Answer:
a) 235.62in³
b) 904.78in³
Step-by-step explanation:
a) The formula to find the volume of a cylinder is:
[tex]V = \pi r^2h[/tex]
We are given that r = 5 and h = 3, so we can just plug in and solve:
[tex]V = \pi(5)^2(3) = 235.62in^3[/tex]
b) The formula to find the volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
We are given that the diameter is 12in, which means that the radius (r) must be 6in (half the diameter). Now, we can plug in and solve:
[tex]V = \frac{4}{3}\pi (6)^3 = 904.78in^3[/tex]
Which value is an output of the function?
Answer: An output is the function
Step-by-step explanation:
Students were surveyed to find out the most popular pizza topping. According to the bar graph, how many students were surveyed?
A) 42
B) 44
C) 46
D) 48
The total number of students surveyed = 44 students
The answer is option D.
What is a bar graph?
A bar graph is a graph that presents categorical data with rectangular bars. The heights are proportional to the values that they represent. The bars can be plotted vertically or horizontally.A bar graph shows comparisons among different categories.
According to the given graph, the total number of students is equal to the sum of all the students in each vertical column.
∴tota students surveyed=12+8+9+15=44 students answer.
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What is the system of equations by graphing
Answer:
(x, y) = (0, 4)
Step-by-step explanation:
The two lines intersect at their y-intercept: (x, y) = (0, 4).
Identify the function in which y varies directly with x
Answer:
y = kx
Step-by-step explanation:
You'll need to share the possible answer choices in all future posts.
A function in which y varies directly with x has the form
y = kx, where k is the constant of proportionality.
With more data, it'd be possible for you and me both to identify this constant.
To identify if a function represents a direct variation relationship between \( y \) and \( x \), we need to determine if the function can be written in the form \( y = kx \), where \( k \) is a non-zero constant known as the constant of variation.
Here are the steps to determine if a function shows that \( y \) varies directly with \( x \):
1. Have a function \( f(x) \) to test. The function should be expressed in terms of \( x \).
2. Attempt to write the function in the form \( y = kx \).
3. Analyze the function:
- If there are no constant terms (that is, no term without \( x \)) and the only term is a multiple of \( x \), then the function shows direct variation. The coefficient of \( x \) is the constant \( k \).
- If there is a constant term not involving \( x \) (other than when \( x = 0 \)), or if \( x \) is raised to a power other than 1, then \( y \) does not vary directly with \( x \).
Let's look at a few examples:
**Example 1**: \( f(x) = 3x \)
This function is in the form \( y = 3x \), which matches the direct variation form \( y = kx \). Here \( k = 3 \). Therefore, \( y \) varies directly with \( x \).
**Example 2**: \( g(x) = 5x^2 \)
\( g(x) \) does not show direct variation because it does not have the form \( y = kx \); instead, \( x \) is raised to the second power, so it cannot represent a direct variation.
**Example 3**: \( h(x) = -2x + 1 \)
\( h(x) \) has a constant term, \( +1 \), which means it does not match the form \( y = kx \) for direct variation since \( y \) should have no constant term other than the coefficient of \( x \). Thus \( y \) does not vary directly with \( x \).
**Example 4**: \( j(x) = \frac{1}{4}x \)
\( j(x) \) reflects a direct variation. The function can be written as \( y = \frac{1}{4}x \), so \( y \) varies directly with \( x \) with a constant of variation \( k = \frac{1}{4} \).
In conclusion, to determine if \( y \) varies directly with \( x \) within a given function, you only need to inspect the function's form to ensure it is a linear equation with a slope \( k \) and no constant term (other than 0 when \( x = 0 \)).
Please answer correctly thank you!
If you rotate the triangle so that the 6 is on the bottom, the two sides are both 6.2.
Because the two sides are equal the two angles at the bottom would also be equal. One is given as 61 degrees, so the other bottom angle is also 61 degrees.
The three inside angles of a triangle need to equal 180, so X would equal 180 minus the two bottom angles.
X = 180 - 61 - 61 = 58 degrees.
