Answer:
x = 12Step-by-step explanation:
The statement
The value of y varies inversely as the square of x is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of proportionality
To find the value of x when y = 1 first find the formula for the variation
y = 16 x = 3
k = yx²
k = 16(3)²
k = 16 × 9
k = 144
The formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
We have
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
We have the final answer as
x = 12Hope this helps you
Con proceso por favor
Answer:se
Step-by-step explanation:
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
The smaller of two numbers is one-half the larger, and their sum is 27. Find the numbers. Answer: The numbers are ___ ___ ___
Answer:
the smaller is 9 while the digger is 18
In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?
Simplify the expression using the order of operations. 2[16-5⋅2]÷4
Answer:
3.
Step-by-step explanation:
Solve in the order of pemdas.
Answer:
[tex]\boxed{\sf 3}[/tex]
Step-by-step explanation:
Solve brackets first.
[tex]2[16-5 \cdot 2]\div4[/tex]
Multiply the terms in the brackets.
[tex]2[16-10]\div4[/tex]
Subtract the terms in the brackets.
[tex]2[6]\div4[/tex]
Divide the numbers.
[tex]2(\frac{6}{4} )[/tex]
Multiply.
[tex]\frac{12}{4} =3[/tex]
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs
of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3
contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb
drawn from it at random is found to be defective. Find the probability that the box
selected was Box 2.
Answer:
1/6
Step-by-step explanation:
As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.
The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2 divided by total number of defective bulbs.
P(defective in box 2)= N(defective in box 2)/N(defective total)
As we know there is only 1 defective lamp in box 2.
So N(defective in box 2)=1
Total number of defective bulbs is Box1- 2 defective bulbs, box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.
So N(defective total)=6
So P(defective in box 2)=1/6
Please help with 4d.
Answer:
(Hemingway, The Old Man and the Sea)(Orwell, 1984)Step-by-step explanation:
A short web search will turn up the authors of the given titles:
The Old Man and the Sea - Hemingway
Huckleberry Finn - Twain
Moby D.ick - Melville
1984 - Orwell
Crime and Punishment - Dostoevsky
Datguy323 is going to complain again. What's the variables for: [tex]x^2+y^2=29\\x+y=7[/tex]
y<4
Answer: :o I FINALLY MADE IT
(5, 2)
x = 5
y = 2
Step-by-step explanation:
First, I graphed both equations. They meet at the points (5,2) and (2,5). Because y < 5, the solution is (5, 2)
Hope it helps <3
Answer:
[tex]x=5\\y=2[/tex]
Step-by-step explanation:
[tex]x^2 +y^2 =29[/tex]
[tex]x+y=7[/tex]
Solve for x in the second equation.
[tex]x+y=7[/tex]
[tex]x+y-y=7-y[/tex]
[tex]x=7-y[/tex]
Plug in the value for x in the first equation and solve for y.
[tex](7-y)^2 +y^2 =29[/tex]
[tex]y^2-14y+49+y^2 =29[/tex]
[tex]2y^2-14y+20=0[/tex]
[tex]2(y-2)(y-5)=0[/tex]
[tex]2(y-2)=0\\y-2=0\\y=2[/tex]
[tex]y-5=0\\y=5[/tex]
[tex]y<4[/tex]
[tex]y=2[/tex]
[tex]y\neq 5[/tex]
Plug y as 2 in the second equation and solve for x.
[tex]x+y=7[/tex]
[tex]x=7-y[/tex]
[tex]x=7-2[/tex]
[tex]x=5[/tex]
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represents the length then the length can be found by solving the equation:
If x represents the length, then the length can be found by solving the equation: x(x-4)=140
Answer: x(x-4) = 140 This equation can be solve to find the length.
Step-by-step explanation:
If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x for it to equal 140 because 140 is the area.
x(x-4) = 140 solve for x
[tex]x^{2}[/tex] - 4x = 140 subtract 140 from both sides
x^2 - 4x - 140 = 0 find a number that the product is 140 and the sum is -4
-14 and 10 works out.
