Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS.
Figures are not drawn to scale.
Answers
The measure of side RS is 7.6 units .
Similar quadrilaterals:
A quadrilateral's interior angles add up to 360 degrees. Two quadrilaterals are said to be identical when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).
The corresponding angles of similar quadrilaterals should be equal in accordance with the similarity of quadrilaterals. Since we know that every angle in a square is 90 degrees, every matching angle in any two squares will be the same.
In the given question ,
Quadrilateral MNOP is similar to quadrilateral QRST .
[tex]\frac{ON}{NM} =\frac{RS}{RQ} \\\\\frac{2}{4} = \frac{RS}{15.2} \\\\\frac{1}{2} =\frac{RS}{15.2} \\\\RS=\frac{15.2}{2} \\\\RS=7.6units[/tex]
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Related Questions
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
2.25 inches
4.5 inches
6.75 inches
12.75 inches
Answers
The height of the cylindrical tub of ice cream is 6.75 inches.
What is the surface area of a cylinder?A cylinder is a 3 dimensional shape which has a curved side and two circular surfaces. The total surface area can be determined by the expression;
total surface area of a cylinder = 2πr^2 + 2πrh
where r is the radius of it circular surface, and h is its height.
Considering the given question, we have;
total surface area of a cylinder = 2πr^2 + 2πrh
But total surface area = 183.69 square inches
r = D/2
= 6/ 2
r = 3 inches
Thus,
183.69 = 2*3.14*3^2 + 2*3.14*3*h
= 56.52 + 18.84h
183.69 - 56.52 = 18.84h
127.17 = 18.84h
h = 127.17/ 18.84
= 6.75
The height of the cylindrical tub of ice cream is 6.75 inches.
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Answer: The answer is (C) 6.75
Step-by-step explanation:
The formula for Surface Area is: SA = 2πr^2 + 2πrh
Let's do the first part: 2πr^2
So you need to find the radius, which is half the diameter. 6 is the diameter so half that, and you get 3.
Now, times 3 by itself
3 * 3 = 9
And then times 9 by 2
9 * 2 = 18
And times 18 by pi, 3.14
18 * 3.14 = 56.52
Now that we have our first value, lets move on to the second part of the formula: 2πrh
So we need the diameter, and the question gives us the value of the diameter.
6 is the diameter
so times 6 by pi, 3.14
6 * 3.14 = 18.84h (leave h there because we don't know the height)
Now do this:
183.69 = 56.52 + 18.84h
You cannot add 56.52 and 18.84h because they are not like terms
So take away 56.52 from both sides
56.52 - 56.52 = 0
183.69 - 56.52 = 127.17
Now divide 127.17 by 18.84h
127.17/18.84 = 6.75 inches
Here is proof that my answer is correct. I have a photo of my results and it shows that 6.75 inches is correct. Here is the photo:
Have a an amazing day
Can anyone write the quadratic of the equation in factored form?
Answers
The factored form of the quadratic equation is given as follows:
y = 3(x + 0.6667)(x - 6).
How to obtain the factored form of the quadratic equation?The quadratic equation for this problem is defined as follows:
3x² - 16x - 7 = 5.
3x² - 16x - 12 = 0.
The coefficients are given as follows:
a = 3, b = -16, c = -12.
Hence the discriminant is of:
D = (-16)² - 4(3)(-12)
D = 400.
Then the roots are of:
x = (16 - sqrt(400))/6 = -0.6667.x = (16 + sqrt(400))/6 = 6.Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:
y = 3(x + 0.6667)(x - 6).
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Is -9(k-5+2k-8) and -27k+117 equivalent expressions
Answers
-9(k-5+2k-8) and -27k+117 are equivalent expressions since the solution of -9(k-5+2k-8) = -27k+117.
