4. What is the solution to the system of equations?

Hint: Solve each equation for y first, then graph.

5. What is the solution to the system of equations?

There are a lot of questions here. I'll do problems 7 and 8 to get you started.

====================================================

Problem 7

The given equations are

y = x^2 + 5x - 2

y = 3x - 2

Since both right hand sides are equal to y, we can equate them, get everything to one side, and solve

x^2 + 5x - 2 = 3x - 2

x^2 + 5x - 2 - 3x + 2 = 0

x^2 + 2x = 0

x(x + 2) = 0

x = 0 or x + 2 = 0 ........ zero product property

x = 0 or x = -2

Now plug each x value back into one of the original equations given

If x = 0, then

y = 3x-2

y = 3*0-2

y = -2

Making (0,-2) as one solution. Repeat for the x value x = -2

y = 3x-2

y = 3(-2)-2

y = -8

The point (-2, -8) is the other solution to the system.

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

Answer: There are two solutions and they are (0, -2) and (-2, -8)

====================================================

Problem 8

y = -x^2 - 3x + 2

y = x + 6

We'll use the same idea as before

y = -x^2 - 3x + 2

x + 6 = -x^2 - 3x + 2

x + 6 + x^2 + 3x - 2 = 0

x^2 + 4x + 4 = 0

Now factor the left side to solve for x

(x+2)(x+2) = 0

(x+2)^2 = 0

x+2 = 0

x = -2

Use this x value to find y

y = x+6

y = -2+6

y = 4

Or we can cay

y = -x^2 - 3x + 2

y = -(-2)^2 - 3(-2) + 2

y = 4

We get the same y value either way.

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

Answer: There is one solution and it is (-2, 4)

Answer:

BMI is 24.9

Step-by-step explanation:

In order to calculate the student's BMI we first need to convert her weight into kilograms and her height into meters. We know that there are 39.37 inches in a meter and every foot has 12 inches. Therefore, since the student is 5ft 4 inches, this means she is 64inches tall. Now we can divide this by 39.37 to find her height in meters

64 / 39.37 = 1.6256 meters

Now we need to calculate her weight in kilograms. Since there are 2.20462 pounds in 1 kilogram, we simply divide her weight by 2.20462.

145 / 2.20462 = 65.7709 kilograms

Now we use the BMI formula to solve for the students BMI

BMI = [tex]\frac{mass}{height^{2} }[/tex]

BMI = [tex]\frac{65.7709}{1.6256^{2} }[/tex]

BMI = [tex]\frac{65.7709}{2.6425}[/tex]

BMI = 24.88

Therefore we can see that the students BMI is 24.9

Answer:

$330

Step-by-step explanation:

[tex]\frac{24}{198} =\frac{40}{x}[/tex]

Cross multiply:

24x= 198(40)

to get x=330

Answer:

[tex]f(-1)=\frac{-1}{2}[/tex]

[tex]g(-2)=\frac{5}{32}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

[tex]f(x)=\frac{2x-1}{2x^3-8x}[/tex]

[tex]g(x)=\frac{2x-1}{2x^3+8x}[/tex]

f(-1) is x = -1

g(-2) is x = -2

Step 2: Evalaute

f(-1)

g(-2)

And we have our final answers!

Answer:

2

Step-by-step explanation:

Answer:

The Function rule for line is: [tex]\mathbf{y=-\frac{13}{5}x}[/tex]

Option A is correct option.

Step-by-step explanation:

Find a function rule for the line that passes through the origin (0,0) and the point (5, - 13)

The function rule is of form: [tex]\mathbf{y=mx+b}[/tex]

where m is slope and b is y-intercept

Finding slope:

The formula used to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have [tex]x_1=0, y_1=0, x_2=5, y_2=-13[/tex]

Putting values and finding slope

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-13-0}{5-0}\\Slope=\frac{-13}{5}\\Slope=-\frac{13}{5}[/tex]

Finding y-intercept

We will use point(0,0) to find y-intercept

[tex]y=mx+b\\0=-\frac{13}{5}(0)+b\\0=0+b\\b=0[/tex]

So, y-intercept is 0

The Function rule for line having slope m=-13/5 and y-intercept b=0:

[tex]y=mx+b\\y=-\frac{13}{5}x+0\\y=-\frac{13}{5}x[/tex]

So, The Function rule for line is: [tex]\mathbf{y=-\frac{13}{5}x}[/tex]

Option A is correct option.

Answer:

Third option is the correct answer

Step-by-step explanation:

[tex] f(x) = 2x^2 - 4x[/tex] is the correct answer.

