Final answer:
The volume of the triangular pyramid is calculated using the formula V = 1/3 × base area × height. With a base area of 330 square yards and height of 18 yards, the volume is found to be 1,980 cubic yards. Therefore, the correct answer is C.
Explanation:
The volume of a triangular pyramid can be calculated using the formula V = 1/3 × base area × height. Given that the base area is 330 square yards and the height of the pyramid is 18 yards, we can calculate the volume by substituting these values into the formula: V = 1/3 × 330 × 18 = 1980 cubic yards. Therefore, the correct answer is C. 1,980 yd³.
The volume of the triangular pyramid is 1,980 cubic yards, making the correct answer option C.
To find the volume of the triangular pyramid, we first need to determine the area of the base triangle. Since the base has an area of 330 square yards, we can use the formula for the area of a triangle, which is 1/2 * base * height. Let's denote the base of the triangle as b and the height as h. We can rearrange the formula to solve for b:
[tex]\[ 330 = \frac{1}{2} \times b \times h \][/tex]
Given that the height of the pyramid is 18 yards, we can plug this value in and solve for the base:
[tex]\[ 330 = \frac{1}{2} \times b \times 18 \][/tex]
330 = 9b
[tex]\[ b = \frac{330}{9} \][/tex]
b = 36.67
Now, we have the base length of the triangle. Next, we can calculate the volume of the pyramid using the formula for the volume of a pyramid, which is [tex]\( \frac{1}{3} \times base\ area \times height \)[/tex]. Let's denote the volume as V:
[tex]\[ V = \frac{1}{3} \times 330 \times 18 \][/tex]
V = 1980
So, the volume of the pyramid is 1980 cubic yards. Therefore, the correct answer is option C: 1,980 yd.
1. if f(x)=1-x^2 and g(x)=1-x which is the rule of function (f-g)(x)
A. 1+x
B. -x^2+x
C. -x^2-x+2
D. x^3-x^2-x+1
2. For the pair of functions, f and g, find (f•g)(x) and (g•f)(x).
f(x) = 3+x, g(x) = x^2 + 1
PLEASE HELP
QUESTION 1
If f(x)=1-x² and g(x)=1-x,
Then,
(f-g)(x)=f(x)-g(x)
This implies that,
[tex]( f - g)(x) = 1 - {x}^{2} - (1 - x)[/tex]
[tex]( f - g)(x) = 1 - {x}^{2} - 1 + x[/tex]
We simplify to get,
[tex]( f - g)(x) = - {x}^{2} + x[/tex]
The correct choice is B.
QUESTION 2
Given:
f(x)=3+x
and
[tex]g(x) = {x}^{2} + 1[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x)=f( {x}^{2} + 1 )[/tex]
[tex](f\circ g)(x)=3 + {x}^{2} + 1[/tex]
[tex](f\circ g)(x)= {x}^{2} +4[/tex]
Also,
[tex](g\circ f)(x)=g(f(x))[/tex]
[tex](g\circ f)(x)=g( 3+ x)[/tex]
[tex](g\circ f)(x)= {(3 + x)}^{2} + 1[/tex]
[tex](g\circ f)(x)= 9 + 6x + {x}^{2} + 1[/tex]
[tex](g\circ f)(x)= {x}^{2} + 6x + 10[/tex]
The length of a chord is equal to its distance to the center of the circle. A second chord in the same circle is twice as long as the first one. How far is the second chord from the center?
Answer:
The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.
Step-by-step explanation:
The length of the chord AB is the same as the distance OC from the center to the cord. Let OC=2x, then CA=x. By the Pythagorean theorem, the radius r of the circle is
[tex]r^2=OC^2+AC^2,\\ \\r^2=(2x)^2+x^2=5x^2,\\ \\r=\sqrt{5}x.[/tex]
The length of the arc ED is 4x.
Consider right triangle EFO. In this triangle, EF=2x, EO=r, then the distance OF is
[tex]OF^2=OE^2-EF^2,\\ \\OF^2=5x^2-(2x)^2=x^2,\\ \\OF=x.[/tex]
The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.
