Factor completely.
X^4-10x^2+24

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Step-by-step explanation:

Given function is:

[tex]h(x) = \frac{5}{2}x+4[/tex]

In order to find the inverse:

Replacing h(x) with y

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

Replacing x with y and y with x

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

Solving for y

[tex]x = \frac{5}{2}y+4\\x - 4 = \frac{5}{2}y+4-4\\x-4 = \frac{5}{2}y\\y = \frac{2}{5}(x-4)\\y = \frac{2x-8}{5}[/tex]

Replace y with h^(-1)(x)

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Hence,

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Keywords: Inverse, Functions

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Last year's salary is $32000

Step-by-step explanation:

We will use the linear equations to solve the given problem

Let x be the last years salary

then

0.06x will be the raise in the salary

This year's salary is $33920

So,

[tex]x+0.06x=33920\\1.06x=33920[/tex]

Dividing both sides by 1.06

[tex]\frac{1.06x}{1.06}=\frac{33920}{1.06}\\=32000[/tex]

Hence,

Last year's salary is $32000

Keywords: Percentage, Linear equations

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Answer:

50, 62

The drawing will help

Answer:

Step-by-step explanation:

[tex]a(1)=2\\\\a(2)=a(1)+12=2+12=14\\\\a(3)=a(2)+12=14+12=26\\\\a(4)=a(3)+12=26+12=38\\\\a(5)=a(4)+12=38+12=50\\\\a(5)=a(5)+12=50+12=62[/tex]

If you want the formula.

It's an arithmetic sequence with the first term 2 and common difference 12.

The explicit formula of an arithmetic sequence:

[tex]a(n)=a(1)+(n-1)d[/tex]

d - common difference

Substitute:

[tex]a(n)=2+(n-1)(12)[/tex]        use the distributive property

[tex]a(n)=2+12n-12[/tex]

[tex]a(n)=12n-10[/tex]

Answer:

f(x) = |x| or f(x) = x² etc.

Step-by-step explanation:

There are several functions that gives positive value for entire interval [-3,-2].

Like the function, y = |x| , where if you put any negative value of x, the resulting output of the value of y is always positive. Therefore, for domain of [-3,-2] the range of the function will be [3,2]

Again, the function y = x², where if you put any negative number as a value of x, the corresponding value of y will be always positive.

Therefore, for domain of [-3,-2] the range of the function will be [9,4] (Answer)  

Answer:

a is 7.5

b is 67.5

c is 100

d is let me think on d

Answer:

a is 7.5

b is 67.5

c is 100

d is for every 7.5

Answer:

Ivan isn't the son

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

Answer:

x = -10

Step-by-step explanation:

-16 = 8x/5

-80 = 8x

x = -10

Answer:

38/3 km per hour

Step-by-step explanation:

3 1/6=19/6

1/4=0.25

(19/6)*4=38/3

Answer:

h=11.3 and c=8(or 8.1 depending on what you do first)

Step-by-step explanation:

so we do the same thing like last time and 8√2 rounded is 11.3, and 7/√3, or 7√3/3 is 4( 4.04 gets rounded down). now we multiply by two because of the theorems and get 8(if this is wrong then try 8.1 because the answer differs depending on what you do first.)

Answer:

[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]

Use formula:

[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]

Since [tex]\cos x<0,[/tex] then

[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]

By definition,

[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]

Answer:

The slope is 1/2.

Step-by-step explanation:

m=(-2-(-4))/(7-3)=(-2+4)/4=1/2

Cancelling out both the -6 we get 12=0 which is not true, hence the equation is incorrect.

Answer:

(9 x+6)   =  3( 3x + 2)

(3x+2) represent the cost of each ticket.

Step-by-step explanation:

Here, the given expression representing  the cost for three friends to go to the movies  is  : (9 x+6 )

Now,simplifying the given expression, we get:

(9 x+6)   =  3( 3x + 2)

So, the given expression represents 3 times ( 3x + 2 ).

So, here (3x+2) represent the cost of each ticket.

And the expression 3 ( 3x+2)  represent the cost 3 tickets combined.

Answer:

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Step-by-step explanation:

1. Let's review carefully all the steps taken by Noa to calculate the difference of the circumferences of the two trees.

Circumference Tree 1 = 37 5/8 inches around

Circumference Tree 2 =  45 1/3 inches around

Step 1: 45 1/3- 37 5/8

The measures are correct, no issues copying them.

Step 2: 45 8/24 - 37 15/24

Noa looked for common denominators

1/3 * 8/8 = 8 /24 is correct; 5/8 * 3/3 = 15/24 is also correct.

Step 3: 44 32/24 - 37 15/24

Noa looked for making the fraction part higher on the left side:

45 8/24 = 44 32/24 is correct because 24/24 = 1

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Answer:

step 4 is correct so D

Step-by-step explanation:

i just took the test

Answer:

65%

Step-by-step explanation:

Cross, multiply and divide method has saved my life with these problems, heres how to do it.

Set up like this:

143 x

------- = -------

220 100

Multiply 143 by 100, then divide that by 220.

x= 65, so she has read 65%

Final answer:

Olivia has read approximately 65% of her 220-page novel by reading 143 pages.