What are equivalent expressions?Equivalent expressions are algebraic expressions that produce the same answer when being simplified. They are said to be a similar expression for whatsoever process used to solve the expression, either by substitution of values or applying mathematical property, they tend to produce equivalent expressions at the end. The equality sign is used between two algebraic expressions that are said to be equivalent.
Given that:
= -9(k-5+2k-8)
Open brackets
= -9k + 45 - 18k + 72
= -27k + 117
Therefore, we can say -9(k-5+2k-8) and -27k+117 equivalent expressions are equivalent expressions.
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Marvin lives in stormwind city and works as an engineer in the city of ironforge. In the morning, he has 3 33 transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same 3 33 choices for his trip home. If marvin randomly chooses his method of travel in the morning and in the evening, what is the probability that he teleports at least once per day?.
Answers
The probability that he teleports at least once per day is [tex]\frac{5}{9}[/tex].
the Marvin must select one of the three transportation alternatives at random.
The likelihood of selecting any one of the three alternatives is the same since the selection is random.
The likelihood of successful teleportation on the first try is:
[tex]P_t=\frac{1}{3}[/tex]
Consequently, the likelihood that you do not teleport is
q=1-p
q=1-[tex]\frac{1}{3}[/tex]
q=[tex]\frac{2}{3}[/tex]
The likelihood that the Marvin won't teleport when leaving for work and returning from work is as follows:
P=[tex]\frac{2}{3}[/tex]×[tex]\frac{2}{3}[/tex]
P=[tex]\frac{4}{9}[/tex]
As a result, the probability that someone will teleport at least once is:
P=1-[tex]\frac{4}{9}[/tex]
P=[tex]\frac{5}{9}[/tex]
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what are the ordered pairs of the solution for this system of equations f(x) = x^2 -2x+3 ; f(x) = -2x + 12
Answers
You have $4.00 and you need to make copies of a flyer at a store that charges $0.30 per copy. Find the inequality that responds the number of copies you can make. Use c as the variable. What is the maximum number of copies you can afforded to make?
Answers
The required number maximum number of copies can be afforded c < 13.33.
What is inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have $4.00 and you need to make copies of a flyer at a store that charges $0.30 per copy.
Here,
Let the number of copies be c,
According to the question,
0.30c < 4
c < 4/ 0.30
c < 13.33
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\int x^(2)(1)/(\sqrt(x^(2)-4))dx
Answers
The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].
What is integration?Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
The integration equation is given below.
[tex]\begin{aligned} \rm I = \int _1^2 \sqrt{x^2 - 4} \ dx \end{aligned}[/tex]
We know that the formula is given as,
∫√(x² - a²) dx = (x/2)√(x² - a²) + (a² / 2) log [x + √(x² - a²)]
Then by the integration, we can write it as,
[tex]\begin{aligned} \rm I &= \int _1^2 \sqrt{x^2 - 4} \ dx \\\rm I &= \int _1^2 \sqrt{x^2 - 2^2} \dx\\\rm I &= \left [ \dfrac{x}{2}\sqrt{x^2-2^2} + \dfrac{2^2}{2} \log (x + \sqrt{x^2 - 2^2}) \right ]^2_1\\\end{aligned}[/tex]
Simplify the equation further, then we have
I = [(1/2) i√3 + 2 log (1 + 3i)]
The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].
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17. The record low temperature in Missouri was −40°F, set February 13, 1905. The record high temperature of 118°F was set July 14, 1954, in the same city: Warsaw, Missouri. The Missouri mean temperature is 55°F. Determine whether the record high or the record low is closer to the mean temperature than the other record, and how much closer is it? Make sure you show your work to support your answer.
Answers
Answer:
The record high temperature of 118°F is 63°F higher than the mean temperature of 55°F. The record low temperature of -40°F is 95°F lower than the mean temperature of 55°F. The record high temperature of 118°F is closer to the mean temperature than the record low temperature of -40°F by 32°F.