Draw a triangles with sides of 9 cm, 7 cm, and 5 cm. Find its perimeter
The perimeter is 21 cm.
thanks
Answer:
12 + √74 cm
Step-by-step explanation:
The perimeter (literally meaning "around measure") is the length around an area, shape, or boundary. Here, we have a right triangle, and the legs of that right triangle measure 5 cm and 7 cm. Using the Pythagorean theorem, we can find the hypotenuse (we'll call it h):
[tex]5^2+7^2=h^2\\25 + 49=h^2\\74=h^2\\\sqrt{74}=h\\[/tex]
Adding all the lengths together, we find a perimeter of
5 + 7 + √74 = 12 + √74 cm
Solve the equation below algebraically for the exact value of x.
6 - 2(x + 5) = 42
Answer:
x= -19
Step-by-step explanation:
6-2(x+5)=42
6-2x-10=42
-4-2x=42
-2x=38
x= -19
Solve the following system by any method
please and thanks!
Answer:
B infinitely many solutions
Step-by-step explanation:
8x+9y = -5
-8x-9y =5
Add the two equations together
8x+9y = -5
-8x-9y =5
-------------------
0 = 0
This is always true, so we have infinite solutions
Answer: B
Step-by-step explanation:
There are infinite ways to solve this solution. If you plug it in, you can get the answer of infinite.
2-(-8c)+24-7c simplified
Answer:
26+c
Step-by-step explanation:
The given expression 2-(-8c)+24-7c simplifies to 26 + c by removing the parenthesis, changing the sign of -8c to +8c, combining like terms, and adding the constants.
The equation 2-(-8c)+24-7c simplifies by applying the distributive property and combining like terms. We first remove the parentheses and change the sign of the term inside, which is -8c, to a positive. Then we combine the like terms, -8c and -7c. The equation simplifies to:
2 + 8c + 24 - 7c = 2 + 24 + (8c - 7c) = 26 + c
So, the given expression simplifies to 26 + c.
Maria wrote the equation log(x/2)+log(20/x2) What is the solution to Maria’s equation?
Answer:
log x - log 2 + log 20 - 2 log x
Step-by-step explanation:
We need to solve the equation:
[tex]log(\frac{x}{2}) + log(\frac{20}{x^2})[/tex]
We know that log(x/y) = log x - log y and
log(x^2) = 2logx
Solving we get:
[tex](log x - log 2) + (log20 - log x^2)\\(log x - log 2) + (log20 - 2 log x)[/tex]
The solution is:
log x - log 2 + log 20 - 2 log x
Answer:
The solution to Maria's equation is x=5/4
98% of the mules who were surveyed said that stubbornness was a good character trait. If 343 mules gave this response, how many were surveyed in total?
Do a part over whole fraction
98% is a part of 100%
343 is a part of the number of mules who were surveyed in an unknown quantity.
You can set what you know into two proportions equal to each other:
[tex]\frac{98}{100} =\frac{343}{x}[/tex]
***x is the unknown value
Now you can cross multiply/butterfly
98x = 34300
Isolate x by dividing 98 to both sides of the equation
98x/98 = 34300/98
x = 350
This means that a total of 350 mules were surveyed
Hope this helped!
~Just a girl in love with Shawn Mendes
how do you plot f(x)= (x + 4) ^2
I hope this helps please tell me if it doesn’t
if 2x- 3 + 3x = 28 what is the value of x
Answer:
x= 31/5 (Exact form)
x= 6.2 (Decimal Form)
x= 6 1/5 (Mixed number form)
Step-by-step explanation:
write 6.04 x 10 to the power of -3 as an ordinary number
Answer: 0.00604
Step-by-step explanation: 10^-3 would be 0.001. If you multiply that by 6.04, you will get 0.00604
I hope that helps! :D
Kyle needed about 1 liter of water to fill a container. Did Kyle most likely fill a small glass, a spoon, or a vase?
The answer is vase.
A spoon is less than 3 ounces for sure.
A small glass is 8 ounces or less.
A vase is probably a liter of more.
Good luck!
What is the solution of square root x^2 + 49=x+5
Answer:
-44
Step-by-step explanation:
√x²+49=x+5
X+49=x+5
x-x=5-49
=-44
Answer:
x = 12/5
Step-by-step explanation:
[tex]\sqrt{x^{2}+49 } = x +5[/tex]
Square both sides: ([tex]\sqrt{x^{2} +49}[/tex])[tex]^{2}[/tex] = (x+5)[tex]^{2}[/tex]
[tex]x^{2} + 49 = (x+5)(x+5)\\[/tex]
[tex]x^{2} +49[/tex] = [tex]x^{2} + 10x + 25\\[/tex]
49 = 10x + 25
24 = 10x
[tex]\frac{12}{5}[/tex] = x
Which basic calculation or process in mathematics relates to factors?
Final answer:
Dimensional analysis, also known as the factor-label method, is a mathematical process related to factors, specifically used for unit conversions and complex computations to ensure correct units are obtained in the results.
Explanation:
The basic calculation or process in mathematics that relates to factors is known as dimensional analysis or the factor-label method. This method is integral in solving problems involving unit conversions and more complex computations, where the orientation of factors according to their units is essential to ensure that quantities cancel out or combine correctly to give a result with the desired units.
Through the factor-label method, we can transform quantities into different units by multiplying by conversion factors, which are ratios that equal one, to achieve the intended units for the result. This approach ensures that we conduct operations on the units of the quantities in the same way we do on the numbers.
For example, if we want to convert meters into inches, we multiply the quantity in meters by a conversion factor that expresses the number of inches in a meter. This factor, being a ratio of inches to meters, aligns the units so that 'meters' cancel out, leaving only 'inches' in the result.
An online company lets you download songs for 0.99 cents after you have paid a 5 dollar membership fee. Which domain would be most appropriate to calculate the cost to download songs?
1, rational numbers greater than zero
2, whole numbers greater than or equal to one
3, integers less than or equal to zero
4, whole numbers less than or equal to zero
The most appropriate domain to calculate the cost of downloading songs is whole number greater than or equal to one.
What are whole number?Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.
It is most appropriate since numbers of songs downloaded cannot be a negative or part quantity.
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The most appropriate domain for calculating the cost to download songs after paying a membership fee is whole numbers greater than or equal to one, as you cannot download fractional or negative numbers of songs.
Explanation:The most appropriate domain for calculating the cost to download songs, given the information that an online company charges a $5 membership fee and then $0.99 for each song, would be option 2, which is whole numbers greater than or equal to one. The domain is referring to the number of songs you can download after the initial membership fee. Since you cannot download a fraction of a song or a negative number of songs, whole numbers make the most sense in this context. The cost for downloading songs would be the membership fee plus the cost per song times the number of songs downloaded, which is a linear relationship.
Please help! Need to confirm my answers.
Match the exponential functions f(x) and g(x) with their key features.
Answer:
Step-by-step explanation:
Average rate of change is Δy / Δx.
For f(x):
[ f(1) - f(0) ] / (1 - 0)
(1 - 3) / (1 - 0)
-2
For g(x):
[ g(1) - g(0) ] / (1 - 0)
(4 - 3) / (1 - 0)
1
Lawrence got a car loan from a bank, with the car as collateral. What kind of loan did he get?
A. a secured loan
B. an unsecured loan
C. a fixed-rate loan
The answer is A. A secured loan, hope this helps!
Answer:A, a secured loan
Step-by-step explanation:
Angles A and B are complementary. Angle A has a measure of (3x +10). Angle B has a measure of (2x +5). What is the value of x?
Answer:
15
Step-by-step explanation:
Complementary angles mean the two angles add up to 90 degrees. So the step by step would look like this;
3x + 10 + 2x + 5 = 90
5x + 15 = 90
5x = 90 - 15
5x = 75
x = 75/5
x = 15 :)
If the angles A and B are complementary then the value of x is 15.
Complementary angles are two angles whose sum is 90 degrees. In this case, angle A and angle B are complementary, so we can set up an equation based on their measures:
(3x + 10) + (2x + 5) = 90
Now, combine like terms:
3x + 2x + 10 + 5 = 90
Combine the x terms and constants:
5x + 15 = 90
Next, isolate the x term:
5x = 90 - 15
5x = 75
Finally, solve for x by dividing both sides by 5:
x = 75 / 5
x = 15
Therefore, the value of x is 15.
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Which of the following is a polynomial function in factored form with zeros at 0, -3, and 4
Answer:
Option A is correct.
Step-by-step explanation:
The polynomial with factors with zeros at 0,-3 and 4 means
x=0 and x =-3 and x=4
this can be written as:
x=0, x+3 =0 and x-4=0
or
x(x+3)(x-4) =0
or
f(x) = x(x+3)(x-4)
So, Option A is correct.
Determine which statements are true regarding the given solid. Check all that apply.
The three-dimensional solid is a hexagonal pyramid.
The three-dimensional solid is a hexagonal prism.
The solid can be created by stacking the same-size hexagons vertically.
The solid can be created by stacking dilated hexagons vertically.
Point D is the apex of the pyramid.
option A, D, and E
I just took it on edge
The true statement regarding the shape are:
The three-dimensional solid is a hexagonal pyramid.The solid can be created by stacking dilated hexagons vertically.Point D is the apex of the pyramid.Base: The bottom surface of a pyramid is a polygonal shape, such as a square, rectangle, triangle, or any other polygon. The base is typically larger in area compared to the other faces.
Faces: Pyramids have triangular faces that slope inward from the edges of the base to a single point at the apex. The number of faces depends on the number of sides of the base polygon.
Vertices: A pyramid has several vertices where the edges of the base meet the triangular faces, and one vertex where all the triangular faces converge at the apex.
Edges: The edges of a pyramid are the lines where the faces intersect. For example, a square pyramid has 8 edges (4 from the base and 4 connecting the base to the apex).
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?
y = x – 12
y = x – 4
y = x + 2
y = x + 6
Answer:
y = x - 4
Step-by-step explanation:
y - 4 = x - 8
y = x - 4
Answer:
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8).
To find slope intercept form of a equation of a line we solve for y
[tex]y - 4 = (x - 8)[/tex]
We remove the parenthesis
[tex]y -4 =x - 8[/tex]
To get y alone, we need to add 4 on both sides
[tex]y -4+4=x - 8+4[/tex]
[tex]y=x -4[/tex]
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
which expression is equivalent to 6e+3(e-1)
6e + 3(e - 1)
6e + 3e - 3
9e - 3
Answer: Equivalent expression would be 9e-3.
Step-by-step explanation:
Since we have given that
[tex]6e+3(e-1)[/tex]
As we need to simplify the above expression:
First we open the brackets :
[tex]3(e-1)=3e-3[/tex]
Now, add it to 6e.
So, it becomes,
[tex]6e+3e-3\\\\=9e-3[/tex]
Hence, equivalent expression would be 9e-3.
marcia makes a cut through a block of frozen spinach, as shown. what are the dimensions of the exposed cross section?
The answer is D. 6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
Hope this helps!
6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
What is cross-section?A cross section is the non-empty intersection of a solid body in three dimensions with a plane in geometry and science, or its equivalent in higher dimensions. Multiple parallel cross-sections are produced when an item is cut into slices.
Given,
6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
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-7 2/3 + ( -5 1/2 ) + 8 3/4 = ?
A: -4 5/12
B: -21 11/12
C: -4 2/3
D: 6 7/12
Answer:
-4 5\12
Step-by-step explanation:
Identify the Least Common Denominator, 12, then just simply evaluate.
Which equation can be used to solve forB?
Answer:tan 30 = 5/b
Step-by-step explanation:
From the diagram line BC is opposite to the angle 30 and line AC is adjacent to that same angle
From trigonometric ratios
Tan 30 = opposite /adjacent
Answer:
The correct answer is first option
Step-by-step explanation:
Points to remember
Trigonometric ratio
Tan θ = Opposite side/Adjacent side
From the figure we can see that a right angled triangle ABC
BC = 5 cm, <A = 30° and <C = 90°
To find the correct equation
We have,
Tan θ = Opposite side/Adjacent side
Tan 30 =BC/AC
Tan 30 = 5/b
The correct answer is first option.
Find the slop of the line shown.
Answer:
1/3
Step-by-step explanation:
Look up on google "how to find slope" and your answer will be right at the top
The answer is x=3 since its a vertical line. hope this helps.please add brainliest
How to round 2.06 to the amount to the nearest dollar
it would be 2.00 it’s closer to 2.00 than 3.00