The value of x in the rectangle is -5 + 5√3.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides are parallel to each other.
Therefore, the area of a rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
length = x + 10
width = x
Hence,
50 = x(x + 10)
50 = x² + 10x
x² + 10x - 50 = 0
using quadratic formula,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 1
b = 10
c = -50
Therefore,
x = [tex]\frac{-10+\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex] and x = [tex]\frac{-10-\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]
Hence,
x = -5 + 5√3 and x = -5 - 5√3
Therefore, we can't use negative values
The value of x = -5 + 5√3
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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.
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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Evelyn deposited $90 in an account
earning 10% interest compounded
annually.
To the nearest cent, how much interest
will she earn in 1 year?
Use the formula B = p(1 + r)², where B is
the balance (final amount), p is the
principal (starting amount), r is the
interest rate expressed as a decimal, and t
is the time in years.
The compound interest earned by Evelyn in one year is $9.
Evelyn has a bank account. She deposited $90 in her account. She earns 10% interest on her deposited money. The interest earned is compounded annually. We need to calculate the interest earned by her in one year, to the nearest cent.
We need to calculate the compound interest. The formula is given below.
B = p(1 + r)^t
The variables 'B', 'p', 't', and 'r' represent the final amount, the initial amount, the time duration, and the rate of interest, respectively.
B = $90(1 + 0.1)^1
B = $90*1.1
B = $99
The final amount in her bank account after one year is $99. The interest earned is the difference between the final and the initial amount. Let the variable 'I' represent the interest earned.
I = B - p
I = $99 - $90
I = $9
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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!
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 (-∞,∞)
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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50 Points pls help!
Question: Fred drew the footprint of a stage he was planning to build for his band on a coordinate plane. He decided he wanted to make it smaller because he wanted to make sure it fit at every venue.
Please help me solve letter A and B :)
Answer:
A) Picture added,B) 26 units.=========================
Part AThe smaller figure is added, considering the coordinates of the image follow the rule:
(x, y) → (0.5x, 0.5y)Smaller stage is in blue. See attached
Part BSince each side is half the original, the perimeter of the image is half the larger one:
P = 52/2 = 26 unitsWhat 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
Lamar will run at most 37 miles this week. So far, he has run 22 miles. What are the possible numbers of additional miles he will run?
The possible numbers of additional miles that Lamar can run are all the solutions of the inequality:
0 ≤ x ≤ 15
What are the possible numbers of additional miles?We know that Lamar will run at most 37 miles this week, and he already did run 22 miles, then the (maximum) distance left this week is:
D = 37mi - 22mi = 15mi
So he can run at most 15 miles, this means that he can run any distance between 0 miles and 15 miles by the end of the week.
So, if we define x as the distance that he will run on the week (in miles), then we can write the inequality:
0 ≤ x ≤ 15
so the possible numbers of additional miles he will run on this week are all the values of x that are a solution for the above inequality.
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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]
If the triangle equals 12cm in perimeter, what's the equation for the triangle with 5cm,3cm, and a missing number labeled as P
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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What characteristics of something that is cyclical
Answer: regularly patterned or that occur in regular intervals.
Step-by-step explanation: took it
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.
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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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
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
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.
Which graph has a domain of all real numbers greater or equal to 6?
Answer:
Step-by-step explanation
C
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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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
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 $26.27
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What’s the answer someone please help
Answer:
Step-by-step explanation:
Ok:
1. This is a percent problem!
45/100*15=
675/100=
6.75
2. Subtract:
15-6.75=
8.25$
Answer: 8.25$
Si un bolso costaba$40.000 y tiene un descuento de un 10%¿cual es el precio final del bolso?
El precio final, esto es, el precio con descuento, del bolso es igual a $ 36.000.
¿Cómo calcular el precio final del bolso?
En este problema debemos determinar el precio final de un bolso (C') adquirido por un cliente con descuento, igual al precio original (C) menos el descuento, descrito en la siguiente fórmula:
C' = C · (1 + r / 100)
Donde r es la tasa de descuento. Nótese que existe descuento para 0 < r < 100.
Si sabemos que C = 40.000 y r = - 10, entonces el precio final del bolso es:
C' = 40.000 · (1 - 10 / 100)
C' = 36.000
El precio final del bolso es igual a $ 36.000.
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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
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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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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Which theorem or postulate could be used to prove the congruence of the triangles?
please answer this question. I get my cat taken away if I dont
Answer: -3
Step-by-step explanation: Used calculator