Use the table to identify values of pand a that can be used to factor
x2 + x - 12 as (x + p)(x+q).

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

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

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: 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.

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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:

What is the question?

Answer:

F = -3.2 is the answer

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.

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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:

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:

$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:

[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]

Step-by-step explanation:

[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x+7-7>17-7\\\\5x>10\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{10}{5}\\\\x>2[/tex]

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:

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:

[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: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:

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:

The sequence of transformation is reflected across the y-axis and translated 2 units down

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) translate h units to the right

∴ Its image is (x + h , y)

- If point (x , y) translate h units to the left

∴ Its image is (x - h , y)

- If point (x , y) translate k units up

∴ Its image is (x , y + k)

- If point (x , y) translate k units down

∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of figure ABCD are:

  A (-1 , 3) , B (1 , 0) , C (2 , 3) , D (1 , 4)

∵ The vertices of figure A"B"C"D" are:

  A" (1 , 1) , B" (-1 , -2) , C" (-2 , 1) , D" (-1 , 2)

* Lets compare between ABCD and A"B"C"D"

∵ All x-coordinates has opposite signs

  -1 ⇒ 1 , 1 ⇒ -1 , 2 ⇒ -2 , 1 ⇒ -1

∴ The ABCD is reflected across the y-axis

∵ All y-coordinates subtracted by 2

 3 ⇒ 1 , 0 ⇒ -2 , 3 ⇒ 1 , 4 ⇒ 2

∴ The ABCD is translated 2 units down

* The sequence of transformation is reflected across the y-axis

  and translated 2 units down

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

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.

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:

[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:

41.7 % to the nearest tenth.

Step-by-step explanation:

5 out of did not arrive on time.

As a percentage this is 5*100 / 12

= 41.7 % .

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

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°.

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:

the answer to that is the very first response.

Step-by-step explanation:

you see, 6(4x+5) is equal to saying (6•4x) + (6•5). hope this helped!

It’s the first answer choice, the second answer choice, and the forth one.

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:

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:

I am pretty sure the answer would  be A.

Answer:

124.7 in²

Step-by-step explanation:

A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.

So, we can calculate the area of one right triangle and multiply by 12.

The formula for the area of one triangle is

A = ½bh

Step 1. Calculate the length of the side a

Per the Pythagorean Theorem,

[tex]\begin{array}{rcl}h^{2} + \left(\dfrac{a}{2}\right)^{2} & = & a^{2} \\\\6^{2} + \dfrac{a^{2}}{4} & = & a^{2}\\\\36 & = &\dfrac{3a^{2}}{4}\\\\144 & = & 3a^{2}\\\\\end{array}\\\\[/tex]

[tex]\begin{array}{rcl}a^{2} & = & \dfrac{144}{3}\\\\a & = & \dfrac{12}{\sqrt{3}}\\\\a & = & \dfrac{12\sqrt{3}}{3}\\\\a & = & 4\sqrt{3}\\\\\end{array}[/tex]

2.Calculate the area of a small triangle

The base of a small triangle is  

b = ½a = ½ × 4√3 = 2√3

The area of one small triangle is

A = ½ bh = ½× 2√3 × 6 = 6√3 in²

3. Calculate the area of the hexagon

A = 12 × 6√3 = 72√3 = 124.7 in²

To find the area of a regular hexagon, use the formula A = (1/2) x Perimeter x Apothem, find the side length with the apothem, calculate the perimeter, and then apply the values to the formula.

To find the area of a regular hexagon with an apothem of 6 inches, you can use the formula for the area of a regular polygon, which is A = (1/2) x Perimeter x Apothem. A regular hexagon can be split into six equilateral triangles, which means each side of the hexagon is equal in length. Since the apothem corresponds to the height of each of these triangle components, you can use the fact that in an equilateral triangle, the ratio of the side to the apothem is √3:1 to find the side length. Once the side length (s) is known, you can find the perimeter (P) of the hexagon by multiplying the side length by six. Then, plug the perimeter and the apothem into the formula to calculate the area.

Step 1: Calculate the side length (s).

Step 2: Calculate the Perimeter (P).

Step 3: Calculate the area (A).