Explanation:

To calculate the percent of the novel that Olivia has read, we use the formula: (number of pages read ÷ total number of pages) × 100%. Olivia has read 143 pages of a 220-page novel. Therefore, the calculation is (143 ÷ 220) × 100%, which simplifies to approximately 65%.

The steps to solve the problem are given below:

Step 1: 143 / 220 = 0.65

Step 2: 0.65 x 100 = 65%

So, Olivia has read about 65% of the novel.

When trying to find the point-slope equation of a line you need to pick a point and plug it into the plain equation with your slope.

-3 = 1/3(-1) +b

Multiply your slope with your x

-3 = -1/3 +b

Move the -1/3 to the other side by doing the opposite operation, in this case being addition.

-3 +1/3 = b

-2 2/3 = b

y = 1/3x - 2 2/3

This is an incomplete question, here is a complete question.

Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3:1 How many tablespoons does Debnil have?

A. 1/18

B. 1/2

C. 2

D.18​

Answer : The correct option is, (C) 2

Step-by-step explanation :

As we are give that Debnil has 6 teaspoons of salt.

The ratio of teaspoons to tablespoons is 3 : 1.

It means,

if he has 3 teaspoons then he has 1 tablespoons

if he has 1 teaspoons then he has [tex]\frac{1}{3}[/tex] tablespoons

So,

if he has 6 teaspoons then he has [tex]6\times \frac{1}{3}=2[/tex] tablespoons

Therefore, Debnil have 2 tablespoons of salt.

The number of tablespoons that debnil has is;

C: 2

We are told that;

Thus, if the total spoons is x. Then;

¾x = 6

Thus;

x = (4 × 6)/3

x = 8 spoons

Thus, number of tablespoons she has = 8 - 6 = 2

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I can't really give an explanation, since it's just multiplication, so here are the answers:

1. 32

2. 12

3. 24

4. 40

5. 20

6. 12

7. 12

Answer:

y=x

Step-by-step explanation:

Answer:

y = x

because it's at 1y axsis, and 1x axsis

The value of x is determined as 64 by solving the first equation. This value is then used to find the percentage n, which turns out to be 16%.

First, let's solve the equation 125% of x is 80. 1.25 times x equals 80. Therefore, x equals 64. Now, we can use that value to solve the second equation, x is n % of 400. This means 64 is what percent of 400. Expressing this as a proportion: 64/400 = n/100. Evaluating this gives n = 16%.

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Answer:

L=15  W=12   15*12 = 180

Step-by-step explanation:

W*L = area

W*(W+3) = 180

Do the distributive

W^+3 W-180=0

Find 2 numbers that when multiplied ,the result is -180

and when added the result is 3

      - 12* 15  = -180

        -12 +15 = 3

Answer:

wheres the answer choices

Answer:

t=3

Step-by-step explanation:

Answer:

The function f(x) has a hole at point x = - 5.

Step-by-step explanation:

We are given a function as

[tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]

Now, we have to describe where the function has a hole.

Now, [tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]

⇒ [tex]f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}[/tex]

Therefore, the common factor of the numerator and denominator is (x + 5).

Now, (x + 5) = 0

⇒ x = - 5

Therefore, the function f(x) has a hole at point x = - 5. (Answer)

By factoring and simplifying the function f(x)=(x^2+7x+10)/(x^2+9x+20), we find a hole at x=-5. This is because -5 was an excluded value in the original function, but does not cause the denominator to be zero in the simplified function.

The given function is f(x) = (x^2+7x+10) / (x^2+9x+20). To find where the function has a hole, we need to factor both the numerator and the denominator. We also must exclude any values of x that would cause the denominator to be zero as these are undefined in the function.

The numerator factors into (x+2)(x+5), and the denominator into (x+4)(x+5). If we simplify, the x+5 term will cancel out, leaving us with f(x) = (x+2)/(x+4).

Originally, x could not be equal to -4 or -5, as these would make the denominator zero. In the simplified function, only x=-4 causes the denominator to be zero. But since x=-5 was an excluded value in the original function, that indicates there is a 'hole' at x=-5 on the function.

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A 6-pack of t-shirts for $3.12 because 3.12 ÷ 6 is 0.52

Answer:

the last one is the least expensive it's only $0.52

Step-by-step explanation:

$2.24 ÷ 8 = $0.56

$3.00 ÷ 3 = $1.00

$4.24 ÷ 8 = $0.53

$3.12 ÷ 6 = $0.52

Answer:

$960.95

Step-by-step explanation:

The question is about finding the final amount after 4 years of a $700 investment with 8% interest, compounded quarterly. This can be solved using the compound interest formula.

The subject of your question pertains to compound interest in mathematics. Given the parameters, we want to find the amount after 4 years when $700 is invested at an interest rate of 8%, compounded quarterly. To solve this, we can use the compound interest formula, A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal form), 't' is the time the money is invested for in years, and 'n' is the number of times that interest is compounded per year. Plugging the values in, we get A = $700(1 + 0.08/4)^(4*4) which gives us the total amount after 4 years.

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Answer:

I would marry Ino from Naruto

Step-by-step explanation:

Plz mark brainliest

Answer:

my bestfriend jaheim

Step-by-step explanation: