4 (y + z); use y = 5 and z = 4

Answer:5 units

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Given

4x - 3y = 12 ( subtract 4x from both sides )

- 3y = - 4x + 12 ( divide terms by - 3 )

y = [tex]\frac{4}{3}[/tex] - 4 ← in the form y = mx + b

Answer:

The three even, consecutive integers are 72, 74, and 76.

Step-by-step explanation:

Let a be the first even integer.

Then the other two consecutive integers, b and c, will be represented by:

[tex]\displaystyle b = a + 2 \text{ and } \\ \\ c = b + 2 = (a + 2) + 2 = a + 4[/tex]

One-sixth of the smallest (that is, a) is three less than one-tenth the sum of the other two even integers (that is, b and c).

Therefore:

[tex]\displaystyle \frac{1}{6} a = \frac{1}{10}\left( b +c\right) - 3[/tex]

Solve for a. Substitute:

[tex]\displaystyle \frac{1}{6} a =\frac{1}{10}\left((a+2)+(a+4)\right) - 3[/tex]

Simplify and solve for a:

[tex]\displaystyle \begin{aligned} \frac{1}{6} a &= \frac{1}{10}(2a + 6) - 3 \\ \\ \frac{1}{6} a &= \frac{1}{5} a + \frac{3}{5} - 3\\ \\ -\frac{1}{30} a &= -\frac{12}{5} \\ \\ a &= 72\end{aligned}[/tex]

Hence, the first even integer is 72.

Therefore, the two other consecutive even integers must be 74, and 76.

In conclusion, the three even, consecutive integers are 72, 74, and 76.

There seems to be one character missing. But I gather that f(x) needs to satisfy

• [tex]x^3[/tex] divides [tex]f(x)[/tex]

• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

[tex]f(x) = x^5 + \cdots[/tex]

Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and

[tex]f(x) = x^3 p(x)[/tex]

where [tex]p(x)[/tex] is degree-2, and we can write it as

[tex]f(x)=x^3 (x^2+ax+b)[/tex]

Now, we have

[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]

so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write

[tex]p(x)^2 = (x-1)^3 q(x)[/tex]

where [tex]q(x)[/tex] is degree-1.

Expanding the left side gives

[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]

and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with

[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]

If the remainder is supposed to be zero, then

[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]

Adding these equations together and grouping terms, we get

[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]

Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,

[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]

So, we end up with

[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]

Hey there! I'm happy to help!

We see that at AB is halfway across our line. We see that AC is the total line.

So, to find the other half, we have to subtract AB from AC, which will give us the value of BC.

We first will subtract our x values.

3x-x=2x

And then we subtract our numbers.

-6-5=-11

So, BC is 2x-11.

Have a wonderful day and keep on learning! :D

Answer:

Step-by-step explanation:

Since B is the midpoint, we have:

Substitute and solve for x:

Find BC:

Answer:

2x²+16x + 24

Step-by-step explanation:

(x + 6) ( 2x + 4)

x ( 2x + 4) + 6 ( 2x + 4)

2x² + 4x + 12x + 24

2x² + 16x + 24

Hope this helps

The polynomial function [tex](x + 6)(2x + 4)[/tex] expressed as a trinomial is [tex]2x^2 + 16x + 24[/tex].

Given data:

The polynomial function is represented as A.

Now, the value of [tex]A=(x + 6)(2x + 4)[/tex].

On simplifying the equation:

From distributive property to multiply the terms:

[tex]A=x * 2x + x * 4 + 6 * 2x + 6 * 4[/tex]

[tex]A=2x^2 + 4x + 12x + 24[/tex]

On simplifying the equation:

[tex]A=2x^2 + 16x + 24[/tex]

Hence, the trinomial is [tex]2x^2 + 16x + 24[/tex].

To learn more about polynomial equations, refer:

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The answer is in the above picture.

Answer:

a =15, b=2

Axis of Symmetry = [tex]\frac{-b}{2a}[/tex]

[tex]=\frac{-2}{2 * 15}[/tex]

= [tex]-\frac{1}{15}[/tex]

To find the y-value for the vertex sub in the axis of symmetry for x

[tex]y=15(-\frac{1}{15} )^{2}+2(-\frac{1}{15} )-8\\\\=-\frac{121}{15}[/tex]

∴ Vertex [tex](-\frac{1}{15}, -\frac{121}{15} )[/tex]

Step-by-step explanation:

Answer:

(a+b+c) (x+y+z)

Step-by-step explanation:

hope this helps to uh

Step-by-step explanation:

x+y+z+bx+by+bz+cx+cy+cz

Take Like terms

x+bx+cx+y+by+cy+z+bz+cz

x(b+c)+y(b+c)+z(b+c)

(x+y+z)(b+c)

hope it helps

Answer:

16,500

Step-by-step explanation:

thats it

Step-by-step explanation:

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Hi! I'm happy to help!

Point slope form states that y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]). m represents your slope (rise/run) and [tex]y_{1}[/tex] and [tex]x_{1}[/tex] represent your first y and x points, and y and x represent your second y and x points. We already have our equation here:

y - 4 = 1/4(x- 8)

Now, let's dive into what slope-intercept form is. Slope intercept form states that y=mx+b. m represents our slope, b represents our y intercept, y represents a y point, and x represents the corresponding x point.

Since we know our m, we can solve for b, by using our other numbers. Let's use our first set of coordinates.

4=1/4(8)+b

4=2+b

2=b

Now our second set to double check:

2=1/4(0)+b

2=0+b

2=b

We know that b must equal 2, so our equation must be y=1/4x+2, which is  option 3.

You should pick option 3.

(y-intercept is where the line hits the y-axis(when x=0). We could've used our second coordinates (0,2), where x equals 0 to know that 2 is the y-intercept (b). This shortcut only works on specific problems though.)

I hope this was helpful, keep learning! :D

Answer:

5(2x + 8) = –33 + 53

10x + 40 = –33+53

10x= –33+53–40

10x = –20

x = –20/ 10

x = – 2

I hope I helped you^_^

Answer:

Remaining balance is $12.2

Step-by-step explanation:

see all steps in picture.

Janet can purchase 36.67 sets of cutlery if each set costs $0.75.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

Janet has $65 to spend on paper goods and cutlery, and the paper goods will cost $37.50,

So, she has $65 - $37.50 = $27.50 remaining to spend on cutlery.

Each set of cutlery costs $0.75,

So, Janet can purchase sets of cutlery :

⇒ $27.50 / $0.75

Apply the division operation, and we get

⇒ 36.67

Since it's not possible to buy a fraction of a set, Janet can only buy 36 sets of cutlery.

Therefore, she can purchase 36.67 sets of cutlery.

To learn more about the division operation click here :

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Answer:

FREEEEEEE POINTSSSSSSS

Step-by-step explanation:

Steps:-

First put the vertices on graph and find Triangle ABC .

Then Transact it the give amount i.e 5units and get A'B'C'

9514 1404 393

Answer:

  AC = AB

Step-by-step explanation:

The attached diagram shows the only segments that are the same length are ...

  AC = AB

__

A and B lie on the same vertical line, 5 units apart. A and C are separated by 3 units vertically and 4 units horizontally, so AC is the hypotenuse of a 3-4-5 right triangle.

Answer:

540 square feet worth of paper

Step-by-step explanation:

This is an area problem. Area is length multiplied by width. The provided length is 30 feet and the provided width is 18 feet. When they are multiplied, you get 540 square feet. Note that the height is the width in this context because if you laid the banner down, 18 would be the width. The banner is being held up, so the 18 feet is called the height.

Answer:

The coordinates are (6.5, 1.7).

Step-by-step explanation:

The difference between A and B's x-coordinate is 15.  7/10 of this is 10.5, which added to -4 gives us an x-coordinate of 6.5.

The difference between A and B's y-coordinate is 11.  7/10 of this is 7.7, which added to -6 gives us a y-coordinate of 1.7.

Therefore, the coordinates are (6.5, 1.7).

Answer:

X>-4

Y>-18

X>-7

I hope this helps

Answer:

Distributive property

Step-by-step explanation:

The 2 shares a product/multiplies with both the 5 and 7.

Step-by-step explanation:

do you happen to have a photo reference your sentence is a bit confusing

Answer:

44 = 4 · g OR g · 4 = 44

Step-by-step explanation:

So first we need to know what a variable is...

A variable is an unknown number in a math sentence

Knowing that we can write the equation.

"44 is the product 4 and Greg's height. Use the variable g to represent Greg's height"

Since we do not know Greg's height that is what we will use variable g to substitute it.

"44 is the product 4 and g"

Now all we have to do is convert this into an equation

(Note: Whenever you see product of something know that it means that you need to multiply)

So your final answer is...

44 = 4 · g

(Explanation: Since it says 44 is the product of then it means it is the answer so we will put an equal sign)

Hope this helps :)

Answer:

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved

Step-by-step explanation:

3x^2 -2x + 1 =3(x^2-2/3x+1/3)

Consider x^2-2/3x+1/3

Remember that (a-b)^2 =a^2-2ab+b^2

x^2=a^2

a=x

-2/3x= -2*x*b

b=1/3

S0 (x-1/3)^2= x^2-2/3x+1/9

x^2-2/3x+1/3= x^2-2/3x+1/9+1/3-1/9= (x-1/3)^2+2/9

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved

The solution for s in the given equation is [tex]s = C-nD[/tex]

The question seems to be incomplete

Here is the complete question:

Solve for s in this equation [tex]D= \frac{C-s}{n}[/tex]   Depreciation.

To solve for s, that means we should make s the subject of the equation

From the given equation,

[tex]D= \frac{C-s}{n}[/tex]

To solve for s, first multiply both sides by n to clear the fraction

We get

[tex]n\times D= n \times \frac{C-s}{n}[/tex]

Then,

[tex]nD = C - s[/tex]

Now, add s to both sides

[tex]nD + s= C - s+s[/tex]

[tex]nD+s = C[/tex]

Then, subtract nD from both sides

[tex]nD-nD+s = C-nD[/tex]

∴ [tex]s = C-nD[/tex]

Hence, the solution for s in the given equation is [tex]s = C-nD[/tex]

Learn more here: https://brainly.com/question/21406377

Step-by-step explanation:

f(g(x))=(3x+1)^2 +2(3x+1) -4

=9x^2 +6x +1 +6x +2 -4

=9x^2 +12x +(-1)

Answer:

Distance btw (-2, -2) and (8, -6) is (10, -4)

Step-by-step explanation:

I. Give (-2, -2) is A and (8, -6) is B

                     B - A = 8 - (-2) in x

                              = -6 - (-2) in y

                    So B - A = 10, -4

II. You can prove the answer by A.value + (10, -4) = B.value

Hope that help :D

Hi ;-)

[tex]\text{A}=(-2,-2) \ \text{and} \ \text{B}=(8,-6)\\\\|AB|=\sqrt{(8-(-2))^2+(-6-(-2))^2}\\\\|AB|=\sqrt{(8+2)^2+(-6+2)^2}\\\\|AB|=\sqrt{10^2+(-4)^2}\\\\|AB|=\sqrt{100+16}\\\\|AB|=\sqrt{116}\rightarrow\boxed{|AB|=2\sqrt{29}} \ (\text{because} \ 116=4\cdot29)[/tex]

Answer:1 3/4

Step-by-step explanation:

Answer:7/4=1 3/4

Step-by-step explanation:

it is like this,7,we can think of 8,which would 2,but it is 7,so we drop down to 1 whole.Then we have 3 remaining,which makes 1 and 3/4