Triangle ABC has coordinates A(0, 1), B(0, 2), and C(3, 2). If ΔABC ≅ ΔEDF, what is the measure of DF?

Answer:

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\cos A = \frac{1}{2}[/tex]

Required

Determine [tex]\cos(\frac{1}{2}A)[/tex]

To do this, we make use of the following identity

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}[/tex]

Substitute: [tex]\cos A = \frac{1}{2}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}[/tex]

Solve the numerator

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}[/tex]

Rewrite as:

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}[/tex]

Take square roots

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]

Answer:

216 degrees.

Step-by-step explanation:

put it through the formula and set the formula equal to 6/5 pi. then solve.

Answer:

 65 in

Step-by-step explanation:

Given:

In triangle ABC, a=74.1, b= 60.8, c=114.2.

To find:

The measure of angle C.

Solution:

According to the Law of cosine:

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

Substituting [tex]a=74.1,b= 60.8,c=114.2[/tex], we get

[tex]\cos C=\dfrac{(74.1)^2+(60.8)^2-(114.2)^2}{2(74.1)(60.8)}[/tex]

[tex]\cos C=\dfrac{5490.81+3696.64-13041.64}{9010.56}[/tex]

[tex]\cos C=\dfrac{-3854.19}{9010.56}[/tex]

[tex]\cos C=-0.42774145[/tex]

Taking cos inverse on both sides, we get

[tex]C=\cos^{-1}{-0.42774145}[/tex]

[tex]C=115.324312[/tex]

[tex]C=115.3^\circ[/tex]

Therefore, the correct option is d.

Answer: 16 hours

Step-by-step explanation:

Given

Carla earns [tex]\$5[/tex] for each hour she works

Last week she earned $148 total including [tex]\$68[/tex] tip

So, the sum of hourly income and must be equal to the total money earned

Suppose she works for [tex]x[/tex] hours

[tex]\Rightarrow 5x+68=148[/tex]

[tex]\Rightarrow 5x=148-68\\\Rightarrow 5x=80\\\Rightarrow x=16\ \text{hours}[/tex]

Thus, she works 16 hours last week

Answer:

($42 × 7)  - ($8.25 × 8)

Step-by-step explanation:

Given that

Mike saves $42 a week for 7 weeks

And, his 8 day vacation, he plans to spend $8.25 each day

We need to find out the expression of how much he would have left

So,

Since the amount $42 is for a week

So for 7 weeks, it would be

= $42 × 7

And, he spends $8.25 each day,

And, for 8 days, it would be

= $8.25 × 8

So, the expression is

= ($42 × 7)  - ($8.25 × 8)

Answer

A

Step-by-step explanation:

Answer:

hope this helps you out good luck

Answer:

The roots are x=2, 4

Step-by-step explanation:

The roots of the parabola are where the graph crosses the x axis .

The graph crosses the x axis at x=2 and x=4

The roots are x=2, 4

Answer:

a

Step-by-step explanation:

bc look

Answer: 24

Step-by-step explanation:

Given

Simra has an 8-carat diamond

She cuts small pieces of [tex]\frac{1}{3}[/tex] carat

Suppose she cuts x pieces of diamond

[tex]\therefore x=\dfrac{8}{\frac{1}{3}}\\\\\Rightarrow x=8\times 3\\\Rightarrow x=24[/tex]

She has now 24 pieces of diamond.

Answer:

B) 10 cm

Step-by-step explanation: since DC scaled up to 10 cm and they were both originally 6cm, RU would be 10cm.

Answer: they both have four sides (quadrilateral)

Step-by-step explanation:

Answer:

Quarderlaterals with reflecting (or parrel) sides of the same length.

Step-by-step explanation:

Squares always have 4 equal sides

Parrallegrams always have two sides that are parrel to each other that are the same lenghth.

Answer:

red = y=(x+5)/4 -1

Step-by-step explanation:

https://www.emathhelp.net/calculators/algebra-2/parabola-calculator/?ft=vp&vx=-5&vy=-1&px=-7&py=0&ppdir=x

use this very good calculator

Answer:

p - 7 = 42

Step-by-step explanation:

"Less than" might make you think of the  <  sign, but that's a mistake.  The expression  7 < p = 42  makes no sense!  In fact, that would say, "7 is less than p and p = 42."

To find 7 less than a number, you subtract 7 from the number.  You start with the number, then subtract 7.

p - 7 = 42

Answer: B

Step-by-step explanation:

the formula for area of a triangle is base times height divided by 2

to get the base do 12.3 x 2 = 24.6

24.6 x 25.6 = 629.76

629.76/2 = 314.88

the answer would be B

(sorry for saying the answer was A at first, i forgot to find the full base)

Answer:

B. 314.9m

Step-by-step explanation:

First, let's take a look at the formula of a triangle.

A=[tex]\frac{1}{2}[/tex](b * h) ALSO WRITTEN AS- A= [tex]\frac{(b*h)}{2}[/tex].

So, as you can see, there is only half the base provided. To get the other half, just multiply it by 2. You get 24.6m as the base.

The height is provided. It's 25.6m. Plug in your base and height values and slove.

A=[tex]\frac{24.6m * 25.6m}{2}[/tex]

A= [tex]\frac{629.76}{2}[/tex]

A= 314.88m

You then round to the nearest tenth.

The final answer is A=314.9m.

Answer:

d) [tex]\frac{9\pi }{4}[/tex]

Step-by-step explanation:

[tex]\frac{9\pi }{4} = 2\pi + \frac{\pi }{4}[/tex]

The correct options are a and d because -7pi/4 and 9pi/4 are the required angles.

Important infromation:

The angles [tex]\theta\pm 2n\pi [/tex] represent the same point on the unit circle as [tex]\theta[/tex].

It means,  [tex]\dfrac{\pi}{4}\pm 2n\pi [/tex] represents the same point on the unit circle as [tex]\dfrac{\pi}{4}[/tex].

The required angles are:

[tex]\left\{...,\dfrac{\pi}{4}-4\pi,\dfrac{\pi}{4}-2\pi, \dfrac{\pi}{4},\dfrac{\pi}{4}+2\pi,\dfrac{\pi}{4}+4\pi,...\right\}[/tex]

[tex]\left\{...,-\dfrac{15\pi}{4},-\dfrac{7\pi}{4}, \dfrac{\pi}{4},\dfrac{9\pi}{4},\dfrac{17\pi}{4},...\right\}[/tex]

Therefore, the correct options are a and d.

Find out more about 'Angles' here:

https://brainly.com/question/23475646

Answer:

Obtuse triangle.

Step-by-step explanation:

A obtuse triangle has one angle that is larger than 90 degrees. There is a angle with 95 degrees.

Answer:

c = 25

Step-by-step explanation:

First, you can divide by 18 on both sides:

18 (c - 19) = 108

÷ 18             ÷18

c - 19 = 6

To isolate the variable c, you can add 19 on both sides:

c - 19 = 6

  +19   +19

c = 25

Answer:

c= 25

Step-by-step explanation:

108/18 = 6

6 +19 = 25

Answer: $3204.06

Step-by-step explanation:

Here's the complete question:

Arnetta's monthly gross pay is $4,200. Federal withholding is 16.05% of her pay. Her other deductions total $321.30. Find her net pay.

First, we calculate the Federal witholding which will be:

= 16.05% × $4200

= 0.1605 × $4200

= $674.10

The total deduction will now be:

= $674.10 + $321.30

= $995.40

The net pay will now be:

= Gross pay - Total deductions

= $4,200 - $995.40

= $3204.06

Therefore, Arnetta’s net pay is $3204.06

Given:

The logarithmic expression is:

[tex]\log_718[/tex]

To find:

The equivalent expression of given expression by using change-of-base formula.

Solution:

The change-of-base formula is:

[tex]\log_ba=\dfrac{\log_ca}{\log_cb}[/tex]

The given expression is:

[tex]\log_718[/tex]

Using the change-of-base formula, we get

[tex]\log_718=\dfrac{\log_c18}{\log_c7}[/tex]

Where, is a constant and c>0.

Let [tex]c=10[/tex], then

[tex]\log_718=\dfrac{\log_{10}18}{\log_{10}7}[/tex]

Therefore, the correct option is a.

Answer:

answer is 52.5

Step-by-step explanation:

hope it helps

Answer:

361 tiles

Step-by-step explanation:

Answer:

361 1-ft square tiles.

Step-by-step explanation:

The area of the room is a square. It has the same length on each side.

To find how many square tiles you need to cover the floor of the room you need to find the area.

Squares are easy to find the area of because you only need to multiply both sides by each other.

19x19=361

To multiply easier, you can 19 by 10 which equals 190.

Then you can add.

190+190

100+100=200

90+90=180

200+180=380

380-19=361

Answer:

I think it's 886.7

Step-by-step explanation:

hope this helps sorry if incorrect have a good rest of your day/night :) ❤

Answer:

The answer is B. 9.7

Step-by-step explanation:

sin 14°=x/40

=> sin 14° X 40 = x

∴ x = 9.67≈ 9.7

Answer:

x = -0.8 and 10.8

Step-by-step explanation:

Given the equation x2 – 10x – 8= 0

Using the general formula

x = -b±√b²-4ac/2a

x = -(-10)±√(-10)²-4(1)(-8)/2(1)

x = 10±√100+32/2

x =10±√132/2

x = 10±11.489/2

x = 10-11.489/2 and 10+11.489/2

x = -1.489/2 and 21.489/2

x = -0.8 and 10.8