Evaluate. (4/5)3 A.64/125 B.4/125 C.64/5 D.12/5

A right triangle, DEF, is shown below. What is sin FDE?

RoseWind [281]

Answer:

22.6°

Step-by-step explanation:

Reference angle = <FDE

Side opposite to <FDE = 5

Hypotenuse = 13

The trigonometric ratios to apply is:

$sin(\theta) = \frac{opp}{hyp}$

Plug in the values

$sin(\angle FDE) = \frac{5}{13}$

$sin(\angle FDE) = 0.3846$

$\angle FDE = sin^{-1}(0.3846)$

$\angle FDE = 22.6$ (nearest tenth)

3 0

3 years ago

Find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5.

Elena-2011 [213]

Let's notice, the focus is at (5,0) and the directrix at x = -5.

keep in mind that there's a distance "p" from the vertex to either of those fellows, therefore, if the focus is at 5,0 and the directrix x = -5, the vertex is half-way between them, check the picture below.

notice the distance "p" there, now, is a horizontal parabola, opening to the right, meaning the value for "p" is positive, or just 5, thus

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})}
\\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}})
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=0\\
k=0\\
p=5
\end{cases}\implies (y-0)^2=4(5)(x-0)\implies y^2=20x
\\\\\\
\cfrac{y^2}{20}=x\implies \cfrac{1}{20}y^2=x$

8 0

3 years ago

The data set shows the number of hours per week that each student in a class spends studying at home. What is the shape of the d

AVprozaik [17]

Answer:

The answer is symmetrical

Step-by-step explanation:

x

x x x

x x x x x

x x x x x x x

___________________________

1 2 3 4 5 6 7

4 0

3 years ago

Steve opens a bank account with a simple annual interest rate of 5%. After four years, how much interest will Steve earn on an i

Marysya12 [62]

Steve will earn $160 interest after four years ⇒ 1st answer

Step-by-step explanation:

The formula of the simple interest is I = Prt, where

P is the initial deposit
r is the annual rate in decimal
t is the time of investment

∵ Steve opens a bank account with a simple annual interest rate of 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ His initial deposit is $800

∵ He will put the money for four years

∴ t = 4

- Substitute all these values in the formula above

∵ I = 800(0.05)(4)

∴ I = 160

Steve will earn $160 interest after four years

Learn more:

You can learn more about the interest in brainly.com/question/13018049

#LearnwithBrainly

7 0

3 years ago

Read 2 more answers

Reduce to simpleast form. -5/8 - (-4/3)=

vfiekz [6]

$-\frac{5}{8} -(-\frac{4}{3} )= -\frac{5}{8}^{(3} + \frac{4}{3}^{(8} = \frac{-15+32}{24}= \frac{17}{24}$

3 0

3 years ago

Evaluate. (4/5)3 A.64/125B.4/125C.64/5D.12/5