Find the area of the shaded sector.

85.64 m2
64.25 m²
7.75 m²
92.99 m²

Answer:

The answer is x= [tex]\frac{9+\sqrt{69}}{2}[/tex], x= [tex]\frac{9-\sqrt{69}}{2}[/tex]

Step-by-step explanation:

x^2=a

-9x=b

3=c

Plug into formula.

Equation: [tex]\frac{9+-\sqrt{(-9)^2-4(1)(3)}}{2}[/tex]

Simplify the equation.

Equation: [tex]\frac{9+-\sqrt{81-12}}{2}[/tex]

Subtract 81 and 12.

Equation: [tex]\frac{9+-\sqrt{69}}{2}[/tex]

Spit into two equations

Equation 1: [tex]\frac{9+\sqrt{69}}{2}[/tex]

Equation 2: [tex]\frac{9-\sqrt{69}}{2}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

What is a Ratio?

This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.

Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Answer:

Step-by-step explanation:

the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning

Answer: 54

Step-by-step explanation:

1) First, we need to find what 'x' is. We know that the exterior angles of a triangle equal to 360. So, we will add up all the expressions and set them equal to 360.

7x-2 + 9x-31 + 4x +33 = 360.

2) We will add all the like terms, which will give us: 20x + 0 = 360. We don't need to add the 0.

3) Now, we will isolate the 'x' by dividing 360 by 20 and we will get: x= 18.

4) To find the measure of angle DCE, we just have to substitute x in '7x-2' with 18, which then would equal to: 124.

5) Now, that we have the adjacent angle of DCE, we just have to subtract 124 from 180, and we will get the answer.

6) Angle DCE equals to 54.

The initial saving of the Winston was $55952.48

Compound interest is when you receive interest on both your interest income and your savings.

According to the question given,

Let the initial savings amount be P

We know Compound interest =

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per year

t = number of time periods elapsed

Given,

A = $65000

t = 3 years

r = 5% = 0.05

n = 2 *12 = 24

So

65000 = P(1 + (0.05/24))^72

P =  $55952.48

Therefore the initial savings was  $55952.48

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Answer:

m=4

Step-by-step explanation:

look at the traingle formed with line with points (6,5) and (4, -3)

look at change in y (how tall the triangle is) and change in x (the base of triangle)

change in y=8

change in x=2

m=rise/run also known as change in y/change in x

=8/2

=4

note that this is a positive gradeint line

Answer:

Step-by-step explanation:

Vertex (a max) is at (-3, 2).

Axis of symmetry is the vertical line x = -3.

y-intercept is (0, -1)

You can read this info directly from the illustration.

Answer:

15

Step-by-step explanation:

5x + 15 <= 90

5x<=75

x=15

Answer:

15 roses

Step-by-step explanation:

90 (Amount Santo wants to spend)

15 (Shipping fee)

You first subtract Shipping Fee from the total amount Santo wants to spend

90-15=75

Next it's time to figure out how many roses he can buy with the $75

Each roses is $5, so you divide the left over money after shipping by the price of the rose.

75÷5=15

Answer:

the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.

Answer:

x < 1

Step-by-step explanation:

x - 4 < - 3

 + 4    +4                        Do inverse operations by adding 4 on both sides

    x < 1

Therefore, the answer is x < 1.

(It isn't allowing me to attach a photo but I am just going to try make a visual of the graph below)

<------------------------------o------------------>

-4    -3    -2    -1     0    1     2    3      4

The circle is open because based on the concept that in inequalities, less/greater than and/or equal to (such as these ≥ ≤ ) signs are graphed with closed circles, while less/greater than (like these > <) signs are graphed with open circles. The direction of the arrow is moving to the left on the number line because all possible values for x would be less than 1. When graphing the inequality you would use a solid line rather than a dashed line (I had to improvise since I could not attach an image).

Answer:

3/2

Step-by-step explanation:

5x-7=-11x-25

5x+11x=-25+7

16x=18

x=18/16

x=3/2

Answer:

x = 5

Step-by-step explanation:

i will insert an image of my work below

Answer:

2.5

Step-by-step explanation:

Taking eguation i

4x+y=13

x= 13-y/4

Taking equation ii

x-y = 2

Substituting the value of x in eq i from ii

x- y =2

13-y/4- y=2

13-y-y=2×4

13-2y =8

-2y=8-13

y=-5/-2

Therefore y=2.5

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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The best answer is t = 7. Option C

A quadratic equation is simply defined as an equation that could be rearranged in standard form.

It is also described as an algebraic equation having the highest exponent of as 2.

