Which choice names a radius of circle F? a. AF b. AB c. AC d. BE

The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their master Trigonomos

VikaD [51]

Answer:

60.2 m

Step-by-step explanation:

Let x represent the width of the river. The distance from the point across from the tree to the second point is 15 m. The angle from this point to the tree across the river is 76°.

This makes the side opposite the angle x, the width of the river. It also means the 15 m side is adjacent to this angle.

The ratio opposite/adjacent is the ratio for tangent; this gives us the equation

x/15 = tan(76)

Multiply both sides by 15:

15(x/15) = 15(tan(76))

x = 15(tan(76)) ≈ 60.2

5 0

3 years ago

When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

aleksandr82 [10.1K]

Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

We have to sum 528 and three times the number, so we have $528+3x$

Then, we have to subtract this number from $x^2$ , so we have

$x^2-(3x+528)$

The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

$x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24$

But we know that x is positive, so we only accept the solution $x = 27$

6 0

2 years ago

Q3. Kylie sits two maths test. She scores 19/25 in the first one, and 16/20 in the second one.

Rina8888 [55]

She done better at the 2nd test because she only got 4 wrong but on the first test she got 6 wrong.

7 0

2 years ago

Read 2 more answers

Drako found an emerald in a cave at a depth between -1/2 and -1 2/3 meters which number could represent the depth which the emer

oksian1 [2.3K]

Answer:

$-\frac{3}{4}$ meters

Step-by-step explanation:

From the answer choices, we basically need to find which of them is between $-\frac{1}{2}$ and $-1\frac{2}{3}$

Converting all of them to decimals would make it really easier:

So we need to find number between -0.5 and -1.67

Answer choice A is -2.33

Answer choice B is -0.75

Answer choice C is -0.25

Answer chioce D is -1.83

So which number, from the choices, is between -0.5 & -1.67?

Clearly, it is -0.75, or, $-\frac{3}{4}$ meters

5 0

3 years ago

Read 2 more answers

What is the completely factored form of f(x)=x^3+4x^2+7x+6?

Reptile [31]

we are given

$f(x)=x^3+4x^2+7x+6$

We will use rational root theorem to find factors

We can see that

Leading coefficient =1

constant term is 6

so, we will find all possible factors of 6

$6=\pm 1,\pm 2,\pm 3,\pm 6$

now, we will check each terms

At x=-2:

We can use synthetic division

we get

$f(-2)=0$

so, x+2 will be factor

and we can write our expression from synthetic division as

$f(x)=x^3+4x^2+7x+6=(x+2)(x^2+2x+3)$

$f(x)=(x+2)(x^2+2x+3)$

now, we can find factor of remaining terms

$x^2+2x+3=0$

we can use quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

we can compare our equation with quadratic equation

we get

$a=1,b=2,c=3$

now, we can plug these values

$x=\frac{-2+\sqrt{2^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}$

$x=-1+\sqrt{2}i$

$x=\frac{-2-\sqrt{2^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}$

$x=-1-\sqrt{2}i$

so, we get

$x=-1+\sqrt{2}i,\:x=-1-\sqrt{2}i$

so, we can write factor as

$x^2+2x+3=(x-(-1+\sqrt{2}i))(x-(-1-\sqrt{2}i))$

so, we get completely factored form as

$f(x)=(x+2)(x-(-1+\sqrt{2}i))(x-(-1-\sqrt{2}i))$ ...............Answer

7 0

2 years ago