The perimeter of the resulting hexagon is 60 meters.
What is the perimeter of the image of a hexagon as a result of a dilation?
In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Scale factorP(x, y) - Original pointP'(x, y) - Resulting pointThe perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):
p' = k · p
If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:
p' = (4 / 3) · (45)
p' = 60
The resulting hexagon has a perimeter of 60 meters.
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
x^2+32x+116=12x
Answer:
x=246 or x=-266
Step-by-step explanation:
First you bring 12x to the other side and simplify to give
x²+20x+116=0
Then solve by completing the square:
(x+10)²-100+116=0
(x+10)²+16=0
(x+10)²=-16
x+10=±256
x=±256-10
x=246 or x=-266
Hope this helps
scot is picking out a pumpkin to buy at the local pumpkin farm. Each pumpkin costs $5.00 plus $0.35 per pound. Which equation represents the price of a pumpkin, p, that is x pounds
The equation represents the price of a pumpkin is p = 5 + 0.35x
The cost of each pumpkin = $5.00
The cost of the pumpkin per pound = $0.35
Consider the price of the pumpkin = p
Consider the number of pounds = x
The equation is the mathematical statement that shows the relationship between two expression with an equal sign. In equation the inequality will not be a part. The expression is the combination of two expression and an equal sign
Then the equation will be
p = 5 + 0.35x
Hence, the equation represents the price of a pumpkin is p = 5 + 0.35x
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What is the domain and range of the relation shown in the table?
X Y
2 0
-1 4
4 2
-3 0
A. domain:{−3,−1,2,4}, range:{0,2,4}
B. domain:{0,2,4}, range:{−3,−1,2,4}
C. domain:{−3,−1,2,4}, range:{y|y∈R}
D. domain:{x|x∈R}, range:{0,2,4}
The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.
This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.
Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.
By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:
Domain = {−3, −1, 2, 4}.
Range = {0, 2, 4}.
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The surface area of a square pyramid is 96 square feet. The height is two-thirds of the length of the base edge.
What is the length of the base edge?
The length of the base edge of the pyramid is 1.71 feet
What is surface area of a pyramid?In order to find the total surface area, we will need to add up the areas of the base and the three other sides. SA=B+12(P×h), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid.
If l is the length of the square base and h is the height of the pyramid, then h =2/3l
from the formula, SA= B+12(P×h)
the perimeter of a square is 4l
the base area of square is l^2
therefore 96= l^2+ 12(4l×2/3l)
96= l^2+ 12×8/3l^2
96=l^2+32l^2
96= 33l^2
divide both sides by 33
l^2= 96/33
l=√2.91
l=1.71 feet
therefore the length of the base edge is 1.71 feet
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Which theorem or postulate could be used to prove the congruence of the triangles?
Angelica purchases $25.75 worth of cosmetics online. There is a 2% processing fee. What is the total cost of the cosmetics? Round to the nearest cent
26.27
Step by step
2/100 = 0.02
0.02 x 25.75 = 0.51
0.51 + 25.75 = 26.26 rounding is 26.27
The total cost of the cosmetics including 2% processing fee rounded up to the nearest cent is $26.27
The cost of the cosmetics is $25.75
The 2% processing fee is calculated as follows:
2/100 × $25.75 = $ 0.515
The total cost including processing fee is $25.75 + $ 0.515 = $26.265 rounded up to $26.27
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4. Find the measure of
TIL
110
40 50 60
140 130 120 110 100 sp 80 70 60
0 120 130
35 degrees
135 degrees
145 degrees
O95 degrees
Answer:
145 degrees
Step-by-step explanation:
The side through L is at a 35 degree angle, and the side through N is at a 180 degree angle. Taking the difference, we get 145 degrees.
How many grams of H2SO4 are needed to prepare 5.0 L of a 2 M H2SO4 solution?
980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.
