The values of x, y and z are 5, 18 and 12 using the congruent triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
In congruent triangles all the sides are equal, with respect to the other triangle.
Calculation:Given that ΔUVW≅ΔTSR.
We can see that in TSR triangle the lengths of TR and TS are given as 50 and 53 now the remaining side RS is 5y-33 as we know that both triangles are similar we compare side RS with side VW
i.e..,
5y-33 = 57
5y = 90
y = 18
So we can now compare vertices vertex V is vertex R , vertex W is vertex S and vertex U is vertex T.
So equating the sides of triangles we get,
12x-7 = 53 and 3z+14 = 50
12x = 60 3z = 36
x= 5 z = 12
The values of x, y and z are 5, 18 and 12 using the similar triangles properties and triangles sum properties.
To know more about triangles, visit:
brainly.com/question/1058720
#SPJ1
Use the figure to decide the type of angle that describes 6 and 4
Answer:
Explanation:
A gas station is 28 kilometers away. How far is the gas station in miles
Answer:
17.394
Step-by-step explanation:
conversion
28 kilometers to miles
1 kilometer = 0.621371 miles
0.621371 miles * 28 kilometers
\(=\fbox{17.3984 miles}\)
3 by 5 ratio 8 by 9
Answer:
5:24
Step-by-step explanation:
Given data
3 by 5
=3*5
=15
8 by 9
=8*9
=72
Hence the ratio is
15:72
Equivalent to
5:24
The graph of a line has a slope of 3 and passes through the point (-4,-5).
What is the equation of the line in point-slope form?
Answer:
3x - y + 7 = 0
Step-by-step explanation:
The given point is , ( -4 , -5) and the slope is 3. The point slope form is ,
=> y - y₁ = m( x - x₁)
=> y - (-5) = 3 { x - (-4) }
=> y +5 = 3( x + 4 )
=> y + 5 = 3x + 12
=> 3x - y + 12 - 5 = 0
=> 3x - y +7 = 0
Hence the equation of the line is 3x - y + 7 = 0 .McKenna is volunteering in the media center at school. She has 125 books that need to go on the shelves. Each shelf holds 25 books.
Which expression can be used to figure out how many shelves will be needed to hold all of the books?
A) 125 ÷ 25
B) 125 x 25
Eliminate
C) 125 – 25
D) 125 + 25
Answer:
A would be the answer this is because we need to fit 125 book in shelves that fit 25 books so it would be division
Answer: the answer would be a
Step-by-step explanation:
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
Read more on graphs:
https://brainly.com/question/19040584
#SPJ1
What is the weight of a 35.01-carat diamond in grams and ounces? Use 1 carat = 0.2 gram, 1 carat = 3.086 grains, and 1 ounce = 437.5 grains.
The weight of a 35.01-carat diamond is
(Round to two decimal places as needed.)
The weight of a 35.01-carat diamond is oz.
The weight of a 35.01-carat diamond in grams and ounces
7.002gram0.247 ouncesHow to determine the weight of a 35.01-carat diamond in grams and ouncesInformation given in the question include
1 carat = 0.2 gram,
1 carat = 3.086 grains,
1 ounce = 437.5 grains.
The conversion of the weight units using the given variables can bbe done as follows
1 carat = 0.2 gram
35.01-carat diamond = ?
cross multiplying gives
1 * ? = 35.01 * 0.2
? = 7.002gram
1 carat = 3.086 grains
35.01-carat diamond = ?
cross multiplying gives
1 * ? = 35.01 * 3.086
? = 108.041 grains
That is 35.01-carat diamond = 108.041 grains
1 ounce = 437.5 grains
? = 108.041 grains
cross multiplying gives
437.5 * ? = 108.041 * 1
? = 108.041 /437.5
? = 0.247 ounces
Learn more on conversion of diamond weights at:
https://brainly.com/question/2134107
#SPJ1
QUESTION : find the measure of angle A
Hint : solve for x then replace in angle A
please help !
Angle A should be 40 since x=10
Answer:
X=10°
Step-by-step explanation:
on the picture
if it's helpful ❤❤❤❤
THANK YOU.
Please help me will mark Brainliest
if the earthquake has stronger magnitude what does it mean
Answer:
Step-by-step explanation:
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.
A checking account's balance is -$275.20. An overdraft fee of $18.00 is applied to the account. Suppose $325.00 is deposited into the account. Which statements are correct?
A) After the deposit, the balance is $31.80.
B) After the deposit, the balance is $60.02.
C) After the deposit, the balance is -$49.80.
D) After applying the overdraft fee, the balance is -$293.20
E) After applying the overdraft fee, the balance is -$257.20.
Answer
the answers are A and D
Step-by-step explanation:
will you please give me brainiest
Answer:
A) After the deposit, the balance is $31.80.
