Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.

Answer:

45

Step-by-step explanation:

1/3 of 90

= 1/3 * 90

= 90/3

= 30

Let the missing number be x.

2/3 of x

= 2/3 * x

= 2x/3

30 = 2x/3

Cross multiply,

2x = 30 * 3

2x = 90

x = 90/2

x = 45

Hence,

the missing number is 45.

Option d is the correct answer. All real numbers are greater than or equal to 2.

Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).

Thus Option d is the correct answer. All real numbers are greater than or equal to 2.

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Answer:

y= -1/5x+5

STEP BY STEP EXPLAINATION:

m = slope = -1/5

c = y-intercept = 5

equation of a straight line:

y=mx+c

so.

y= -1/5x+5

Answer:

h'(z) = 2

Step-by-step explanation:

(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
         (-1)(-2z+11)
         2z-11

Now, let's find the derivative:
h'(z) = 2

Answer:

B

Step-by-step explanation:

We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3

Answer:

34

Step-by-step explanation:

Substitute values given into expression and simplify  :

5(2) + 6(4) =

10 + 24 =

34

Hope this helped and have a good day

The equation represents the class's model of the population over time will be P = 50(2)^(n/12). Then the correct option is D.

Consider the function:

y = a (r)ⁿ

Where n is the number of times this growth occurs, a = initial amount, and r = increasing amount of growth.

A biology class at Central High School predicted that a local population of animals will double in size every 12 years.

The population at the beginning of 2014 was estimated to be 50 animals.

If P represents the population n years after 2014.

Then the equation represents the class's model of the population over time will be

[tex]\rm P = 50(2)^{n/12}[/tex]

Then the correct option is D.

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Answer: D is correct

Step-by-step explanation:

The function f(x) = 2x -14 is a polynomial function

The equation of the function is given as:

f(x) = 2x -14

A polynomial is represented as:

f(x) =ax^n + bx^(n - 1)....... + c

Where n is at least 1.

The function f(x) = 2x -14 is a polynomial with a degree of 1

Hence, the function f(x) = 2x -14 is a polynomial function

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Answer:

The representative sample contained more girls than boys.

Step-by-step explanation:

Since there is roughly 1.5x more girls than boys, the sample size will likely contain more girls than boys when chosen at random.

Answer:

D

Step-by-step explanation:

The model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

"It is a diagram that represents data in an organized manner."

"It is the height of the object above the surface of the ground."

For given question,

The graph shows the altitude, in feet, of a model rocket t seconds after launch.

From the graph we can observe that the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

Therefore, the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

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8.57 liters glucose (in liters) is needed for 30 units of blood.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

For 7 units of blood = 2 l of glucose needed.

Foe 1 units of blood, glucose needed = 2/7

For, 30 units of blood , glucose needed = 8.57 liters

Hence, 8.57 liters glucose (in liters) is needed for 30 units of blood.

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15

Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.

Multiple of 10

Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).

So, 10% of 50 is 5.0.

Then, to find 30%, multiply 5 by 3.

30% of 50 is 15.

Multiplication

The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).

Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.

So, this once again shows that 30% of 50 is 15.

Answer:

Step-by-step explanation:

The ratio of boys to girls in a school is 4:5. There are 220 boys in the school. How many students attend the school?​

find the number of girls

4 : 5 = 220 : x

x = 5 * 220 : 4

x = 275

sum boys and girls

220 + 275 =

495 (your answer)

check

4 : 5 = 220 : 275

4 : 5 = 4 : 5

the answer is good

Answer:

6 is the average

Step-by-step explanation:

You add all the numbers together

7 + 5 + 10 + 2 + 8 + 4 = 36

and then divide by the amount of numbers

36/6=6

Answer:

30

Step-by-step explanation:

Given:

Brian Height = 6 feet

Brian Shadow Height = 4 foot

Flag Shadow Height = 20 foot

Flag Height = Unknown ??

