The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12m.

Calculate the length of EF, one of the horizontal edges of the block.

Answer: 1/4 ( 12x + 24 ) -9x=−6x+6

Answer: 10 , 11 , 12

Step-by-step explanation:

Let the integers be : x , x + 1 and x + 2

the smallest multiplied by 3 implies 3x

From the first statement

3x = 18 + (x+2)

3x = 18 + x + 2

3x - x = 18 + 2

2x = 20

x = 10

Therefore : the numbers are : 10 , 10 + 1 and  10 + 2

the numbers are : 10 , 11 , 12

Answer:

10,11,12

Step-by-step explanation:

3 consecutive integers...x and x + 1 and x + 2

3x = x + 2 + 18

3x = x + 20

3x - x = 20

2x = 20

x = 20/2

x = 10

x + 1 = 10 + 1 = 11

x + 2 = 10 + 2 = 12

ur numbers are 10, 11, and 12

The domain and the range of the functions is real numbers. Hence, option A is correct.

We need to determine the domain and range of the function  [tex]\bold{f(x)=-35x^3}[/tex].

Let us define the domain and the range of the function:

Domain:

When all the possible values of an independent variable for which we get the real value of a dependent variable then the values of the independent variables is called domain of the function.

Range:

All the possible values of the function is called the range of the function. Range is the sub-set of co-domain.

Now,

For the given function [tex]f(x)=-35x^3[/tex].

No value of x can restrict the above function hence its domain is real number that is [tex](-\infty, +\infty)[/tex].

And, range of the function is also the same [tex](-\infty, +\infty)[/tex].

Thus, the domain and the range of the functions is real numbers. Hence, option A is correct.

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The domain and range of the cubic function f(x) = -35x^3 are both all real numbers, because there are no restrictions on x and the function's output covers all real values.

The function described is f(x) = −35x^3. The domain of a polynomial function, which includes cubic functions like this one, is all real numbers because there are no restrictions on the values that x can take. Therefore, the domain is (−∞, ∞). Since the leading coefficient of the cubic term is negative, the ends of the graph will go towards negative infinity as x goes to positive and negative infinity. Therefore, the range of the function is also all real numbers, which we write as (−∞, ∞).

Question:

What is the numerator of the simplified sum?

x/x^2 +3x+2 + 3/x+1

Answer & Step-by-step explanation:

The given equation is as follows.

       \frac{x}{x^{2}+3x+2} + \frac{3}{x+1}

Taking L.C.M, the equation will become as follows.

      \frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)}  ........ (1)

Factorize the equation x^{2}+3x+2 in the denominator as follows.

        x^{2}+3x+2

      =  x^{2} + 2x + x + 2  

      = x(x+2) + 1(x + 2)  

      = (x+1)(x+2) ........ (2)

Put the factors in equation (2) in to equation (1), then the equation will become as follows.

     \frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)}

    = \frac{x^{2}+x +3x^{2}+9x+6)}{(x+1)(x+2)(x+1)}

    = \frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}

Now, factorize the numerator as follows.

      \frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}

   = \frac{4x^{2}+4x+6x+6}{(x+1)^{2}(x+2)}

   = \frac{4x(x+1) + 6(x+1)}{(x+1)^{2}(x+2)}

   = \frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}

Cancelling (x+1) from both numerator and denominator. Then the equation will be written as follows.

      \frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}

    = \frac{(4x+6)}{(x+1)(x+2)}

The numerator of simplified sum is (4x+6).

4x+6
C on Edge 2022



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Answer:

  C  1

Step-by-step explanation:

BC is perpendicular to AB, so has a slope that is the negative reciprocal of that of AB:

  BC slope = -1/(AB slope) = -1/-1 = 1

Dilating the triangle has no effect on the slope.

The slope of B'C' is 1.

an example of an equivalent inequality is

5+(-m) is greater than or equal to 20

Answer:

3

Step-by-step explanation:

Answer: B. y = 2/3 x - 13/3

Step-by-step explanation:

two lines are said to be parallel if they have the same slope.

To find the slope of line K we will use the formula fro calculating slope which is :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 2

[tex]x_{2}[/tex] = 8

[tex]y_{1}[/tex] = -3

[tex]y_{2}[/tex] = 1

substituting into the values into the formula , we have :

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

m = [tex]\frac{4}{6}[/tex]

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

Therefore : the slope of line K = [tex]\frac{2}{3}[/tex] , this means that any line that will be parallel to K must have a gradient of [tex]\frac{2}{3}[/tex].

The only line that has a gradient of [tex]\frac{2}{3}[/tex] is the line y = 2/3x - 13/ 3 ,this means that the line is parallel to Line K

Answer:

Option C) 144 centimeters squared.

