USE THE FACTOR THEOREM
YES OR NO

The solution set for each rational inequality:

Case 1: - 9 ≤ x < - 5

Case 3: Every real number except x = 1.

In this problem we find two cases of rational inequality, whose solution sets can be found by using algebra properties and sign laws. Now we proceed to solve on each case:

Case 1

(3 · x + 7) / (x + 5) ≥ 5

(3 · x + 7) / (x + 5) - 5 ≥ 0

[(3 · x + 7) - 5 · (x + 5)] / (x + 5) ≥ 0

(- 2 · x + 18) / (x + 5) ≥ 0

- 2 · (x - 9) / (x + 5) ≥ 0

The inequality is positive for - 9 ≤ x < - 5.

Case 3

(- x² - 1) / (- x² + 2 · x - 1) > 0

[(- 1) · (x² + 1)] / [(- 1) · (x² - 2 · x + 1)] > 0

(x² + 1) / (x² - 2 · x + 1) > 0

(x² + 1) / (x - 1)² > 0

The inequality is positive for all real number except x = 1.

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The transformation of f(x) to g(x) is (a) f(x) is shifted up 1 unit to g(x).

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the graph, we can see that

So, we have

Difference = 1 - 0

Evaluate

Difference = 1

This means that the transformation of f(x) to g(x) is (a) f(x) is shifted up 1 unit to g(x).

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Answer:

14

Step-by-step explanation:

line from center to chord bisect chord

so x = 14

Answer:

1,110

Step-by-step explanation:

it's that because I added it all up in got thatv

The total distance between the buildings is 150 meters. In the event a map placed one is to 5000 scales then it projects one unit on the map represents 5000 units in the actual world.

We can apply this ratio to alter the distance on the map to the actual distance between the buildings or objects in the given case that the distance is shown as 3 centimeters then the actual distance in meters is followed 1 centimeter on the map represents 5000 centimeters in the real world.

1 cm on the map = 5000 cm in the actual world

3 cm on the map = (3 x 5000) cm in the actual world
= 15000 cm in the actual world
To alter cm to meters, we need to can apply division by 100 since there are 100 cm in a meter. So, the actual distance between the two buildings is:
15000 cm / 100 = 150 meters
The real distance between the two buildings is 150 meters.
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The length of OP in the given circle figure is 2.

We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,

A = (A/360)*πr²

Here length of OP represents the radius of the circle with center O.

Let OP = R.

The area of the whole circle will be = πR²

Given that the sector which intends an angle of 72 degrees in center has area 4π/5.

According to the condition,

(72/360)* πR² = 4π/5

R²/5 = 4/5

R² = 4

R = 2 [since length cannot be negative so the negative value of square root is ignored.]

Hence the length of OP is 2.

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Answer:

the temperature at 7 am was -36.7 degrees.

Step-by-step explanation:

Let's denote the temperature at 7 am by "x". Since the temperature increased by 8.4 C between 7 am and 11 am, we can set up the equation:

x + 8.4 = -28.3

Subtracting 8.4 from both sides, we get:

x = -36.7

Therefore, the temperature at 7 am was -36.7 degrees.

The value of B is 6 when the value of sin x degrees equals to 4/5.

In the given triangle diagram, the opposite side of x = 3b

The hypotenuse of the given triangle = 22.5

Given triangle is a right-angled triangle, in trigonometry, we know that in a right-angled triangle the sin x = opposite side of x / hypotenuse side

So, sin x = 3b/22.5

But, the given value is 4/5. So,

3b/22.5 = 4/5

3b = 90/5

3b = 18

b = 18/3

b = 6

From the above explanation, we can conclude that the value of b is 6.

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b) Josh would pay $741.15 for the refrigerator at the department store with 10% discount.

c)  The true statement is: Josh would pay more for the refrigerator at the superstore.

(b) If the department store marks up the wholesale price of the refrigerator by 50%, then the price at the store would be:

Wholesale price + (50% x Wholesale price) = $549 + (0.5 x $549) = $823.50

If Josh would receive a 10% discount off the in-store price, then the price he would pay would be:

In-store price - (10% x In-store price) = $823.50 - (0.1 x $823.50) = $741.15

(c) If the superstore marks up the wholesale price of the refrigerator by 40%, then the price at the store would be:

Wholesale price + (40% x Wholesale price) = $549 + (0.4 x $549) = $768.60

Therefore, Josh would pay $768.60 for the refrigerator at the superstore.

