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Answer:

Step-by-step explanation:

Solving for x

The solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]

The given polynomial is [tex]x^3 - 7x^2 - x + 7 = 0[/tex]

We can observe that the polynomial has a common factor of (x - 1).

By dividing the polynomial by (x - 1), we can simplify the equation:

[tex](x - 1)(x^2 - 6x - 7) = 0[/tex]

Now we have factored the polynomial equation as a product of two factors, [tex](x - 1)[/tex] and [tex](x^2 - 6x - 7).[/tex]

To find the solutions, we set each factor equal to zero and solve for x.

Setting [tex](x - 1) = 0[/tex], we get [tex]x = 1.[/tex]

Now, let's solve the quadratic factor [tex](x^2 - 6x - 7) = 0[/tex]

Using factoring or the quadratic formula, we find the roots of the quadratic equation:

[tex]x^2 - 6x - 7 = 0[/tex]

[tex](x - 7)(x + 1) = 0[/tex]

Setting each factor equal to zero:

[tex]x=7[/tex] and [tex]x=-1[/tex]

Therefore, the solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]

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Answer:

hi answers b or a

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer:

g(x) = f(x) + 5

Step-by-step explanation:

C

Answer: g(x) = f(x) - 5

Step-by-step explanation:

y = mx + b

The Graph of g(x) is 5 units down from the graph of f(x)

Answer: I think the answer is b

Step-by-step explanation:

Total number of parts = 3 + 2 = 5 parts

[tex]each \: part \: = \frac{(540 \div 5)}{2} \: m[/tex]

[tex] \\ each \: part \: = \frac{108}{2} m \: \\ \\ each \: part \: = 54 \: m[/tex]

Then , the length of this triangle :

[tex]54 \times 3 \: m[/tex]

[tex] = 162 \: m[/tex]

Then , the width of this triangle will be :

[tex]54 \times 2 \: m[/tex]

[tex]108 \: m[/tex]

∴ The length of this rectangle is 162 m and the width of this rectangle is 108 m .

Answer:

r=4.5% daily

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

[tex]P=P_o(1+r)^t[/tex]

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.

Substitute the given values into the model function:

[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]

Simplifying:

[tex]4.09=(1+r)^{32}[/tex]

We need to solve for r. Taking the 32nd root:

[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]

Simplifying:

[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]

Solving:

[tex]r=1.045-1\Rightarrow r=0.045[/tex]

r=4.5% daily

Answer:

x = 7

Step-by-step explanation:

Set the equations equal to each other, since the two angles are congruent.

x + 16 = 4x - 5 now solve

21 = 3x

x = 7

Answer:

Step-by-step explanation:

Answer:

31 is correct guys

Step-by-step explanation:

Since the data is incomplete, for the given question the required average rate of change is given by 15 + 3h.

Given that,
For a function j(x), the difference quotient is 3x2 + 3xh + h2.

The average rate of change of j(x) over the interval [–1, 6] is to be determined.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is independent while Y is the dependent variable.

Here, the average rate of change = f(6) - f(-1) / (6 + 1)
So,
f(6) = 108 + 18h + h²
f(-1) = 3 - 3h + h²

Now,
average rate of change = [(108 + 18h + h²) - (3 - 3h + h²)]/(7)
                                        = [105 + 21 h ] / 7
                                         =   15 + 3h

Thus,  the required average rate of change is given by 15 + 3h.

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Answer:

x=3

Step-by-step explanation:

0 = x -3

-x = -3

change the sign to positive so x= 3

Answer:

8 subtract 1 sides fraction

Answer:

8 subtract 1 sides fraction

Step-by-step explanation:

Answer:

answer

Step-by-step explanation:

step by step explanation

Answer:

B. 61

Step-by-step explanation:

Given:

∆PQR ≅ ∆PQS

PQ = 2x + 41

QS = 7x - 24

QR = 3x + 16

Required:

Numerical value of PQ

SOLUTION:

First, create an equation to find the value of x as follows:

Since both triangles are congruent, therefore:

QS = QR

7x - 24 = 3x + 16 (Substitution)

Collect like terms

7x - 3x = 24 + 16

4x = 40

Divide both sides by 4

4x/4 = 40/4

x = 10

Find PQ by plugging x = 10 into PQ = 2x + 41

PQ = 2(10) + 41

PQ = 20 + 41

PQ = 61

Answer:

Opction b)

The maximum area that can be enclosed by the fencing

Step-by-step explanation:

I took the test

The solution is, A(w), represents the maximum area that can be enclosed by the fencing.

Here, we have,

If the width of the garden is w (in yards), then the length of the garden is (150-w) and the area is ...

 A(w) = w(150 -w) = -(w² -150w)

 A(w) = -(w² -150w +75²) +75²

 A(w) = -(w -75)² +5625

In this vertex form, the vertex is (75, 5625).

