As calculated with the help of Pythagorean theorem, The ladder will reach 19.36 feet high on the building.
What is Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle. The square whose side is the hypotenuse, or the side across from the right angle, has an area equal to the sum of the areas of the squares on its other two sides. The Pythagorean equation, which connects the lengths of the sides B, P, and the hypotenuse H, can be used to express this theorem.
H² = B² + P²
As given in the question,
the length of the ladder is 20 ft. which will work as a hypotenuse of a right angled triangle,
The base is 5 ft.
we need to find the perpendicular line to the base.
Applying Pythagorean theorem.
H² = B² + P²
20² = 5² + P²
400 = 25 + P²
400 - 25 = P²
P = 19.36 ft.
Therefore, the ladder will go 19.36 ft. high on the building.
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What is reciprocal of -4/1
Answer:
-1/4
Step-by-step explanation:
A reciprocal is simply defined as the inverse of a value or a number. So if we have a fraction of - 4/1 we can just flip the numerator and the denominator to get -1/4.
Graph triangle ABC with vertices A(6,-2), B(8, -6), and C(4,-8) and its image after the following transformations. Give the coordinates of the final image.
A’(___,___)
B’(___,___)
C’(___,___)
Answer:
Step-by-step explanation:
When you rotate 270 degrees counterclockwise, (a,b) turns to (b,-a)
So,
A'(-2,-6)
B'(-6,-8)
C'(-8,-4)
:]
Use point-slope form to write the equation of a line that passes through the point
(−11,−14) with slope 1.
The equation of the line that passes through the point (−11,−14) is y = x - 3.
What is the slope of the line?
A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
We have,
The line that passes through the point (−11,−14)
With Slope (m) = 1,
The general equation of a straight line is
y = mx + c,
where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
so here,
y = mx + c,
(-14) = 1(-11) + c
c = -14 + 11
c = -3
The equation becomes:
y = x - 3.
Hence, the equation of the line that passes through the point (−11,−14) is
y = x - 3.
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You have a piece of fabric with an area of 32 1/3 ft.² if there are five people in your group what is the area of fabric that each person can use
Answer:6.47 ft^2
Step-by-step explanation:
Cassie is swimming backstroke for her team at the Tri-County Swim Meet. The fastest time so far is 49.25 seconds. Cassie wants to either beat or tie for the fastest time.
Let t represent the time, in seconds, Cassie hopes to achieve. Which inequality models the story?
The inequality that models Cassie situation is t ≥ 49.25
How to use inequalities to represent a situation?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Cassie is swimming backstroke for her team at the Tri-County Swim Meet. The fastest time so far is 49.25 seconds. Cassie wants to either beat or tie for the fastest time.
The inequalities that models the story is as follows:
let
t = time in secondsCassie has to equal the record or beat the record.
Therefore, the inequalities that represent the story is t ≥ 49.25
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You are selling hats and mittens at a craft fair. You hope to have $240 in sales. Hats cost $10 and mittens cost $6. a) write an equation in standard form. b) Graph the equation using x- and y- incercepts. (Show your work)
a) The linear equation is given as follows: 10x + 6y = 240.
b) The graph of the linear function is given by the image shown at the end of the answer.
How to define the linear function?The first step is defining the linear function is identifying the variables, which are given as follows:
Variable x: number of hats purchased.Variable y: number of mittens purchased.You hope to have $240 in sales. Hats cost $10 and mittens cost $6, hence the equation is given as follows:
10x + 6y = 240.
The x-intercept is the point (x,0), hence:
10x = 240
x = 24.
The y-intercept is the point (0,y), hence:
6y = 240
y = 40.
Then the line is traced connecting the points (0,40) and (24,0), with only positive values, as they represent countable amounts.
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What is the perimeter of triangles a, b, and c? DONT EXPLAIN, JUST ANSWER ROUNDED TO THE NEAREST TENTH.
The perimeter of the triangle passing through the points A, B, C is 27.5 cm.
What is a perimeter?A triangle's perimeter and side lengths are measured in the same unit. If the sides' lengths are measured in a different unit, first convert them to that unit. Example 1: Calculate the triangle's perimeter from the information provided. A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is its outermost boundary.
There are many uses in real life for perimeter calculations. The length of fence needed to enclose a yard or garden is known as the calculated perimeter.