So we can use cross multiplication

6/4 = x/20

6×20/4 = x

6×20 =120

120÷4 = 30

So x= 30, which is the Flag Height

I wish that I helped you with this.

As per linear equation, the  height of the flag pole is 30 feet.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, Brian is 6 feet tall and cast a 4 feet shadow.

Therefore, the ratio of Brain and it's shadow is

= 6/4

= 1.5

A flag pole cast a 20 foot shadow.

Therefore, the height of the flag pole is

= 20 × 1.5 feet

= 30 feet.

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Using the equation of the proportional relationship:

Average rate of speed = 60

Time taken to go 300 miles = 5 hrs

Distance travelled in 2.5 hrs = 150 miles

A equation of a proportional relationship models the relationship between two variables, x and y, that has a constant of k. It is expressed as y = kx.

Given the following:

Equation: d = 60t

d = distance in miles

t = time in hours

Average rate of speed for the bus = k = 60

Time (t) it would take to go 300 miles (d):

300 = 60(t)

300/60 = t

t = 5 hours

Distance (d) it would travel in 2.5 hours (t):

d = 60(2.5)

d = 150 miles

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Answer:

47.1408

Step-by-step explanation:

They gave us the percentage of a number and wants us to find the whole

to do that we will use the following equation:

46.116*100/4.5 = 47.1408 is the number we are looking for.

The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The set of output of the function is a multiple of 40 from 200 to 640

The input of the function can be found as follows:

The camp can only run if we have at least 5 students.

The limits of student is 16.

Therefore, the input are  {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.

Therefore,

R(n) = 40n

R(5) = 40(5) = 200

R(16) = 40(16) = 640

The output are multiple of 40 from 200 to 640

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Answer:

25%

Step-by-step explanation:

percent = part/whole × 100%

percent = 9/36 × 100%

percent = 25%

Answer:

25%

Step-by-step explanation:

If you divide 36 by 9 you get 4.  If you do the same for 100, and divide by four, you get 25.  Therefore, 9 is 25% of 36.

Answer: 6:1

Step-by-step explanation:

Answer:

The answer is in Step.

Step-by-step explanation:

Domain: (- inf, + inf)

Range: (- inf, 3]
Increasing: (- inf , 0)

Decreasing: (0 , + inf)
Positive: (- 1 , 1 )
Negative: (- inf , -1) , (1 , + inf)

Maximum: (0,3) or just 3.

Minimum: None.
x-int: -1, 1
y-int: 3

Answer:

D.

Step-by-step explanation:

Use Quadratic formula

x =  [-b +- sqrt (b^2 - 4ac) ]  / 2a     with a = 6   b = -24    c = 1

  to find

         x = 2 ± sqrt (23/6)

Answer:

x=1

Step-by-step explanation:

4x=4

(Linear equation)

Solved:-

Transpose 4 from LHS to RHS:

[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]

[tex] \rm = > x = \tt1 [/tex]

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Based on the calculations, the area of the shaded region is equal to 22 square foot.

By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:

Area of shaded region = Area of square - Area of circle.

Note: The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.

Radius = diameter/2 = 10/2 = 5 feet.

For the area of square, we have:

Area of square = S²

Area of square = 10²

Area of square = 100 square foot.

For the area of circle, we have:

Area of circle = πr²

Area of circle = 3.14 × 5²

Area of circle = 78.5 square foot.

Substituting the parameters into the formula, we have;

Area of shaded region = Area of square - Area of circle.

Area of shaded region = 100 - 78.5

Area of shaded region = 21.5 ≈ 22

Area of shaded region = 22 square foot.

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Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.

Answer:

60

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

given

3[tex]\sqrt{2}[/tex] × 5[tex]\sqrt{8}[/tex]

= 3 × 5 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex]

= 15 × [tex]\sqrt{16}[/tex]

= 15 × 4

= 60