the dimensions of a rectangle can be expressed as x-3 and x+8. If the area of the rectangle is 42 square feet. Find the dimensions of the rectangle.
Answers
the area of a rectangle=length*width
let
length=x-3
width=x+8
area=42 ft²
so
42=(x-3)*(x+8)----------> x²+8x-3x-24=42--------> x²+5x-66=0
using a graph tool-------> to resolve the second order equation
see the attached figure
the solution is
x=6
hence
length=x-3------> 6-3-----> 3 ft
width=x+8 ------> 6+8----> 14 ft
the answer is
the dimensions of the rectangle are 3 ft x 14 ft
Related Questions
A cylinder has a radius of 10m and a 8m. What is the exact volume of the cylinder?
160 TT m3
80 TT m3
800 TT m3
18 TT m3
Answers
Please help with geometry
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[tex]a=503ft=\dfrac{503}{3}yd\approx168yd\\\\b=516ft=\dfrac{516}{3}yd=172yd\\\\\sin38^o\approx0.616[/tex]
Substitute:
[tex]A_\Delta=\dfrac{1}{2}\cdot168\cdot172\cdot0.616\approx8,877yd^2[/tex]
Find the missing values given that cos(theta) = 1.
Sin(Theta):
Csc(Theta)
Sec(Theta):
Cot(Theta):
Answers
cos(theta) = 1---------> the value of cos is positive
then
angle theta------> could be in the first or fourth quadrant
Part 1) find sin theta
sin² theta+cos² theta=1------> sin² theta=1-cos² theta----> 1-1²----> 0
sin theta=0
Part 2) find csc theta
csc theta=1/sin theta
but sin theta =0
therefore
csc theta-------> it does not exist, it is not defined
Part 3) find sec theta
sec theta=1/cos theta
cos theta=1
so sec theta=1/1----> sec theta=1
Part 4) find cot theta
cot theta=cos theta/sin theta
but sin theta=0
therefore
cot theta-------> it does not exist, it is not defined
9) If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
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_____________
The coach attempts to determine an association between shirt size and hat size. Which is most likely true?
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Answer:
There is likely an association because 0.8 is not similar to ≈ 0.33.
I NEED HELP ON THIS EQUATION PLEASE (:
Answers
45 = Length x 10
Length = 45 ÷ 10 = 4.5 in
Answer: 4.5 in
Solve 5x = 10x - 5(2x-3) for x. Show your work.
Answers
Eliminate parentheses using the distributive property.
... 5x = 10x -10x +15
Collect terms, then divide by the coefficient of x.
... 5x = 15
... x = 3
The base of a triangular prism is a right triangle with hypotenuse 10 m long and one leg 6 M. If the height of the prism is 12 M, what is the volume of the prism
Answers
Use a^2 + b^2 = c^2
Then find the volume.
Step One
a^2 + b^2 = c^2
c = 10
b = 6
Find a
a^2 + b^2 = c^2
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 100 - 36
a^2 = 64
a = sqrt(64)
a = 8
Step Two
Find the volume
a = 8
b = 6
h = 12
V = 1/2 * a * b * h
V = 1/2 * 8 * 6 * 12
V = 288 m^3 <<<<<<< answer
The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.
Answers
[tex] G_{1}[/tex]: The larger square garden.
[tex] G_{2}[/tex]: The smaller square garden.
Given that both of then have square areas, then:
[tex] A_{G1} = L_{G1}^{2} [/tex]
[tex] A_{G2} = L_{G2}^{2} [/tex]
Being [tex] L_{G1} [/tex] the side of the larger garden and [tex] L_{G2} [/tex] the side of the smaller garden as shown in the figure.
The larger square garden at Volterra Hall has sides twice as long as the smaller square garden, thus:
[tex] L_{G1} = 2L_{G2}[/tex]
Together the gardens cover 18,000 square feet, so:
[tex]A_{G1} + A_{G2} = L_{G1}^{2} + L_{G2}^{2} = 18000[/tex]
Then:
[tex](2L_{G2})^{2} + L_{G2}^{2} = 18000[/tex]
[tex]4L_{G2}^{2} + L_{G2}^{2} = 18000[/tex]
[tex]5L_{G2}^{2} = 18000[/tex]
[tex]L_{G2}^{2} = 3600[/tex]
[tex]L_{G2} = \sqrt{3600}[/tex]
[tex]L_{G2} = 60[/tex]
[tex]L_{G1} = 2L_{G2} = 2(60) = 120[/tex]
Therefore:
Each side of the larger square garden is [tex] 120 ft [/tex] and each side of the smaller one is [tex] 60 ft[/tex] each. These are the dimensions.
Which one is it? Will give brainiest
Answers
180° - 180° + 34° + 103°
34° + 103°
137°
~C
Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?
