Solve for x. Use the completing the square method. x² + 8x = 7

Answer:

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Step-by-step explanation:

First we have to factor the equation:

[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex]

The commom factor of first three terms and [tex]105x[/tex] is [tex]3x[/tex]. Note that [tex]105x=3x(35)[/tex]

[tex]3x(2yz+10y+7z+35)+2yz+10y+7z=812[/tex]

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z)=812[/tex]

In order to have two equal factors add 35 both sides:

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z+35)=847[/tex]

Let's factor [tex](2yz+10y+7z+35)[/tex]

[tex](2yz+10y+7z+35) \Rightarrow 2y\left(z+5\right)+7\left(z+5\right) \Rightarrow \left(z+5\right)\left(2y+7\right)[/tex]

Now we have:

[tex]3x(z+5)\left(2y+7\right)+\left(z+5\right)\left(2y+7\right)=847[/tex]

[tex](3x + 1) (2y + 7) (z + 5) = 847[/tex]

Now it is the interesting part: You have to figure out that 3 numbers multiplied by each other will result in 847.

We have [tex]847 = 7 \cdot 11 \cdot 11[/tex]

Let's try

[tex]2y+7=7\\2y=0[/tex]

I will stop right here. This is not true.

Let's try then

[tex]2y+7=11\\2y=4\\y=2[/tex]

Now let's try

[tex]z+5 = 11\\z=6[/tex]

Now let's try

[tex]3x+1=7\\3x=6\\x=2[/tex]

Note that in this case I didn't considered [tex]3x+1=11[/tex] because it would not be an integer.

Therefore,

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Answer:

12 units

Step-by-step explanation:

distance formula

Answer: 1p/5

Step-by-step explanation:

Answer:

Gina will eat  pound cheese for lunch each day

Explanation

Amount of cheese bought = 1 pound and the amount of cheese used =  pound

So, the remaining amount of cheese

As this  pound cheese is splitting into 5 equal parts, so the amount of each part will be:  ÷ 5 =  ×  =  pound

So, Gina will eat  pound cheese for lunch each day.

Step-by-step explanation:

Answer:

y+6 = -2(x-4)

Step-by-step explanation:

Point slope form is given by

(y-y1) = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

(y - -6) = -2( x-4)

y+6 = -2(x-4)

The value of x must be equal to 1000

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as

For x > 0 , a > 0, and a ≠1,

y= logₐ x if and only if x = a^y

Then the function is given by

f(x) = logₐx

Given here  log x= 3 ⇒x=10³

                                 ⇒x=1000

Hence, The value of x must be equal to 1000

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What is the slope of the first line?  

✔ –5

What is the slope of the second line?  

✔ 2

How many times do the lines intersect?  

✔ 1

How many solutions does the system have?  

✔ 1

Answer:

Step-by-step explanation:

-5x - 1 = 2x + 6

-7x - 1 = 6

-7x = 7

x = -1

y = -5(-1) - 1 = 5 - 1 = 4

(-1. 4)

first slope: -5

second slope: 2

once

one

Step-by-step explanation:

if you have a whole number and fraction you can simply at them together, which results in what's called mixed number .

example : the mixed number 8 3/4 is understood to mean the same thing as

8 + 3/4.

Answer:

3) 10^12

4) 0.99^4

8) x^12

9) 3/4^6

Step-by-step explanation:

10^(6+5+1)

0.99^(3+1)

x^(6+2+4)

3/4^(2+2+2)

3) 10^12=1000000000000

4)0.99^4=0.96059601

8)x^12

9)(3/4)^6=0.1779...

Answer:

C

Step-by-step explanation:

Since triangles TUS and QRS are similar, if TUS is isosceles then so is QRS. This means that all corresponding proportions are at a constant ratio. So if TS=US, QT=RU and therefore a=7. Hope this helps!

