what is the factorization of the polynomial below? x^2+6x+8

Answer: 72and 108

Step-by-step explanation: that is the correct answer don’t be a fool

Answer:

B (6,12)

Step-by-step explanation:

The distance from point A (6,5) to point B should be 7.

A- (6,5)-> (7,5) is 1 unit right

B- (6,5)-> (6,12) is 7 units up

C- (6,5)-> (6,7) is 2 units up

D- (6,5)-> (12,5) is 6 units up

Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x

The number of students in his class be y

According to the question he gave every student 4 pieces in the class

The pieces he gave to everyone become 4y.

Note that 4 here means he had given four to each

and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y....

Answer:

After 2.9 years the town's tax status will change

The towns tax status change within the next 3 years

Step-by-step explanation:

The question below is

Will the towns tax status change within the next 3 years ?

Let

y -----> the population of a small town

t ----> the number of years

we have a exponential function of the form

[tex]y=a(b)^{t}[/tex]

where

a is the initial value

b is the base

In this problem

[tex]a=9,400\ people[/tex]

[tex]b=100\%-14.3\%=85.7\%=85.7/100=0.857[/tex]

substitute

[tex]y=9,400(0.857)^{t}[/tex]

Remember that

The town's tax status will change once the population is below 6,000 people

so

The inequality that represent this situation is

[tex]9,400(0.857)^{t}< 6,000[/tex]    

Solve for t

[tex](0.857)^{t}< 6,000/9,400[/tex]

Apply log both sides

[tex](t)log(0.857)< log(6,000/9,400)[/tex]

[tex]-0.067t< -0.1950[/tex]

Multiply by -1 both sides

[tex]0.067t > 0.1950[/tex]

[tex]t > 2.9\ years[/tex]

so

After 2.9 years the town's tax status will change

therefore

The answer is

Yes, the towns tax status change within the next 3 years

the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.

To find out after how many years the population of the town would decrease to below 6,000 people, we start with the current population and apply the annual exponential decrease. The population decreases at a rate of 14.3% each year, which means the remaining population each year is 85.7% (100% - 14.3%) of the previous year. Starting with a population of 9,400 people, we need to solve for t in the inequality 9400  × (0.857)^t < 6000. We take the natural logarithm of both sides to solve for t:

ln(9400 × (0.857)^t) < ln(6000)

t × ln(0.857) < ln(6000) - ln(9400)

t > (ln(6000)-ln(9400)) / ln(0.857)

Using a calculator, we find that:

t > 7.17

Therefore, the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.

Answer:

WoodChuck-Prairie Dog

WoodChuck-Beaver

WoodChuck-Chipmunk

PrairieDog-Beaver

PrairieDog-Chipmunk

Beaver-Chipmunk

Answer:

A chipmunk and a beaver

The difficulty between theorems and proofs in geometry is subjective. Theorems are proven true statements, while proofs are the logical processes used to establish the truth of theorems. Students may find one harder than the other depending on their individual abilities and understanding.

In the study of geometry, students often ask which are harder: theorems or proofs. To address this, it's important to understand the nature of both. A theorem is a statement that has been proven to be true through a logical sequence of statements, starting from agreed-upon assumptions, known as axioms. The Pythagorean Theorem, for instance, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem provides a consistent and reliable outcome as long as the arithmetic is carried out correctly.

On the other hand, a proof is the process by which a theorem is shown to be true. Proofs involve a series of logical deductions from accepted principles and previously proven theorems. They are essentially the 'work' or argument that establishes the truth of a theorem. In any proof, each step must logically follow from the previous ones based on established geometric postulates and existing theorems. Therefore, a proof can be viewed as a bridge that connects the basic assumptions of geometry to the theorem being proven.

Whether theorems or proofs are harder is subjective and depends on the student's strengths. Some students find memorizing theorems challenging, while others may struggle with the logical sequence and creativity required to craft proofs. Nonetheless, the study of geometry contributes valuable reasoning skills and knowledge that connects fundamental truths of mathematics to practical applications in the real world, like engineering and physics.

Answer: I believe the last numbers are $3.40 and $2.75

Step-by-step explanation:

5.35 minus 4.70 equals 0.65 and that is continually going so you should subtract each number by 0.65 to get the next. If that makes sense

Final answer:

The cost for Mrs. Beusse to buy 100 personalized pencils is $405.00.

Explanation:

According to the chart, the cost of pencils depends on the number of pencils being purchased. For 1-20 pencils, the cost is $5.35 each. For 21-40 pencils, the cost is $4.70 each. For 41-60 pencils, the cost is $4.05 each. Since Mrs. Beusse needs to buy 100 personalized pencils, we need to determine which price range this falls into. 100 pencils falls within the range of 81-100, so the cost per pencil will be $4.05.

Therefore, the total cost for 100 personalized pencils will be $4.05 x 100 = $405.00.

Answer: r = -10

Step-by-step explanation:

Move variable to the left , collect like terms, then divide both sides by 2.

Answer:

r = -10

Step-by-step explanation:

Your equation is 6r = 4r - 20

To solve this equation, find out r's value.

To do that, you must get r alone on one side of the equation

6r = 4r - 20

[Subtract 4r from both sides]

2r = -20

[Now divide both sides by 2]

r = -10

So, the answer to this equation is r = -10

I hope this helps! :)

Step-by-step explanation:

y = x - 2

x + y = 12

Substitute the first expression for y into the second equation.

x + (x - 2) = 12

2x - 2 = 12

2x = 14

x = 7

Now plug into either equation to find y.

y = 7 - 2

y = 5

So the solution is (7, 5).

Answer:

51 in² is the area of the shape.

Step-by-step explanation:

Note that there is a triangle, as well as a Parallelogram.

First, solve for the measurement for the Parallelogram. The Parallelogram has sides that measure 6 in. & 7 in. respectively.

Note the measurement of the left length, which is 13. The right length is 7. To solve for the length of the triangle, subtract the two:

13 - 7 = 6

The triangle length is 6.

To solve for the triangle width, subtract the part from the total:

6 - 3 = 3

The triangle width is 3.

Note that the area of the triangle is found using the formula: Area = 1/2base x height (or length x width). Plug in the corresponding numbers to the corresponding variable.

A = 1/2(3)(6)

A = (3)(3)

A = 9

The triangle's area is 9 in².

Solve for the area of the parallelogram:

6 x 7 = 42

The parallelogram's area = 42 in².

Add the two measurements together:

42 + 9 = 51

51 in² is the area of the shape.

~

The above composite shape can be divided into :

●  A Rectangle with Length 7 in. and Width 6 in.

●  A Right angled Triangle with base 3 in. and height 6 in.

Let us first find the Area of Rectangle :

We know that - Area of a Rectangle is given by : Length × Width

[tex]:\implies[/tex]  Area of Rectangle = (7 × 6) in²

[tex]:\implies[/tex]  Area of Rectangle = 42 in²

Now, Let us find the Area of Right angled Triangle :

[tex]\mathsf{We\;know\;that - Area\;of\;a\;Triangle\;is\;given\;by : \dfrac{1}{2} \times base \times height}[/tex]

[tex]\implies \mathsf{Area\;of\;Right\;angled\;Triangle = \dfrac{1}{2} \times 3 \times 6\;(in^2)}[/tex]

[tex]:\implies[/tex]  Area of Right angled Triangle = (3 × 3) in²

[tex]:\implies[/tex]  Area of Right angled Triangle = 9 in²

Area of the Composite shape :

●  Area of Rectangle + Area of Right angled Triangle

[tex]:\implies[/tex]  Area of the Composite shape = (42 + 9) in²

[tex]:\implies[/tex]  Area of the Composite shape = 51 in²

Answer: THIRD OPTION.

Step-by-step explanation:

Given the trapezoid in the figure, you know the coordinates of  two points:

(0,c) and (a,b)

You can observe that the point (a,b) and the point P have the same x-coordinate, because both points are "a" units from the origin.

Then, the x-coordinate of P is:

[tex]x=a[/tex]

Now, in order to find the y-coordinate of the point P, you need to remember that when the line touches the x-axis, the value of "y" is equal to zero. Therefore, the y-coordinates of the point P is:

[tex]y=0[/tex]

Then the answer is:

[tex](a,0)[/tex]

Answer: 14.9

I have to write this in order to have enough characters.

7.45 divided by 0.5 equals 14.9. This is calculated by converting the divisor 0.5 to a whole number and doing the same operation on the dividend, then performing the division.

Dividing Decimals

To find what 7.45 divided by 0.5 is, one approach is to think of 0.5 as one-half, so you are essentially finding out how many halves there are in 7.45. Another way to approach this is to manipulate the numbers to make the division easier. Since 0.5 is equivalent to the fraction 1/2, dividing by 0.5 is the same as multiplying by 2 (which is the reciprocal of 0.5). Here are the steps to perform the division:

Therefore, 7.45 divided by 0.5 equals 14.9.

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Answer:

The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]

In this problem we have

[tex]a=300\ ft[/tex]

[tex]b=250\ ft[/tex]

[tex]c=420\ ft[/tex] ----> is the greater side

substitute and solve for angle C

[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]

[tex]176,400=152,500 -150,000cos(C)[/tex]

[tex]cos(C)=[152,500-176,400]/150,000[/tex]

[tex]cos(C)=-0.1593[/tex]

[tex]C=arccos(-0.1593)=99.2\°[/tex]

Answer:

the answer is that D is false

Step-by-step explanation:

the relative frequency chart shows that 0.35 of her total freshman and sophomores take biology (Bottom left corner of the chart).

Answer: D

Step-by-step explanation: Apex said so

Answer:

The total area is [tex]16\sqrt{3}\ units^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the regular pyramid is equal to the area of its four triangular faces

Each face is an equilateral triangle

so

Applying the law of sines

The surface area is equal to

[tex]SA=4[\frac{1}{2}b^{2}sin(60\°)][/tex]

we have

[tex]b=4\ units[/tex]

[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]

[tex]SA=4[\frac{1}{2}(4)^{2}\frac{\sqrt{3}}{2}][/tex]

[tex]SA=16\sqrt{3}\ units^{2}[/tex]

Answer:

16 sqrt 3

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

The formula for right triangular prisms is simple; 1/2 × a × b × c. So simply plug in your numbers (doesn't matter the order you plug in).

1/2 × 12 × 5 × 3 = 90

Answer:90

Step-by-step explanation:

Answer:

1. [tex]m=1\frac{1}{14}[/tex]

2. undefined

3. [tex]-6[/tex].

4. [tex]2\frac{1}{3}[/tex].

5. [tex]2[/tex].

6.  [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

1. The required line passes through [tex](3,0),(-11,-15)[/tex]. The slope of the line joining the points  [tex](x_1,y_1),(x_2,y_2)[/tex] is given by the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]

Either of them yields the same result.

Substitute [tex]x_1=3,y_1=0,x_2=-11,y_2=-15[/tex] into the first formula to get,

[tex]m=\frac{-15-0}{-11-3}[/tex] [tex]\implies m=\frac{-15}{-14}=\frac{15}{14}[/tex]

You can write this as a mixed number to obtain:

[tex]\implies m=1\frac{1}{14}[/tex]

2. The given line passes through [tex](4,-8),(4,13)[/tex].

Observe that the first coordinates are the same for both points. This implies that, the line is vertical.

The slope of all vertical lines are undefined.

3. The average rate of change of the function [tex]y=f(x)[/tex] on the interval [tex][a,b]\:\:or\:\:a\le x\le b[/tex] is given by:

[tex]ARC=\frac{f(b)-f(a)}{b-a}[/tex].

The given function is [tex]f(x)=x^2-4x[/tex]

[tex]f(-2)=(-2)^2-4(-2)=12[/tex]

[tex]f(4)=(4)^2-4(4)=0[/tex]

[tex]ARC=\frac{f(4)-f(-2)}{4--2}[/tex].

[tex]ARC=\frac{0-12}{6}=-6[/tex].

4. The given function is [tex]f(x)=2^x-1[/tex]

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

[tex]f(3)=2^3-1=7[/tex]

[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].

[tex]ARC=\frac{7-0}{3}=2\frac{1}{3}[/tex].

5. From the graph

[tex]f(3)=7,f(0)=1[/tex]

[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].

[tex]ARC=\frac{7-1}{3}[/tex].

[tex]ARC=\frac{6}{3}=2[/tex].

6. The given equation is :

[tex]2y-7x=-4[/tex]

Add [tex]7x[/tex] to both sides.

[tex]2y=7x-4[/tex]

Divide through by 2.

[tex]y=\frac{7}{2}x-2[/tex]

Compare this function to [tex]y=mx+b[/tex]

The slope is [tex]m=\frac{7}{2}[/tex]

Answer:

B. 1.81

Step-by-step explanation:

Simply divide [tex]\frac{6.98}{3.86}[/tex] to get [tex]1.8082...[/tex].

This is closer to [tex]1.81[/tex] than it is to [tex]1.80[/tex], so that is how it is rounded.

Then, you have your answer.

Answer:

0

Step-by-step explanation:

We find the determinant of a matrix by the method below. If we have a matrix:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

The determinant is [tex]ad-bc[/tex]

Now, using cramer's rule, we find x-value by the formula:

[tex]x=\frac{D_x}{D}[/tex]

Where D is the determinant of the original problem and [tex]D_x[/tex] is the determinant of the x-value matrix. How do we get those?

To get original matrix and thus D, we set up the matrix as the coefficients of x and y (s) of both the equations and to get matrix of x-value and thus [tex]D_x[/tex], we replace the x values of the matrix with the numbers in the right hand side of the 2 equations. We show this below:

To get D:

[tex]\left[\begin{array}{cc}3&4\\1&-6\end{array}\right] \\D=(3)(-6)-(1)(4)=-18-4=-22[/tex]

To get [tex]D_x[/tex]:

[tex]\left[\begin{array}{cc}12&4\\-18&-6\end{array}\right] \\D_x=(12)(-6)-(-18)(4)=0[/tex]

Putting into the formula, we get:

[tex]x=\frac{D_x}{D}=\frac{0}{-22}=0[/tex]

Thus, the value of x is 0

Answer: 9

Step-by-step explanation:

Answer:

the remainder is 9

Step-by-step explanation:

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

         0        4        10

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

         4        10       9 -> Remainder

So the remainder is 9

Answer:

The slope is [tex]m=\frac{5}{4}[/tex]   or  [tex]m=1.25[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]A(9,7)\ B(5,2)[/tex]

Substitute the values

[tex]m=\frac{2-7}{5-9}[/tex]

[tex]m=\frac{-5}{-4}[/tex]

[tex]m=\frac{5}{4}=1.25[/tex]

Answer:

a=3

b=12

c=13

Step-by-step explanation:

(see attached)

The value of 'a' is 3, 'b' is 12, and 'c' is 13 and this can be determined by using the arithmetic operations.

Given :

Expression -  [tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}=2^c[/tex]

The value of a, b, and c can be determined by following the below calculations:

[tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}[/tex]

Further, simplify the above expression:

[tex]\dfrac{2^5\times (2^3)^4}{2^5}=\dfrac{2^5\times (2^a)^{4}}{2^4}[/tex]

the above equation holds good when the value of 'a' is 3.

[tex]\dfrac{2^5\times 8^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}[/tex]

Further, simplify the above expression:

[tex]\dfrac{2^5\times 2^{12}}{2^5}=\dfrac{2^5\times 2^b}{2^4}[/tex]

the above equation holds good when the value of 'b' is 12.

[tex]\dfrac{2^5\times 2^{12}}{2^5}=2^c[/tex]

Further, simplify the above expression.

[tex]\dfrac{2^{17}}{2^4}=2^c[/tex]

[tex]2^{13}=2^c[/tex]

the above equation holds good when the value of 'c' is 13.

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Answer:

The solution of the equation f (x) = g (x) is the same as the coordinates of the intersection.

Exaple in the attachment.

f(x) = g(x) → x = -2, y = -1 or x = -1 and y = 0 or x = 1 and y = 2.

Answer:

He will run 31.6 miles in two weeks.

Step-by-step explanation:

6 days a week = 2.3 miles

6 days · 2 weeks = 12 days total running 2.3 miles

1 day a week = 2 miles

1 day · 2 weeks = 2 days total running 2 miles

(12 · 2.3) + (2 · 2)

27.6 + 4

31.6 miles

Answer:

с. 57°

Step-by-step explanation:

The measure of the exterior angle of a triangle is equal to sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

57° is the value of y.

A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side

Given

The measure of the exterior angle of a triangle is equal to the sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

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Answer:

1. k(x) = (3g + 5h)(x) = -24x+40

2. k(x) = (h - g)(x)  = 0

3. k(x) = (g + h)(x) = -6x+10

4. k(x) = (5g + 3h)(x) = -24x+40

5. k(x) = (3h - 5g)(x) = 6x-10

6. k(x) = (5h - 3g)(x) = 10-6x

Step-by-step explanation:

Given

h(x) = 5 - 3x

and

g(x) = -3 x + 5

1. k(x) = (3g + 5h)(x)

3*g(x) = 3(-3 x + 5)

=> -9x+15

5*h(x) = 5(5 - 3x)

=>25-15x

(3g + 5h)(x)=3*g(x)+5*h(x)

= -9x+15+25-15x

=-9x-15x+15+25

=-24x+40

2. k(x) = (h - g)(x)

(h - g)(x) = h(x) - g(x)

= 5 - 3x -(-3 x + 5)

=5-3x+3x-5

= 0

3. k(x) = (g + h)(x)

(g+h)x = g(x) + h(x)

= -3 x + 5 + 5 - 3x

= -6x+10

4. k(x) = (5g + 3h)(x)

5*g(x) = 5(-3 x + 5)

=-15x+25

3*h(x) = 3(5 - 3x)

=15-9x

(5g + 3h)(x) = 5*g(x) + 3*h(x)

= -15x+25+15-9x

= -15x-9x+25+15

=-24x+40

5. k(x) = (3h - 5g)(x)

(3h - 5g)(x) = 3*h(x)-5*g(x)

=15-9x-(-15x+25)

=15-9x+15x-25

=-9x+15x+15-25

=6x-10

6. k(x) = (5h - 3g)(x)

5*h(x)-3*g(x) = 25-15x - (-9x+15)

= 25-15x+9x-15

= 25-15-15x+9x

=10-6x

Answer:

1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x

6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x

Answer:

Exact Form:

1190/ 3

Decimal Form:

396. 6

Mixed Number Form:

396  2 /3

Step-by-step explanation:

Final answer:

The volume of the triangular prism with a triangle base of 14 units and height of 17 units and a prism height of 5 units is 595 cubic units.

Explanation:

To find the volume of a triangular prism, we need to first find the area of the base triangle and then multiply it by the height of the prism. The formula for the volume of a triangular prism is given by V = (base area)  imes (prism height). However, we need to be clear about what the given 14 and 17 represent. Assuming they stand for base and height of the triangle, respectively, the area of the base triangle is A = (1/2)  imes base  imes height = (1/2)  imes 14  imes 17. Multiplying this area by the prism height of 5 units gives us the volume of the prism.
Calculating the base area: A = (1/2)  imes 14  imes 17 = 119 square units. The volume is then V = 119  imes 5 = 595 cubic units. Therefore, the volume of the triangular prism is 595 cubic units.

The triangles cross the center of the circle CAD is the same as CBD.

The answer is B) 40 degrees.

Answer:

Step-by-step explanation:

You need an x value to determine what number to multiply that will give you three numbers that are in the ratio of 3:1:4

Let the number = x

Set the equation up as 3x + x + 4x = 500

3x + x + 4x = 500           Combine the left

8x = 500                         Divide both sides by 8

x = 500/8                        Divide by 8.  

x = 62.5

So 3x = 3*62.5 = 187.5

1x       = 1 * 62.5 =  62.5

4x      = 4 * 62.5 = 250    The total should be 500

Answer:

{187.50, 62.50, 250}

Step-by-step explanation:

Add up the numbers in the ratio:  Add up 3, 1 and 4.  We get 8.

Then we divide up 500 into eight parts, each 62.5.

The ratio we are to follow is 3:1:4.

3 parts of 62.5 each comes out to 187.5;

1 part of 62.5 each comes out to      62.5; and

4 parts of 62.5 each comes out to 250.

If we have done this correctly, these 3 results add up to 500:

187.50

 62.50

250

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

   500

So, 500 divided up in the ratio 3:1:4 is {187.50, 62.50, 250}