The volume of the building in the shape of a square pyramid is 252720 m³
In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangle faces that meet above its base (the apex).
The building is in the shape of a square pyramid.
The base of the building is 54 meters long.
The height of the building is 260 meters.
The volume of the right square pyramid is given as:
V = ( 1/3)a²h
Where a is the base and h is the height.
Now we have,
a = 54 meters and h = 260 meters
Then the volume of the building is:
V = ( 1/3)a²h
V = ( 1/3 ) × ( 54 )² × 260
V = ( 1/3 ) × 54 × 54 × 260
V = 758160/3
V = 252720 m³
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Ebony is cutting dough for pastries in her bakery. she needs all the pieces to be congruent triangles and has ensured that segment ef ≅ segment on and ∠mon ≅ ∠gef. what would ebony need to compare in order to make sure the triangles are congruent by sas? segment om and segment ef segment eg and segment om segment nm and segment fg segment eg and segment mn
The parts of the triangles Ebony needs to compare so as to make sure both triangles are congruent by SAS are;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]What are congruent triangles?Two triangles are said to be congruent when the three sides and three interior angles of one triangle have the same measure as the three sides and the three interior angles of the other triangle.
The given triangles are ∆MON and ∆GEF
The segments and angles that Ebony has ensured are congruent are;
[tex] \overline{EF} \cong \overline{ON}[/tex]
[tex] \angle{ MON} \cong \angle{ GEF}[/tex]
The method by which Ebony intends to use to make sure that the two triangles are congruent, SAS, Side–Angle–Side congruency postulate.
The Side–Angle–Side congruency postulate states that two triangles are congruent if two sides and an included angle in one triangle are congruent to the corresponding two sides and included angle in the other triangle.
Given that the sides that form included angles with [tex] \angle{ MON} [/tex] are [tex] \overline{ON}[/tex] and [tex] \overline{OM}[/tex] and the sides that form an included angle with [tex] \angle{ GEF}[/tex] are [tex] \overline{EF} [/tex] and [tex] \overline{EG} [/tex], the other segments Ebony needs to compare are therefore the segments;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]
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what is the volume of the following triangular prism? 288 ft^3480 ft^396 ft^3576 ft^3
The volume of the triangular prism = base area x height
Since its base is a right triangle, then
[tex]B\mathrm{}A=\frac{1}{2}\times leg_1\times leg_2[/tex]From the figure leg1 = 6 ft and leg2 = 8 ft
[tex]\begin{gathered} BA=\frac{1}{2}\times6\times8 \\ BA=24ft^2 \end{gathered}[/tex]Now multiply it by the height of the prism
Since its height = 12 ft, then
[tex]\begin{gathered} V=24\times12 \\ V=288ft^3 \end{gathered}[/tex]The answer is A
Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)x^, when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
X 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Using exponential functions, it is found that:
a) Lisa's account has $763 after 5 years.
b) Xavier's account has $897 after 5 years.
c) The difference is of $134.
What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^x[/tex]
In which the parameters are described as follows:
a is the initial value of the function, that is, the value of the function when x = 0.b is the rate of change of the function.Lisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200, b = 270/200 = 1.35.
Hence his function is:
[tex]g(x) = 200(1.35)^x[/tex]
In 5 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa: [tex]f(5) = 250(1.25)^5 = 763[/tex]Xavier: [tex]g(5) = 200(1.35)^5 = 897[/tex]The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
897 - 763 = $134.
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At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional?
The quantities Choose... proportional.
The dollar cost y and the amount of yogurt are proportionate
The formula is y = 0.08x
If y fluctuates as directly as x, you may express it as y = kx.
Where k is the proportionality constant.
Determine the value of the proportionality constant. When y = 2.56 and x = 32, you get:
y = kx
k = y/x
k = 2.56/32
k = 0.08
The equation is then: y = 0.08
Check to see if they are directly proportionate. Substitute the amount of yogurt purchased by Jonah. The outcome must be $0,48:
y = 0.08 (6) (6)
y = 0.48
The cost and amount of yogurt are proportionate in a straightforward manner.
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Use the given graph to complete the table. Then write an equation representing the relationship.
The equation of the relation is y = 3/2x.
x | y
0 0
2 3
4 6
How to Write the Equation that Represents a Proportional Relationship?To write the equation for the proportional relationship between two variables, x and y, find the unit rate, k, which is k = y/x.
Substitute the value of k into y = kx to write the equation of the relationship.
Using a point on the line, (2, 3):
k = y/x = 3/2
Substitute k = 3/2 into y = kx:
y = 3/2x
Using the equation, substitute each of the values of x in the table to get the corresponding value of y:
For 0:
y = 3/2(0)
y = o
For 2:
y = 3/2(2)
y = 3
For 4:
y = 3/2(4)
y = 6
The table is:
x | y
0 0
2 3
4 6
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Kareem went for a drive in his new car. He drove at a speed of 63 miles per hour for 157.5 miles. For how many hours did he drive?
Answer: He drove for 2 hours and 30 minutes. Hope you do great! :)
Answer:2.5 hours
Step-by-step explanation:
A piece of pipe that is 8 feet long is cut into 1/4 ft pieces. How many pieces can be cut from the pipe?
Responses
A 30 pieces
B 28 pieces
C 8 pieces
D 32 pieces
Answer:it is 32 peices d
Step-by-step explanation:
what is problem 2/7i
2/7√-1........ ....................... . .
Write the equation in standard form, x(x+3)=0
Answer:
x²+3x=0
Step-by-step explanation:
Just distribute and simplify.
find X. (this is multiple choice the options are 3, 49, or 27
QUICKLYYY
Which situation below has the lowest constant of proportionality?
A) 40 ounces of fabric softener cost $20.00.
B) 20 ounces of powder laundry detergent costs $4.00.
C) 30 ounces of laundry scent boosters cost $12.12.
D) 90 ounces of liquid laundry detergent cost $36.00.
Answer: D
Step-by-step explanation:
Because I can math
Express the ratio below in its simplest form.
6
:
2
:
6
Answer:
3 : 1 : 3
Step-by-step explanation:
6 : 2 : 6 ← divide each part ot the ratio by 2
3 : 1 : 3 ← in simplest form
Convert 838% to an improper fraction written in its simplest form
To convert percent to a number divide it by 100
Then to convert 838% to a number divide it by 100
[tex]838\text{ \%=}\frac{838}{100}[/tex]To simplify divide up and down by 2
[tex]\begin{gathered} \frac{838}{100}=\frac{\frac{838}{2}}{\frac{100}{2}} \\ \frac{838}{100}=\frac{419}{50} \end{gathered}[/tex]The improper fraction is 419/50 in the simplest form
A student is working on finishing a scale
model of the Eiffel Tower. The actual
tower is 1,083 feet tall and 410 feet wide
at the base. If the model currently has a
base that is 0.75 feet wide, which would
be the scale factor of the model to the
tower?
1:410
3: 1640
1:0.75
The scale factor of model to the tower is 3:1640.
What is scale factor?The scale factor states the scale by which a figure is bigger or smaller than the original figure.
In other words, scale factor is a ratio between two corresponding sides of similar figures.
Therefore, the actual tower is 1,083 feet tall and 410 feet wide at the base.
The scale model currently has a base that is 0.75 feet wide.
Therefore, the scale factor of the model can be calculated as follows;
The scale factor can be written as a ratio or fraction.
The scale factor of the base to the model is the same with the height of the tower to the model.
0.75 : 410
multiply both side by 100
75 : 41000
divide both sides by 25
Therefore,
3 : 1640
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Please help me. I’ve tried but I kept getting it wrong for some reason
Answer:
43
Step-by-step explanation:
Trust me, this is the right answer.
Answer:
Rate of change =$43
Step-by-step explanation:
Rate of change is also known as the gradient or slope
Gradient= y2 - y1 / x2 - x1
The Xcoordinate is usually written first.
Y2 = 384
Y1= 169
X2=8
X1= 3
Rate of change= 384- 169 /8-3
= 215/5
= $ 43
francesco obtains a loan of $18,965.00. the loan has a simple interest rate of 3%. how much interest will francesco owe at the end o the first year
The interest owned by Francesco at the end of one year would be $19023.69.
What is the formula to calculate the simple interest on a given principle amount?
The simple interest on a given principle amount [P] at rate [r%] for [t] years is given by -
I = (P x r x t)/100
Given is Francesco who obtains a loan of $18,965.00 at an interest rate of 3% for 1 year.
From the data given, we can write -
Principle amount = [P] = $18,965.00
Rate = [R] = 3%
Time = [T] = 1 year
Now, using the formula for calculating the simple interest, we get -
I = PRT/100
Substituting the values -
I = (18965 x 0.3 x 1)/100
I = (18965 x 0.3)/100
I = 189.65 x 0.3
I = 58.69
Amount = P + 58.69 = 18965 + 58.69 = 19023.69
Therefore, the interest owned by Francesco at the end of one year would be $19023.69
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I need help with this question
Answer:
x = 7
Step-by-step explanation:
For line q and line r to be parallel lines,
the angle with a measure of 108 and the angle represented with measure 15x + 3 must be alternate interior angles which means two angles have equal measures so we can write the following equation:
15x + 3 = 108 subtract 3 from both sides
15x = 105 divide both sides by 15
x = 7
F (x) =3x+2 and g (x) = x^2 - x, find the value F(8)
The value of F(8) is 26.
What is function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
F (x) =3x+2
Now, F(8)= 3x+2
=3(8) +2
=24 +2
=26
Hence, the value of F(8) is 26.
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Divide.
(24x³ - 2x² + 3x-9) ÷ (6x - 5)
Your answer should give the quotient and the remainder.
Answer: 4x^2 + 3x + 3
Step-by-step explanation:
Solve for x.
5(2x - 1) = 6
a. x = 1/10
b. x = 11/10
c. x = 1/2
Answer:
b
Step-by-step explanation:
5(2x - 1) = 6 ← distribute parenthesis on left side
10x - 5 = 6 ( add 5 to both sides )
10x = 11 ( divide both sides by 10 )
x = [tex]\frac{11}{10}[/tex]
point slope that is parallel and passes through (-1,-1)
The equation of line parallel to the given line is y = x + 2
Given,
The points that the line passes, (x, y) = (-1, -1)
Slope of the line, m = 1
We have to find the equation of line that is parallel to the given line.
Slope of parallel lines will be same.
So, equation be like:
y = mx + b
y = 1x + b
Here, we can use points and find y intercept:
That is,
-1 = 1 × -1 + b
-1 = -1 + b
b = 1 + 1
b = 2
So, the equation of line be like, y = 1x + 2
That is,
The equation of line parallel to the given line is y = x + 2
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Kayla's mom left a 20% tip for a restaurant bill that was $35. She used the expression 1.20 (35) to find the total cost. Which equivalent expression could she also use to find the total cost?
O 35 +0.2
O (1+0.2)35
O 1+0.2(35)
O 1.02(35)
The equivalent expression which could be used to find the total cost is; ( 1 + 0.2 ) 35.
What is the equivalent expression to the given expression 1.20 (35)?It follows from the task content that the expression which is equivalent to 1.20(35) as given in the task content is to be determined.
Since the given expression whose equivalent is to be determined is; 1.20 (35).
Since a 20% tip indicates a 0.2 fraction of the whole, the resulting equation is therefore;
( 1 + 0.2 ) 35.
And ultimately, the required equivalent expression is; (1 + 0.2) 35.
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5k-3(2k-2/3)-9=0 what is equal to k
[tex]5k - 6k + 2 - 9 = 0 \\ - k - 7 = 0 \\ - k = 7 \\ \frac{ - k}{ - 1} = \frac{7}{ - 1} \\ k = - 7[/tex]
ATTACHED IS THE SOLUTION
Choose ALL answers that describe the quadrilateral PQRS if PQ = RS, QR =SP, and diagonals have equal length: PR = QS.
○ parallelogram
○ rectangle
○rhombus
○square
○ trapezoid
answer:It's a rectangle
There are two cars, green car (gc) and a blue car (bc). gc is $15 plus $0.50 per mile driven, bc is $25 plus $0.15 per mile. how many miles do both cars have to drive to cost the same amount?
The number of miles that both the green car and the blue car have to drive to cost the same amount is equal to 28.5 miles.
The number of miles both cars have to travel to cost the same amount can be determined using an algebraic expression. An algebraic expression can be defined as a mathematical equation consisting of both letters and numbers.
As the green car (gc) cost $15 plus $0.50 per mile and the blue car (bc) costs $25 plus $0.15 per mile, an algebraic expression for this problem can be given as follows;
15 + 0.50(x) = 25 + 0.15(x)
Solving for x;
0.50x - 0.15x = 25 - 15
0.35x = 10
x = 10 / 0.35
x = 28.5
Hence, both cars have to drive 28.5 miles to cost the same amount.
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find the larger of 2 consecutive intergers if 4 times the smaller is 53 more than 3 times the larger
The larger of the two consecutive numbers is 57
What is a consecutive number?
Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a difference of 1 between them. If n is a number, then examples of consecutive numbers would be n, n+1, and n+2. and 1, 2, 3, 4, 5, and so on.
From the question,
Let's say the smaller integer is x
Then the larger integer will be (x + 1)
According to the question,
4 times the smaller = 4x
3 times the larger = 3(x + 1)
⇒ 4x = 3(x + 1) + 53
⇒ 4x - 3x = 56
⇒ x = 56
(x + 1) = 57
Therefore, the larger of the two consecutive numbers is 57
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The daily changes in the barometric pressure for four days are −0.05, 0.09, −0.04, and −0.08 inches. The mean change after five days is −0.01 inch. What is the change on the fifth day? Write your answer as a decimal.
The change on the fifth day is 0.03.
What is a mean?A mean simply means the average of.a set of numbers.
Based on the information given, let the change in the fifth day be x. This will be illustrated as:.
= (-0.05 + 0.09 - 0.04 - 0.08 + x)/ 5 = -0.01
Crops multiply
-0.08 + x = -0.05
Collect like terms
x = -0.05 + 0.08
x = 0.03
The change is 0.03.
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you've done a ton of original research for a statistics project, but you just can't prove your hypothesis that the majority of college students adore katy perry. rather than admit that only .9% of students can tolerate kp, you move the decimal point and declare that 90% of students are katycats. this is an example of:
This is an example of remix plagiarism.
Remix plagiarism includes collecting information from different sources, combing together into one work by using the method of paraphrasing, and claiming it as your work.
The person basically changes the language of the statements and fit the topic under his or her name. Here the hypothesis that majority of college students adore katy perry, rather use the statement "90% of students are katycats".
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Each statement is either a phrase or a clause.
Drag each statement into the correct column of the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Phrase Clause
Answer:
phrase- around the corner- very slowly- Peter and michael
clause- put in the closet- when i go to school
Step-by-step explanation:
A clause is a collection of words with a subject and a verb. The words that make up a phrase do not include a subject or a verb.
Hope this helps! \( ﾟヮﾟ)/
Step-by-step explanation:
phrase- around the corner- very slowly- Peter and michael
clause- put in the closet- when i go to school
Step-by-step explanation:
A clause is a collection of words with a subject and a verb. The words that make up a phrase do not include a subject or a verb.
Solve for a, b, and c.
a =
b=
C=
C
40⁰