Answer:
242 mm²
Step-by-step explanation:
Given 2 similar figures with
ratio of sides = a : b, then
ratio of areas = a² : b² and
ratio of volumes = a³ : b³
Here the ratio of volumes = 27 : 1331, hence
ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11, thus
ratio of areas = 3² : 11² = 9 : 121
let x be the surface area of the larger figure then by proportion
[tex]\frac{18}{9}[/tex] = [tex]\frac{x}{121}[/tex] ( cross- multiply )
9x = 18 × 121 ( divide both sides by 9 )
x = [tex]\frac{18(121)}{9}[/tex] = 2 × 121 = 242
The surface area of the larger figure is 242 mm²
What is the sum of the geometric series 243-162+108.....+64/3
Answer:
[tex]\frac{463}{3}[/tex]
Step-by-step explanation:
The given geometric series is:
243-162+108.....+64/3
The first term is [tex]a=243[/tex].
The common ratio is:
[tex]r=\frac{-162}{243}=-\frac{2}{3}[/tex]
The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.
The complete series is
243-162+108-72+48-32+64/3
The sum is:
[tex]243+108+48+64/3-162-72-32=\frac{463}{3}[/tex]
Question 29
Find the short leg
Plz help
Answer:
7
Step-by-step explanation:
Since the triangle is right we can use the cosine ratio to find IR
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{IR}{TR}[/tex] = [tex]\frac{IR}{14}[/tex]
Cross- multiply
IR = 14 × cos60° = 14 × 0.5 = 7
Plz help me with this
Answer: A) y = -4
Step-by-step explanation:
The midline is usually at y = 0. In the given equation, the graph is shifted down 4 units so the new midline is at -4.
What is the measure of bac
50
80
100
130
Answer:
80
Step-by-step explanation:
The measure of a triangle is 180.
Answer: The answer to your question is 80
Step-by-step explanation: The first thing you do is set up your problem to find the side measure of bac, which is an angle they are looking for. The problem would look like this:
180-50+50
180-100
=80 degrees
Nate is wrapping a present the gift is a right rectangular prism with the base measuring 15“ x 12“ and a height of 8 inches what is the surface area?
Write an equation of the line that is perpendicular to the line y = 2x + 8, and which passes through the point (6,-2).
A) y = 2x + 4
B) y = -2x + 1
C) y = -
1
2
x - 4
D) y = -
1
2
x + 1
Answer:
y = -1/2 x + 1
Step-by-step explanation:
Lines that are perpendicular to each other have slopes that are negative reciprocals. You get the negative reciprocal of a number by flipping the fraction for the slope, then changing the positive/negative.
The lines are written in slope-intercept form, y = mx + b.
"x" and "y" are points on the line.
"m" is the slope.
"b" is the y-intercept.
In y = 2x + 8, the slope is 2. Find its negative reciprocal.
Write the slope as a fraction.
[tex]m=2=\frac{2}{1}[/tex]
Flip the fraction.
[tex]m=\frac{1}{2}[/tex]
Change the negative/positive.
[tex]m=-\frac{1}{2}[/tex] This is the slope of the perpendicular line.
Now we need to find the y-intercept, "b", for our line. We know m = -1/2, and we know a random point (6, -2). Points are written (x, y), which mean x = 6 and y = -2. Substitute the values of the point and the slope into y = mx + b.
[tex]y = mx + b[/tex]
[tex]-2 = -\frac{1}{2}*6 + b[/tex] Multiply (-1/2)(6) by combining into the numerator
[tex]-2 = -\frac{6*1}{2} + b[/tex] Simplify numerator
[tex]-2 = -\frac{6}{2} + b[/tex] Reduce fraction
[tex]-2 = -3 + b[/tex] Isolate "b" now
[tex]-2 + 3 = -3 + b + 3[/tex] Add 3 to both sides
[tex]1 = b[/tex] Solved for "b"
[tex]b=1[/tex] Write the variable on the left side for standard formatting
b = 1 and m = -1/2
Substitute them into slope-intercept form for the final answer.
y = -1/2 x + 1
To find the equation of a line perpendicular to a given line and passing through a specific point, use the negative reciprocal of the original line's slope. Applying this to the point-slope form of the line equation gives y = -(1/2)x + 1, which is the correct answer as per the given options.