The graph of area versus width is a parabola that opens downward, so the vertex second coordinate is the maximum area that can be enclosed.

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Answer:

Henry’s unit rate is 0.7 miles per hour. Clark’s unit rate is 1.5 miles per hour . So, Ckark is faster.

Step-by-step explanation:

Distance covered by Henry is represented by y = 0.7x, where x = time (hrs), and y = distance (miles).

Distance covered in 1 hour by Henry would be:

y = 0.7(1) = 0.7 miles per hour

Distance covered by Clark in 1 hour = 1.5 miles per hour

Ckark covers more miles per hour than Henry covers in one hour, therefore, Ckark is faster.

Answer:

20

Step-by-step explanation:

angles on a straight line

(x+20)+7x

open bracket

8x +20 = 180

collect like terms

8x= 180-20

8x=160x

x=160/8

x =20

Answer:

1. 6 to 2 and 9 to 3

2. Any ratio that is not equivalent to 3 to 1. For example, 4 to 11.

Step-by-step explanation:

Given:

Height of box = 5 inches

Breadth (width) of box = 4 inches

Length of box = 3 inches

Volume of box = 5 • (3 • 4) cubic inches

To find:

The explanation for the parentheses in the expression 5•(3•4)

Solution:

We know that,

Volume of a box is

[tex]Volume = length \times breadth \times height[/tex]

Area of a rectangle is

[tex]Area = length \times width[/tex]

Now,

Volume of box = 5 • (3 • 4) cubic inches

In this expression, (3 • 4) represents the product of length and with of the box. So, it means represents area of the base of box and after multiplying the base area with height we get the volume of the box.

Therefore, the parentheses in the expression 5•(3•4) represents the base area of the box.

Answer:

3 ÷ 1/3 = 9

Step-by-step explanation:

= 3 ÷ 1/3

= 3/3 (3/1) ÷ 1/3

= 9/3 × 3/1

= 9/1

= 9

Answer:

  -9.5

Step-by-step explanation:

The slope (m) is the ratio of the change in y to the change in x:

  m = (y2 -y1)/(x2 -x1)

  m = (10-(-9))/(-3-(-1)) = 19/-2

  m = -9.5

The slope of that line is -9.5.

__

The graph shows the line through those points, written in point-slope form.

Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1.  So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series.  So an =│an│and both series converge (p series with p > 1).  This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series.  bn = 1 / (8 + n), which diverges.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Answer:

Step-by-step explanation:

-x + 9x = -4

8x = -4

x = -4/8

x = -1/2

Answer:

Length = 74 feet,

Width = 65 feet

Step-by-step explanation:

If length = l, width = w;

l = 9 + w (Given)

2l + 2w = 278 (Definition of perimeter)

Substitute "9 + w" for l in the second equation;

2(9 + w) + 2w = 278 -> Distribute the "2"

18 + 2w + 2w = 278 -> Combine like terms

18 + 4w = 278 -> Subtract 18 on either side

4w = 260 -> Divide either side by 4

w = 260/4 = 65 feet

l = 9 + 64 = 74 feet

Answer:

a) A = (5, 1), b) A = (1,11)

Step-by-step explanation:

given A is (2,3), question a is represented by a shift of this point 3 units to the right, and 2 units down which means (x,y) → (x +3, y - 2) or T(3,-2)(x,y). (2,3) → (x + 3, y - 2) = (2 + 3, 3 - 2) = (5, 1).

Question b represents a shift of this point one unit to left, and 8 units up which is represented by (x,y) → (x -1 , y + 8) or T(-1,8)(x,y).

(2,3) → (x - 1, y + 8) = (2 - 1 , 3 + 8) = (1, 11).

Answer:

#23 is x+27°=27

2x-17°=-17

#24 is x+23°=23

x+54°=54

#25 is x+79°=79

2x-37°=-37

#26 is 3x+71°=71

5x+37°=37

Step-by-step explanation:

how you ask because when it is like x+55° and 6x+88° that means its going to be a positive number.

but when it is like 5x-78° that means its going to be a negative number.

remember this +=positive and -=negative

hope this helped you out!

Answer:

65 pounds of cashews 35 pounds of almonds

Step-by-step explanation:

do you do vla in ohio? I have the same questions you do

Answer:

36

Step-by-step explanation:

it took David's car 90 seconds  and chris's car 54 seconds so that means

90-54=36

The number of seconds would they meet again at the starting point will be 270 seconds.

The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.

David's car would cover one lap of the Indy 500 in about 90 seconds. Chris’s car could cover one lap in about 54 seconds.

If both cars left the same starting point at the same time. Then the number of seconds would they meet again at the starting point will be given as,

L.C.M. = 90, 54

L.C.M. = 2 x 3 x 3 x 5, 2 x 3 x 3 x 3

L.C.M. = 2 x 3 x 3 x 3 x 5

L.C.M. = 270 seconds

The number of seconds would they meet again at the starting point will be 270 seconds.

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