#1
Volume
πr²hπ(5)²(4)100π3.14(100)314cm³#2
Radius=10/2=5cm
Volume
4/3πr³4/3π(5)³125(4/3π)500π/3523.3cm³#3
Volume
π(4/2)²(7)2²(7π)28π87.92in³#4
V=1/3a²hV=1/3(81)h27h=297h=11cm#5
radius=8/2=4
Volume
π(4)²(10)160π502.4cm³502.4mLAnswer:
1) 314 cm³
2) 523.33 cm³
3) 87.92 in³
4) 11 cm
5) 502.4 cm³
Step-by-step explanation:
Part 1[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 5 cmh = 4 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]
Part 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]
Given:
d = 10 cm ⇒ r = 5 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]
Part 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 4 in ⇒ r = 2 inh = 7 inπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]
Part 4[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]
Given:
Volume = 297 cm³Area of base = 81 cm²[tex]\implies 81=a^2[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9\: \sf cm[/tex]
Substitute the given values into the formula and solve for h:
[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]
Part 5[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 8 cm ⇒ r = 4 cmh = 10 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]
the function f and g are defined follows. f(x)= x+6/x^2-12x+36 g(x) = x+7/x^2-49 for each function, find the domain. write each answer as an interval or union of intervals
Domain of f(x) is {x | x ≠ 6} and Domain of g(x) is {x | x ≠ +7 and x ≠ +7}.
How to find the domain of a function?The domain of a function is the set of all input values that make the function possible.
Now, for f(x) = (x + 6)/(x² - 12x + 36)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 12x + 36 = 0
Solving this using quadratic formula gives; x = 6. Thus, domain of f(x) is;
Domain = {x | x ≠ 6}
Now, for g(x) = (x + 7)/(x² - 49)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 49 = 0
Solving this using quadratic formula gives; x = +7 or -7. Thus, domain of g(x) is; Domain = {x | x ≠ +7 and x ≠ +7}
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A rectangular parking lot has a length that is 5 yards greater than the width the area of the parking lot is 300 yd.² find the length and width
Answer:
width=5yd and length=10yd
Step-by-step explanation:
To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)
We know that Area (A) = Length (L) * Width (W)
You know Area (A) = 50 sq. yds.
You don't know anything about the width, so let's just say Width (W) = x
And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd
Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.
Well, now just plug in. What does W equal and L equal?
From above we plug in and can say that 50 sq yd = x * (x + 5 yd).
Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).
Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:
0 = x^2 + 5x - 50
Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.
I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that
0 = x^2 + 5x - 50 = (x + 10)(x - 5)
And so you know that x = -10 or 5.
Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.
mark me brainlistUse the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (8 points) Part B: Find (a - b) (x). Show your work. (8 points) Part C: Find (a - b)(x). Show your work. (9 points) Part D: Find a(b(x)]. Show your work. (10 points)
a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]
b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]
The lines below are parallel. If the slope of the green line is -3, what is the slope of the red line?
Answer:
The lines would be equal, meaning the slope of the red line is also -3.
Step-by-step explanation:
SIMPLE:
Parallel lines have the same slope.
An arithmetic sequence is defined as follows:
a₁ = 92
a₁ = a₁-1-8
Find the sum of the first 28 terms in the sequence.
Answer:
-448
Step-by-step explanation:
The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.
Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d
__
series sumUsing the above formula with a1=92, d=-8, and n=28, the sum is ...
S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448
The sum of the first 28 terms of the sequence is -448.
What is the perimeter of this composite figure?
4 cm
6 cm
Find a coterminal angle between 0° and 360°.
780
for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.
solve the following absolute value equation.
−8 − 2 |5X – 17| = −14
If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to
-8 - 2 (5x - 17) = -14
-8 - 10x + 34 = -14
-10x = -40
x = 4
If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have
-8 - 2 (-5x + 17) = -14
-8 + 10x - 34 = -14
10x = 28
x = 2.8
What number would you add to both sides of x² + 7x = 4 to complete the square?
Answers:
A. 2²
B. 7²
C. 7²/2
D. [⁷/2]²
The number would you add to both sides of x² + 7x = 4 to complete the square option C 7²/2.
What is completing the squares method for solving the quadratic method?Suppose the considered quadratic equation is of the form
ax^2 + bx + c = 0
Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic.
The given quadratic equation is
x² + 7x = 4
add 7²/2 to both sides of x² + 7x = 4 to complete the square
7²/2 = 49/4
x² + 7x + 49/4 = 4+ 49/4
(x + 7/2)² = 4+ 49/4
Thus, option C 7²/2 is correct.
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A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
Answer:
20 I guess
Step-by-step explanation:
because maybe 1 is 9
The diagram shows a right angled triangle. 7cm and 11cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
The size of the unknown angle "x".
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question we'll have to use cos because hypotenuse and adjacent is given.
