1) The sum of the two numbers is 36 and their difference is 9. Find the average of the two numbers.

Let's find sides one by one

[tex]\\ \tt\hookrightarrow a^2=2^2+3^2=4+9=13\implies a=\sqrt{13}=3.2[/tex]

[tex]\\ \tt\hookrightarrow b=\sqrt{2^2+4^2}=\sqrt{20}=4.2[/tex]

[tex]\\ \tt\hookrightarrow x=\sqrt{1^2+4^2}=\sqrt{17}=4.1[/tex]

Now

[tex]\\ \tt\hookrightarrow s=\dfrac{4.2+4.1+3.2}{2}=5.7[/tex]

Apply herons formula

Area

[tex]\\ \tt\hookrightarrow \sqrt{5.7(5.7-3.2)(5.7-4.1)(5.7-4.2)}=\sqrt{5.7(2.5)(1.6)(1.5)}=5.84units^2[/tex]

A: f(x)=8x-2

1. Switch the f(x) to y

y=8x-2

2. Switch y to x and x to y

x=8y-2

3. Solve for y:

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

1. Add 2 to both sides.

 x=8y-2

+2     +2

2. Divide both sides by 8.

x+2=8y

---     ---

8       8

1/8x+1/4=y

3. Write in f-inverse form

f^-1(x)=1/8x+1/4  

B: g(x)=2/3x+6

1. Switch the g(x) to y

y=2/3x+6

2. Switch y to x and x to y

x=2/3y+6

3. Solve for y:

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

1. Subtract 6 from both sides.

x=2/3y+6

-6        -6

2. Multiply both sides by 3/2 (to cancel out the 2/3)

x-6=2/3y

2/3x-4=y

3. Write in f-inverse form

g^1(x)=2/3x-4

C: h(x)-4x-12

1. Switch the h(x) to y

y=-4x-12

2. Switch y to x and x to y

x=-4y-12

3. Solve for y:

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

1. Add 12 to both sides.

x=-4y-12

+12    +12

2. Divide both sides by -4

x+12=-4y

------    ---

-4        -4

-1/4x-3=y

3. Write in h-inverse form

h^2(x)=-1/4/x-3

Answer:

y = 2x + 1 --> linear

y = -4x + 7 --> non-linear

Not a solution for a linear system.

Step-by-step explanation:

for (a), y = 2x+1, substitute the x and y values. keep in mind, that in a linear pair, (x, y). So, for the first equation you get:

7 = 2x3 + 1. This is correct, because 6 + 1 is 7. Therefore, (a) is linear.

for (b), we have to substitute our values again. You get:

7 = -4x3 + 7, which is

7 = -12+7, which is not true. So, (b) is not linear.

This means that for the linear pair (3, 7), it does not satisfy both equations, which means that it is not a solution for the linear system.

Answer: 3:2 is the scale he should use

Step-by-step explanation: You simplify 24/16 by the GCF (greatest common factor) The GCF of 24 and 16 is 8 so [tex]\frac{24}{16}[/tex] ÷ [tex]\frac{8}{8}[/tex] = [tex]\frac{3}{2}[/tex]. 3/2 could also be written as a scale or ratio which is 3:2.

Answer:

The y intercept should be 9 and the graph is incorrect.

On the interval {x, 7} , the x-value at which the average rate of change is 56, is 4 and 7.

Table is a way to represent the data of the two or more variable.

To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.

The table of the given x value is,

x          3,     4,     5,     6,     7

f(x)      12,   24,   28,   96,   192

The average rate of change of value is the ratio of overall change of function output value to the input value.

For the input values of 4 and 7 let's find the average rate of change,

[tex]r=\dfrac{192-24}{7-4}\\r=\dfrac{168}{3}\\r=56[/tex]

Hence, on the interval {x, 7} , the x-value at which the average rate of change is 56, is 4 and 7.

Learn more about the data table here;

https://brainly.com/question/15602982

Answer:

4

x-value is the average rate of change 56

Answer:

[tex]r=\frac{a-p}{pt}[/tex]

Step-by-step explanation:

Solve [tex]a=p+prt:[/tex]

[tex]r=\frac{a-p}{pt}[/tex]

The volume of a cylinder is the amount of space in it

The radius of the cylinder is 3 feet

The volume of a cylinder is:

[tex]V = \pi r^2 h[/tex]

Where r represents the radius, and h represents the height

So, we have:

[tex]108\pi = \pi r^2 * 12[/tex]

Divide both sides by 12pi

[tex]9 = r^2[/tex]

Take the square roots of both sides

3 = r

Rewrite as:

r = 3

Hence, the radius of the cylinder is 3 feet

Read more about volume at:

https://brainly.com/question/10171109

Answer:

A circle has a worth of 0. If your talking about the corners.

Answer:

31.47

Step-by-step explanation:

WX - 11

3.1 x 13.7 - 11

42.47 -11

=31.47

Hi!

I can help you with joy!

All we have to do here is plug in the numbers.

wx-11

(3.1)(13.7)-11

Multiply:

42.47-11

Subtract:

31.47 (Answer)

I hope this helps!

Ask me if you have any questions.

~Misty~

-[tex]\bf{Silent~[/tex]-

Probabilities are used to determine the chances of events

The probability that the salesman left his sunglasses in the first store is 0.16

The given parameter is:

p = 1/5 ---- the probability that he left his sunglass

The probability that he did not leave his sunglass would be:

q= 1- 1/5

Evaluate the difference:

p = 4/5

So, the probability that the salesman left his sunglasses in the first store is:

Pr = 1/5 * 4/5

Evaluate the product

Pr = 4/25

Express as decimal

Pr = 0.16

Hence, the probability that the salesman left his sunglasses in the first store is 0.16

Read more about probabilities at:

https://brainly.com/question/25870256

The resultant polynomial which is the correct simplification and demonstration of the closure property of give expression is,

[tex]-5x^3 +4x^2- 5x[/tex]

This resultant expression is polynomial.

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The given expression in the problem is,

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

Let the resultant polynomial of the above expression is f(x). Therefore,

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

To solve the above polynomial, open the bracket by multiplying the sign with inside values as,

[tex]3x^3 +2x^2 - 5x - 8x^3 +2x^2[/tex]

Separate the same power terms of the variables as,

[tex]f(x)=3x^3- 8x^3 +2x^2 +2x^2- 5x\\f(x)=-5x^3 +4x^2- 5x[/tex]

The resultant polynomial which is the correct simplification and demonstration of the closure property of give expression is,

[tex]-5x^3 +4x^2- 5x[/tex]

This resultant expression is polynomial.

Learn more about polynomial here;

https://brainly.com/question/24380382

Answer:

8.5 in

Step-by-step explanation:

step 1

to find the width, the equation would be:

P/2-L

step 2-plug in

43/2-13=

8.5

Answer:

Step-by-step explanation: 10 + 10 = 20

46 - 20 = 26

26 divided by 2 = 13

Answer:

[tex]x = 14 - 3[/tex]

Step-by-step explanation:

*The key word 'less than' means to subtract.

x + 3 = 14 is incorrect. Kiran isn't adding weight to his backpack.

In other words, the backpack didn't increase in pounds.

3(x) = 14 is incorrect. Multiplying is irrelevant to this problem, it's not saying Kiran's backpack is 3 times a number equal to Clare's backpack weight.

x = 143 is incorrect. This equation is unrealistic.

x = 14 - 3 is correct. This equation is explaining that Kiran's backpack is 3 pounds less than Clare's backpack (14)

Answer:

42 square cm

Step-by-step explanation:

6 x 14 = 84. 84 divided by 2 = 42.

a = b x h divided by 2

Answer:

s is the independent variable and d is the dependent variable.

Step-by-step explanation:

--------- :)

Answer:

9) y=(-6-3x)/2                 10) y=(2x+15)/3            11) y=8+4x

12) y=1/2x+6                   13) y= (8-3x)/-4            14) y= (10-6x)/-2

Step-by-step explanation:

The methods I used are known as float and ping, and escalator:

9) We can float the 3x to the other side to make

2y=-6-3x

We now escalate the 2 down to make:

y= [tex]\frac{-6-3x}{2}[/tex]

10) We simply escalate the 3 down to give:

y= [tex]\frac{2x+15}{3}[/tex]

11) We simply float the -4x to the other side:

y=8+4x

12) For this question, it will be better to expand the bracket first:

y-8=-1/2x-2

Now we float the -8 to the other side to give:

y=-1/2x-2+8

Which can be simplified to give:

y=1/2x+6

13) We simply float the 3x to the other side to give:

-4y=8-3x

Now we escalate the -4 down to give:

y= [tex]\frac{(8-3x)}{-4}[/tex]  
14) We float the 6x to the other side to give:

-2y=10-6x

Now we escalate the -2 down to give:

y= [tex]\frac{10-6x}{-2}[/tex]

Answer:

D. Subtraction Property of Equality

Step-by-step explanation:

D. Subtraction Property of Equality

From 6-7, you subtract 132 from both sides. You can only do this because of the subtraction property of equality which essentially means that if you subtract something from one side of the equation, you also have to subtract it from the other side. In this case, you subtract 132 from both sides, therefore it is D.

Answer:

If P(x) has the roots -11 and 6, then its multipliers can be written as

Step-by-step explanation:

P(x)=(x+11)(x-6)

P(x)=x2-6x+11x-66

P(x) = x2+5x-66

Answer:

-33

Explanation:

29-(-36-(-27-31)+40)=

29-(-36-(-56)+40)=

29-(-36+58+40)=

29-62=-33

Answer:

With exponents:

Without exponents

Step-by-step explanation:

Factorization of 36:

Factorization of 45:

-Chetan K

Answer:

The Prime factorization of 36 and 45 is 3²

36 = 2 × 2 × 3 × 3

= 2² × 3²

45 = 3 × 3 × 5

= 3² × 5

Prime Factorization = 3²

____________________

Answer:

a) There will be approximately a water depth of 7.5 meters after 3h

b) Approximately 2.5 hours have passed when there is 8 m of water in the tank.

Step-by-step explanation:

a) Look for the y-value when the x-value is 3.

b) Look for the x-value when the y-value is 8.

*The y-axis is the depth (m), and the x-axis is the time (h).

Answer:

5 if the value of y become 5 it makes this true

Hi! Let's solve this inequality!

Move 12 to the right side, using the opposite operation.

y>17-12

y>5

Thus, any value of y greater than 5 will make this inequality true.

Let's try 6, since 6 is greater than 5.

12+6>17

18>17

Yeah, it worked :)

Thus, any value of y greater than 5 will make this inequality true.

Hope it helps!

Enjoy your day!

Please feel free to ask if you have any doubts.

[tex]\bf{M^a^g^i^c^a^l[/tex]

Answer:

96cm

Step-by-step explanation:

The exponential function represented in the table is given by:

[tex]F(x) = 16\left(\frac{3}{2}\right)^x[/tex], which means that option F is correct.

It is modeled by:

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

In which:

Considering the table, that has points (2,36) and (3,54), we have that:

[tex]36 = ab^2[/tex]

[tex]a = \frac{36}{b^2}[/tex]

[tex]54 = ab^3[/tex]

[tex]54 = \frac{36}{b^2} \times b^3[/tex]

[tex]36b = 54[/tex]

[tex]b = \frac{3}{2}[/tex]

Hence:

[tex]y = a\left(\frac{3}{2}\right)^x[/tex]

When x = 2, y = 36, hence:

[tex]y = a\left(\frac{3}{2}\right)^x[/tex]

[tex]36 = a\left(\frac{3}{2}\right)^2[/tex]

[tex]\frac{9}{4}a = 36[/tex]

[tex]a = 16[/tex]

Hence, the function is:

[tex]F(x) = 16\left(\frac{3}{2}\right)^x[/tex], which means that option F is correct.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

21

Step-by-step explanation:

On the left side, 2 multiply by 3 is 6. So you can do the same thing to the right side. 7 multiply by 3 is 21.

<A+<B+<C=180(sum of triangle)

55+65+<C=180

120+<C=180

<C=60

Answer:

Percent increase : 20%

Step-by-step explanation:

First month: 4,264 phone calls.

Second month: 25% more phone calls than in the first month.

To know the total phone calls received during this month you must take 25% of 4,264 and then add it to the 4,264 call of the first month:

64,264*25%=1,066

Total phone calls of the second month: 1,066+ 4,264= 5,330

You can also calculate the total phone calls of the second month by multiplying 4264 times 1,25 because times 1 is the same number and times 0,25 is the percent increase in the number of calls:

4,264*1,25= 5,330

Third month: 6,396 phone calls

To know the percent increase in the number of phone calls from the second month to the third month you must use the percent change formula:

Percent change: ((value2-value1)/ value 1 )*100%

Value 2: phone calls received during the third month

Value 1: phone calls received during the second month

Percent change: ((6,396-5,330)/ 5,330 )*100%

Percent increase: 20%

Brainliest?!

Answer:

4,3

Step-by-step explanation:

1 plus 3 equals 4.

-3 plus 6 equals 3.