Answer:
x = 8
measure of each side = 27 units
Step-by-step explanation:
Properties of an equilateral triangle:
Regular polygon with 3 sidesAll 3 sides are equal in lengthAll 3 interior angles are congruentIf ΔGHJ is an equilateral triangle, the side measures are equal.
\(\implies \sf GH = HJ = GJ\)
\(\implies (5x-13)=(11x-61)=(7x-29)\)
To solve for x, choose 2 side lengths, equate them, and solve for x:
\(\implies \sf GH=HJ\)
\(\implies 5x-13=11x-61\)
\(\implies 5x-13 - 5x =11x-61 - 5x\)
\(\implies -13=6x-61\)
\(\implies -13+61=6x-61+61\)
\(\implies 48=6x\)
\(\implies 48 \div 6=6x \div 6\)
\(\implies x=8\)
To find the measure of each side, substitute the found value of x into one of the side expressions:
\(\begin{aligned}\implies \textsf{GH}&=5(8)-13\\& =40-13\\& =27\end{aligned}\)
Therefore, x = 8 and the measure of each side is 27 units.
Equilateral triangles have same sides
GH=HJ5x-13=11x-6111x-5x=-13+616x=48x=8Length of each side
5(8)-1340-1327Can someone help me with this one problem?
A pool is filling with water at a rate of 45 gallons every 5 minutes,
How many gallons of water will be in the pool in one hour?
Write and solve a proposition that the teacher can use to estimate how many students in the whole school would choose the aquarium.
Answer:
Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:
Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100
We can plug in the values we know:
80 / x = p / 100
where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.
We can solve for "x" by cross-multiplying and simplifying:
8000 = px
x = 8000 / p
Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:
(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction
This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:
p / 100 = 80 / 210
p = 38.1
So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:
80 / x = 38.1 / 100
Cross-multiplying and solving for "x", we get:
x = 209.71
Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.
Step-by-step explanation:
Answer:
The teacher surveyed a total of:
80 + 60 + 30 + 40 = 210 students.
If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.
The relative frequency of students choosing the aquarium in the sample is:
80/210 = 0.38
This means that approximately 38% of the students in the sample chose the aquarium.
To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:
0.38 x 1000 = 380
Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.
Find the equation of a straight line cutting off the y-intercept 4 from the axis of y and inclined to 60° with the positive direction of X-axis.
The linear function is given as follows:
\(y = \sqrt{x} + 4\)
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The y-intercept is of 4, hence the parameter b is given as follows:
b = 4.
The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:
m = tan(60º)
\(m = \sqrt{3}\)
Thus the function is given as follows:
\(y = \sqrt{x} + 4\)
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Simplify the expression.
−6−7
Answer:
-13
Step-by-step explanation:
subtract 7 from -6
Answer: -13
Step-by-step explanation: When you have two numbers with negative signs, you add them but you keep the negative sign.
Therefore, -6-7 = -13
For the future, know these rules for signs when adding, subtracting, dividing and multiplying:
When adding two negative numbers, you add but keep the negative sign like in the above problem.
When adding a positive and negative, you subtract but keep the sign of the highest number. Example: -4+9 = 5 or -11+3 = -8.
When multiplying two negatives or positives numbers, the answer will be positive. When multiplying negatives x positive = negative.
The same applies to division. (-)/(+) = (-) or (+)/(-) = (-)
(-)/(-) = (+)
Hope this explanation and rules help.
PLEASE HELP WILL MARK BRAINLIEST
Answer:
b,a,c
Step-by-step explanation:
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
Ebony earned scores of 70 , 72 , 89 , 92 , 89 and 80 on six math tests. Determine her score on the seventh test if her average for the seven tests was 80? Enter your answer as a whole number
Answer:
70
Step-by-step explanation:
TAKE MY POINTS pleaseeee
Answer:
156 M
Reasoning you add How far He has walked from his starting point
Step-by-step explanation:
Answer: 156 m here u go
The first bus stop on a bus route is 4 miles from school. How many yards is the first bus stop from school?
Answer:
7040 yards
Step-by-step explanation:
1 mile = 1760 yards
1 x 4 miles = 1760 x 4 yards
4 miles = 7040 yards
Answer this. Please LOL NOW
Answer:
A
Step-by-step explanation:
Took this test
Can you find the surface area of a rectangular prism 2,3,4
Answer:
48
Step-by-step explanation:
4*2*3 for the 4 flaps
2*4*3 for the 2 tops
(4*2*3) + (2*4*3) = 48
Answer:
52 square inches
Step-by-step explanation:
to find the surface area of a rectangular prism the formula is
S.A.=2(l*w+l*h+w*h)
2(4*3+4*2+3*2)
=52 square inches
here l is length w is width and h is height
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 8x3/5 + 3x−4/5
Answer:
\(\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\)
Step-by-step explanation:
Given the function: \(f(x)=\dfrac{8x^3}{5}+3x-\dfrac{4}{5}\)
To take the antiderivative (or integral) of a function, we follow the format below.
\(f(x)=x^n\\$Then its antiderivative\\Antiderivative of f(x)$=\dfrac{x^{n+1}}{n+1}\)
Therefore, the antiderivative of f(x) is:
\(=\dfrac{8x^{3+1}}{5(3+1)}+\dfrac{3x^{1+1}}{2}-\dfrac{4}{5}x+C\\=\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\)
We want to check our result by differentiation.
\(\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\right)\\=\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}\right)+\dfrac{d}{dx}\left(\dfrac{3x^{2}}{2}\right)-\dfrac{d}{dx}\left(\dfrac{4}{5}x\right)+\dfrac{d}{dx}\left(C\right)\\\\=\dfrac{32x^{3}}{20}+\dfrac{6x}{2}-\dfrac{4}{5}+0\\\\=\dfrac{8x^{3}}{5}+3x-\dfrac{4}{5}\)
Find two numbers whose sum is 9 and their difference is 60.
Smaller-
Large number-
Answer:
Step-by-step explanation:
x+y = 9
x-y = 60
-----------
2x = 69
x = 34.5
y = 9-x = -25.5
smaller number: -25.5
larger number: 34.5
Need help alegbra!!! Look at photo for question!!
Answer
74+2
Step-by-step explanation:
I want a correct answer you can take your time. If I was born on December 24, two thousand and four and my classmate was born on April 9, two thousand and six, how many months, years and days are we apart?
Answer:
5years, 3months, 16 days
Circle 1 is centered at (−4,−2) and has a radius of 3 centimeters. Circle 2 is centered at (5,3) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes.
The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of .
The circles are similar because you can translate Circle 1 using the transformation rule (9, 5) and then dilate it using a scale factor of 2.
To prove that Circle 1 and Circle 2 are similar, we need to identify the transformations that can be applied to Circle 1 to obtain Circle 2.
First, let's consider the translation of Circle 1. The translation rule is given by (a, b), where a represents the horizontal shift and b represents the vertical shift.
In this case, to translate Circle 1 to align with Circle 2, we need to shift it 9 units to the right and 5 units up. Therefore, the translation rule for Circle 1 is (9, 5).
Next, let's consider the dilation. A dilation is a transformation that changes the size of the figure but preserves its shape. The scale factor, denoted by k, determines the amount of scaling. In this case, Circle 1 needs to be dilated to match the size of Circle 2.
The scale factor can be determined by comparing the radii of the two circles. The radius of Circle 1 is 3 centimeters, while the radius of Circle 2 is 6 centimeters. The scale factor is obtained by dividing the radius of Circle 2 by the radius of Circle 1: 6/3 = 2.
Therefore, the transformation applied to Circle 1 to prove that the circles are similar is a translation by (9, 5) followed by a dilation with a scale factor of 2.
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The difference of three times a number and 4 is 14. Find the number.
Answer:
x=6
Step-by-step explanation
you have to build up simple equation for this.
3x-4=14
3x=18
x=6
Hope this will be helpful =)
Solve by graphing. Round each answer to the nearest tenth.
6x^2 + 31x = 12
How do you figure out division expression with answer of 19.1
Answer:
its 5823
Step-by-step explanation:
help urself
hi im doing homework i hate i-ready so yea can someone answer this please?
Weight of Omar after 4 weeks is 9.4375 pounds.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Weight of Omar at the time of birth = 8 pound 3 ounces
Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces
New weight of Omar
= (8 lb 3 ounces) + 20 ounces
= 8 lb + 23 oz
As, we know 16 ounces = 1 pound
23 ounces = 1.4375 pound
Now, total weight of Omar after 4 weeks = 8 lb + 23 oz
≈ 8 lb + (1.4375) lb
≈ 9.4375 pounds
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A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
100 points!!!!!! What is the value of this question ? please help quick !!!!!!!!!!!!!!!
Answer:
1/2
Step-by-step explanation:
y varies directly with x.
y is -50 when x is 10
What is x when y is 15?
Suppose
x = [?]
X
The value of x is -3 when value of y = 15 by using the property proportion as x and y are directly related to each other.
What is direct relation?
Two variables x and y are directly related to each other if x increases or decreases the value of y also increases or decreases proportionally.
We are given that value of y is -50 then value of x is 10
We have to find the value of x when y is 15
We solve it using proportion
we have,
10/x = -50/15
On separating the variable from the constant and then simplifying we get,
x=-3
Hence the value of x is -3 when y is 15
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can someone pls help answer this
Answer:
Small: 7
Large:13
Step-by-step explanation:
I worked it out, hope this helps
Answer:
Answer:
Small: 7
Large:13
Step-by-step explanation:
I worked it out, hope this helps
solve 5xln2=(2x+1)ln3
Answer:
hhhhhhhhghhhgggghhhhhhhhhhhhhhhhh
Sean received both the 5th highest and the 5th lowest mark in the class. How many students are there in the class?
Answer:
There are 9 people in the class.
Step-by-step explanation:
Sean received the 5th highest grade in his class meaning that there are 4 people in front of him who got a higher grade. This also means that Sean has 4 people behind him who have lower grades. So,
4+4+1 (Sean himself) = 9 people
The number of students in the class is given by the sum of the frequency
of each score.
There are at least 9 students in the class.Reasons:
When the class scores are arranged in increasing order, we have;
Sean's position = 5 th = The fifth lowest score
Therefore;
The number of scores lower than Sean's score = 4When the scores are arranged in decreasing order, we have;
Sean's position = 5 th = Fifth highest score
Therefore;
The number of scores higher than Sean's score = 4The total number of different scores in the class = 4 + 1 + 4 = 9Given that two or more students can have the same score, the frequency
of each score, determines the number of students in the class, we have;
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Solve the equation for x.
(x=21)= 103
X =
Answer:
Step-by-step explanation:
I don't know if you made a mistake when typing but I am guessing you meant x - 21 = 103
(x-21) = 103 Add 21 to each side
x - 21 + 21 = 103 + 21
x = 124
The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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You are considering two possible marketing campaigns for a new product. The first marketing campaign requires an outlay next year of 2M, and then will pay 0.24M in all subsequent years. The second marketing campaign requires an outlay of 3M next year and then will pay 0.27M in all subsequent years.
What is the IRR for the first marketing campaign?
The IRR is a used by to estimate the profitability of the marketing campaigns.
The IRR for the first marketing campaign is 12%.
The given parameters are:
First marketing campaign
\(\mathbf{Outlay\ Next\ Year = 2M}\)
\(\mathbf{Subsequent\ Years = 0.24M}\)
Second marketing campaign
\(\mathbf{Outlay\ Next\ Year = 3M}\)
\(\mathbf{Subsequent\ Years = 0.27M}\)
The IRR of the first marketing campaign is calculated as follows:
\(\mathbf{IRR = \frac{Subsequent\ Years}{Outlay\ Next\ Year}}\)
So, we have:
\(\mathbf{IRR = \frac{0.24M}{2M}}\)
Cancel out common factors
\(\mathbf{IRR = \frac{0.24}{2}}\)
\(\mathbf{IRR = 0.12}\)
Express as percentage
\(\mathbf{IRR = 0.12 \times 100\%}\)
So, we have:
\(\mathbf{IRR = 12\%}\)
Hence, the IRR for the first marketing campaign is 12%.
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A coin has a diameter of 22 millimeters. What is the area of the coin? Use 3.14 for T. Round your answer to the nearest tenth.
Answer:
The answer to the question was
379.9