When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.
what is volume ?It is also known as the object's capacity. The fundamental equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. The math is the same regardless of how you refer to the different dimensions. For example, you can substitute "depth" for "height." Volume is used to describe an object's capacity. Volume can also be used to describe how much space a three-dimensional object occupies.
given
The ratio of their volumes is always one to three
Since the volume of a prism is 108 cubic meters,
a pyramid's volume is 1/3 * 108, or 36 cubic meters.
When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.
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The sum of the two digits number is nine
If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.
What is a digit?
In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.
The first equation is as given t + u = 9
Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.
The second equation is t = (1/2)u => u = 2t
When we replace this in first equation we get -
t + 2t = 9
3t = 9
t = 9/3
t = 3
When we replace it again in the equation -
u = 2 t
= 2 · 3
= 6
The requested number is 36.
Therefore, the number is 36 and the second equation is t=u/2.
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Please hep pls easy easy proportional relationship
Answer:
Below
Step-by-step explanation:
A) Juan reads at 57 pages /hr
B) Juan reads 9 pages more per hour (57-48) than Lexi
in 7 hours this will be 7 hr * 9 p/hr = 63 pages
The function () =
40+700
represents the average cost (in dollars) of making items. How
many items must be made for the average cost to fall to $5
The number of items must be made for the average cost to fall to $5 wil be; 900.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).
We are given that function = 40x +700 represents the average cost (in dollars) of making items.
Then the item made for function average cost to fall to $5.
= 40x + 700
= 40(5) + 700
= 200 + 700
= 900
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3(4x-10)= 2(3x-30) help
The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's solve for x:
3(4x - 10) = 2(3x - 30)
First, we can simplify both sides by distributing the coefficients:
12x - 30 = 6x - 60
Next, we'll move all the x terms to one side of the equation and the constants to the other side:
12x - 6x = -60 + 30
Simplifying further:
6x = -30
Finally, we can solve for x by dividing both sides by 6:
x = -5
Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
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the volum of the wood in a tree varries directly as height and the square of length
Answer:
The volume of wood in a tree varies directly with the height and the square of the length of the tree. This means that if we increase the height of the tree, the volume of wood in the tree will also increase, and if we increase the length of the tree, the volume of wood will increase by the square of that increase.
This relationship can be expressed mathematically as:
V = khl^2
Where V is the volume of wood in the tree, h is the height of the tree, l is the length of the tree, and k is a constant of proportionality.
This relationship is based on the assumption that the cross-sectional area of the tree remains constant, and that the volume of wood in the tree is directly proportional to the height and the square of the length of the tree.
Calculate the given angle, to the nearest degree,
55
33
44
Answer:
Step-by-step explanation:
1 radian is equal to 180^0/Pi
[tex]55=55*\frac{180}{\pi y} \\=54.97787[/tex]
Solve the formula A=1/2(a+b) for a
The equation for a is a=2A-b
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: A=1/2(a+b)
a=2A-b
Hence, the equation for a is a=2A-b
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Help Its geometry, I'm struggling
Answer:
[tex]y=\frac{3}{4}x-\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]m_{\parallel}=\frac{3}{4} \\ \\ y-1=\frac{3}{4}(x+6) \\ \\ y-1=\frac{3}{4}x-\frac{9}{2} \\ \\ y=\frac{3}{4}x-\frac{7}{2}[/tex]
suppose we want to choose 7 objects without replacement from 11 distinct objects  how many ways can this be done if the order of the choices is relevant
In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.
What is permutation?
An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.
We want to choose 7 objects without replacement from 11 distinct objects
So, since the order of the choices is relevant, we will use permutation.
Therefore,
⇒nPr = n! ÷ (n - r)!
⇒11P7 = 11! ÷ (11 - 7)!
⇒11P7 = 11! / 4!
⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)
⇒11P7 = 1663200 ways
Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.
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solve the inequality 27>b+57
Answer:
b < -30
Step-by-step explanation:
27 > B + 57 Subtract 57 from both sides
27 - 57 > b +57 - 57
-30 > b
or
b < -30
The figure below is composed of square ABCD and equilateral triangle
Answer: 225°
Step-by-step explanation:
The correct option is D)
Refer Figure
Given:
ABCD is a square
ABP is an equilateral triangle
AB=BP=BC (△ABP is equilateral and AB and BC belong to a square, hence all are equal)
∠ABC=∠ABP+∠PBC=60°+∠PBC
90°−60°=∠PBC
∠PBC=30°
In △BPC
BP=BC
∠BPC=∠BCP= 2
180−∠PBC
( angles opposite to equal sides of a triangle are equal)
∠APC=∠APB+∠BPC=(60+75)°=135°
Hence, Reflex ∠APC=(360−135)°=225°
Find the length of ST
Answer:
ST = 10
Step-by-step explanation:
Δ RSQ and Δ RTP are similar by the AA postulate , then
the ratios of corresponding sides are in proportion , that is
[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )
[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
RT = 3 × 5 = 15
Then
ST = RT - RS = 15 - 5 = 10
Let me know if I got this right
What is the solution to the equation?
lnx−ln(4x−1)=ln5
Enter your answer in the box. Enter any fractions as simplified fractions.
Answer:
x = 5/19
Step-by-step explanation:
For left side, apply logarithm division property:
[tex] \displaystyle{ \ln a - \ln b= \ln \left( \dfrac{a}{b} \right)}[/tex]
Hence:
[tex] \displaystyle{ \ln \left( \dfrac{x}{4x - 1} \right) = \ln 5}[/tex]
Since both sides have same ln, we can cancel ln both sides:
[tex] \displaystyle{ \dfrac{x}{4x - 1} = 5}[/tex]
Solve the equation for x:
[tex] \displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = \dfrac{5}{19}}[/tex]
Therefore, x = 5/19
During a series of plays in a football game, a running back carried the ball for the yardages given by 6, -3, 2, -1, 7,
-4, and -2. Find his total yards and his average yards per carry.
The total yards for the running back was
(Simplify your answer.)
Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.
Define area.Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.
Here,
We find w = 56, which indicates that the parallelogram has a length of 56 yards.
Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.
The rectangle's length is shown to be 118 yards.
The size of the playing area is accordingly 118 yard by 56 yards.
As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.
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Which is the mode for the data set? -1,0,3,4,-3,-1
Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data set is,
⇒ -1, 0, 3 ,4, -3, -1
Now, We know that;
The mode is the value that appears the most often in the data set.
Here, In the data set - 1 is most often number.
So, The mode of data set = - 1
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Equivalent fractions to 30/10
Answer: 3/1. 6/2. 9/3. 12/4. 15/5. 18/6. 21/7. 24/8. 27/9 and many more
Step-by-step explanation:
Can somebody please tell me how to Solve Systems by Elimination? I don't understand it at all and I'm staying up all night trying to figure it out. I especially don't understand the co-efficient part.
An example is:
2c+3d=12
5c-d=13
What would the answer be to that? Please provide an explanation!
Solving the example, hope it will help you with better understanding.
Given system:
2c + 3d = 125c - d = 13We need to eliminate one of the variables c or d. Let us eliminate d.
We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.
Demonstrating how it works:
2c + 3d = 12, we leave it as is
5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39
Now add up the two equations:
2c + 15c + 3d - 3d = 12 + 39, eliminated d17c = 51 solving for cc = 51/17c = 3Now we can find the value of d:
2c + 3d = 122*3 + 3d = 126 + 3d = 123d = 6d = 2Our solution is:
c = 3, d = 221⁄2
yards of thread to make 4⁄6
of a sock. How many yards of thread will it take to
make an entire sock?
The yards of thread that will take to make an entire sock will be 3 3/4 yards.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, 2 1/2 yards of thread to make 4 /6
of a sock.
The yards of thread that will take to make an entire sock will be:
= 2 1/2 ÷ 4 / 6
= 5 / 2 × 6/4
= 30 / 8
= 15 / 4
= 3 3/4 yards.
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can someone help me with this please?
could the answer be;
a.) px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3
b.) px=-3x^3-2x²-6x-16,r(x)=-117, and q(x)=x-3
c.) px=-x^3+4x²+12x+16,r(x)=-117, and q(x)=x-3
d.) px=-x^3+4x²+14x+45,r(x)=-0, and q(x)=x-3
The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
(-x^4+7x^3+2x+3)/ (x-3)
=-x² + 4x² + 12x + 38 + 117/(x - 3)
Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
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57. In the standard (x,y) coordinate plane, define the
h-v distance between. 2 points to be the length, in
coordinate units, of the shortest path between the
2 points using only horizontal and vertical segments.
The expression (5-2) +13-(-4) gives the
h-v distance between which of the following pairs of
points?
A.(3, 5) and (-4, 2)
B.(3, 5) and (-2,-4)
C. (5.-4) and (-2, 3)
D. (5,-2) and (3, 4)
E. (5, 2) and ( 3,-4)
A vertical line in geometry is one that crosses the page from top to bottom.
What is meant by horizontal and vertical segments?A vertical line in geometry is one that crosses the page from top to bottom. Its cousin is the horizontal line that spans the page from left to right. A horizontal line and a vertical line are perpendicular.
Businesses utilize segmentation as a marketing strategy to focus on a certain market segment or type of customer. While vertical segmentation sharpens your marketing emphasis to target customers in a smaller demographic, horizontal segmentation entails offering a product to a broad range of consumers.
A horizontal object is one that is perpendicular to the horizon. Due to the fact that vertical is the polar opposite of horizontal, anything that forms a 90° (right angle) with either the horizontal or the horizon is referred to as vertical. This means that the horizontal line is one that crosses from left to right. Mathematical applications of the horizontal and vertical.
Therefore, the correct answer is option C. (5.-4) and (-2, 3).
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So far this semester, Franco is averaging a score of 70.7 points on math tests, which is 1% higher than his average last semester. What was the average of his scores last semester?
help me pleasee
Which expression is the least absolute value |-28| |-1| |6| |15|
Answer: |-1|
Step-by-step explanation:
So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)
measurements of angles
Step-by-step explanation:
10x + 17 + 8X - 31 + 6x - 8 = 180
Use this equation and solve this equation and you will find the answer
how do write 3n - 6 as a phrase in words
Find the value of x in the
following parallelogram:
2x - 5
X + 10
x=[?]
The value of x in the following parallelogram is 15
What is a parallelogram?You should recall that a parallelogram is a quadrilateral whose opposite sides are equal and parallel
The given sides are
2x - 5 and X + 10This means that
X + 10 = 2x -5
Collecting like terms we have
x-2x = -5-10
-x = -15
Dividing by -
We have x= 15
Therefore x is 15 in the parallelogram.
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Unit 11 volume and surface area homework 2 area of sectors
Answer:
2. KI = 20 ft 119 M K 4. YZ = 14.2 m 2 6. PO = 2.8 in R 311 8. WZ = 5.3 km w z 108
Step-by-step explanation:
What’s the tangents ratio for F?
5/4
5/3
4/3
3/4
The tangent ratio of F by using the rule from trigonometry is 4/3
What is the trigonometry ratio?Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.
The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;
Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.
Therefore, the tangent ratio for F is:
tan θ = 8/6
This can be reduced to 4/3
Therefore, we can conclude that the tangent ratio of F is 4/3.
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The tallest tree in the United States is the coast redwood and your deer Smith State Park in California. It is 321 feet tall suppose you are 5‘,8“ tall and cast a shadow that is 2 feet at a certain time of day about how long is the trees shadow at the same time of day convert five point 5‘8“ to feet
The shadow of the tree at the same time of day was 113.29 foot long.
What is foot?Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).
In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.
We know that
1 feet = 12 inches
So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet
Now, lets find the shadow of tree
5[tex]\frac{2}{3}[/tex]/2 = 321/x
x = 113[tex]\frac{5}{11}[/tex]
x = 113.29
Thus, the tree's shadow at the same time of day was 113.29 foot long
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Angles 3 and 4 are supplementary. The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
1. What is the measure of Angle 3?
2. What is the measure of Angle 4?
The values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
Given ,
What are supplementary angles ?
The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .
Angles 3 and 4 are supplementary.
The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
So,
∠3 + ∠4 = 180 degrees.
∠3 = 180-∠4 - equation 1
∠3 = 35 + (1/4 ) ∠4 - equation2
As equation 1 and 2 are equal
hence,
180-∠4 = 35 + (1/4) ∠4
180-35 = ∠4 + (1/4) ∠4
145 = ((1/4)+1) ∠4
145 = (5/4) ∠4
∠4 = 145 * 4 / 5
∠4 = 29*4
∠4 = 116
∠3 = 180-116
∠3 = 64
Hence the values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
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ILL GIVE BRAINLIEST IF CORRECT NEED HELP ASAP PLS
Answer: y=2x-15
Step-by-step explanation:
Answer:
y=1/2x + 15
Since,her original flight plan time is X and hence the flight will reach 2 times faster the X becomes X/2 and the additional time 15 minutes which has already been delayed.So,she will arrive her destination in(1/2X+15)min from 4:00 p.m.
*mark me brainliest