From the figure,
The triangle is passing through the points A(4, 0), B(-6, 5), C(3, 3)
By using distance formula, we have to calculate the lengths of AB, BC, CA
Length of AB=√(-6-4)²+(5-10)²
=√125
Length of BC=√(3+6)²+(3-5)
=√85
Length of CA=√(3-4)²+(3-10)²
=√50
The perimeter of a triangle=AB+BC+CA
=√125+√85+√50
=11.18+9.22+7.07
=27.47≈27.5
Therefore, the perimeter of the triangle is 27.5 cm.
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The value of t is 41 more than 24
Answer:
t=24+41=65
Step-by-step explanation:
The value of t>24 and is 41 more than 24. So 24+41=t.
24+41=65, so t=65.
-Hope this helped & Happy Holidays!
dr. holmes reported inferential statistics in the results section of her study to show the probability of future outcomes. in this study inferential statistics help psychologists obtain the goal of
This study inferential statistics help psychologists obtain the goal of Prediction.
What is prediction in statistics?
Predictions are frequently made using measurements. For instance, they can assist in making predictions about a 4-year-future old's height, which pupils are more likely to thrive in a certain academic programme, or which job candidates have the best chances of success.a prediction of what you believe the future will hold: Please don't expect me to predict anything about the meeting tomorrow.Rain is expected this afternoon, according to every local weather forecaster. She says she has the ability to foretell the future. The outcome of the election is difficult to foresee. Although it was widely believed that the store would fail, it has done extremely well. The forecast for sales is the same as last year.To know more about predictions check the below link:
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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
c(x) = 5.50 + 20.50x
c(x) = 5.50x + 20.50
c(x) = 5.50 + 21.60x
c(x) = 5.50x + 21.60
Answer:
c(x) = 5.50 + 21.60x
Step-by-step explanation:
To start, we are told that the service fee of 5.50 is added to the set price per ticket. So we can automatically eliminate B and D
Now, to find how much it costs per ticket, we have to divide 108.00 by 5 since we are told that it costs $108 to buy 5 tickets
108.00/5 = 21.60
This means that it costs $21.60 per baseball ticket
So the third answer choice is correct
the arguments supplied to the if function, in order, are the condition for execution,
As per the concept of function, the arguments supplied to the IF function, in order, are the condition for execution, the result if condition is true, and the result if condition is false.
What is meant by function?
In math, function refers an expression, rule, or law that defines a relationship between one variable also known as the independent variable and another variable also known as the dependent variable.
Here we need to find the missing term of the given statement the arguments supplied to the if function, in order, are the condition for execution.
Here we have given that, the if function refers decision-making statement that guides a program to make decisions based on specified criteria.
When the IF statement executes one set of code if a specified condition is met (TRUE) or another set of code evaluates to FALSE.
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Given 5.05(−14.6), find the product. 651.11 7.38 −9.55 −73.73
Answer:
Step-by-step explanation: -73.73 D, If its not and its like A,B, or C and one of them is -73.73 its still going to be correct
a sample of a radioactive substance decayed to 93% of its original amount after a year. (round your answers to two decimal places.) (a) what is the half-life of the substance?
The half-life of the substance is of 10.31 years.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
a sample of a radioactive substance decayed to 93% of its original amount after a year.
The half-life is t for which:
exp(-0.067 t) = (0.5)
ln(0.5) = -0.067 t
t = 10.31 years.
Hence the half-life of the substance is of 10.31 years.
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Use long division to divide. SEE EXAMPLE 1
15. x³ + 5x²-x-5 divided by x - 1
16. 2x³ + 9x² + 10x + 3 divided by 2x + 1
17. 3x³ - 2x² + 7x + 9 divided by x² – 3x
18. 2x46x² + 3 divided by 2x - 6
Use synthetic division to divide. SEE EXAMPLE 2
Answer:
Step-by-step explanation:
eazy 102
an urn contains 5 green balls and 3 red balls . what is the probability that when two balls are selected at random with no replacement , both are green ? ( round to three decimal places)
By using probability, it can be calculated that
Probability that when two balls are selected at random with no replacement , both are green = 0.357
What is probability?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Number of green balls = 5
Number of red balls = 3
Total number of balls = 5 + 3 = 8
Probability that when two balls are selected at random with no replacement , both are green = [tex]\frac{5}{8} \times \frac{4}{7} = \frac{5}{14} = 0.357[/tex]
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One side of a rectangular yard is bounded by the side of a house. The other three sides are to be fenced with 86 ft of fencing. The length of fence opposite the house is 13 ft less than either of the other two sides. Find its length and width.
