Answers
Related Questions
Difference of two numbers is 8. find the smallest possible product.
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Find the area of the shaded region. Thanks!
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now, let's rationalize the denominator for "r" first.
also notice, that section is just 1/4 of the area of that circle, so, let's just find the area of the whole circle with that "r", get one-quarter of it, and subtract it from the half of the area of the square.
[tex]\bf r=\cfrac{8}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies r=\cfrac{8\sqrt{2}}{2}\implies \boxed{r=4\sqrt{2}} \\\\\\ \stackrel{\textit{area of that circle}}{A=\pi (4\sqrt{2})^2}\implies A=\pi (16\cdot 2)\implies A=32\pi \\\\\\ \textit{how much is one-quarter of that?}\quad \cfrac{32\pi }{4}\implies \boxed{8\pi }\\\\ -------------------------------\\\\[/tex]
[tex]\bf \stackrel{\textit{area of the square}}{A=8\cdot 8}\implies A=64\qquad \stackrel{\textit{half of that square's area}}{32}\\\\ -------------------------------\\\\ \textit{shaded region}\implies \stackrel{\stackrel{\textit{half of that square}}{area}}{32}~~-~~\stackrel{\stackrel{\textit{one-quarter of the circle}}{area}}{8\pi }[/tex]
Answer:
-8π + 32
6.8675
Step-by-step explanation:
So we know that the are of the square is 64, and we know that the equation for the are of the shaded region is Area of square - 1/4 area of circle with a radius of 4√2 - area of 90/45/45 triangle with side lengths of 8 and 8.
s = square area
c = circle area
t = triangle area
∆ = shaded region area
∆ = s - 1/4c - t
input the numbers that we have for those variables:
∆ = 64 - 1/4(100.53) - 32
∆ = 64 - 25.1325 - 32
∆ = 32 - 25.1325
shade region approximate ≈ 6.8675
or to get an exact answer in terms of pi
∆ = 64 - 1/4(32π) - 32
∆ = 32 - 8π
shaded region = -8π + 32
just added this because it is hard to pick out the actual answer in the other person's answer.
PLEASE HELP!!!!!!!!!
solve for x
-2(x+1/3)+9x=4
x=
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-2x - 2/3 + 9x =4
7x - 2/3 = 4
7x = 4 + 2/3
7x = 14/3
/7 /7
x = 2/3
If $5000 is invested at 7.8% interest compounded monthly, how much would you have after 54 months?
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5000 x (1+0.078/12)^54
5000 x (1.0065)^54
$7094.37
The table below represents the atmospheric temperature at a location as a function of the altitude:
Altitude
(in thousand feet)
x
15
20
25
30
Temperature
(in °C)
f (x)
4
−6
−16
−26
The average rate of change of the function between x = 15 to x = 25 is ___degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.
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from x15 to x 25 is 4 - -16 = -20 degree change
25 -15 = 10000 feet
-20/10 = -2 degrees every 1000 feet
Answer: The average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.
Step-by-step explanation:
The average rate of change of a function y=f(x) from [tex]x_1\ to\ x_2[/tex]is given by :-
[tex]k=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{-6-4}{20-15}[/tex]
Now, by the given table the average rate of change of the function between x = 15 to x = 25 will be :_
[tex]k=\frac{-16-4}{25-15}=\frac{-20}{10}=-2[/tex]
Hence, the average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.
Find the geometric mean of 6 and 7.
A. √42
B. 4√3
C. 7
D. 42
Please select the best answer from the choices provided.
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The Arithmetic Mean: (this is the mean we are used to seeing)
[tex]m= \frac{a+b+c}{n} [/tex]
(n= number of variables, in this case n=3)
To Find the Geometric Mean of n #'s:
[tex]m_{geometric} = \sqrt[n]{a*b} [/tex]
(n= number of variables, in this case n=2)
So, using this information we can find the geometric mean of 6,7 by plugging them into the equation as "a" and "b". n=2 (when n=2 a square root can be used)[tex]m_{geometric} = \sqrt[n]{a*b}[/tex]
[tex]m_{geometric} = \sqrt{a*b} [/tex]
[tex]m_{geometric} = \sqrt{6*7} [/tex]
[tex]m_{geometric} = \sqrt{42} [/tex]
So the answer in this case is A.[tex] \sqrt{42} [/tex]
which graph shows the inequality y>-2
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Find y'' by implicit differentiation .4x3 + 5y3 = 9
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Differentiating with respect to x, we have
[tex]12x^2+5(3y^2)(y')=0[/tex],
that is
[tex]12x^2+15y^2y'=0[/tex].
This means that [tex]\displaystyle{y'= -\frac{12x^2}{15y^2}=- \frac{4x^2}{5y^2} [/tex]
Differentiating again, using the quotient rule for the right hand side expression:
[tex]\displaystyle{y''=- \frac{4}{5}\cdot \frac{2xy^2-2yy'x^2}{y^4}= \frac{-8xy^2+8yy'x^2}{5y^4} [/tex]
y'' by implicit differentiation is y'' = -16x/5y^3.
To find y'' by implicit differentiation, we need to differentiate both sides of the equation .4x3 + 5y3 = 9 twice with respect to x.
First, we differentiate both sides once with respect to x to find dy/dx. This gives us:
12x^2 + 15y^2 (dy/dx) = 0
Next, we differentiate both sides once again with respect to x to find d^2y/dx^2 (y''). This gives us:
24x + 30y^2 (dy/dx) + 15y^2 (d^2y/dx^2) = 0
We can now solve for d^2y/dx^2 (y'') by substituting dy/dx from the first equation into the second equation. This gives us:
24x + 30y^2 (-12x^2/15y^2) + 15y^2 (d^2y/dx^2) = 0
Simplifying this equation, we get:
d^2y/dx^2 = -16x/5y^3
Therefore, y'' = -16x/5y^3.
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the image from reflecting a figure in the third quadrant over the x-axis
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Therefore, the image from refrecting a figure in the third quadrant over the x-axis is in the second quadrant.
You give up a full time salary of 45,000 a year to go to school for 2 years the total cost of going to school is 30,000, if want to be able to recover your investment in 5 years or less what is the minimum salary you would need to earn upon earning your degree?
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I would say that this person has lost out on 2 years salary while in school plus 5 year repayment period. Total amount divided over 5 years is:
( (2+5)(45,000) + 30,000 ) / 5 =
(7(45,000)+30,00)/5 = 69,000 salary
Answer:
69,000
Step-by-step explanation:
Given,
There is loss of 45,000 per year for two years,
So, the total lost = 2 × 45000 = 90,000
Also, the cost of school going = 30,000
∴ the total recovering amount = 90,000 + 30,000 = 120,000
If this amount must recover in 5 years or less than 5,
Then, the minimum recovering amount per year = [tex]\frac{120000}{5}[/tex] = 24,000
Now, the original salary per year = 45,000
Hence, the new salary per year = original salary + recovering amount
= 45,000 + 24,000
= 69,000
I’ll mark brainliest!!!!!! Please help me someone, anyone
What is the value of x ?
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1. y and x have a proportional relationship, and y = 7 when x = 2. What is the value of x when y = 21?
2. y and x have a proportional relationship, and y = 9 when x = 2. What is the value of y when x = 3?
3.he table shows a proportional relationship.
x y
2 2.8
4 5.6
6 8.4
8 11.2
Complete the equation that represents the table.
Enter your answer as a decimal in the box. y = ____x
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Answer: 6
Step-by-step explanation:
For what values of x and y must each figure be a parallelogram?
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(6x - 180)° = 180°
6x = 360°
x = 60°
5(60)-180= 300-180=120°
The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?
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Translation of a function y = h(x) up/down the y-axis is given by y = h(x) + a for translation 'a' unit up and y = h(x) - a for translation 'a' unit down
So, translating f(x) = x² eight units right and two units up gives:
g(x) = (x-8)² + 2
Please help thank you.
30 points.
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The sum of all angles with a polygon with n sides is
180(n-2)
We have 20 sides.
180(20 -2) = 180 * 18
= 3240
Thus, the sum of all angles is 3240 degrees.
The second choice is your answer.
Question 2:
First, let's calculate the sum of all the angles.
180(12 - 2) = 1800
Now, divide that by the number of sides to get the measure of one angle.
1800/12 = 150
Your answer is the last choice.
Question 3:
Do the same as we did in question 2, but instead of 12 sides, there are 6 sides.
A regular hexagon has an interior angle measure of 120 degrees.
(Note: you should remember that for future reference).
Now, let's form the following equation
3x = 120
Divide both sides by 3
x = 40
The first choice is your answer.
Have an awesome day! :)
1. 3240. 20 gon is called an isogon
2.150 because the formula for the interior angle or regular polynomials is [tex] \frac{180(n-2)}{n}[/tex]
3.3x = 120
Divide both sides by 3
x = 40
The product of two consecutive even integers is 80. find all such pairs of integers
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The possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given product of two consecutive even integers is 80.
Assume that the first integer is [n]. Then the second integer will be [n + 2]. According to the question, we can write -
n x (n + 2) = 80
n² + 2n = 80
n² + 2n - 80 = 0
n² + 10n - 8n - 80 = 0
n(n + 10) - 8(n + 10)
(n - 8)(n + 10) = 0
n = 8 and n = - 10
If → n = 8 then (n + 2) = 10.
If → n = - 10 then (n + 2) = -8.
Therefore, the possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
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Final answer:
The consecutive even integers whose product is 80 are 8 and 10. This is found by setting up an equation for consecutive even integers and factoring the number 80.
Explanation:
The question is asking to find two consecutive even integers whose product is 80. When two numbers are consecutive even integers, they can be represented as n and n + 2, where n is an even integer. To find these numbers, we set up the equation n(n + 2) = 80.
First, we need to find two numbers that multiply to give 80. We can start by listing the factors of 80: 1 x 80, 2 x 40, 4 x 20, 5 x 16, 8 x 10. Since we are looking for even integers, we pick the pairs where both numbers are even: 4 x 20, 8 x 10. However, the numbers must also be consecutive even integers, which is the case for the pair 8 and 10, but not for 4 and 20.
Therefore, the pair of consecutive even integers that multiply to give 80 are 8 and 10.
How do I simplify ((3x^2+12x+12)/(2x^2+x-6))/((4x^2-9)/(3x^3+x^2-10))
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[tex]= \dfrac{3(x + 2)^2}{(2x - 3)(x + 2)} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]
[tex]= \dfrac{3(x + 2)}{2x - 3} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]
[tex]= \dfrac{3(x + 2)(3x^3+x^2-10) }{(2x - 3)^2(2x + 3)} [/tex]
What is the mixed number for -10.125
Write in simplest form please!
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Hope this helps!
the -10 is ur whole number...it stays ur whole number
the 0.125....the last digit (5) is in the thousandths place...so put it over 1000
-10 125/1000 reduces to -10 1/8 <==
Two months ago, the mean daily rainfall in a local city was 9.4 cm. The mean absolute deviation was 3.5 cm. Last month, the mean daily rainfall in that city was 11.5 cm, and the mean absolute deviation was 1.6 cm.
Which statement about the rainfall is true?
More rain fell two months ago than last month.
About the same amount of rain fell two months ago as last month.
Last month, the amount of rain that fell each day varied about the same as the month before.
Last month, the amount of rain that fell each day varied less than the month before.
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Answer:
C
Step-by-step explanation:
Last month, more rain fell compared to two months ago, and there was less variation in the daily rainfall.
Explanation:To determine whether more rain fell two months ago or last month, we need to compare the mean daily rainfall and the mean absolute deviation for both months. Two months ago, the mean daily rainfall was 9.4 cm with a mean absolute deviation of 3.5 cm. Last month, the mean daily rainfall was 11.5 cm with a mean absolute deviation of 1.6 cm.
Thus, based on this information, we can conclude that more rain fell last month. The mean daily rainfall was higher and the mean absolute deviation was lower. This indicates that there was less variation in the amount of rain that fell each day last month compared to two months ago.
Which proportion could be used to solve the question?
What percent of 80 is 23?
A. p/23 = 80/100
B. p/80 = 23/100
C. p/100 = 23/80
D. none could be used
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C. can be used to solve it
other way is: p/100 *80 = 23
0.8p = 23
p = 23/0.8 = 28.75
What is the equation of the line shown in this graph?
pls help
Answers
the line of the graph is vertical since both x coordinates are the same ( both are -2)
so the equation would be x = -2
What is the length of the hypotenuse of 385.7 and 321.84?
Answers
Pythagorean theorem: 385.7^2 + 321.84^2=hypotenuse^2
hypotenuse=502.34
The table below represents ordered pairs of a function. Which change could be made so that the relation in the table is no longer a function
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Gina bought 2.3 pounds of red apples and 2.42 ponds of green apples. They were on sale for 0.75 a pound. How much did the apples cost altogether?
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Solve for y 3x-4y=10
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or,4y=3x-10
or,y=(3x-10)/4
so,y=3/4 x-5/2
The sum of two integers is 28, and their product is 192. what are the two integers?
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The product of 12 and 16 is 192, and the sum is 28.
write an equation for the line that passes through (2,-5) and is parallel to 3x+4y=8
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4y = -3x + 8; slope = -3
parallel lines, slope is the same so slope = -3
passes through (2,-5)
y = mx + b
b = y - mx
b = -5 - (-3)(2)
b = -5 + 6
b = 1
equation
y = -3x +1
hope it helps
The equation of the line which is parallel to the line 3x+4y=8 and passes through the point (2,-5) is y = -3/4x - 1/2.
Explanation:The given equation is 3x+4y=8, which is a linear equation. To make this simpler, we can isolate 'y' to make it in the form 'y = mx + b', where 'm' is the slope. When we do this, we get y = -3/4x + 2, so the slope of this line is -3/4.
Next, we know that parallel lines have the same slope. Therefore, the equation of the line parallel to the given line and passing through (2, -5) will also have a slope of -3/4. Using the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line, and 'm' is the slope, we can substitute the given values.
Therefore, y - (-5) = -3/4(x - 2), simplifying this gives us the equation of our line: y = -3/4x - 1/2.
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Which is harder linear algebra or abstract algebra?
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Linear algebra
I've always had trouble with graphs and it's much better if the algebra is similar to arthemetic
The vertex of the graph of a quadratic function is (–2, –9) and the y-intercept is (0, –5). Which of the following is the equation of the function? A. y = x2 +10x + 2 B. y = x2 +10x – 2 C. y = x2 – 2x – 5 D. y = x2 + 4x – 5
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Find the quotient of 3 2/5 and 3 2/6. Express your answer in simplest form.