The height of the school is 8.5 m.
For a project in his Geometry class, Jacob uses a mirror on the ground to measure the height of his school building.
To find out how tall is the school:
An image is always formed at the back of a mirror. Thus, the appropriate option is -8.75 m. The flagpole is 8.75 m tall.
Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{1.65}{1.7}[/tex]
Tan θ = 0.9706
θ = [tex]Tan^{-1} 0.9706[/tex]
= [tex]44.2^{o}[/tex]
θ = [tex]44.2^{o}[/tex]
Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{h}{8.75}[/tex]
0.9706 = [tex]\frac{h}{8.75}[/tex]
h = 0.9706 x 8.75
= 8.49275
h = 8.5 m
Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.
Hence the answer is the height of the school is 8.5 m.
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Choose the equation that represents the graph shown
Answer:
[tex]y=|x|-4[/tex]
Step-by-step explanation:
The vertex of the graph is at (4, 0).
This eliminates all of the options except for [tex]y=|x|-4[/tex].
In the following figure, AD is the bisector of ZBAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that AAEG = AAFG by the AAS congruence postulate. Do you agree or disagree? Explain.
I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent
The AAS have it that the two triangles being compared should have their two angles and the side not included being equal
The Angle - Angle - Side = AAS, here include
< FA,G - < AFG - AG
< EAG - < AEG - AG
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There are 100 items in a garage sale. 30% of the items are sold during the first hour of the sale. If 10 items are sold during the second hour, what percent of the items have not been sold?
The percentage of items that have not been sold is: 60%
In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.
Percent in itself stands for out of 100.
Let the total number of items= i
Let the percentage be represented as= p
Then,
i=100 (Given in the question)
Let the number of items sold in the first hour be= a
Let the number of items sold in the second-hour be= b
Since,
p= Given Value/Total value x100
thus,
a/100x100=30%
The hundreds cancel out.
Thus, a=30 -(i)
The number of items sold in the second hour= b
b=10 (provided in the question) -(ii)
Let the total number of items sold be=T
The total number of items sold= a+b
From (i) and (ii)
Total number of items sold=30+10
Thus,
Total number of items sold=40 -(iii)
Number of items that have not been sold(n)=100-(a+b)
=100-T
= 100-40
From (iii)
n = 60 -(iv)
Then,
Percentage of items that have not been sold = n/100x100
From -(iv)
= 60/100x100
Canceling hundred by hundred
= 60%
Thus,
Answer: The percentage of items that have not been sold is: 60%
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a coin is flipped eight times. each result is either a heads or a tails. how many possible outcomes contain at least 33 tails ?
The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.
The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:
[tex]\frac{8!}{3!5!} + \frac{8!}{4!4!} + \frac{8!}{5!3!} + \frac{8!}{6!2!} + \frac{8!}{7!1!} + \frac{8!}{8!0!}[/tex]56 + 70 + 56 + 28 + 8 + 1= 219Hence, the possible outcomes that contain at least three tails are 219.
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Type the missing number to complete the proportion.
18 orders in 2 days = 9 orders in
days
Answer:
18 orders in 2 days 9 orders in 1 day
Answer:
Step-by-step explanation:
9x2=18 which is 2 days so 9x1= 9 which is one day
Math help needed (grade 9)
Step-by-step explanation:
volume = base area × height
= (1/2×12×16)×10
=960cm3
surface area:
1. triangle area = 1/2×12×16=96cm2
2.bottom area = 12×10=120cm2
3.side area = 16×10=160cm2
4.slope area = 10×20=200cm2
5.add everything and remember you have two triangle
surface area= 96×2+120+160+200 =672cm2
order the sides DEF from shortest to longest
From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.
Triangle:
The polygon with three edges known as sides and three vertices are known as triangle.
Given,
Here we have the triangle with their corresponding angle.
Now, we have to order the sides from shortest to longest.
Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.
By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.
In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.
From values, the shortest to longest the order is written as DE, DF and EF.
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A student was asked to name all values of n that make the relation a function. Correct the error.
{(2,8), (6,0), (4,2), (2n,n)}
n can be any value except 2,6, or 4
The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.
The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.
The known elements of the set A in the question are; 2, 6, and 4
The elements of the set A are known as the domain of the function.
The known element of the set B are 8, 0, and 2
The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)
To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4
Therefore;
n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2
The correct statement is therefore;
n can be any value except 1, 3, or 2
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the population of a city increases by 4,000 people each year. in 2005 the population is projected to be 450,000 people. what is an equation that gives the city's population p (in thousands of people) x years after 2010
Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
As given in the question,
Let 'p' represent the population in thousands of people.
Let x represents the number of years.