The length of one side is 20 ft and the other side of the yard is 33 ft.
Let the length of the side opposite to the house be x ft.
We know that the yard to be fenced is rectangular. Hence the opposite sides of the yard are going to be equal.
It is given that the side opposite to the wall is 13 ft less than the length f the other two sides.
Hence the length of the side adjacent to the house will be
(x + 13) ft
The fencing needs to be done on these three sides. We already know that the length that has been fenced is 86 ft.
Hence, we get
x + x + 13 + x + 13 = 86
or, 3x + 26 = 86
or, 3x = 86 - 26
or, 3x = 60
or, x = 60/3
or, x = 20.
Hence the length of one side is 20 ft and the length of the other side is
20 + 13
= 33 ft.
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Solve for x given the diagram
Answer:
x=4
Step-by-step explanation:
If we were to perform a reduction, the scale factor would be ½. This means we have to divide by 2. 14÷2=7 and 12÷2=6.
Line segment AB is equal to 7.
Line segment BC is equal to 6.
AB: If you want to double check, 4+3=7
BC: 2×4=8 and 8-2=6
If AGHJ is isosceles,
find the value of x.
G
38°
H
J
(14x + 1)
The value of x from the given isosceles triangle GHJ is 5.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
In the given isosceles triangle GHJ, GJ=GH, ∠G=38° and ∠J=(14x+1)°.
Since, sides GJ=GH
∠J=∠H
Now, ∠G+∠J+∠H=180° (Angle sum property of a triangle)
⇒ 38°+(14x+1)°+(14x+1)°=180°
⇒ 28x+40°=180°
⇒ 28x=140°
⇒ x=140/28
⇒ x=5
Therefore, the value of x is 5.
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"Your question is incomplete, probably the complete question/missing part is:"
If triangle GHJ is isosceles find the value of x.
Suppose S is the set of integers that are multiples of 3, and T is the set of integers that are odd. Prove that |S| = |T| by constructing a bijection between S and T.
The bijection could be defined from the set of numbers and it is proved.
We can define a bijection f from S to T as follows: for any integer x in S, let f(x) = x + 1.
To show that f is a bijection, we need to prove that it is both injective and surjective.
To prove that f is injective, suppose f(x) = f(y) for some x, y in S. Then x + 1 = y + 1, which means x = y. Thus, f is injective.
To prove that f is surjective, let y be an arbitrary element of T. Since y is odd, we can write y = 2n + 1 for some integer n. Now consider the element x = 3n in S. We have f(x) = x + 1 = 3n + 1 = y, so f is surjective.
Therefore, f is a bijection from S to T, so |S| = |T|.
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Select the correct answer.
AC and BD are diagonals of quadrilateral ABCD is quadrilateral ABCD a parallelogram? Explain
D
с
OA. Yes, because the diagonals bisect each other
OB. Yes, because the sides are congruent.
OC. No, because the diagonals bisect each other.
OD. No, because the sides are congruent.
The given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
Given:
AC and BD are diagonals of quadrilateral ABCD.
From diagram we can see that the measure of AO and OC is same which is 4.
Also measure of BO and OD is same which is 6.
That is diagonals bisects each other.
Hence, the given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.
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Find a difference equivalent to the product
(x - y)11.4.
Answer:
11.4x-11.4y
Step-by-step explanation:
Distribute the 11.4
11.4x-11.4y
x-2/x-4+x-6/x-8=6 2/3
Answer:x=8.47
Step-by-step explanation:
Number 15 is the question
The coordinate after reflection over y- axis is
A' ( 8 , 1),
B' (0 , -2)
C'( -3, 5)
What is Reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Given:
A( -8, 1), B(0, -2) and C(3, 5).
As, The rule for a reflection over the y -axis is (x,y)→(−x,y) .
So, the coordinate after reflection is
A' ( 8 , 1),
B' (0 , -2)
C'( -3, 5)
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What is Y in the math?