What is Sulfuric acid?Sulfuric acid, also known as sulphuric acid or oil of vitriol in the past, is a mineral acid made up of the elements hydrogen, oxygen, and sulfur with the chemical formula H₂SO₄. It is a viscous liquid that is miscible with water. It has no color or smell.Sulfuric acid can irritate the nose and throat, burn the eyes, burn holes in the stomach if eaten, cause severe skin burns, and make breathing difficult if inhaled.So, the grams of H₂SO₄ needed will be:
Calculate to prepare 5.0L of a 2M solution.98g/mol × 5mol × 2mol /L = 980g H₂SO₄Therefore, 980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.
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julia rides her bike at a rate of 1/2 mile per 1/9 of an hour. how far does she ride in one hour
Answer:
4.5 miles
Step-by-step explanation:
0.5 of a mile per 1/9 of an hour.
rate x time=distance and you need to find distance for one hour not 1/9 so multiply it by 9 so
0.5*9=4.5, 1/9*9=1
rate time distance
4.5 * 1 = d
4.5*1=d
4.5=d
so the distance traveled in one hour is 4.5 miles
Answer:
4.5 miles
Step-by-step explanation:
Given:
Julia rides her bike at a rate of 1/2 mile per 1/9 of an hour.Let x be the distance Julia rides in one hour.
Create an equivalent ratio of miles to hours:
[tex]\implies \dfrac{1}{2}:\dfrac{1}{9}=x:1[/tex]
[tex]\implies \dfrac{\frac{1}{2}}{\frac{1}{9}}=\dfrac{x}{1}[/tex]
[tex]\implies \dfrac{1}{2}\times \dfrac{9}{1}}=x[/tex]
[tex]\implies \dfrac{9}{2}=x[/tex]
[tex]\implies x=4.5[/tex]
Therefore, Julia rides 4.5 miles in one hour.
Help Pls Help I need it in 10 mins!!!!!!!!!!!!!!PLS
The point (6,2) is reflected over the -axis and then the image is translated 4 units right and 3 units down. What is the absolute difference between the coordinates of the final image?
Answer:
When we reflect over the x-axis the answer will be (6, -2)
Then when we go 4 units right it will turn into (10,-2)
And lastly, when we go 3 units down, it will be (10,-5)
The Answer is (10,-2)
(Brainiest is optional)
(a) The amount of pure acid in 40 oz of 20% acid solution is oz.
(Type an integer or a decimal.)
neverminding the jumbled wording
how much is 20% of 40?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 40}}{\left( \cfrac{20}{100} \right)40}\implies 8[/tex]
please answer this question. I get my cat taken away if I dont
Answer: -3
Step-by-step explanation: Used calculator
ANSWER THIS QUESTION FOR BRAINLISTEST
The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)
How to Interpret Mathematical Transformations?We are given from the question that the triangle P'Q'R' was transformed from the triangle PQR.
We see from the image that the coordinates of the original triangle PQR are;
P(-1, 1)
Q(2, 0)
R(-1, -2)
We also see that the coordinates of the transformed triangle P'Q'R' are;
P(-5/2, 5/2)
Q(5, 0)
R(-5/2, -5)
Thus, we can conclude that the transformation rule used here is;
(x, y) → (⁵/₂x, ⁵/₂y)
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how do you estimate the product of 5 1/3 and 4 7/8
Malik created a model of a rectangular flag.
His model is 10 inches long and the actual flag is 25 inches long.
How many times wider is the actual flag than Malik's model?
Answer:
2.5x
Step-by-step explanation:
Given information for width:
Model: 10 in.
Real: 25 in.
Solve: How much times wider is real than model?
To find this, lets divide 25in. by 10in to find the scale factor.
25/10 = 2.5
2.5
We can verify this by multiplying 10 by 2.5
10 x 2.5 = 25
Zach loves to compete in triathlons. At a race a few months ago, he finished in 280 minutes. Yesterday, he completed another triathlon and finished in 294 minutes. What was the percent of increase in Zach's finishing time?
The percent of increase in Zach's finishing time is 5%.
How to calculate the percentage?From the information, at a race a few months ago, he finished in 280 minutes and yesterday, he completed another triathlon and finished in 294 minutes.
The increase in time will be:
= New time - Old time
= 294 - 280
= 14 minutes
The percentage increase will be:
= Increase in time / Original time × 100
= 14 / 280 × 100
= 1/20 × 100
= 5%
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Deon, Jerome, Lamar, and Terell are practicing for the meter relay race. The school record for the race is 49.6 seconds. The fastest time that each boy ran a 100-meter sprint in practice is shown in the table. If each of the boys can run their best 100-meter sprint during the race, can they beat the school record?
Answer: Yes
Step-by-step explanation:
Add all of their best times.
11.9 + 12.6 + 12.52 + 11.95 = 48.97
48.97 < 49.6
helppppppppppppppppppppppppppppppppppp pls can you show me how to write out each problem and solve it
Answer:
1) 1.96
2) 6
3) 4/3
Step-by-step explanation:
think of exponents as repeated multiplication. the exponent is how many times you're going to multiply the number itself by.
1) [tex]1.4^{2}[/tex] is really just 1.4 * 1.4, which you can solve by long multiplication or a calculator to get 1.96
2) for this one, you can rewrite the expression as a fraction. you'll also want to use PEMDAS, starting with the parentheses
[tex]\frac{300}{ 2(0.5+4.5)^{2}}\\\\\frac{300}{2*(5)^2}\\\\\frac{300}{2*25} \\\\\frac{300}{50} = 6[/tex]
3) [tex](\frac{1}{2})^{3} = \frac{1}{2} *\frac{1}{2} *\frac{1}{2} = \frac{1}{8} \\[/tex]
you can rewrite the division as a fraction again, only this time. you can change the subtraction to the reciprocal of the denominator
[tex]\frac{1}{3} / (2*\frac{1}{8} )= \frac{1}{3} / \frac{1}{4} = \frac{1}{3} * 4 = \frac{4}{3}[/tex]
hope this helped!
what is the functional for seven less than 3/5 of B is A
The mathematical expression is 3/5b -7 = a.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
7 less than three fifths of b is a
So, the mathematical expression for the above statement is
(3/5)b - 7 = a
3b - 35 = 5a
3b- 5a= 35
Hence, the mathematical expression is 3/5b -7 = a.
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Which option shows the equation for the line in the graph?
Responses
y=−5x−5y is equal to negative 5 x minus 5
y=3x−10y is equal to 3 x minus 10
y=−3x−10y is equal to negative 3 x minus 10
y=−10x−3
The option that shows the equation for the line in the graph is
y=−3x−10y is equal to negative 3 x minus 10How to obtain the equation of the line in the graphA graph is a pictorial representation of data. The graph shows a linear function which will be written in the slope intercept form form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
calculation of slope
The points used for the slope is gotten from the graph as B(-5. 5) (-2, -4)
m = (y₂ - y₁) / (x₂ - x₁)
substituting the values
= ( -4 - 5 ) / ( -2 - -5 )
= -9 / -2 + 5
= -9 / 3
= -3
y intercept, c
this is a point where the graph cuts the y axis
c = -10
hence the equation is written using y = mx + c and substituting the values
y = -3x - 10
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What’s the answer someone please help
Answer:
Step-by-step explanation:
Ok:
1. This is a percent problem!
45/100*15=
675/100=
6.75
2. Subtract:
15-6.75=
8.25$
Answer: 8.25$
Mitzi looked up prices of thirteen used Chevrolet HHR retro" tracks in the classified ads and found these prices: 8,500, 8,500, 8,500, 9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000
The price range of the Chevrolet HHR retro will be $14,500.
What is the range of the data?The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.
The given data as:
$8,500, $8,500, $8,500, $9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000
According to the given information, the required solution would be as:
The maximum value of data = $23,000
The minimum value of data = $8,500
The range of the data = The maximum value of data - The minimum value of data
Substitute the values in the above formula,
The range of the data = 23,000 - 8,500
Apply the subtraction operation to get the answer
The range of the data = 14,500
Therefore, the price range of the Chevrolet HHR retro will be $14,500.
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The question seems to be incomplete the correct question would be:
Mitzi looked up prices of thirteen used Chevrolet HHR retro" tracks in the classified ads and found these prices: 8,500, 8,500, 8,500, 9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000. Find the range of the data.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x−3y= −21
Answer:
y=4/3x +7
Step-by-step explanation:
4x - 3y = -21
Move 4x to the other side
-3y = -21 -4x
Next divide the other side by -3
y= 7 +4/3x
Move numbers around
y = 4/3x + 7
What is the slope-intercept form of the equation of the line that passes through the points (7,-5) and (3,- 9)?
y=x-4
y = x + 12
y=x-12
y = x + 5
Answer:
y = x - 12
Step-by-step explanation:
slope = (-9 - (-5))/(3 - 7) = -4/(-4) = 1
y = mx + b
y = x + b
-5 = 7 + b
b = -12
y = x - 12
What characteristics of something that is cyclical
Answer: regularly patterned or that occur in regular intervals.
Step-by-step explanation: took it
1/2 of a number is 15 more than 1/7 of the same number. find the number.
Answer:
42
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] x = [tex]\frac{1}{7}[/tex]x + 15 Clear the fraction by multiplying all the way through by 14
7x = 2x + 210 Subtract 2s from both sides
5x = 210 Divide both sides by 5
x = 42
If the triangle equals 12cm in perimeter, what's the equation for the triangle with 5cm,3cm, and a missing number labeled as P
the mean age for all foothill college students for a recent fall term was 33.2. the population standard deviation has been pretty consistent at 15. suppose that twenty-five winter students were randomly selected. the mean age for the sample was 30.4. we are interested in the true mean age for winter foothill college students. let x
Lower Limit = 24.52
Upper Limit = 36.28
Error Bound = 5.88
Lower Limit: - The Lower Limit for every class is the smallest value in that class. For example: 5 is a lower lower limit for the set S= { 5,8,42,34}
Upper Limit: - A value that is greater than or equal to every element of a set of data. For example: - { 3,5,11,20,22} is a upper bound of 22.
Given that,
Population Mean,μ = 33.2
sample Mean, χ (x bar) = 30.4
sample Size, n = 25
α (Alpha) = 0.05
Population standard deviation,σ = 15
95% confidence interval:
μ ± z critical σ / √n
Putting the values, we get,
z critical at α0.05 = ± 1.96
30.4 ±1.96( 15/√25) = 30.4 ± 5.88 = (24.52,36.28)
a) Lower Limit = 24.52
b) Upper Limit = 36.28
c) Error Bound =
Margin of Error = z critical × σ /√n
= 1.96 × 15/√25
= 1.96 × 15/5
= 5.88
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If r(x) = 2x² and w(x) = x-2, what is the range of (wor)(x)?
The given function are
r(x) = 2 - x² and w(x) = x - 2
(w*r)(x) can be obtained by multiplying the both function together
So, (w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)
(w*r)(x) = x (2-x²) - 2(2-x²)
= 2x - x³ - 4 + 2x²
∴ (w*r)(x) = -x³ + 2x² + 2x - 4
It is a polynomial function with a domain equal to R
The range of (w*r)(x) can be obtained by graphing the function
To graph (w*r)(x), we need to make a table between x and (w*r)(x)
See the attached figure which represents the table and the graph of (w*r)(x)
As shown in the graph the range of (w*r)(x) is (-∞,∞)
Which graph has a domain of all real numbers greater or equal to 6?
Answer:
Step-by-step explanation
C