Answer: The length and width are 20 square centimeters and 8 square centimeters
Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.
Answer:
length = 20 cm and width = 8 cmStep-by-step explanation:
l - length
w - width
length and width are in a ratio of 5:2
[tex]\dfrac{l}{w}=\dfrac{5}{2}[/tex] cross multiply
[tex]2l=5w[/tex] divide both sides by 2
[tex]l=\dfrac{5w}{2}[/tex]
the area is 160cm²
[tex]lw=160[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}l=\dfrac{5w}{2}&(1)\\lw=160&(2)\end{array}\right[/tex]
Substitute (1) to (2):
[tex]\left(\dfrac{5w}{2}\right)(w)=160\\\\\dfrac{5w^2}{2}=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=\sqrt{64}\\\\w=8[/tex]
Put the value of w to (1):
[tex]l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20[/tex]
The graph shows the population of deer for the past 5 years. what is the approximate difference in the growth rate of the two populations?
WILL GIVE BRAINLIEST
Answer:
The approximate difference in the growth rate of the two populations is 40%.
Step-by-step explanation:
The general exponential growth model is
[tex]y=a(1+r)^t[/tex]
Where, a is initial value, r is growth rate and t is time.
In the given graph, red curve passing through the points (2,22.5) and (3,33.75).
[tex]22.5=a(1+r)^2[/tex] .... (1)
[tex]33.75=a(1+r)^3[/tex] .... (2)
Divide the equation (2) by equation (1).
[tex]1.5=1+r[/tex]
[tex]0.5=r[/tex]
The graph rate of red curve is 50%.
In the given graph, purple curve passing through the points (7,19.4) and (8,21.4).
[tex]19.4=a(1+r)^7[/tex] .... (3)
[tex]21.4=a(1+r)^8[/tex] .... (4)
Divide the equation (4) by equation (3).
[tex]1.1031=1+r[/tex]
[tex]0.1031=r[/tex]
[tex]0.1\approx r[/tex]
The graph rate of red curve is 10%.
The approximate difference in the growth rate of the two populations is
[tex]50-10=40\%[/tex]
Therefore the approximate difference in the growth rate of the two populations is 40%.
Caroline measured the weight of a dog that came into the veterinary clinic. She determined that her measurement had a margin of error of 0.05 kilogram. What could be the measured weight of the dog?
Answer:
9.2 kilo grams
Step-by-step explanation:
Find the future value and interest earned if $8706.54 is invested for 8 years at 6%
Answer:
Flat 12,885.68
Compound 13,876.90
Step-by-step explanation:
Flat rate (6% of only the amount you invested originally per year (based on investment) -
(8706.54*.06)*8+8706.54=12885.68 (rounded)
Compound interest (6% interest on total money earned per year(based on amount invested previous year).)
(((((((8706.54*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)=13,876.90
The future value of the investment is $13876.90 and the interest earned is $5170.36.
To solve this problemWe can use the following formulas:
Future value = [tex]Principal * (1 + Interest rate)^N^u^m^b^e^r ^o^f^ y^e^a^r^s[/tex]
Interest earned = Future value - Principal
Substituting the known values into the formulas, we get:
Future value =[tex]$8706.54 * (1 + 0.06)^8 = $13876.90[/tex]
Interest earned = $13876.90 - $8706.54 = $5170.36
Therefore, the future value of the investment is $13876.90 and the interest earned is $5170.36.
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Help plz I don’t understand this like at all!!!
Answer:
x is less than or equal to 3.5
Step-by-step explanation:
For this you can any variable but let’s use d representing the distance that Jonathan ran.
Hmm
D_>3.5+5
In other words d is less than or equal to 3.5 plus 5
Hope this helped u :)
If m<1= 10x + 4 and m<2 =5x-4 find m<2
Answer:
m∠2 = 56°
Step-by-step explanation:
Given;
m∠1 = 10x + 4 and m∠2 = 5x - 4
Angles 1 and 2 are supplementary angles meaning that they add up to 180°
i.e,
(10x + 4) + (5x - 4) = 180°
10x + 5x + 4 - 4 = 180°
15x = 180°
x = 180/15 = 12
m∠2 = 5(12)° - 4° = 60° - 4° = 56°
Vera runs a stable. 15 horses currently board at the stable, and 7 of them are palomino.
What is the probability that a randomly chosen horse will be palomino?
Simplify your answer and write it as a fraction or whole number.
