The number of students enrolled at a college is 14,000 and grows 5​% each year.

Answer:

Step-by-step explanation:

Consider the product ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

You will notice that the linear term (a+b)x has a coefficient (a+b) that is the sum of the factors of the constant term (ab).

For problems like this, it is useful to be able to factor the constant term, so you can choose the factors with the appropriate sum.

Signs are important. If the constant is positive, its factors will have the same sign, both positive or both negative. If the constant is negative, its factors will have opposite signs.

__

1. b^2 +13b +36

Factors of 36 are ...

  36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6

The sums of these are 37, 20, 15, 13, and 12. So, the factor pair we're looking for is 4 and 9. The factorization is ...

  = (b +4)(b +9)

__

2. c^2 +4c -45

The middle term is positive, so the larger magnitude factor will be positive. Factors of -45 are ...

  -45 = -1·45 = -3·15 = -5·9

Sums of these factors are 44, 12, 4. So, the factor pair we're looking for is -5 and 9. The factorization is ...

  = (c -5)(c +9)

__

3. k^2 +5k +6

  6 = 1·6 = 2·3 . . . . sums are 7 and 5  ⇒  factors of interest are 2 and 3

  = (k +2)(k +3)

Answer:

[tex]3[/tex]

hope this helps

Answer:

Number 7

Step-by-step explanation:

That's the one that is at the bottom and the corresponding tubes lead to the one being the first to be filled

Answer:

The debt snowball method is a debt reduction strategy where you pay off debt in order of smallest to largest, gaining momentum as you knock out each balance. When the smallest debt is paid in full, you roll the money you were paying on that debt into the next smallest balance.

Step-by-step explanation:

Answer:

a debt reduction str

ategy where you pay off debt in order of smallest to largest, gaining momentum as you knock out each balance.

Step-by-step explanation:

The straight line distance is 5 miles from starting point.

Step-by-step explanation:

Driving 3 miles north and 4 miles east and then the straight line distance will form a right angled triangle.

Answer:

E2020 A, B, D

Step-by-step explanation:

The probability of P(D|F), P(E|D), and P(F|E) are 6/34, 7/25, and 8/18 options (A), (B), and (D) are correct.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we can see in the Venn diagram the data is shown.

P(D | F) = The probability of event D that depends on the event F.

P(D|F) = 6/34

Similarly:

P(E|D) = 7/25

P(F|E) = 8/18

Thus, the probability of P(D|F), P(E|D), and P(F|E) are 6/34, 7/25, and 8/18 options (A), (B), and (D) are correct.

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Answer:

Yes, because the linear function  x - y = 5 is a function

Step-by-step explanation:

x - y = 5  can look like   y = x - 5  with slope 1 and y-intercept -5

so this is a function  which makes set K a function.

Answer:

[tex] f(0) = 1 [/tex]

Step-by-step explanation:

The initial value is the value when x = 0.

[tex] f(x) = 4^x [/tex]

For x = 0,

[tex] f(0) = 4^0 [/tex]

[tex] f(0) = 1 [/tex]

Step-by-step explanation:

The difference is 1 times +3 is like 1×3=3

Unlike 1 times 1 + 3 =1×1+3=4

Answer:

Step-by-step explanation:

1x +3 is like 1×3=3

1 x 1 + 3  is basically 1×1+3=4

Answer:

x = 1

Step-by-step explanation:

Download photomath and you can find out.

Answer:

Part A: What is the y-intercept for f(x)? Write your answer as a fraction.

-1/3

Part B: What is the x- intercept for f(x)?

undefined

Part C: Find f(-1)

-1

Step-by-step explanation:

Hope this helps those on Section 7 Topic 4

Answer:

A

Step-by-step explanation:

I believe a is true but I'm not a hundred percent sure

Answer:

Answer A

Step-by-step explanation:

13/14 goes to 26/28, which is greater than 25/28.

