The pentagonal prism below has a height of 4 units and a volume of 164 units^3
Find the area of one of its bases.
The calculated area of one of its bases is 41 square units
How to find the area of one of its bases.From the question, we have the following parameters that can be used in our computation:
Volume = 164 cubic units
Height = 4 units
using the above as a guide, we have the following:
Base area = Volume / Height
substitute the known values in the above equation, so, we have the following representation
Base area = 164/ 4
Evaluate
Base area = 41
Hence, the area of one of its bases is 41 square units
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A line passes through (4,5) and (8,9)
Step-by-step explanation:
Hey there!
The equation of a st.line passing through points (4,5) and (8,9) is;
\((y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)\)
Put all values.
\((y - 5) = \frac{9 - 5}{8 - 4} (x - 4)\)
Simplify them to get equation.
\((y - 5) = \frac{4}{4} (x - 4)\)
\((y - 5) = 1(x - 4)\)
\((y - 5) = x - 4\)
\(x - y + 1 = 0\)
Therefore the required equation is: x - y + 1=0.
Hope it helps...
Please help me if possible
Answer:
obtuse triangle
Step-by-step explanation:
Answer:
its right angled triangle ! hich grade r u in ?
Simplify fully125y2/10xy
Answer:
12.5y/x
Step-by-step explanation:
125y²/10xy = 12.5y/x
the average height of a certain age group of children is 53 inches. the standard deviation is 4 inches. if the variable is normally distributed, find the probability that a selected individual's height will be less than 45 inches.
The probability that a selected individual's height will be less than 45 inches is approximately 0.0228.
We can use the normal distribution to find the probability that a selected individual's height will be less than 45 inches. We'll need to first calculate the z-score for a height of 45 inches, and then use a standard normal distribution table or calculator to find the corresponding probability.
The formula for calculating the z-score is:
z = (x - μ) / σ
Where x is the height we're interested in, μ is the population mean (given as 53 inches), and σ is the population standard deviation (given as 4 inches).
Plugging in the values, we get:
z = (45 - 53) / 4 = -2
Now, we can use a standard normal distribution table or calculator to find the probability of a z-score less than -2. Using a table, we find that the probability is approximately 0.0228.
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please help ill mark brainliest
Answer:
D
Step-by-step explanation:
Answer:
D. y=2x-3
Step-by-step explanation:
Just plug the values in!
(x,y)
(7)=2(5)-3
(13)=2(8)-3
Pls I need help with this
Answer:
umm I think I know hold on
The two tables below show the amount of tip, y, included on a bill charging x dollars.
Restaurant A
х
10
20
30
5
Restaurant B
х
25
50
75
y
1
2.
3
✓x
10
15
Which compares the slopes of the lines created by the tables?
O The slope of the line for Restaurant B is 5 times greater than the slope of the line for Restaurant A.
O The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.
The slope of the line for Restaurant B is 5 times greater than sie slope of the line for Restaurant A.
The slope of the line for Restaurant B is 10 times greater than the slope of the line for Restaurant A.
Answer:it’s B I did the test
Step-by-step explanation:
3/2 x -6
hahshdnndndndjd
Solve (x + 3)(x - x = 0. (2 points) x = 3, x = -8 O x = -3, x = 8 x = 3, x = 8 O x = -3, X = -8
answer:
the answer is -3 and 8
Step-by-step explanation:
we will place -3 in the equation
(x+3)(x-x)=0
(-3+3)=0 (because -3+3 will cut down together)
we will place two 8(eights) in the equation
(8-8)=0
final answer is
(0)(0)=0
so -3 and 8 fits well in the equation
When two angles in a plane share a vertex and a side but no common interior points, they are called.................. angles?
When two angles in a plane share a vertex and a side but no common interior points, they are called adjacent angles
What is Adjacent angles?The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.
When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.
Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.
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The contents of a cell in a spreadsheet are shown below. 3.9157E+9 What number do the contents of the cell represent? A. 3,915,700,000 B. 39,157,000,000,000 C. 0.0000000039 D. 0.0000000004
Answer:
the answer is c
Step-by-step explanation:
what is this i need help ASAP
Answer:
The first and fourth statement.
Step-by-step explanation:
1. - 3 - 12/3 + 5
= - 3 - 4 + 5
= - 7 + 5
= - 2
- 2 < 0
4. 4 - 2 - 3/2
= 2 - 3 / 2
= 1 / 2
1 / 2 > 0
Hope this helped! ^^
Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.
14. Write the point-slope form of the function that has a slope of -3 and passes through the
point (11,2).
Answer:
y-2=-3(x-11)
Step-by-step explanation:
point-slope form is y-y1=m(x-x1), where (x1,y1) is the ordered pair of the coordinates given, and m is the slope of the line.
y-2=-3(x-11)
What combination of transformations is shown below?
A) reflection, then translation
B) rotation, then translation
C) reflection, then rotation
D) rotation, then reflection
Answer:
d)rotation then reflection
Step-by-step explanation:
Answer:
D) rotation, then reflection
Find the slope of the line with points (-1,-2) (2,7)
Answer:
3
Step-by-step explanation:
You may use this formula to find the slope of a line going through points \((x_1,y_1) \text{ and } (x_2,y_2)\):
\(\frac{y_2-y_1}{x_2-x_1}\)
Notice the numerator is just a subtraction of the y's while the denominator is a subtraction of the x's. The order you choose your y's on top will matter to how you subtract the x's.
You could just line up the points and remember that the y difference goes on top and the x difference goes on bottom.
This is my favorite way.
(-1 , -2)
minus
(2 , 7)
---------
-3 -9
The slope is -9/-3 or 3.
You could do it the other way:
(2 , 7)
minus
(-1 , -2)
--------------
3 9
The slope is 9/3 or 3.
How do you find the mean of a set?
Mean mode formula - Mean = {Sum of Observation} ÷ {Total numbers of Observations}
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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in triangle ABC, AB = 6 cm, BC = 13cm and angle ACB = 23 degrees. Calculate angle BÁC, which is obtuse.
Answer:
\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)
Step-by-step explanation:
\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)
g etween two variables may be explained away by the presence of another variable that accounts for the original correlation. These relationships are known as
A spurious correlation is a correlation between two variables that appears to be causally linked but is actually due to the influence of a third variable that is not considered. The correct answer is spurious correlation.
Spurious correlations are correlations that exist between two variables, but they are not actually causally related to one another, despite the fact that they appear to be causally related at first glance. The relationship between two variables may be accounted for by a third variable that was previously overlooked or not considered, causing the original correlation to be explained away. Spurious correlations are commonly found in science and research, and they can lead to misleading results if not properly identified and accounted for. It is critical to account for all potential confounding variables in order to establish causal links between variables and avoid spurious correlations. Therefore, researchers must carefully consider all variables that might influence the relationship between two variables to avoid drawing inaccurate conclusions.
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What is the rank of Matrix 3x3?
A 3x3 matrix, the rank can be 0, 1, 2, or 3, depending on the values of the entries in the matrix.
The rank of a matrix is the number of linearly independent rows or columns in the matrix. The rank of a 3x3 matrix can be found by performing row reduction to obtain an echelon form, and then counting the number of non-zero rows.
For example, let's consider the following 3x3 matrix:
a11 a12 a13
a21 a22 a23
a31 a32 a33
Performing row reduction, we can obtain an echelon form:
a11 a12 a13
0 a22' a23'
0 0 a33'
Here, a22' and a33' represent the pivots of the matrix, and the number of non-zero rows in the echelon form is equal to the rank of the matrix.
Therefore, for a 3x3 matrix, the rank can be 0, 1, 2, or 3, depending on the values of the entries in the matrix.
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A scale drawing of a lake has a scale of 1 cm to 40 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing?
Answer:
25cm
Step-by-step explanation:
Jamal groups 8 blocks as 5 blocks and 3 blocks What is another way to group the 8 blocks
Answer:
1 block and 7 blocks
Step-by-step explanation:
You can split 8 blocks into 1 and 7.
Hope this helps :)
If someone said you could be at an wlevation of 0 feet, where would you be?
I NEED ANSWERS PLZ ASAP
Answer:
Sea level.
Step-by-step explanation:
Can someone please help me with this
In the trigonometric function, the value of \(sin\theta = \frac{1}{2}\) and \(cos\theta=\frac{\sqrt3}{2}\).
What is trigοnοmetric functiοn?The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.
Here the given \(\theta = \frac{-\pi}{6}\)
Now put \(\theta = \frac{-\pi}{6}\) into sin\(\theta\) then,
=> sin \((\frac{-\pi}{6})\)
=> \(\frac{1}{2}\)
Now put \(\theta = \frac{-\pi}{6}\) into cos\(\theta\) then,
=> cos \((\frac{-\pi}{6})\)
=> \(\frac{\sqrt3}{2}\)
Hence the value of \(sin\theta = \frac{1}{2}\) and \(cos\theta=\frac{\sqrt3}{2}\).
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n this assignment, you will explore how to find the number of different species of fish in a pond by looking at a random sample of the fish.
Which phrase best describes the total number of brook trout in the pond?
the population of brook trout
the proportion of brook trout
the sample of brook trout
the population of fish
Answer:the population of brook trout
Step-by-step explanation:
186:403 in simpleast form
Answer:
6:13
Step-by-step explanation:
both are divisible by 31
use the laplace transform to solve the given integral equation. f(t) + t (t − τ)f(τ)dτ 0 = t
f(t) = L^(-1){1 / (s^2 + s)} Inverse Laplace transform tables or techniques, determine the time-domain function f(t) that satisfies the given integral equation.
The Laplace transform is a powerful mathematical tool that can be used to solve complex integral equations, like the one you've provided: f(t) + t * ∫(t - τ)f(τ)dτ = t.
To solve this equation using the Laplace transform, follow these steps:
1. Apply the Laplace transform to both sides of the equation. The Laplace transform of f(t) is F(s), and the Laplace transform of t is 1/s^2. The integral equation becomes:
L{f(t)} + L{t * ∫(t - τ)f(τ)dτ} = L{t}
F(s) + L{t * ∫(t - τ)f(τ)dτ} = 1/s^2
2. Next, apply the convolution theorem to the integral term. The convolution theorem states that L{f(t) * g(t)} = F(s) * G(s). In this case, f(t) = t and g(t) = (t - τ)f(τ):
F(s) + L{t} * L{(t - τ)f(τ)} = 1/s^2
3. Now, substitute the known Laplace transforms for t and f(t):
F(s) + (1/s^2) * F(s) = 1/s^2
4. Combine the terms containing F(s):
F(s) * (1 + 1/s^2) = 1/s^2
5. Isolate F(s) by dividing both sides of the equation by (1 + 1/s^2):
F(s) = (1/s^2) / (1 + 1/s^2)
6. Simplify the expression for F(s):
F(s) = 1 / (s^2 + s)
7. Finally, apply the inverse Laplace transform to F(s) to obtain the solution for f(t):
f(t) = L^(-1){1 / (s^2 + s)}
Using inverse Laplace transform tables or techniques, you can determine the time-domain function f(t) that satisfies the given integral equation.
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2. Which point is located on the line represented by the equation y + 4 =-5(x-3)? (1 poir
0(-4,-5)
0(-5,-4)
O(3.-4)
0(-3, 4)
Answer:
0(-3, 4)
Step-by-step explanation:
I got it right
Point (3, - 4) is located on the line represented by the equation
y + 4 =- 5(x - 3).
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Equation is y + 4 = -5(x - 3).
We'll confirm the points by the given options putting the value of x and checking the corresponding y value.
y + 4 = -5(x - 3).
y + 4 = - 5x + 15.
y = - 5x + 11.
By going through the options we conclude that at x = 3, y = - 4.
So, The point is (3, - 4).
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The parabolic path of a performer who is shot out of a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in fleet), has a vertex of (60,50) and a y-intercept of (0,30). Write an equation of the parabola. The performer lands in a net 80 feet from the cannon. What is the height of the net?
\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}\)
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y =f(2x)
b.
y = f(ç)
C.
2y = f (x)
d.
2 = f (x)
Enter
Therefore , the solution of the given problem of equation comes out to be option c is correct 2y = f(x) .
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation
y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.
Therefore, the vertically scale factor is equal to 1/2:
=> y = (1/2)f(x)
This problem can be solved by multiplying it by two and yields the following solution:
=> 2y = f(x)
thus , option c is correct
Therefore , the solution of the given problem of equation comes out to be option c is correct 2y = f(x) .
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