What is the area of the smaller square? *


16
32
36
81

There are different kinds of math problem. There will be 11 rats in sewer #1.

The term  word problems is known to be problems that are associated with a story, math, etc. They are known to often vary in terms of technicality.

Lets take

sewer #1 = a

sewer #2 = b

sewer #3 = c

Note that   A=B-9

So then you would have:

A=B-9

B=C- 5

A+B+C=56

Then you have to do a substitution so as to find C:

(B- 9) + (C-5) + C = 56

{ (C- 5)-9} + (C-5) + C = 56

3C - 19 = 56

3C = 75

B = C- 5

B = 25 - 5

Therefore, B = 20

A = B - 9

= 25 - 9

=11

Therefore, there are are 11 rats in sewer #1

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Answer:

10+5 =15 thanks for asking

Answer: 47.28 miles

Step-by-step explanation: 5.91 times 8= 47.28

Here we are given that ;

[tex]{:\implies \quad \sf f(x)=x^{2}-81}[/tex]

Differentiating both sides w.r.t.x ;

[tex]{:\implies \quad \sf f^{\prime}(x)=\dfrac{d}{dx}(x^{2}-81)}[/tex]

[tex]{:\implies \quad \sf f^{\prime}(x)=\dfrac{d}{dx}(x^{2})-\dfrac{d}{dx}(81)}[/tex]

[tex]{:\implies \quad \sf f^{\prime}(x)=2x^{2-1}-0}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{f^{\prime}(x)=2x}}}[/tex]

This is the required answer

By using what we know about octagons, we will see that:

For an octagon of side length S, the area is:

A = 2*(1 + √2)*S^2

In this case, the area of the smaller octagon is:

19.28 in^2 =  2*(1 + √2)*S^2

Solving for S we get:

S = √( 19.28 in^2/(2*(1 + √2))) = 2.03 in

If we apply an enlargement of a factor 3.5, the new side length is:

S' = 3.5*2.03 in = 7.11 in

Then the area of the larger octagon is:

A' = 2*(1 + √2)*(7.11 in)^2 = 244.89 in^2

b) For an octagon of side length S, the radius is:

R = S*√(1 + 1/√2)

Then the radius of the larger octagon is:

R' = (7.11 in)*√(1 + 1/√2) = 9.29 in

Then the diameter of the box must be:

D = 2*R' = 2*9.29 in = 18.58 in

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Answer:

19.6

Step-by-step explanation

= Sum of terms / number of terms

= ( 20 + 19 +18+ 20 +19 +22 ) / 5

= 19.6

Answer:

Step-by-step explanation:

Answer:

  Tina is 12 and MIna is 15

Step-by-step explanation:

Age problems can often be worked by backing out any of the changes in age so as to match the conditions specified at a given time.

Here, the ratio is given for now. The sum of the two ages is 6 years less now than it will be after 3 years, so is now 33 -6 = 27.

The sum of ratio units now is 4+5 = 9, so each ratio unit stands for 27/9 = 3 years of age. The ratio of current ages is ...

  3×4 : 3×5 = 12 : 15

Tina is 12 and MIna is 15.

_____

Check

After 3 years, their ages will be 15 and 18, which will total 33.

Using an exponential function, it is found that the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868}[/tex]

Which means that approximately 16.22 mg remain.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the equation is:

[tex]f(h) = m(0.5)^h[/tex]

We work with a 50 mg Cobalt-60 sample, hence m = 60, and considering a half-life of 5.3 years, in 10 years we have h = 10/5.3 = 1.8868. Hence the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868} = 16.22[/tex]

Approximately 16.22 mg remain.

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Answer:3 or 3/10

Step-by-step explanation:

The value of x in the diagram is 8 feet that makes the combined area of the house and the porch to be 733 ft²

Combined area = big rectangle + smaller rectangle - triangle

Hence:

733 = (13 * (59 - x)) + (x * 9) - 0.5(9 - 7) * (x - 6)

733 = 767 - 13x + 9x - x + 6

x = 8 feet

The value of x in the diagram is 8 feet that makes the combined area of the house and the porch to be 733 ft²

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The inputs of the function are -8, 2, 4, and 6.

The input is the number that we put into the given function to get the output function.

x  and y of the function are given below

X    –8      2     4    6

f(x)  –6    –3     1     5  

From the given table, the inputs are given as the set of x values.

outputs are given as the set of y values. here, x is the input value that gives the output f(x).

