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Norma-Jean [14]
2 years ago
10

Factor the Following Expression using the greatest common monomial factor. (x^p+2)(y^p+2) + (x^p+2)(y^p-1) + (x^p+1)(y^p+1) + (x

^p+1)(y^p-1)
Mathematics
1 answer:
igomit [66]2 years ago
4 0
As written, there is no common monomial factor. We assume you intend to factor ...
x^{p+2}y^{p+2}+x^{p+2}y^{p-1}+x^{p+1}y^{p+1}+x^{p+1}y^{p-1}\\\\=(x^{p+1}y^{p-1})(xy^{3}+x+y^{2}+1)
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Car A travels 20 mph faster than Car B. In the same time that Car A travels 252 miles, Car B travels 196 miles. Find their speed
RoseWind [281]

<u>Answer:</u>

A = 70

B = 90

<u>Step-by-step explanation:</u>

We know that Car A travels 20 mph faster than Car B.

Assuming the speed of Car B to be x and the speed of Car A to be x+20, we can write:

\frac{196}{x} =\frac{252}{x+20}

Taking the reciprocal of both sides to make x the subject:

196(x+20)=252x

196x+3920=252x

252x-196x=3920

56x=3920

x=70 ---> speed of Car A

Finding the speed of Car B: x+20 = 70+20=90

Therefore, the speed of Car A = 70 and the speed of Car B = 90.

8 0
3 years ago
Write a polynomial function of least degree with integral coefficients that has the given zeros.
densk [106]
The zeroes are
0, -5, 3 + i (and its conjugate)

The factors are
x (x + 5) (x - (3 + i)) (x - (3 - i))
Expanding...
(x² + 5x)((x - 3) - i) ((x - 3) + i)
(x² + 5x)((x - 3)² - i²)
(x² + 5x)(x² - 6x + 9 - (-1))
(x² + 5x)(x² - 6x + 10)
x⁴ - 6x³ + 10x² + 5x³ - 30x² + 50x
x⁴ - x³ - 20x² + 50x
4 0
2 years ago
Keisha swims 18 ft from one side of her circular pool to the other, swimming straight through the center. She then swims one tim
elena-s [515]

Answer:

Swimming one time around the pool is 56.5 ft

Step-by-step explanation:

Swimming 18 ft from one side of her circular pool to the other, swimming straight through the center means the circular swimming pool has a diameter of d=18 ft.

The circumference of the circle is calculated using:

c = \pi \: d

where d=18 is the diameter and π=3.14 as given.

We substitute the values to get:

c = 3.14 \times 18

c = 56.52

We approximate to the nearest tenth to get:

c = 56.5ft

6 0
2 years ago
A line is defined by the equation y = 2/3 x - 6 The line passes through a point whose y-coordinate is 0. What is the x-coordinat
Iteru [2.4K]

Answer:

x = 9

Step-by-step explanation:

Use the equation of the line, and let y = 0. Then solve for x.

y = 2/3 x - 6

Let y = 0:

0 = 2/3 x - 6

Add 6 to both sides.

6 = 2/3 x

Multiply both sides by 3/2.

3/2 * 6 = x

x = 9

8 0
3 years ago
A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchase
Alona [7]

Answer:

The customer can conclude that the company's claim is correct

Step-by-step explanation:

The percentage of lids that has a free yogurt coupon = 20%

The number of cups a loyal customer purchases = 85 yogurt cups

The number of cups that contained a coupon = 12 (14.1%)

The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes

The interval obtained = (0.044, 0.238)

Therefore, the range of proportion within which the true proportion exists is 0.044 < \hat p < 0.238

The range of percentage within which the true percentage exist is therefore;

0.044 × 100 = 4.4%  < \hat p × 100 < 0.238 × 100 = 23.8%

Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.

4 0
2 years ago
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