The distance between the second chord from the center of the circle is 'a' (half the length of the first chord).
What is a chord?A circle chord is a straight line segment with both endpoints on a circular arc.
As the length of a chord is equal to its distance to the center of the circle, therefore, the length of the chord and the distance to the center of the circle is 2a. Thus, In ΔAOB the length of the third side of the triangle can be written as,
[tex]OA^2= OB^2+AB^2\\\\OA^2 =(2a)^2+a^2\\\\OA^2=5a^2\\\\OA = a\sqrt5[/tex]
Now, OA and OQ are the radii of the circle and the length of the radius of the circle is a√5 units.
Now, the length of the second chord in the same circle is twice as long as the first one, therefore, the length of the half chord is 2a. Therefore, in ΔAOB the length of the perpendicular side of the triangle can be written as,
[tex]OQ^2=OP^2+PQ^2\\\\(a\sqrt5)^2= OP^2+(2a)^2\\\\5a^2-4a^2=OP^2\\\\OP = a[/tex]
Hence, the distance between the second chord from the center of the circle is 'a' (half the length of the first chord).
Learn more about Chord:
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How can you calculate realative frequencies as percents?
Answer:
1. Count the total number of items. In this chart the total is
2. Divide the count (the frequency) by the total number.
3. Then, convert it to a percent.
Erik is 4.23 feet tall. Stacy is 4.3 feet tall. Who is taller? Explain. Plssss answerrr
Answer:
Stacy
Step-by-step explanation:
4.23 < 4.3
Stacy is 0.07 feet taller than Erik, as of the given conditions.
Given that,
Erik is 4.23 feet tall. Stacy is 4.3 feet tall.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?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,
Heights
Stacy = 4.3 feet
Erik = 4.23 feet
Difference = 4.3 - 4.23 = 0.07 feet
Thus, Stacy is 0.07 feet taller than Erik, as of the given conditions.
Learn more about arithmetic here:
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can someone help me?
The correct answer is B.
Hope this helps.
Answer:
San Fransisco
Step-by-step explanation:
If Geneva is 12°C colder than her hometown, this means that her hometown is 12°C warmer than -3°C.
Since warmer means a higher number, we find 12 + -3, which is 9°C.
The town that is 9°C is San Fransisco.
Carly draws quadrilateral JKLM with vertices J(-3,3), K(3,3), L(2,-1),and M(-2, -1). What is the best way to classify the quadrilateral?
Answer:
Trapezoid
Step-by-step explanation:
The points are shown in the attached graph.
You can clearly see from the picture that it is a "Trapezoid".
Trapezoid is basically a quadrilateral (4 sided-figure) that has 1/2 pair of parallel sides.
On the other hand, a parallelogram has 2 pair of parallel sides.
Thus, a parallelogram is a special type of trapezoid where there are 2 pair of parallel sides. But trapezoid need not be a parallelogram.
The picture shows 1 pair of parallel sides, hence it is a trapezoid.
Which table shows a no change linear relationship?
A)
x y
4 55
7 60
10 65
13 70
B)
x y
10 -16
15 -18
20 -20
25 -22
C)
x y
14 12
20 12
26 12
32 12
D)
x y
4 10
7 14
10 18
13 22
Answer:
C
Step-by-step explanation:
Each of the tables is a linear relationship. Linear relationships increase or decrease steadily by adding or subtracting a constant. Table A increases by 5. Table B decreases by 2. Table C doesn't change. Table D increase by 4.
A "no change" means the y values never change. The constant is 0 and is a horizontal line. Table C is the solution.
Answer:
Option C.
Step-by-step explanation:
Linear relationship : If the relation between variables is represent by a non vertical straight line, then it is called a linear relationship.
Horizontal line is a special case of linear relationship. It is know as no change linear relationship. It means the output value remains same for each input value.
In option C, the given table is
x y
14 12
20 12
26 12
32 12
Only in option C, the y-values are constant. So, it represents no change linear relationship.
Therefore the correct option is C.
Desmond knows that 2 cakes will feed 11 people. If he is inviting 58 people to his parents' anniversary party, how many cakes will he need?
5 cakes
6 cakes
10 cakes
11 cakes
To feed 58 people at the party there should be 10 cakes.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Desmond knows that 2 cakes will feed 11 people. If he is inviting 58 people to his parent's anniversary party.
The number of cakes for 58 people will be calculated as,
11 people = 2 cakes
1 person = 2 / 11
58 people = ( 58 x 2 ) / 11
58 people = 10 cakes
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what is the answer to this problem? simplify 3^5*3^4
Answer:
3^9
Step-by-step explanation:
We we multiply exponents with the same base, we can add the exponents
a^b * a*c = a^(b+c)
3^5 * 3^4
3^(5+4)
3^9
Will give brainlly
ABCD =JKLM
What angle in the first quadrilateral corresponds to J?
A
B
C
D
Answer:
A
Step-by-step explanation:
With this question, its actually way easier than you think. If you want to find corresponding angles, you have to find a way to make the shapes overlap to be exactly the same. If they cannot be exactly the same, there will not be corresponding angles. For this, if you rotate quadrilateral 90 degrees counter-clockwise, you will see that the shapes look the same. Then you can just match up the angles that have the same degree measure (or just look the same for simplicity) and you have your answer. The answer is actually in the question too. ABCD=JKLM, but each letter is actually in the right place. A=J B=K C=L D=M.
Hope this helped! ^-^
let f(x)=2/5x^2 -2. the function g(x) is a vertical stretch of f(x) by a factor of 2 what is the equation of g(x)?
Answer:
g(x) = 4/5 x² - 4
Step-by-step explanation:
∵ f(x) = 2/5 x² - 2
∵ f(x) stretched vertically by scale factor 2
∴ g(x) = 2[f(x)]
∴ g(x) = 2[2/5 x² - 2] = 4/5 x² - 4
The resulting function is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \).[/tex].
Given the function f(x) = [tex]\( \frac{2}{5}x^2 - 2 \)[/tex] and the function g(x) representing a vertical stretch of f(x) by a factor of 2, we need to find the equation of g(x).
A vertical stretch of a function f(x) by a factor of k means multiplying the function by k. Here the factor k is 2.
So, the equation of g(x) will be:
g(x) = 2 * f(x)Substitute f(x) into the equation:
g(x) = 2 * [tex]( \( \frac{2}{5}x^2 - 2 \))[/tex]Distribute the 2:
g(x) = [tex]\( \frac{4}{5} x^2 - 4 \)[/tex]Therefore, the equation for g(x) after a vertical stretch by a factor of 2 is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \)[/tex].
A local grocer cut his marketing budget by 57% last year. He spent only $650 on marketing this year and is happy with his decision. How much did the grocer spend on marketing last year?
I know that the answer is $1511.63, I just need to know the math of how we get that answer.
To find out how much the grocer spent on marketing last year, we need to set up an equation with x as the original budget. By solving the equation, we find that the grocer spent approximately $1511.63 on marketing last year.
Explanation:To find out how much the grocer spent on marketing last year, we first need to determine the original marketing budget. Since the grocer cut their marketing budget by 57%, this means they spent only 43% of their original budget this year. Let's represent the original budget as 'x'.
Set up an equation: 43% of x = $650Convert 43% to decimal form by dividing by 100: 0.43x = $650Solve for x by dividing both sides of the equation by 0.43: x = $650 / 0.43Calculate the value of x using a calculator or long division: x ≈ $1511.63Therefore, the grocer spent approximately $1511.63 on marketing last year.
Which pair of expressions has equivalent values?
Answer:
first one
Step-by-step explanation:
first one
1^13 = 1
1^15 = 1
P.S.
