By using scale factor formula we can evaluate the measure of side EF.
What happens when we dilate a triangle?When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.
How do you find scale factor?The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.
Therefore,
2/3 =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF
EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]
By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.
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Find out the answer to 4x+12=63
Answer:
The answer to this question is x= 51/4
Anybody know the answer to this ?
On solving the provided question, we can say that - the data from graphs represents a curvilinear and straight graph.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
Here,
in graphs,
as per data we can say that there two types
one is curvilinear and other is straight graph.
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Lena decides to make 1 batch of mac-and-cheese
and 3 pizzas. How many tablespoons of basil does
she need?
On solving the provided question, we can say that - equation at factors x= -3 that value of a is = 33
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
4x^2 + 5x - 8
x = -3
36 + 15 -8
33
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please assist with helping in the image below!!
Arjun is hiking from a mountain lodge to a nearby summit. The probability that he will take the longest trail is 59. The odds against Arjun taking the longest trail are _[blank]_.
What odds best complete the sentence?
Enter your answer as “m:n{}^{\prime\prime} where m and n are the smallest integers possible, like this: 3:2
The odds against Arjun taking the longest trail are 4 : 9 .
How to find the probability ?The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.
This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:
= 1 - 5 / 9
= 4 / 9
When given as a ratio, this would be:
= 4 : 9
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Please help!
ponential functions are in the form y = a(b)'.
What values of b make it an exponential growth function?
What values of make b it an exponential decay function?
Please hurry, it's due in two days
Answer:
C (3, -2) is in the Fourth Quadrant.
The equation of the line is Y=2
The Line x=-1 would be a straight vertical line on the point x=-1.
Step-by-step explanation:
I have attached three pictures, one of all the quadrants labeled for you to help in the future, one of a visual of y=2 with the points labeled, and one of a visual of the line x = -1.
7•e^.1t =47 express the solution as a logarithmic in base e
Answer:
The value of t is 19.04
Step-by-step explanation:
[tex]7e^{0.1t} = 47\\[/tex]
[tex]e^{0.1t} = \frac{47}{7}[/tex]
take log both sides :
[tex]ln(e^{0.1t}) = ln(\frac{47}{7}) \\0.1t = 1.9042\\t = \frac{1.9042}{0.1}\\t = 19.04[/tex]
how do i solve -2.4>b/-2.5 step by step
Step-by-step explanation:
hope this helps....see above for answer
Write 108:96 in the form 1:n.
Answer:
it will be [tex]1:\frac{8}{9}[/tex]solvve for z: (1st answer or nice and detailed answer brainliest)
1/2z+5=57
[tex]\dfrac{1}{2} z+5=57[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{2} z+5-5=57-5[/tex]
[tex]\dfrac{1}{2} z=52[/tex]
Multiply both sides by 2:
[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]
[tex]\fbox{z = 104}[/tex]
Answer:
z=104
Step-by-step explanation:
1/2z=57-5
1/2z=52
1/2z*2=52*2
1z=104
1/1z=104/1
z=104
find the number that makes the ratio equivalent to 1:8
Answer:
2:16
Step-by-step explanation:
maybe i don't know im not smart but that is the ratio equalivent i guess i have to make this 20 words long soooo
Answer:
To find the number that makes the ratio equivalent to 1:8, we need to set up the ratio as a fraction and solve for the missing value.
The ratio 1:8 can be written as the fraction 1/8. In this case, the missing value is the numerator (1) and the known value is the denominator (8). To solve for the missing value, we can multiply both the numerator and denominator by the same value.
For example, if we multiply both the numerator and denominator by 2, we have:
1/8 = (12)/(82) = 2/16
If we multiply both the numerator and denominator by 4, we have:
1/8 = (14)/(84) = 4/32
If we multiply both the numerator and denominator by 5, we have:
1/8 = (15)/(85) = 5/40
In each of these cases, the ratio is still equivalent to 1:8, but the missing value (the numerator) is different. In general, we can multiply the numerator and denominator by any value to find the missing number that makes the ratio equivalent to 1:8.
