What is the area of the composite figure

The area of the triangle is 18.6 units²

Given data ,

Let the triangle be represented as ΔABC

Now , the sides of the triangle are

We can use the law of cosines to find the length of the third side of the triangle:

c² = a² + b² - 2ab cos(C)

c² = 5² + 8² - 2(5)(8)cos(79°)

c ≈ 9.05

Now, we can use Heron's formula to find the area of the triangle:

s = (5 + 8 + 9.05)/2 = 11.525

A = √(s(s-a)(s-b)(s-c))

A = √(11.525(11.525-5)(11.525-8)(11.525-9.05))

A ≈ 18.6

Hence , the area of the triangle is approximately 18.6 square units

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Answer:

This line passes through (0, -9)

Slope = 2

y = 2x-9

Step-by-step explanation:

Slope intercept form is : y=mx+b (m = slope, b= y-intercept)

First, let's distribute the 2 to the (x-6).

y-3 = 2x-12

Second, set it into slope intercept form (y = mx+b) by adding 3 to both sides.

y = 2x-9

This will be the equation in slope intercept form.

After looking at the the slope intercept form, we know that m = the slope. So the since the 2 is in the place of m when in slope intercept form, m=2. this would mean that the slope = 2.

Y-intercept is the point when the line touches the y-axis. To find the y-intercept, x would have to equal 0. This would mean that the point would have to be (0, y). After looking at the slope intercept form, and comparing it with our equation in slope intercept form, we know that -9 is in the place of b. This would mean that b = -9. This would also mean that the y-intercept is equal to -9. Therefore, the point would be (0, -9).

Answer:

Step-by-step explanation:

Formulas:

A = (pi)(radius^2)

C = (pi)(Diameter)

Find the radius

81pi = pi * (r)^2

r^2 = 81

r = 9

Use radius to find diameter

D= 2r

D = 18

Use circumference formula

C = 18π

The value of x, considering the rectangle given at the end of the answer, is given as follows:

x = 8.

From the rectangle given at the end of the answer, the bases are given as follows:

For a rectangle, the bases are congruent, meaning that they have the same measure.

Considering that the bases are congruent, the value of x is obtained as follows:

4(x - 7) = 2(10 - x)

4x - 28 = 20 - 2x

6x = 48

x = 48/6.

x = 8.

The rectangle is given by the image presented at the end of the answer.

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The values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25

From the question, we have the following parameters that can be used in our computation:

The right triangle

The values of sin (A) and sin (B) can be calculated using

sin = opposite/hypotenuse

Using the above as a guide, we have the following:

sin(A) = 14/50

sin(B) = 48/50

Simplify the equations

sin(A) = 7/25

sin(B) = 24/25

Hence, the values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25

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Answer=

-17/12 should be subtracted from-5/12 to get the answer 1

Mark me as brainlist pls...

Answer:

-5,0,1,2,3

Step-by-step explanation:

in a number line the negative numbers are always on your left hand side and as you head to the right they increase thus becoming positive integers

a) The temperature in Juneau was 23°F lower than in Atlanta.

b) The temperature in Milwaukee at noon would be -3°F.

(a) The temperature difference between Juneau and Atlanta is:

= -3 - (-26)

= 23°F lower in Juneau

Therefore, the 6 a.m. temperature in Juneau was 23°F lower than in Atlanta.

(b) Since the temperature in Milwaukee had risen by 11°F, its temperature at noon would be:

= -14 + 11

= -3°F

Therefore, the temperature in Milwaukee at noon would be -3°F.

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Answer: 23.666

(if you would like an explanation please let me know)

There are 35 potential pass codes. The Option B.

A pass code means string of characters used as a password to gain access to a computer or smartphone.

To get number of potential pass codes, we will combinations formula with repetition [tex](n + r - 1)[/tex]  choose r.

n = number of options

r = length of the pass code.

The number of potential pass codes is:

= (5 + 3 - 1) Choose 3

= 7 Choose 3

= (7 x 6 x 5) / (3 x 2 x 1)

= 210 / 6

= 35.

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The domain of the step function f(x) is given as follows:

{x | -4 < x ≤ 4}.

For the function graphed at the end of the answer, we have that:

Hence the domain of the step function f(x) is given as follows:

{x | -4 < x ≤ 4}.

The function is given by the image presented at the end of the answer.

