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motikmotik
3 years ago
7

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1 at x=−5.

Mathematics
1 answer:
satela [25.4K]3 years ago
3 0

Answer:

P(x) = -0.7(x-5)^{2}(x+5)

Step-by-step explanation:

Root multiplicity of 2 means the root is repeated 2 times. Root multiplicity of 1 means root is repeated only once.

A polynomial of degree 3 means the largest exponent of x is 3.

Here, the polynomial P(x) has root 5 with multiplicity 2 and -5 with multiplicity 1.

So, P(x) = a(x-5)^{2}(x+5)

Where, a is a constant.

Now, it's given that the y intercept is -87.5. Therefore, value of x at y intercept is 0.

We obtain a by plugging in -87.5 for P(x) and 0 for x.

-87.5=a(0-5)^{2}(0+5)

-87.5=a(25\times5)\\ a=-\frac{87.5}{125}=-0.7

Therefore, the polynomial P(x) is given as:

P(x) =-0.7(x-5)^{2}(x+5)

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Bobby earns $9 per hour plus commission. Last week he worked 32.5 hours
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Answer:

Step-by-step explanation:

32.5*9=292.5

add the commission - $28.75

292.5+28.75= $321.25

8 0
1 year ago
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A city has a population of 310,000 people. Suppose that each year the population grows by 9%. What will the population be after
Leno4ka [110]

Answer: 644,800

Step-by-step explanation:

This can also be solved using the terms of Arithmetic Progressions.

Let the 13 years be number of terms of the sequences (n)

Therefore ;

T₁₃              = a + ( n - 1 )d , where a = 310,000 and d = 9% of 310,000

9% of 310,000 = 9/100 x 310,000

                        = 27,900

so the common difference (d)

                     d = 27,900

Now substitute for the values  in the formula above and calculate

T₁₃              = 310,000 + ( 13 - 1 ) x 27,900

                  = 310,000 + 12 x 27,900

                  = 310,000 + 334,800

                  = 644,800.

The population after 13 years = 644,800.

 

3 0
2 years ago
For triangle ABC with sides a,b and c the law of cosines states
grigory [225]

Answer:

SAS

Step-by-step explanation:

Looking for the third side given the other two sides and the angle between them

c² = a² + b² - 2abcosC

6 0
2 years ago
Answer this and I’ll mark you the Brainlest
Elena-2011 [213]

Answer:

D. 88

Step-by-step explanation:

if you add the given numbers up (equals 100) them subtract it from 540(the degrees of a Pentagon) you get 440. then divide that by 5 (number of xs left) you get 88. You can plug in 88 for x and check but I already did, I hope this helps you lemme know if it does :)

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3 years ago
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In the diagram below, P and Q are points on a circle with centre O.
Gnoma [55]

Answer:

<h2>∠PQT = 72°</h2>

Step-by-step explanation:

According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.

Also from the diagram, ∠OQP + ∠PQT = ∠OQT;

∠PQT  = ∠OQT -  ∠OQP

Given ∠OQP = 18° and ∠OQT = 90°

∠PQT = 90°-18°

∠PQT = 72°

8 0
3 years ago
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