Answers
The angle directly across from the 32 is also 32 degrees because it uses the same lines at the same angles. That's the Vertical Angles Theorem. The line straight across means that is 180 degrees, which is already split in half by the visible 90 degree angle (given by the box in the corner). Since all the angles are on the same side of the line, the 180 degree angle, they should add up to equal 180 degrees. Also, since 90 is half of 180, the 32 degree angle and the x angle should just add up to equal 90 degrees. So, 90 minus 32 equals 58.
Related Questions
Alex painted 178 ft2 of his apartment’s walls with 13 1 3 gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 ft2 of his apartment, does he have enough paint? Complete a true statement
Answers
From multiplcation operation, Alex has enough paint to cover 1,000 ft² of his apartment. The true statement is 2 gallons of paint will cover 1068 ft², Alex have enough paint of quantity 2 gallons.
We have Mr. Alex painted his apartment. Area of his apartment'walls = 178 ft²
Quantity of paint used by him to paint his apartment'walls with area 178 ft² =\( \frac{1}{3} \: \: gallons\)
Total quantity of paint used in all
= 2 gallons
We have to check the provide paint is enough or not to cover 1,000 ft² of his apartment. Let the required paint for 1000 ft² be x gallons. Using multiplcation, 1/3 gallons quantity of paint will cover the area of apartment = 178 ft², so, 1 gallons quantity of paint will cover the area of apartment = 178 ×3 ft²= 534 ft²
Now, 2 gallons quantity of paint will cover the area of apartment = 2× 534 ft² = 1068 ft²> 1000 ft²
But he wants to paint 1000 ft² of his apartment in 2 gallons quantity (x=1.9 gal ). So, he has enough paint to paint his apartment.
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Complete question:
The above figure complete the question.
Alex painted 178 ft2 of his apartment’s walls with 1/3 gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 ft2 of his apartment, does he have enough paint? Complete a true statement
TRUE/FALSE. post-implementation evaluation primarily is concerned with assessing the quality of a new system.
Answers
True. Post-implementation evaluation refers to the process of evaluating the performance and effectiveness of a new system after it has been implemented.
It involves assessing the extent to which the system meets the intended objectives, as well as its overall quality and impact on the organization. The evaluation can be carried out through various methods such as user feedback, performance metrics, and system testing.
Therefore, post-implementation evaluation is primarily concerned with assessing the quality of a new system and its ability to deliver the expected benefits to the organization.
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1 year = 12 months
3/4 year =
Answers
Answer:
3/4 year = 9
Step-by-step explanation:
To find 3/4 of a year you first need to find 1/4 of a year so you do 12/4 and get 3. Now we know that 1/4 of a year is 3 months so you just multiply that by 3 to get 9. So 3/4 of a year is 9 months.
I hope this helps!
Your answer to 3/4 of a year is 9 months
HELPPPPPPPPPPPPPPPPPPP!
Answers
Answer: Real, equal, rational.
Step-by-step explanation:
\(-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.\)
what is the perimeter of 7%
Answers
Answer:
solve the following questions 2x+3=24
what is the ratio of 3:4
Answers
The simplified or reduced ratio "3 to 4" tells us only that, for every three men, there are four women. The simplified ratio also tells us that, in any representative set of seven people (3 + 4 = 7) from this group, three will be men. In other words, the men comprise 73 of the people in the group.
Hi there!
Answer:
\(\boxed{6:8}\)
Step-by-step explanation:
3 : 4 = 600 : 800
\(3 : 4 = 1 : 1.3333333333333= 0.75 : 1\)
\(3\\3 + 4\\= 42.857142857143%\) ( don't mind theis part because idk how make the chart )
Have a great day/night!
rewrite: as a power of five:125;625;15625
Answers
Answer: 125 = 5³
625 = 5⁴
15625 = 5^6
Step-by-step explanation:
Tge question simply states that we should write the numbers given below in power of 5 and the number goes thus:
125 = 5 × 5 × 5 = 5³
625 = 5 × 5 × 5 × 5 = 5⁴
15625 = 5 × 5 × 5 × 5 × 5 × 5 = 5^6
What's the standard deviation of the sum of two independent random variables, each of standard deviation of 3 and 4
Answers
The standard deviation of the sum of the two independent random variables is 5.
The standard deviation of the sum of two independent random variables is equal to the square root of the sum of the variances of each random variable.
To find the standard deviation of the sum of two independent random variables, you can use the following formula:
Standard deviation of the sum (σ_sum) = √(σ₁² + σ₂²)
Here, σ₁ and σ₂ are the standard deviations of the two independent random variables.
Given: σ₁ = 3 and σ₂ = 4
Now, plug the values into the formula:
σ_sum = √(3² + 4²) = √(9 + 16) = √25 = 5
So, the standard deviation of the sum of the two independent random variables is 5.
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The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Answers
Answer:
A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground
Step-by-step explanation:
f(t) = 4t^2 − 8t + 7
Factor out 4 from the first two terms
f(t) = 4(t^2 − 2t) + 7
Complete the square
(-2/2)^2 =1 But there is a 4 out front so we add 4 and then subtract 4 to balance
f(t) = 4( t^2 -2t+1) -4 +7
f(t) = 4( t-1)^2 +3
The vertex is (1,3)
This is the minimum since a>0
The minimun is y =3 and occurs at t =1
Answer:
The above answer is correct.
Step-by-step explanation:
if a = 1 3 5 and b equals to 1 3 5 find a into B and Plot the co-ordinate in graph paper
Answers
To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.
Given:
a = [1, 3, 5]
b = [1, 3, 5]
To find a · b, we multiply the corresponding components and sum them:
\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)
So, a · b equals 35.
Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.
On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.
First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.
Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).
The graph paper would show a single point labeled 35 on the number line.
Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.
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Each chart has which three components (choose three)?
A. Forecast of customer
B. A center line representing the average
C. An upper line representing last week's sample
D. A lower line representing last week's sample
E. An upper line representing the maximum acceptable variation upwards
F. A lower line representing the maximum acceptable variation downwards
G. A center line representing the maximum acceptable variation centrally
Answers
Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.
Each chart has the following three components:
1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.
2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.
3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.
These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.
In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.
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A test contains 50
multiple choice questions. Suppose that one gets 2
marks for every correct answer and 1
mark is deducted from the student’s score for every incorrect answer. If Robin attempted all the questions and scored 58
on the test, then find the number of questions he attempted correctly.
Answers
Answer:
I don't know if it is correct.Let's assume that the number of questions Robin attempted correctly is x.
For each correct answer, Robin gets 2 marks, so the total marks earned from correct answers would be 2x.
For each incorrect answer, 1 mark is deducted, so the total marks deducted would be 50 - x.
Given that Robin scored 58 on the test, we can set up the equation:
2x - (50 - x) = 58
Simplifying the equation:
2x - 50 + x = 58
3x - 50 = 58
3x = 58 + 50
3x = 108
x = 108 / 3
x = 36
Therefore, Robin attempted 36 questions correctly.1⁄4 + 4⁄8 + 4⁄6 = ???
Answers
☁️ Answer ☁️
Exact form:
17/12
Decimal:
1.416
mixed:
1 5/12
Hope it helps.
Have a nice day hyung/noona ￣▽￣
K As a town gets smaller, the population of its high school decreases by 4% each year. The senior class has 250 students now. In how m students? Write an equation. Then solve the equation. Write an equation to represent this situation. Let n be the number of years before the class will have 100 students. 0 (Type an equation using n as the variable. Use integers or decimals for any numbers in the equation.) Solve the equation. In n = years the senior class will have about 100 students. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
Answer:
y = 250(0.96^n)
Step-by-step explanation:
You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.
Exponential equationThe exponential equation will have the form ...
y = a·b^x
where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.
ApplicationYou have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...
y = 250(0.96^n)
100 studentsThe population will reach 100 students when n has the value that satisfies ...
100 = 250·0.96^n
0.4 = 0.96^n . . . . . . . . . divide by 250
log(0.4) = n·log(0.96) . . . . . take logarithms
n = log(0.4)/log(0.96) ≈ 22.45
The senior class will have about 100 students in 22.45 years.
__
Additional comment
The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.
compare the square root of one hundred sixty and one hundred sixteen ninths using <, >, or =.
Answers
The comparison between the square root of one hundred sixty and one hundred sixteen ninths is √160>√116/9.
To compare the square roots of 160 and 116/9, follow these steps:
We need to first find the square roots of these two numbers. The square root of 160 =√(16×10)=4√10= 12.65, rounded to two decimal places. The square root of 116/9 can be simplified as follows:√(116/9) = √(116)/√(9) = (2√(29))/3=3.59.Now, we can compare the two values: 12.65 > (2√(29))/3. Therefore, the answer is 12.65 > (2√(29))/3.The comparison between the square root of one hundred sixty and one hundred sixteen ninths is √160>√116/9, which is also 12.65>3.59
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Strat
1. Brenna cuts wood for a fire. She can cut a log into thirds in 10 min.
How long would it take Brenna to cut a similar log into sixths?
Answers
Brenna would take 20 min to cut the same wood into sixths.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10
x = 0.3 cuts per minute for single wood,
Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min
Thus, Brenna would take 20 min to cut the same wood into sixths.
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If a: b = 1:2 and b; c = 3:4, find a : c.
Answers
Answer:
Step-by-step explanation:
b:c= 3:6
Answer:
Step-by-step explanation:
We know that:
a : b = 1 : 2 (or a = (1/b)*b)
b : c = 3 : 4 (or b = (3/4)*c)
So, we can substitute the value of b from the second equation into the first equation to get the ratio of a : c:
a = (1/b)*b = (1/((3/4)c))((3/4)c) = (4/3)(1/c)*c = (4/3)*1 = 4/3
So, the ratio of a : c is 4 : 3.
Alternatively, we can use the cross-multiplication method to find the ratio.
a : b = 1 : 2, and b : c = 3 : 4
so a4 = b3, and b4 = c3
so a4 = c3
so a:c = 3:4
In this way also we got the ratio of a:c as 3:4
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
Answer: the answer is 189
Step-by-step explanation:
) The value of shares, t years after their floatation on the stock market, is modelled by V=10e 0.09t
Find the initial value of these shares and values after 5 years, 10 years and 12 years, respectively. Round your answer to two decimal places. [9 marks] During a recession, a firm's revenue declined continuously so that the total revenue (TR) in t years' time is modelled as TR=10e −0.19t
(in million dollars) Calculate the current revenue and revenue in 5 years' time. After how many years the revenue of this firm is going to drop to $1 million? Round your answer to two decimal places.
Answers
After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.
The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t
The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,
we get
V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.
The values after 5 years, 10 years and 12 years, respectively are:
For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars
The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)
The current revenue is the total revenue when t = 0.
So, putting t = 0 in TR = 10e−0.19t, we get
TR = 10e−0.19 × 0= 10e0= 10 million dollars
Revenue in 5 years' time is TR when t = 5.
So, putting t = 5 in TR = 10e−0.19t, we get
TR = 10e−0.19 × 5≈ 4.35 million dollars
To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.
Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1
Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303
Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.
So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.
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In a recent tennis tournament, women playing singles matches used challenges on 135 calls made by the line judges. Among those challenges, 36 were found to be successful with the call overturned.
a. Construct a 95% confidence interval for the percentage of successful challenges.
b. Compare the results from part (a) to this 95% confidence interval for the percentage of successful challenges made by the men playing singles matches: 23.6%
Answers
a) The 95% confidence interval is 18.95% to 34.49%. b) The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%.
To construct a 95% confidence interval for the percentage of successful challenges made by women playing singles matches, we can use the formula for the confidence interval for a proportion. The formula is:
Confidence Interval = p ± Z * \(\sqrt{p(1-p)/n}\)
Where:
p is the sample proportion (successful challenges / total challenges)
Z is the z-score corresponding to the desired confidence level
n is the sample size
a. Let's calculate the confidence interval for the percentage of successful challenges made by women:
Sample size (n) = 135
Number of successful challenges (x) = 36
Sample proportion (p) = x/n
p = 36/135 ≈ 0.2667
To find the z-score corresponding to a 95% confidence level, we need to calculate the critical value. Since the sample size is large enough (n > 30), we can approximate the critical value using the standard normal distribution.
The z-score corresponding to a 95% confidence level (two-tailed test) is approximately 1.96.
Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667(1-0.2667)/135}\)
Calculating the confidence interval:
Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667*0.7333/135}\)
= 0.2667 ± 1.96 * \(\sqrt{0.19511/135}\)
= 0.2667 ± 1.96 * 0.03943
≈ 0.2667 ± 0.07723
The lower bound of the confidence interval is:
0.2667 - 0.07723 ≈ 0.1895
The upper bound of the confidence interval is:
0.2667 + 0.07723 ≈ 0.3449
Therefore, the 95% confidence interval for the percentage of successful challenges made by women is approximately 18.95% to 34.49%.
b. To compare the results with the 95% confidence interval for the percentage of successful challenges made by men (23.6%), we can observe that the confidence interval for women does not overlap with the value for men.
The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%. This suggests that there may be a significant difference in the percentage of successful challenges made by women compared to men.
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Help with explaining please thank you
Answers
For given triangle, the value of x is 22.
In this question, we have been given three angles of triangle.
We need to find the value of x.
We can observe that (6x - 7)° is an exterior angle.
So, the third angle of the triangle is 180° - (6x - 7)°
We know that the sum of the all angles of the triangle is 180°
2x° + (103 - x)° + [180° - (6x - 7)°] = 180°
2x + 103 - x + 180 - 6x + 7 = 180
2x - x - 6x + 103 + 180 + 7 = 180
-5x + 290 = 180
-5x = 180 - 290
-5x = -110
x = 22
Therefore, for given triangle, the value of x is 22.
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(6x+1/2)+(2x-8 1/2)Simplify the expression.
Answers
Answer:
simplified = 8x - 8
Step-by-step explanation:
trust me :)
PArt 1
Let x be a random variable that represents level of glucose in the blood (mg per deciliterof blood) a er a 12-hour fast. The glucose level is approximately normal with a mean of 85 and a standard deviation of 25.
a. What is the probability that a sample of 10 people have a mean glucose level less than 84.5?
b. What is the probability that a sample of 100 people have a mean glucose level less than 84.5?
Answers
a. The probability that a sample of 10 people has a mean glucose level less than 84.5 is 47.48%. b. The probability that a sample of 100 people has a mean glucose level less than 84.5 is or 42.07%.
To calculate the probabilities in this scenario, we will use the properties of the normal distribution and the central limit theorem. The central limit theorem states that for a large sample size, the distribution of the sample mean approaches a normal distribution, even if the underlying population distribution is not normal. In both cases, we can use the z-score formula to find the probabilities.
a. For a sample of 10 people:
The mean of the sample mean is equal to the population mean, which is 85. The standard deviation of the sample mean (also known as the standard error) is given by the population standard deviation divided by the square root of the sample size: 25/sqrt(10) ≈ 7.9057.
To find the probability that the sample mean is less than 84.5, we calculate the z-score:
z = (84.5 - 85) / 7.9057 ≈ -0.0634
Using a standard normal distribution table or a calculator, we find that the probability corresponding to a z-score of -0.0634 is approximately 0.4748, or 47.48%.
b. For a sample of 100 people:
Similarly, the mean of the sample mean is still 85, but the standard deviation of the sample mean (standard error) is now 25/sqrt(100) = 2.5.
To find the probability that the sample mean is less than 84.5, we calculate the z-score:
z = (84.5 - 85) / 2.5 = -0.2
Using the standard normal distribution table or a calculator, we find that the probability corresponding to a z-score of -0.2 is approximately 0.4207, or 42.07%.
Therefore:
a. The probability that a sample of 10 people has a mean glucose level less than 84.5 is approximately 0.4748, or 47.48%.
b. The probability that a sample of 100 people has a mean glucose level less than 84.5 is approximately 0.4207, or 42.07%.
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Solve algebraically, show all steps, and round 3 decimal places
Answers
Answer:
x = 1.523
Step-by-step explanation:
Given
\(\quad\quad e^{x-1} = 3^{2-x}\)
we are asked to solve for x
Take natural logs on both sides:
\(\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)\)substitute on left side of original eqn
\(\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\\)
Therefore we get
\(\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)\)
But ln(e) = 1
So we get
\(x - 1 = (2-x)\;\ln(3)\\\\\)
So the expression becomes
\(x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)\)
Add \(x\ln(3)\) on both sides:
x + x ln(3) - 1 = 2ln(3)
Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1
x(1 + ln(3)) = 2 ln3 + 1
ln(1 + \ln(3)) = 2.09861
2ln(3) + 1 =3.1972
So we get
x(2.0986) = 3.1972
x = 3.1972/2.0986 = 1.52349
Rounded to 3 decimal places, the answer is 1.523
Plzzzz Help me 50 points!!!!
Answers
Will the given side lengths from a right triangle?yes or no 4.5,6and 7.5
Answers
Yes it is possible.
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I REALLY NEED HELP
find the area of the composite figure
Pleassssessee help me
Answers
Answer:
The area of the triangle is 70.805 ft squared
Step-by-step explanation:
The local middle school has students 2924 The principal wants the students in groups of 24 for an assembly How many groups of students will there be?
Answers
Answer:
1239 it is 1239 I think I have same test
A rectangular garden is 15 ft longer than it is wide. Its area is 6750 ft 2 . What are its dimensions
Answers
Answer:
450 x 15 = 6750 ft 2
Step-by-step explanation:
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is——
x+1
x +10
x - 10
x + 9
Answers
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is x + 9.