P(palomino) =
Answer:
47%
Step-by-step explanation:
you would take the number of palomino horses and divide that by the total number of horses like this:
7 / 15 = 0.46666667
which would be rounded to 0.47
which equals 47%
so the probability of randomly choosing a palomino horse would be about 47%
i hope this helps :)
q=p/r+s make p the subject
Answer:
see explanation
Step-by-step explanation:
Given
q = [tex]\frac{p}{r}[/tex] + s ( subtract s from both sides )
q - s = [tex]\frac{p}{r}[/tex]
Multiply both sides by r
r(q - s) = p
BRAINLIEST + POINTS NEED HELP!
Answer:
ohh tough one let me figure this out
Step-by-step explanation:
brb
afk
9a^2+1/9a2-2-12a+4/3a
hope it helps you!!!!!!!!!!!
Melanie paid $42.50 for 3 adult tickets and 2 student tickets at Theater A. Drew paid $47 for 4 student tickets and 2 adult tickets at Theater A. Theater B charges $9 for each adult ticket and $7 for each student ticket.
Which of the following statements is TRUE?
A
The price for each adult ticket is the same at both theaters
B
The price for each student ticket is the same at both theaters.
C
The price of an adult ticket at Theater A is $0.50 less than the price of an adult ticket at Theater B.
D
The price of a student ticket at Theater B is $0.50 less than the price of a student ticket at Theater A.
Answer:
B. The price for each student ticket is the same at both theaters
Correct Option is B.
System of Linear equations:
A system of linear equations is a set of equations which are satisfied by the same set of variables.
Ex : 2x - y = 12 , x - 2y = 48
Here,
Let's take adult ticket price in theatre A = x
And the student ticket price in theatre A = y
So, (Given), 3x + 2y = $42.50 (Melanie paid)
=> 2y = $42.50 - 3x --(1)
Also given, 2x + 4y = $47 (Drew paid)
=> 4y = $47 - 2x
2(2y) = $47 - 2x
Now, substitute 2y value from eq-(1), we get
2($42.50 - 3x) = $47 - 2x
$85 - 6x = $47 - 2x
=> $85 - $47 = 6x - 2x
=> $38 = 4x
=> x = ($38)/4 => 9.5
Substitute x value in eq-(1), we get
2y = $42.50 - 3(9.5) => y = $7.
In the given options only Option B is the correct answer.
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How can I show that 0.2 is greater than 0.18
Answer:
Step-by-step explanation:
By showing that 0.20 is greater than 0.18 by doing 0.20-0.18 which gives a positive 0.02, thich means that its greater.
0.2 is greater than 0.18.
What inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have to Compare 0.2 and 0.18.
First we have two digits in 0.18 after decimal.
Then, make 0.2 with two digits after decimal as 0.20.
Now, compare the after decimal value
20 > 18
So, 0.2 is greater than 0.18.
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Which lists all of the y-intercepts of the continuous function in the table?
A (0,0)
B (-1,0), (2,0)
C (-1,0), (0, 0)
D (-1,0), (0, 0), (2,0)
Answer:
A (0,0)
Step-by-step explanation:
When a function intersects the y-axis then the point of intersection is called y-intercept of the function,
Also, for y-intercept x = 0.
That is, if f(x) is the function then its y-intercept is (0, f(0) )
By the given table for x = 0, f(x) = 0
Hence, the y-intercept of the given function is (0,0),
Option A is correct.
Answer:
A trust
Step-by-step explanation:
If the area of a circle measures 9π cm2, what is the circumference of the circle in terms of π?
A) 3π cm
B) 6π cm
C)
9/4
π cm
D)
9/2
π cm
Answer: option B
Step-by-step explanation:
The circumference of a circle can be calculated with this formula:
[tex]C=2\pi r[/tex]
Where "C" is the circumference of the circle and "r" is the radius of the circle.
The area of a circle can be calculated with:
[tex]A=\pi r^2[/tex]
Where "r" is the radius.
Knowing the area, you can solve for the radius:
[tex]r^2=\frac{9\pi cm^2}{\pi }\\\\r=\sqrt{\frac{9\pi cm^2}{\pi } }\\\\r=3cm[/tex]
Substituting into [tex]C=2\pi r[/tex], you get that the circumference of this circle is:
[tex]C=2\pi (3cm)=6\pi\ cm[/tex]
Answer:
B
Step-by-step explanation:
The area (A) of a circle = πr² ← r is the radius
here A = 9π, hence
πr² = 9π ( divide both sides by π )
r² = [tex]\frac{9\pi }{\pi }[/tex] = 9
r = [tex]\sqrt{9}[/tex] = 3
The circumference (C) of a circle is C = 2πr, hence
C = 2π × 3 = 6π → B
plz asap 1. (5 points) What is the value of x? Show all of your work. Round your answer to the nearest tenth.
41.2 in.
35.7 in.
Answer:
X = 20.6 inches
Step-by-step explanation:
Pythagorean Theorem: [tex]A^{2} =B^{2} +C^{2}[/tex]
A = 41.2 in, while B = 35.7 in and we are solving for C.
[tex]41.2^{2} = 35.7^{2} +C^{2}[/tex]
[tex]1697.44 = 1274.49 + C^{2}[/tex]
Now solve for C
[tex]422.95 = C^{2}[/tex]
Take the square root
[tex]20.5657482237 = C[/tex]
What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?
Answer: B.) f(x) => -∞ as x => -∞; f(x) => +∞ as x => +∞
The graph touches, but does not cross, the x–axis at x =__
The graph of the function crosses the x–axis at x = ___
Answer:
Step-by-step explanation:
f(x) = x⁵ – 8x⁴ + 16x³
As x approaches +∞, the highest term, x⁵, approaches +∞.
As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).
Now let's factor:
f(x) = x³ (x² – 8x + 16)
f(x) = x³ (x – 4)²
f(x) has roots at x=0 and x=4. x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.
The graph crosses the x-axis at x=0.
Answer:
Part 1. B
Part 2. 4, 0
Step-by-step explanation: Edge 2023
What is the factores form of x^12y^18+1
Answer:
factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]
Step-by-step explanation:
We need to find factors of [tex]x^{12}y^{18}+1 can\,\,be\,\, written\,\, as\,\,\\(x^2y^3)^6 + 1\\It\,\, can\,\, be\,\, further\,\, written\,\, as\\((x^2y^3)^2)^3 +1\\Using\,\, the\,\, formula\,\, a^3+b^3 = (a+b)(a^2-ab+b^2)\\Here \,\, a = (x^2y^3)^2 and y = 1\\((x^2y^3)^2)^3 +(1)^3= ((x^2y^3)^2+1) (((x^2y^3)^2)^2 -(x^2y^3)^2 +1)\\= (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]
So, factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]
For the inverse variation equation xy=k what is the constant of variation k when x=-3 And y=-2
ANSWER
The constant of variation is 6.
EXPLANATION
The inverse variation equation is:
[tex]xy = k[/tex]
We want to find the constant of variation, when x=-3 and y=-2.
We substitute the values for x and y to get,
[tex] - 3 \times - 2 = k[/tex]
Multiply out the left hand keeping in mind that negative times negative yields a positive result.
This implies that;
[tex]k= 6[/tex]
Hence the constant of variation is 6.
Answer:
The constant of variation k is 6.
Step-by-step explanation:
Given that there is inverse variation between x and y with equation
[tex]xy=k[/tex]
we have to find the constant of variation k when x=-3 and y=-2
The inverse variation equation is:
[tex]xy = k[/tex]
To find constant of variation we substitute the values of x and y
Put x=-3 and y=-2
[tex](-3)\times (-2)=k[/tex]
Solve LHS by multiplying
This implies
[tex]k= 6[/tex]
Hence the constant of variation is 6.
What is the arc length of the semicircle?
The arc is equal to the half of circumference.
The formula for circumference is [tex]C=2\pi r=2\pi 11=22\pi\approx69.11[/tex]. Now divide that by 2 and you get [tex]69.11\div2\approx\boxed{34.56}[/tex]
Semicircular arc has a length of approximately 34.56
Hope this helps.
r3t40
PLEASE HELP RIGHT AWAY
Still second graph from top down is the good one
I just need 23 please
Answer:
The answer is D
Answer:
The answer is A
What are the steps to find (2+2i)(5+3i)?
Answer:
Step-by-step explanation:
(2+2i)(5+3i)
(2)5+(2)3i=10+6i
(2i)5+(2i)3i=10i+6i^2
10+6i+10i+6i^2
6i^2+6i+10i+10
6i^2+16i+10
To find the product of (2+2i)(5+3i), apply the distributive property to multiply each part. The result is 10 (real*real), 6i (real*imaginary), 10i (imaginary*real), and -6 (imaginary*imaginary, since i^2=-1), which are summed to give 4 + 16i.
Explanation:The product of two complex numbers, such as (2+2i)(5+3i), can be found by using the distributive property (also known as foil - first, outer, inner, laters). In this case:
First, multiply the real parts: 2*5 = 10. Second, multiply the outer parts: 2*3i = 6i. Then, multiply the inner parts: 2i*5 = 10i. Lastly, multiply the imaginary parts: 2i * 3i = 6i^2. But, since i^2 = -1, this becomes -6.