Explanation:The subject of the question is about writing the equation of a line that is perpendicular to another line, specifically y = 2x + 8, and passes through a specific point (6, -2). The concept involved here is the slope of the lines. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Since the slope of our given line is 2, the slope of the line that is perpendicular to this would be -1/2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes, we can substitute m = -1/2 and (x1, y1) = (6, -2). Therefore, the equation of the line is y = -(1/2)x + 1.
The correct answer from the given options is (D) y = -(1/2)x + 1.
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PLEASE ANSWER ASAP! THANK YOU! SUPER EASY! Mrs. Davis is planning to put a circular rug in her living room. The circumference of the rug is 31.4 ft. Use this information to answer the following questions. Use 3.14 for π. C=πD. A = π r^2.
Answer:
Part A) The diameter of the rug is [tex]10\ ft[/tex]
Part B) The radius of the rug is [tex]r=5\ ft[/tex]
Part C) The area of the rug is [tex]78.5\ ft^{2}[/tex]
Step-by-step explanation:
Part A) Find the diameter of the rug
we know that
The circumference of a circle (circular rug) is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]C=31.4\ ft[/tex]
[tex]\pi=3.14[/tex]
substitute the values and solve for D
[tex]31.4=(3.14)D[/tex]
[tex]D=31.4/(3.14)=10\ ft[/tex]
Part B) Find the radius of the rug
we know that
The radius of a circle (circular rug) is half the diameter
we have
[tex]D=10\ ft[/tex]
[tex]r=D/2[/tex]
substitute
[tex]r=10/2=5\ ft[/tex]
part C) What is the area the rug is covering?
The area of the circle (circular rug) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=5\ ft[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]A=(3.14)(5)^{2}[/tex]
[tex]A=78.5\ ft^{2}[/tex]
what is the range of 4,5,10,10,16
Range is the biggest number minus the smallest from the list.
R = 16 - 4
R = 12
The range is 12.
The length And width of a rectangle each less than 1 unit long. Which statement is true about the area of the rectangle?
Area is calculated by multiplication of dimensions:
length×width= Area
both are lesser than 1, let's say 0.5 and 0.9 as examples.
0.5×0.5=0.25
0.9×0.9=0.81
you see the area is less than one and area can never be negative so first answer is the right answer.
The correct statement is option a. The area is between 0 square units and 1 square units
What is a rectangle?Any 2-diamensional figure bounded by 4 sides in which opposite sides are equal and parallel and all the 4 angles are right angled.
How to find which statement is true about the area of the rectangle?The area of rectangle can be calculated by the formula = Length x breadth( or width)Here the length and width of a rectangle each less than 1 unit long.Now, 0 unit<length<1 unit
0 unit<width<1 unit
∴ Area of the rectangle = (length x width)
We know that if any quantity whose value lies between 0 and 1 is multiplied to another quantity whose value also lies between 0 and 1 ,then the answer will also lie between 0 and 1.If the values of both the quantities are 1, then the product will be 1⇒ 0 square units <Area of the rectangle <1 square units
∴ The area of the rectangle is between 0 square units and 1 square units
The first option matches with the answer.
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Find the value of x if y = 1/4x and 5x-8y=33.
Answer:
x = 11
Step-by-step explanation:
Given the 2 equations
y = [tex]\frac{1}{4}[/tex] x → (1)
5x - 8y = 33 → (2)
Substitute y = [tex]\frac{1}{4}[/tex] x into (2)
5x - 8( [tex]\frac{1}{4}[/tex]x ) = 33
5x - 2x = 33
3x = 33 ( divide both sides by 3 )
x = 11
Answer:
11
Step-by-step explanation:
Given that ,
⇒ y = 1/4x and
⇒ 5x - 8y = 33
We can write 1st equation as ,
⇒ 4y = x
Put x = 4y in 2nd Equation ,
⇒ 5*4y - 8y = 33
⇒ 20y - 8y = 33
⇒ 12y = 33
⇒ y = 33/12
Put this in 1st ,
⇒ 33/12 = 1/4 x
⇒ x = 33/12 × 4
⇒ x = 33/3
⇒ x = 11 .
What is 70 times five
Answer:
350
Step-by-step explanation:
Answer:
350
Step-by-step explanation:
First, do 7 x 5
7 x 5 is 35
Now just add a zero to the end to get 350
I hope this helps! :)
In the 30-60-90 triangle below, side s has a length of _
length of
_and side q has a?
(e) is the homogeneous mixture
Answer:
it is E
Step-by-step explanation:
Just finished the test
40 POINTS NEED HELP FAST(sqrt is a radical)
1.)simplify:
sqrt425
sqrt628
sqrt128
2.)add:
-2sqrt7+3sqrt7
3.)subtract:
-3sqrt12-3sqrt3-3sqrt20
4.)multiply:
3sqrt3(3sqrt8)
3sqrt3(4-3sqrt5)
1)5sqrt17,2sqrt157,8sqrt2
2)sqrt7
3)-3(3sqrt3+2sqrt5)
4)18sqrt6,12sqrt3-9sqrt15
This question is confusing the bejubes out of me =(
Answer:
Final answer is [tex]c=12t[/tex].
Step-by-step explanation:
Given that the amount c of energy you burn and the time t you spend exercising, if you burn calories at a rate of 12 Cal/min.
Now we need to write a function rule for the relationship between c and t.
given that cal/min=12
or [tex]cal/min=12/1[/tex]
or [tex]c/t=12[/tex]
or [tex]c=12t[/tex]
Hence final answer is [tex]c=12t[/tex].
Help with this question !
Answer:
see explanation
Step-by-step explanation:
Given
T= 2π[tex]\sqrt{\frac{L}{g} }[/tex]
Square both sides
T² = 4π² [tex]\frac{L}{g}[/tex] ( divide both sides by 4π²
[tex]\frac{T^2}{4\pi ^2}[/tex] = [tex]\frac{L}{g}[/tex]
Multiply both sides by g
L = [tex]\frac{gT^2}{4\pi^2 }[/tex]
Find the radius of the circle whose equation is x^2 + y^2 = 4.
Answer:
Radius = 2.
Step-by-step explanation:
We have been given equation of the circle which is [tex]x^2 + y^2 = 4[/tex].
Now we need to find the radius of the given circle [tex]x^2 + y^2 = 4[/tex].
To find that let's compare with the formula of the circle with standard equation of the circle [tex]x^2 + y^2 = r^2[/tex], where r is the radius.
We get [tex]r^2 = 4[/tex]
take square root of both sides.
[tex]r=2[/tex]
Hence radius of the given circle is r = 2.
PLEEEAAAASE HELLP!!!Tina is making a cylindrical sandbox that has a radius of 2 feet. She bought 18.84 cubic feet of sand for the sandbox. Which height does she need to make the sandbox to fit all the sand?0.5 ft, 0.75 ft, 1 ft, 1.5 ft.
Answer:
Step-by-step explanation:
The answer is 1.5 ft i just took the test
Answer:
The correct option is 4.
Step-by-step explanation:
The volume of a cylinder is
[tex]V=\pi r^2h[/tex]
where, r is radius of the base and h is height of the cylinder.
It is given that the radius of the cylindrical sandbox is 2 ft and the volume of cylindrical sandbox is 18.84.
[tex]18.84=(3.14)\times (2)^2\times h[/tex] [tex][\because \pi=3.14][/tex]
[tex]18.84=(3.14)\times 4\times h[/tex]
[tex]18.84=12.56\times h[/tex]
[tex]\frac{18.84}{12.56}=h[/tex]
[tex]1.5=h[/tex]
The height of the sandbox is 1.5 ft. Therefore the correct option is 4.
You are able to bike 20 miles in the same time that your friend ran 3 miles. If your speed was 5 miles per hour faster on average than your friend's speed, what was the average speed of your friend?
Answer:
Step-by-step explanation:
Givens
d = 20 for the bike
d1 = 3 for the person
rate of person = r
rate of bike = r + 5
Formula
d = r*t; t = d/r
Solution
t is the same for both
20/(r + 5) = 3/r Cross multiply
20*r = 3*(r + 5) Remove the brackets.
20*r = 3r + 15 Subtract 3r from both sides.
20r - 3r = 3r - 3r + 15 Combine
17r = 15 Divide by 17
r = 15/17
r = 0.8824 miles per hour running
according to the graph what is the value of the constant in the equation below
Answer: D or 36 just answered on apex
Step-by-step explanation:
To find the constant in an equation with a graph, examine the graph's features such as slope, intercept, or specific data points and compare them with theoretical constants provided, like k1, k2, k3, k4, and K3.
Explanation:The value of the constant in the equation being discussed is related to graphing functions and the characteristics of lines and curves on a graph. In general, when determining a constant from a graph in mathematics, it is essential to look at certain features such as the slope, the intercept, or specific data points depending on the context of the problem. For instance, if we are trying to find a constant of proportionality (k), we might use a linear fit of data points to determine the slope, which then gives us the value of k. Similarly, other constants may be deduced by comparing the theoretical values with the actual data points on the graph.
To determine the value of a constant such as k in a force (F) versus displacement (x) graph, one would label the transition region of the graph and use the given constants (e.g., k1, k2, k3, k4, K3) to measure the force. The slope (m) of the line on the graph is representative of how the value changes along the graph and is calculated using the change in y over the change in x. In situations where the graph does not display a constant force, the value may be represented by the area under the force versus distance graph.
which equation includes the minimum or maximum of f as a number that appears in the equation?
Answer:
Option A
Step-by-step explanation:
The parent function [tex]y=x^2[/tex] has a minimum [tex](0,0)[/tex].
If we map [tex]x\mapsto x-1[/tex] we get [tex]y=(x-1)^2[/tex]. This is a horizontally translated copy of the parent function, so the minimum is still 0.
Then if we map [tex]f(x)\mapsto f(x)-4[/tex] we have [tex]y=(x-1)^2-4[/tex]
This is a vertical translation 4 units down, so now the minimum is -4, which appears in the equation.
The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
First of all, all the function mentioned does not have a maximum, but have the same minimum, at (1, -4).
But, as of the appearance equation f(x) = (x - 1)² - 4 includes the minimum. because when terminating x it gives minimum y and when terminating it gives x minimum.
Thus, The required equation which includes the minimum or maximum of f is given as f(x) = (x - 1)² - 4. Option A is correct.
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What is the answer to adding 5/16 1/2
Answer:
1 1/3
Step-by-step explanation:
(5/6 x 1/1) + (1/2 x 2/3) + ?
the answers to that are 5/6 and 3/6 so
5/6 + 3/6 = ???
5 + 3/ 6 = 8/6
8 divided by 2/ 6 divided by 2 = 4/3
so divide the numerator and denominator 4 divided by 3
then convert that to a mixed number
1 1/3
Answer:
13/16.
Step-by-step explanation:
1/2 = 8/16 so:
5/16 + 1/2
= 5/16 + 8/16
= 13/16 (answer).
what is the sum of -5/7 + 4/7?
Answer:
1/7
Step-by-step explanation:
Answer: -1/7
Step-by-step explanation: Since the fractions have the same denominator you can add them together without trying to have to change it
|x−3| =4 help me, please
Answer:
x=-1 or x=7
Step-by-step explanation:
|x−3|=4
x-3=-4 or x-3=4
x=-1 or x=7
I neeed help please?!!!!
Answer:
(3,-3)
Step-by-step explanation:
An ordered pair is written with X first, then Y (X,Y).
X is the left and right axis Y is the up and down axis.
The dot is at X = 3 and Y = -3
It would be written as (3,-3)
Which ordered pair could be removed so that the set of
ordered pairs is a function?
(4, -2)
(-3,2)
(3, 4)
(1,1)
The answer is (-3,2) because when it’s present in the graph the graph would not pass the vertical line test.
Another way to think about it is that -3 (input) has more than one output.
Answer:
The answer is (-3, 2)
Step-by-step explanation:
Let's define the two sets
A = {4, -3, 3, 1} and B = {-2, 2, 4, 1 -3}, so that the set of ordered pairs is a function , we should have that to every element from the first set (in this case A) corresponds (or is associate to) an element (and only one element) from the second set (in this case B). But we have that the element -3 in the set A (the domain) is related to the elements 2 and -3 which belong to the set B (the codomain), this in not allowed by the definition of function. So in order to the set of ordered pairs is a function we should remove the pair (-3, 2).
7. Two angles are vertical in relation. One angle is 2y and the other angle is y +130. Find each
angle measure. Is your answer reasonable? Explain how you know.
TV BOF
To solve for the vertical angles, we set up the equation 2y = y + 130. Solving for y gives us 130, and substituting back, we get each angle measures 260 degrees, which is reasonable since vertical angles are equal.
Explanation:Two angles are vertical angles, which means they are opposite each other when two lines intersect and they are equal in measure. The problem states that one angle is 2y and the other is y + 130. Since vertical angles are equal, we can set up the equation 2y = y + 130.
Now, we solve for y:
To check if the answer is reasonable, we can note that vertical angles must be equal, and both our calculated angles are 260 degrees, confirming they are equal and thus reasonable.
Which equation represents y = −x^2 −2x + 3 in vertex form
Final answer:
The equation y = -x² - 2x + 3 can be expressed in vertex form as y = -(x + 1)² + 4.
Explanation:
The equation y = -x² - 2x + 3 can be expressed in vertex form as:
y = -(x + 1)² + 4
To convert the equation to vertex form, we need to complete the square. Here are the steps:
Factor out a common negative from the first two terms: y = -1(x² + 2x) + 3
Take half the coefficient of x (-2/2 = -1) and square it: (-1)² = 1
Add the squared value inside the parentheses and subtract it outside: y = -(x² + 2x + 1) + 3 - 1
Simplify: y = -(x + 1)² + 2
The vertex form of the equation is y = -(x + 1)² + 4.
the ratio of teachers to student is 1 to 26. Find an equivalent ratio
To find an equivalent ratio, multiply both the numerator and denominator of the given ratio by the same number. In this case, multiplying both 1 and 26 by 2 gives us an equivalent ratio of 2:52.
Explanation:To find an equivalent ratio, we can multiply or divide both the numerator and denominator of the given ratio by the same number. In this case, we can multiply both the numerator and denominator of the ratio 1:26 by 2 to get an equivalent ratio. Therefore, the equivalent ratio is 2:52.
NEED HELP FAST!!!!!!!!!
h= k/j
Multiply by j for the left and right hand side
(h)(j)= k/j(j)
Cross out j and j for the right hand side.
hj= k
answer is : k= hj
I think this is the answer
ANSWER
[tex]k = hj[/tex]
EXPLANATION
The given formula is:
[tex]h = \frac{k}{j} [/tex]
We want to solve this formula for k.
Let us multiply both sides by j.
[tex]h \times j = \frac{k}{j} \times j[/tex]
Cancel the common factors.
[tex]hj = k[/tex]
Or we rewrite to obtain,
[tex]k = hj[/tex]
k is now isolated on one side of the equation.
Tamara wants to find the distance from (2, –10) to other points. For which points in the same quadrant as (2, –10) could Tamara use a number line to find the distance
Answer:
(2,-2)
(10,-10)
(2,-9)
(7,-10)
Step-by-step explanation:
The given point is (2,-10)
This point is in the fourth quadrant.
To be able to use the number line to find the distance between this point , (2,-10) and another point in the fourth quadrant, the second point must have the same x-coordinate with this point or the same y-coordinate with this point.
Answer:
A
B
D
E
Step-by-step explanation:
simple stuff i know