The general formula that describes the variation is T² = 18a³/d²
Direct variation: When a variable x changes directly with another variable y, it is written in this form;x ∝ y.
This can then be written as;
x = ky
Where;
k = constant rate of change.
Inverse: When one variable x changes in the opposite direction to another variable y, it is written in this form; x ∝ 1 / y This can then be written as; x = k (1/y) Where; k = constant rate or variationCombined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;x ∝ (y/z)
This can then be written as;
x = k (y/z)
Where;
k = constant rate or variation
The square of T varies directly with the cube of a and inversely with the square of d.
Note that
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝ a³/d²
T² = k (a³/d²)
Since;
T = 4 when a = 2 and d = 3
We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;
(4)² = k (2³/3²)
16 = k (8/9)
8k = 16 x 9
8k = 144
k = 144/8
k = 18
Therefore, The overall formula for describing the variation is
T² = 18 a³/d²
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Which of the following statements are true about a reflection? Select all that apply. © An image created by a reflection will always be congruent to its pre-image. • Corresponding angles and segments are always congruent in a reflection of a figure. • Reflections can only be constructed across horizontal or vertical lines. D Reflections may change the size of a pre-image. • An image and its pre-image are always the same distance from the line of reflection.
True statements about reflection are:
(A) A reflection's image will always be congruent to its pre-image.(B) In a figure reflection, corresponding angles and segments are always congruent.(E) The distance between an image and its pre-image from the line of reflection is constant.What do we mean by reflection?The change in direction of a wavefront at an interface between two different media that causes the wavefront to return to the medium from which it originated is referred to as reflection. Light, sound, and water wave reflections are common examples. A reflection's image will always be congruent to its pre-image.In a figure reflection, corresponding angles and segments are always congruent.The distance between an image and its pre-image from the line of reflection is constant.The description of reflection is similar to three options given in the question which are option (A), (B) and (E).
Therefore, true statements about reflection are:
(A) A reflection's image will always be congruent to its pre-image.(B) In a figure reflection, corresponding angles and segments are always congruent.(E) The distance between an image and its pre-image from the line of reflection is constant.Know more about reflections here:
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The correct question is given below:
Which of the following statements are true about a reflection?
Select all that apply.
A. An image created by a reflection will always be congruent to its pre-image.B. Corresponding angles and segments are always congruent in a reflection of a figure.C. Reflections can only be constructed across horizontal or vertical lines.D. Reflections may change the size of a pre-image.E. An image and its pre-image are always the same distance from the line of reflection.Answer:
A. An image created by a reflection will always be congruent to its pre-image.
B. Corresponding angles and segments are always congruent in a reflection of a figure.
E. An image and its pre-image are always the same distance from the line of reflection.
Are correct !!
write 101 in binary form
Answer:
1100101
Step-by-step explanation:
5w + 10x . quick answer!
Answer:
you can not do that. They are not like terms. Even though they are raised to the same power, they don't have the same variable
Step-by-step explanation:
Members of a baseball team raised $1128.75 to go to a tournament. They rented a bus
for $856.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
-2(3x + 6) > 4(x + 7)
Give an example of each type of number.
18. a real number between √13 and 14
19. an irrational number between 5 and 7 pleaseee!!!!!!
Examples of each type of number are shown:
A real number between √13 and √14: 3.61An irrational number between 5 and 7: 5.1234567What are real numbers and irrational numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, in other words, cannot be expressed as the ratio of two integers.(A) A real number between √13 and √14:
We can say that many real numbers lie between √13 and √14.3.61, 3.62, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, 3.69, 3.70, 3.71, 3.72, and 3.73.(B) An irrational number between 5 and 7:
Consider the following irrational numbers between 5 and 7: 5.1234567, 5.5768576, 6.12134567, and so on.Between 5 and 7, there are an infinite number of irrational numbers.Therefore, examples are:
A real number between √13 and √14: 3.61An irrational number between 5 and 7: 5.1234567Know more about real numbers here:
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yall help me pwease im so bad at math
Answers are in bold
4x-62x/5x - 74/e6(9+x)x(13-6)10x+12(20/x) + 7(x - 16)/2==========================================================
Explanations:
"Four times a number" gives us "4x". We then subtract off 6.The expression 2x represents "2 times a number", aka "the product of 2 and a number". We then divide that expression over 5 to get the quotient.Take any number x, and subtract off 7. For instance, if x = 10, then x-7 = 10-7 = 3, which shows that 3 is 7 less than 10.The term "quotient" means "result of division". So we divide 4 over 'e'The expression 9+x is the sum of 9 and some unknown number. The 6 out front means we multiply 6 with (9+x).The term "difference" means we'll be subtracting the terms."ten times a number" translates to 10x, in which we increase that by 12 to get 10x+12The portion 20/x is the quotient of 20 over x. This is similar to problem 4. Then we increase the (20/x) by 7 to get (20/x) + 7The x-16 part is the difference of x and 16. That result is then divided in half.Given m/n find the value of x (8x+10)=(6x+30)
The value of x from the given expression is 10
Solving linear expressionsLinear function are functions that has a leading degrees of 1. Given the expression below;
(8x+10)=(6x+30)
Collect the like terms
8x - 6x = 30 - 10
2x = 20
Divide both sides by 2
2x/2 = 20/2
x = 10
Hence the value of x from the given expression is 10
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joyce paid $90 for an item at the store that was 40 percent of the original price. what was the original price?