Answers
thus the equation will be as follows:
y=a(x-k)(x-h)
where:
(x-k) and (x-h) are the factors:
thus
y=a(x+7)(x-3)
y=a(x^2+4x-21)
But, when x=1, y=32
plugging this in the equation we get:
32=a(1^2+4(1)-21)
32=a(1+4-21)
32=-16a
hence:
a=-2
thus the eqiation will be:
y=-2(x^2+4x-21)
hence the equation is:
y=-2x^2-8x+42
The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].
To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.
[tex]y = k*(x+7)(x-3)[/tex]
[tex]y = k *(x^2 + 4x - 21)[/tex]
[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]
[tex]y = -2(x+7)(x-3)[/tex]
[tex]= -2(x^2 + 4x - 21)[/tex]
[tex]= -2(x^2 +4x ) -42[/tex]
[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]
[tex]= 2 (x+2)^2 -50[/tex]
If you take 5 quizzes and get scores of 95%, 95%, 80%, 85%, and 75%, how would you find your mean quiz score?
Answers
The mean of the quiz scores is given by the equation M = 86 %
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the mean of the quizzes be represented as M
Now , the equation will be
Let the number of quizzes be n = 5
Let the scores of each quizzes be represented by set A
Set A = { 95% , 95%, 80%, 85%, 75% }
So , the mean of the quizzes M = sum of the quizzes / number of quizzes
Substituting the values in the equation , we get
The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5
The mean of the quizzes M = ( 430/5 )
The mean of the quizzes M = 86 %
Therefore , the value of M is 86 %
Hence , the mean of the quizzes is 86 %
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I don’t really get how to do this?
Answers
There is the smaller non-shaded box though of 7 * 2 = 14.
Take the difference of the two by doing 120 - 14 = 106 and that's your answer.
106 m²
Find the area of the unshaded region
The unshaded region is a rectangle. Its area will be
A = L * W
L = 7 m
W =2 m
Area = 7 * 2 = 14 m^2
Step Two
Find the Area of the entire region, both shaded and unshaded areas.
A = L * W
L = 10 m
W = 12 m
Area = 12 * 10 = 120 m^2
Step Three
Find the area of the shaded region.
Shaded Area = whole area - unshaded region
Shaded Area = 120 m^2 - 14 m^2
Shaded Area = 106 m^2
Answer: 106 m^2
Mrs. rifkin had 84 oranges. 24 of her oranges were rotten; the rest were either ripe or unripe. there were 18 more ripe oranges than unripe oranges. find the ratio of the number of ripe oranges to the number of rotten oranges to the number of unripe oranges.
Answers
There were 39 ripe oranges
There were 24 rotten oranges
and there were 21 unripe oranges
for a total of 84 oranges.
Sam is making a histogram of the height in inches of all 250 students in his grade. The shortest person is 48 inches and the tallest is 60 inches. How wide should his x-axis intervals be? A) 2 B) 5 C) 8 D) 12
Answers
i need to have 20 characters so ...
Answer:
The answer is A) 2.
Step-by-step explanation:
The best way would be to use intervals of 2.
We know that the shortest persons 48 inches and the tallest 60 inches.
The difference between the tallest person and the shortest is:
60 - 48 = 12 inches
Since the difference is small, we might use intervals smaller than 12 because if we used intervals of 12, we wouldn't know for sure the heights of the other students, and we would have to estimate their heights.
Using intervals of 8 would be the same, we would have to estimate the heights of most students.
Using 5 , would also not be a good choice because 5 is not a multiple of 48, 60 or 12, therefore, that
Therefore, 2 would be the best option, as you don't have to estimate and the intervals would match the shortest and tallest height.
A triangle has sides with lengths: 6, 9, and 5. How do you find the area of the triangle using Heron's formula?
Answers
a=6
b=9
c=5
s=(a+b+c)/2
s=(6+9+5)/2
s=10
Δ=√10(10-6)(10-9)(10-5)
Δ=10√2 sq. units
OR
Δ=14.14 sq. units
divide (x^3-20x+16)divide (x-4)
Answers
here is your answer
mark it as brainliest if it is helpful to you......
how do you evaluate 71 - b, if b is 27
Answers
Find the volume of a cube that is 7 cm on each edge.
Answers
V=a^3
our a=7
V=343 cm^3
Final answer:
The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).
Explanation:
To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:
V = 7 cm imes 7 cm imes 7 cm = 343 cm3
So the volume of the cube is 343 cubic centimeters (cm3).
!!!!!!!!!!!!!which answe
Answers
Answer:
When we toss a coin we have 50% of probability to get a tail and 50% probability to get heads.
If we toss the coin 8 times, in order to find P(T=6), we need to use the binomial distribution:
[tex]P = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of successes we want
p = probability of success
Therefore:
[tex]P(T=6) = \frac{8!}{6!(2)!} 0.5^{6} (1-0.5)^{2} [/tex]
= 28 · 0.015625 · 0.25
= 0.109375
Hence, the probability of getting 6 tails out of 8 tosses is D) 10.94%.