Population projected in 2005 = 450,000 people
= 450 ( in thousand people)
Population increases by 4000 people each year that is equal to 4 (in thousand of people)
Required equation to represent the population in x years ( in thousand of people ) is given by:
p = 4x + 450
Population in 2010 is equal to :
p = 4 ( 2010 - 2005) + 450
= 4(5) + 450
= 20 + 450
= 470 ( in thousand of people)
= 470,000 people
Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
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A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If ( x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.
Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:
(x, y) → (SFx, SFy) = (0.4x, 0.4y)
Where:
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Complete Question:
A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
answer choices
(0.4x, 0.4y)
(x + 20, y + 20)
(x + 0.4, y + 0.4)
(20x, 20y)
what is (2 x 10 to the power of 5) divided by (4 x 10 to the power of 2)
there is a line whose slope is 1 and whose y-intercept is -9, what is its equation in slope-intercept form?
a multiple choice test consists of six questions, each of which has five choices. each question has exactly one correct answer. william guesses randomly at each answer. what is the probability that he gets four or fewer questions correct? (round your answer to four decimal places.)
The probability that he gets four or fewer questions correct is 0.9984
Let p be probability of getting correct answer and q be probability of getting in correct answer.
Number of trails : n = 6
Number of Successes : x = 4
By using binominal distribution ,
P(x≤4) = 1 - P(x>4)
= 1 - [P(x = 5) + P(x = 6)]
= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]
solving combination ,
= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]
= 1 - (24 + 1 / 625)
= 1 - 25 / 625
= 624/625 = 0.9984
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Select the type of cross section formed when a triangular pyramid is cut parallel to its
base.
Please help pleaseee
According to the Pythagoras theorem, the value of x is 13.76
Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.
Given,
Here we have the triangle with the side values.
Now, we have to find the value of x through this given values.
In order to calculate the value of x,
First, we need the value of the side KM.
Let us consider the value of KM is y.
Then according to the concept of Pythagoras theorem,
The value of y is calculated as,
=> (12.3)² = y² + (5.4)²
=> 151.29 = y² + 29.16
=> y² = 122.13
=> y = 11.05
Therefore, the value of the hypotenuse x is calculated as,
=> x² = (11.05)² + (8.2)²
=> x² = 122.13 + 67.24
=> x² = 189.37
=> x = 13.76
Therefore, the value of x is 13.76.
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pls give answer pls pls
Answer:
k = 13
Hope this helps : )
Step-by-step explanation:
To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.
1. Divide 7 on both sides of the equal sign.
7k = 91
7 7
2. Answer.
The 7 cancels out so we are left with k = 13 since
91 ÷ 7 = 13
k = 13
3. Check.
Plug in the variable "k."
7(13) = 91
91 = 91 ✓
If you roll a die three times, how many different sequences are possible? a. 6 cubed = 216 b. 3 superscript 6 baseline = 216 c. 3 superscript 6 baseline = 729 d. 6 cubed = 729
Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex] =216
What is outcome of an event?
Suppose an event is happening. The result of the event is called outcome of the event.
For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die
Number of outcomes of rolling a die first time = 6
Number of outcomes of rolling the die second time = 6
Number of outcomes in rolling a die third time = 6
Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]
= [tex]6^3[/tex]
= 216
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A line passes through the point
(8, 7) and has a slope of 4
Write an equation in slope-intercept form for this line.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 4}(x-\stackrel{x_1}{8}) \\\\\\ y-7=4x-32\implies {\Large \begin{array}{llll} y=4x-25 \end{array}}[/tex]
Answer:
y = 4x -25
Step-by-step explanation:
y = 4x + b
we must find the y intercept
plug in the point
7 = 4(8) + b
7 = 32 + b
subtract 32 from both sides
-25 = b
the y intercept is -25
plug in -25 for b
y = 4x - 25
Evaluate the expression for the given value of the variable. 52+1/5(-1/2)
The simplified form of the expression 52 + 1/5(-1/2) is [tex]\frac{519}{10}[/tex]
What is a fraction?A fraction is a ratio of two integers.
The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.
52 + 1/5(-1/2)
Multiply out the fraction
we have
52 + (-1/10)
52 - 1/10
to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes
520/10 - 1/10
simplifying the numerator we have,
[tex]\frac{520 - 1}{10}[/tex] = [tex]\frac{519}{10}[/tex]
In conclusion the solution to 52+1/5(-1/2) is [tex]\frac{519}{10}[/tex]
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A rectangle is 25 cm on one side and 6 cm on another side. What is the perimeter?
Answer:
31
Step-by-step explanation:
about 310 000 t of atlantic cod were caught in 1991. in 2001 the mass of the cod caught was 87% less. HOw much cod was caught in 2001
Number of Atlantic cods caught in the year 2001 is; 40300 t
How to solve percentage word problems?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;
Percentage = (value / total value) * 100%
Now, we are told that;
Number of Atlantic cods caught in 1991 = 310000 t
We are told that in the year 2001, there were 87% less caught. Thus;
Number by which it was reduced = 310000 * 87% = 269700
Thus;
Number of Atlantic cods caught in the year 2001 = 310000 - 269700
Number of Atlantic cods caught in the year 2001 = 40300 t
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Solve the equation or formula for the variable indicated.
X-2y=1
Answer:
Step-by-step explanation:
-2y = -x -1
2y = x+1
y = 1/2x+1/2
Pls help me thank you
The value of y is x/2 + c/5
Given,
In the question:
5x - 7y = 3y - 2c
To find the value of y.
Now, According to the question:
The equation is given as:
5x - 7y = 3y - 2c
Combine the like terms:
-7y - 3y = -5x - 2c
Calculate the sum or difference:
-10y = -5x - 2c
y = -5x/-10 - 2c/-10
Calculate the product or quotient :
y = x/2 + c/5
Hence, The value of y is x/2 + c/5
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wilma can mow a lawn in 120 minutes. vanessa can mow the same lawn in 80 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
Working together, they can mow the yard in 48 minutes.
Given data;
A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?
Let 't' is their time in minutes working together.
Add their rates of working to get their rate working together,
Wilma's rate: [ 1 lawn ] / [ 120 min ]
Vanessa's rate: [ 1 lawn ] / [ 80 min ]
Rate working together: [ 1 lawn ] / [ t min ]
1/120 + 1/80 = 1/t
Multiply both sides by 240t;
2t + 3t = 240
5t = 240
t = 48
It takes them 48 min to mow the lawn working together.
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Please help me Find the slope of the line
Answer:
Step-by-step explanation:
d- down four then right three
necesito saber como se resuelve
La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.
¿Cómo resolver un ecuación exponencial?
Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.
Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:
f(x) = 9ˣ⁺¹ - 28.3ˣ - 3
g(x) = 0
La solución es todo punto tal que f(x) = g(x).
A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.
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Which description matches the graph of the inequality y <|x-2| + 1
A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
What is inequality?
Inequality is a relationship between two expressions or values that is not equal to each other.
This inequality may be written in two ways:
(a) y < x - 2 + 1
or
y < x - 1
(b) y < -x +2 + 1
or
y < -x + 3
A graph of the inequality is shown below. The shaded region satisfies the inequality.
Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
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4) A pizza shop sells pizzas that are 12 inches (in diameter) or larger. A 12 inch cheese pizza costs $9. Each additional inch costs $1.75, and each additional topping costs $0.50. Write an equation that represents the cost of a pizza. Be ure to specify what the variables represent.
The equation to represent the cost is C = 8 + 1.50x + 0.75y.
To write an equation that represents the cost of a pizza.
An equation that represents the cost of a pizza will be
C = 9 + 1.75x + 0.50y
Fixed cost = $9
Cost of additional inch = 1.75x
Cost of additional topping = 0.50y
Total cost (C) will then be:
= 9 + (1.75 × x) + (0.50 × y)
C = 9 + 1.75x + 0.50y
Hence the answer is, the equation to represent the cost is C = 8 + 1.50x + 0.75y.
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(3s+2f=18)
(2s+3f=15.75)
Answer:
(s, f) = (4.5, 2.25)
Step-by-step explanation:
You want the solution to the simultaneous equations ...
3s+2f = 182s+3f = 15.75SolutionWriting these in general form, we have ...
3s +2f -18 = 0
2s +3f -15.75 = 0
Using the "cross-multiplication method" for solution, we find ...
∆1 = (3)(3) -(2)(2) = 5
∆2 = (2)(-15.75) -(3)(-18) = 22.5
∆3 = (-18)(2) -(-15.75)(3) = 11.25
s = ∆2/∆1 = 22.5/5 = 4.5
f = ∆3/∆1 = 11.25/5 = 2.25
The solution is (s, f) = (4.5, 2.25).
__
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A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. What is the length of the third side of the triangle?
x + 13
2x + 13
5x − 5
12x + 3
The length of the third side of the triangle is 2x+13.
According to the question,
We have the following information:
A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.
We know that perimeter of triangle is the sum of all three sides of triangle.
Let's take its third side to be y.
So, we have the following expression:
3x+2x-5+y = 7x+8
5x-5+y = 7x+8
Adding 5 on both the sides:
5x+y = 7x+8+5
5x+y = 7x+13
Subtracting 5x from both the sides:
y = 7x-5x+13
y = 2x+13
Hence, the correct option is B.
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Answer:
B. 2x+13
Step-by-step explanation:
I got it right on the test