Since x represents the input values and y represents the output values.

So, inputs of the function are -8, 2, 4 and 6

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The area of waffle in the cone is the amount of space covered by the waffle

The cone has 5630 square millimeter of waffle

The surface area of a cone is calculated using:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

For the complete 72 mm tall cone, we have:

Height (h) = 72 mm

Radius (r) = 42 mm/2 = 21 mm

So, the surface area is:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

A = 3.142 * 21 * (21+[tex]\sqrt{[/tex](72^2 + 21^2))

Evaluate

A = 3.142 * 21 * (21+75)

A = 6334.272

When the cone is cut at the top, we have:

Height (h) = 24 mm

Radius (r) = 14 mm/2 = 7 mm

So, the surface area is:

A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))

A = 3.142 * 7 * (7+[tex]\sqrt{[/tex](24^2 + 7^2))

Evaluate

A = 3.142 * 7 * (7 + 25)

A = 703.808

Calculate the difference (d) between the areas

d = 6334.272 - 2.5*703.808

Evaluate

d = 5630.464

Approximate

d = 5630

Hence, the cone has 5630 square millimeter of waffle

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Sales tax amount:-

Price:-

Answer:

$17,280

Step-by-step explanation:

Given

Solving :

Answer: x = 5, y = 7

Step-by-step explanation:

First, put the variables together/rearrange:

y - x = 2 & 5x - 4y = -3

Cancel out variable x by multiply the first equation by 5:

5y - 5x = 10 & 5x - 4y = -3

Add equations:

y = 7

Then determine x by plugging y back into the first equation y = x + 2:

x = 5

Answer:

D

Step-by-step explanation:

I have done this before
Top row units is 8 i then multiplied both sides so 5*2 which = 10 then multiplied 8*10 to get 80

Answer:

80 square units (D)

Step-by-step explanation:

Base is 16 units, height is 5 units. 16 * 5 = 80

Step-by-step explanation:

x = "a number"

x/-5 - 18 > 3

Answer:

64

Step-by-step explanation:

(-2(-4))^2

8^2

64

hope that helps

Answer:

diameter is half the value of circumference 15/2 =7.5 diameter

Answer:

Question (a)

Given equation:

[tex]8^{2x} = 32^{x+3}[/tex]

8 can be written as [tex]2^3[/tex]

32 can be written as [tex]2^5[/tex]

Therefore, we can rewrite the equation with base 2:

[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]

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

Question (b)

To solve:

[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]

Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]

[tex]\implies 2^{6x} = 2^{5x+15}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :

[tex]\implies 6x = 5x+15[/tex]

Subtract [tex]5x[/tex] from both sides:

[tex]\implies x = 15[/tex]

Answer:

10. s = 1.50x

11. s = 28x + 5

Step-by-step explanation:

10. s (money); so multiply x (the amount of pencils) by the price which is 1.50. Which is equal to 112.50.

11. s (money); multiple x (the amount of shoes) by the price, 28, which equals 84. Then add 5 for the shipping. This equals 89.

Answer:

L= 12

Step-by-step explanation:

area= L×B

108= 9×L

108= 9L

Divide both sides by 9

108/9= 9L/9

L= 12

Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:

[tex]A(t) = 64(0.5)^t[/tex]

32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:

[tex]A(4) = 64(0.5)^4 = 4[/tex]

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Answer:

$26.42

Step-by-step explanation:

P = 30 * 0.82 * 1.074 = 26.42

Step-by-step explanation:

I don't understand this question

come again

Step-by-step explanation:

-4-(3)=-7

step two

3+(-5)=-2

step three

4+6=10

step four

-5-9=-14

step five

-4+(-9)=-13

Answer:

a) -4 - ( 3) = - 7

b) 3 + ( -5) = 3 - 5 = -2

c) 4 + 6 = 10

d) -5 -9 = - 14

e) -4 + ( -9) = -4 -9 = - 13...

Answer:

1

Step-by-step explanation:

definite integral from 0-2 of root x dx

root x = x^½

integral of x^½ = ⅔x^(3/2)

The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

[tex]V(n) = n * 1[/tex]

This gives

[tex]V(n) = n[/tex]

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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Answer:

Dividing by same signs give a positive answer.

Dividing by different signs give a negative answer.

Step-by-step explanation:

Quotient is just a term for the answer given by a division problem.

positive/positive = positive

positive/negative = negative

negative/positive = negative

negative/negative = positive