D) After applying the overdraft fee, the balance is -$293.20
Step-by-step explanation:
How are these two scenarios different: 3 people went to the zoo and tickets cost
$15 each in comparison to: 3 people go to the carnival, where tickets cost $15
each and parking costs $10.*
FOR BRAINLIST!!!!
Write the absolute value of each number. 1. -2/8 2. 3 ¾
Jo has a 10 GB monthly cell phone plan. Jo has used 8 GB in the first 10 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answer:
Step-by-step explanation:
1st 10 days - 8 GB
2nd 10 days - 8 GB
3rd 10 days - 8 GB
________________
30 days - 24 GB
A triangular pane of glass has a height of 32 inches and an area of 352 square inches. What is the length of the base of the pane?
The required length of the base of the triangular pane of glass is 22 inches.
We know that the formula for the area of a triangle is:
Area = 1/2 * base * height
We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:
352 = 1/2 * base * 32
Multiplying both sides by 2 and dividing by 32, we get:
base = 22
Therefore, the length of the base of the triangular pane of glass is 22 inches.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
the linear equation y=1/2x+1 is represented by the graphed line. A second linear equation is represented by the data in the table. X(-2,0,2,4) Y(7,6,5,4) .In which square is the solution located
Answer:
Correct Answer is D
Step-by-step explanation:
Answer:
Yeah it's "D"
Step-by-step explanation:
Have a Jocular Day
During one year, the population of a town increased by 2% but during the next year it diminished by 2%. If at the end of the second year the population was 6,25,000, what was the population at the beginning?
Answer:
614,818.71
Step-by-step explanation:
hope it helps
Answer:
6,25,250
Step-by-step explanation:
let initaial population be "x"
after increasing by 2%
x'=x+x*2%
x'=102x/100
x' is decreased by 2% and population reached 625000,so,
625000=102x/100-2%*102x/100
625000=102x/100-51x/2500
625000=2499x/2500
2499x=625000*2500
x=1562500000/2499
x=625250.1
complete population is only counted so,
x=625250
initial population =625250
HELLPP 8 MINUTES LEFT!!!!!!!!For the following graph, identify the intervals of increase
ANSWERS IN PICTUREEEEE
Answer:
it is b
Step-by-step explanation:
On a map, the scale shown is 1 inch : 5 miles. If
a wildlife refuge is 50 square miles, what is the
area of the refuge on the map?
Use the proportion to solve for x.
1 in. 2
25 mi2
x in. ²
50 mi²
Cross
multiplication
can help!
=
The area of the wildlife refuge is [?] square
inches on the map.
Enter
Answer:
Step-by-step explanation:
6
what is the mean,median,mode and range or the data set 4, 7, 3, 7, 7, 12,
Answer:
the mean is6.7 the mode is 7 and the range is 9
Step-by-step explanation:
Natalie borrowed money from her parents to pay for a trip.
Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed.
The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks.
Number of Weeks Natalie Has Paid,
�
w
Amount Natalie Still Owes,
�
d
0
0
$
180
$180
2
2
$
162
$162
4
4
$
144
$144
6
6
$
126
$126
8
8
$
108
$108
Part A
How much does Natalie pay her parents each week?
$
per week
Part B
Write a function that shows the relationship between the amount Natalie still owes,
�
d, and the number of weeks she has paid,
�
w.
Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
We can see that Natalie is reducing the amount she owes by $18 every two weeks.
Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.
This means that after n weeks, the amount she still owes is:
$180 - $18n
Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:
$180 - P
After two weeks, she will owe:
($180 - P) - P = $180 - 2P
After four weeks, she will owe:
($180 - 2P) - P - P = $180 - 4P
After six weeks, she will owe:
($180 - 4P) - P - P = $180 - 6P
And after eight weeks, she will owe:
($180 - 6P) - P - P = $180 - 8P
We can set up an equation using the information we have:
$180 - 8P = $108
Solving for P, we get:
P = $9
Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
To learn more about the linear equation;
https://brainly.com/question/29739212
#SPJ1
The complete question:
Natalie borrowed money from her parents to pay for a trip. Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed. The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?
Week 0 = $180
Week 2 = $162
Weeks 4 = $144
Week 6 = $126
Week 8 = $108
Show the algorithm/abstract strategy to justify the 3/5?
The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.
To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.
Algorithm/Abstract Strategy:
Start with the numerator, which is 3.
Identify the denominator, which is 5.
Interpret the fraction as a ratio or comparison between the numerator and denominator.
Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).
Perform the division: 3 ÷ 5.
Simplify the division to its simplest form, if necessary.
The result of the division, in this case, is the decimal representation of the fraction.
If required, convert the decimal representation to a percentage or any other desired form.
For example, if we perform the division 3 ÷ 5, the result is 0.6.
So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.
For similar question on algorithm/abstract strategy.
https://brainly.com/question/31332020
#SPJ8
Milan made a shirt using 5/8 yards of yellow fabric and 1/4 yards of green fabric. How many more yards of yellow fabric did Milan use?
Answer:
Milan used \(\frac{3}{8}\) more yards of yellow fabric than green fabric.
Step-by-step explanation:
The goal is to subtract 1/4 from 5/8.
\(\frac{5}{8}-\frac{1}{4}\) This is your original equation. To subtract, the fractions must
have common denominators (the same number on the bottom.
Therefore, you must find the LCM (least common multiple) of 4
and 8, which is 8. Convert 1/4 to 2/8 by multiplying the
numerator and denominator by 2.
\(\frac{5}{8}-\frac{2}{8}\) Now, subtract the numerators. 5-2=3. Leave the denominator.
\(\frac{3}{8}\)
I don’t understand this can someone help me
Answer:
\( \sqrt[3]{432 {x}^{5} } \\ \\ 432 = 6 \times 6 \times 6 \times 2 = {6}^{3} \times 2 \\ {x}^{5} = x \times x \times x \times x \times x = {x}^{3} \times {x}^{2} \\ \\ \sqrt[3]{432 {x}^{5} } = 6x \sqrt[3]{2 {x}^{2} } \)
I hope I helped you^_^
Solve the given equation.
8 to the power of x/ 4= 16
Answer:
x=8
.....................
You may need to use the appropriate technology to answer this question. The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.
Quality of Management Reputation of Company
Excellent Good Fair
Excellent 40 25 8
Good 35 35 10
Fair 25 10 12
Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.
a. State the null and alternative hypotheses.
b. Find the value of the test statistic. (Round your answer to three decimal places.)
c. Find the p-value. (Round your answer to four decimal places.)
Answer:
Step-by-step explanation:
The null and alternative hypothesis:
\(H_o \text{: Quality of management and reputation of company are independent}\)
\(H_a \text{: Quality of management is not independent of the reputation of company }\)
The observed values:
Excellent Good Fair Total
Excellent 40 25 8 73
Good 35 35 10 80
Fair 25 10 12 47
Total 100 70 30 200
The expected values = (Row total/column total)/grand total)
Excellent Good Fair
Excellent 36.5 25.55 10.95
Good 40 28 12
Fair 23.5 16.45 7.05
O E (O - E)²/E
40 36.5 0.3356
35 40 0.6250
25 23.5 0.0957
25 25.55 0.0118
35 28 1.7500
10 16.45 2.5290
8 10.95 0.7947
10 12 0.3333
12 7.05 3.4755
9.951
\(X^2 = \sum \dfrac{(O-E)^2}{E} \\ \\ \mathbf{X^2 = 9.951}\)
Degree of freedom \(df = (r-1)(c-1)\)
\(df = (3 - 1 ) (3 - 1)\)
\(df = (2)(2)\)
\(df = 4\)
Using Excel formula =CHIDIST(x²,d.f)
The P-value = 0.0413
At a local college, 61 of the male students are smokers and 549 are non-smokers. Of the female students, 156 are smokers and 444 are non-smokers. A male
student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Do not round your answer. (If necessary, consult a list of formulas.)
The probability of randomly selecting a male student and female student are non-smokers is 0.6771
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
According to the given question:
Number of male students are smokers = 61
Number of male students are non smokers = 549
Total number of male students = 610
Number of female students are smokers = 156
Number of female students are non smokers = 444
Total number of female students = 600
Probability that both are non smokers is given by
P (non-smoker males) x P (non-smoker females)
= \(\frac{549}{610} . \frac{444}{600}\)
= 0.915 x 0.74
= 0.6771
Therefore the probability that both male and female are non-smokers is 0.6771.
To know more about probability visit
https://brainly.com/question/16887898
#SPJ1
3 tickets to the museum cost $12.75. At this rate, what is the cost of:
A. 1 ticket?
B. 5 tickets?
Answer:
1 ticket - $4.25
5 tickets - $21.25
Step-by-step explanation:
12.75/3=4.25 which is one ticket then take the price of one ticket and multiply it by 5, 4.25*5=21.25.
9 = -4+u
what’s the answer
Steps to solve:
9 = -4 + u
~Add 4 to both sides
13 = u
Best of Luck!
I need the area choices below
Answer:
Area of the shape is 244.98cm² is B
Step-by-step explanation:
Area of shape=Area of semi circle+Area of trapezoid
A=1/2 πr² + 1/2(a+b)h
A=1/2×3.142×7² + 1/2(14+18)10.5
A=1/2×3.142×49 + 1/2×32×10.5
A=76.98+168
A=76.98+168
A=244.98cm²