Comparing the prices, we can see that Josh would pay less for the refrigerator at the department store after factoring in the discount:

Price at department store = $741.15

Price at superstore = $768.60

So the true statement is: Josh would pay more for the refrigerator at the superstore.

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The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0

From the question, we are to calculate the probability of choosing a ball numbered 29

From the formula for probability

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given information,

"A lottery game contains 28 balls numbered 1 through 28"

This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.

Now,

We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,

Number of favorable outcomes = 0

Total number of possible outcomes = 28

Thus,

Probability of choosing a ball numbered 29 = 0/28

Probability of choosing a ball numbered 29 = 0

Hence,

Probability of choosing a ball numbered 29 is 0

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Answer:

$\boxed{52}$ dog owners would be expected to brush their dog's teeth.

Step-by-step explanation:

Answer:  D.  -1

Step-by-step explanation:

Your equation:

[tex]\sqrt[4]{(\sqrt[3]{64}) ^{2} } =(\frac{1}{2} )^{x}[/tex]       >We are going to work from the inside first then out

                                   The cube root of 64 is 4 because 4*4*4=64

[tex]\sqrt[4]{(4) ^{2} } =(\frac{1}{2} )^{x}[/tex]            > 4² = 4*4=16

[tex]\sqrt[4]{(16) } =(\frac{1}{2} )^{x}[/tex]           > the 4th root of 16 is 2 because 2*2*2*2=16

[tex]2 =(\frac{1}{2} )^{x}[/tex]                   > if you have the same bases you can set the

                                   exponents equal.  They are not the same but we

                                    are going to make them the same.  

[tex]2^{1} =(\frac{1}{2} )^{x}[/tex]                  > 2 is the same as 2^1,  i can make the bases the

                                   same if I can make the 2 a reciprocal.  That

                                   happens when I take the negative exponent of the

                                   number

[tex](\frac{1}{2} )^{-1} =(\frac{1}{2} )^{x}[/tex]             >Now that my bases are the same, I can make the

                                exponents =

-1 = x

Answer:

the answer to the question provided is y = x

Using cluster estimation, the team's finishing time is 188 seconds.

We are given that the Team's average time is 47 seconds which means all players finishes in 47 seconds.

The Cluster Estimation means a method used to estimate sum & product when the numbers that we are adding or multiplying cluster near to a same number .

Here, all given time cluster near to the average time i.e., 47 seconds.

So, the team's finishing time will be:

= 47 + 47 + 47 + 47

= 4 × 47

= 188 seconds

Therefore, the team's finishing time is 188 seconds.

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Answer:

9) 36     36  and   36 (all three sides equal)

10) 3.1    3.1  and  3.3  (two sides equal)

Step-by-step explanation:

#9

This is an equilateral triangle so all three sides are equal
Expressions for two of the sides are 6y and 4y + 12

Set these expressions equal to each other and solve for y:
6y = 4y + 12
6y - 4y = 12
2y = 12
y =6

So the side with expression 6y becomes 6 · 6 = 36

Since it is an equilateral triangle, each of the three sides is 36

#10
This is an isosceles triangle with side 2x + 1.7 = x + 2.4

Solve for x:
2x + 1.7 = x + 2.4

2x - x = 2.4 - 1.7
x = 0.7

So the side with x + 2.4 = 0.7 + 2.4 = 3.1 same as the side with 2x + 1.7

The third side with 4x + 0.5 = 4(0.7) + 0.5 = 2.8 + 0.5 = 3.3

So the sides of this triangle are 3.1, 3.1 and 3.3

The total cost of the fence needed for the Perimeter of the work site is $8,800. So the answer is option B.

Because the question involves many units of measurement, we must convert them all to the same unit in order to determine the answer.

1/4 mile is equivalent to 1320 feet (1 mile = 5280 feet).

The length of the fence required to surround the work site equals the perimeter of the work site. To calculate the length of the fence in yards, divide 1320 feet by 3 (since a yard is 3 feet long).

1320 feet ÷ 3 = 440 yards

So the length of the fence needed is 440 yards.

The fence costs $20.00 per yard, thus to get the total cost, multiply the length of the fence by the cost per yard:

440 yards x $20.00/yard = $8,800.00

Therefore, the total cost of the fence needed for the perimeter of the work site is $8,800.00.

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Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".

Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.

No, Michael is not correct.

Translating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.

In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.

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The area of the shaded part is 42.14 ft² .

Area of the shaded part of the figure = area of square - area of quarter circle

Area of shaded part of the figure = s² - 1/4πr²

Where s = 14 ft and r = 14 ft

Substitute into the formula:

Area of shaded part = 14² - 1/4(3.14)(14²)

                                  = 42.14 ft²

Therefore, the area of the shaded part is: 42.14 ft² .

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Complete Question

Check image

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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The equation of the line representing Main Street is option C. y = -2x + 11

The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.

[The product of slopes of perpendicular Lines is -1.)

y - 1 = -2 (x -5)

y - 1 = -2x +10

y = -2x + 10 + 1

y = -2x + 11

Therefore, the best choice is option C. y = -2x + 11

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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.

We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).

Using the point-slope form of a line, we have:

y - 3 = 2(x - 0)

y - 3 = 2x

y = 2x + 3

Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.

To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:

y - 1 = -1/2(x - 5)

y - 1 = -1/2x + 5/2

y = -1/2x + 7/2

Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).

Answer: 64

Step-by-step explanation:

multiple all of them

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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The ladder will reach up the side of the house to a height of approximately 47.1 feet.

We can use the Pythagorean theorem to solve this problem. Let x be the distance between the base of the ladder and the house after Jevonte pulls the ladder 3 feet farther from the house. Then, we have a right triangle with legs x and 48 feet, and hypotenuse 52 feet (the length of the ladder).

Using the Pythagorean theorem, we have:

x² + 48² = 52²

Simplifying, we get:

x² + 2304 = 2704

x² = 400

x = 20

Therefore, Jevonte pulls the ladder 3 feet farther from the house, so the ladder is now 23 feet away from the house. The ladder will reach up the side of the house to a height of:

√(52² - 23²) = 47.1 feet (rounded to the nearest tenth)

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x = -6.

[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]

Applying the distributive property of multiplication on the left hand side:

[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]

Applying the distributive property of multiplication:

[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]

Check the image below to see an illustration of this process.

[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]

Now simplifying on the right hand side (applying the same logic as last step).

[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]

[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]

[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]

[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]

[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]

That's correct!

x = -6 is the corect answer.

The required value of y is 14 units for the given right triangle.

14. It is required to find the value of y.

According to the attached figure, we have a right triangle that has:

Length of AB = x units

Length of BC = 7 units

Length of AC = y units

∠ABC = 90°

∠BAC = 30°

As per the sine ratio, it can be written as follows:

sin 30° = BC/ AC

1/2 = 7/y

Apply the cross-multiplication, and we get

y = (7)(2)

y = 14 units

Therefore, the required value of y is 14 units for the given right triangle.

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Answer:

83

Step-by-step explanation:

Add them all together and then divide by 10 (which is the number of digits there are)

Answer:9.125

Step-by-step explanation:

The recursive formula for the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The first term of the sequence is given as follows:

[tex]a_1 = -\frac{1}{8}[/tex]

Each term is the previous term multiplied by two, hence the common ratio is given as follows:

q = 2.

Then each term is the previous term multiplied by two, and the recursive rule is given as follows:

[tex]a_n = 2a_{n - 1}[/tex]

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Answer:

So we can be 95% confident that the true proportion of people with kids in the population is between 0.044 and 0.096.

Step-by-step explanation:

To construct a confidence interval, we need to use the formula:

CI = p ± zsqrt((p(1-p))/n)

Where:

CI = confidence interval

p = sample proportion (in this case, 42/600 = 0.07)

z = the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval)

n = sample size (in this case, 600)

Plugging in the numbers, we get:

CI = 0.07 ± 1.96sqrt((0.07(1-0.07))/600)

Simplifying this, we get:

CI = 0.07 ± 0.026

Therefore, the 95% confidence interval for the true population proportion of people with kids is:

0.044 ≤ p ≤ 0.096