Sum these results together: 10 + 6i + 10i - 6. Thus, (2+2i)(5+3i)= 4 + 16i.
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hailey had 4 3/8 cup of cherries she used 5/8 of the cherries to bake muffins how many cups of cherries did she use
Answer:
2 31/32 cups used
Step-by-step explanation:
We have 4 3/8 cups cherries
Change this to an improper fraction
4 3/8 = (8*4+3)/8 = 38/8
We use 5/8 of the cherries
38/8 *5/8
190/64
Change this back to a mixed number
64 goes into 190 2 times
190 - 128 =62 left over
2 62/64
2 31/32 cups used
A group of friends went to play minigolf at Adventureland. Anna's score was 262 putts, Daniela's score was 313 putts, Luiza's score was 393 putts, and Vera's score was 323 putts. Find the mean absolute deviation (MAD) of the data set.
Answer:
35.25
Step-by-step explanation:
There are 4 data:
262, 313, 393, and 323
The formula for MAD (mean absolute deviation) = [tex]\frac{SUM(|x_{i}-XBar|)}{n}[/tex]
Where x_i are the each individual values (stated)
XBar is the average value
n is the number of data
First, let's find XBar, or the average. We add up all the 4 numbers and divide by 4 to get:
XBar = (262+313+393+323)/4=322.75
Now, let's calculate MAD:
MAD = [tex]\frac{|262-322.75|+|313-322.75|+|393-322.75|+|323-322.75|}{4}\\=35.25[/tex]
MAD = 35.25
Answer:
31.5
Step-by-step explanation:
Which point is located at (6,1)?
A) T
B) V
C) W
D) X
Go 6 units in X axis and 1 unit in Y axis and you get V.
Alternative B
Answer:
B, Point V
Step-by-step explanation:
find 6 on the x-axis and go up 1, you will find point V
What is the value of x?
Answer:
x = 127°
Step-by-step explanation:
We are given a polygon which has six sides but all the sides and angles are not equal so it is an irregular hexagon.
We know that the sum of the measures of the interior angles of a polygon with n sides is given by: [tex](n-2)\times180[/tex].
[tex](6-2)\times180 = 112+133+128+100+120+x[/tex]
[tex] 7 2 0 = 5 9 3 + x [/tex]
[tex] x = 7 2 0 - 5 9 3 [/tex]
x = 127°
For example of 100 students the median is 90
Answer:
How is that possible
Step-by-step explanation:
So..... what is the question ?
HELP *EASY* What is the area of a trapezoid if the bottom of the trapezoid is 12cm, the top of the trapezoid is 9cm, and the height of the trapezoid is 3.5cm?
Answer:
A = 36.75 cm^2
Step-by-step explanation:
The area of a trapezoid is found by
A = 1/2 (b1+b2) *h
where b1 and b2 are the bases and h is the height
A = 1/2 (12+9) *3.5
A = 1/2(21)*3.5
A = 36.75 cm^2
graph of which exponential function passes through the points (0,4) and (1,24)?
Answer:
see explanation
Step-by-step explanation:
The exponential function is of the form
y = a [tex]b^{x}[/tex]
Substitute the given points into the equation to find a and b
Using (0, 4), then
4 = a[tex]b^{0}[/tex] ⇒ a = 4
Using (1, 24), then
24 = 4 [tex]b^{1}[/tex] ⇒ b = 6
Exponential function is
y = 4 × [tex]6^{x}[/tex]
The equation of the exponential function that passes through the points (0,4) and (1,24) is y = 4(6)^x.
Explanation:To find the equation of the exponential function that passes through the points (0,4) and (1,24), we can use the general form of an exponential function: y = ab^x, where a is the initial value and b is the growth/decay factor.
Using the point (0,4), we plug in x=0 and y=4 to get the equation 4 = ab^0, which simplifies to a = 4.
Using the point (1,24), we plug in x=1, y=24, and a=4 to get the equation 24 = 4b^1, which simplifies to b = 6.
Therefore, the equation of the exponential function is y = 4(6)^x.
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Find the value of y. Cos 21=9/y
y=9.64
—————
cos21=9/y
Cross Multiply
ycos21=9
Divide both sides by cos21 to isolate y
9/cos21 = 9.640304943
y=9.64
The perimeter of rectangle abcd is 28 and the area is 45.what is the new perimeter and area after the rectangle has been dilated by a scale factor of 4?
Answer is
New perimeter = 112
See photo