Answer:
Step-by-step explanation:
answer is $100.00 is original price
40% of 100 = $90
solve the following absolute equation 2|3x-4|+8=6
Answer:
"No solution" is the answer
Step-by-step explanation:
(4^6) (4^−8)?????????????
Answer:
1/16
in decimal form it is:
0.0625
Step-by-step explanation:
Numbers from greatest to least
A triangle has two sides of lengths 10 and 14. What value could the length of
the third side be? Check all that apply.
A triangle having two sides of lengths 10 and 14 will have the third side length less than 24.
As per the question statement, We are given a triangle that has two sides of lengths 10 and 14 and we are asked about the length of the third side.
Before solving the question, we should be well aware of the the theorem of triangle side sum property.
"According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."
The sum of length of two sides are = [tex]10+14=24[/tex]
Hence the length of third side has to be less than 24 as per the theorem.
Triangle side sum property: "According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."To learn more about triangles and its properties, click on the link given below:
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Suppose M is the midpoint of FG. Find the missing measure FM = 3x - 4, MG = 5x - 26
Answer:
FG=58 X=11
Step-by-step explanation:
I'm assuming your looking for the whole segment. What I did was 3x-4=5x-26. We first have to find X. So just use the equation to find X. You should get X=11 if you did it the way I set it up. Then you plug it in with the measures you got. So FM = 3(11)-4 and 5(11)-26. You should get 29 for both. If your looking for FG, you would add those two together. So 29+29= 58. FG=58. there you go.
if the sides in a parallelogram are 3 cm and 5 cm, can the diagonal in the parallelogram be 10 cm? 8 cm? 4 cm? why?
The diagonal of the parallelogram be 10 cm or 8 cm.
What is defined as the parallelogram?A parallelogram is just a quadrilateral with two parallel sides (and therefore opposite angles equal).
A rhombus is a quadrilateral to equal sides, while a rectangle is a parallelogram with all right angles. Furthermore, because a square is a degenerate situation of a rectangle, rectangles and squares are both special kinds of parallelograms.A parallelogram's opposite sides are all the same length.A parallelogram's adjacent or adjoining angles add up to 180°.A parallelogram's diagonals cross each other.For the given case.
The sides of the 3 cm and 5 cm. As, these two side are the adjacent sides of the parallelogram, the diagonal formed will be the closing side of the triangle.
As, the diagonal is the longest side of the triangle, thus its value must be greater than other side.
This is possible with the diagonal values of 10 cm and 8 cm.
Thus, 10 cm and 8 cm are the correct values for the diagonal of parallelogram.
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You decide to save money to purchase an automobile. You save $1,500 and the total cost of the
new automobile is $27,890. The dealership offers to loan you the remaining amount, in order to
purchase the automobile, at 5.25% annual interest for 66 months.
3. What is the principal of the loan?
Show your work here:
4. What is the total amount of interest that you will have paid on the loan when the
automobile is paid off?
Show your work here:
The principal for the loan is $27,890.
The total amount of interest to be paid on the loan, at a rate of 5.25% after 66 months is $8053.24
How to find the principalThe principal is the amount of money to be paid for the automobile which is $27,890.
How to find the interest
from simple interest formula = ( principal * time * rate ) / 100
given data
principal = $27,890
time = 66 months
rate = 5.25%
converting the time to years gives
time = 66 / 12
time = 5.5 years
simple interest = ( 27 890 * 5.5 * 5.25 ) / 100
simple interest = 805 323.75 / 100
simple interest = $8053.24
We can therefore say that the amount of interest paid on the loan at a rate of 5.25% after 66 months is $8053.24
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The formula C = P(1-d) is used to find the cost of an item that is discounted.
C represents the cost of an item after a discount. P represents the original price of an item, and d is the amount of the discount
written as a percent in decimal form.
Solve for d.
A d-1-
B d-1-2
C d=1+%
D d=-1
The value of the discount d is given by [tex]\\\\d=1-\frac{C}{P}[/tex] .
A reduction in price that is often offered for early or quick payment or to a select group of customers is called discount.
The amount that results from subtracting the cost of production from the purchasing price is called the profit.The cost is the total amount needed to create a good or provide a service.Selling price is the cost at which something actually sells.Profit = sell price-cost priceDiscount = Marked price - sell priceGiven expression for the Profit , cost price and discount as
[tex]or, C = P(1-d)[/tex]
Here d is the discount , P is the profit and C is the cost price.
Now solving the equation for d we get:
[tex]or, C = P(1-d)\\\\or,\frac{C}{P} =1-d\\\\or, d+\frac{C}{P}=1\\\\or, d=1-\frac{C}{P}[/tex]
Hence the expression for calculating the discount d is given by
[tex]\\\\d=1-\frac{C}{P}\\[/tex] .
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Solve the system by substitution or elimination.
y = 2x+8
y = 3x - 1
A sampling interval of 5 (selecting every fifth unit) was used to select a sample from a population of 1000. how many elements are to be in the sample?
200 elements are required to be in the sample.
What is a sampling interval of a population?The sampling interval is the frequency with which data is collected. The sampling interval is computed by the division of the total population size by the required sample size.
So, from the information given:
The total population N = 1000The sampling interval (i) = 5The elements that are required to be in the sample i.e. the sample size (n) can be computed by using the formula:
[tex]\mathbf{i = \dfrac{N}{n}}[/tex]
[tex]\mathbf{ n= \dfrac{N}{i}}[/tex]
[tex]\mathbf{ n= \dfrac{1000}{5}}[/tex]
n = 200 elements.
Therefore, we can conclude that 200 elements are required to be in the sample.
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show that these statements about the integer x are equivalent: (i) 3x 2 is even, (ii) x 5 is odd, (iii) x2 is even.
All the above statements are proved using proof by contraposition.
What is proof by contraposition?Proof by contrapositive, also known as proof by contraposition, is an inference technique used in mathematics where a conditional statement's contrapositive is used to infer the conditional statement's conclusion. To put it another way, the conclusion "if A, then B" is inferred by building a proof of the claim "if not B, then not A" instead. This method is frequently chosen if the contrapositive is more straightforward to establish than the first conditional statement.
The term "contraposition" describes a proving strategy known as "proof by contraposition," which involves drawing an inference from a conditional statement to its logically equivalent contrapositive. The antecedent and consequent of a sentence are inverted and flipped in the contrapositive.
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what would the sum of x and 16 is less than 32 look like in a problem?
What is the probability of not drawing a queen from a standard deck of 52 cards?
The probability of not drawing a queen from a standard deck of 52 cards is 12/13
How to determine the probability of not drawing a queen from a standard deck of 52 cards?In a standard deck of 52 cards, we have
Total number of cards = 52
Queen cards = 4
The probability of not drawing a queen from a standard deck of 52 cards is calculated as
P = 1 - P(Queen)
Where
P(Queen) = Queen cards/Total number of cards
So, we have
P(Queen) = 4/52
Substitute P(Queen) = 4/52 in the equation P = 1 - P(Queen)
This gives
P = 1 - 4/52
Evaluate the difference
P = 48/52
Simplify
P = 12/13
Hence, the probability of not drawing a queen from a standard deck of 52 cards is 12/13
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Answer:
12/13
Step-by-step explanation:
Got it right on the test.
Find the distance between the two points.
(-9,9) and (-16,33)
The distance is
(Type an exact answer, using radicals as needed.)
The distance between the given two points is 25.
