Answer: 56.25 = u
Step-by-step explanation:
1) Multiply 3 on both sides to leave u by itself
18.75 = u/3
18.75*3 = u
56.25 = u
Question is down below, match the answer choices with the units.
whichWe define:
• A = original area = 100 sq units,
,• A' = dilated area.
If we dilate a trapezoid in a scale factor k, the area scales as:
[tex]A\rightarrow A^{\prime}=k^2\cdot A\text{.}[/tex]Using the area A = 100 sq units, we have:
[tex]\begin{gathered} A^{\prime}=k^2\cdot100\text{ sq units,} \\ k^2=\frac{A^{\prime}}{100\text{ sq units}}, \\ k=\sqrt[]{\frac{A^{\prime}}{100\text{ sq units}}}\text{.} \end{gathered}[/tex]This formula gives as the scale factor k for witch we must dilate the trapezoid to have an area A'.
1) For A' = 6400 sq units, we have:
[tex]k=\sqrt[]{\frac{6400\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{64}=8.[/tex]2) For A' = 100 sq units, we have:
[tex]k=\sqrt[]{\frac{100\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{1}=1.[/tex]3) For A' = 25 sq units, we have:
[tex]k=\sqrt[]{\frac{25\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{\frac{1}{4}}=\frac{1}{2}.[/tex]4) For A' = 900 sq units, we have:
[tex]k=\sqrt[]{\frac{900\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{9}=3.[/tex]Answers
• 8
,• 1
,• 1/2
,• 3
Which term describes the red curve in the figure below?
A. Hyperbola
B. Ellipse
C. Circle
D. Parabola
Use the following image to complete the sentences describing the ratio of spots to eyes.
A ladybug with 2 eyes and 6 spots.
A ladybug with 2 eyes and 6 spots.
There are 6 spots for every
eyes.
There are
spots for every 1 eye.
Using ratios, the sentences are completes as follows:
There are 6 spots for every 2 eyes.There are 3 spots for every 1 eye.What is the ratio between two amounts?The ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
Between two amounts b and a, the ratio is given by the division of b by a, as follows:
r = b/a.
This means that the ratio between two amounts is not commutative, meaning that the order of the amounts matters.
A ladybug with 2 eyes and 6 spots, hence the first sentence is given as follows:
There are 6 spots for every 2 eyes. (ratio is the number of eyes for 6 spots).
The number of spots per eye is the ratio of the number of spots and the number of eyes, as follows:
Spots per eye = 6 spots/2 eyes = 3 spots per 1 eye.
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The average temperatures across Washington, Texas, Oklahoma, New York, Missouri, Hawaii and Michigan are48°F, 65°F, 60°F, 45°F, 54°F, 64°F, 70°F, and 45°F respectively.Find the median
SOLUTION
Let's list the values first. These are
48, 65, 60, 45, 54, 64, 70 and 45
Now, we have to arrange these values from the smallest to the largest. Doing this we have
45, 45, 48, 54, 60, 64, 65, 70.
The median will be between the middle items which are 54 and 60. So we will find the median by the following way
[tex]\begin{gathered} \text{Median = }\frac{54+60_{}}{2} \\ \text{Median }\frac{114}{2} \\ \text{Median = 57} \end{gathered}[/tex]Therefore, the Median is 57°F
find the sum of the measure of the angle of a three sided polygon
The sum of the interior angles of a polygon is given by the formula:
Sum = (n - 2)180
where n is the number of sides of the polygon
Since the polygon is a three-sided polygon, n = 3
Sum = (3 - 2)180
Sum = 1 x 180
Sum = 180
Simplify three raised to the fourth power raised to the negative one power
one over three raised to the fourth power
one over three raised to the power of negative four
negative three raised to the fourth power
three raised to the power of the third power
The result of the given expression is one over three raised to the fourth power.
what is logarithmic equation ?
Logarithm , the exponent or power to which a base must be raised to yield a given number.