[tex]x^{2}[/tex] - 14x + 10x - 140 = 0 factor by grouping
x(x -14) 10(x-14) = 0 factor out x-14
(x-14) ( x+10) = 0 set them both equal zero.
x-14= 0 or x+10 = 0
x = 14 or x= -10
Since -10 can't represent a distance, the answer is 14.
Check.
In this case the length is 14 and if the width is 4 less than the length then we will subtract 4 from 14.
14- 4 = 10 so the width is 10.
14 * 10 = 140
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years
Answer:
The value of annuity is [tex]P_v = \$ 7929.9[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 250[/tex]
The interest rate is [tex]r = 5\% = 0.05[/tex]
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is [tex]t = 10 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)
substituting values
[tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]
[tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]
[tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]
[tex]P_v = \$ 7929.9[/tex]
Question 15
1 pts
The cost of three avatars and three bats is $29.85. The cost of
three avatars and two bats is $23.90. How much will you pay
altogether if you purchase one of each.
O $5.95
O $8.92
$9.95
O $10.99
O $11.00
1 pts
Question 16
9
Answer:
$9.95.
Step-by-step explanation:
Let's say that you are buying a avatars and b bats.
3a + 3b = 29.85
Divide all terms by 3.
a + b = 9.95
You will pay $9.95 if you buy one of each.
Hope this helps!
What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes
Answer:
Step-by-step explanation:
I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be
(All of that is my point of view)
Average temperature 30 °
So :
30 ÷ 15 = 2 °
30 ÷ 10 = 3 °
30 ÷ 5 = 6 °
A rectangle is to be inscribed in a right triangle having sides of length 6 in, 8 in, and 10 in. Find the dimensions of the rectangle with greatest area assuming the rectangle is positioned as in Figure 1. Figure1
Answer: width = 2.4 in, length = 5
Step-by-step explanation:
The max area of a right triangle is half the area of the original triangle.
Area of the triangle = (6 x 8)/2 = 24
--> area of rectangle = 24 ÷ 2 = 12
Next, let's find the dimensions.
The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.
length = 10 ÷ 2 = 5
Use the area formula to find the width:
A = length x width
12 = 5 w
12/5 = w
2.4 = w
The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.
Let the length and width of the rectangle be x and y.
Then Area of the rectangle = xy
Now, from the triangle we can conclude that
[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]
Put the value of y in Area we get
[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]
Differentiating it w.r.t x we get
[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]
Put A'(x)=0 for maximum /minimum value
[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]
Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]
Therefore the area of the rectangle is maximum for x=3 inch
Now,
[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]
Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.
Learn more:httpshttps://brainly.com/question/10678642
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
Find the area of the shaded region if the dimensions of the unshaded region are 14ft x 18ft . Use 3.14 for π as necessary. Answer Asap Please! That would be greatly appreciated! PLEASE HELP ME ON THIS ASAP FIRST ANSWER GETS BRAINLIEST
Answer:
867.44 ft²
Step-by-step explanation:
The area of the shaded region is A = 196π + 252.
We have the dimensions of the unshaded region are 14ft x 18ft.
We have to find the area of shaded region.
What is the area of a Rectangle and a Circle?The area of a rectangle is -
A(R) = Length x Breadth = L x B
and the area of Circle is -
A(C) = [tex]\pi r^{2}[/tex]
According to the question -
Dimensions of the unshaded region -
L = 18ft
B = 14ft
Area of the shaded region (A) = Total Area - Area of Rectangle
Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.
Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)
Total Area = 196π + 504
Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252
Hence, the area of the shaded region is A = 196π + 252.
To solve more questions on Area of Figures, visit the link below -
https://brainly.com/question/9720037
#SPJ2
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation for this absolute value function when y=0? A 0=|x+2|+3 B 0=|x−2|+3 C 0=−|x+2|+3 D 0=−|x−2|+3
Answer:
Option D.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is a constant, (h,k) is vertex.