1 to the exponent of any number is equal 1
Answer:
1¹³ and 1¹⁵
Step-by-step explanation:
The answer does not change however we add or reduce the exponents. This is the uniqueness of the integer 1. When the others are tried, 6¹=6 and 9¹=9
7⁸=5764801 and 8⁷=2097152
9²=81 and 4³=64
Therefore the integer 1 is the only number that is not affected by exponents.
The number of bacteria y in a certain area doubles every hour x which function could be used to model this situation
The function could be used to model this situation is D. y = 2ˣ.
The function that could be used to model the situation where the number of bacteria, y, in a certain area doubles every hour, x, is: D. y = 2ˣ
This function represents exponential growth, where the number of bacteria doubles every hour.
The variable x represents the number of hours, and 2^x represents the doubling of the bacteria population over time.
please help me with this
Answer:
s - 8
Step-by-step explanation:
TO find the function rule, substitute (s-2) in place of v. Then simplify.
h(v) = v - 6
h(s - 2) = (s - 2) - 6
h(s - 2) = s - 8
A scale on a blue print drawing of a house shows that 666 centimeters represents 333 meters. What number of centimeters on the blue print represents an actual distance of 272727 meters?''
Answer:
545454
Step-by-step explanation:
This is a ratio. you take 666/333 = x/272727. Basically tis says 666 cm to 333 m is equal to some number of centimeters to 272727 meters. Then just solve for x. 272727(666/333) = 545454.
Another way of looking at it is what did we multiply 333 by to get 666. Answe is 2, so we do the same for 272727. 2*272727 = 545454
If you wanted to you could have also converted units so everything was in either centimeters of meters, but as long as you keep things in the right order this works.
Answer: the number of centimetres is 54cm
Step-by-step explanation:
Given that 6 centimeters represents 3meters.
The number of centimeters on the blue print that will represent an actual distance of 27meters will be Y
6 : Y = 3 : 27
That is
6/Y = 3/27 = 1/9
Cross multiply
Y = 54 cm
All rectangles are parallelorams.Are all parallelograms rectangles? Explain
Answer:
See explanation
Step-by-step explanation:
Definitions of parallelogram and rectangle:
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
A rectangle is a parallelogram with four right angles.
This gives us that each rectangle is a parallelogram.
But an arbitrary parallelogram can have angles that are not necessarily right (for example, 60°, 120°, 60°, 120°). Thus, there are a lot of parallelograms that are not rectangles.
f(x)=3 over x+2-x-3 squared what is f(7)
Answer:
[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]
Step-by-step explanation:
We are given the following function of x and we are to find the value of [tex] f ( 7 ) [/tex]:
[tex] f ( x ) = \frac { 3 } { x + 2 } - \sqrt { x - 3 } [/tex]
Substituting the given value (7) in the above function to get:
[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]
[tex] f ( 7 )= \ frac{3}{7+2}-\sqrt{7-3}[/tex]
[tex] f(7) = \frac { 3 } { 9 } - \sqrt { 4 } [/tex]
[tex]f(7)=\frac{1}{3}-2[/tex]
[tex]f(7)=\frac{1}{3}-\frac{6}{3}[/tex]
[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]
How do you solve this
zoom out a little i cant see it that well
What is the result of 3÷3/5
A.1/9
B.1/5
C.5
D.9
I WILL MARK BRAINLIEST AND GIVE ALL STARS with 30 points!
Answer:
C
Step-by-step explanation:
To divide 3 by 3/5
Leave the 3, change division to multiplication and turn the fraction upside down, that is
3 ÷ [tex]\frac{3}{5}[/tex]
= 3 × [tex]\frac{5}{3}[/tex]
= [tex]\frac{3(5)}{3}[/tex] = [tex]\frac{15}{3}[/tex] = 5 → C
Raeana is twice as old as Madeline, and Laura is 10 years older than Raena. If Laura is 50 years old, how old is Madeline? Define your variables.
Answer: Madeline is 20 yrs old
Step-by-step explanation:
If Laura is 50 and she is 10 years older than Raena then Raena is 40 that would then make Madeline 20 years old.
Final answer:
To determine Madeline's age, we set up an equation based on the given relationship and solved it to find that Madeline is 20 years old.
Explanation:
To solve the question about Raeana, Madeline, and Laura's ages, we first define the variables. Let's denote Madeline's age as M. Since Raeana is twice as old as Madeline, Raeana's age would be 2M.
The problem states that Laura is 10 years older than Raeana, making Laura's age 2M + 10. Given that Laura is 50 years old, we can set up an equation: 2M + 10 = 50.
Now, we solve for M:
Subtract 10 from both sides of the equation to isolate the term with M on one side: 2M = 40.
Divide both sides by 2 to solve for M: M = 20.
Therefore, Madeline is 20 years old.
A motorcycle dealer paid a certain price for a motorcycle and marked it up by 1/5 of the price he paid. Later, he sold it for $14. What is the original price?? PLZZ I will give you 100 pointd
Answer:
$11.67
Step-by-step explanation:
14 (the price he sold it for) = x + 1/5(x) (how much he upped the price)
14 = 6/5x
x = 11.67
To check find 20% of 11.67 which is 2.33 and add them together, which equals $14, so it checks out.
Answer:
$35/5 = $11.666666667 ≈ $11.67Step-by-step explanation:
A motorcycle dealer paid a certain price for a motorcycle
certain price = x
And marked it up by 1/5 of the price he paid.
marked price = 6/5x
Because x + 1/5x = 6/5x
Later, he sold it for $14.
6/5x = 14
1/5x = 14/6
x = 14/6 * 5
14 * 5 = 70
70/6 = 35/3
x = 35/3
x = 35/3 = $11.666666667
Substitute this back in to check it's right.
11.666666667 * 6/5 = 14
simplify (-2x-9)(-4)
Answer: [tex]8x+36[/tex]
Step-by-step explanation:
To simplify the expression you must apply the Distributive property.
Keep on mind that:
- According to the Distributive property, the product of the difference is equal to the difference of the products:
[tex]a(b-c)=ab-ac[/tex]
- Remember the multiplication of signs:
(-)(-)=+
(+)(+)=+
(-)(+)=-
Then, you obtain the following:
[tex](-2x-9)(-4)=8x+36[/tex]
Answer: The correct answer is 8x - 36.
Step-by-step explanation: I am 98% sure.
The description below represents Function A and the table represents Function B: Function A The function is 2 more than 5 times x. Function B x y −1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions?
Answer:
The slope of Function A is greater than the slope of function B while the y-intercept of Function B is greater than the y-intercept of function A.
Step-by-step explanation:
Function A is f(x) = 5x + 2
The slope is 5 and the y-intercept is (0, 2).
Function B. The slope is (5-2) / (0- -1) = 3.
also (8-5) / (1 - 0) = 3
The slope is 3.
The y-intercept is at (0, 5) because one point on the graph is (0, 5).
Answer:
Their slopes are equal but y-intercepts are not equal.
Step-by-step explanation:
Its simple arithmatics
21....................
Answer:
The answer is (b) ⇒[tex]\frac{d^{5} }{2\sqrt{c} }[/tex]
Step-by-step explanation:
∵ [tex]\frac{\sqrt{c^{2}d^{6}}}{\sqrt{4c^{3}d^{-4}}}[/tex]
∵ √x² = x ⇒ that means to cancel the square root divide
the power by 2
∴ [tex]\sqrt{c^{2}d^{6}}=cd^{3}[/tex]
∵ √4 = 2 ⇒ √2×2 = √2² = 2
∵ √c³ = [tex]c^{\frac{3}{2}}[/tex]
∴ [tex]\sqrt{4c^{3}d^{-4}}=2c^{\frac{3}{2}}d^{-2}[/tex]
∴ [tex]\frac{cd^{3}}{2c^{\frac{3}{2}}d^{-2}}[/tex]
∵ In the same base with multiplication we add the power,
in same base with division we subtract the power
∴ [tex]\frac{1}{2}c^{1-\frac{3}{2}}d^{3-(-2)}=\frac{1}{2}c^{\frac{-1}{2}}d^{5}=[/tex]
[tex]\frac{d^{5}}{2c^{\frac{1}{2}}}=\frac{d^{5}}{2\sqrt{c}}[/tex] ⇒ [tex]c^{\frac{1}{2}}=\sqrt{c}[/tex]
∴ The answer is (b) ⇒ [tex]\frac{d^{5}}{2\sqrt{c}}[/tex]
Answer:
b. [tex]\frac{d^{5}}{2\sqrt{c} }[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{\sqrt{c^2d^6} }{\sqrt{4c^3d^{-4}} }[/tex]
We simplify the radicand using the property; [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{\sqrt{d^{6--4}} }{\sqrt{4c^{3-2}} }[/tex]
[tex]\frac{\sqrt{d^{10}} }{\sqrt{4c^{1}} }[/tex]
[tex]\frac{d^{5}}{2\sqrt{c} }[/tex]
Complete the factorization of 3x2 – 10x + 8.
3x2 – 10x + 8 = (x –
)(
x – 4)
Answer:
We shall use the method of splitting the middle term
To factorize
3x² - 10 x + 8
We need two numbers which add to give -10 and multiply to give 3 × 8 = 24
The numbers are -6 & -4
(-6)+(-4) = -10
(-6)(-4) = 24
So we shall split -10x as -6x - 4x
We get
3x² -10x + 8
= 3x² -6x -4x+8
Taking out 3x common from first two terms & -4 from the lest two terms we get
= 3x(x-2)-4(x-2)
Taking out (x-2) common we get
= (x-2)(3x-4)
So
3x² - 10x + 8 = (x-2)(3x-4)
Answer:
2 and 3
Step-by-step explanation:
on EDGE 2021
Plz help me with it
Answer: a. 1
Step-by-step explanation:
[tex]\sqrt{2x+7}+1=\sqrt{2x+14}\\\\(\sqrt{2x+7}+1)^2=(\sqrt{2x+14})^2\\\\2x+7+2\sqrt{2x+7}+1=2x+14\\\\2x+8+2\sqrt{2x+7}=2x+14\\\\2\sqrt{2x+7}=6\\\\\sqrt{2x+7}=3\\\\(\sqrt{2x+7})^2=(3)^2\\\\2x+7=9\\\\2x=2\\\\x=1\\\\\\Check:\\\sqrt{2(1)+7}+1=\sqrt{2(1)+14}\\\\\sqrt9+1=\sqrt16\\\\3+1=4\ \checkmark[/tex]
Given the graph of a circle and a line, how many solutions to the system of equations exist?
-no solutions
-one
-two
-three
Answer:
First Option
Step-by-step explanation:
The number of solutions is given by the values in which the equation of the circumference is equal to the equation of the line.
In other passwords the number of solutions is equal to the number of times the line intersects or touches the circumference.
Notice in the graph that the line does not touch the circumference.
Therefore for this case there are no solution
Answer:
The answer is A (no solution)
Step-by-step explanation:
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed. x + y ≤ 6 x ≤ 4
Answer: The graph is attached.
Step-by-step explanation:
The region is limited by two lines:
[tex]x+y=6[/tex] and [tex]x=4[/tex]
You can write the first inequlity [tex]x+y\leq6[/tex] in the following form:
[tex]y\leq-x+6[/tex]
This region are all the values for which the y-axis is less than the line f(x)=x+6 (all the values under the line).
The other inequality x ≤ 4 are all the values for which the x-axis is less than the line x=4 (all the values to the left of the line).
Observe the graphs attached.
Answer:
its this one
Step-by-step explanation:
What is the volume of a cylinder with a radius of 7 feet and a height of 12 feet? Use 3.14 for pi. Round your answer to the nearest hundredth. (4 points)
1,846.32 cubic feet
1,950.25 cubic feet
1,999.21 cubic feet
2,000.31 cubic feet
Answer:1846.32
Step-by-step explanation:
3.14 times 7 squared times 12 equals 1846.32
The answer should be 1846.32 ft³