You borrow $200 from a relative for six months. You agree to pay compound interest at
the rate of 1% per month. How much interest will you pay your relative when you return the
money at the end of the six months?
a.
$201.00
c.
$12.30
b.
$11.66
d.
$210.00
Answers
Answer: D (210.00)
Step-by-step explanation:
According to the formula of compound INTEREST this is correct
If 1/5+1/5=a/5 then a=
Answers
Answer: a = 2 because 1 + 1 = 2
Step-by-step explanation:
Maurice has completed 48 pages of the research paper he is writing. That is 80% of the required length of the paper. What is the required length of the paper? The required length of the paper is pages.
Answers
Answer:
We can use the proportion:
48 pages / x = 80% / 100%
where x is the required length of the paper in pages.
First, we can simplify the right-hand side of the equation:
80% / 100% = 0.8
Next, we can solve for x by cross-multiplying:
48 pages / 0.8 = x
x = 60 pages
Therefore, the required length of the paper is 60 pages
Solve. 1. Denver is called the Mile-High City because it is at an altitude of 1 mile. How many feet is this? Can some one please help asap?
Answers
One mile is equal to 5,280 feet. Therefore, to convert the altitude of Denver from miles to feet, we can multiply by 5,280:
1 mile × 5,280 feet/mile = 5,280 feet
So, Denver's altitude of 1 mile is equal to 5,280 feet.
answer the question. if you get it correct ill give it 5 stars and the brainiest.
Answers
(x^2 - 7x - 18)/(x + 2) = x - 9 can be simplified by multiplying both sides of the equation of x + 2. The new equation is x^2 - 7x - 18 = x^2 - 7x - 18. Therefore the equation's solution is all real numbers.
Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05What does Bob conclude? A)Bob gives up on his research becauser=.05 means there is no relationship of any kind between bedrooms and selling price. B) Bob continues his research because even though there is no linear relationship here, there could be a different relationship.
Answers
Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.
Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.
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The graph shows the number of game systems sold
since 2015. Based on this information, which function
best models the number of game systems sold in
millions x years since 2015?
Answers
Step-by-step explanation:
so, for x = 0, y = 30.5
that means the first answer is out.
for x = 1, y = 21.35
so, only
y = 30.5(0.7)^x
can be right.
all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).
and to verify :
30.5 × 0.7¹ = 30.5 × 0.7 = 21.35
correct.
A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were defective. A store clerk generates random numbers to simulate a random sample of this shipment. The clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through 5,000 represent working MP3 players. The results are given.
2,806 623 232 3,955 3,799 657 2,140 262 844 561
Based on this sample, how many of the MP3 players might the clerk predict would be defective?
The manager would expect _________ defective players in the shipment.
Answers
The manager would expect 1000 defective players in the shipment.
How to find the defective members in a sample?A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.
The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.
The results are given AS:
2,806 623 232 3,955 3,799 657 2,140 262 844 561
This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.
( Since the number 232 and 262 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )
Hence, the Probability that the mp3 players were defective is:
P( defective)=2/10=1/5
Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:
P( defective)×5000
= 1/5 × 5000
= 1000.
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Create an imaginary profile for someone who CAN be claimed as a dependent and someone who CANNOT be claimed as a dependent on taxes. Be sure to include their age and at least TWO details that explain why they can or cannot be claimed as a dependent.
Answers
Example: a mother wants to place her child as a dependent, she has to make sure she qualifies and is the right age. The child is 16, is the child the right age? The answer to that is yes. The child has to be under age 19 or 24 if they are a full-time student. The child qualifies to be a dependent for the mother.
2 example: a woman wants to make her spouse a dependent but she has to make sure he qualifies. The spouse is not a U.S citizen so he cannot be a dependent. She must find someone else who can be.
Hal sold a box of 30 books at a yard sale for a total of $62.16. He sold the paperback books for $1.78 each and sold the hardcover books for $2.51 each.