The coordinates of two points given to us are (-9, 9) and (-16, 33).The length of the line segment connecting two places is defined as the distance between them. The length of the line segment connecting the specified coordinates can be used to compute the distance between two locations in coordinate geometry.The distance (d) between the two points whose coordinates are (x1, y1) and (x2, y2) is given by the formula:d² = (x2-x1)² + (y2-y1)² We will apply the above formula.d² = (-16-(-9))² + (33-9)²d² = (-16 + 9)² + (33-9)²d² = (-7)² + (24)²d² = 49 + 576d² = 625d = √625d = 25Thus, the distance between the given points is 25.To learn more about distance, visit :
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HII HELP PLEASE! I DONT UNDERSTAND
Answer:
C
Step-by-step explanation:
3x^2-30x=72
3(x^2-10x)=72
x^2-10x=24
Then do the subtitules
Answer:C
Give me brainlliest
Answer: C x = -2
Step-by-step explanation:
[tex]3x^{2} - 30x - 72 = 0[/tex]
[Add 72 on both sides]
[tex]3x^{2} - 30x = 72[/tex]
[Factorise Left Hand Side of equation to get 3 on one side of a bracket]
[tex]3(x^{2} -10x) = 72[/tex]
[Divide each side by 3 to just get the brackets and the x's on one side]
[tex]x^{2} -10x = 24[/tex]
[Minus 24 on both side as the equation must = 0]
[tex]x^{2} -10x-24=0[/tex]
[Solve the square on the left hand side]
[tex](x-12)(x+2)=0[/tex]
[Solve for x on left hand side - two possible answers]
[tex]x-12=0 \\ x=12[/tex]
[tex]x+2=0\\x=-2[/tex]
[The answer '12' is not in the option for the question so '-2' is the answer]
please help with problem 25
I am writing this because the app says the answer is to short
PLEASE HELP!! i’ll give brainliest
AE = EB and CF = FB
ca = 18
de = 7
cb = 14
fe = [?]
Answer:
by comparing the two triangles,
we take the ratio of each side to be equal
Step-by-step explanation:
By comparing the sides of the triangles,
we take the ratio of each sides to each other
de/cb = fe/ca
de.ca = fe.cb
fe = (de.ca)/cb
fe = (7* 18)/14
fe = 9
The measure of side FE of triangle DEF is FE = 9
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ABC
Now , let the second triangle be DEF
And triangle ABC and DEF are similar triangles
So , corresponding sides of similar triangles are in the same ratio
And , AE = EB and CF = FB
From the similar triangle theorem ,
EF / AC = DE / CB
Substituting the values in the equation , we get
EF / 18 = 7 / 14
Multiplying by 18 on both sides of the equation , we get
EF = ( 7 x 18 ) / 14
EF = 18/2
EF = 9
Therefore , the value of EF is 9
Hence , the measure of side EF is 9
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9. The volume of a box in cubic feet can be expressed as V(x) = x³ - 3x² - 10x or as the product of three linear factors with integer coefficients. The width of the box is 5-x. What is the length, width, and height of the box in factored form? A. -x(5-x)(x+2) B. X(5-x)(x+2) C. X(5-x)(x-2) D. -x(5-x)(x-2)
The length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
The box is in the shape of a cuboid
The volume of a cuboid = l b h, where l is the length, b is the breath or width and h is the height
Putting the values of width and volume in the formula
x³ - 3x²-10x = l ×(5-x) × h
This becomes a cubic equation
l × h = (x³-3x²-10x)/ 5-x
l × h = -x²-2x
l × h = -x(x+2)
Now, putting the value of l × h in the equation we get
v= -x ( x+ 2) (5-x)
v = -x (x-5)(x +2)
Hence, the length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
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a pizza parlor can make 100 pizzas in an evening. they make 40 pepperoni pizzas and 60 extra cheese pizzas. they are producing each pizza at the lowest possible cost. 100 people order pizza, but 50 people would like a pepperoni pizza and 50 would like an extra cheese pizza. this pizza parlor is what?
Technically efficient, is what pizza parlor is but not allocatively efficient nor economically efficient
What is meant by Technical efficiency? Give an example.
The effectiveness with which a several set of inputs is employed to generate an output is called as technical efficiency. Technical efficiency refers to a company's ability to generate the highest amount of output from the least amount of inputs, such as labor, capital, and technology.
Technical effectiveness eliminates the wants for resource unemployment.
Consider the following example : Using its present staff and robot count, a company manufactures 300 automobiles every week. if 320 was the highest possible output.
The company's technical efficiency rate is (300/320) = 93.75%.
In this example , certain employees and factor inputs are underutilized, and some potential production is lost.
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If FG = 2x, GH = x-1, and FH = 5 what is GH?
Answer:
GH = 1
Step-by-step explanation:
Finding the value of x,
→ FG + GH = FH
→ 2x + x - 1 = 5
→ 3x = 5 + 1
→ x = 6/3
→ [ x = 2 ]
Now the value of GH is,
→ GH = x - 1
→ GH = 2 - 1
→ [ GH = 1 ]
Hence, the value is 1.
PLS HELP!!!
John simplified the expression
-3 X (3 + 12 ÷ 3) - 4.
Word Pro
For his first step, he added 3 + 12 to get 15. What
was John's error? Find the correct answer.
Answer:
Correct answer : -21x - 4
John's error : He added the number inside the parenthesis, instead he should've divided first then added the number.
I hope you get it