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What is the area of this triangle?
Enter your answer as a decimal in the box round only your final answer to the nearest tenth.

Not sure what the question is, but I guess it's to prove that

[tex]\cos3A=4\cos^3A-3\cos A[/tex]

Expand the left side as

[tex]\cos3A=\cos(2A+A)=\cos2A\cos A-\sin2A\sin A[/tex]

and use the double angle identities to write

[tex]\cos3A=(\cos^2A-\sin^2A)\cos A-2\sin^2A\cos A[/tex]

[tex]\cos3A=\cos^3A-3\sin^2A\cos A[/tex]

Recall the Pythagorean identity:

[tex]\cos3A=\cos^3A-3(1-\cos^2A)\cos A[/tex]

[tex]\cos3A=\cos^3A-3\cos A+3\cos^3A[/tex]

[tex]\implies\cos3A=4\cos^3A-3\cos A[/tex]

as required.

Answer:

Step-by-step explanation:

Use Pythagoras theorem

a = √ 8² + 5² = 9.4

b = √ 17² - 12² = 12.0

Answer: a=9.4 b=12.0

Step-by-step explanation:

Answer:

The height of the prism is [tex]7.5\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base of prism

H is the height of the prism

Find the area of the base B

[tex]B=(5)(8)=40\ ft^{2}[/tex]

we have

[tex]V=300\ ft^{3}[/tex]

substitute in the formula and solve for H

[tex]300=40(H)[/tex]

[tex]H=300/40[/tex]

[tex]H=7.5\ ft[/tex]

In a parallelogram, opposite angles are congruent.

This means that the four angles of the parallelogram are:

[tex]L = x+40,\quad M = 3x,\quad N = x+40,\quad O = 3x[/tex]

Moreover, the sum of the interior angles of a polygon with n sides is 180(n-2). So, the sum of the interior angles of a parallelogram is 360.

This means

[tex]L+M+N+O = 360 \iff 2(x+40)+2(3x) = 2x+80+6x = 360 \iff 8x = 280 \iff x = 35[/tex]

And since [tex]O=3x[/tex], we have [tex]O=3\cdot 35=105[/tex]

Answer:

Angle O(3x) is =105 degrees or C

Answer:

Part 2) Option A: 25

Part 3) Option C: 16

Part 4) Option D: 20

Part 5) pentagon

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

so

[tex]V- E+ F=2[/tex]

Part 2) we have

vertices: 11

Edges: 34

Faces: ?

substitute the values in the formula and solve for F

[tex]11- 34+ F=2[/tex]

[tex]-23+ F=2[/tex]

Adds 23 both sides

[tex]F=2+23[/tex]

[tex]F=25[/tex]

Part 3) we have

Edges: 36

Faces: 22

Vertices: ?

substitute the values in the formula and solve for V

[tex]V- 36+ 22=2[/tex]

[tex]V- 14=2[/tex]

Adds 14 both sides

[tex]V=2+14[/tex]

[tex]V=16[/tex]

Part 4) we have

Faces: 12

Vertices: 10

Edges: ?

substitute the values in the formula and solve for E

[tex]10- E+ 12=2[/tex]

[tex]- E+ 22=2[/tex]

Subtract 22 both sides

[tex]- E=2-22[/tex]

[tex]- E=-20[/tex]

Multiply by -1 both sides

[tex]E=20[/tex]

Part 5) we know that

The cross section of the figure is a plane figure with five straight sides and five angles

therefore

The figure is a pentagon

Answer:

Team E appears to have the larger mean weight.

Step-by-step explanation:

After seeing the dot plot of two teams i.e. Team E and Team F the conclusion that can be drawn regarding the larger mean of the team is that:

Team E is expected to have larger mean since the dots are for the higher values of weights  and hence will result in higher mean. whereas for team F the dots or frequencies are for smaller weights and hence will result in a less mean as compared to team E.

Hence, Team E appears to have the larger mean weight.

Answer:

team E

Step-by-step explanation:

Answer:

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot.  

This line may pass through some of the points, none of the points, or all of the points.

Step-by-step explanation:

1.  Prepare a scatter plot of the data on graph paper.

2.  Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3.  Find two points that you think will be on the "best-fit" line.  