Answer:

$7.50

Step-by-step explanation:

Answer:

$22.50

Step-by-step explanation:

My bad lol, I posted the answer under the wrong thing.

Answer:

The coordinates of point that divides the given line in ratio 1:2 are (-1,-6)

Step-by-step explanation:

Given that:

(x1,y1) = (-6,-10)

(x2,y2) = (9,2)

If a point (x,y) divides a line into ratio m:n, the coordinates can be found out by the formula

[tex](x,y) = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})[/tex]

As given ratio is: 1:2

so m= 1

n = 2

Putting the values in the formula we get

[tex]= (\frac{(2)(-6)+(1)(9)}{1+2} , \frac{(2)(-10)+(1)(2)}{1+2})\\=(\frac{-12+9}{3} , \frac{-20+2}{3})\\=(\frac{-3}{3} , \frac{-18}{3})\\=(-1,-6)[/tex]

Hence,

The coordinates of point that divides the given line in ratio 1:2 are (-1,-6)

Answer:

x = 9.5

x = 9 1/2

x = 19/2

All answers are the same, just different ways of denoting it.

Step-by-step explanation:

-4 + 5x - 7 = 10 + 3x - 2

Simplify both sides, by combining like terms

-4 + 5x - 7 = 10 + 3x - 2

-11 + 5x = 8 + 3x

Inverse operations

-11 + 5x = 8 + 3x

+11           +11

5x = 19 + 3x

-3x         -3x

2x = 19

/2     /2

x = 9.5

Answer:

25000

Step-by-step explanation:

25 * 1000 = 25000

25000 milliliters

Convert 25 liters to milliliters

Answer:

[tex] y = \frac{1}{2}x + \frac{1}{4} [/tex]

Step-by-step explanation:

Equation in slope-intercept form is given as [tex] y = mx + b [/tex]

An equation parallel to [tex] y = \frac{1}{2}x + \frac{5}{2} [/tex] would have the same slope as the equation.

The slope (m) of the line would be ½.

m = ½.

Given that this same line runs through or contains (³/2, 1), we cam find the value of b (y-intercept) by substituting m = ½, x = ³/2, and y = 1 in [tex] y = mx + b [/tex].

Thus:

[tex] 1 = (\frac{1}{2})(\frac{3}{2}) + b [/tex]

[tex] 1 = \frac{3}{4} + b [/tex]

Subtract both sides by ¾

[tex] 1 - \frac{3}{4} = b [/tex]

[tex] \frac{1}{4} = b [/tex]

To derive the equation, substitute m = ½, and b = ¼ in [tex] y = mx + b [/tex].

✔️The equation is:

[tex] y = \frac{1}{2}x + \frac{1}{4} [/tex]

Answer:

A. HL

B. SAS

C. SSS

May I have brainliest please? :)

The triangles can be proved congruent by HL, SSS, and SAS congruence, the correct option is A, B, and C.

A right triangle is a triangle in which the measure of one of the angles is 90 degrees.

The triangle given is are triangles ABR and ACR

They share a common side AR

∠ABR = ∠ACR = 90 degree.

AB ≅ AC

BR ≅ CR

The triangles can be proved congruent by,

HL- Height Length congruence for a right-angle triangle

SSS -  All the sides are equal and,

SAS - The two sides and the included angle is equal.

Your question seems incomplete, the complete question is attached with the answer.

To know more about Right Angled Triangle

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Answer:

A.  [tex]f(n) =0.2n+4.8[/tex]

B. The y intercept is 4.8

Step-by-step explanation:

Given

[tex]a_n= 5 + 0.2(n-1)[/tex]

Solving (a): Write as a function.

To do this, we simply substitute f(n) for [tex]a_n[/tex]

[tex]a_n= 5 + 0.2(n-1)[/tex] becomes

[tex]f(n)= 5 + 0.2(n-1)[/tex]

Open Bracket

[tex]f(n) = 5 + 0.2n-0.2[/tex]

Collect Like Terms

[tex]f(n) =0.2n-0.2 + 5[/tex]

[tex]f(n) =0.2n+4.8[/tex]

B. The y intercept.

To get the y intercept, we set n to 0

i.e

[tex]f(0) =0.2 * 0+4.8[/tex]

[tex]f(0) =0+4.8[/tex]

[tex]f(0) =4.8[/tex]

Hence, the y intercept is 4.8

Answer:

7.22

Step-by-step explanation:

Use a calculator

Answer:

19 x 0.38 = 7.22

Step-by-step explanation:

if the number you are multiplying by is smaller than 1, it's always smaller than the beginning number.

