Factor the trinomial x^2+8x+7

Answer:

Part 1) An expression for the area of the inner square is [tex]x^{2}=0.75(20)^{2}[/tex]

Part 2) The area of the entire garden is [tex]400\ ft^{2}[/tex]

Part 3) 75% of the area of the entire garden is [tex]300\ ft^{2}[/tex]

Part 4) The equation is [tex]x^{2}=300[/tex]

Part 5) The solutions of the quadratic equation are [tex]x=(+/-)17.3\ ft[/tex]

Part 6) The solution that best describes the side length of the inner square is [tex]x=17.3\ ft[/tex]

Step-by-step explanation:

Part 1) What is an expression for the area of the inner square?

we know that

The area of the inner square is equal to

[tex]A=x^{2}[/tex]

[tex]A=0.75(20)^{2}[/tex]

so

[tex]x^{2}=0.75(20)^{2}[/tex]

Part 2) What is the area of the entire garden?

The area of the entire garden is

[tex](20)^{2}=400\ ft^{2}[/tex]

Part 3) What is 75% of the area of the entire garden?

we know that

[tex]75\%=75/100=0.75[/tex]

so

[tex]0.75*(400)=300\ ft^{2}[/tex]

Part 4) Write an equation for the area of the inner square using the expressions from Steps 1 and 3

[tex]x^{2}=0.75(20)^{2}[/tex]

[tex]x^{2}=300[/tex]

Part 5) Solve the quadratic equation. Round to the nearest tenth of a foot

we have

[tex]x^{2}=300[/tex]

square root both sides

[tex]x=(+/-)\sqrt{300}[/tex]

[tex]x=(+/-)17.3\ ft[/tex]

Part 6) Which solution to the quadratic equation best describes the side length of the inner square?

[tex]x=(+/-)17.3\ ft[/tex]

so

The solution that best describes the side length of the inner square is

[tex]x=17.3\ ft[/tex]

because

The side length can not be a negative number

the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.

from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.

the standing up sides are simply rectangles of 8x3.

if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312[/tex]

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ First, according to PEMDAS, you need to do multiplication and division from left to right.

3*6=18

Then, you divide that by 8:

18/8=2.25

Final answer:

2.25

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

With Remainder: 2 R2

Step-by-step explanation:

Multiply 3 and 6

= 18

Divide 18 and 8 = 2 R2

If you need it without the remainder, put it in the comments and I'll give it without the remainder.

Answer:

6 = 2 • 3  

8 = 23  

18 = 2 • 32

Answer:

72

Step-by-step explanation:

Consider the least common multiple of 6 and 8

The multiples of 6 are : 6, 12, 18, 24, 30, 36, ......

The multiples of 8 are : 8, 16, 24, 32, 40, ......

The common multiple is 24 or 48 or 72

The multiples of 18 are : 18, 36, 54, 72, 90, ....

Since 72 is a common multiple of 8 and 6 and also a multiple of 72

Then the least common multiple of 6, 18 and 8 is 72

Answer:

1oz cost $0.39 which will be the unite rate

Step-by-step explanation:

Answer:

$0.39 per oz

Step-by-step explanation:

[tex]\frac{6}{2.34} =\frac{1}{x} \\\\6x=2.34\\\\x=\frac{2.34}{6} \\\\x=0.39[/tex]

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

We have

[tex]2r=4\ in\to r=2\ in\\\\H=8\ in[/tex]

Substitute:

[tex]V_1=\pi(2^2)(8)=\pi(4)(8)=32\pi\ in^3[/tex]

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

We have

[tex]r=2\ in\\\\H=0.7\ in[/tex]

Substitute:

[tex]V_2=\dfrac{1}{3}\pi(2^2)(0.7)=\dfrac{1}{3}\pi(4)(0.7)=\dfrac{1}{3}\pi(2.8)=\dfrac{2.8\pi}{3}=\dfrac{28\pi}{30}=\dfrac{14\pi}{15}\ in^3[/tex]

The volume of the plastic object:

[tex]V=V_1-V_2[/tex]

[tex]V=32\pi-\dfrac{14\pi}{15}=\dfrac{480\pi}{15}-\dfrac{14\pi}{15}=\dfrac{466\pi}{15}\\\\\pi\approx3.141\\\\V\approx\dfrac{466}{15}\cdot3.141\approx97.6[/tex]

Answer:

A. 8 cm sq

Step-by-step explanation:

Find the scale factor

new width/original width

8/1.6=5

calculate length of original rectangle

new length/scale factor

25/5=5cm

Find area of original rectangle

A=l×w

A=1.6×5=8cm²

A is the answer

You find the scale factor by doing 8÷1.6 which = 5

Then you do 25÷5=5

And then times 5 and 1.6 together to get 8cm sq

Answer:

Communative: 12 x 5= 5 x 12 Associative: (5) + 6 = (8) + 3 Identity: 5 x 1= 5

Step-by-step explanation:

Commutative 3+4=4+3

Associative (1+2)+3= 1+(2+3)

Identity x+0=x

Answer:

Step-by-step explanation:

[tex]g(x) =\frac{1}{2} f(x+3)+\frac{1}{2}[/tex]

Following changes are made in f(x) i.e. Line m to get g(x) i.e. the Line m'

1) Multiplication of f(x) by 1/2

Multiplying the function by a number indicates dilation. So this means Line m is dilated by a factor of 2. The dilation in this case is compression. So the function is being compressed by a factor of 2.

2) Addition of 3 to x

Addition of a value directly to x shifts it horizontally towards left. So Line m is shifted 3 units to left.

3) Addition of 1/2 to function value

Addition of a number to function value indicates vertical upward shift. So the Line m is shifted up by 1/2 units

Therefore, the correct answers are:

Answer:

I have tried the answer given on Math Nation and it told me the answer was wrong. The answers are:

Step-by-step explanation:

The given polynomial 2x-4 is of degree 1 and is typically referred to as a linear polynomial because its highest power of the variable is 1.

The polynomial in question is 2x-4. It's important to note that the degree of a polynomial is the highest power of the variable that appears in the polynomial. In this case, the highest power of the variable 'x' is 1. Therefore, the polynomial 2x-4 is of degree 1. It is referred to as a linear polynomial because linear polynomials always have a degree of 1.

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The polynomial 2x-4 is a first-degree polynomial, also known as a linear polynomial.

The given expression, 2x-4, is a polynomial. A polynomial is a mathematical expression composed of variables and coefficients. In this case, the variable is 'x' and the coefficients are '2' and '-4'. This specific polynomial is of first degree, because the highest power of the variable 'x' is 1. Therefore, the given expression is a linear polynomial.

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subsitute values

4(2) + 1/3 (3)^2

8 + 1/3 (9)

8 + 3

11

Answer:

x + 3

Step-by-step explanation:

Factor out the greatest common factor from f(x), which is x²

We get f(x) = x²(x + 3)

The (x + 3) factor is a linear component

Lines are in the form of y = mx + b, here we have y = x + 3

Answer: {(5,0), (3,4)}

Step-by-step explanation:

You can apply the Substitution method:

- Solve for y from the second equation.

- Substitute into the first equation and solve for x.

Then:

[tex]y=10-2x[/tex]

[tex]x^2+y^2=25\\x^2+(10-2x)^2=25\\[/tex]

(Remember that: [tex](a\±b)^2=a^2\±2ab+b^2[/tex])

[tex]x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3[/tex]

Substitute the values obtained into one of the original equation and solve for y:

[tex]2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4[/tex]

The solution set is: {(5,0), (3,4)}

|4x-2|=-6 because an absolute value can’t be equal to a negative

Answer:

see explanation

Step-by-step explanation:

given

[tex]\frac{x8x^2-8}{4x+4}[/tex] , x ≠ - 1

The x ≠ - 1 means that x cannot take the value of - 1 as this would make the denominator equal to zero which would make the fraction undefined.

Factor the numerator/ denominator

8x² - 8 = 8(x² - 1) ← factor out 8 from both terms

x² - 1 ← is a difference of squares, hence

8x² - 8 = 8(x - 1)(x + 1)

4x + 4 = 4(x + 1) ← factor out 4 from both terms

Thus the fraction now simplifies to

[tex]\frac{8(x-1)(x+1)}{4(x+1)}[/tex]

Cancel the 8 and 4 by 4 and cancel the factor (x + 1), leaving

=  2(x - 1) = 2x - 2 ← in the form ax + b

Answer:

its b  because i took a test

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

¹²/₇

Step-by-step explanation:

Model ⁴/₇ × 3

Assume that you have three pies, each dived into seven slices.

There are only four slices remaining in each pie, that is, there is ⁴/₇ pie in each pie plate

The picture represents ⁴/₇ × 3.  

Model the product

Now, transfer slices to get as many filled pie plates as possible.

Count the total slices.

You have 12 slices, and each slice represents ⅐ of a pie.

You have ¹²/₇  pie.

∴ ⁴/₇ × 3 = ¹²/₇

Answer:

Step-by-step explanation:

Seven

I imagine that 7 is the one giving you the problem. There are 29 steps between where A is and where B is. The problem is in the directions. If you follow the first direction, there are 29 squares separating them meaning that B and starts on square 31 and A starts on one. If, however, you read on, your find out that B actually starts on 29. Which is it? If you follow the first direction, you get the both land on 13. Here's how.

A's motion is 3 up 1 back. His net motion is that  he moves 2 forward.

B's motion is 5 down and 2 up. His not motion is - 3 each time

A                          B

1                            31

3                            28

5                            25

7                             22

9                             19

11                             16

13                             13

=============================

Let's do it again starting with the second direction

A                              B

1                               29

3                              26

5                               23

7                                20

9                                17

11                                14

13                                11 and they miss  but keep going. You might have to go another round

15                                 8

17                                  5

19                                  2 Now if you try going forward you can't so B uses As  rule.

21                                  4

23                                  6

25                                  8  And these two will never meet on this round.

I think you should follow the first rule.

27                                   10

28                                   12

25                                   14

22                                    16

19                                      18 another miss.    

Well you can carry it on. I would ask your teacher about this one.

Eight

I can give you an answer, but I don't know how you would find it on your own. The smallest number I found was 301

You can see that 2 and 5 do leave a remainder of 1.

You can also see the 301 / 3 leaves a remainder of 1

What about 4? 301 / 4 = 75 with a remainder of 1.

301 / 6 = 50 with a remainder of 1.

301/7 = 43 with no remainder.

What a strange question.

All of these from 2 to 6 divide into 300 evenly. 301 gives a remainder of 1.

But 301 = 7 * 43

Nine

Let the smaller to the 2 angles = x

Therefore the larger one is 3x + 2

The third angle = 90 degrees.

3x + 2 + x + 90 = 180                    Combine like terms on the left.

4x + 92 = 180                                Subtract 92 from both sides.

4x = 180 - 92

4x = 88                                          Divide by 4

x = 88/4

x = 22

So the three angles are

22

66 + 2 = 68

90

This problem seems much easier than the other 2.

Answer:

yes

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction of two whole numbers, like 3/1 (3), 8/10 (0.8), or even something crazy like 23784/924433 (0.0257...). ... For example, pi and the square root of two cannot be expressed as a fraction of two whole numbers, so they are both irrational.

No 23/3 is a rational number.

Irrational numbers are real numbers that cannot be represented as simple fractions. An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.

Given here the number N=23/3 which is of the form p/q where p,q are integers, thus N is a rational number.

Hence, N is not a irrational number.

Learn more about irrational numbers here:

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Answer:

20 x 31= 620 ft of fence

Step-by-step explanation:

This is the answer.

Answer:

4.23691242438e+12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The solutions are (-2 , 0) and (1 , 3)

Step-by-step explanation:

∵ -x² + 4 = x + 2

* y = -x² + 4 ⇒ is quadratic represented by parabola

 The parabola open downward because coefficient of x² is negative

 The x-coordinate of its vertex = -b/2a, where b is the

  coefficient of x and a is the coefficient of x²

∴ x = 0/2(-1) = 0

∴ The y-coordinate of the vertex = (0)² + 4 = 4

∴ The maximum point of the parabola is (0 , 4)

∵ -x² + 4 intersects x-axis at y = 0

∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4

∵ x² = 4

∴ x = ±√4 = ± 2

∴ the parabola intersects x-axis at -2 , 2

∵ y = x + 2 represented by a line its slope = 1

  It intersects y-axis at 2

∵ x + 2 intersects x-axis at y = 0

∴ x + 2 = 0

∴ x = -2

∴ The parabola and the line intersect each other at

  x = -2 and y = 0

To find all the point of intersection between the 2 equations we will solve them as a system of equations

∵ y= -x² + 4  and y = x + 2

∴ -x² + 4 = x + 2

∴ -x² + 4 - x - 2 = 0

∴ -x² - x + 2 = 0 ⇒ × -1

∴ x² + x - 2 = 0 ⇒ factorize

∴ (x + 2)(x - 1) = 0

∴ x + 2 = 0 ⇒ x = -2

∴ x - 1 = 0 ⇒ x = 1

* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)

* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)

The solution graphically

Answer:

The graph consists of a parabola and a line. The parabola opens down and has a vertex of (0, 4). The line has a slope of 1 and a y-intercept of 2

c:

Final answer:

By applying the Pythagorean theorem, we find that the sum of the squares of the two shorter sides of triangle STV (7 and 11) is not equal to the square of the longest side (14). Therefore, triangle STV is not a right triangle.

Explanation:

To determine if triangle STV with sides of 7, 11, and 14 is a right triangle, we can apply the Pythagorean theorem, a² + b² = c², where c is the hypotenuse (the longest side of the triangle) and a and b are the other two sides. For triangle STV, assume that the side with a length of 14 units is the hypotenuse, and the sides with lengths of 7 and 11 units are the other two sides.

Now, let's calculate:

a² = 7² = 49

b² = 11² = 121

a² + b² = 49 + 121 = 170

c² = 14² = 196

Since 170 does not equal 196, the sums of the squares of the sides do not equal the square of the hypotenuse. Therefore, triangle STV is not a right triangle.

Answer:

Step-by-step explanation:

Answer: D. 0.75

Step-by-step explanation: The bus was late 15 out of 20 times. Therefore, the experimental probability that the bus will be late is 0.75.

Answer: 8.8pi

Step-by-step explanation:you have to divide 12 by 1.35 then you get your answer.

Answer: 0, I think?

Step-by-step explanation: In order to do this equation, we want to get the variable on one side. In order to do this, we add 7 to both sides to cancel out the -7's. Now, we divide 9 on both sides, giving us 0.

Answer:

1. 50

2. They are congruent

3. They are equidistant

4. No, a chord has endpoints on the edges of a circle while a radius has endpoints on the center of the circle and an edge.

5. Since the chords are not congruent, the lines cannot be congruent.

Step-by-step explanation:

Using Theorem 84, we can find that since CA = BD, the corresponding arcs are congruent. Using this theorem, we can find the answers to the rest of the questions.

Answer:

x > 80,000

Step-by-step explanation:

3600+1.02x<2000+1.04x

The first thing we need to do is to isolate the x's and get all of them on one side, let's start off by subtracting 2,000 from both sides of the equation.

1,600+1.02x<1.04x

Now, subtract 1.02x from both sides to get both the x's on one side.

1600<0.02x

Divide by 0.02 to solve for x.

80,000<x

We can flip the sign and swap the places of the number and variable so that x is on the left side.

x > 80,000

To solve the inequality 3600+1.02x<2000+1.04x algebraically, follow the steps: Move terms, combine like terms, simplify, and isolate x.

To solve the inequality 3600+1.02x<2000+1.04x algebraically, we can follow these steps:

By following these steps, we can find the value of x that satisfies the inequality.

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Answer: Vertical angles and linear pairs of angles

Step-by-step explanation:

1) Vertical angles are angles that are opposite each other when two straight lines intersect

2) A linear pair of angles is formed when two lines intersect. They are linear if they are adjacent angles formed by two intercepting lines. Linear pairs of angles add up to 180 degrees.