3t40

Answer:

A $20 comic book is reduced to $17

Step-by-step explanation:

Consider the provided information.

A bookstore is having a sale. All comic books are reduced 15%.

We need to Fill the blank to show a  correct representation of this sale.

A $20 comic book is reduced to?​

The cost of books are reduced to 15% that means now you need to pay only 85% of the price.

Therefore,

[tex]\frac{85}{100}\times 20=0.85\times20 =17[/tex]

Hence, A $20 comic book is reduced to $17

[tex]\bf a^{-4}+b^2\implies \cfrac{1}{a^4}+b^2\qquad \begin{cases} a=2\\ b=\frac{3}{4} \end{cases}\implies \cfrac{1}{2^4}+\left( \cfrac{3}{4} \right)^2\implies \cfrac{1}{16}+\cfrac{3^2}{4^2} \\\\\\ \cfrac{1}{16}+\cfrac{9}{16}\implies \cfrac{1+9}{16}\implies \cfrac{10}{16}\implies \cfrac{5}{8}[/tex]

Answer:

Radius of the cone's base is 3x ....

Step-by-step explanation:

We have given that the volume of a cone is 3πx³

Height = x units.

The volume of a cone of radius r and height h units is given by:

V= 1/3 π r² *h

Simply plug the values given in the question into the above mentioned equation:

1/3πr²*x = 3*π*x³

1/3r²*x= 3x³

r² = 3*3*x³/x

r²=9x²

Taking square root at both sides we get:

√r² =√9x²

r = 3x

Thus the radius of the cone's base is 3x.

Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x

Step-by-step explanation: I just paid for this answer

Answer:

C) 360pi in2

Step-by-step explanation:

Given:

radius, r= 10in

height, h=26in

surface area of the cone, T.S.A= ?

T.S.A=πrl +πr^2

         =π(10)(26) +π(10)^2

         =260π+100π

         =360π^2 !

Answer:

[tex] y = 6(2.5)^x [/tex]

Step-by-step explanation:

[tex] y = ab^x [/tex]

Use (0, 6) and solve for a:

[tex] 6 = ab^0 [/tex]

[tex] 6 = a \times 1 [/tex]

[tex] a = 6 [/tex]

Use a = 6 and (1, 15) and solve for b.

[tex] 15 = 6b^1 [/tex]

[tex] 15 = 6b [/tex]

[tex] 6 = 2.5 [/tex]

[tex] y = 6(2.5)^x [/tex]

Answer:

see explanation

Step-by-step explanation:

Obtain the exponential function by substituting the given points into the equation.

Equation in form

y = a [tex]b^{x}[/tex]

Using (0, 6), then

6 = a [tex]b^{0}[/tex] = a ⇒ a = 6

Using (1, 15), then

15 = 6 [tex]b^{1}[/tex] = 6b ( divide both sides by 6 )

[tex]\frac{15}{6}[/tex] = b, hence

b = [tex]\frac{5}{2}[/tex]

Exponential equation is y = 6 [tex](\frac{5}{2}) ^{x}[/tex]

Answer:

It is the second statement.

Step-by-step explanation:

y = 25(3)^(n - 1)   where y = the number of fleas and n = the number of days.

On day 1,  y = 25 3^0 = 25

On day 2, y = 25(3^1 = 75

On day 3, y = 25(3) ^2 = 225  and so on.

Exponential growth.

Answer: Second Option

Step-by-step explanation:

Initially there are 25 fleas, and each day triples the amount.

So:

Day 1: 25

Day 2: [tex]25 * 3 = 75[/tex]

Day 3: [tex]25 * (3) ^ 2 = 225[/tex]

Day 4: [tex]25 * (3) ^ 3 = 675[/tex]

Day n: [tex]25 * (3) ^ {n-1}[/tex]

Note that the function that models the number of fleas for day n is an exponential growth function with an increase factor of 3 and an initial quantity of 25. Therefore, the answer is the second option.

Chapter : Linear equations

Lesson : Math of Junior High School

2x - 3 + 3x = -28

= 5x - 3 = -28

= 5x = -28 + 3

= 5x = -25

= x = -25 / 5

= x = 5

For this case we must find the value of "x" of the following expression:

[tex]2x-3 + 3x = -28[/tex]

We add similar terms:

[tex]5x-3 = -28[/tex]

We add 3 to both sides of the equation:

[tex]5x = -28 + 3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]5x = -25[/tex]

We divide between 5 on both sides of the equation:

[tex]x = \frac {-25} {5}\\x = -5[/tex]

ANswer:

[tex]x = -5[/tex]

Answer:

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

Step-by-step explanation:

If the equation of the line is

[tex]y=mx+b,[/tex]

then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.

Rewrite the equation of the line in the slope form

[tex]y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1[/tex]

Thus, the slope of the line is

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

The slope of a line whose equation is [tex]y-4 = \frac{5}{2}(x-2)[/tex] is [tex]\frac{5}{2}[/tex]

In this case;

The equation in question is;

[tex]y-4 = \frac{5}{2}(x-2)[/tex]

Combining like terms;

[tex]y= \frac{5}{2}x-5+4[/tex]

The equation of the line is

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

From the equation the slope of the line is [tex]\frac{5}{2}[/tex], while

The y-intercept is -1

Keywords: Slope, Equation of a straight line, y-intercept,  

Level: High school  

Subject: Mathematics  

Topic: Equation of a straight line  

Sub-topic: Slope/gradient of a line

Answer:

B.

Step-by-step explanation:

The triangle is equilateral, therefore its angles are 60°.

Answer:

B: (2, -1)

Step-by-step explanation:

1) First isolate the y in both equations

2) Set the equations equal to each other

3) Solve for x (you should get 2 and 5)

4) Insert the x values back in to get your y values

5) You should have gotten (2, -1) and (5, 2)

These are your two answers, but the question is only asking for one solution and (5,2) isn't one of the options, so it has to be (2,-1).

Answer:

[tex]24x -{6x}^{2} = 0 \: matches \: with \: 6x(4 - x) \: and \: the \: solution \: x = 0 \ \: or \: \: x = 4[/tex]

[tex]2 {x}^{2} + 6x = 0 \: matches \: with \: 2x(x + 3) = 0 \: and \: the \: solution \: x = 0 \: or \: x = - 3[/tex]

[tex]4x - {x}^{2} = 0 \: matches \: with \: x(4 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 4[/tex]

[tex]14x - {7x}^{2} = 0 \: matches \: with \: 7x(2 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 2

[/tex]

Answer:

[tex]z=\frac{63}{4}[/tex]

Step-by-step explanation:

When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.

This is represented by the following equation

[tex]y = kx[/tex]

Where k is the constant of proportionality

When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.

This is represented by the following equation

[tex]y = \frac{k}{x}[/tex]

In this case we know that:

z varies directly with [tex]x^4[/tex] and inversely with y.

We write this as:

[tex]z = k\frac{x ^ 4}{y}[/tex]

We know that When [tex]x = 2[/tex] and [tex]y = 4,\ z = 3[/tex].

So we use this information to find the constant k

[tex]3 = k\frac{2 ^ 4}{4}[/tex]

[tex]3 = k\frac{16}{4}[/tex]

[tex]3 = 4k[/tex]

[tex]k = \frac{3}{4}[/tex]

So the equation is:

[tex]z = \frac{3}{4}\frac{x ^ 4}{y}[/tex]

Finally when x = 4 and y = 9 then:

[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]

[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]

[tex]z=\frac{63}{4}[/tex]

Answer:

False.

Step-by-step explanation:

The function f(x) =2x is not an logarithmic function. Rather, it is a linear function. The reason for this is that in f(x) = 2x, there is no log or ln involved on the right hand side of the equation. It is the polynomial of the first degree, which means it is a straight line function. It is important to note that for any value of x, the value of the function changes with the same proportion. This is because the derivative of the function is a constant, which means that the rate of change is constant. The graph of the function will be a line passing from the origin and (1,2) and will have the positive slope. Therefore, f(x) is not a logarithmic function, which means that the statement is false!!!

Answer:

Sweater =400 grams

Hat =80 grams

Scarf =75 grams

Step-by-step explanation:

The amount of wool used to make a sweater, a hat and a scarf=555 grams

Let the amount of wool used to make a sweater be = x

The amount of wool for the sweater =x/5

The amount of wool used for the scarf=x/5 -5

Total amount of wool used = x+(x/5)+(x/5-5)

x+x/5 +x/5-5=555

Multiply all through by the LCM 5

5x+x+x-25=2775

7x=2800

x=400

Sweater =400 grams

Hat=400/5=80 grams

Scarf =400/5 -5=75 grams

Answer:

B

Step-by-step explanation:

The answer is in the the question "What angle is included by line segments AB and BC?".

I see B in both of those line segments so they both must share the angle B.

Answer:

<B

Step-by-step explanation:

The included angle is the angle between the two sides AB and BC

The included angle is angle B

Answer:

Answer in picture.

Step-by-step explanation:

First step: You must plot the point (-3,5).

To graph this point, start at the origin.  

The point says move left 3 and up 5 and put your dot (your point).

Second step: Use your slope to find a second point to plot.  The slope is [tex]\frac{-1}{2}[/tex].

Slope is rise/run.  So it says down 1 and right 2.

So starting at the first point you plotted and you count down 1 and then go right 2 and put your second point.

Third step: Connect the two points with a straight-edge. Extend in both directions.

The two points I used to graph my line is (-3,5) and (-1,4).

Step-by-step explanation:

[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\Delta y-\text{run up (+) or down (-)}\\\\\Delta x-\text{run to the right (+) or to the left (-) }\\\\\text{We have}\ slope=-\dfrac{1}{2}=\dfrac{1}{-2}\to\Delta y=1\ (\text{1 unit up}),\ \Delta x=-2\ (\text{2 units to the left})\\\\\text{Mark the point (-3, 5) in the coordinates system. Go 1 unit up}\\\text{and 2 units to the left. Mark next point.}\\\text{Draw a line passing through the given points.}\\\\\bold{Look\ at\ the\ picture.}[/tex]