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Answer:

The leading coefficient is 5, the degree is y+1

Step-by-step explanation:

The polynomial 12+5x^y+4x has two terms, 12 and 5x^y+4x. The leading coefficient of the polynomial is 5, which is the coefficient of the term with the highest degree. The degree of the polynomial is y+1, which is the highest power of x in any term of the polynomial after like terms have been combined. The degree is determined by adding the exponents of the variables in the term with the highest degree, which is 5x^y in this case. The exponent of x is 1 and the exponent of y is y, so the degree is y+1. Therefore, the leading coefficient is 5 and the degree is y+1.

Step-by-step explanation:

To solve the equation 3/(n-1) = 2n/(n+4), follow these steps:

Step 1: Cross-multiply to eliminate the fractions.

3 * (n + 4) = 2n * (n - 1)

Step 2: Distribute the terms on both sides.

3n + 12 = 2n^2 - 2n

Step 3: Move all terms to one side and set the equation to zero.

2n^2 - 5n - 12 = 0

Step 4: Factor the quadratic equation, if possible. In this case, we can factor by finding two numbers that multiply to -24 and add to -5.

(2n + 3)(n - 4) = 0

Step 5: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

2n + 3 = 0 or n - 4 = 0

Step 6: Solve for 'n' in each equation.

2n + 3 = 0 => n = -3/2

n - 4 = 0 => n = 4

So, there are two possible solutions for 'n': -3/2 and 4.

Answer: n= 4 , (-3/2)

Step-by-step explanation:

Your goal is to isolate n by getting it by itself

Multiply both sides by (n-1) to get 3 = ((2n)(n-1))/(n+4)

Use distributive property on the 2n * (n-1) to get 3 = (2n^2 - 2n)/(n+4)

Multiply both sides by (n+4) to get 3n + 12 = 2n^2 - 2n

Subtract 12 and 3n from both sides to get 2n^2 - 5n -12 = 0

Solve the quadratic using any method you like

Factoring would give you (n - 4)(2n + 3) = 0

So n= 4 and -3/2

Answer:

Step-by-step explanation:here it is. you did not say which grade ...

but hoping ok method .

If x represents the number of hats sold, the expression representing Geoff's earnings is 15x.

An algebraic expression is a mathematical statement that combines variables, constants, values, numbers, and other quantities based on mathematical operands but without using equal symbols (=).

The selling price per handknit hat = $15

The total cost of materials (yarn) for making the hats = $45.

Let the number of hats sold = x

Total earnings from the sales = 15x

Total cost = $45

Net earnings = 15x - 45

Thus, the expression that represents Goefft's earnings from the sale of handknit hats is 15x.

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Answer:

2

Step-by-step explanation:

To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.

First, we identify the values of a, b, and c:

a = -3

b = 1

c = 12

Next, we substitute these values into the discriminant formula:

b^2 - 4ac = (1)^2 - 4(-3)(12) = 145

Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.

Answer:

1.430

Step-by-step explanation:

1.430 x 10^-2

Answer:

Therefore, Connor is correct in his explanation that the ratio of white to black marbles is 4:11.

Step-by-step explanation:

Connor is correct in his reasoning. Let's break down the problem step by step to understand why.

Given:

Ratio of white marbles to red marbles = 2:3

Ratio of red marbles to black marbles = 6:11

To find the ratio of white to black marbles, we can follow these steps:

Step 1: Consider the black marbles as the whole unit.

Let's assume there are 11 black marbles (since the ratio of red to black marbles is 6:11).

Step 2: Determine the number of red marbles.

Since the ratio of red marbles to black marbles is 6:11, out of the assumed 11 black marbles, there are (6/11) * 11 = 6 red marbles.

Step 3: Determine the number of white marbles.

Using the ratio of white marbles to red marbles (2:3), we can find the number of white marbles. Since the ratio is 2:3, the number of white marbles would be (2/3) * 6 = 4.

Step 4: Find the ratio of white to black marbles.

Now that we have determined there are 4 white marbles and 11 black marbles, the ratio of white to black marbles is indeed 4:11.

a) Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount. b) , the difference in the final payment between choices 1 and 2 is $1,107.60.

a. The cash discount on the printer is calculated as 2% of the list price:

Cash discount = 2% * $860 = $17.20

Using the formula:

Interest = Principal * Rate * Time

Principal = Amount borrowed = List price - Cash discount = $860 - $17.20 = $842.80

Rate = 6% per year = 6%/100 = 0.06

Time = 30 days (since the terms are 2/10, n/30)

To convert the interest to a 360-day basis, we use the formula:

Interest = Principal * Rate * (Time/360)

Interest = $842.80 * 0.06 * (30/360) = $5.60733

Therefore, Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount.

b. Choice 1 for the computer involves paying $150 per month for 17 months, with the 18th payment paying the remainder of the balance. Choice 2 involves paying 6% interest for 18 months in equal payments.

