Answer:
x=21
Step-by-step explanation:
The angles of a triangle always add up to 180°
71+62+(2x+5)=180
First add 71 and 62
133+(2x+5)=180
Then you subtract 133
2x+5=47
Subtract 5 too
2x=42
Then divide by 2
x=21
We can check our answer by adding all the angles
71+62+(2*21+5)
71+62+(42+5)
71+62+47=180
The perimeters of the
square and the rectangle
below are the same. Write
and solve an equation to find
the value of x.
3x
x-2
Area =
121 in 2
Answer:
Step-by-step explanation:
A formula is a method that has been proven to work when solving specific types of problems.
Let’s explore some of those familiar formulas by looking at rectangles, squares, area and perimeter.
The perimeter of a figure is the distance around the figure. Perimeter is the sum of all of the sides in a square or rectangle. Since a rectangle has two sets of parallel sides, the formula for determining perimeter of a rectangle is:
and
Let’s look at an example.
[Figure 2]
The rectangle above shows its dimensions. Find the perimeter.
First, substitute the values for the width and the length into the perimeter formula.
Next, complete the multiplication and addition to find the perimeter.
The answer is 42.
The perimeter of the rectangle is 42 inches.
Area is the amount of square units inside the figure. Area is found by multiplying the . The formula for finding the area of a rectangle is:
You can use the dimensions from the rectangle above to find the area of this rectangle.
First, fill the values for and into the formula for area.
Next, solve for the area by multiplying.
The answer is 108.
The area of the rectangle is .
Notice that the unit of measurement for area is squared. That is because you multiplied a unit measure times itself: . Area is always written in square units.
You can also find the perimeter and area of a square. Remember that a square has four equal sides given the symbol . You can use the following formula for finding the perimeter of a square:
Let’s look at an example.
A rectangle has a length of 12 feet and a perimeter of 72 feet. Write and solve an equation to determine the width of the rectangle.
First, substitute the values for the perimeter and the length into the perimeter formula.
Next, complete the multiplication.
Then, subtract 24 from both sides to get your variable alone on the right side.
Then, multiply both sides by the reciprocal of 2 to isolate your variable.
The answer is 24.
The width of the rectangle is 24 feet.
Examples
Example 1
Earlier, you were given a problem about Raj and his garden fence.
He knows that the area of the land is 240 square feet, the length of one side is 15 feet, and needs to know the width of the land.
First, substitute the values for the area and the side length into the area formula.
Next, multiply both sides by the reciprocal of 15 in order to isolate the variable .
The answer is 16.
The width of Raj’s garden is 16 ft. Therefore the dimensions of the garden are 16 ft by 15 ft.
Example 2
A square has a perimeter of 196 inches. Determine the length of one side of the square.
First, substitute the value for the perimeter into the perimeter formula.
Next, multiply both sides by the reciprocal of 4 to isolate your variable.
The answer is 49.
Example 3
Find the perimeter of the following square if the side length is 4.5 inches.
First, substitute the value for the side length into the perimeter formula.
Next, multiply by 4 to solve for the perimeter.
The answer is 18.
Example 4
Can you find the area of the square in Example 1?
First, substitute the value for the side length into the area formula.
Next, multiply to solve for the area.
The answer is 20.25.
The area of the square is .
Example 5
A square has an area of 144 sq. meters. What is the side length?
First, substitute the value for the area into the area formula.
Next, take the square root of the area to isolate . Remember that the opposite of square is square root.
The answer is 12.
Solve for X please!!!!!!!!!!!!! I need this answer ASAP
2x + 1/3x = 21
We know:
we can add/subtract the same expression to both sides of the equation to get an equivalent equation;we can multiply/divide both sides of the equation by the same non-zero number to get the equivalent equation.Equivalent equations are algebraic equations that have identical solutions.
We have the equation:
[tex]2x+\dfrac{1}{3}x=21[/tex]
SOLUTION:multiply bot sides by 3
[tex]3\cdot2x+3\!\!\!\!\diagup\cdot\dfrac{1}{3\!\!\!\!\diagup}x=3\cdot21\\\\6x+x=63\\\\7x=63[/tex]
divide both sides by 7
[tex]\dfrac{7\!\!\!\!\diagup x }{7\!\!\!\!\diagup}=\dfrac{63}{7}\\\\\boxed{x=9}[/tex]
Answer:
x = 9
Step-by-step explanation:
Given equation,
→ 2x + (1/3)x = 21
Now the value of x will be,
→ 2x + (1/3)x = 21
→ (6/3)x + (1/3)x = 21
→ (7/3)x = 21
→ 7x = 21 × 3
→ 7x = 63
→ x = 63/7
→ [ x = 9 ]
Hence, the value of x is 9.
A store received shipment of 37 tvs valuad at 625 each what is the total value. Of the shipment
A store received shipment of 37 tvs valued at 625 each what is the total value of the shipment?
37 * $625 = $23,125
Shaylee is determining if 6 is the solution to the equation.
42 ÷ w = 7 for w = 6
First, Shaylee must substitute
for
.
To simplify, Shaylee must divide
by
.
First Shaylee must substitute 6 for w. To simplify, Shaylee must divide
42 by 6.
What is division?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
In this equation we have
42 ÷ w = 7
The question has already specified the value of w as 6
Hence we would have to remove w and replace it with the value six 6.
This is
42 ÷ 6
Next we have to find the value or the answer when we do this division. This can be easily done with a calculator
42 ÷ 6 = 7
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the owner of a convenience store has determined that their daily revenue has mean $7200 and standard deviation $1200. the daily revenue totals for the next 30 days will be monitored. expressing the probability to four decimal places and for two points, what is the probability that the mean daily revenue for the next 30 days will exceed $7000?
The probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.
Define the term z score?The Z-score indicates the discrepancy between a given value and the standard deviation. The Z-score, also referred to as the median score, indicates how often standard deviations an actual data point deviates from the mean.The formula for the z score is-
z = (x - μ)/σ
In which,
z = standard scorex = observed value (= $7000)μ = mean ( = $7200)σ = standard deviation (=$1200)Put the value in formula
z = (7000 - 7200)/1200
z = - 0.16
Thus,
P(x > $7000) = P(z > - 0.16)
See the p- value for obtained z from negative z score table.
P(x > $7000) = 0.4760
Thus, the probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.
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Which of the following represents an equation in standard form for the line that passes through (3, -1) and (-5, -3).
O A y-tx-1
OB 7x-4y = 1
OC. x - 4y = 7
D 4x-y=7
Answer:
Step-by-step explanation:
y = ¼x + (-7/4) is the standard form for the line that passes through (3, −1) and (−5, −3)
What is Slope intercept form?
y=mx=c is the slope intercept form of a line, m is the slope.
We need to find equation of line passing through (3, −1) and (−5, −3)
First we need to calculate slope 'm'.
slope m = y2- y1 / x2-x1
y2=-3, y1=-1, x2=-5, x1=3
m= -3 - (-1)/(-5)-3 = -2/-8=1/4
Equation of line, y=mx+c
find C in the equation (y=mx+c)
C = y-mx
C = -1-1/4(3)= -7/4
now replace the values you find in the equation (y=Mx+C)
y =1/4x-7/4
Hence y =1/4x-7/4 is the equation of line passes through (3, −1) and (−5, −3).
i need help also i don't know what to do with x. 3(4x-12) = 84
Answer:
x=10
Step-by-step explanation:
3(4x-12)=84
12x-36=84
+36. +36
12x=120
/12. /12
x=10
Hopes this helps please mark brainliest
Find the Error When graphing the equation y=−3x+2, a student plotted the y-intercept at 2, then moved down 3 units and to the left 2 units because the slope is negative, so both rise and run are negative. Find his error and correct it.
Which selections describe an error that the student made and give the correct response? Select all that apply.
Multiple select question.
A)
The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −31 .
B)
The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.
C)
The student plotted the y-intercept at 2, instead of at −3. The y-intercept should be −3, because when x=0, you get y=−3.
D)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the left 1 unit, because the slope is −3−1, not −3−2.
E)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 2 units, because the slope is −32, not −3−2.
F)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −31, not −3−2.
*also need this one*
Answer:
A, B, F
Step-by-step explanation:
You want to know the errors made in graphing y = -3x +2 by plotting the y-intercept of 2 and then plotting another point 3 down and 2 left of that.
PlotThe appropriate graph would be created by plotting the y-intercept at 2, then moving down 3 units and 1 unit right from there, because the slope is -3.
ErrorsThe y-intercept is correctly plotted at y=2.
The next point is incorrectly plotted down 3 units and 2 units left of the y-intercept. It should be plotted down 3 units and 1 unit right.
The slope is -3, or -3/1. For a negative slope, the rise or run, but not both, will be negative. We don't know the student's rationale for using 2 as the "run" in ...
slope = rise/run
The best error descriptors seem to be ...
A) The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −3/1 .
B) The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.
F) After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −3/1, not −3/−2.
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a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 90% confidence level, what size of sample is needed? give your answer in whole people.
For the specified requirements, 105 sample size are required.
Given that,
Confidence Interval = 90
Margin of error (m) =0.08
We know , to find Sample size for estimating a population proportion
n = (Z*/m)² P(1-P)
where , m is margin of error
P is estimated proportional value.
If we have no preconceived of the value of the population proportion
, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.
for a 90% confidence interval ,
Z* = 1.645 , m=0.08
Using equation we get
n = (1.645/0.08)²(0.5)( 1 - 0.5 )
By solving,
n =105.3 = 105
The necessary sample size is 105
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The dimensions of two rectangular prisms are shown below. How much more volume does the larger prism have than the smaller prism?
Answer:16/25 :D
Step-by-step explanation:does that help :3
Write the equation of the line that passes through the points (−3,−5) and (−2,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Expand and Simplify (x+5)(x-2)
Answer:
[tex]x^2+3x-10[/tex]
Step-by-step explanation:
To expand you must do this:
[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]
Is g = 10 a solution to the inequality below?
g≤ 4
yes
Submit
S
Answer:
yes it is
atleat i think
whats the product of 23 and 39
Answer:
Step-by-step explanation:
1. Product means multiplying sign in math
23*39=897
2. Answer: 897
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Dimensions of the area enclosed is l = 800 ,b = 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and breadth.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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Write the polynomial in standard form. Then
name the polynomial based on its degree and number of terms.
3. g-6g³+10g²-3
a. 6g³-10g²+g-3; cubic trinomial
b. -3+g+10g²-6g³; cubic binomial
c. -6g³+10g²+g-3; cubic polynomial
d. 10g³-6g²+g-3; quadratic binomial
At 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
If he continues at this rate, at what time will he reach `10000` steps?
To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
The time will be calculated as,
2000 steps ⇒ 23 minutes
1 Step ⇒ 23 / 2000 minutes
10000 steps ⇒ ( 23 x 10000) / 2000 minutes
10000 steps ⇒ 115 minutes
The time of covering 10000 steps will be at 9:55.
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a fruit stand has to decide what to charge for their produce. they need \$10$10dollar sign, 10 for 444 apples and 444 oranges. they also need \$12$12dollar sign, 12 for 666 apples and 666 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange?
No, we cannot find a unique price for an apple and an orange
Let the price of an apple be $x and that of orange be $y.
Condition 1.
They need $10 for 4 apples and 4 oranges.
Then, 4x + 4y = 10
or, 2x + 2y = 5 .....(1)
Condition 2.
They need $12 for 6 apples and 6 oranges.
Then, 6x + 6y = 12
or, 2x + 2y = 5 .....(2)
Two identical linear equations have been discovered.
They do, however, create a system of dependent linear equations that reduces to:
2x + 2y = 5
There are infinite possible solutions to this linear equation.
Thus, we get the conclusion that an apple and an orange cannot have different prices.
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the probability of serena serving an ace n tennis is 0.15, and the probability that she double faults is 0.25. what is the probability that serena does not serve an ace or a double fault?
The probability that Serena does not serve an ace or a double fault is 0.63..
Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .
We have following information,
The probability of Serena serving an ace in tennis (p) = 0.15
Probability that she double faults(q) = 0.25
The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85
let A and B be two events Serena not serving an ace and she double faults respectively.
Events A and B are not mutually exclusive events .
i.e, P(A ∩ B ) =/ 0
when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.
So, the probability of intersection of event A and B = 0.85/2 = 0.47
Adding Rule for probabilities is
P(A or B ) = P(A) + P(B) - P(A ∩ B)
The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47
= 1.10 - 0.47 = 0.63...
Hence, the probability that Serena does not serve an ace or double fault is 0.63..
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Headphones were bought for $44. Coupon code got 20% off then a 5% processing fee was after the discount. How much was the processing fee?
The processing fee was = $36.96
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
let the price of headphones be= x
44*20/100=8.844-8.8=35.235.2*5/100=1.7635.2+1.76= 36.96Hence,The processing fee was = $36.96
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Im not sure how to do this, could one of you give me the answer on how to do this?
Answer:
2x+4=52
2x+19=67
2x+13=61
(I gotta be honest I can’t fully remember how to name the angles but to not set you astray I just put the equation each angle goes to)
x=24
Step-by-step explanation:
the sum of all three angles is equal to 180 degrees
So we can add all of these angles and set it equal to 180 like this
(2x+19)+(2x+4)+(2x+13)=180
Simplify by adding common terms
6x+36=180
-36. -36
6x=144
/6. /6
x=24
So now to find the angles we just fill in x with 24
2(24)+4
48+4
52
2(24)+19
48+19
67
2(24)+13
48+13
61
Hopes this helps please mark brainliest
PLEASE HELP I REAALLY NEED HELP!
The domain of the exponential function in this problem is given as follows:
0 ≤ n ≤ 5.
How to obtain the domain of the exponential function?The exponential function in this problem is defined by the rule presented as follows:
g(n) = 10(1.02)^n.
In which the variables are listed as follows:
n is the number of days.g(n) is the height of flower after n days.When the study was finished, the height of the flower was of 11.04 inches, hence the day at which the study was finished is obtained as follows:
10(1.02)^n = 11.04
(1.02)^n = 11.04/10
log[(1.02)^n] = log(11.04/10)
Applying the logarithm of power property, we have that:
nlog(1.02) = log(11.04/10)
n = log(11.04/10)/log(1.02)
n = 5.
The domain is the number of days for which the student was realized, hence:
0 ≤ n ≤ 5.
As the number of days cannot assume negative values.
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One bulldozer clears land twice as fast as another. Together they clear a large tract in 1.5 hours. How long would the larger bulldozer take?
The larger bulldozer would take about 30 minutes.
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if 269 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? round your answer to four decimal places.
The probability will be 0.9940.
The provided parameters are
p = 0.05 (the true proportion or the mean )
n = 269 ( sample size )
we can calculate standard deviation as follows
σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
σ = 0.0132
Now the values that 'x' can take are
x = [tex]x_{1}[/tex] ± [tex]x_{2}[/tex]
x = 0.05 + 0.03, 0.05 - 0.03
x = 0.08 , 0.02
Also the z-score is
z = (x - μ)/σ
z = [tex]\frac{0.08-0.05}{0.0132}[/tex] , [tex]\frac{0.02-0.05}{0.0132}[/tex]
z = 2.27 , -2.27
we now find the p-values for the z-scores
p values are = 0.9970 , 0.0030
The difference in these values will give the probability
∴ P = 0.9970 - 0.0030
P = 0.9940
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Suppose loga(2) = b and loga(3) = c. Compute loga(108/a^3)
In accordance with algebra properties and relationship between logarithms and powers, the logarithm ㏒ₐ (108 / a³) is equal to the pseudolinear expression 2 · b + 3 · c - 3.
How to solve a logarithmic expression
In this problem we must determine the base of a given set of logarithms by using algebra properties and relationships between powers and logarithms. Now we proceed to solve:
Step 1 - We get the following equations:
㏒ₐ 2 = b, ㏒ₐ 3 = c
Step 2 - Now we add the other logarithm:
㏒ₐ (108 / a³)
Step 3 - By logarithm properties:
㏒ₐ 108 - ㏒ₐ a³
㏒ₐ (2² · 3³) - 3 · ㏒ₐ a
㏒ₐ 2² + ㏒ₐ 3³ - 3 · 1
2 · ㏒ₐ 2 + 3 · ㏒ₐ 3 - 3
Step 4 - By Step 1:
2 · b + 3 · c - 3
The logarithm ㏒ₐ (108 / a³) is equivalent to 2 · b + 3 · c - 3.
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What is the value of y in the equation 2(2y − 16) = 0? (5 points)
a 4
b 6
c 8
d 9
Answer:
the options are wrong
Step-by-step explanation:
open the bracket2(2y)2(-16)=04y-32=0make y the subject of formulary=-32÷4y=-8Answer:
C. 8
Step-by-step explanation:
2 x 8 = 16
16 - 16 = 0
2 x 0 = 0
This square based pyramid
30 cm
is cut horizontally at a height of 15 cm
to leave this frustum
R
15 cm
10 cm
1 xarea of base x perpendicular height
Vol = x
10 cm
Calculate the volume of the frustum.
Answer:
875 cm³
Step-by-step explanation:
You want the volume of the 15 cm high frustum of a 30 cm high pyramid with a 10 cm square base.
Pyramid volumeThe volume of a pyramid is given by the formula ...
V = 1/3Bh
Where B is the area of the base:
B = s²
For the given pyramid, the volume is ...
V = 1/3(10 cm)²(30 cm) = 1000 cm³
Frustum volumeThe volume of the frustum is the volume of the whole pyramid, less the volume of the part that is cut off. The part that is cut off has dimensions that are 1/2 of those of the whole pyramid, so its volume is ...
V = (1/2)³ × (1000 cm³) = 125 cm³
Then the volume of the remaining frustum is ...
1000 cm³ -125 cm³ = 875 cm³
The volume of the frustum is 875 cm³.
__
Additional comment
The volume can also be calculated from the areas of the two bases of the frustum and its height.
V = (1/3)(B₁ +B₂ +√(B₁B₂))h
The top base is 5 cm square, so this evaluates to ...
V = (1/3)(100 cm² +25 cm² +√(100·25) cm²)(15 cm) = 1/3(175 cm²)(15 cm)
V = 875 cm³
Which of the following expressions represents the distance between -3/4 and -0.2 on a number line?
The expression that represents the distance between -3/4 and -0.2 on a number line is |-3/4 + 0.2|
What is distance?The distance between points on a number line is the number of units or points between these points
How to determine the distance?From the question, we have the following parameters that can be used in our computation:
Distance between -3/4 and -0.2 on a number line
This means that
Endpoints = -3/4 and -0.2
These endpoints can be represented as
Endpoint 1 = -3/4
Endpoint 2 = -0.2
The distance between these endpoints is then calculated as
Distance = |Endpoint 1 - Endpoint 2|
Substitute the known values in the above equation, so, we have the following representation
Distance = |-3/4 - -0.2|
Evaluate the difference
Distance = |-3/4 + 0.2|
Hence, the distance expression is |-3/4 + 0.2|
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The range of f(x) = |x| is y ≥ 0. If a < 0 and b ≠ 0 for g(x) = a|x| + b, what is the range of function g?
The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.
Range of a functionIt follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.
Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).
However, the possible values of constant, b include all real numbers except 0.
On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.
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the mayor of a town has proposed a plan for the construction of an adjoining community. a political study took a sample of 1600 voters in the town and found that 34% of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 31%. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is 2.59.
What is Test Statistics?A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
Here, the percentage of residents favored construction is 34%.
[tex]p\leq 0.31\\p > 0.31[/tex]
The test statistics is given by,
[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]
Here n=1600, P=0.34 and p=0.31,
Putting the values,
[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]
Test Statistics = 2.59
Therefore, the value of test statistics is 2.59.
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