Answer:

4x2+216x-684x

Step-by-step explanation:

solnA) The dimensions of the table are in inches

Let

x=the thickness of the border

we know that the table and the border must have an area of 3,276 square feet

convert the dimensions of the table to feet

remember that; 1ft =12in

36in=3ft

72in=6ft

i.e; 3,276 = (6+12x)*(3+2x)

solve for x

3276=6×3+ 6×2x +2x×3+ 4x²

3276=18+12x+6x+4x²

4x²+18x+18-3276=0

4x²+18x-3258

solnB) The dimensions of the table are in feet

Let

x=the thickness of the border

we know that the table and the border must have an area of 3,276 square feet

i.e 3,276 = ()×()

solve for x

3,276 = 72×36 + 72×2x + 2x×36 + 4x²

3,276 = 2,592 + 144x + 72x + 4x²

4x² + 216x + 2,592 + 3276 = 0

4x²+216× - 684= 0

therefore; the quadratic equation can be used to determine the thickness of the border =

4x² + 216x - 684 = 0

Answer:

0, 1, 2

Step-by-step explanation:

Hi there!

A quadratic function can have either 0, 1 or 2 x-intercepts. This means that the graph of a quadratic function can intercept the x-axis 0, 1 or 2 times.

Attached are some graphical representations of all three cases.

I hope this helps!

Answer:

49.15 m

Step-by-step explanation:

Length of the string is the hupotenuse: 60

Height of the kite is the opposite: X

sin(55) = opposite/hypotenuse

sin(55) = X/60

X = 60sin(55)

X = 49.14912266 m

Work Shown:

5(3-x) < -2x+6

15-5x < -2x+6 .... distribute

15-5x+5x < -2x+6+5x ... adding 5x to both sides

15 < 3x+6

15-6 < 3x+6-6 ... subtracting 6 from both sides

9 < 3x

3x > 9 ... flip both sides of inequality, flip the inequality sign

3x/3 > 9/3 ... dividing both sides by 3

x > 3

Notice that when going from 3x > 9 to x > 3, the inequality sign does not flip. The sign only flips if you divided both sides by a negative number.

Answer: your graph should look like the picture down below!!

Step-by-step explanation:

Vetex: (0,80)

Focus: (0, 5119/64)

Axis of symmetry: x=0

The graph for the given exponential function is shown in the figure.

An exponential function is defined as a function with a positive constant other than 1 raised to a variable exponent. It is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

For the given situation,

The exponential function is h = -16t^2+80.

Plot this exponential function in the graph.

We can obtain the graph shown below.

From the graph, the vertex is (0,80)

Hence we can conclude that the graph for the given exponential function is shown in the figure.

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Answer:

Step-by-step explanation:It’s actually the fourth one because all of them equal 2187 the only one is the last one because it equals 1/2187

Answer:

45

Step-by-step explanation:

Answer:

41 Units

Step-by-step explanation:

You have to use Pitagora.

Diagonal (d) = √9²+40² = √1681 = 41

The length of a diagonal is 41 units.

Using Pythagorean theorem formula

Diagonal (d) =√width²+length²

Let plug in the formula

Diagonal (d)=9²+40²

Diagonal (d) =81+1600

Diagonal (d)=√1681

Diagonal (d) =41 units

Inconclusion the length of a diagonal is 41 units.

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Answer:

87.92 m

Step-by-step explanation:

The formula to calculate the circumference of the circle is:

Diameter * Pi  ---->  28 * 3,14

Final answer:

The circumference of a circle with a 28 meter diameter is calculated using the formula C = \\(pi) \\times d, resulting in 87.92 meters as the circumference.

Explanation:

The question requires us to find the circumference of a circle given its diameter, which measures 28 meters. To calculate the circumference, we use the formula C = \\(pi) \\times d, where \\(pi) is approximately 3.14 and d is the diameter of the circle. Since the diameter is 28 meters, the circumference is calculated as follows:

C = 3.14 times 28 m = 87.92 m.

Therefore, the circumference of the circle is 87.92 meters.

Answer:

C. 75 inches

Step-by-step explanation:

well if it's a rectangle then we would do A = L x W we are told the Width and the Area

344 = L x 16

344 / 16 = 21.5

P = L + L + W + W

16 + 16 + 21.5 + 21.5

16 + 16 = 32

21.5 + 21.5 = 43

32 + 43 = 75

the perimeter is 75 inches

Final answer:

To find the perimeter of the rectangle, we calculate the length by dividing the area by the width and then apply the perimeter formula. We find that the length is 21.5 inches and the perimeter is 75 inches.

Explanation:

To find the perimeter of the rectangle when the area is 344 square inches and the width is 16 inches, we need to use the area formula of a rectangle, which is Area = length × width. Since we have the area and the width, we can calculate the length:

Divide the area by the width to find the length: Length = 344 sq in / 16 in = 21.5 in.

Now, use the perimeter formula: Perimeter = 2 × (length + width).

Substitute the length and width into the formula: Perimeter = 2 × (21.5 in + 16 in) = 2 × 37.5 in = 75 inches.

The correct answer is C. 75 inches.

Answer:

age of Sam= 15 years

age of Nina  = 25 years

Step-by-step explanation:

Let  Nina's age be X years

Let  Sam's age be Y years

Five years ago Nina's age will be X- 5 years

Five years ago Sam's age will be Y- 5 years

Given in question

Five years ago, Nina was twice as old as Sam

writing it mathematically using X and Y we have

Nina's age = 2 * Sam's age

X- 5 = 2 *(Y- 5)

X = 2 *(Y- 5) + 5 = 2Y - 10 + 5 = 2Y - 5  _________________equation A

__________________________________________________________

Five years in future Nina's age will be X+ 5 years

Five years ago Sam's age will be Y+ 5 years

Given in question

In five years, she will be 1.5 times as old as Sam

writing it mathematically using X and Y we have

Nina's age = 1.5 * Sam's age

X+5 = 1.5 *(Y+ 5)

X = 1.5*(Y+5) -5 = 1.5Y +7.5 - 5 = 1.5Y +2.5  _________________equation B

_______________________________________

in equation A we have X = 2Y - 5

in equation B we have X = 1.5Y + 2.5

equating equation A and B  we have

2Y - 5 = 1.5Y +2.5

=> 2Y - 1.5Y = 2.5 + 5

=> 0.5Y = 7.5

=> Y = 7.5/0.5 = 15

from equation A we have

X = 2Y - 5  (substituting the value of Y = 15 in equation we have)

X = 2*15 - 5 = 25

Therefore age of Sam= 15 years

age of Nina  = 25 years

Answer:

Nina's 25 and Sam's 15

Step-by-step explanation:

Answer:

1,4,6

Step-by-step explanation:

Answer:

I got 300, though it's not in the answer choices

Step-by-step explanation:

Separate them into two separate rectangles

5×10×4= 200cm

5×5×4= 100cm

=300cm^2

Answer:A

Step-by-step explanation:

The cost function for Natalie's clothing store per month is C = 10.25n + 725.

The cost function for Natalie's clothing store per month can be calculated by adding up all the costs she incurs. This includes the cost of the gym shorts, the cost of the boxes for the shorts, the cost of the bags, and the monthly expenses for rent, electricity, and advertising.

The cost of each pair of shorts is $7, the cost of each box is $3, and the cost of each bag is $0.25. The monthly expenses are $650 for rent, $55 for electricity, and $20 for advertising.

Therefore, the cost function for Natalie's clothing store per month can be expressed as: C = 7n + 3n + 0.25n + 650 + 55 + 20, where n represents the number of gym shorts sold.

Simplifying the expression, we get: C = 10.25n + 725

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Answer:

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

Step-by-step explanation:

x+y=5

y=5-x

x-y=a

x-(5-x)=a

2x-5=a

2x=a+5

x=[tex]\frac{a+5}{2}[/tex]  

x+y=5

[tex]\frac{a+5}{2}[/tex]  +y=5

y=5-[tex]\frac{a+5}{2}[/tex]  

Answer:

x=5/2 + a/2,  y= 5/2 - a/2

Step-by-step explanation:

We can solve this system using addition of the equations

x+y=5

x-y=a

2x  =(5+a)

x=(5+a)/2= 5/2 +a/2

x=5/2 +a/2

x-y=a

y = x - a , x=5/2 + a/2

y= 5/2 + a/2-a

y= 5/2 - a/2

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Answer:

maybe D

Step-by-step explanation:

I'm thinking D because if do

[tex] - 6 - 4 = - 10[/tex]

but also it doesn't make 16 when you do

[tex]4 \times 6 = 24[/tex]

Answer:

C

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 3) and (x₂, y₂ ) = (3, 1)

d = [tex]\sqrt{(3-8)^2+(1-3)^2}[/tex]

  = [tex]\sqrt{(-5)^2+(-2)^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex] → C