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The surface area of a prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the base of the prism

P is the perimeter of the  base

L is the length or height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ cm^2[/tex] ---> the base is a right triangle

Find the perimeter of the base P

[tex]P=3+4+5=12\ cm[/tex] ---> is the perimeter of a triangle

we have

[tex]L=11\ cm[/tex]

Find the surface area SA

[tex]SA=2(6)+12(11)=144\ cm^2[/tex]

Answer:

144

Step-by-step explanation:

The average speed is 135.26 miles per hour

Solution:

Given that, woman traveled 2445.9 miles in 18 hours five minutes

To find: Average speed of her flight in miles per hour

Let us first convert 18 hours 5 minutes to hours

We know that,

[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]

Therefore,

[tex]5 \text{ minute } = \frac{5}{60} \text{ hour } = 0.083 \text{ hour }[/tex]

Thus we get,

18 hours five minutes = 18 hour + 0.083 hour = 18.083 hour

Given that, distance = 2445.9 miles

Average speed is given by formula:

[tex]Average\ speed = \frac{distance}{time}\\\\Average\ speed = \frac{2445.9}{18.083}\\\\Average\ speed = 135.26[/tex]

Thus average speed is 135.26 miles per hour

Answer:

4 : 2

Step-by-step explanation:

The two triangles Δ ABC and Δ A'B'C' are similar.

Here, ∠ A = ∠ A' = 104°, ∠ B = ∠ B' = 50° and ∠ C = ∠ C' = 26°.

Now, the length of AB and the length of A'B' are 4 cm and 2 cm respectively.

Again, the length of BC and the length of B'C' are 9 cm and 4.5 cm respectively.

Therefore, [tex]\frac{AB}{A'B'} = \frac{BC}{B'C'} = \frac{CA}{C'A'} = \frac{4}{2} = \frac{9}{4.5} = 2[/tex]

Hence, the ratio of the corresponding side lengths is 4 : 2. (Answer)

Answer:

4:2

Step-by-step explanation:

Answer:

Step-by-step explanation:

recall that for a radical expression, the following apply

[tex]\sqrt[x]{y} = y^{\frac{1}{x} }[/tex]

compare this with our case, we can clearly see that

x = 4 and y = 10,

substituting into the above equation gives:

[tex]\sqrt[4]{10} = 10^{\frac{1}{4} }[/tex]

The expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].

The general equation of a exponential relationship is -

y = Aeˣ

The general equation of a quadratic equation is -

y = ax² + bx + c

Given is the following expression -

[tex]$\sqrt[4]{10}[/tex]

We can write the given expression in the form of exponential expression as -

y = [tex]$(10)^{\frac{1}{4} }[/tex]

Therefore, the expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].

To solve more questions on exponential function, visit the link below-

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Answer:

3000 inches cubed

Step-by-step explanation:

I hope this help sorry if I'm wrong

Answer:

it's 1480

Step-by-step explanation:

I just did it on imagine math :)

Answer:

.45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

If you divide 45 by 100, the decimal point will move two times to the left because there is two 0's in 100, making it 0.45

-5x(-7x^3)

Because -7x^3 is in parentheses, you add the degrees together:

35x^4

Answer:

the answer would be 5w-20 after distribution

Answer: 5w + (-20)

Step-by-step explanation: So let's simplify this problem using the distributive property. The first thing we want to do is change the minus to plus a negative.

Now we can distribute or multiply the 5 by each of the terms inside the set of parentheses.

So we get 5(w) + 5(-4) and this simplifies to 5w + (-20).

Answer:

Step-by-step explanation:

in order to be like terms, they have to have the same variable (and exponent, if there is any).....or be just a constant with no variables (just a number)

like terms in 12a - 7 + 7a + 12b are :

12a and 7a....because they have the exact same variable (a)

12b....no like terms

-7...no like terms

so ur answer is : 12a and 7a

Answer:

20

Step-by-step explanation:

Add 4 to 46 = 52

Divide 52 by 2 = 26

Finally, subtract 6 to get 20

Answer:

-2

Step-by-step explanation:

Answer:

-1+y=-1

y=0

Step-by-step explanation:

cuz you basically add 1 to both sides

Could I get more context about the question? If I had more numbers then I could solve it.

Answer:

When solving equations you goal is to get x by itself so

18-6.3x=49.5 (first step would be to minus 18 from each side)

-6.3x=31.5 (18-18=0, 49.5-18=31.5) (now you want to divide each side by -6.3)

x=-5 (-6.3/-6.3=1, 31.5/-6.3=-5)

Your final answer is

x=-5

Hope this helps ;)

The premium of the policy is approximately $64,198.32.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To calculate the premium of the policy, we need to take into account the probability of the person dying in the next 20 years and the payout of the policy.