Which system of equations can be used to determine the number of $1.78 paperback books, x, and the number of $2.51 hardcover books, y, that were
sold at the yard sale?
Answers
Answer:
Step-by-step explanation:
Let x be the number of $1.78 paperback books and y be the number of $2.51 hardcover books that were sold. The total number of books is x + y = 30 and the total amount of money earned is $62.16. The cost of the paperback books is x * $1.78 and the cost of the hardcover books is y * $2.51.
So, we have the following system of equations:
x + y = 30 (the total number of books is 30)
x * $1.78 + y * $2.51 = $62.16 (the total amount of money earned is $62.16)
This system of equations can be used to determine the number of $1.78 paperback books and the number of $2.51 hardcover books that were sold at the yard sale.
Below are the dimensions for a US postal office box that you are wrapping as a gift.
Explain how to find the surface area of this box. You may explain using words or numerically.
also there is a 12in 2in and 8in on it
Answers
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Area = length x breadth
To find the surface area of the postal box, we first find the area of each sides of the box and add them together.
Top and bottom area = L x B = 12 x 8 = 96inches² x 2 = 192inches²
Front and back areas = L x B = 12 x 2 = 24inches² x 2 = 48inches²
Area of the sides = L x B = 8 x 2 = 16inches² x 2 = 32inches²
Total surface area will be 192 + 48 + 32 = 272inches²
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What is the standard form for seven squared
Answers
Therefore, after answering the given query, we can state that the as we can multiply it as 7 multiply by 7 = 7*7 = 49.
what is multiply?Multiplication is one of the four matrix multiplication, along with arithmetic, addition, and subtraction. Multiplication in mathematics is the process of repeatedly combining subgroups of the same size. Multiplication is calculated using the formula multiplicand multiplier gives product. multiplicand: Starting number, to be more exact (factor). as a separator, use number two (factor). The result is what remains after splitting both the multiplicand and the multiplier. There are numerous additions necessary when adding numbers. similar to 5 x 4 = 5 x 5 x 5 x 5 = 20. What I did was multiply 5 by 4. Because to this, multiplication is frequently referred to as "doubling."
The standard form for seven squared is 49.
as we can multiply it as 7 multiply by 7 = 7*7 = 49.
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Find the percent of the quantity.
150% of 56 =
Answers
Answer:
84
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
To solve for 150% of 56, we can multiply 56 by 150%.
56 × 150% = 84Therefore, 150% of 56 is 84.
the data set shows the numbers of hours students study the week before the a test. find an interpert the mean absolute deviation of the data.
1, 2, 5,5,5,5,6,7,8,9.
Answers
The answer is 1.6!!!
How old are?
PLEASSEEEEEE HELPPPPP ASAPPP IM SO SORRY BUT THIS IS THE LAST ONE FOR TODAY I THINKK
Solve for x and y
Answers
The value of x and y in the right triangle are as follows:
x = 15√3 units
y = 30 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.
The side x and y can be found using trigonometric ratios,
tan 60° = opposite / adjacent
tan 60° = x / 15
cross multiply
x = 15 tan 60°
x = 15 × √3
x = 15√3 units
Let's find y as follows:
cos 60° = adjacent / hypotenuse
cos 60° = 15 / y
cross multiply
y = 15 / cos 60
y = 15 ÷ 1 / 2
y = 15(2)
y = 30 units
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What is stoichiometry formula?
Answers
Stoichiometry formula is founded on the basis that law of conservation of mass where the total mass of the reactants = total mass of the products.
What is Stoichiometry?This is referred to as the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers.
The stoichiometry of a balanced chemical equation identifies the maximum amount of product that can be obtained. The stoichiometry of a reaction describes the relative amounts of reactants and products in a balanced chemical equation.
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I NEED HELP ASAP Please and Thank You!
Answers
An exponential decay function that shows the relationship between y and t is y = 16,000 (0.74)^t.