Simplifying exponential equation
Exponential equations are inverse of logarithmic equation. Exponential equation is expressed as y = ab^x
Given the expression below;
(3⁴)⁻¹ = 3⁻⁴
According to the law of indices
a^-n = 1/a^n
Using this law above, this will be expressed as;
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
Hence the result of the given expression is one over three raised to the fourth power
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Two ways to write k/3+16
The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3
How to rewrite the expression?From the question, the expression is given as
k/3+16
Start by factoring 1/3 out of the first term
So, we have the following expression
1/3k + 16
The above is one of the ways of rewriting the expression
Another way is by taking the LCM
So,we have
k/3+16 = (k + 48)/3
Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3
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Jacob is preparing a monthly budget. His net pay is $1, 350 every two weeks, and his monthly rent is $936. What percentage
of his monthly budget should Jacob allocate for rent?
The percentage of monthly budget should Jacob allocate for rent is 27.7%.
What is termed as the percentage?A percentage is a ratio with the second term being 100. Percentage refers to parts per hundred. The term is derived from the Latin word per centum, that also means "per hundred." In mathematics, the symbol% stands for percent.For the given question;
Jacob's two week earning is $1,350.
Jacob's one week earning will be $1,350/2 = $675.
Considering there are 5 weeks in a months.
Jacob's one month earning will be $675×5 = $3,375.
The total monthly rent = $936.
Let 'x' be the percentage Jacob pay for the rent.
Then,
x% of 3,375 = 936
Simplifying the expression.
3,375x/100 = 936
x = 93,600/3,375
x = 27.7 %
Thus, the percentage of monthly budget should Jacob allocate for rent is 27.7%.
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Graphing proportional relationships
Answer:
hello fríend nose inglus
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10.
Rectangle C has length 30 and width 15,
B? If so, what is the scale factor?
a, Is Rectangle A a scaled copy a of Rectangle
b. Is Rectangle B a scaled copy of Rectangle
A? If so, what is the scale factor?
C. Explain how you know that Rectangle C is not a scaled copy a of Rectangle B.
d. Is Rectangle
A.a scaled copy of Rectangle
C? If so, what is the scale factor?
Answer:
A. Yes, Rectangle A is a scaled copy of rectangle B.
B. Yes, Rectangle B is a scaled copy of rectangle A.
C. No, Rectangle A is not a scaled copy of rectangle C.
Step-by-step explanation:
Rectangle A has dimensions 12x8 and Rectangle B has length 15x10.
We see that sides of A and B are proportional because
[tex]\frac{12}{15} = \frac{8}{10}[/tex]
So we say that since sides are proportional A and B are similar or scaled copy of each other.
Since A is smaller and B is bigger, a is 0.8 scaled copy of B. Similarly B has an enlargement scale factor = 1.25 Rectangle C has 30x15, not proportion with sides of A and B. Hence we find that C is neither a scaled copy of A nor B
Hope this helps! :))
Solve the system.
x - 5y + 4z=27
4x-3y-z-23
3x + 3y - 6z=-9
Answer:
Step-by-step explanation:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-5y+4z=27,4x-3y-z=23,3x+3y-6z=-9 Tiger Algebra Solver.
Solve the system of linear equations using the substitution method.
5x - 2y = 3 and y = 2x
A. (3, 6)
B. (1, 4)
C. (1, 6)
D. (1, 9)
Answer:
the answer is A. (3,6)
Step-by-step explanation:
5x - 2y = 3
5x - 2(2x) = 3
5x - 4x = 3
x = 3
y = 2x
y = 2(3)
y = 6
1 point
Which graph represents the solution x > 3?
Graph 1 represents the solution x > 3.
In Graph 1, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to positive infinity but 3 would not be considered. The highlighted side is toward the positive side.
In Graph 2, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to negative infinity but 3 would not be considered. The highlighted side is toward the negative side.
In Graph 3, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to positive infinity and 3 would be considered as well. The highlighted side is toward the positive side.
In Graph 4, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to negative infinity and 3 would be considered as well. The highlighted side is toward the negative side.
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1. Few months ago, Frank purchase stock for
$6, 150. Last week he sold the stock for. $8,250.
what was his gross capital gain?
Frank's gross capital gain was $2,100.
What is gross capital gain?
the discrepancy between the overall cost base of your asset and your capital gains. Your share of the capital gain - If more than one person owns this asset, your share of the gain is equal to the percentage of the asset that you personally hold.
You want the gross capital gain resulting from selling a stock purchased for $6,150 and sold for $8,250.
Capital Gain
The capital gain resulting from the sale is the difference between the selling price and the purchase price:
gain = selling price - purchase price
gain = $8,250 -6,150
gain = $2,100
Frank's gross capital gain was $2,100.
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How much simple interest does $2,560 earn in 17 months at a rate of 1*1/8 Round to the nearest cent.
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.
The formula for simple interest is:
Simple Interest = (Principal × Rate × Time) / 100
Where I am interested
P ⇒ amount deposited.
R ⇒ interest rate
T ⇒ period for investing
Given that the time is 17 months = 17/12 years
1 and 1/8 = 1.125
I = 2,560 ×17/12 × 1.125/100
= 2560 × 17/12 × 0.01125
= $185.86667
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
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in triangle ABC , angle A = 30 degrees and angle C = 35 degrees. what is angle B degrees?
Answer:
115°
Step-by-step explanation:
The sum of the three angles in a triangle is always 180°
m∠A + m∠B + m∠C = 180°
m∠B = 180 - m∠A - m∠C
m∠B = 180 - 30 - 35 = 115
Which is a formula that can be used to find the area of one triangular section of the door? How do you know the formula work?
A formula that can be used to find the area of one triangular section of the door is; (1/2) * Area 0f rectangle
How to find the Area of the triangle?
From the attachment, we can say let us;
Denote the Length as L
The width as w.
Area of a triangle is given by the formula;
A = 1/2 * base * height
The area of the rectangle is:
A = Length * Width
From the attachment, we can see that the rectangle is divided into two equal triangular sections.
This implies that, the area of one of the triangular sections is half the area of the rectangle. Thus;
Area of Triangle = (1/2) * Area 0f rectangle
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Find the value of r in the equation below.X-17 = 12
Answer : x = 39
We are given the equation
x - 17 = 12
First, isolate the value of x
When you isolate the value of x, the figure 17 cross the equality sign and change to positive
x = 12 + 17
x = 39
a pyramid has an isosceles , triangle base with sides 25,25 and 48 units . the height of the pyramid is 30 units . calculate The volume of the pyramid
A pyramid has an isosceles triangle base with sides of 25,25 and 48 units.
The height of the pyramid is 30 units. The volume of the pyramid is 13What is the volume?We have a pyramid with four sides and a square base. Two-thirds of the pyramid's sides make up its height. The volume of a pyramid is 1, and we need to determine which of them matches our volume. Third, multiplying the length by the width gives us our base's area, which is s times s, or s square.This tells us that our base's height is equal to two-thirds of its side because it is a square base.
That makes it 2 to times s, or 2 s over 3. So we incorporate that into our equations next. We have a volume that is equal to 1/s squared / 2 / s spanning 3 points.Therefore, a pyramid has an isosceles triangle base with sides of 25,25, and 48 units.
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What is 2 5/8 as a equivalent percent
2 5/8 as an equivalent percent is 262.50%.
What is the percent?Percentage is the rate of a number expressed as fraction out of 100. Percentage is a measure of frequency. The sign that represents percentage is %. In order to change a number to a percentage, multiply the number by 100.
A mixed number is a non-integer that is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator. An example of a mixed number is 2 5/8
In order to convert the mixed number to percentage, multiply it by 100:
2 5/8 x 100
21/8 x 100 = 262.50%
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- Nathaniel Barnes obtained a single-
payment loan of $1,200 to purchase a
computer. He agreed to repay the loan in
120 days at an ordinary interest rate of 7%.
What is the maturity value of his loan?
Answer: 1.25
Step-by-step explanation: Divide 1,200 in 7 days and the aswer is 1.25
–8(y-7)=2y+6Simplify your answer as much as possible
You have the following equation:
-8(y -7) = 2y + 6
In order to solve for y, proceed as follow:
-8(y -7) = 2y + 6 expand the factor right side
-8y + 56 = 2y + 6 subtract 2y and subtract 56 both sides
-8y - 2y = 6 - 56 simplify
-10y = -50 divide by -10 both sides
y = -50/(-10)
y = 5
Hence, the value of y is 5
Ollie borrowed $5000 for 3 years at a compound interest rate of 10%.
How much did Ollie pay back?
Answer: Assuming interest rate is yearly, Ollie would have to pay back 6, 655 dollars :)
Step-by-step explanation:
The formula for compound interest is
Y = P(1 + r/m)^mt, with P being the initial deposit (5000), r being the interest rate (0.10), m being the amount of times it is compounded per year (1), and t being the number of years (3).
Write and Solve Equations in Context
A group of friends wants to go to the amusement park. They have $246.75 to spend
on parking and admission. Parking is $14, and tickets cost $33-25 per person,
including tax. Write and solve an equation which can be used to determine 2, the
number of people who can go to the amusement park.
Equation:
?
Answer: 2 =
Answer:
8 people
Step-by-step explanation:
117.50 - 5.50 = 112
112 ÷ 14.8 = 7.56756756757, but you round it up to 8, so the answer is 8 people.
need help btw the last two i guessed the last to boxes so yea
Answer:
Everything is right. No need to change anything.
Please Help Please ASAP
The graph of the inequality y < 1 - 3x is in the attachment below.
How to Graph an Inequality?Given the inequality, y < 1 - 3x, we need to determine if the line of the inequality graph will be dashed or solid, the slope (m) of the line, and the y-intercept (b).
The slope (m) of the inequality y < 1 - 3x is -3. This means the line would be a declining line where the rise/run = -3.
The y-intercept (b) of the inequality y < 1 - 3x is 1. This means the line would intercept the y-axis at y = 1.
The boundary line of the inequality graph for y < 1 - 3x would be a dashed line because of the inequality sign "<". It also means the shaded part would be below the boundary line, because, the inequality sign, "<" means the the values are not included.
The graph that will represent the inequality given is the image attached below.
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The student council at Baker High School is planning a dance. The table shows their budget. What is the student council’s expected profit?
Item. Funds raised. Expenses
Dance tickets. $400
DJ fuze. -250
Decorations. -125
The student council’s expected profit as per given budget is equal to $25.
As given in the question,
Budget decided by the student council at Baker High School while planning a dance.
Total expenses on the items used for the dance
DJ fuze. : $250
Decorations. : $125
Total expenses done by student council for dance
= $( 250 +125)
=$375
Total funds raised by dance performance is equal to
Dance tickets. $400
Total revenue =$400
Revenue >Expenses
Student council’s expected profit= $(400 -375)
= $25
Therefore, the student council’s expected profit as per given budget is equal to $25.
The complete question is:
The student council at Baker High School is planning a dance. The table shows their budget. What is the student council’s expected profit?
Funds raised:
Dance tickets : $400
Expenses:
DJ fuze. : $250
Decoration : $125
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Daisy has two measuring jugs, A and B, which can hold a combined volume of
900 ml.
Daisy fills jug A with water. She then fills jug B by pouring in water from jug A.
After this, there is 500 ml of water remaining in jug A.
Work out the volume of each measuring jug.
Help please
Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Daisy has two measuring jugs, A and B, that together have a capacity of 900 ml, A jug of water is filled by Daisy. Afterward, she transfers water from jug A into jug B. Following this, jug A has 500 ml of water left.
Total volume = volume in jug A + volume in Jug B
If there are 500 ml of water remaining in jug A.
900 ml = 500 ml + volume in Jug B
volume in Jug B = 900 - 500
volume in Jug B = 400 ml
Thus, Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
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nouOR
36, 27,
81
4'
Find the 10th term.
Submit Answer
Answer:
177
Step-by-step explanation:
Answer: a_10 = 177147/65536. Write the general term through the pattern:: a_n = 36 3/4 n - 1 Substitute and calculate:: a_10 = 177.
11. Tom borrowed some money from his father seven months ago. Every month,
he pays back $400 to his father. Currently, he owes $2,500.
a) How much will he owe his father three months from now?
b) How much money did he borrow from his father?
In three months, he will owe his father $2500 less $1200, or $1300.
One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
Tom's payment for 7 months is 400 * 7 = $2800.
He borrowed $5300 ($2500 plus $2800).
His monthly payment for three months is 400*3.
In three months, he will owe his father $2500 less $1200, or $1300.
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