It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.
[tex]y=a|x-2|+3[/tex] ...(1)
It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.
[tex]0=a|5-2|+3[/tex]
[tex]-3=3a[/tex]
[tex]-1=a[/tex]
Put a=-1 in (1).
[tex]y=(-1)|x-2|+3[/tex]
[tex]y=-|x-2|+3[/tex]
Now, put y=0, to find the equation for this absolute value function when y=0.
[tex]0=-|x-2|+3[/tex]
Therefore, the correct option is D.
Answer:
I got this question on my test and I answered D cause if you look up the graph it matches the question
Step-by-step explanation:
D 0=−|x−2|+3
The perimeter of an equilateral triangle with a side length of 12 units is:
Answer:
Hey there!
An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.
Thus, the perimeter for this equilateral triangle would be 3(12)=36
Hope this helps :)
Answer:
[tex]\boxed{Perimeter = 36 \ units}[/tex]
Step-by-step explanation:
Perimeter = sum of all sides
Perimeter = 12 +12 + 12
Perimeter = 36 units
Simplify the expression.(4+2i)-(1-i)
ANSWER :
6i - (1-i)
Step - by - step explanation:
( 4 + 2i ) - ( 1 - i )
( 4 + 2 × i) - ( 1 - i )
( 6× i ) - ( 1 - i )
= 6i- (1-i)
Hope this helps and pls mark as brainliest :)
Factor.
-7x2 + 49x
-7(x - 7)
01 - 7x2 + 49x)
-x(x – 7)
-7x(x – 7)
Answer:
Option 1: -7x (x - 7)
Step-by-step explanation:
Factor -7x out of -7x^2.
= -7x (x) + 49x
Factor -7x out of 49x.
= -7x (x) -7x (-7)
Factor -7x out of -7x (x) - 7x (-7).
= -7x (x - 7)
(Also I took the test and got this answer right)
A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is cubic units. A cylinder with the same height and radius as the cone will have a volume of cubic units. If a sphere has the same radius as the cylinder, its volume is the volume of the cylinder.
The above question is not complete because it was not written and arranged properly
Complete Question
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Answer:
1) Volume of the cone = 134.04cubic units
2)Volume of the cylinder = 402.12cubic units
3) Volume of the sphere= 268.08 cubic units. Hence, if a sphere has the same radius as the cylinder, its volume is 2/3 times the volume of the cylinder.
Step-by-step explanation:
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
Volume of a cone = 1/3πr²h
h = 8 units
r = 4 units
Volume = 1/3 × π × 4² × 8
134.04cubic units
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
Volume of a cylinder = πr²h
Height and radius is the same as that of the cones hence,
h = 8 units
r = 4 units
= π × 4² × 8
= 402.12cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Volume of a Sphere = 4/3πr³
r = radius of the cylinder = 4 units
Volume of a Sphere = 4/3 × π × 4³
= 268.08 cubic units.
From the above question, we are asked to compare the volume of the sphere with the volume of the cylinder
Volume of the sphere : Volume of the cylinder
268.08 cubic units : 402.12 cubic units
268.08/402.12 = 2/3
Therefore, the volume of the sphere is 2/3 times the volume of the cylinder
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes
Answer:
The class width is [tex]C_w \approx 13[/tex]
Step-by-step explanation:
From the question we are told that
The upper class limits is [tex]max = 121[/tex]
The lower class limits is [tex]min = 14[/tex]
The number of classes is [tex]n = 8 \ classes[/tex]
The class width is mathematically represented as
[tex]C_w = \frac{max - min}{n }[/tex]
substituting values
[tex]C_w = \frac{121 - 14}{8 }[/tex]
[tex]C_w = 13.38[/tex]
[tex]C_w \approx 13[/tex]
Since
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))