What is an exponential decay function?An exponential decay function is one of the two types of exponential functions, including an exponential growth function.
Exponential functions are depicted as y = abˣ, where "a" is a constant, b is the base and x is the variable exponent.
The purchase value of a car = $16,000
Annual decreasing rate in value = 26%
Decayed value after 1 year = 0.74 (1 - 26%)
Let the number of years after the purchase = t
Let the resale value of the car after t years = y
Exponential Function:Resale value after t years, y = 16,000 x (1.074)^t
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How many minutes are in 3 5/12 hours
Answers
Answer:
205
Step-by-step explanation:
3hrs is 180 min
5/12 hours is just 25 min
180+25=205
Answer:
205 minutes
Step-by-step explanation:
*60 minutes = 1 hour
3 x 60 = 180
5/12 x 60 = 5/12 x 60/1 = 300/12 = 25
180 + 25 = 205 minutes
The graph below belongs to which function family?
50
linear
O quadratic
cubic
4
32
+++
2+
1
-10-6-4-2₁
-2+
& A w
2 4 6 8 10 X
Answers
Answer:
Step-by-step explanation: n The graph is of an absolute value function. Step-by-step explanation: For x ≥ 0, the graph is given by. ⇒ x + 2y = 6. ⇒. ⇒ ........ (1).
Missing: 50 32 2₁
Hope that helps:)
A square lawn has an area of 1922 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?
A.43.84 B.21.92 C.62 D.31
Answers
The radius of the circle is 21.92 feet
What is the radius of the circle?From the question, we have the following parameters that can be used in our computation:
A square lawn has an area of 1922 square feet
This means that
Area = 1922
Take the square root of both sides to determine the side length
side length = 43.84
This represents the circle diameter
So, we divide by 2
radius = 21.92
Hence, the radius is 21.92
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Pls help will mark Brainly est pls help
Answers
Step-by-step explanation:
We can find the other point using the axis of symmetry.
The axis of symmetry for a parabola passes through the x coordinate of the vertex.
So our axis of symmetry is x=4, which is a vertical line.
For any point on a parabola curve except the vertex, there will two points that share the same y value. The two x coordinates of those points midpoints should be the axis of symmetry.
So,
If we know (0,-6) and the vertex is 4, let's find the other point
[tex]( \frac{0 + b}{2} = 4[/tex]
[tex]b = 8[/tex]
So our other point is
(8,-6).
So the answer to #1 is we found point (8,-6) by using the axis of symmetry. By reflecting the point (0,-6) about the vertical line x=4, we end up getting the point (8,-6)
To find q, q(x) has the same vertex, so it is (4,10).
We know the axis of symmetry is x=4, we also know the y intercept is 18 so we have point (0,18)
Using the axis of symmetry we will get (8,18).
So the graphs above are the graphs of p and q
The graph facing upwards is q
The graph facing downwards is p.
For #2, you can say we know the vertex is (4,10) and using the y intercept and axis of symmetry we found the other point on the curve.
I don't fully see the table but if the other coordinates have a higher y value, the vertex is a minimum.
Else, of the other coordinates have a lower y value, the vertex is a maximum.
Suppose the account in #3 above paid interest quarterly instead of annually. Find the account balance after 5 years.
Answers
The account with compound interest of 7.2 % quarterly after 5 years is given by A = $ 1,428.75
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after compound interest be represented as A
Now , the equation will be
The initial principal amount = $ 1000
The rate of interest r = 7.2 %
The number of times interest is applied n = 4 ( quarterly )
The number of years b = 5 years
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
A = 1000 ( 1 + 0.072/4 )⁴ˣ⁵
On simplifying the equation , we get
A = 1000 ( 1 + 0.018 )²⁰
On further simplification , we get
A = 1000 ( 1.018 )²⁰
A = $ 1,428.75
Hence , the amount after 5 years is $ 1,428.75
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