When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.
what is direct variation ?equation that can be used to explain the mathematical relationship between two variables, where one variable is equal to a constant multiplied by the other. A direct variation's (proportional relationship's) graph is a straight line that pierces the origin. On a graph of direct variation, the graph will always pass through (1, k), where k is the proportionality constant. Direct variation refers to a change in one quantity that directly affects the other. The complete opposite of this is inverse variation.
The equation that describes this variation is:
h =kx
1st Data 2nd Data
s=22 m s = 40 m
h=6 stories h = find 2nd
k=find 1st k = 0.27 story/m
Find k: Find h :
h=kx h = kx
6 stories=k(22 m) h = ( 0.27 story/m ) ( 40 m)
k=6 stories/22 m h = 10 stories
k=0.27 story/m
so its direct variation .
When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.
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a builder wishes to fence in 60,000m of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost 20 per meter, while the fence for the other three sides will cost 10 per meter. how much of each type of fence should the builder buy to minimize the cost of the fence
The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.
To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.
To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:
2x + 2y = 60,000
To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:
60,000 - x = 3x + 2y
The total length of the three sides that are not the front is 3x + 2y.
Now we can calculate how much the builder will pay for each type of fence:
Cost of front fence = $20/m * x = $20xCost of other three sides = $10/m * (3x + 2y) = $30x + $20yTotal cost of the fence = $20x + $30x + $20y = $50x + $20y
To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.
However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:
x meters of $20/m fence for the front side3x + 2y meters of $10/m fence for the other three sides.This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.
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HELP!!!! if you answer you get 20 points.
Answer:
Very last choice is the answer.
Step-by-step explanation:
Remark
The thing that is most important is that the horizontal line connect h and the radius is parallel to the cut of the sphere if it was placed right in the middle. That line swings around as though the center was a pivot.
Solution
So what you have is a circle when that line goes around that part of the sphere. To find the length of that line, use the Pythagorean Theorem. Call the line r1.r1 ^2 = r^2 - h^2So the area is pi * r1^2Area = pi (r^2 - h^2)The very last one is the answer.what is the answer????
Answer:
x = 11.2
Step-by-step explanation:
[tex]\frac{6.4}{x}[/tex] = [tex]\frac{4}{7}[/tex]
4x = 44.8
x = 11.2
Nick is driving from Brookville to Kansas City, a distance of more than 325 miles, to watch the Bengals play the Chiefs in the playoffs. After driving 75 miles, Nick stops for gas. Write and solve an nequality to determine how much farther Nick has to drive to reach Kansas City.
The distance that Nick has to drive to reach Kansas will be at least 250 miles.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Since Nick is driving from Brookville to Kansas City, a distance of more than 325 miles and after driving 75 miles, Nick stops for gas.
An inequality to determine how much farther Nick has to drive to reach Kansas City will be:
x > 325 -75
x > 250
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If x = 6 and y = − 2 , evaluate the following expression: 2 x y
Answer:
-24
Step-by-step explanation:
2(6)(-2)
Donald has xxx twenty-dollar bills and 111 ten-dollar bill. How much money does Donald have? Write your answer as an expression.
Answer:
20x + 10
Step-by-step explanation:
Given that :
Number of $20 bill = x
Number of $10 bill = 1
Total amount of money can be expressed as :
Σ(Value of bill * number of bill)
Hence,
($20 * x) + ($10 * 1)
20x + 10
The expression for the amount of money Donald has is : 20x + 10
A stack of identical 8-centimeter-by-10-centimeter rectangular playing cards is sitting on a table. The stack is 1 centimeter high and has a volume of 80 cubic centimeters. The table is bumped and the stack of cards is shifted so that the stack is no longer a right rectangular prism, but all of the cards are still part of the stack.
Which of the following statements are true of the shifted stack of cards? Select all that apply.
A) The shifted stack of cards has a volume of 80 cubic centimeters because it has the same base area and height.
B) The area of a card at any location in the stack remains the same.
C) The width of the stack from the leftmost edge to the rightmost edge will remain 10 centimeters because the volume is the same.
D) Cavalieri’s principle cannot be applied to the volume of the stack because the stack is a rectangular prism instead of a cylinder.
E) The area of the middle card in the stack is 40 square centimeters because it is half of 80.
Answer: A, B, C.
If the stack of cards are shifted so it is not straight, it still has everything the same.
What type of line is Y 0?
If the value of y = 0, then it make the straight line on the graph.
The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.
Here we have the expression y = 0.
And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.
Therefore it represent the x-axis.
Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.
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What additional information would be necessary to determine sin a without using the Pythagorean theorem explain brainly?
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulae.
In order to determine sin a without using the Pythagorean theorem, we will need to have the value of the opposite side and angle. Sin (a) = opposite / hypotenuseHere, the hypotenuse is not given, so we will need to have the value of the opposite side and angle (a) in order to determine sin a without using the Pythagorean theorem.
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•225+225 = ?
•5/25 = ?
•78-8 = ?
•13*1 = ?
Step-by-step explanation:
hope it is helpful to you
help with this please.
please help me if you can! ( links= report )m
Answer:
Volume (V) = 2522.0 mm^3
Step-by-step explanation:
The volume of cylinder is :
V = π r 2 h
We know that the height (h) is 19.
We also know the radius (r) is 13/2 = 6.5
So,
V = π 6.5^2*19
V = 2522.0 mm^3
h=?ft
what is the correct answer
Answer:
h = 4 ft
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 8 and h = 3 , then
A = 8 × 3 = 24 ft²
Now consider the other base b = 6 with perpendicular height h , then
6h = 24 ( divide both sides by 6 )
h = 4
5
6
Harder Questions
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Question Progress
b)
nth term:
87%
The terms in this sequence increase by the same amount each time.
19
34
a) Work out the missing terms.
b) Work out, in terms of n, the nth term of the sequence.
Type here to search
O
RI
E
Does anyone know c & d please
Answer:
c = 100 or 10^2
d = 3125 or 5^5
Step-by-step explanation:
c. the answer for C is 10^2 because you just subtract the exponents same goes for d.
can someone please tell which congruency do you use and how?
To prove that ΔABC is isosceles.
Properties of an isosceles triangle.An isosceles triangle is a type of triangle in which the length of its two sides, and measure of its two internal angles are equal. When a bisector of an angle is drawn to one of the internal angles of the triangle, two congruent triangles of corresponding properties are produced.
To prove that ΔABC is isosceles, we have:
<CAD ≅ <BAD (definition of an angle bisector)
CD ≅ BD (definition of a midpoint)
AC ≅ AB (congruent sides of an isosceles)
<ACD ≅ <ABD (congruent internal angles of an isosceles)
<ADC ≅ <ADB (definition of right angle)
Therefore it can be concluded that;
ΔABC is an isosceles triangle (Angle-Side-Side theorem)
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How is 0.1363636363636363636... written as a fraction in simplest form?
.
Answer:
3/22
Step-by-step explanation:
There's a very neat trick for this kind of problem.
First, choose a letter to represent the number.
n = 0.1363636...
Observe that there is a 2-digit block that repeats ("36"), but that block does not repeat immediately to the right of the decimal point. Do two muliplications, one to put the decimal point in front of the repeating block, the other to put the decimal point after the block.
10n = 1.363636...
1000n = 136.363636...
Here comes the cool part: subtract the first equation from the second.
990 n = 135 See? The repeating decimal parts, all lined up as they are, subtract to zeros.
Finally, n = 135/990 = 15/110 = 3/22
the sum of 8 times a number and 6 is 3
Answer:
Sum means '+'
is means '='
a number means 'x'
3x + 6 = 8
I hope this helped!
Approximately 3.4% of Americans are vegetarian. If we ask a random sample of 36 people, what is the probability that exactly 4 of them are vegetarian?
Answer:
0
Step-by-step explanation:
Given: 3.4% of Americans are vegetarian.
sample size = 36 people
Therefore, 3.4% of 36 = 1.224.
Hence, out of 36 people only 1.224 people which is approximately 1 is vegetarian.
So, the probability of exactly 4 people being vegetarian out of 36 people would be zero.
As out of 36 only 1 was vegetarian.
Hence, the correct answer would be 0
5. Michael has of 3 boxes of a dozen doughnuts for his class of 30 students. Does
he have enough doughnuts for each student to get a whole doughnut? Why or
why not?
Yes Michael has 36 doughnuts 6 extra
3*12=36
36>30
Please help!! I will give brainliest and no links!! Also please do it in a picture model “standard algorithm” please do both questions!
Find the quotient of 4,611 divided by 21.
Answer:
1. 219.571428571
2. 150.314285714
Toss a coin 10 times and record how many times you tossed heads.
a) What is your experimental probability of tossing heads?
b) What is the theoretical probability of tossing heads?
c) Compare the two probabilities and determine if you are considered to be
"lucky" at tossing heads.
d) If you were to toss the coin 100 times, what would you expect the
experimental probability of heads to be? Defend your answer.
To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the probability of tossing heads is 0.000976.
What is probability?Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.
Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.
P(getting heads on one toss) = 1/2
P(getting all heads in 10 tosses)=(1/2)¹⁰
=1/1024
=0.000976
Therefore, the probability of tossing heads is 0.000976.
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Which triangles are congruent? 30° 110° A 30° 45° B 110° 40 C С
Answer:
It would be triangles A & C
Step-by-step explanation:
This is because all of the angles within triangle add up to 180, with this, you can do the following to find the missing sides:
Tri A:
180-110-30 = 40
Tri B:
180-45-30 = 105
Tri C:
180-110-40 = 30
When you do this, look at the angles of the triangles. You see that Triangle A with the angles 110, 30, and 40 all match with those seen in Triangle C.
Therefore, the two triangles are congruent.
PLEASEEEE HELP I WILL MARK BRAINLIST
Find the value of x such that the data set has the given mean.
102. 119. 107, 115, 106, x; mean 119
Answer:
Integer - 72
Decimal - 72.3
Answer:
.here is the answer ............
The Reed family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There are 4 beds, 3 desks, and 1 dresser to select from. How many different furniture sets could they select?
Answer:
12.
Step-by-step explanation:
right!!
use your calculator to determine the percent of each number a.1% of 28 =
Answer:
0.28
Step-by-step explanation:
1% = 0.01
0.01 × 28 = 0.28
483000 in standard form
Answer:
483000
Step-by-step explanation:
To write a linear expression in standard form, rearrange the terms in alphabetical order.
Answer:
48300000
We can write the above number as
4.83 x 10000000
=4.83 x 10 ^7
decide whether the function is a polynomial function. If so right it in standard form and state it’s degree type in leading coefficient if so write it in standard form and state its degree type in leading coefficient P(x)=-3x^2+10-4x
For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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. The ratio of the area of circle A to the area of circle B is 12/5. What is the ratio of their circumferences?
Answer:
1.5
Step-by-step explanation:
a : b = 1 : 12/5
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
Let the radius of circle a = 1
Area of circle A = 1π
Radius of circle A = square root of 12/5 = 1.5
The circumference of a circle = 2nr
n = 3.14
circumference of circle A = 2 x n x 1 = 2n
circumference of circle B = 2 x n x 1.5 = 3n
ratio of circumference = 3n / 2n = 1.5
I don’t if is good and the last I don’t know how to do it
From the given data, the first and third graph are correct.
1. For the first graph,
the two equation are -
y = -2x - 4
-4x + y = 2
Let us check the common points for the given graph,
(-1,-2)
y = -2x - 4 - 4x + y = 2
-2 = -2(-1) - 4 -4(-1) + (-2) = 2
-2 = -2 2 = 2
Hence it is correct.
2. For the second graph,
y = -3/2x - 2
y = -1/4x + 3
Common points are - (4,4)
y = -3/2x - 2 y = -1/4x + 3
4 ≠ -8 4 ≠ 2
Hence it is not correct.
3. For the third graph,
y = -5
y = 3x + 1
Common points are - (-2,-5)
y = 3x + 1
-5 = -5
Hence it is correct.
The correct graph for 2, graph is below,
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