For choice 1:

Remaining balance = List price - (17 * Monthly payment)

Remaining balance = $4,020 - (17 * $150) = $4,020 - $2,550 = $1,470

For choice 2:

Interest = Principal * Rate * Time

Principal = Amount borrowed = List price = $4,020

Rate = 6% per year = 6%/100 = 0.06

Time = 18 months

To convert the interest to a 12-month basis, we use the formula:

Interest = Principal * Rate * (Time/12)

Interest = $4,020 * 0.06 * (18/12) = $362.40

The final payment difference between choices 1 and 2 is:

Final payment difference = Remaining balance - Interest

Final payment difference = $1,470 - $362.40 = $1,107.60

Therefore, the difference in the final payment between choices 1 and 2 is $1,107.60.

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We are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.

This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.

Hence, Using a t-distribution with 86 degrees of freedom (n-1), and a 95% confidence level (α=0.05), the critical value for the two-tailed test is 1.992.

The standard error can be calculated as:

SE = SD / √n = 15.6 / √100 ≈ 1.56

The margin of error (ME) can be calculated as:

ME = t x SE = 1.992 x 1.56 ≈ 3.11

The 95% confidence interval (CI) is then:

CI = mean ± ME = 5.9 ± 3.11 = (2.79, 9.01)

Therefore, we are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.

This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.

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The complete table for the linear function y = -2x + 8 is:

x y

1 6

2 4

3 2

4 0

5 -2

The given function is y = -2x + 8, which represents a linear equation in the slope-intercept form. In this form, the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

Comparing the given equation with the slope-intercept form, we can see that the slope of the line is -2, which means that the line goes down by 2 units for every 1 unit it moves to the right. The y-intercept of the line is 8, which means that the line intersects the y-axis at the point (0, 8).

The complete table:

x y

1 6

2 4

3 2

4 0

5 -2

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The complete question:

Complete the following table as per the function y = -2x + 8.

x         y

1

2

3

4

5

The value of the volume of this rectangular pyramid is,

⇒ V = 192 m³

We have to given that;

In rectangular pyramid,

Lenght = 8 m

Width = 9 m

Height = 8 m

Hence, The volume of this rectangular pyramid is,

⇒ V = 1/3 x Length x width x height

⇒ V = 1/3 × 8 × 9 × 8

⇒ V = 192 m³

Thus, The value of the volume of this rectangular pyramid is,

⇒ V = 192 m³

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Option C. It t will take approximately 5.923 hours to drive the same distance at 65 miles per hour.

t = k / r

where k is the constant of variation.

First, we need to find the constant of variation, k, using the given information:

t = 7 hours when r = 55 mph

7 = k / 55

To find k, multiply both sides by 55:

k = 7 * 55 = 385

Now that we have the constant of variation, we can find the time it will take to drive the same distance at 65 mph:

t = k / r

t = 385 / 65

t ≈ 5.923 hours

So, it will take approximately 5.923 hours to drive the same distance at 65 miles per hour.

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Answer:

Let s be the number of squares and t be the number of triangles.

s + t = 17---->4s + 4t = 68

4s + 3t = 64---->4s + 3t = 64

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

t = 4, s = 13

4 triangles, 13 squares

Answer:

x = the number of kg of cement

3x = number of kg of sand

4x = number of kg of gravel

x + 3x + 4x = 480

8x = 480, so x = 60

60 kg of cement

3(60) = 180 kg of sand

4(60) = 240 kg of gravel

Bob will need 180 kg of sand.

Answer:

f(x)= - [x] + 3

Step-by-step explanation:

because it describes a negative slope and 3 units up from the origin

Complete sentence is,

The square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16

We have to given that;

Taking the square root of a number technically results in two solutions.

Here, The number is,

⇒ 16

Take square root as;

⇒ √16

⇒ ± 4

Since, 4² = 16

And, (- 4)² = 16

Thus, We get;

the square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16.

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[tex] {77.05 \: m}^{2} [/tex]

hope this is correct