Let P be the probability of the person dying in the next 20 years, and let A be the administrative costs of the policy.

Then the expected value of the payout of the policy is:

E(payout) = P x $60,000

And the expected value of the cost of the policy (including administrative costs) is:

E(cost) = P x premium + A

We want to find the premium of the policy, so we can rearrange this equation to solve for the premium:

premium = (E(cost) - A) / P

Substituting the given values, we get:

P = 0.072698

A = $75

E(payout)

= P x $60,000

= 0.072698 x $60,000

= $4,361.88

Now we need to calculate the expected value of the cost of the policy.

The cost of the policy includes both the payout (if the person dies) and the administrative costs (whether or not the person dies).

So we can write:

E(cost) = E(payout) + A x (1 - P)

where (1 - P) is the probability that the person will not die in the next 20 years.

Substituting the given values, we get:

E(cost) = $4,361.88 + $75 x (1 - 0.072698) = $4,746.88

Finally, we can calculate the premium of the policy:

premium = ($4,746.88 - $75) / 0.072698 = $64,198.32

Therefore,

The premium of the policy is approximately $64,198.32.

Learn more about expressions here:

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hope it helps I just did it

Answer:

y=3x-13

Step-by-step explanation:

1) find slope

5--1/8-4=6/2=3

2) (y--1)=3(x-4)

y+1=3x-12

y=3x-13

Answer:

No Solution

Step-by-step explanation:

4x-2y=8

y=2x+1

Make the first equation into where it says y=.

-2y=-4x+8

y=2x-4

Substitute either equation into the other as y=.

2x+1=2x-4   or    2x-4=2x+1

Switch terms around so they're with their like terms. Make sure it becomes the opposite when switching.

2x-2x=-1-4    or    2x-2x=4+1

0=-5                     0=5

Since x did not come back to equal an answer, this problem is not workable. There is no solution to it. If you were to do it a different way, there still would not be a solution to it.

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Step-by-step explanation:

Let,

x be the number of candles sold by Julio in first week.

According to given statement;

Candles sold in first week = x

He sold twice the number of candles the second week as he did the first week.

Candles sold in second week = 2x

In the third week, Julio sold 4 less than the number he sold the first week.

Candles sold in third week = x-4

Total candles sold = First week + Second week + Third week

Total candles sold = x+2x+(x-4)

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Keywords: addition, variable

Learn more about addition at:

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Answer:

The value of A in the given graph of the equation is 1

That is A=1

Step-by-step explanation:

Given graph of the equation is Ax+2y=-2

Given that the equation of line Ax+2y=-2 passes through the point (2,-2)

Let (x,y) br the point (2,-2)

Therefore we have that

A(2)+2(-2)=-2

2A-4=-2

2A-4+2=-2+2

2A-2=0

2A=2

[tex]A=\frac{2}{2}[/tex]

Therefore A=1

Therefore the value of A in the given graph of the equation is 1

Answer:

  3.25

Step-by-step explanation:

The slope of the line is ∆y/∆x = (-2-1)/(7-3) = -3/4.

The point-slope form of the line with slope m through (h, k) is ...

  y -k = m(x -h) . . . . . . . . . . we have m=-3/4, (h, k) = (3, 1)

  y -1 = -3/4(x -3)

The y-intercept is the point on the line where x=0. For x=0, the value of y is ...

  y = -3/4(-3) +1 = 9/4 +4/4

  y = 13/4 = 3 1/4

The y-intercept is 3 1/4.

Answer:

Step-by-step explanation:

5x - y = 3.......(1)

2y = 10x+2.....(2)

Rearranging (2)

-10x + 2y = 2......(3)

Multiply equation (1) by 2

10x - 2y = 6..........(4)

Adding (3) and (4)

-10x + 10x + 2y - 2y = 2 + 6

No solution since both x and y are eliminated.

Answer:

d^2 - π(d/2)^2

Step-by-step explanation:

Since the diameter of the circle is equal to the side of a square (d), that means that we have a circle inscribed in square.

If we draw a square and inscribe a circle in it, all parts of the square outside the circle will be waste, in this particular case.

If we want to find the area of the wasted material we need to subtract the area of the circle from the area of the square.

Area of the circle is:

P1 = πr^2, r being the radius

Since radius is half the diameter, that means that:

P1 = π • (d/2)^2

Area of the square whose side is d is:

P2 = d^2

So, the area of wasted material is:

P = P2 - P1

P = d^2 - π(d/2)^2