Calculate the hypotenuse. Find the missing side of each triangle, leave your answers in simplest radical form.

Answer:

7. B

Step-by-step explanation:

The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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Answer:

7.5

Step-by-step explanation:

multiply like normal math . then add the decimal point after 1 number

Answer:

B) Wx is equal to WX.

When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.

Answer:

v = 141.76 m/s

Step-by-step explanation:

Given that,

The ball reaches the ground with a velocity of 4.43h m/sec.

We need to find the velocity of the ball at a height of 32 m.

Since, v = 4.43h

Put h = 32 m in the above expression.

v = 4.43(32)

v = 141.76 m/s

So, the velocity of the ball is equal to 141.76 m/s.

Answer:

−3/2

Step-by-step explanation:

Hope this helps

:D

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

32 ounces

Step-by-step explanation:

1 lb = 16 ounces

2 lbs = 2 * 16 = 32 ounces

Answer:

The answer is letter B

Step-by-step explanation:

We know obviously when you are multiplying (since it is how MANY he ran that we are multiplying to get total distance), you don't add 1 or 3 to the numbers. We also know he did not run the 26 mile course 13 times, so the only answer choice that is feasible and/or even remotely correct would be B.

Answer:

Step-by-step explanation: true

Answer:

4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

Given

2 dozen Muffins; 3 cups of flour and 1 cup of sugar

Required

Determine the cups of flour if 18 muffins is used

First, we have to determine the proportion of the number of muffins used previously and now;

Represent this with p;

\(p = \frac{2\ dozen}{18}\)

\(p = \frac{2 * 12}{18}\)

\(p = \frac{24}{18}\)

\(p = \frac{4}{3}\)

Multiply this to the previous cups of flours and sugars;

Cups of flour = p * previous cups of flour

\(Cups\ of\ flour = \frac{4}{3} * 3\)

\(Cups\ of\ flour = 4\)

Cups of Sugar = p * previous cups of sugar

\(Cups\ of\ sugar= \frac{4}{3} * 1\)

\(Cups\ of\ sugar= \frac{4}{3}\)

Hence, 4 cups of flour is needed and 4/3 cups of sugar

Answer:

Step-by-step explanation:

Restate the problem:

 "  29% of x is $28.9 million"

   (29/100)x = $28.9 million  

          [in word (story) problems "of" usually means multiply]

          29% may be written as (29/100) or 0.29 as needed by the problem.

   x = (100/29)($28.9 million)

   x ≅  $99.655 million

   x ≅ $100 million         [rounded

Answer:

-107

Step-by-step explanation:

x4-5^3+ 3^2-2x + 7

2x−109/x−1

1   2   −109

    2

second step

1   2                    -109

                    1 * 2 = 2

    2 (-109) + 2 = -107

Coefficients are 2, and -107

Therefore the quotient is 2 and the remainder is -107

The total cost of his groceries in dollars and cents is 91.35 on 8.75% sales tax.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

Sales tax is an indirect fee that is always applied at the point of exchange or purchase and is calculated as a percentage of the item's worth. Retail, manufacturing, wholesale, use, and value-added taxes are the various types of sales taxes (VAT). Note: As of July 1, 2017, the Goods and Services Tax (GST) has taken the place of the Sales Tax.

Sales tax = 8.75%

⇒  8.75/100 × 84

⇒ 7.35

Total price = 7.35 + 84

⇒ $ 91.35

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Answer:

A

Step-by-step explanation:

Divide them both by 2 an you get 5 and 2. Since the question says girls to boys then you out the girls first. so 5:2

Based on the information given, the number of milligrams that will remain after 59 hours will be 13.125 milligrams.

Since after 40 hours, 25 mg of the substance has been removed, therefore, the rate per hour will be:

= 25/40 = 0.625.

The amount that will be removed in 59 hours will be:

= 59 × 0.625 = 36.875

The number of milligrams that will remain will be:

= 50 - 36.875 = 13.125 milligrams

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A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

Solution :

Given :

Sample mean, \($\overline x = 714.2$\)

Sample size, n = 40

Standard deviation, s = 83.2

∴ The null hypothesis is \($H_0 : \mu = 703.5$\)

   Alternate hypothesis is \($H_a : \mu > 703.5$\)

Test statistic :

\($z = \frac{\overline x - \mu}{s / \sqrt n}$\)

\($z = \frac{714.2-703.5}{83.2 / \sqrt {40}}$\)

z = 0.813

Now at α = 0.05, for a right tailed,

\($z_{critical} = 1.645$\)

Since, \($z < z_{critical}$\) , we fail to reject the null hypothesis.

The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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Answer: D. (-2,0) and (9,0)

Step-by-step explanation:

When you equate the factors to 0 you get

(X+2) = 0

X = -2

(X-9) = 0

X= 9

Here the Y value is 0 as you find the factors of x when the Y value is 0.

So the answer is (-2,0) and (9,0)

Answer: EDMENTUM AND PLATO

D.) (-2,0) and (9,0)

Step-by-step explanation:

Answer:

its positive 29 since you dividin a negative 1 and a negative divided by a negative is a positive

Step-by-step explanation:

Answer:

Assuming you're hoping to solve the inequality for x, x > 29

Step-by-step explanation:

When dividing both sides of an inequality by -1, the sign will be reversed. In this case, the sign will change from a less than to a greater than, meaning -x < -29 => x > 29.

The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

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Answer:

1. y = -2x+5

2. y = 3/4 - 3

3. intercept = -5 slope =  4/3

4. intercept = 1 slope = -1/2

The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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The width of the shape is 4.2 units

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

Surface Area = 54 square units

Length = 2 units

Height = 3 units

The surface area of the shape can be calculated using the following formula

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

2 * (2 * Width + 2 * 3 + Width * 3) = 54

Divide both sides by 2

So, we have

2 * Width + 2 * 3 + Width * 3 = 27

Subtract 6 from both sides

2 * Width + Width * 3 = 21

This gives

Width * 5 = 21

Divide both sides by 5

Width = 4.2

HEnce, the width is 4.2 units

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Answer:

44 ft/s

Step-by-step explanation:

Answer:

a) 4.55% probability that both adults dine out more than once per week.

b) 61.80% probability that neither adult dines out more than once per week.

c) 38.20% probability that at least one of the two adults dines out more than once per week.

d) An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.

Step-by-step explanation:

The adults are selected without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

800 adults, so \(N = 800\)

171 dine out at a resaurant more than once per week, so \(k = 171\)

2 are chosen, so \(n = 2\)

a. Find the probability that both adults dine out more than once per week.

This is P(X = 2).

\(P(X = 2) = h(2,800,2,171) = \frac{C_{171,2}*C_{629,0}}{C_{800,2}} = 0.0455\)

4.55% probability that both adults dine out more than once per week.

b. Find the probability that neither adult dines out more than once per week.

This is P(X = 0).

\(P(X = 0) = h(0,800,2,171) = \frac{C_{171,0}*C_{629,2}}{C_{800,2}} = 0.6180\)

61.80% probability that neither adult dines out more than once per week.

c. Find the probability that at least one of the two adults dines out more than once per week.

Either none dines out more than once per week, or at least one does. The sum of the probabilities of these events is 100%. So

p + 61.80 = 100

p = 38.20

38.20% probability that at least one of the two adults dines out more than once per week.

d. Which of the events can be considered unusual? Explain.

An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.