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2 years ago

Find the value of each variable. Answer in simplest radical form.

Mathematics

1 answer:

Vlada [557]2 years ago

8 0

Answer:

x = 5√3; y = 5

Step-by-step explanation:

Finding y: The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:

sin 30° = 1/2 = y/10

Solve the equation of ratios

1 y

-- = ----- using cross-multiplication first: 2y = 10 → y = 5

2 10

We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:

x² + y² = 10² = 100 → x² = 100 - y² = 100 - 5² = 75

If x² = 75, then x = ±√75 = ± (√25)·(√3) → ±5√3

Since lengths are always positive, take x = 5√3 as the answer.

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The sum of a number and its opposite equals zero

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Answer:

Yes,its true

Step-by-step explanation:

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3 years ago

Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)

Rom4ik [11]

Answer:

Step-by-step explanation:

Given : $p(x)=x^{3} +6x^{2} -7x-60$

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, $\text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Since constant term = -60

Leading coefficient = 1

$\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}$

$\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}$

Thus the possible roots are $\pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60$

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is $x^{2} +x-12$

And remainder is 0 .

So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting

$x^{2} +x-12=0$

$x^{2} +4x-3x-12=0$

$x(x+4)-3(x+4)=0$

$(x-3)(x+4)=0$

Thus x-3 and x+4 are the other two factors

So , p(x)=(x+5)(x-3)(x+4)

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3 years ago

Read 2 more answers

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Sonbull [250]

Answer:

Step-by-step explanation:

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8 0

2 years ago

Solve. for. c m=c-s

podryga [215]

Answer:

s-c= m c

Step-by-step explanation:

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2 years ago

A packet of 33 Marbles needs to be split between Gavin and Howard in the ratio of 5:6. How many marbles will each boy get.

Eduardwww [97]

Answer:

15 and 18

Step-by-step explanation:

33 split into groups of 5 and 6

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