May I have brainliest please? :)

Answer:

x=5

Step-by-step explanation:

Let's solve your equation step-by-step.

4x+10=30

Step 1: Subtract 10 from both sides.

4x+10−10=30−10

4x=20

Step 2: Divide both sides by 4.

4x /4 = 20/4

x=5

The value of x that satisfies the equation 4x + 10 = 30 is x = 5.

Here,

To solve the equation 4x + 10 = 30,

we want to find the value of x that makes the equation true.

Step 1: Isolate the variable term.

First, we want to get rid of the constant term 10 on the left side of the equation.

We can do this by subtracting 10 from both sides of the equation:

4x + 10 - 10 = 30 - 10

Simplifying:

4x = 20

Step 2: Solve for x.

Next, we want to isolate the variable x on one side of the equation.

Since 4 is multiplied by x, we can undo this by dividing both sides of the equation by 4:

4x / 4 = 20 / 4

Simplifying:

x = 5

Step 3: Check the solution.

To verify that our solution is correct, we can substitute the value of x back into the original equation:

4x + 10 = 30

Substitute x = 5:

4(5) + 10 = 30

Simplifying:

20 + 10 = 30

30 = 30

Since both sides are equal, our solution x = 5 is correct.

Therefore, the value of x that satisfies the equation 4x + 10 = 30 is x = 5.

To learn more on equation click:

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Answer:

3

Step-by-step explanation:

(1/2) / (1/6)

(1/2) * (6/1) = 6/2 = 3

Answer:

you prove her wrong with dem facts!

Answer:

3 1/8

Step-by-step explanation:

You can rewrite 1 1/4 as 1 2/8, so adding them you'd get 2 9/8, or 3 1/8

Answer:

1.7^3

Step-by-step explanation:

i cannot see your answer options so I hope this helps!!!!

Answer:

xfghzfgfrxeshixeah

Step-by-step explanation:

LG's SSL looks sl lid

Answer:

it is 12 people

Step-by-step explanation:

i looked it up on Google. all you have to do is type in 25 percent of 48

Answer: Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. ... Volume is often quantified numerically using the SI derived unit, the cubic metre.

Step-by-step explanation:

SI unit: Cubic metre

Other units: Litre, fluid ounce, gallon, quart, pint, ...

In SI base units: 1 m3

Dimension: L3

Answer:

f(h)=2d+4.3

= 2 x 1.5+4.3

  h=7.3ft

Answer:

1.[tex]y=-6x+6, y=\frac{6}{5} x+\frac{18}{5}, y=\frac{6}{11} x+\frac{42}{11}[/tex]

2.[tex]y=-\frac{1}{2} x+2\frac{1}{4} , x=2, y=-\frac{7}{6}x+\frac{43}{12}[/tex]

Step-by-step explanation:

A(−3, 0), B(0, 6), and C(4, 6)

using the midpoint formula: [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] we can find all of their midpoint which is necessary to complete question 1 and 2

Mid AB=(-1.5, 3), Mid BC=(2, 6), Mid AC=(0.5,3)

Next, we have to find the slope of from the vertex and the midpoint of each side. We use the slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

You would get -6, 6/5, and 6/11.

Next you substitute in the coordinates for the equation of each for example: y=-6x, you switch in the set of cords AB which is (-1.5, 3). 3=-6(-1.5)+z and find that z=6, so the equation is y=-6x+6. As for the rest, repeat the same process until you find all 3 cords. You should get an answer of [tex]y=-6x+6, y=\frac{6}{5} x+\frac{18}{5}, y=\frac{6}{11} x+\frac{42}{11}[/tex]

For question 2,

The line has to be perpendicular bisector to the midpoint, signifying that it has to split 2 angles into congruent angles and a side into half. In order to do that we need to first find the opposite reciprocal of each side's slope. Which means we need to once again use the slope formula and get the opposite reciprocal by [tex]-\frac{1}{slope}[/tex]. For all the opposite reciprocal slopes you get will be incorporated into the final formulas. That gives us the slopes of -1/2, 0 and -7/6. Then do the same process of matching cords with these incomplete equations and you can find the final equations of [tex]y=-\frac{1}{2} x+2\frac{1}{4} , x=2, y=-\frac{7}{6}x+\frac{43}{12}[/tex]

I hope that helped with your question!! :)

Also I'm an RSM student too and I didn't know how to do them before so I searched it up.

Answer:

-1 and 0                              

-2/3 lies between numbers -1 and 0

Answer:

D

Step-by-step explanation:

Have a great da༼ つ ◕_◕ ༽つy!