The y is the variable that used in the different situations like to find the unknown variable, graphing, and function
y in the math is usually used as the variable in function, graphing etc.
y variables can be used in the equation to find the unknown values in the equation
Example = 5y + 10 = 15
Similarly in the graphing the y is used in the slope intercept form
The slope intercept form is
y = mx + b
Y can be used in the function as well
Example: y = 2x + 4
Therefore, the y can be used as the variable in the different situation
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what is the solution to 12-3/4(8f-5/3+4f+2/3)?
Answer:
51/4 - 9f
Step-by-step explanation:
Answer:
12 3/4 -9f
Step-by-step explanation:
You want the simplified form of the expression 12-3/4(8f-5/3+4f+2/3).
SimplificationWe can simplify inside parentheses first. This consists of combining like terms.
= 12 -3/4((8+4)f +(-5/3+2/3)) = 12 -3/4(12f -1)
Then the distributive property is applied, and like terms are combined (again).
= 12 -9f +3/4
= 12 3/4 -9f
ovement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Solve for k, the constant of variation, in an inverse variation problem, where x = 3.3 and y = 24.
Ok = 79.2
Ok = .14
Ok=7.3
Ok = 20.7
Submit
Pass
The constant of proportionality in the inverse variation is 79.2
Constant of ProportionalityConstant of proportionality is defined as the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities:
Direct Variation Inverse Variation.This is often determined because of the formula used.
Given that the variation here is an inverse variation.
y ∝ 1/ x
y = k / x
k = y₁x₁ = y₂x₂ = y₃x₃
However, in this question, we can simply represent the constant of proportionality as
k = yx
Substituting the values given into the formula above;
k = 24 * 3.3
k = 79.2
The constant of proportionality is 79.2
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If you take a number, times by 3 then add 5. You get the same as if you took the
number, times by 7 then subtract 8. What is the number?
The number is 4.
If you take a number, times by 3 then add 5, you get (3x + 5).
If you take the same number and times by 7 then subtract 8, you get (7x - 8).
Set the equations equal to each other:
3x + 5 = 7x - 8
Subtract 3x from both sides:
5 = 4x - 8
Add 8 to both sides:
13 = 4x
Divide both sides by 4:
4 = x
Therefore, the number is 4.
the longest professional tennis match ever played lasted a total of 11 hours and5minutes. how many minutes was this?
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes 665 in minutes or 665 minutes.
Given that:
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes.
Time = 11 hours and 5 minutes
We know that,
1 hour = 60 minutes.
Also, need to know that 1 minute = 60 seconds.
So, multiply hours by 60 to convert hours into minutes and add it with minutes to find the value of time in minutes.
i.e. Time = 11 x 60 minutes + 5 minutes
∴Time = 660 minutes + 5 minutes
= 665 minutes
Hence, 665 minutes was the time the longest professional tennis match ever played lasting a total of 11 hours and 5 minutes.
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3) Find the value of FD. bited F 12 12 13x - 16 E 4x+11 D
The Length of FD = 26 cm
According to the given information
FE = FC = 12cm
As FE, FC both are radius of circle
The tangent segments to a circle from a external point are equal
Hence
CD = ED
13x - 16 = 4x + 11
13x - 4x = 11 + 16
9x = 27
x = 27/9
x = 3
CD = 13x - 16
= 13 × 3 - 16
= 23 cm
ED = 4x + 11
= 4 × 3 + 11
= 23 cm
In Triangle FED
FE is perpendicular to ED
According to Pythagoras Theorem
[tex]FD^{2}= FE^{2}+ED^{2}[/tex]
= [tex]12^{2}+ 23^{2}[/tex]
= 673
FD = 26 cm approx.
The Length of FD = 26 cm
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There were 425 guests at a hotel. 170 guests ordered food. what percentage of the guests ordered food?
There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.
Define percentage.A percentage is a fraction of a whole in mathematics, which is denoted by the symbol per 100. A single unit out of a hundred, or one hundredth of something, is represented as a single percent, such as 1%. The Latin phrase per centum, which means by the hundred, is where the word percent originates. Percentage does really refer to a hundredth or 1/100 of something.
Given,
Total number of guests = 425
Guest who ordered food = 170
For percentage,
Value/ Total × 100%
170/425 × 100%
0.4 × 100%
40%
There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.
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