For example, if we multiply both the numerator and denominator by 10, we have:
1/8 = (110)/(810) = 10/80
In this case, the missing value (the numerator) is 10, which makes the ratio equivalent to 1:8.
Step-by-step explanation:
What are the 3 types of translation?
When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.
The three types of translation in math are
horizontal translationvertical translationcompression translationWhen the object moves either from left to right or from right to left it is known as vertical translation.
The movement in up or downward direction of the graph is known as horizontal translation.
The domain of the function remains same in both the cases.
A translation in which the size of the object decreases or is compressed is known as the compression translation.
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How many solutions does 2 variables have?
A linear equation in two variables has only 1 solution.
Now, According to the question:
Let's know:
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equation in two variables, it has two solutions.
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0.
A linear equation in two variables has only 1 solution.
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What is the median of the following 9 numbers: 23, 15, 32, 27, 19, 11, 30, 19, 22?
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
The median for odd data will be
Median = [(n + 1) / 2]th
The median for even data will be
Median = {[n / 2 + (n + 2)/ 2] / 2}th
The data is given below.
23, 15, 32, 27, 19, 11, 30, 19, 22
Arrange the data in ascending order. Then we have
11, 15, 19, 19, 22, 23, 27, 30, 32
Then the median of the following 9 numbers is calculated as,
Median = [(9 + 1) / 2]th
Median = (10 / 2)th
Median = 5th
Median = 22
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
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A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 15 hours, to the nearest whole number?
The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.
Given that,
P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.
In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,
Therefore,
P_0 = 7100
d = 2
t = 15
so,
P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235
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18 points ! The shape of Gretchen's data can be described as 1) skewed left 2) skewed right 3) symmetrical.
Because of this, the 1) mean 2) median would be the best measure of center for this data set. The actual value for the best measure of center is 1) 7, 2) 9, 3) 9. 1, 4) 9. 6
The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.
What is skewed left?A distribution that is left-skewing has a lengthy left tail.
Distributions that are negatively skewed are also known as left-skewed distributions.
This is due to the number line having a significant negative tail.
Additionally, the peak is to the left of the mean.
The right tail of a right-skewed distribution is lengthy.
It's a widespread misperception that "peakness" is defined by the distribution's peak.
To put it another way, a peak that leans left indicates a left-skewed distribution.
Hence, The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.
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What is the slope of the line that passes through the points (1, 6) and (13, 2)? Write your answer in simplest form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]
Homer Simpson left an estate of $2.4 million. He left 10% to Springfield University, 15% to the First Church of Springfield, $600,000 to his wife Marge, and the remainder to be divided among his three children. How much did each child receive?
Hello there!
Answer:
$400'000
Step-by-step explanation:
Estate -- $2.4 million or $2'400'000
Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000
First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000
Wife will receive $600'000
Total: $240'000 + $360'000 + $600'000 = $1'200'000
Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000
So each child will receive: $1'200'000 / 3 = $400'000
Answer: Each child of Homer Simpson gets $400000.
Step-by-step explanation:
Homer Simpson left 10% of his estate, or (10/100) x $2.4 million
= $ (10/100)x2400000= $240000
$240,000 to Springfield University.
He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000
= $360000
So 360,000 to the First Church of Springfield.
So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)
=$1200000
$1,200,000 to organizations and his wife.
That means the remainder of the estate, $2.4 million - $1,200,000
= $2400000-1200000
= $1200000
1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3
=$400000
Answer: $400000.
the current ratio of Sara's sales to Ravi's sales is 100:2 would you earn a greater total commission with Sara or Ravi?
as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?
One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current sales ratio and commission rates.
Which of Sara and Ravi guarantees more earnings after apprenticeship?As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.
Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.
Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.
Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.
Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.
Ultimately, one would earn more if one apprenticed for Sara.
Complete question; Sara's pieces of art sell for $25 each your commission is 60%.
Ravi's pieces of art sell for $2000 each and your commission is 25%.
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use your calculator to determine the percent of each number a.1% of 28 =
Answer:
0.28
Step-by-step explanation:
1% = 0.01
0.01 × 28 = 0.28
What are my financial goals? What major purchases should I save for?
It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.
I need to factor completely to get an answer for
r²+3r-28
I need to get factors in parenthesis like (r +/- #) (r +/- #)
I need it before tomorrow
Answer:
(r + 7)(r - 4) = 0
Step-by-step explanation:
r² + 3r - 28 = 0
(r + 7)(r - 4) = 0
r = -7, 4
What is a 2 step problem?
A 2-step problem is a mathematical problem that can be solved using two steps or operations. These types of problems are typically simple and can be solved using basic arithmetic or algebraic concepts.
For example, a 2-step problem could involve solving for one variable in one equation and then substituting that value into another equation to find the value of a second variable.
For example:
2x+3y=10 and 3x-2y=5
Here, first step would be to solve for x in the first equation by isolating x and in the second step we can substitute that value of x in the second equation to solve for y.
It can also refer to a problem that can be solved in two steps by breaking the problem down into simpler parts. For example, a 2-step problem in geometry could involve finding the area of a shape by first finding the area of one part of the shape and then adding that to the area of another part of the shape.
In general, 2-step problems are not complex and can be solved easily by breaking down the problem into simpler parts and solving each part separately.
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What is the product of 2p 7 3p2 4p 3?
The product of 2p 7 3p2 4p 3 is 756p7.
What is product in math?Product in math is the result of multiplying two or more numbers, variables, or algebraic expressions together. It is often denoted by the symbol 'x' or by juxtaposition, such as writing "ab" instead of "a x b". The product of two numbers is the same as the result of the first number multiplied by the second. Product is a fundamental concept in mathematics and is used in many different types of equations and calculations.
This can be calculated by multiplying the terms together.
First, multiply the terms in each parenthesis.
2p 7 is 14p, 3p2 is 9p2, and 4p 3 is 12p3.
Then, multiply the three terms together, 14p x 9p2 x 12p3, which equals 756p7.
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how do I find the slope of these points
(8,-4) and (2,-4)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]
Amrita divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (USE π=22/7 )
The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.
Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs
Step 1: Calculate the circumference of the original circle.
Circumference of a circle = 2πr
Circumference of the circle with a radius of
7 cm = 2πr = 2 × 22/7 × 7 = 44 cm
Step 2: Calculate the perimeter of each semicircular shape disc.
The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.
Perimeter of each semicircular shape disc
= 44 cm/2
= 22 cm
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A fisherman illegally drops some fish into a pond, and they quickly propagate (reproduce). The population growth of the new specifies is modeled by P(x) = 6∙2x, where x is the time in weeks following the moment he dropped the fish into the pond. How many fish are in the pond after 3 months? (assume there are four weeks in a month) a. 48 b. 8, 916 c. 24,576 d. 72
The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.
what is exponential function ?A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.
Given that,
When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.
According to the question,
P(x) = 6bˣ
Put p(x) = 51 and x = 6
51 = 6b⁶
17/2 = b⁶
b = [17/2]¹/⁶
b = 1.43
The b value that must be simplified is given as 1.43. A is the proper answer.
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Given function g, which is defined by g(x)=x to the power of 3 -x , what is the value of g(3)?
Really sorry, misunderstood the equation. This is the answer though.
Answer:
24
Step-by-step explanation:
We have our function g(x) = [tex]x^{3}[/tex] - x
Now, we will substitute 3 in for x, giving us:
[tex]3^{3} - 3[/tex]
Now, we will simplify our exponent, giving us:
27 - 3 = 24
So your answer is 24.
Hope this helped!
Find the length and width of the actual room, shown in the scale drawing. Then find the area of the actual room. Round the final answer, if necessary, to the nearest tenth.
The actual dimensions are 9.75 feet and 7.5 feet. The area will be 73.125 square feet.
What is the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). The scale factor is defined as the proportion of the new image's size to that of the previous image.
Here the scale factor for the given image is 2 inch = 3 ft.
The measure of the actual dimensions will be calculated as,
2 in = 3 ft
1 in = 3/2 ft
6.5 in = 6.5 x 3 / 2 = 9.75 ft
5 in = 5 x 3 / 2 = 7.5 ft
The actual area will be calculated as,
Area = 9.75 x 7.5
Area = 73.125 square feet
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