Answer:
I think it's D
Step-by-step explanation:
Anyone know this geometry question?
Answers
Solve for m -20+14m=10m+16
Answers
-10m. -10m
-20+4m=16
+20. +20
4m=36
/4. /4
m=9
PLEASE HELP ME FIND THE VALUE OF X
25 POINTS
Answers
Pythagorean theorem:
c^2 = a^2 + b^2
a = 6 and c =√117
to find b:
b^2 = c^2 - a^2
b^2 = (√117)^2 - 6^2
b^2 = 117 - 36
b^2 = 81
b = √81
b = 9
answer:
x = 9 cm
Answer:
the answer is x = 9 cm
Step-by-step explanation:
Aaron took three times as many pictures as jennifer.jennifer has 16 fewer pictures than aaron.which system of equations can be used to find the number of oictures each person took?
Answers
J=Jennifer
a=3j
j=a-16
Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet
Answers
Area=250×25=6250 ft²
but 1 acre= 43560 ft²
thus converting our area to acres we get:
6250/(43560)
=0.1435 acres
thus the population density will be:
(Population)/(area)
=15/0.1435
=104.544 trees/acre
The perimeter of the rectangle below is 90 units. find the length of side vy . write your answer without variables.
Answers
we know that
perimeter of a rectangle=2*[base+height]
base=3y+1
height=2y+3
perimeter=90 units
so
90=2*[(3y+1)+(2y+3)]-----> 90=2*[5y+4]----> 10y+8=90----> y=8.2 units
base=3y+1-----> base=3*8.2+1-----> 25.6 units
height=2y+3----> height= 2*8.2+3---> 19.4 units
the answer is
the length of side vy is (2y+3)-----> 19.4 units
the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.
It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.
To find the dimensions, we set up an equation using the formula for the perimeter:
90 = 2 * [(3y + 1) + (2y + 3)]
This equation represents that the perimeter is equal to twice the sum of the base and height.
The equation is then simplified:
90 = 2 * [5y + 4]
By dividing both sides by 2, it becomes:
5y + 4 = 45
Solving for y:
5y = 45 - 4
5y = 41
y = 41 / 5
y = 8.2 units
So, the value of y is correctly determined as 8.2 units.
With the value of y known, the base and height expressions are evaluated:
Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`
Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`
The dimensions of the rectangle are correctly calculated as follows:
Base: 25.6 units
Height: 19.4 units
It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.
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What is the vertex of the absolute value function defined by f (x) = |x - 7| + 1?
A. (7,1)
B. (-7, -1)
C. (-7, 1)
D. (7, -1)
Answers
We have: f(x) = |x - 7| + 1
shift the graph of the function y = |x| 7 units right and 1 unit up. Then the vertex of function f is (7; 1).
Your answer is A. (7; 1)
Look at the picture.
Determine whether quantities vary directly or inversely and find the constant of variation. It takes four identical water pumps 6 hours to fill a pool. How long would it take three of these same pumps to fill the pool, assuming they all pump at the same rate?
Answers
Let the number of water pumps be n and the time taken to fill the pool is t.
Now, we can see that higher the number of water pumps, lesser the time to fill the pool.
It means quantities vary indirectly.
Thus, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]
Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.
Thus, we have
[tex]4=\frac{k}{6} \\ \\ k=24[/tex]
Hence, constant of variation is 24.
Now, we have to find the time that three pumps will take to fill the same pool.
[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]
Hence, it will take 8 hours to fill the pool by three identical pumps.
What are the period and amplitude of the function?
A) period 3, amplitude 1.5
B) period 3, amplitude 3
C) period 4, amplitude 1.5
D) period 4, amplitude 3
Answers
Answer:
Option: A is the correct answer.
A) Period: 3 , amplitude : 1.5
Step-by-step explanation:
We know that Period of a function is the smallest value such that the function repeats after a fixed time.
and also the amplitude of the function is the height above or below the mid-line.
After looking at the graph we see that the period of the function is: 3
Since the function is repeating itself after every x=3.
Also, the mid-line of the function is: y= -0.5.
Hence, the height above the mid-line is: 1+0.5 = 1.5
Hence, amplitude= 1.5
Can derivatives be used to measure the the slope of the tangent line at x=a
Answers
For example, picture the graph of the following function:
[tex]f(x) = x^2[/tex]
The slope is constantly changing at every x-value, so to find the slope at x=a, we find the derivative of the function.
[tex]f'(x)=2x[/tex]
Once we have the derivative, simply plug in a for x to find the slope of the line tangent to f(x) at x=a.
For example, at x=5:
[tex]f'(5)=2(5)[/tex]
The slope of f(x) at x=5 is 10.