4.  We are choosing the points (9, 260) and (30, 530).  

You may choose different points.  

5.  Calculate the slope of the line through your two points (rounded to three decimal places).

[tex]\frac{530-260}{30-9} =\frac{270}{21} =12.857[/tex]

6.  Write the equation of the line.  

[tex]y-y_{1} m(x-x_{1} )\\y-260=12.857(x-9)\\y=12.857(x-9)+260[/tex]

7.  This equation can now be used to predict information that was not plotted in the scatter plot.  

Question: Predict the total calories based upon 22 grams of fat.

y=12.857(22-9)+260

y=12.857(13)+260

y=427.141

ANS: 427.141 calories

The equation for the line of best fit is written as ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope determined by minimizing the sum of squared errors (SSE). You substitute various x-values to calculate the resulting y-values, then plot these points to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are used to measure the goodness of fit.

To write an equation for the line of best fit, or the least-squares regression line, you would use the formula ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. Generally, 'b' is determined by minimizing the sum of the squared differences between the observed (actual) and predicted values of y, also known as the sum of squared errors (SSE). To do this, you would typically use statistical techniques or software that perform these calculations. Let's consider an example, the equation of the best-fit line is ŷ = -173.51 + 4.83x. Here, -173.51 is the value of 'a', and 4.83 is the value of 'b'.

While working with any specific equation, you can create a table of values by substituting different values for 'x' and calculating the resulting values for 'y'. You then plot these points and draw a line through them to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are also used to measure the goodness of fit of the regression line.

Remember, while your sample data might give you a best-fit line for your sample, testing the significance of the correlation coefficient is needed to confirm the suitability of this line for the overall population.

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Answer:

4 pounds

Step-by-step explanation:

"About" means that you are rounding. Most of the time, when you are rounding food, you generally round to the next whole number. In this case, it is 3.75, so you round to 4.

Jolie bought ~4 pounds of turkey.

The reason you round up, is because you can have less than amount, but generally not more. Also, food's weight can change depending on temperature, heat, how it is at the moment (cooked, non-cooked, mashed, processed, unprocessed, etc.).

~

Answer:

c.

Step-by-step explanation:

The number 64 is a perfect cube and square also. Option C: Cube and square

In mathematics, a perfect cube is a number that is the cube of an integer.

In other words, it is the product obtained when an integer is multiplied by itself twice.

Since perfect square is a number system that can be expressed as the

square of a given number from the same system.

The perfect cube of 4 is 64 because 4 x 4 x 4 = 64.

Hence, option B is correct.

The perfect Square of 8 is 64 because 8 x 8 = 64.

Hence, option A is correct.

Learn more about perfect square;

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Final answer:

The number of 4-letter passwords using the letters A-Z with repetition allowed is 456,976, while without repetition it's 358,800.

Explanation:

When calculating the number of 4-letter passwords that can be made using the letters A through Z, two scenarios are considered: one where repetition of letters is allowed, and one where it is not allowed.

Scenario a) Repetition of letters is allowed

For each position in the 4-letter password, there are 26 possibilities (since there are 26 letters in the alphabet). Because repetition is permitted, each of the four positions can be filled by any of the 26 letters. Thus, the total number of possible passwords can be found by multiplying the number of choices for each position: 26 x 26 x 26 x 26 = 456,976.

Scenario b) Repetition of letters is not allowed

When repetition of letters is not allowed, the number of choices decreases for each subsequent position in the password. The first position can be filled by any of the 26 letters, the second can be filled by 25 remaining letters (since one letter has been used), the third position by the 24 remaining letters, and the fourth by 23 remaining letters. Thus, the calculation would be: 26 x 25 x 24 x 23 = 358,800.

Look at the image below :)

In case you didn't know, corresponding angles are equal to each other and are on the same side of the traversal

Therefore the answer is angle CGH

Hope this helped!  

Answer:

Step-by-step explanation:

When two lines are crossed by another line, the angles in matching corners are called corresponding angles.

When the two lines are parallel Corresponding Angles are equal.

∠AFG and ∠CGH are corresponding angles.

The lines AB and CD are parallel, therefore m∠AFG = m∠CGH.

∠CGH and ∠DGH are supplementary angles.

Therefore m∠CGH + m∠DGH = 180°

Substitute m∠DGH = 54°:

m∠CGH + 54° = 180°          subtract 54° from both sides

m∠CGH = 126°

Therefore m∠AFG = 126°.

Amount spent on vacation=$7920,

Let Mike monthly salary be x,

11% of X= $7920,

[tex] \frac{11}{100} \times x = 7920[/tex]

[tex]11x = 7920 \times 100[/tex]

[tex]x = 792000 \div 11[/tex]

[tex]x = 72000[/tex]

Answer: 720

Step-by-step explanation: divide 7920 into 11 and you will get your answer.

For this case we have that by properties of logarithm that:

[tex]log_ {b} (a) = c[/tex] is equivalent to the following expression:

[tex]b ^ c = a[/tex]

We have the following expression:

[tex]log_ {7} () = - 3[/tex]

Then, according to the property we have:

[tex]7 ^ {- 3} =[/tex]

ANswer:

[tex]7 ^ {- 3} =[/tex]

Option A

Answer:

[tex]\large\boxed{A)\ y=-2x+15}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(10,\ -5).[/tex]

[tex]\text{Put the coordinates of the point to the equation.}\ x=10,\ y=-5:\\\\-5=-2(10)+b\\\\-5=-20+b\qquad\text{add 20 to both sides}\\\\b=15[/tex]

Answer:

Jim is 5, Dad is 20

Step-by-step explanation:

Since dad is 4 times as old as Jim that means 5 x 4=20 and in ten years Jim will be 15 and Dad will be 30 and 15 x 2 is 30.

Hope this helps!

Answer:

Step-by-step explanation:

I believe the correct option would be the 1st option because I just took the test and I got this correct! Hope this helps :)

Answer:

Summation: [tex]\sum_{n=1}^4(3n+12)[/tex]

Explicit formula: [tex]a_n=3n+12[/tex]

Step-by-step explanation:

The given series is 15 + 18 + 21 + 24.

The first term of this series is [tex]a_1=15[/tex].

The common difference is [tex]d=18-15=3[/tex]

The explicit formula is given by: [tex]a_n=a_1+d(n-1)[/tex].

We plug in the known values to get:

[tex]a_n=15+3(n-1)[/tex]

[tex]a_n=15+3n-3[/tex]

The explicit formula is [tex]a_n=3n+12[/tex]

The summation that represents the series is: [tex]\sum_{n=1}^4(3n+12)[/tex]

Answer:

3 12

Step-by-step explanation:

Answer:

$600

Step-by-step explanation 50 dollars every month for 12 months you would do 12 *50 and it gives you 600

Answer:

By the end of 12 months, Esther would have $600.

Step-by-step explanation:

As Esther deposits $50 each month in her account, and the account does not produce interests, it is just an addition of money each time she puts $50 in it. That money won't increase until she puts another $50 at the end of the following month. Therefore, by the end of twelve months, she would have $600 (50 x 12 = 600).

Answer:

2/15

Step-by-step explanation:

We need to find the difference between the houses

Peter - Natalie

3/10 - 1/6

Get a common denominator of 30

3/10 * 3/3 - 1/6*5/5

9/30 - 5/30

4/30

Divide top and bottom by 2

2/15

Answer:

I am pretty sure the answer would  be A.

Answer:

[tex] \sqrt{20} + \sqrt{45} - \sqrt{32} = [/tex]

[tex] \sqrt{4} \sqrt{5} + \sqrt{9} \sqrt{5} - \sqrt{16} \sqrt{2} = [/tex]

[tex]2 \sqrt{5} + 3 \sqrt{5} - 4 \sqrt{2} = [/tex]

[tex]5 \sqrt{5} - 4 \sqrt{2} [/tex]

2√5 + 3√5 - 4√2 = 5√5 - 4√2. To simplify the expression with square roots, evaluate each square root separately and then combine the results.

To simplify the expression, simplify each square root individually:

Then substitute these values back into the original expression: 2√5 + 3√5 - 4√2 = 5√5 - 4√2.

Answer:

Correct choice is D). 8y + 96​.

Step-by-step explanation:

Given expression is [tex]8\left(y+12\right)[/tex].

