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3 years ago

What are the missing angle measures in triangle ABC?

Mathematics

2 answers:

Finger [1]3 years ago

5 0

we know that

In the right triangle ABC

∠ $A+$ ∠ $B=90$ ------> by complementary angles

Step $1$

Find the measure of angle B

we know that

$tan\ B=\frac{opposite\ side\ angle\ B}{adjacent\ side\ angle\ B}$

in this problem

$opposite\ side\ angle\ B=7in\\ adjacent\ side\ angle\ B=5in$

$tan\ B=\frac{7}{5} \\ \\ B=arc\ tan\frac{7}{5} \\ \\ B=54.5\ degrees$

Step $2$

Find the measure of angle A

$A+B=90\\ A=90-B\\ A=90-54.5\\ A=35.5\ degrees$

therefore

the answer is the option

35.5° and 54.5°

RideAnS [48]3 years ago

3 0

35.5° and 54.5°

solve though tangent

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Fernando followed two diagonal paths, Paths 1 and 2, to get from his house, F, to a neighborhood corner store, C, as shown below

aleksandrvk [35]

Answer:

42 meters

Step-by-step explanation:

Given

See attachment for complete question

Required

Calculate distance FC

FC is calculated as:

$FC = Path\ 1 + Path\ 2$

Where

$Path\ 1 = FB$

$Path\ 2 = BC$

Considering $\triangle FEB$ , we have:

$FB^2 = FE^2 + BE^2$ --- Pythagoras theorem

Where

$FE = FD - BA$

$FE = 22m - 15m$

$FE = 7m$

and

$BE = CD - CA$

$BE = 32m - 8m$

$BE = 24m$

So:

$FB^2 = FE^2 + BE^2$

$FB^2 = 7^2 +24^2$

$FB^2 = 49 +576$

$FB^2 = 625$

Take square roots of both sides

$FB = 25$

So:

$Path\ 1 = 25$

Considering $\triangle BAC$ , we have:

$BC^2 = BA^2 + AC^2$ --- Pythagoras theorem

Where:

$BA = 15$ and $AC = 8$

So, we have:

$BC^2 = 15^2 + 8^2$

$BC^2 = 225 + 64$

$BC^2 = 289$

Take square roots of both sides

$BC = 17$

So;

$Path\ 2= 17$

Recall that:

$FC = Path\ 1 + Path\ 2$

$FC = 25 + 17$

$FC = 42$

6 0

3 years ago

Y = 2x + 3 y = -2x + 15 Can you please explain how to get the answer.

-Dominant- [34]

Answer:

$x = 3$ and $y = 9$

Step-by-step explanation:

Given:

$y = 2x + 3$ .......................... equation i

$y = -2x + 15$ ........................ equation ii

since y is equals to the two functions , we can equate the two values of y . That is , equate equation i and ii , we have

$2x + 3 = -2x + 15$

Add $2x$ to both sides , we have

$2x + 2x + 3 = -2x + 2x + 15$

$4x + 3 = 15$

subtract 3 from both sides , we have

$4x = 12$

divide both sides by 4 , then

$x = 3$

substitute $x = 3$ into equation i to get the value of y , that is

$y = 2(3) +3$

$y = 6 + 3$

$y = 9$

Therefore :

$x = 3$ and $y = 9$

4 0

3 years ago

Read 2 more answers

the numerator of a fraction is 2 less than its denominator. when both numerator and denominator are increased by 3, the fraction

Dmitriy789 [7]

First denominator -- x
first numerator ---- x-2 

new denominator -- x+3 
new numerator ---- x+1 

(x-2)/x + 3/20 = (x+1)/(x+3) 
times 20x(x+3) , the LCD 
20(x+3)(x+1) + 3x(x+3) = 20x(x+1) 
expanding and simplifying gave me 
x^2 + 3x - 40 = 0 
(x-5)(x+8) = 0 
x = 5 or x=-8 

if x=5, the original fraction was 3/5 
if x=-8 the original fraction was -10/-8 or 5/4 

check for 3/5 , new fraction would be 6/8 or 3/4 
3/5 + 3/20 = 12/20 + 3/20 = 15/20 = 3/4 

but for 5/4, new fraction would be 8/7 
5/4 + 3/20 = 28/20 = 7/5 ≠ 8/7 
BUT, if we take the unsimplified fraction -10/-8 , new fraction would be -7/-5 = 7/5 

So the original fraction would be 3/5 for sure, but 
also the unsimplified fraction -10/-8

7 0

3 years ago

Read 2 more answers

the empire stat building in new york city is 1454 feet tall a model building is 24 inches tall what is the ratio of the model to

Blizzard [7]

I believe the answer is 6

6 0

3 years ago

A research report describing the results from a repeated-measures t test states that "t(22) = 1.71, p > .05."

Aleonysh [2.5K]

Answer:

b) Fail to reject the null hypothesis with a sample of n = 23 participants

Step-by-step explanation:

Hello!

A "Repeated-measures t-test" is also known as "paired sample t-test" In this type of test you have only one sample and you measure two variables of interest to each experimental unit. Since both study variables are measured in the same units they are said to be dependent.

The most common example of this type of test is the "before-after treatment" experiment.

The degrees of freedom of this experiment are

, so if the test was conducted under a t₂₂ distribution, then the sample size was n= 23 experimental units. Remember if you use the p-value approach, to make a decision over the null hypothesis you have to compare it to the level of significance following the decision rule:

If the p-value ≤ α, you reject the null hypothesis.

If the p-value > α, you do not reject the null hypothesis.

In this example is specified that the p-value is greater than the level of significance, then the decision is to not reject the null hypothesis.

With all this in consideration, the correct option is b)

U hope you have a SUPER day!

6 0

3 years ago