Answers
let's recall Cavalieri's Principle, solids with equal altitudes and cross-sectional areas at each height have the same volume, so even though this cylinder is slanted with a height = x and a radius = 8, the cross-sectional areas from the bottom to top are the same thickness and thus the same area, so its volume will be the same as a cylinder with the same height and radius that is not slanted.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=8\\ h=x\\ V=768\pi \end{cases}\implies 768\pi =\pi (8)^2(x)\implies 768\pi =64\pi x \\\\\\ \cfrac{768\pi }{64\pi }=x\implies 12=x[/tex]
Related Questions
Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (–10, 6), (4, 6).
Answers
Answer:
[tex]\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1[/tex]
Step-by-step explanation:
The standard equation of a horizontal hyperbola with center (h,k) is
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
The given hyperbola has vertices at (–10, 6) and (4, 6).
The length of its major axis is [tex]2a=|4--10|[/tex].
[tex]\implies 2a=|14|[/tex]
[tex]\implies 2a=14[/tex]
[tex]\implies a=7[/tex]
The center is the midpoint of the vertices (–10, 6) and (4, 6).
The center is [tex](\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)[/tex]
We need to use the relation [tex]a^2+b^2=c^2[/tex] to find [tex]b^2[/tex].
The c-value is the distance from the center (-3,6) to one of the foci (6,6)
[tex]c=|6--3|=9[/tex]
[tex]\implies 7^2+b^2=9^2[/tex]
[tex]\implies b^2=9^2-7^2[/tex]
[tex]\implies b^2=81-49[/tex]
[tex]\implies b^2=32[/tex]
We substitute these values into the standard equation of the hyperbola to obtain:
[tex]\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1[/tex]
[tex]\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1[/tex]
I really need help with this I don’t understand
Answers
Answer:
Step-by-step explanation:
There is not possible solution in the real number system or the complex field.
Oddly, before I answer your question, I would point out that the equation given is a perfectly legitimate equation in some computer languages. It has the meaning of
Take the current value in memory location x Subtract 5 from it. Put the new result in memory location x.But that is not what you are being asked about.
The blank you could put in 4
so 4 = 4 - 5
4 = - 1
The second blank will give you the result of 4 = - 1 which can't be true in a million years.
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines?
Answers
Feel free to ask for any doubts.
Please mark Brainliest if this helps!
L•W•H L=8 W=31 H=20 I keep getting the answer wrong please help
Answers
Answer:
4960.
Try that, And good luck
Answer:
lwh = 4960
Step-by-step explanation:
To solve for volume, we use the formula V = lwh. Let's plug in our values:
lwh = l*w*h
= 8*31*20
= 4960
is 5 a soluation to the equation? 3x(+1)=7(×-2)-3
Answers
Answer:
x=5
Step-by-step explanation:
If the equation is:
3(x+1)=7(x-2) -3
Solution:
Multiply (x+1) by 3 and (x-2) by 7
3x+3 = 7x-14 -3
3x+3 = 7x -17
Now combine the like terms:
3+17 = 7x-3x
20 = 4x
Now divide both the terms by 4
20/4 = 4x/4
5 = x
You can write it as x=5
Thus the value of x is 5 ....
what is 1/3 to the power of -4
Answers
First, to get applied by the fraction rule: [tex]\displaystyle\frac{3^4}{1}[/tex], then, the applied rule [tex]\displaystyle\frac{a}{1}=a[/tex]. Finally, simplify to find the answer. [tex]\displaystyle3^4=3*3*3*3=81[/tex], the correct answer is 81. I hope this will help you. Have a wonderful day!
[tex]\left(\dfrac{1}{3}\right)^{-4}=3^4=81[/tex]
If g(x) = 3(x + 10), what is the value of the
function when x = -8?
O
-8
-2
24
Answers
Answer:
6 which is none of your answers.
Are you sure your function is right?
Is value to plug in x=-8?
Step-by-step explanation:
To find the value of the function at x=-8, you replace x with -8 in the function.
g(x)=3(x+10)
g(-8)=3(-8+10)
g(-8)=3(2)
g(-8)=6
g(-8) = 6.
The value of g(x) = 3(x + 10) when x = -8 is:
Substituting x = -8 in the function g(x)
g(-8) = 3 (-8+ 10)
Solving the operation in the parenthesis
g(-8) = 3 (-8 + 10)
g(-8) = 3 (2)
Solving the multiplication
g(-8) = 6
For which rational expression is -5 an excluded value of x?
Answers
Ration expressions cause excluded values wherever the denominator equals zero.
So, for any expression like
[tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]
-5 is an excluded value if [tex]g(-5)=0[/tex]
For example, the simplest one would be
[tex]h(x) = \dfrac{1}{x+5}[/tex]
In fact, if you try to evaluate this function at -5, you'd have
[tex]h(-5)=\dfrac{1}{5+5}=\dfrac{1}{0}[/tex]
which is undefined, and thus you can't evaluate the function, and thus -5 is an excluded value.
Answer:
6/x+5
Step-by-step explanation:
what can go in to 12 and 57??
Answers
Hijk is definitely a parallelogram. true or false?
Answers
The correct answer is: True
A parallelogram means that the lines will not intersect.
As you can see the ^ on both sides witch indicates that they will not touch.
Hope this helps! :3
The figure Hijk is definitely a parallelogram is true.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We are given that;
The figure of parallelogram
Now,
IH is parallel to JK
IJ is parallel to HK
Angle H and angle J are equal by alternate interior angles
Therefore, by given parallelogram the answer will be true.
Learn more about parallelogram;
https://brainly.com/question/28854514
#SPJ7
what is 99.96 rounded to the nearest tenth
Answers
Answer:
It is 100. You round the 6 to the 9 which makes the 9 round the 99 which makes it 100.
Step 1: Choose a point on the line, such as (2, 5).
Step 2: Choose another point on the line, such as (1, 3).
Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is .
Step 4: Substitute those values into the point-slope form.
y – y1 = m(x – x1)
y – 3 = (x – 1)
Answers
Answer:
y-3=2(x-1)
Step-by-step explanation:
So it looks like your line goes through (2,5) and (1,3) based on what you have said.
Looking at 5 to 3, that is down 2.
Locking at 2 to 1, that is left 1.
So the slope is -2/-1 =2/1=2.
Plug in the (x1,y1)=(1,3) and slope=m=2.
So using point slope form we have y-3=2(x-1).
Answer:
Step 3
Step-by-step explanation:
Just did the test
What is the greatest common factor of the polynomial below?
30x^3-20x
Answers
Answer:
10x
Step-by-step explanation:
The greatest common factor of the polynomial 30x³ - 20x is 10x.
Option B is the correct answer.
We have,
To find the greatest common factor (GCF) of the polynomial
30x³ - 20x, we need to determine the largest expression that can be factored out from both terms.
Let's look at the coefficients first.
The coefficients of the terms are 30 and -20.
Both numbers are divisible by 10, so we can factor out 10.
Now let's consider the variable, x. In the first term, we have x³, and in the second term, we have x.
The lowest power of x that appears in both terms is x, so we can factor out x.
Putting it together, we can factor out the GCF of 10x:
GCF(30x³ - 20x) = 10x
Therefore,
The greatest common factor of the polynomial 30x³ - 20x is 10x.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
What is the solution to the following equation?
3(x-4)-5= x-3
Answers
Answer:
x = 7Step-by-step explanation:
[tex]3(x-4)-5=x-3\qquad\text{use the distributive property}\\3x-12-5=x-3\\3x-17=x-3\qquad\text{add 17 to both sides}\\3x-17+17=x-3+17\\3x=x+14\qquad\text{subtract}\ x\ \text{from both sides}\\3x-x=x-x+14\\2x=14\qquad\text{divide both sides by 2}\\\dfrac{2x}{2}=\dfrac{14}{2}\\\\x=7[/tex]
Find the value of a in the picture
Answers
Answer:
= 52°
Step-by-step explanation:
The obtuse angle at O is twice the angle made at the circumference /by the same segment b.
=52×2=104°
The base angles that are made by isosceles triangle that has the apex with angle 104° equal to (180-104)/2=38°
The radii of a circle are equal and meet tangents at right angles.
Angle a= 90-38= 52°
What is the rate of change for this set of ordered pairs ?
X | 0 | 1 | 2 | 3 | 4
y | 7 | 12 | 17 | 22 | 27
A)2
B)2.5
C) 5
D)4
Answers
Answer:
Option C is correct.
Step-by-step explanation:
The rate of change can be found by finding the slope of given ordered pairs.
y₂=12, y₁=7,x₂=1,x₁=0
rate of change = y₂-y₁/x₂-x₁
rate of change = 12-7/1-0
rate of change = 5/1 = 5
Now considering next two points,
y₂=17, y₁=7,x₂=2,x₁=1
rate of change = y₂-y₁/x₂-x₁
rate of change = 17-12/2-1
rate of change = 5/1 = 5
So, the rate of change for this set of ordered pairs is 5.
Option C is correct.
Question 3
1 pts
8 men and 6 women apply for a job at a new startup. How many
ways can 4 of the applicants be selected for a second interview?
Answers
Answer:
1001 ways
Step-by-step explanation:
Total number of people who applied for the job = 8 + 6 = 14
Number of people to be chosen = 4
This is a combination problem because the order of selection does not matter. A group selection involves the combinations. So here we have to find the combinations of 14 people taken 4 at a time. The formula for the combination is:
[tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]
Here, n is the total number of objects which is 14 in this case.
r is the number of objects to be chosen which is 4 in this case.
Using these values, we get:
[tex]^{14}C_{4}=\frac{14!}{4!(14-4)!}\\\\ = \frac{14!}{4! \times 10!}\\\\ =1001[/tex]
Thus, there are 1001 ways to select 4 applicants from 8 men and 6 women for the second interview.
(x+2) is one of the factors of the polynomial x³+13x²+32x+20. Find its remaining factors.
A little help....
Answers
Answer:
x^2+11x+10
or
(x+1)(x+10) since you can factor x^2+11x+10
Step-by-step explanation:
Let's do synthetic division.
We are dividing by x+2, so -2 will be on the outside. Like this:
-2 | 1 13 32 20
| -2 -22 -20
|___________________________
1 11 10 0
The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.
The other factor we found by doing this is (x^2+11x+10).
You can find more factors by factoring x^2+11x+10.
Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).
identify the image of triangle XYZ for a composition of 50 degrees rotation and a 40 degrees rotation, both about point y
Answers
Answer:
a
Step-by-step explanation:
Given:
triangle XYZ is rotated by a composition of 50°+40°=90° both about point y
Now when a geometrical figure is rotated by any degree then its shape or size does not change and remain same.
As the triangle is rotated clockwise by 90 degrees about point y then diagram attached is formed .
option a is correct.
Answer:
The correct option is A.
Step-by-step explanation:
If the direct of rotation is not mentioned, then it is consider as counterclockwise rotation.
It is given that triangle XYZ rotated 50 degrees and a 40 degrees, both about point Y.
It means the figure triangle XYZ rotated 90 degrees counterclockwise about the point Y.
In option A, triangle XYZ rotated 90 degrees counterclockwise about the point Y.
In option B, triangle XYZ rotated 180 degrees counterclockwise about the point Y.
In option C, triangle XYZ rotated 270 degrees counterclockwise about the point Y.
In option D, triangle XYZ rotated 360 degrees counterclockwise about the point Y.
Therefore the correct option is A.
choose the equation that represents a line that passes through points -3,2 and 2,1
5x+y=-13
5x-y=17
x-5y=-13
x+5y=7
Answers
bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{1-2}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]
[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies y=-\cfrac{1}{5}x-\cfrac{3}{5}+2\implies y=-\cfrac{1}{5}x+\cfrac{7}{5} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y)=5\left( -\cfrac{1}{5}x+\cfrac{7}{5} \right)}\implies 5y=-x+7\implies \blacktriangleright x+5y=7 \blacktriangleleft[/tex]
The equation of the line passing through points (-3,2) and (2,15) is calculated using the point-slope formula after calculating the slope. The derived equation is y = 2.6x + 7.8.
Explanation:The question is asking to find the equation of the line that passes through two given points: (-3,2) and (2,15). To tackle this, firstly we need to calculate the slope (m) of the line, which is given by the formula: (y2 - y1) / (x2 - x1). Secondly, we apply the point-slope formula, y - y1 = m(x - x1), where (x1, y1) can be either point.
Now, calculating the slope using the given points, we find (15-2) / (2- (-3)) equals to 13/5 or 2.6. Next, we use the point-slope formula to write the equation. If using point (-3,2) we find y - 2 = 2.6 (x - (-3)). Thus, the equation for the line that passes through (-3,2) and (2,15) is y = 2.6x + 7.8 after simplifying the equation.
Learn more about Equations of Line here:https://brainly.com/question/35492661
#SPJ3
Tangent wz and secant WV intersect at point W. Find the length of YV If necessary, round to the hundredths place.
A 2.67
B5
с.9
D. 10
Answers
Answer:
Option B. [tex]YV=5\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem, states that If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
In this problem
[tex]WZ^{2}=WV*WY[/tex]
substitute and solve for WV
[tex]6^{2}=WV*4[/tex]
[tex]WV=36/4=9\ units[/tex]
we have that
[tex]WV=WY+YV[/tex]
substitute
[tex]9=4+YV[/tex]
[tex]YV=9-4=5\ units[/tex]
Prove that the diagonals of a rectangle bisect each other.
The midpoint of BD is _____
Answers
Answer:
a,b
Step-by-step explanation:
in the rectangle when bisected
if mid point is taken as O
BO=OD
AO=OC
X=2a
mid point of X=2a/2=a
Y=2b
y mid point = b
The midpoint of BD will be ( a,b ) so option (C) will be correct.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other terms, a line segment is merely a section of a larger, straight line that extends indefinitely in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
The midpoint of a line associated with two coordinates is given by
(x₁ + x₂)/2 and (y₁ + y₂)/2
Given that B (0,2b) D (2a,0)
So midpoint
(0 + 2a)/2 and (2b + 0)/2
⇒ (a,b) so the midpoint will be this.
For more about line segment
https://brainly.com/question/25727583
#SPJ5
brianna is graphing the function f(x)=x^2+6x+5. what x intercepts should brianna use to graph f(x)
Answers
Answer:
x = - 5, x = - 1
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
x² + 6x + 5 = 0 ← in standard form
Consider the factors of the constant term (+ 5) which sum to give the coefficient of the x- term ( + 6)
The factors are + 5 and + 1, since
5 × 1 = 5 and 5 + 1 = + 6, hence
(x + 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 )
x + 1 = 0 ⇒ x = - 1 ⇒ (- 1, 0)
Answer:
-5 -1
Step-by-step explanation:
on edge
Convert each angle measure to Radion measure 45°
Answers
Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
To convert from degrees to radians
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
given degree measure = 45°, then
radian = 45 × [tex]\frac{\pi }{180}[/tex] ( divide 45 and 180 by 45 )
= [tex]\frac{\pi }{4}[/tex]
Answer:
π/4 radians.
Step-by-step explanation:
To convert to radians we multiply degrees by π/180.
So 45 degrees = 45 * π / 180
= π/4 radians.
a portion of road A climbs steadily for 154 feet over a horizontal distance of 2200 feet. a portion of road B climbs steadily for 153 feet over a horizontal distance of 3400 feet. which road is steeper?
Answers
Answer:
Road A
Step-by-step explanation:
The slope of road A is:
154 / 2200 = 0.07
The slope of road B is:
153 / 3400 = 0.045
Road A has the larger slope, and is therefore steeper.
The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. By calculating this ratio for both Road A and Road B, we find that Road A, with a ratio of 0.07, is steeper than Road B, which has a ratio of 0.045.
Explanation:The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. This is equivalent to finding the slope in mathematics. We can calculate this for both Road A and Road B:
For Road A, the slope can be calculated as rise over run, or 154 feet over 2200 feet, yielding approximately 0.07. For Road B, applying the same formula gives 153 feet over 3400 feet, resulting in a slope of about 0.045.
Comparing these two results, it is clear that Road A, with a slope of 0.07, is steeper than Road B, which has a slope of 0.045.
Learn more about Slope Calculation here:https://brainly.com/question/33539953
#SPJ11
A pair of shoes costs $89.99. They are on sale for 30% off. The store charges a 6.5% sales tax. What is the final cost? Round to the nearest cent.
Answers
Final answer:
The final cost of the shoes after a 30% discount and a 6.5% sales tax is $67.08, with each step of the calculation rounding to the nearest cent.
Explanation:
Calculating Final Price with Discount and Sales Tax
To calculate the final cost of a pair of shoes with an original price of $89.99 and a discount of 30%, along with an additional 6.5% sales tax, follow these steps:
Calculate the discount amount by converting the percentage to a decimal (30% = 0.30) and multiplying it by the original price: $89.99 × 0.30 = $26.997. Round this to the nearest cent: $27.00.Subtract the discount from the original price to get the discounted price: $89.99 - $27.00 = $62.99.Find the sales tax by converting the 6.5% to a decimal (6.5% = 0.065) and multiplying by the discounted price: $62.99 × 0.065 ≈ $4.09435. Round this to the nearest cent: $4.09.Add the sales tax to the discounted price to find the final cost: $62.99 + $4.09 = $67.08.The final cost of the shoes after applying the discount and including sales tax is $67.08.
Which of the following graphs is described by the function given below? y = 2x 2 + 6x + 3
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=2x^{2}+6x+3[/tex]
This is the equation of a vertical parabola open up
The vertex is a minimum
Convert to vertex form
Complete squares
[tex]y-3=2x^{2}+6x[/tex]
Factor the leading coefficient
[tex]y-3=2(x^{2}+3x)[/tex]
[tex]y-3+4.5=2(x^{2}+3x+2.25)[/tex]
[tex]y+1.5=2(x^{2}+3x+2.25)[/tex]
Rewrite as perfect squares
[tex]y+1.5=2(x+1.5)^{2}[/tex]
The vertex is the point (-1.5,-1.5)
Find the zeros of the function
For y=0
[tex]2(x+1.5)^{2}=1.5[/tex]
[tex](x+1.5)^{2}=3/4[/tex]
square root both sides
[tex]x+\frac{3}{2} =(+/-)\frac{\sqrt{3}}{2}[/tex]
[tex]x=-\frac{3}{2}(+/-)\frac{\sqrt{3}}{2}[/tex]
[tex]x=-\frac{3}{2}(+)\frac{\sqrt{3}}{2}=\frac{-3+\sqrt{3}}{2}=-0.634[/tex]
[tex]x=-\frac{3}{2}(-)\frac{\sqrt{3}}{2}=\frac{-3-\sqrt{3}}{2}=-2.366[/tex]
Find the y-intercept
For x=0
[tex]y=3[/tex]
The y-intercept is the point (0,3)
therefore
The graph in the attached figure
Answer: graph a
Step-by-step explanation: a p e x
What is the average rate of change for this quadratic function for the interval
from x= 2 to x = 4?
Answers
Answer:
-6
Step-by-step explanation:
The average rate of a function f(x) on the interval from x=a to x=b is [tex]\frac{f(b)-f(a)}{b-a}[/tex].
So in the problem you have from [tex]x=2[/tex] to [tex]x=4[/tex].
The average rate of the function from x=2 to x=4 is
[tex]\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}[/tex].
Now we need to find f(4) and f(2).
f(4) means what is the y-coordinate that corresponds to x=4 on the curve.
f(4)=-15 since the ordered pair at x=4 is (4,-15).
f(2) means what is the y-coordinate that corresponds to x=2 on the curve.
f(2)=-3 since the ordered pair at x=2 is (2,-3).
So let's plug in those values:
[tex]\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}[/tex].
Now we just simplify:
[tex]\frac{-15+3}{2}[/tex]
[tex]\frac{-12}{2}[/tex]
[tex]-6[/tex]
Graph the system of equations on graph paper to answer the question.
{y=25x+4
{y=2x+12
What is the solution for this system of equations?
HELP PLS!!
Answers
Answer:
[tex]x = \frac{8}{23} \: \: \: \\ y = \frac{292}{23} [/tex]
Answer:
-5, 2
Step-by-step explanation:
Find X. Round to the nearest tenth if necessary.
Answers
Answer:
3.2
Step-by-step explanation:
If there are 2 secont lines intersecting inside a circle like the picture shown, then the theorem tells us that "the product of 2 segments of one secant line is equal to the product of 2 segments of other secant line"
Thus, we can say that:
x * 10 = 8 * 4
10x = 32
x = 32/10
x = 3.2