Now question says to simplify that expression using distributive property then find the correct matching choice from the given choices:

A). 8y=12

B). 20y

C). 20 - y

D). 8y + 96​

So let's distribute 8 by using distributive property

[tex]a\left(b+c\right)=a\left(b\right)+a\left(c\right)[/tex]

[tex]8\left(y+12\right)=8\left(y\right)+8\left(12\right)[/tex]

[tex]8\left(y+12\right)=8y+96[/tex]

Hence correct choice is D). 8y + 96​.

Answer:

What is the question?

Answer:

F = -3.2 is the answer

Answer: I believe it is A

Step-by-step explanation:

In this table, you have to look at multiple things in the table. So you have to look at where it says Under 40 and that don't read the paper. So according to what I learned with this, you would have to do 36/40 and then get 0.9 which would be in percent form: 90 %.

I would recommend looking at another person's response also, before you submit this question. But hope this helps!

The probability that a person surveyed is under and does not get the news by reading the paper is A; 90%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

So,

P(a person is under 40 and doesn't get the news by reading the paper)

= 36/40

= 0.90

= 90 %  

Hence, option A is correct.

Learn more about probability here;

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Answer: 1. 266

             2. 72

1. 95 : 15 = ___ : 42

Form a proportion. Let x be the missing term.

[tex]\frac{95}{15} = \frac{x}{42}[/tex]

Solve for x by cross-multiplying.

[tex]15x = 95(42)\\15x = 3990\\x = 266[/tex]  

2. 98 : 112 = 63 : ___

Form a proportion. Let x be the missing term.

[tex]\frac{98}{112} = \frac{63}{x}[/tex]

Solve for x by cross-multiplying.

[tex]98x = 112(63)\\98x = 7056\\x = 72[/tex]

Answer:

-3x+25

16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

-5(3 - 5) + 2(3) =

-5(-2) + 2(3)

10 + 6 =

16

Answer:

The camper will use all 6 storage compartments, with 2 sleeping bags in the one that is not completely filled.

Step-by-step explanation:

If 6 storage compartments can each hold 3 sleeping bags, 18 (6*3) sleeping bags in total will be able to be stored.

We only have 17, which is one bag less than 18, so we can think of it as having one compartment with one bag less than all the others (they have three). Therefore, there are 2 sleeping bags in that storage compartment.

We can also divide 17 by 3 to find how many compartments will be filled. The remainder is the number of bags in the one that is not completely full.

17/3 = 5 r2

But because the camper still needs to put those two sleeping bags in a compartment, they will use 6.

5 compartments will be completely used, and the 6th compartment will contain 2 sleeping bags.

To determine how many storage compartments will be used for storing 17 sleeping bags, when each compartment can hold 3 sleeping bags, we can divide 17 (the total number of sleeping bags) by 3 (the capacity of each compartment):

Therefore, 5 compartments will be completely used, and the 6th compartment will contain 2 sleeping bags.

Answer:

90

Step-by-step explanation:

A right triangle is a triangle that has a right angle.  A right angle is an angle that is 90 degrees.

A 90 degree angle. That’s the answer .

Answer:

a. blue 16x + 5

a. red 4x + 5

b. 12x

c. blue 53

c. red 17

Step-by-step explanation:

a.

The perimeter of a polygon is the sum of the lengths of the sides of the polygon.

Blue triangle:

side lengths: 4x + 2, 5x - 4, 7x + 7

perimeter = 4x + 2 + 5x - 4 + 7x + 7 = 16x + 5

Red triangle:

side lengths: x + 3, x + 7, 2x - 5

perimeter = x + 3 + x + 7 + 2x - 5 = 4x + 5

b.

We subtract the perimeter of the red triangle from the perimeter of the blue triangle.

16x + 5 - (4x + 5) =

= 16x + 5 - 4x - 5

= 12x

c.

Blue triangle:

perimeter = 16x + 5 = 16(3) + 5 = 48 + 5 = 53

Red triangle:

perimeter = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:c 4

Step-by-step explanation:because ti is in the middle

Answer:

1+1+2+3+3+3+4+4+4+4+4+5+5+5+5+6+6+6+7+7/20 is 78.35

Step-by-step explanation: