The length of a rectangle is twice its width. If the area of the rectangle is
32cm2, find the perimeter.
Answers
Before we find the perimeter, first we must know length and width.
Let width = x
The question says that the length of a rectangle is twice its width. Therefore the length is 2×x or two times of width which equal to 2x.
The area of rectangle is given as 32 cm^2.
Do you remember the rectangle area formula? If not then it is:
[tex] \large \boxed{ \tt{A = width \times length}}[/tex]
Since A is area - substitute A = 32 in. As for width, we substitute in x and length in 2x.
[tex] \large{32 = x \times 2x}[/tex]
Since x multiplies by another x. It becomes x squared.
[tex] \large{32 = 2{x}^{2} }[/tex]
Next, we divide 2 by both sides since we want to solve for x.
[tex] \large{ \frac{32}{2} = {x}^{2} }[/tex]
Simplify 32/2 in simplest form.
[tex] \large{16 = {x}^{2} }[/tex]
Square both sides so we can get rid the x squared, leaving only x.
[tex] \large{ \sqrt{16} = \sqrt{ {x}^{2} } }[/tex]
Normally, when solving quadratic equation, you must write plus or minus. However, for this circumstance - we are solving a variable for length and width which cannot be negative. Therefore
[tex] \large{4 = x}[/tex]
After we solve for x. Substitute x = 4 in width = x and length = 2x.
[tex] \large{ \tt{width = x = 4}} \\ \large{ \tt{length = 2x = 2(4) = 8}}[/tex]
When we multiply these two numbers, we get 32 cm^2.
Next, we find the perimeter. The formula of perimeter for rectangle is:
[tex] \large \boxed{ \tt{P = (width + length) \times 2}}[/tex]
We know width and length which are 4 and 8 in order. Substitute in the formula.
[tex] \large{P = (4 + 8) \times 2} \\ \large{P = 12 \times 2} \\ \large \boxed{P = 24}[/tex]
Hence, the perimeter is 24.
Answer
The perimeter for the rectangle is 24.after you list the factors, you have to read the question back .. the question the length of the rectangle is twice the width .. so 4 × 8 is the correct answer .. and you do as usual to calculate the perimeter ..
Related Questions
For what values of b will F(x) = logo x be a decreasing function?
A. b>0
B. 0
C. b< 0
D. O >b>-1
Answers
[tex]f(x) = \log_b(x)[/tex] is a decreasing function when [tex]0 < b < 1[/tex]
This is because we can use the change of base formula to say
[tex]\log_b(x) = \frac{\log(x)}{\log(b)}[/tex]
If b is between 0 and 1, not including either endpoint, notice how the log(b) term is negative.
For example, if b = 0.5, then log(b) = log(0.5) = -0.301 approximately. I'm using log base 10 to get log(0.5) = -0.301
So for b = 0.5, we have,
[tex]\log_{0.5}(x) = \frac{\log(x)}{\log(0.5)} \approx \frac{\log(x)}{-0.301} \approx -3.322\log(x)[/tex]
The log(x) part on its own is always increasing. The negative coefficient out front flips it to always decreasing.
By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex]decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D) #SPJ5
How to define the behavior of a logarithmLogarithms are trascendent functions whose form is defined by the following expression:
[tex]\log _{b} x[/tex] such that [tex]x = b^{a}[/tex], where b > 0.
Where b is the base of the power.
Whose rules are described below:
The logarithm is an increasing function if its base is less than 1.The logarithm is a decreasing function if its base is greater than 1.By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex] is a decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D)
RemarkThe statement is poorly formatted and reports several mistakes. Correct form is shown below:
For what values of b will [tex]F(x) = \log_{b} x[/tex] be a decreasing function?
A. b > 0
B. 0
C. b < 0
D. 0 < b < 1
To learn more on logarithms, we kindly invite to check this: https://brainly.com/question/20785664 #SPJ5
Given circle and circle with radii of 6cm and 4cm respectively.
Compare the length of EF and GH.
The length of EF is ____the length of GH
The length of EF is___
The length of GH is ___
Answers
Solution :
Given that :
The radius of circle A = 6 cm
The radius of circle C = 4 cm
In circle A
[tex]\angle EAF = \theta = 140^\circ[/tex]
The length of arc EF = [tex]$2 \pi r \times \frac{\theta}{360^\circ}$[/tex]
[tex]$=2 \times 3.14 \times 6 \times \frac{140^\circ}{360^\circ}$[/tex]
= 14.653 cm
In circle C
[tex]\angle GCH = \theta = 140^\circ[/tex]
The length of arc GH = [tex]$2 \pi r \times \frac{\theta}{360^\circ}$[/tex]
[tex]$=2 \times 3.14 \times 4 \times \frac{140^\circ}{360^\circ}$[/tex]
= 9.769 cm
Therefore,
The length of EF is 14.653 cm
The length of GH is 9.769 cm
The length of EF is 1.5 times the length of GH
i.e. 14.653 = 1.5 x 9.769
14.653 = 14.653
Hence proved.
Sandra went to the grocery store with $25 to buy fruit. If she spent $12 on apples and $8 on bananas, which set of equations could be used to find the amount of money Sandra had left?
A. 25 - 12 = 13
13 + 8 = 21
B. 25 + 13 = 38
38 - 8 = y
C. 20 - 8 = y
y + 25 = 37
D. 12 + 8 = 20
25 - 20 = y
Answers
Answer:
D
Step-by-step explanation:
She spent $12 and *$ on two separate things, meaning she spent $20 on both.
So, 12 + 8 = 20.
If she started with 25, we subtract 20 from 25 to get how much she has left.
So, 25 - 20 = y.
Therefore, the answer is D.
Answer:
D
Step-by-step explanation:
I agree with the previous answer, it's D.
Sandra spent $12 on apples and $8 on fruit, so you would add.
That's $20, so to find out how much money she has left you do 25 - 20.
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Answers
So,
1 = 128
2 = 52
3 = 128
4 = 52
Given the equation −4square root of x minus 3 = -12, solve for x and identify if it is an extraneous solution.
A. x = 0, solution is extraneous
B. x = 0, solution is not extraneous
C. x = 12, solution is extraneous
D. x = 12, solution is not extraneous
Answers
Answer:
D. x = 12, solution is not extraneous
Step-by-step explanation:
-4√(x - 3) = -12
Divide both sides by -4
√(x - 3) = 3
Square both sides
x - 3 = 9
add 3 to both sides
x = 12
To see if it's extraneous plug into original problem
-4√(12 - 3) = -12
-4√(9) = -12
-4 * 3 = -12
-12 = -12
not extraneous
Broody is makeing trailmix for a hike he is takeing some friends. He used 6 cups of peanuts,4 cups of cashoe, 3 cups of choclate chips and 2 cups of raisins.Be mixed it all up and put a equal amount of trail mix into 5 bags.How many cups of trail mix did he put in each bag?
Answers
Answer:
The answer is 3.
Step-by-step explanation:
To answer this, you have to find the total amount of cups he had to begin with. You add the cups of peanuts, cashews, chocolate chips, and raisins together, which equals 15 cups. Then, he divided it evenly into 5 bags, which means he put 3 cups of trail mix into each bag.
Find the area of the triangle. Round your answer to the nearest tenth.
B
54 yd
270
А
54 yd
с
a. 742.9 yd?
b. 1,458 yd?
C. 1,323.8 yd?
d. 661.9 yd?
Answers
Answer:
here is the answer bae. Feel free to ask for more
what is the answer to 3x + 2(4x − 6) = 8x + 1
Answers
Answer:
x=13/3
Step-by-step explanation:
Mrs. Clever rolls a number cube once.
x
1 5.
What is the probability of a 4 being on top?
A. O out of 6
B. 1 out of 6
C. 3 out of 6
D. 4 out of 6
חד
6 out of 6
Answers
Answer:
I think it would be 1 out of 6 or B.
Step-by-step explanation:
I think so because there are 6 sides to a cube and if Mrs.Clever only rolls it once then it would be 1 out of 6.
Let g be the function defined by g(x) = x3 + x. If f(x) = g-1(x) and f(2) = 1, what is the value of f ′ (2)?
Answers
Answer:
f'(2) = 1/4
Step-by-step explanation:
We know that:
g(x) = x^3 + x
and f(x) is the inverse function of g(x), such that:
f(2) = 1
this is because:
g(1) = 1^3 + 1 = 2
We want to find:
f'(2)
The general formula for this case is:
if f(x) is the inverse of g(x)
and f(x) = y
then:
f'(y) = 1/g'(x)
Then in this case,
f'(2) = 1/g'(1)
so we just need to differentiate g(x)
g'(x) = 3*x + 1
and:
g'(1) = 3*1 + 1 = 4
Then:
f'(2) = 1/g'(1) = 1/4
f'(2) = 1/4
Solve: 8(x + 4) = 5(x + 3)
ANSWER! PLS
Answers
Answer:
I think -3x-17 sorry if wrong
Step-by-step explanation:
8x+ 32= 5x+15
-3x-17
Answer:
[tex]8(x + 4) = 5(x + 3) \\ 8x + 32 = 5x + 15 \\ 32 - 15 = 8x - 5x \\ [/tex]
-3x-17
help!! pls pls pls help!
Answers
Step-by-step explanation:
Going through this one by one, we can say:
For the first one ("Both functions are increasing on the interval (0, ∞)"), this does not need to be selected. Although h(x) increases as x increases, g(x) (the y value) decreases as the x value increases, or the graph moves to the right.
Next, we have "g(x) is increasing on the interval (-∞, 0)." The -∞ represents when x is at its lowest point, or the leftmost point possible for the curve. 0 represents the middle of the graph, cutting right through the y-axis. As g(x) is only increasing on negative values, this is true. It is important to note that the 0 has a parenthesis next to it, so the value 0 itself, where the graph is not increasing, is not included
After that, we have "The y-intercept of g(x) is greater than the y-intercept of h(x)." The y intercept is when x=0. For g(x), y=9 here, and for h(x), y=1. Thus, g(x) is greater, and this can be selected.
Furthermore, we have "The function h(x) represents a linear function." This means that for each value of x throughout the function, a change in x by 1 always results in the same change in y. When x goes from -1 to 0, h(x) increases by 0.75. When x goes from 0 to 1, h(x) increases by 3. Therefore, as 0.75 is not equal to 3, these are not the same.
Finally, the last statement is g(2) < h(2). As we can see on the graph, as x=2, the line is at g(x) = 5. When x=2, h(x) is 16. As the value of h(x) (16) is greater than the value of g(x) (5) when x=2, this can be selected as well.
I need the answer to 3 times 300
Answers
Answer:
900
Step-by-step explanation:
3*300=900
Answer:
3 x 300=900
brainly me pls
Given the following quadratic equation: 0 = (x - 8) (3x - 5)
Find the solutions (Show all work) need help please
Answers
Answer:
x=8
x=5/3
Step-by-step explanation:
evey bracket equal =0 to get solution
x-8=0
x=8
3x-5=0
3x=5
x=5/3
Answer:
x=5/3 or x=8
Step-by-step explanation:
0=3x^2-29x+40
-3x^2+29x-40=0
(3x-5)(x-8)=0
-3x+5=0 or x-8=0
x=5/3 or x=8
A group of 5 friends shares 35 pieces of candy equally. How many pieces of candy does each friend receive?
Answers
Divide total pieces of candy by total people:
35 / 5 = 7
Each person receives 7 pieces of candy
Answer:
7
Step-by-step explanation:
35 divided by 5 equals 7
Decide if the answer to 8/7 x 12 is less than, greater than, or equal to 12.
A. equal to
B. less than
C. greater than
Answers
Answer:
Option C.
Step-by-step explanation:
Answer:
C. greater than
Step-by-step explanation:
Since 8/7 is greater than 1
multiply it by 12 will result in a larger number.
find the profit on 6000 for one year at 4% per annum
Answers
Answer:
240 dollars.
Step-by-step explanation:
I'd be assuming you mean the returns on interest rate after you put $6000 into the system, kind of like how you get returns after you deposit money at the bank. In that case:
[tex]6000 \cdot (1 + 4%) - 6000[/tex]
[tex]= 6240 - 6000[/tex]
[tex]= 240[/tex] dollars
Of course, you didn't say how frequently the interest rate would be compounded, so this result would be if the interest was compounded yearly.
Hope this helped!
Answer:
$240
Step-by-step explanation:
4% of $6000 = $240
Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.
Answers
Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Meaning of Congruent quadrilateralsA quadrilateral can be defined as a polygon shape that possesses four sides.
Congruent quadrilaterals are those quadrilaterals that are similar in sides and angles.
For example, a parallelogram needs to be proved by both the sides and the angles
In conclusion, Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Learn more about Congruent quadrilaterals: https://brainly.com/question/224113
#SPJ1
The function of g(x) is a transformation of the absolute values parent function which graphs shows g(x)
Answers
==============================================================
Explanation:
f(x) is shown in the blue dashed line, while g(x) is a solid black line.
When going from |x| to 3|x|, we are multiplying each y output value by 3. So a point like (4,4) on f(x) moves to (4,12) on g(x). A point like (-3,3) on f(x) moves to (-3,9) on g(x). And so on.
This will result in g(x) being taller and skinnier/narrower compared to f(x) as shown in graph B. We have vertical stretching going on here.
The vertex of each V shape is the same and that's at the origin (0,0).
No translations (horizontal or vertical shifting) are occurring.
The graph that shows the function g(x) = 3|x| is graph B.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Given that, a function of g(x) is a transformation of the absolute values, we need to find the parent function of g(x)
Function g(x) = 3|x| is a vertical stretch of 3 units of function f(x) = |x|, that is, they keep the same vertex at (0,0), just graph g is stretched, passing at (1,3) instead of (1,1) for example.
Hence graph B is correct.
More can be learned about translation click;
brainly.com/question/27950531
#SPJ7
Find the volume of each shape, please and I will give you a lot of points
Answers
Step-by-step explanation:
1.V=LWH L is the length, W is the width and H is the height.
12×6×3=216
2.V=Ah A is the area of the base, h is the height
18×16=288
3.V=LWH L is the length, W is the width and H is the height
10×14×5=700
Add the Integers
2+(-2)
Answers
Answer:
0
Step-by-step explanation:
2+(-2) is basically 2-2 which is 0
These trapezoids are similar. Which of the following is the correct similarity statement?
Answers
What is the maximum number of right angles that can be contained in a
triangle?
O A. 3
OB. O
O c. 1
OD.2
Answers
Answer:
ONE...
total of three angles that add up to 180
if you had a second, that would be 180 none left for the third angle
Step-by-step explanation:
What’s the perimeter of the pentagon
Answers
Answer:
74 cm
Step-by-step explanation:
Perimeter Pentagon = 48 + (38 - 12)
48 + 26 = 74
74 cm
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
3y - 5 (2x + 3) - 12
Answers
hope this helps :)
Answer:
The answer is 3y - 10x - 27
Which 2 options are correct?
Answers
Answer:
A,C
Step-by-step explanation:
i took the test
PLZZ HELP WILL BRAINLIEST IF CORRECT!!!!
1. Andrea says that there are less numbers to the left side of 7 because the box plot is shorter on that side. Is she correct? Explain your reasoning,
2. Amber says that the data set is left-skewed because the box is farther to the left on the number line. Is she correct? Explain how you know.
Answers
Answer:
Both are wrong
Step-by-step explanation:
Though the box is shorter on the left side, it doesn't mean there are fewer numbers. Box plot tells the range, and not the mode. The box plot tells us that the interquartile range is higher on the right side.
Amber is wrong since the box plot is right-skewed
Pls vote as brainliest
We can conclude that:
1. Andrea is wrong, box plot doesn't imply mode.
2. Amber is wrong, the box plot is right-skewed.
What is a Box Plot?A box plot shows how a data is distributed or spread out.
If a data distribution is right-skewed, the median which is indicated by the vertical line that divides the rectangular box would be closer to the lower end of the box, and also if it has a shorter whisker to the left.
Also, if a data distribution is left-skewed, the median would be closer to the upper end of the box, and also if it has a shorter whisker to the right of the box.
The box plot shown is right-skewed.
Thus, we can conclude that:
1. Andrea is wrong, box plot doesn't imply mode.
2. Amber is wrong, the box plot is right-skewed.
Learn more about box plot on:
https://brainly.com/question/14277132
Please help me solve my problem!!!
Answers
Answer:
360°
Step-by-step explanation:
360°
Answer:
360 degrees
Step-by-step explanation:
For a polygon of n sides, the sum of the measures of the interior angles is
(n - 2)180.
A quadrilateral has 4 sides, so n = 4.
(4 - 2)(180) = 2(180) = 360
Answer: 360 degrees.
HELP!! I tried solving this and cant seem to get it right.
Answers
Answer:
x= 20
y = 10
Step-by-step explanation:
Angles 3x° and 60° are Corrosponding angles so they are equal:
[tex]3x = 60 \\ \frac{3x}{3} = \frac{60}{3} \\ x = 20[/tex]
Angles (5y-5)° and 135° are Cointerior so add to give 180°:
[tex]5y - 5 + 135 = 180 \\ 5y + 130 = 180 \\ 5y = 180 - 130 \\ \frac{5y}{5} = \frac{50}{5} \\ y = 10[/tex]
Substitute y and x into the respective formula's to get your angles.
Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2 2 1 2, start fraction, 1, divided by, 2, end fraction meters. Then he climbed straight up 6\dfrac{3}{4}6 4 3 6, start fraction, 3, divided by, 4, end fraction meters. Eric was wondering what his change in elevation was after these two moves.
Answers
Answer:
Hence, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above. So after the 2 moves, he is up by [tex]4\frac{1}{4}[/tex] meters.
Step-by-step explanation:
Let us assume "negative" as climbing up and "positive" as climbing up. Here we need to find the change in elevation.
[tex]2\frac{1}{2}[/tex] meters down means [tex]-2\frac{1}{2}[/tex]. [tex]6\frac{3}{4}[/tex] meters up means [tex]+6\frac{3}{4}[/tex].Now we have:
[tex]=-2\frac{1}{2} + 6\frac{3}{4}\\\\=-\frac{5}{2} +\frac{27}{4} \\\\=\frac{-5(2)+27}{4} \\\\=\frac{-10+27}{4} \\\\=\frac{17}{4} = 4\frac{1}{4}[/tex]
Answer:
b
Step-by-step explanation: