Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet
What is Pythagoras TheoremPythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:
x² = y² + z²
where x is the hypothenuse and y, z are the legs of the right angle triangle.
To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.
x² = y² + z²
15² = 2² + z²
z² = 15² - 2²
z² = 221
z = √221
z = 14.87 feet
The height is 14.87 feet
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Need help ASAP Geometry Assignment
The figure also has a line symmetry for the vertical line x is 5, and a line symmetry for the horizontal line y is 5 .Therefore the figure has both symmetry
What is meant by line symmetry ?A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it creates a symmetrical split in the figure and the separated pieces look like mirror reflections of one another, we also refer to this line as the axis of symmetry or the mirror line.
An imaginary line that splits a line or shape into two identical parts is called the axis or line of symmetry. The symmetry axis of a parabola will be required of you at higher level mathematics. This u-shaped line on the graph is a parabola.
B) The transformation that maps the figure unto itself are therefore;
1) Rotating the figure 180° about the point (5, 5) which is the center of the figure
2) The figure reflected across the line x = 5 and the figure reflected across the line y = 5
The complete question is : Determine if the figure below has rotational symmetry, line symmetry or both and
describe the transformation that mas the figure onto itself. BE SPECIFIC. You must
name the center of rotation and degree of rotation if it has rotational symmetry or lines of reflection if it has line symmetry
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You want to determine the number of students in your school who have visited an art museum. You survey 36 students in the art club. Twenty-seven have visited an art museum, and nine have not. So, you conclude that 75% of the students in your school have visited an art museum.
Determine whether the conclusion is valid.
Answer:
The sample is large enough, representative of the entire population, and chosen randomly so the conclusion is valid.
The conclusion that 75% of the students in your school have visited an art museum is valid.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
Given that,
Total number of students in the art club being surveyed = 36
Number of students who visited art museum = 27
Number of students who does not visited art museum = 9
Percentage of students who visited art museum = (27 / 36) × 100
= (3/4) × 100
= 0.75 × 100
= 75%
Hence the conclusion that 75% of the students in your school have visited an art museum is valid.
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HELP! The diameter of a circle is 12 cm. Find its area in terms of π. (pi)
The area of the given circle in terms of π is 36π cm².
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
Area = πr²
where 'r' is the radius of the circle
Given that the diameter of the circle is 12 cm, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2
Radius = 12 cm / 2
Radius = 6 cm
Now, we can substitute the radius value into the formula:
Area = π x (6 cm)²
Area = π x 36 cm²
Therefore, the area of the circle in terms of π is 36π cm².
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Make a tree diagram to show sample space. Then select the total number of outcomes.
choosing a card with a square shape or a circle shape and spinning a spinner and it landing on orange, blue, yellow, red, or
green.
a. 5
c.15
b. 10
d. 20
Answer:
B. 10
Step-by-step explanation:
The first choice has 2 options: square or circle
The second choice has 5 options: orange, blue, yellow, red, or green.
2 x 5 = 10 total outcomes
The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
Answer: 12.96
Step-by-step explanation: you should multiply 12 * 0.08 = 0.96
then just add 0.96 + 12 = 12.96
Convert the mixed numbers to improper fractions.
Aim :
We have to convert them into improper fractions as they are into mixed fractions. So let's start..!!
Solution :
1) [tex] \bf{ 1\dfrac{5}{8} }[/tex]
Multiply 8 into 1 and add 5 into it,
[tex]: \: \implies \: \sf{ \dfrac{8 \times 1 \: + \: 5}{8}} \\ \\ : \: \implies \: \sf{ \dfrac{8 \: + \: 5}{8}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{13}{8}}}[/tex]
_______________________________________
2) [tex] \bf{ 4\dfrac{2}{5} }[/tex]
Multiply 4 into 5 and add 2 into it.
[tex]: \: \implies \: \sf{ \dfrac{4\times 5 \: + \: 2}{5}} \\ \\ : \: \implies \: \sf{ \dfrac{20 \: + \: 2}{5}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{22}{5}}}[/tex]
_______________________________________
3) [tex] \bf{ 2\dfrac{6}{8} }[/tex]
Multiply 8 into 2 and add 6 into it after multiplying.
[tex]: \: \implies \: \sf{ \dfrac{2 \times 8 \: + \: 6}{8}} \\ \\ : \: \implies \: \sf{ \dfrac{16 \: + \: 6}{8}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{22}{8}}}[/tex]
The temperature at a location was recorded for 5 days. The median temperature was 72
degrees. On four of the days, the temperatures were 67, 72, 77, and 52 degrees. Which of the
following is not a possible temperature for the fifth day?
83
79
80
70
Answer:
70
Step-by-step explanation:
First, put the values they gave you in order from least to greatest.
52 62, 72, 77
In order for the median to be 72, it has to be in the middle of the data set. Since there are 2 values on the left of 72, there must be 2 values on the right. The data set is also in order from least to greatest, so we know that the last value has to be over 72. Because it is placed to the right of 72. The only value of the options that isn't greater than 72 is 70.
The unlikely temperature of the fifith day is 70.
The The median of an observation is the number that is in the middle of a set of numbers arranged in ascending or descending order.
The median temperature is 72. So, it has to lie in the middle of the observation. Let the temperature of the fifth day be represented with x. The unknown temperature has to be greater than 72 because there are already two numbers less than 72.
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Nassim spends $15.00 on colored pencils, $10.00 on a sketchbook, $3.50 on erasers, and $4.95 on a colored pencil blender. He hands the clerk $35.00.
What could he receive in change?
Answer: 1.55
Step-by-step explanation:
In a classroom, 1 10 of the students are wearing blue shirts , and 2 5 are wearing white shirts. There are 20 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts
Answer:
10 students are wearing shirts other than blue or white.
Step-by-step explanation:
1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.
2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.
Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.
There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.
Please help !! As soon as possible
Answer:
32.9% i think
Step-by-step explanation:
please assist with helping in the image below!!
Find the missing length and area of each figure
LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd
Area = 2 × (1/2) × 6 × 8 = 48 yd²
Which method can you use to prove these triangles congruent?
Answer:
the hl theorem that says that if a leg and a hypotenuse of a right triangle are congruent to a leg and a hypotenuse of another right triangle, the two triangle are congruent
Step-by-step explanation:
The measures of the exterior angles of a triangle are 5x°, 7x°, and 8x°. Find the measure of the largest exterior angle.
Answer:144
Step-by-step explanation:
How do you find the sine cosine and tangent of an acute angle?
The sine , cosine and tangent of an acute angle can be find by using:
Sin θ = Opposite side/HypotenuseCos θ = Adjacent/HypotenuseTan θ = Opposite/AdjacentAcute Angle:
Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.
Sine of an Acute Angle :
The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.
Cosine:
Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.
Tangent:
The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).
So the formula for tan x is:
tan x = sin x/cos x
tan x = opposite side/adjacent side
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in a school, students either study french, german or spanish. They study one language each. 11 percent of students study french 27percent students study spanish. what fraction of the students study German
Answer:
62%
Step-by-step explanation:
First, you got the formulate: 1-27%-11%
Second, calculate the difference: 0.73-0.11
Third, the sum is 0.62
Then you multiply 0.62 ×100\100
Write a single fraction: 0.62×100\100
Calculate the product or quotient: 62\100
100% to a percentage: 62%
That is your answer 62%
help!!!! this is graded and no links!!!
Answer:
30
Step-by-step explanation:
Step 1: Find the area of the whole figure
The whole figure is a rectangle with a width of 4cm and a length of 12cm
The area of a rectangle can simply be calculated by multiplying the width by the length
So area = 4 * 12 which = 48
So the area of the whole figure is 48cm²
Step 2: Find the area of the non shaded area
The non shaded area forms a triangle with a base length of 9cm and a height of 4cm
The area of a triangle can be calculated using this formula
[tex]A=\frac{bh}{2}[/tex] where b = base length and h = height
That being said we plug in the values into the formula
[tex]A=\frac{9*4}{2} \\9*4=36\\\frac{36}{2} =18[/tex]
Hence the area of the non shaded region is 18cm²
Final step: Our last step is to subtract the area of the non shaded region by the area of the whole figure
so the answer = 48 - 18 which equals 30
Hence the area of the shaded region is 30 square centimeters.
PLEASE HELP W THE QUESTIONS IN IMAGE ILL GIVE BRAINLIEST
Answer:
53
Step-by-step explanation:
You spin a spinner with 4 sections numbered 1-4and then flip a coin. List all the possible outcomes with a tree diagram.
Answer:
/ heads
1
\ tails
/ heads
2
\ tails
/ heads
3
\ tails
/ heads
4
\ tails
A stack of 200 file folders is 5. 125 inches tall. A. Elena guesses that each file folder is 0. 035 inches thick. Explain how you know that Elena’s answer is not correct
To know whether Elena is correct or not, you need to find out the height of each stack of file folder.
Assume that all 200 files have the same height.
Let the height of each file folder be m inches.
So, by unitary method the height of each file folder would be,
m = Total height of stack / Number of file folders
here, the total height of stack = 5.125 inches
And the number of file folders = 200
So, m = 5.125 / 200
m = 0.0256 inches
But Elena guesses that each file folder is 0. 035 inches thick.
This means, Elena is wrong as the answer Elena gave is too large than the actual answer.
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Why are sine and cosine ratios always less than 1?
Answer:
Step-by-step explanation:
The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.
What is the x-intercept of the graph of y x2 4x 4?
The x-intercept of the graph of y = x² - 4x + 4 is x = 2.
By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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vvv Please help vvv
Find the value of x.
What is a log 10 transformation?
A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.
The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.
The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.
It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.
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A rectangular school banner has a length of 21 inches and a perimeter of 66 inches. A sign is made that is similar to the school banner and has a length of 7 inches. What is the perimeter of the sign?
The perimeter of the sign is 22 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular school banner has a length of 21 inches and a perimeter of 66 inches.
Let the perimeter of the sign for the length of 7 inches of the banner = x
So, By definition of proportion, we get;
⇒ 21 / 66 = 7 / x
Solve for x;
⇒ x = 7 × 66 / 21
⇒ x = 22
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Here is the histogram of a data distribution. All class widths are 1.
What is the median of the distribution?
A. 7
B. 4
C. 9
D. 5
Answer:
D) 5
Step-by-step explanation:
1,2,2,3,3,3,4,5,6,6,7,7,7,8,9
there are 15 data values so the 8th one is the median
Simplifying algebraic expressions
Answer:
-8
Step-by-step explanation:
7-6x+3x
You have to replace x for a 5.
7-6(5)+3(5)
After this you would multiple all of it.
7-30+15
Then add
7+15=22
-30+22=-8
Answer:
[tex] \sf \: 7 - 6x + 3x = - 8[/tex]
Step-by-step explanation:
Now we have to,
→ find the value of expression.
The expression is,
→ 7 - 6x + 3x
→ using (x = 5)
Let's solve the expression,
→ 7 - 6x + 3x
→ 7 - 6(5) + 3(5)
→ 7 - 30 + 15
→ 7 - 15
→ -8 => final answer
Hence, the answer is -8.
There arent any answers for this one online
Answer:
I believe it is 240 ft
Step-by-step explanation:
Please answer #6a and 6b
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
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slope intercept form of y + 6 = (x - 4)