It is so arranged such that;

It is important to note that the three methods of solving quadratic equation are;

From the information given, we have that the form is;

x² = c

Given  t squared minus 49 = 0

First, represent mathematically

t² - 49 = 0

Now, collect like terms, we have;

t² = 49

Take square root of both sides

t = √49

t = 7

Hence, the equation is  t = 7

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Answer:

138.23 cm²

Step-by-step explanation:

The formula for the area of a sector is given as:

θ/360 × πr²

θ = 110°

Radius = r = 12 cm

Hence

Area of a sector = 110/360 × π × 12²

= 138.23007676 cm²

Approximately, Area of a sector = 138.23 cm²

Answer:

8 x 16 = 128 (area of rectangle)

Area of triangle:

16 - 12 = 4

6 x 4 = 24

24 divided by 2 = 12 (area of triangle)

Now lets add both areas:

128 + 12 = 140 ft2 is your answer.

Therefore , the solution of the given problem of interest rate comes out to be the amount after 5 years is A  ≈ 364.996.

With the help of an interest rate, you can determine how much borrowing will cost you and how much saving will yield. As a result, the interest rate is the cost of borrowing money and, if you're a borrower, it's expressed as a percentage of the total loan amount. An amount, expressed as a percentage of the loan amount, that a borrower is required to pay to a lender as interest during the term of a loan.

Here,

Given : Principal amount : $300

rate of interest :  4%

and time =5 years

Thus , to find the amount after 5 years as compounded

We use , the formula:

=> A = P

=> A  =

=> A =    

=> A  ≈ 364.996

Therefore , the solution of the given problem of percentage comes out to be the amount after 5 years is A  ≈ 364.996.

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The amount after 5 years with compound interest rate is option(A)  = $365. 00.

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields (APY).

Given : Principal amount : $300

rate of interest :  4% (compounded yearly)

time =5 years

Thus , to find the amount after 5 years as compounded we use , the formula:

=> A = P(1 + r/100)^t.

=> A = $300 (1 +4/100)^5

=> A = $300 (104/100)^5

=> A = $300 (1.04)^5

=> A = $300 * 1.2167

=> A = $365.00

The amount after 5 years with compound interest rate is option(A)  = $365. 00.

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Answer:

obtuse angled triangle

Step-by-step explanation:

Given 3 segments , say a, b and c , with c the longest then

• If a² + b² = c² ⇒ right triangle

• If a² + b² > c² ⇒ acute triangle

• If a² + b² < c² ⇒ obtuse triangle

Here c = 17 and 17² = 289

9² + 12² = 81 + 144 = 225

Since 225 < 289 , then triangle is obtuse

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (- 1, 8) ← 2 ordered pairs from the table

m = [tex]\frac{8-6}{-1-1}[/tex] = [tex]\frac{2}{-2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 6 ) , then

6 = - 1 + c ⇒ c = 6 + 1 = 7

y = - x + 7 → B

Answer:

y=7.5x+6.2

Step-by-step explanation:

Hopefully this is the answer

Answer:

y=7.5x+6.2

Step-by-step explanation:

Hopefully this is the answer

The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4

What is a function?

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Given table is

x           f(x)

-1            -5

0             0

1               3

2              4

3               3

4                0

Find the difference to find the degree of the given function

f(x)                 -5           0           3            4         3          0

1st difference        5           3           1            -1          -3

2nd difference              -2          -2        -2          -2

The degree of the function is 2.

The general form of a second-degree function is

f(x) = ax²+bx+c

Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:

f(0) = a×0²+b×0+c

0 = c

Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:

f(1) = a×1²+b×1+0    [since c=0]

3 = a + b ....(i)

Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:

f(2) = a×2²+b×2+0    [since c=0]

4 = 4a + 2b ....(ii)

Solve equations (i) and (ii) by using the elimination method:

Multiply equation (i) by 2 and subtract it from (ii)

4a + 2b  = 4

2a  + 2b  = 6

(-)   (-)         (-)

__________

2a = -2

a = -1

Putting a = -1 in equation (i):

-1 + b = 3

b = 3+1

b = 4

The function is f(x) = -x² +4x

Rewrite the given function in vertex form:

f(x) = -(x² - 4x +4-4)

f(x) = -(x-2)² + 4

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Answer:

m= -1/3

Step-by-step explanation:

slope is rise/run or change in y/change in x

i pick out point (9,0) to (6,1)

the increase in y of this triangle is 1 and increase in x is 3

note that this line will have a negative slope as it goes downwards from left to right instead of upwards

hence m= rise/run= -1/3

Answer:

as a factor 2(x-1) this should help or be the correcr answer

Answer:

(the last one) i think its B

Step-by-step explanation: