Mark the angles and sides of each pair of triangles to indicate that they are congruent

Answers

Answer 1

Answer:

The Corresponding angles and Corresponding sides are shown below,

$\angle RWX=\angle VXW\n\n\angle RXW=\angle VWX\n\n\angle V=\angle R$ and $RW=VX\n\nRX=VW\n\nWX=WX$

Congruent triangles :

Two triangles are said to be congruent, when corresponding sides and corresponding angles of both triangles are equal.

Given that, triangles WXV and XWR are congruent. so that corresponding sides and angles of these triangles are also equal.

Corresponding angles are shown below,

$\angle RWX=\angle VXW\n\n\angle RXW=\angle VWX\n\n\angle V=\angle R$

Corresponding sides are shown below,

$RW=VX\n\nRX=VW\n\nWX=WX$

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Answer 2

Answer: using asa you find that wx=xw and then angle rwx is equal to angle wxv bc of alternate interior angles and then angle xwv is equal to angle rxw also bc of alt int angles

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Does anyone know the answer

A pencil box and a notebook together cost $6.28 the notebook cost $0.70 more than the pencil box . How much does the notebook cost?

Answers

The cost of notebook is $3.49.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the cost of pencil box be x

Let the cost of notebook be y

Total cost = $6.28

⇒ $x+y = 6.28 ----- (1)$

The notebook cost $0.70 more than the pencil box,

⇒ $y=x+0.70 ----- (2)$

Now substitute equation 2 in equation 1,

⇒ $x+x+0.70=6.28$

⇒ $2x=6.28-0.70$

⇒ $x=(5.58)/(2)$

⇒ $x=2.79$

∴ $y=6.28-2.79$

⇒ $y=3.49$

Hence we can conclude that the cost of notebook is $3.49.

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Answer:

the note book costs $5.58

Step-by-step explanation:

you take 6.28 - 0.70

hope this helps ;)

You and two friends are having dinner. The bill is $120. If you split it evenly, how much do you have to pay?

Answers

If you divide 120$ by 2 people it equals to 60$ so each person has to pay 60$

Final answer:

The question pertains to Mathematics, asking how to evenly split a bill. In this case, $120 is divided by three (you and your two friends), resulting in each person paying $40.

Explanation:

The subject of this question is Mathematics, specifically a calculation problem. You are faced with the scenario of splitting a dinner bill evenly with your friends. The bill comes to a total of $120 and you need to split it amongst three people: yourself and two friends.

To calculate this, you simply need to divide the total amount of the bill by the number of people. So, $120 divided by 3 equals $40. Thus, each person will pay $40 to cover the total cost of the meal.

In conclusion, when you divide any amount equally amongst a group of people, you are performing a mathematic operation known as division. In this question, you divide the total cost of the dinner by the number of people to find out how much each person will have to pay. In this case, each person will pay $40.

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A survey found that women’s heights are normally distributed with mean 63.8 in and a standard deviation 2.3 in. A branch of the military requires women’s heights to be between 58 in and 80 in.a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

The percentage of women who meet the height requirement is __%.

For the new height requirements, this branch of the military requires women’s heights to be at least __ in and at most __ in.

Answers

Answer:

a) 99.41% of women meeting the height requirement. There are not many women being denied the opportunity to join this branch of the military because they are too short or too tall.

b) The new requirement is between 58.441 in and 68.515 in.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 63.8, \sigma = 2.3$

A branch of the military requires women’s heights to be between 58 in and 80 in.

a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?

This probability is the pvalue of Z when X = 80 subtracted by the pvalue of Z when X = 58.

If the probability that a woman is accepted on the military is lower than 5%, we say that a woman being accepted into the military is unlikely.

X = 80

$Z = (X - \mu)/(\sigma)$

$Z = (80 - 63.8)/(2.3)$

$Z = 7.04$

$Z = 7.04$ has a pvalue of 1.

X = 58

$Z = (X - \mu)/(\sigma)$

$Z = (58 - 63.8)/(2.3)$

$Z = -2.52$

$Z = -2.52$ has a pvalue of 0.0059

So there is a 1-0.0059 = 0.9941 = 99.41% of women meeting the height requirement. There are not many women being denied the opportunity to join this branch of the military because they are too short or too tall.

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

Tallest 2%: X when Z has a pvalue of 0.98. So X when $Z = 2.05$

$Z = (X - \mu)/(\sigma)$

$2.05 = (X - 63.8)/(2.3)$

$X - 63.8 = 2.3*2.05$

$X = 68.515$

Shortest 1%: X when Z has a pvalue of 0.01. So X when $Z = -2.33$

$Z = (X - \mu)/(\sigma)$

$-2.33 = (X - 63.8)/(2.3)$

$X - 63.8 = -2.33*2.3$

$X = 58.441$

The new requirement is between 58.441 in and 68.515 in.

Base on the questions, which is asking to many questions, ans the following would be the answers,
A. the women that fall between 58 and 80 inches tall would have a probability of 99.416%,
B. the new heights would 58,45 inches and 68,52 inches.

I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarifications

Given x varies inversely with y and xy = 2, what is the value of x when y = 1?a) -1

b) 1/2

c)1

d) 2

Answers

Answer is (d).

Let's take the constant as K.
x=K. (1/y)----(1)'
K= xy
so; according to the data given above K=2.

Let's substitute K=2 & y=1 to ----(1)'

x=2x (1/1)
x= 2×1
so x = 2... :)

Which statement about the solution to the following system of equations is true?3x - 2y = 4
-6x + 4y = -8

A) There is no solution because the equation represents the same line
B) There is no solution because the equations have the same slope
C) There are infinitely many solutions because the lines have the same slope and different y-intercepts.
D) There are infinitely many solutions because the equations represent the same line

Answers

Let's solve and find out.

3x - 2y = 4
-6x + 4y = -8

To solve by elimination, multiply the top equation by 2 to cancel out y-terms.

2(3x - 2y = 4)
6x - 4y = 8

Now, add the equations together.

6x - 4y = 8
-6x + 4y = -8
+___________
0 - 0 = 0

Since we get that 0 = 0, this system has infinitely many solutions. Only graphs that represent the same line have infinitely many solutions, so...

Answer:
D) There are infinitely many solutions because the equations represent the same line

Determine the first expression to evaluate in each problem (3+3)+6÷3+6

Answers

To know what to do first in a math problem we look to order of operations... PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction. So to begin we look for parentheses... do we have any? Why, yes, yes we do. Let's work!

(3+3) + 6 / 3 + 6 =

Add 3+3 in the parentheses. Since there is nothing else, the parentheses can go away.

6 + 6 / 3 + 6 =

Now, any exponents? Nope... Multiplication? Nope... division? Yes! Let's go!

6 + 2 + 6 =

Now all we have left is addition... Go for it!

8 + 6 = 14

Done!

Time for the Order of Operations!
PEMDAS, its easy dont worry!
P for Parenthesis
E for Exponents
M/D for Multiplication/Division
A/S for Addition/Subtraction
we should always follow the order of operations!

(3+3)+6÷3+6
1st step: We've got parenthesis:
(3+3)=(6) done
2nd step: Check for exponents, Looks like we dont have them!
3rd step: M/D? no multiplication, But we do have division.
(6)+6 ÷ 3 + 6
6 + 2 + 6
4th and last step: Finally, we are going to end this!
A/S? Yes!!!! Addition, No Subtraction!
6 + 2 + 6 = 14

Final Answer: 14

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