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3 years ago

10

For the right triangle shown, which expression represents the length of CA?

1 answer:

strojnjashka [21]3 years ago

6 0

Step-by-step explanation:

The attached figure shows a right angled triangle right angle at C. It is required to find the length of CA.

Here, CA = x = perpendicular

BC = base

AB = hypotenuse =7

Angle B is 40 degrees

We know that the ratio of perpendicular to the hypotenuse is equal to sine of angle.

$\sin\theta=\dfrac{P}{H}\\\\\sin(40)=\dfrac{x}{7}$

x is length of CA

$x=7\sin(40)$

So, the correct option is (A).

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Step-by-step explanation:

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3 years ago

Solve 2x2 + 20x = −38. (1 point)

RoseWind [281]

Answer:

The solutions are $x=-5+\sqrt{6}$ and $x=-5-\sqrt{6}$

Step-by-step explanation:

we have

$2x^{2} +20x=-38$

Divide by $2$ both sides

$x^{2} +10x=-19$ ------> $x^{2} +10x+19=0$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +10x+19=0$

so

$a=1\\b=10\\c=19$

substitute

$x=\frac{-10(+/-)\sqrt{10^{2}-4(1)(19)}}{2(1)}$

$x=\frac{-10(+/-)\sqrt{100-76}}{2}$

$x=\frac{-10(+/-)\sqrt{24}}{2}$

$x=\frac{-10(+/-)2\sqrt{6}}{2}$

$x1=\frac{-10(+)2\sqrt{6}}{2}=-5+\sqrt{6}$

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8 0

3 years ago

Read 2 more answers

The net of a square pyramid is shown

Wewaii [24]

Answer:

Option (D)

Step-by-step explanation:

Surface area of a square pyramid is determined from the formula,

Surface area = Area of the square base + 4(Area of one lateral triangular side)

Area of the base = (Side)²

= 8²

= 64 cm²

Area of one lateral triangle = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(8)(8)$

= 32 cm²

Therefore, surface area of the square pyramid = 64 + 4(32)

= 64 + 128

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Therefore, Option (D) will be the correct option.

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3 years ago

What is the range for this data set?<br> 22, 7, 14, 13, 38, 12, 19, <br> 17, 49, 13, 9, 18, 36

Degger [83]

Answer:

from 7 to 49 or (7, 49)

Step-by-step explanation:

Range means the limit of the data set. Basically, the low part of the range is the lowest number in the set and the high part of range is the highest part.

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2 years ago

Factor completely 2x3 + 8x2 + 3x + 12.

goblinko [34]

Answer:

$(2x^2+3)(x+4)$ .

Step-by-step explanation:

$2x^3+8x^2+3x+12$

We need to find the factors of given equation;

Solution:

On Solving the above equation we get;

Now First we will take common factor from first 2 terms which is $2x^2$ we get;

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Hence After factorizing the given equation we get $(2x^2+3)(x+4)$ .

8 0

3 years ago