Answer:

a =7

Step-by-step explanation:

The triangles are similar so we can use ratios

10           10

------  = --------

10+a      10+7

Since the numerators are the same, the denominators have to be the same

10+a = 10+7

a = 7

Answer:

3%

Step-by-step explanation:

Just move the decimal 2 spaces to the right .03 becomes 3% :)

Answer:

[tex]P(x)=x^3-5x^2+2x+8[/tex]

Step-by-step explanation:

If the polynomial has the following zeros: x= 4, x=2, and x=-1, then it must have the following factors which guarantee the polynomial will render zero at the given points:

[tex]P(x)=C (x-4)\, (x-2) \,(x+1)[/tex]

where C is any multiplicative constant. Since there is no other condition imposed on the polynomial, we can adopt a simple constant C = 1 to facilitate our final calculation of writing the polynomial in standard form:

[tex]P(x)=(x-4)\, (x-2) \,(x+1)\\P(x)=(x^2-2x-4x+8)\,(x+1)\\P(x)= (x^2-6x+8)\,(x+1)\\P(x)=x^3+x^2-6x^2-6x+8x+8\\P(x)=x^3-5x^2+2x+8[/tex]

Answer:

It will be letter D and A

Step-by-step explanation:

Letter D, because you are saying that is 25 over 100 and letter A because the equation to find a percentage is:

[tex]\frac{X}{Y}= \frac{PERCENTAGE MISSING}{100}[/tex]

X and Y: will be the information that they give so, the equation and answer will be

[tex]\frac{25}{100} =\frac{x}{100}\\\\ \frac{25* 100 }{100} \\\\\frac{2500}{100} \\\\25%[/tex]

Answer:

D & A

Step-by-step explanation:

Answer:

1) 9 × 2 = 18 cm²

2) 6 cm

3) 9 × 2 × 6 = 108 cm³

Answer:

Base area: [tex]18cm^2[/tex]

Height: 6 cm

Volume: [tex]108cm^3[/tex]

Step-by-step explanation:

Base area:

So the base is the side the right rectangular prism is laying on and in this case it is ABCD and the length and width is 9 and 2 so multiplying that we get [tex]18cm^2[/tex].

Height:

In this scenario of a right rectangular prism any side It is lying on so we will use 6 cm as the height.

Volume:

To find the volume of a rectangular prism you have to use the following formula.

[tex]V=l*w*h[/tex]

The l is length which is 9 cm.

The w is width which is 2 cm.

And the h is height which is 6 cm.

So multiplying all that we get [tex]108cm^3[/tex].

24nk

n=6

k=8

24 × (6) × (8)

24 × (48) = 1152

Answer:

24nk=1152

Step-by-step explanation:

24nk

Substituting the values in the equation

24*6*8

In order to evaluate these values we have to simply multiply the numbers

144*8

I hope it will help you

1152 is the answer

Answer:

I think the answer is the last one

adjacent side / hypotenuse

Answer:

The value of Area of B/Area of A is 0.75.

Step-by-step explanation:

It is provided that:

Consider the diagram below.

The area of a rectangle is:

[tex]\text{Area}=\text{Length}\times \text{Breadth}[/tex]

Compute the area of rectangle A as follows:

[tex]\text{Area of A}=l\times b[/tex]

Compute the area of rectangle B as follows:

[tex]\text{Area of B}=1.25\ l\times \frac{3}{5}\ b=0.75\ (l\times b)[/tex]

Compute the value of Area of B/Area of A as follows:

[tex]\frac{\text{Area of B}}{\text{Area of A}}=\frac{0.75\ (l\times b)}{l\times b}=0.75[/tex]

Thus, the value of Area of B/Area of A is 0.75.

Answer:

f(x) = x² - 81 = ( x+ 9)(x - 9) Difference of two squares

g(x) = x+9/x-9

g(x) . f(x) = x + 9/ x - 9 × (x+9)(x - 9)

= ( x + 9)(x +9)

= ( x + 9)²

= x² + 18x + 81

Hope this helps.

Add 1 to both sides of the equation to get 4x = 4.

Divide both sides by 4 and x = 1.

Answer:

x= 1

Step-by-step explanation:

4x-1=3

    +1 +1

4x=4 (divide both sides by 4 to get x alone)

x=1

Answer:

If f and h are inverses, then:

f (h(x) ) = x   and also

h( f(x) ) = x

Step-by-step explanation:

Inverse function: The function f(x) goes from domain to range and the inverse function f^{-1} goes from Range to domain

Option C is correct

I would appreciate it if you marked me brainliest :)

Answer:

a) g(f(x)) = (sqrt(x - 5))^2 + 1 = x - 5 + 1 = x - 4

b) For f(x), domain is x - 5 >= 0, or x >= 5, so for g(f(x)), the domain is

x >= 5

Since there is nothing attached for me to help you I looked for a website that can find the answer with an explanation. It is called quickmath it’s like a math calculator . Hopefully that helps you .

