the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
Can someone please help me out
Step-by-step explanation:
[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]
Venn diagram of b union b
Answer:
let b union b be
B={2,4,6,8} and B= {1,2,3,4,5}
then B union B = {1,2,3,4,5,6,8}
Step-by-step explanation:
Venn diagram of b union b is in the attachment
Hope it is helpful to you
The height of a baseball in feet can be found by the equation -4.982 – 20t + 1000. How far has the
baseball traveled at t = 6?
Answer:
875.018
Step-by-step explanation:
To solve this, we must plug in 6 for our t value. So, we have the equation:
-4.982 - 20(6) + 1000
Following the rules of PEMDAS, we have:
-4.982 - 120 + 1000 = 875.018
(c+d)^2+11(c+d)+30
Factor completely.
Answer:
firstable give c+b a polynomial value like x
so its will be x^2+11x+30
after the we have to factor it
30=6×5
and 11=6+5
so its will become
(x+6)×(x+5)=x^2+11x+30
x=c+d
(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30
have a great day
The graph f(x) shown below has the same shape as the graph of g(x)=x^2 which of the following is the equation of f(x)
Answer:
Choice D. [tex]F(x)=x^2-4[/tex]
Step-by-step explanation:
Since the graph is translated down 4, it cannot be choice A. or C.Since the graph is concave up, choice B. is ruled out.Leaving choice D. the correct answer.Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
https://brainly.com/question/22213822
i need help ASAP please
Answer:
reflection over Y axis
Step-by-step explanation:
Answer:
I believe it is D) a reflection over the Y-axis
Step-by-step explanation
it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)
[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day
Answer:
3 / 16
Step-by-step explanation:
Let The total amount = x
Fraction eaten on first day = 1/4x
Fraction left = x - 1/4x = 3/4x
Fraction of amount left eaten on second day = 3/4 of 3/4x
3/4 * 3/4x = 9/16x
Fraction left :
3/4x - 9/16x = (12x - 9x) /16 = 3/16x
Hence, fraction left = 3/16
Câu 1: Giá trị
2
3
2020 -5 lim
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n
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bằng:
A.
2.
B.
.
C.
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D.
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Answer:
i dont understan your language plz speak in englosh
HELP PLEASE!!! The expected value of a random variable X is 35. The variable is transformed
by multiplying X by 4 and then adding 1 to it. Find the expected value (mean)
of the transformed variable. A. 135 B.117 C. 154 D.141
Answer:
Expected value x= 35
linear transformation is defined as a + bx
here, b=4, a=1
The transformation is [tex]z=1+4x[/tex]
now, expected value, [tex]l_z=l_z(a+bx)[/tex]
[tex]=l(a)+l(bx)[/tex]
[tex]=a+b\:l\:x[/tex]
substitute the value of a=1, b=4 and l=35
[tex]l_z=1+4\times35[/tex]
[tex]=1+140[/tex]
[tex]=141[/tex]
So, the expected value of the transformed variable is 141.
OAmalOHopeO
=======================================================
Explanation:
Let's consider a set of three values such that they're all equal to 35
{35,35,35}
This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.
If we multiply everything by 4, then we get the new set {140,140,140}
Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.
-----------------------------
You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.
If we quadruple each item, then we have {34,35,36} turn into {136,140,144}
Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.
These are just two examples you could do to help see why the answer is D) 141
-----------------------------
In a more general theoretical sense, we're saying the following
Y = mX+b
E[Y] = E[m*X+b]
E[Y] = E[m*X] + E[b]
E[Y] = m*E[X] + b
where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.
So,
E[Y] = m*E[X] + b
E[Y] = 4*35 + 1
E[Y] = 141
-----------------------------
Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.
A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.
Two boys together have $12. One of them has $10 more than the other. How much money does each of them have
You wait in line for hours to get the new special edition Nikes for $250, but you have to pay 5.3% in Virginia state sales tax. What is the total you will pay?
Answer:
263.25
Step-by-step explanation:
250 x .053 (5.3%) = 13.25 tax
250 + 13.25 = 263.25 price plus sales tax
Answer:
263.25
Step-by-step explanation:
What type of line is PQ¯¯¯¯¯¯¯¯?
A. median
B. angle bisector
C. side bisector
D. altitude
Answer:
angle bisector
Step-by-step explanation:
Since the line divided the top angle into two equal pieces we call this an angle bisector.
in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Answer:
2520 ways
Step-by-step explanation:
Given
[tex]n = 10[/tex]
[tex]r = (2,3,5)[/tex]
Required
The number of selection
First, select 2 people from 10 in 10C2 ways.
There are 8 people, left.
Next, select 3 people from 8 in 8C3 ways.
There are 5 people left.
Lastly, select 5 from 5 in 5C5 ways
So, we have:
[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]
Using combination formula
[tex]Total = 45 * 56 * 1[/tex]
[tex]Total = 2520[/tex]
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
Explain the relationship of the meaning of the word isometric to the properties of an isometric or rigid transformation
Step-by-step explanation:
The iso parts of isometric means same, and It is similar becuase rigid trtransformation and the metric parts means measure. Basically isometric means same measure. Rigid transformation preserve "same measures" like angles and side lengths.
(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).
Answer:
[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]
[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]
[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]
[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x-10[/tex]
[tex]OAmalOHopeO[/tex]
Please help with question thank you
Answer:
The answer is 3x=50-10y
The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent? the number of seconds after the rocket is released the initial height of the rocket the initial velocity of the rocket the height of the rocket after t seconds The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
Answers:
t is the number of seconds after the rocket is released
V(r) is the volume of the ball with radius r.
====================================================
Explanation:
There isn't much to say in terms of explanation. These variables are simply definitions.
What is the area of this triangle
Answer:
14
Step-by-step explanation:
7*4*1/2=14
ahla
S : Assignment
乡,一石
Answer
what's the question?
Step-by-step explanation:
looks like your question is missing information
ASAP HELP!! PLEASEEEE!!
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
A hundred chickadees can eat 100 kg of seeds in 100 days. How many kg of seeds can 10 chickadees eat in 10 days?
Answer:
1 kg
Step-by-step explanation:
Number of chickadees = 100
Quantity of seed eaten = 100 kg
Number of days = 100
Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days
= 100 ÷ 100 ÷ 100
= 1 ÷ 100
= 0.01 kg of seed
How many kg of seeds can 10 chickadees eat in 10 days?
= Quantity of seeds each chickadee eats per day × number of chickadee × number of days
= 0.01 kg × 10 × 10
= 1 kg
10 chickadees eat 1 kg of seeds in 10 days
write 5 lcms of 100 and 120
Answer:
The LCM of 100 and 120 is 600.
The LCM of 5 and 120 is 120.
LCM of 5 and 100 is 100.
Step-by-step explanation:
I think this is the answer . If it is not sorry .
Please help ! pythagoran theaeom ! I need someone to please explain how to answer this ASAP , giving brainlist
Answer:
Floor=2*sqrt(11)
Step-by-step explanation:
Using Pythagoras theorem, we have
Wall^2+Floor^2=(Ladder)^2
Floor^2=12^2-10^2
Floor=sqrt(44)=2*sqrt(11)
Answer:The floor is 6m
Step-by-step explanation:
In this we have to solve to find B
First we know that A^2+B^2+C^2 and we know A is 10 and C is 12 so now we are going square both 10 and 12 which would be 100 and 144 then we subtract each other 144-100=44 and lastly we are going to get the square root of 44 which is 6.
Please give brainlist