[tex]\large\boxed{cos(A)=\frac{adj}{hyp}}[/tex]
Substitute according to the formula.
[tex]cos \: x= \frac{7}{11}[/tex]
We'll have to use cos inverse.
[tex]x={cos}^{-1}(\frac{7}{11})[/tex]
[tex]x=50.47880364[/tex]
[tex]\large\boxed{x=50.5°}[/tex]
Therefore, the size of the unknown angle "x" is 50.5°
The required measure of the angle x is given as 50°.
Given that,
The diagram shows a right-angled triangle. 7cm and 11cm and x degrees.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Apply cosine equation,
cosx = 7 / 11
cosx = cos50
x = 50°
Thus, the required measure of the angle x is given as 50°.
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Write a rule to describe the transformation.
Step-by-step explanation:
The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left
Find the value of x in the diagram below. x =
Answer:
x=101
Step-by-step explanation:
Fun angles......................
Answer:
x = 79°
Step-by-step explanation:
The arrows on the line segments indicate that the lines are parallel.
As the parallel line segments are the same length, the other pair of opposite line segments are also parallel and the same length. Therefore, we can apply the Alternate Interior Angles Theorem.
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, the missing angle in the triangle including angle x is 28°.
Interior angles of a triangle sum to 180°
⇒ 73° + 28° + x = 180°
⇒ x = 180° - 73° - 28°
⇒ x = 79°
please help i need it
Answer:
[tex]4\frac{7}{8}[/tex]
Step-by-step explanation:
The three heaviest eggs are between [tex]1\frac{1}{2}[/tex] and [tex]1 \frac{3}{4}[/tex]
[tex]1\frac{1}{2} +1 \frac{3}{4}/2[/tex][tex]1+1+\frac{2}{4}+\frac{3}{4}/2[/tex][tex]2\frac{5}{4}/2[/tex][tex]1\frac{5}{8}[/tex][tex]1\frac{5}{8}*3=\frac{13}{8}*3=\frac{39}{8} = 4\frac{7}{8}[/tex]Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a triangle? Question 6 options: A) A cut parallel to the vertical axis, directly through the vertical axis B) A cut parallel to the vertical axis, but off the vertical axis C) A cross section cut parallel with the bottom D) Cutting off one of the bottom corners
The plane that would produce a triangle is A, a cut parallel to the vertical axis, directly through the vertical axis.
What is a squared pyramid?
A square pyramid is a geometric shape having four triangles, five faces and a square.
Properties of a squared pyramidIt has a five bases It has four or greater equilateral triangular faces meeting above the baseAll the edges, sides and angles are equalSince the sides are equal, cutting parallel to the vertical axis forms a triangle.
Therefore, a cut parallel to the vertical axis, directly through the vertical axis would produce a triangle.
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Find the area of this triangle.
Answer:
120 ft²
Step-by-step explanation:
The formula to find the area of a triangle is :
Area = [tex]\frac{1}{2}[/tex] × base × height
Given that,
base ⇒ 30 ft
height ⇒ 8 ft
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × base × height
Area = [tex]\frac{1}{2}[/tex] × 30 ft × 8 ft
Area = [tex]\frac{1}{2}[/tex] × 240 ft²
Area = 120 ft²
In this question we are provided with the base and height of a triangle. We are asked to calculate the area of the triangle.
Base = 30 feet
Height = 8 feet
We know,
[tex] \large \star \: \small\boxed{ \rm{ Area_{(triangle)} = \dfrac{1}{2} × b × h}}[/tex]
Where,
b stand for baseh stand for heightSubstituting the values we get
[tex] \small\sf{ Area_{(triangle)} = \dfrac{1}{ \cancel{2}} × 30 × \cancel{8} \: \: 4}[/tex]
[tex] \longmapsto \small\rm Area_{(triangle)} = 30 × 4[/tex]
[tex] \small \underline{ \boxed{\sf {Area_{(triangle)} =120 \: {feet}^{2} }}}[/tex]
Hence,the area of the triangle is 120 feet².
[tex]\underline{\rule{71mm}{3pt}}[/tex]
4. PLEASE HELP!!!!!!
You have a cup with 17 coins inside. The total inside the cup is $5.50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work.
The number of half dollars coins are 5 and the number of the quarters dollars coins are 12.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
You have a cup with 17 coins inside.
The total inside the cup is $5.50.
Let x be the number of half dollars and y be the number of the quarters dollars.
Then the equations will be
x + y = 17 ............1
0.5x + 0.25y = 5.5 ...........2
By solving equations 1 and 2, we have
x = 5 and y = 12
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11.85 is 75% of what number
Answer:
20.14
Step-by-step explanation:
so to find it i added 75% to 11.85 so 11.85 + 75% = 20.14
Hope This Helped
Answer:
15.8
Step-by-step explanation:
11.85/75 = x/100
x = 15.8
11.85 is 75% of 15.8
Brainliest please!
hope this helps :)
james got 19 questions right on a math test. These questions made up 76% of the test.How many questions were there on the test?
Answer:
25 Questions.
Explanation:
Original or full is always 100%
Mentioned:
76% ⇒ 19
=========
1% ⇒ (19 ÷ 76) = 0.25
Solve for Total:
100% ⇒ 0.25 × 100 = 25
Help please ………………….
Answer:
Step-by-step explanation:
make c the subject v=c/4-5
Answer:
c = -v
Step-by-step explanation:
v = [tex]\frac{c}{4-5}[/tex]
v = [tex]\frac{c}{-1}[/tex]
v = -c (anything divided by -1 is the negative itself)
c= -v
Hope this helped and brainliest please
Which expression is equivalent to the given expression
Answer:
i think the answer is A. 2x^3y^2
Consider a triangle ABC like the one below. Suppose that a = 31, b = 23, and c = 20. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1
How to solve the triangle?The figure is not given;
However, the question can still be solved without it
The given parameters are:
a = 31, b = 23, and c = 20
Calculate angle A using the following law of cosine
a² = b² + c² - 2bc * cos(A)
So, we have:
31² = 23² + 20² - 2 * 23 * 20 * cos(A)
Evaluate
961 = 929 - 920 * cos(A)
Subtract 929 from both sides
32 =- 920 * cos(A)
Divide both sides by -920
cos(A) = -0.0348
Take the arc cos of both sides
A = 92.0
Calculate angle B using the following law of sine
a/sin(A) = b/sin(B)
So, we have:
31/sin(92) = 23/sin(B)
This gives
31.0189 = 23/sin(B)
Rewrite as:
sin(B) =23/31.0189
Evaluate
sin(B) =0.7415
Take arc sin of both sides
B = 47.9
Calculate angle C using:
C = 180 - 92.0 - 47.9
Evaluate
C = 40.1
Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
x>3
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
How many 5-digit numbers are there, that are "even"? Show all work/ calculations.
Answer: The correct answer is 13776.
Explanation: There are 3024 five-digit numbers that begin with the digit 4 with no repetition.
A circle has a radius of 3 units and is centered at (-2,-2)) Write the equation of this circle
Answer:
The area is: 28.26 units^2
The diameter is: 18.84 units
Step-by-step explanation:
Area A=pie(3.14)R^2
Diameter D=pie(3.14)R2
Question 3
Points 2
Answered On: 06/15/2022 09:40 AM
A boa constrictor slithers 1/3 feet in 3/4 second. What is its speed in terms of
feet per second?
Reset
Reset
comp
Answer:
18 inches = 1.5 feet
8 inches = 2/3 foot
y = 1.5 + (2/3)x
PLEASE PLEASE HELP
An archer makes two attempts to hit a target, and the probability that he hits the target on any one attempt is 1/7.
What is the probability that the archer will miss the target on both attempts?
A. 1/49
B. 48/49
C. 6/7
D. 36/49
Answer:
The answer would be D.
Step-by-step explanation:
If there is a 1/7 chance that the archer will hit it, there is a 6/7 chance he/she wont. 6/7 times 6/7 is equal to 36/49, getting you your answer of D. I hope this helps! :)
Evaluate 2Tu when T =5 and u=9
Answer:
2Tu = 90
Step-by-step explanation:
You can substitute the values T = 5 and u = 9 into the expression to get: 2 × 5 × 9 which is 90 (2 × 45 = 90)
Hope this helps!
The final result is 90 when T = 5 and u = 9.
Here, we have to evaluate 2Tu when T = 5 and u = 9, we substitute the values of T and u into the expression and perform the operations accordingly.
Given expression: 2Tu
T = 5
u = 9
Now, let's substitute the values:
2 * 5 * 9
Next, perform the multiplication:
2 * 5 = 10
10 * 9 = 90
So, when T = 5 and u = 9, the value of 2Tu is 90.
We get, to evaluate 2Tu, we first multiply T and u together, and then multiply the result by 2.
In this case, we have T = 5 and u = 9.
So, we perform the following steps:
Multiply T and u: 5 * 9 = 45
Multiply the result by 2: 2 * 45 = 90
Thus, the final result is 90 when T = 5 and u = 9.
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Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she strikes it. How long does Marsha have to
react, before the volleyball hits the ground? Round your answer to two decimal
Answer:
0.98 seconds
Step-by-step explanation:
We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.
__
motion equationThe general form of the equation of height for ballistic motion is ...
[tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]
The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.
For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...
h(t) = -16t² +10.5t +5
__
reaction timeMarsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...
a = -16b = 10.5c = 5The solution is ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]
The positive solution is ...
t ≈ 0.976327 ≈ 0.98
Marsha has about 0.98 seconds to react before the volleyball hits the ground.
_____
Additional comment
After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.