Answer:

x = 6

Step-by-step explanation:

3 ln x = ln 216

Rewrite 216 as 6^3

3 ln x = ln 6^3

We know that ln a^b = b ln a

3 ln x = 3 ln 6

x = 6

Answer:

[tex] \sf{ \dfrac{ 3}{5}x + 2 = \dfrac{2}{3} x}[/tex]

[tex] \implies \sf{ \dfrac{2}{3} x - \dfrac{3}{5} x} = 2[/tex]

[tex] \red\star \sf{take \: l.c.m \: of \: 3 \: and \: 5 = 15}[/tex]

[tex] \implies \sf{ \dfrac{10x - 9x}{15} = 2 }[/tex]

[tex] \implies \sf{ \dfrac{x}{15} = 2 }[/tex]

[tex] \implies \sf{x = 2 \times 15}[/tex]

[tex] \implies \sf{x = 30}[/tex]

Answer:

x=30

Step-by-step explanation:

3/5x+2=2/3x

So for solving for x you are going to first try to get x on the same side so move 2/3x to the left side of the equal sign. so it becomes 3/5x-2/3x+2=0 then you are going to combine like terms and subtract 2/3x from 3/5x so it becomes 9/15x-10/15x since they have least common denominater which is 15 so it becomes 9/15 and 10/15 then you subtract them so it is -1/15x+2=0 then you are going to move the 2 to the other side of the equal sign so it is -1/15x=-2 then you are going to divide multiply -15 to both sides to get rid of it from the x side so you can isolate it so therefore the answer is x=30

Answer:

G(x)=-(x+3)+6

Step-by-step explanation:

f(x) means that whatevers in the parentheses is x. In g(x) x is equal to x+3

Answer:

2). Volume = 14400 feet³

3). Volume = 157.5 ft³

Step-by-step explanation:

Both the figures given in the sheet attached are a rectangular pyramid and a triangular prism.

2). In this part of the question solid given is in the shape of an rectangular pyramid.

Volume of this oblique pyramid = [tex]\frac{1}{3}(\text{Base})(\text{Height})[/tex]

Here 'B' = area of the base

h = height of the pyramid

Volume = [tex]\frac{1}{3}(25\times 36)\times 48[/tex]

             = 14400 cubic feet

4). Volume of a triangular cone = (Area of the triangular base)×(height)

                                                    = [tex][\frac{1}{2}(\text{Base})(\text{height})]\times {\text{height of the prism}}[/tex]

                                                    = [tex]\frac{1}{2}(7\times 9)\times {5}[/tex]

                                                    = 157.5 ft³

Answer:

D) 5

Step-by-step explanation:

The smaller triangle is similar to the big triangle with the big triangle with a scale factor of 1.8.

5x × 1.8 = 45

Divide both sides by 1.8

5x = 25

Divide both sides by 5

x = 5

The  solutions of the equation 2x²+7x+3=0 are x=-1/2 and x=-3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is 2x²+7x+3=0

Two times of x square plus seven times of x plus three equal to zero is the form of quadratic.

We can solve the quadratic equation  2x²+7x+3=0 using factoring

Let us find two numbers whose product is 2x²+7x+3=0 and

whose sum is 7.

We can see that 2x²+7x+3=0

Let us factor by grouping

2x²+6x+x+3=0

2x(x+3)+(x+3)

=(2x+1)(x+3).

x=-1/2 and x=-3

Therefore, the solutions are x=-3 and x=-1/2.

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Answer:

30 days

Step-by-step explanation:

There are 6 * 7 = 42 days in 6 weeks.

There are 2 * 6 = 12 weekends in 6 weeks.

42 - 12 = 30

Answer:

30 days

Step-by-step explanation:

Work Shown:

sec(80) = 1/cos(80) = 5.75877048314363 which rounds to 5.76

Make sure your calculator is in degree mode.

Answer:

31.

Step-by-step explanation:

1. Write out the problem.

6w-19 + k; w=8 and k=2

2. Figure out the first part of the problem.

So, if w=8 and 6 and w are next to each other, we should multiply 6*8, which is 48. Next, it says to subtract 19. 48-19=29.

3. Find out what the last part of the problem is.

Since the first part of the problem is 29 and k=2, we should add 29+2=31, which is the final answer.

Hope this helped :)