Factor the following polynomials: a^2+a+72

Answer:

1 2 = 2 4 = 3 6 = 4 8 = etc. All of these fractions are located at the same point on the number line. Therefore, they represent the same number. From the paper folding exercises, we see that increasing both numerator and denominator of a fraction by the same factor gives an equivalent or equal fraction.

Hope this helps :) Just know I tried.

Answer:

Her friend got the better deal.

Step-by-step explanation:

For Jillians equation look at

$22.56/4 = $6.39 per CD

For her friends equation look at

$18.45/3 = $6.15 per CD

Jillian's friend got the better deal because she paid less per CD as shown in the equations above.

Displacement means the distance traveled on a straight line to get to a certain destination. The interpretation of the given equation is option (a):

Given that:

[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]

First, we calculate how far the student traveled to arrive at the school.

This means that we calculate f(0).

So, we have:

[tex]f(0) = (0 + 1)(0 - 2)(0 - 3)[/tex]

[tex]f(0) = ( 1)( - 2)( - 3)[/tex]

[tex]f(0) = 6[/tex]

The student walked 6km to school

When x = 2, it means:

[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]

[tex]f(2) = (2 + 1)(2-2)(2 -3) = 0[/tex]

This means that the student got to school after 2 minutes

When x = 3, it means

[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]

[tex]f(3) = (3 + 1)(3-2)(3 -3) = 0[/tex]

This means that the student walked away, turned back and got to school after 3 minutes.

From the given options, option (a) fits the above description.

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Answer:

Total surface area = 340 cm²

Step-by-step explanation:

Surface area of the given prism = Area of two bases + Area of its lateral surfaces

Area of pentagonal base = [tex]\frac{1}{2}(\text{Apothem)}(\text{Perimeter})[/tex]

                                          = [tex]\frac{1}{2}(3.6)(5\times 5)[/tex]

                                          = 45 cm²

Area of the lateral sides of the prism = Perimeter of the pentagonal base × height

= (5×5)×10

= 250 cm²

Total surface area of the prism = 2(45) + 250

                                                     = 90 + 250

                                                     = 340 cm²

Answer:

x=1 and y=10 (1,10)

Step-by-step explanation:

2+30=32

10=1+9

Answer:

Top is 18, Bottom goes 6 for 12, then 7 for 14, then 10 for 20

Step-by-step explanation:

2 guests = 1 table

Answer:

θ = 35.39°

Step-by-step explanation:

Given that,

Perpendicular, P = 27

Base, B = 38

We need to find the value of angle. Let the angle be θ. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\theta=\tan^{-1}(\dfrac{P}{B})\\\\\theta=\tan^{-1}(\dfrac{27}{38})\\\\\theta=35.39^{\circ}[/tex]

So, the required angle is 35.39°.

Answer:

Step-by-step explanation:

From the first image attached below, we will see the sketch of the curve x = y² & x = 2y

In the picture connected underneath, the concealed locale(shaded region) is bounded by the given curves. Now, we discover the marks of the crossing point of the curves. These curves will cross, when:

[tex]y^2 =2 y \\ \\ or y^2 -2y = 0 \\ \\ y(y-2) = 0 \\ \\ y = 0 \ \ or \ \ y = 2[/tex]

Thus, the shaded region fall within the interval 0 ≤ y ≤ 2

Now, from the subsequent picture appended we sketch the solid acquired by turning the concealed region about the y-axis.

For the cross-sectional area of the washer:

[tex]A (y) = \pi (outer \ radius)^2 - \pi ( inner \ radius )^2 \\ \\ A(y) = \pi (2y^)2- \pi (y^)^2 \\ \\ A(y) = 4 \pi y^2 - \pi y^4 \\ \\ A(y) = \pi( 4 y^2 -y^4)[/tex]

Finally, the volume of (solid) is:

[tex]V = \int^2_0 A(y) \ dy \\ \\ V = \int^2_0 \pi (4y^2 -y^4) \ dy \\ \\ V = \pi \int^2_0 (4y^2 -y^4) \ dy \\ \\ V = \pi \Big[\dfrac{4}{3}y^3 - \dfrac{y^5}{5} \big ] ^2_0 \\ \\ V = \pi \Big [ \dfrac{4}{3}(2)^3-\dfrac{2^3}{5} \Big ] \\ \\ V = \dfrac{64}{15}\pi \\ \\ V = (4.27 ) \pi[/tex]

Answer:

180=2x+ 24( angles opposite to equal sides)

156/2=x

x=78

Step-by-step explanation:

The value of x from the triangle is given by the equation x = 78°

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ABC

Now , the measure of angle ∠A = 24°

It is an isosceles triangle with ∠B = ∠C

So , the measures of the two angles are the same

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

x + x + 24° = 180°

On simplifying the equation , we get

2x = 156°

Divide by 2 on both sides of the equation , we get

x = 78°

Hence , the measure of x = 78°

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Answer:

A (i think)

Step-by-step explanation:

If i'm right please mark me branliest

Answer:

Step-by-step explanation:

k(k+1)(k+2) - 3k(k+1)

k and (k+1) are common to both terms.

k(k+1)(k+2) - 3k(k+1) = k(k+1)[(k+2) - 3] = k(k+1)(k-1)

Answer:

27

Step-by-step explanation:

try that it should work for their

The perimeter of the figure is 60

The side lengths are given as:

11, 22, and 27 meters

The perimeter of the triangle is the sum of its side length.

So, we have:

Perimeter = 11 + 22 + 27

Evaluate the sum

Perimeter = 60

Hence, the perimeter of the figure is 60

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Answer:

y = x + 1

Step-by-step explanation:

We can use the point-slope formula to write an equation for this problem. The point-slope formula states: (y - y1) = m (x - x1)

Where m is the slope and (x1 y1) is a point the line passes through.

Substituting the slope and the values from the point in the problem gives:

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

We can also solve for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: y = mx + b

y - 2 = 1x - 1

y = 1x - 1 + 2

y = 1x + 1 or y = x + 1 * are just the same.

The equation of the line is y = x + 1.

The slope and direction of a line are represented numerically by the line's gradient, which is also referred to as the slope in mathematics.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

And here we have the slope,

m = 1

And (x₁ ,y₁)  =  (1,2)

then the equation of line is

y - y₁ = m (x - x₁)

y - 2 = (x -1)

y = x + 1

Therefore, the equation is y = x + 1.

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Answer:

42

Step-by-step explanation:

divide the total by the cost of each invite

Step-by-step explanation:

9x - 2 = 4x + 8 → (9-4)x = 8 + 2 → 5x = 10 → x = 10/2 = 5

C. multiplication

Multiplication not used

Answer:

Check pdf

Step-by-step explanation:

Step-by-step explanation:

[tex]f( - \frac{3\pi}{2} ) = 0 \\ f(\pi) = 2 \\ f( \frac{\pi}{2} ) = 0 \\ [/tex]

Answer:

Trinomial

Step-by-step explanation:

Its called a Trinomial since it has 3 terms in it                                                                                                                                

Hope its helps!

Answer:

[tex] \color{magenta} \huge{ \boxed{answer}}[/tex]

hopefully help:)

Step-by-step explanation:

Given:

Initial profit = $100,000

Increasing rate of profit = 1.2%

To find:

The function that shows the company's profit as a function of time in years.

Solution:

The exponential growth model is defined as:

[tex]f(t)=a(1+r)^t[/tex]

Where, a is the initial value, b is the growth rate and t is the time period.

Putting a=100,000 and r=0.012, we get

[tex]f(t)=100,000(1+0.012)^t[/tex]

Where, t is the number of years.

Therefore, the correct option is c.

Answer:

m = 4 + (2n)/(3)

Step-by-step explanation:

Move all terms that contain m to the right side and solve it.

Answer:The answer is A)11(9)(4)

Step-by-step explanation:

If you have 9(4)(11) then is would be the one that look just like it but the number are moved like 11(9)(4)

Answer:

The Answer is 11 (9 + 4)

Answer:

32 and 70

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The formula for any geometric sequence is:

[tex]a_n=a_1\cdot r^{n-1}[/tex]

Where aₙ is the value of the nth term, a₁ is the value of the first term, r represents the common ratio, and n represents the term number.

We want the formula for the geometric sequence:

-3, -6, -12, -24, ...

Note that our first term is -3. Hence, a₁ = -3.

Next, each subsequent term is twice the previous term. Hence, our common ratio r = 2.

Therefore, by substitution, we acquire:

[tex]a_n=-3\cdot (2)^{n-1}[/tex]

Our answer is C.

Answer:

y = 23

Step-by-step explanation:

115 = 5y

Divide 5 by both sides of the equation.

y = 23

Answer:

25.5

Step-by-step explanation:

4 x 51 / 8

204/8

25.5

Answer:

Step-by-step explanation:

4×15/8 = 4×(1+⅞) = 4×1 + 4×⅞ = 4 + 7/2 = 4 + 3.5 = 7.5

Answer:

900 cans and bottles.

Hope that helps!

Step-by-step explanation:

360 / 4 = 90

90 x 100 = 900

Hope that helps!

Answer:

x^3+2

Step-by-step explanation: