a pyramid with a square base is cut by a plane that is parallel to its base and 22 units from the base. the surface area of the smaller pyramid that is cut from the top is half the surface area of the original pyramid. what is the altitude of the original pyramid?
The altitude of the original pyramid is about 75.11 units
Given that,
Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :
Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.
(Height ratio)^2 = 1/2
((h -22)/h) ^ 2 = 1/2
(h-22) / h = 1/[tex]\sqrt{2}[/tex]
h-22 = h /[tex]\sqrt{2}[/tex]
h = 75.11 units
Consequently, the original pyramid's altitude is around 75.11 units.
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(d)
After one year, the value of Annie's car had reduced by 20%.
At the end of the second year, the value of Annie's car had reduced by a further 15% of its value at the
end of the first year.
07
(i) Calculate the overall percentage reduction after the two years.
20
What is the mathematical name of the shape
Answer:
Triangular prism
Step-by-step explanation:
If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism
In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.
Based on the given information, answer the questions below. Round each answer to the nearest tenth.
Part A: How tall is the pole? Show your work.
Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.
Part C: How long is Wire 1? Show your work.
A. Applying the trigonometric ratio, the length of pole = 29.6 ft.
B. 23.1 ft.
C. Length of wire 1 = 45.1 feet.
How to Apply the Trigonometric Ratios?The trigonometric ratios are:
sin ∅ = opposite length/hypotenuse length cos ∅ = adjacent length/hypotenuse lengthtan ∅ = opposite length/adjacent length.Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole
∅ = 41°
Opp. = length of pole
Adj. = 34 ft
Substitute
tan 41 = length of pole/34
Length of pole = (tan 41)(34) = 29.6 ft.
Part B:
Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.
∅ = 38
Opp. = x
Adj. = 29.6 ft
Therefore:
tan 38 = x/29.6
x = (tan 38)(29.6)
x = 23.1 ft.
Part C: Use the Pythagorean theorem to find the length of wire 1.
Length of wire 1 = √34² + 29.6²)
= 45.1 feet.
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Drew painted his uncle's barn on saturday. it took him 7 hours to paint the whole barn, and his uncle paid him 133 dollars for his work. what was drew's pay rate, in dollars per hour?
The total amount paid in dollars per hour is $19.
Unitary Method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.
We have to find the amount paid per hour.
Total amount given = $133
Number of hour Barn work = 7 hours
Amount paid per hour = 133/ 7
= $ 19
Therefore the amount paid per hour is $19.
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Donald graphs the distance he walks over time the graph passed through the points (3, 12) and (4, 16)
Using a proportional relationship, it is found that:
A. The slope of the line is of 4.
B. The slope is the same over both segments.
What is a proportional relationship?A proportional relationship is modeled as follows:
y = kx.
Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.
In this problem, the relationship has two points presented as follows:
(3, 12) and (4, 16).
Hence the slope, which is the constant of the relation, is given as follows:
k = 12/3 = 16/4 = 4.
Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:
(1,4) and (3,12): m = (12 - 4)/(3 - 1) = 8/2 = 4.(3, 12) and (4,16): m = (16 - 12)/(4 - 3) = 4.Which are the same slopes.
Missing InformationThe problem is given by the image at the end of the answer.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.
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rachel and robert run on a circular track. rachel runs counterclockwise and completes a lap every 9090 seconds, and robert runs clockwise and completes a lap every 8080 seconds. both start from the same line at the same time. at some random time between 1010 minutes and 1111 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. what is the probability that both rachel and robert are in the picture?
The probability that both Rachel and Robert are in the picture is 3/16.
The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.
Given that
Rachel and Robert both begin at the same point
Rachel completes a lap every 90 seconds.
Robert completes a lap every 80 seconds.
The photographer captures 1/4th of the track, centered on the starting line.
As a result, the photo captures 1/8th of the track on either side of the starting line.
The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.
Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.
Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.
Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).
Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.
i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.
Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}
= {90/8}/60
= 3/16
Therefore the probability that both Rachel and Robert are in the picture is 3/16
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Write an equation in point-slope form for the line that passes through each point
with the given slope. Then graph the equation.
1. (-6, -3), m = -1
2. (-7, 6), m = 0
3. (-2, 11), m=4/3
The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
the graph of the line is shown below .
In the question ,
point on the line and slope of the line is given
So , equation will be
Part(1)
(-6, -3), m = -1
(y -(-3)) = -1(x -(-6))
y + 3 = -1(x + 6)
y + 3 = -x - 6
y = -x -6 -3
y = -x -9
the equation is y = -x -9 .
Part(2)
(-7, 6), m = 0
(y - 6) = 0(x -(-7))
y - 6 = 0(x + 7)
y - 6 = 0
y = 6
the equation is y = 6
Part(3)
(-2, 11), m=4/3
(y - 11) = (4/3)(x -(-2))
y - 11 = (4/3)x + 8/3
y = (4/3)x + 8/3 + 11
y = (4/3)x + 41/3
the equation is y = (4/3)x + 41/3
the graph of all the three equations are shown below .
Therefore , The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
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arturo can have pizza for dinner on any four of the next eight days. how many different ways can he select the days on which to have pizza?
Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.
What is combination?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
In combinations, one can select the items in any order.
Number of combination of a objects chosen from n objects
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
According to the given question:
To select 4 days out of the next 8 days, use combination rule
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]
⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)
⁸C₄ = (8x7x6x5)/(4x3x2x1)
⁸C₄ = 70
Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.
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solve for x and find each angle measure
(7x-32)
(5x-27)
(9x-8)
equation
x:
please help me !!
it’s for a quiz
Answer:
Step-by-step explanation:
187
for g(x)=x to the power of 2 minus x, find g(x) when x=-2
The value of the function g(x) when x = -2 is 6
How to evaluate the function?The definition of the function is given as
g(x)=x to the power of 2 minus x
Rewrite the above function properly
So, we have the following representation
g(x) = x² - x
To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2
This is represented by
Calculate g(x), when x = -2
Substitute -2 for x in the equation g(x) = x² - x
So, we have the following equation
g(-2) = (-2)² - (-2)
Evaluate the exponents
This gives
g(-2) = 4 - (-2)
Evaluate the sum
g(-2) = 6
Hence, the value of the function is 6
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Please help!! Asap screenshot below.
joe and matthew plan to visit a bookstore. based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. a figure is shown with two tables, each with two rows. the top table has a top row that reads number of books joe will buy, 0, 1, 2, and a bottom row that reads probability, 0.50, 0.25, 0.25. the bottom table has a top row that reads number of books matthew will buy, 0, 1, 2, and a bottom row that reads probability, 0.25, 0.50, 0.25. assuming that joe and matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?
The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We are to find the probability where p(x) = 0 and p(y) = 0
This is where we would have
from the table, p(x) = 0 is 0.5
p(y) = 0 is 0.25
0.25 x 0.5 = 0.125
Hence the probability that no books would be bought is 0.125.
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Which equation represents a line that is parallel to the line y = -2/3x + 5? Pls Hurry :/
The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Lines are parallel when they have the same slope.
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = - 2 / 3 x + 5.
The slope of the equation is - 2 / 3.
Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.
2x - 3y = 21
add 2x to both sides of the equation
2x + 2x - 3y = 21 + 2x
- 3y = 2x + 21
divide both ides by - 3
- 3y / - 3 = 2x / -3 + 21 / - 3
y = - 2 / 3 x - 7
Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21
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h(x)=x²+3x-2; 12-h(7)
How would I input 12-h(7) in place of x to solve this function?
Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Answer: love
Step-by-step explanation: love
Total revenue is determined by price
multiplied by output. What is the total
revenue for 95 goods each priced at
$8?
A. $760
B. $450
C. $930
Answer:
A. $760
Step-by-step explanation:
Price: $8
Amount of goods; 95
revenue = price x total units
$8 x 95 = $760 revenue
Cual es el número que sigue en la sucesión 1,3,4,7,11,18
Answer:
29
Step-by-step explanation:
1+3= 4
3+4=7
4+7=11
7+11=18
11+18=29
g:x→0.44√3.2x−4.1 i need to make that into a graph in my calculator but im not sure how
The graph of the given functions is (see in attachments).
From the question, we have
g(x) = 0.44√3.2x−4.1
Graph:
A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.
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What is the nature of the roots for y=2x^2- 5? Use the discriminant to determine the nature of the roots.
The nature of the roots for y=2x²- 5 is there are 2 distinct real roots.
What is the nature of roots?
The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant
Δ > 0 means there are 2 distinct real roots.
Δ = 0 means there are 2 equal real roots or 1 distinct real root.
Δ < 0 means there are no real roots, but 2 complex roots.
Here,
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
b² - 4ac
Substitute the values of a, b, and c.
Evaluate the given equation to find the discriminant, we get
= 0 - 4×2×(-5)
= 41
> 0
Since the discriminant is greater than 0
Hence, there are 2 distinct real roots.
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Ms.emlyn buys a hat and gloves with a coupon for 30% off her entire purchase. the gloves cost $35 before the discount. her bill before tax is $44.80.write an equation to find the original cost of the hat.
The equation to find the original cost of hat is
44.80 = (x + 35) - (x+35)× 10/3
In the given question we have,
Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.
discount on total purchase = 30%
cost of gloves before discount = $35
let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80
total cost ( hat+gloves) before discount= $(x+35)
Now, after sum up all information we get,
$(x+35) - 30%discount on $(x+35) = $44.80
=> x+35 - (x+35)100/30 = 44.80
=> x+35 - (x+35)10/3= 44.80
which is required equation for original cost of hat.
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Given: 2x+3=4x-5
Prove: x=4
Answer:
Step-by-step explanation:
2x + 3 = 4x - 5
4x - 5 = 2x + 3
Step 1 : Add 5 on both sides.
4x = 2x + 3 + 5
4x = 2x + 8
Step 2 : Subtract 2x on both sides.
4x - 2x = 8
2x = 8
Step 3 : Divide 2 on both sides.
x = 8/2
x = 4
Hence proved.
Answer:
Collect like terms
3+5=4x-2x
(note that when - crosses a line it turns to +
8=2x
8/2=2x/2
x=4
Solve :-
[tex]7a - 3 = 3 + 6a[/tex]
Answer:
A=6Step-by-step explanation:
7a-3=3+6aMove 6a to the other side
7a-6a-3=3Subtract 7a and 6a
a-3=3use inverse operations. So add 3 on both sides
a-3+3=3+3~~~~~~~~~Now we have the answer which is a=6Answer:
a = 6
Step-by-step explanation:
The given equation is,
→ 7a - 3 = 3 + 6a
Now the value of a will be,
→ 7a - 3 = 3 + 6a
→ 7a - 6a = 3 + 3
→ a = 3 + 3
→ [ a = 6 ]
Hence, the value of a is 6.
The table shows the probabilities that a biased dice will land on 2, on 3,
on 4, on 5 and on 6.
Number on dice
Probability
1
2
0.1
3
0.17
4
5
6
0.08 0.16 0.14
Paulo rolls the biased dice 300 times.
Work out an estimate for the total number of times the dice will land on 1 or on 5
The total number of times the dice will land on 1 or on 5 is 153.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.All of the probabilities will add up to 1. This gives us the equation.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1
P(1) + 0.65 = 1
P(1) = 1 - 0.66
P(1) = 0.35
We now need to find the probability of 1 or 5.
P( 1 or 5) = P(1) + P(5)
= 0.35 + 0.16
= 0.51
We now use the predicting outcomes formula
Expected = P( 1 or 5) * No. of times
= 0.51 * 300
= 153
Hence, the total number of times the dice will land on 1 or on 5 is 153.
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[tex]x-4/5-x+1/6=1/3[/tex]
The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.
What is an equation?
A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -
y = 5x + 4
2x + 3y = 5x + 8π
cos(ny) = sin(πx)
Given is the following equation -
x - 4/5 - x + 1/6 = 1/3
We have -
x - 4/5 - x + 1/6 = 1/3
x - x - 4/5 + 1/6 = 1/3
- 4/5 + 1/6 = 1/3
Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions
Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions
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WILL MARK BRAINLIEST! Determine the quadratic function of the form f(x)= a(x - h)² + k whose graph is given on the
right.
Answer:the quadratic function in f(x)= a(x-h)^2+k is f(x) = - (x - 2)² + 2.I think this is false";}
Step-by-step explanation:
- 4≤2w + 2 and 3w+1 <4
Answer:
[tex] - 3 \leqslant w < 1[/tex]
Step-by-step explanation:
as shown in picture attached
street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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help meeeeeeeeeeeeeee pleaseee
The vertex of the curve will be at (-2, -4) and the axis of symmetry is at -2
How to illustrate tye information?From the graph, the roots of the equation are -4 and 0, therefore, (x + 4) is a factor and x is also a a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = + 4x
The x coordinate of the vertex =
will be illustrated as:
-b/2a = axis of symmetry
a and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
Then, substitute x = -2 into y = + 4x to find the y-coordinate of the vertex
y = (-2)² + 4(-2)
y = 4 -8
y = -4
vertex = (-2, -4)
The axis of symmetry is -b/2a which is -2
Therefore, the vertex is at (-2, -4).
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