Substitute the length of the sides (8in, 15 in, z) into the Pythagorean Theorem. Then, find the length of the missing side z.
Answers
The length of the missing side z would be 17 units which is determined by Pythagoras's theorem.
What is Pythagoras's theorem?A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
According to Pythagoras's theorem,
⇒ a² + b² = c²
Here, a = 8 b = 15 and c = z
⇒ (8)² + (15)² = z²
⇒ 64 + 225 = z²
Apply the addition operation,
⇒ 289 = z²
⇒ z² = 289
⇒ z = √289
⇒ z = 17
Therefore, the length of the missing side z would be 17 units.
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Related Questions
Question content area top
Part 1
Write the absolute value function as a piecewise-defined function with linear parts.
f(x)=4x+5
Answers
The absolute function f(x) = 4x+5 as a piecewise-defined function is:
f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
Given, the absolute function f(x) = 4x+5
The fundamental tenet of piecewise linear regression is that we should construct the regression function in "pieces" if the data exhibit various linear trends over various parts of the data. The components may or may not be joined.
when 4x+5 < 0
4x < -5
x < -5/4
f(x) = -(4x+5) = -4x-5
when 4x+5 ≥ 0
4x ≥ -5
x ≥ -5/4
f(x) = 4x+5
so f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
since, I x I = { -x , x<0
x , x ≥0}
Therefore, we get the required piecewise-defined function with linear parts.
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Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate.
What option gives possible rates and times for two of his jogs
Answers
5 mph for 2 hours and 4 mph for 3 hours
4 mph for 2.25 hours and 6 mph for 1.5 hours
gives possible rates and times for two of his jogs
1.Let's determine the relationship between the rate of jogging and the time f jog in each scenario.
First Rate = [tex]\frac{6}{1.5} =4[/tex] time = 1.5 hours
Second Rate = [tex]\frac{5}{1.25} = 4[/tex] time = 1.5 hours
As a result, in this instance, the duration of his runs does not appear to be inversely related to their intensity.
2.First Rate = [tex]\frac{5}{2} =2.25[/tex] time = 2 hours
Second Rate = [tex]\frac{4}{3} =1.33[/tex] time = 3 hours
Therefore, in this instance, the duration of his runs appears to be inversely related to his pace.
3.First Rate = [tex]\frac{4}{2.25}[/tex]=1.77 time = 2.25 hours
Second Rate = [tex]\frac{6.5}{1.5} =4[/tex] time = 1.5 hours
Therefore, in this instance, it appears that the duration of his runs is inversely related to his speed.
4.First Rate = [tex]\frac{4.5}{3}[/tex]=1.5 time = 3 hours
Second Rate =[tex]\frac{6}{4} =1.5[/tex] time = 4 hours
Therefore, in this instance, it does not appear that the length of time he runs is inversely related to the speed at which he runs.
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Refer to the figure below if m<2 = (a+15)
, and m<3=(a+35) find the value of a that :-P hi
Answers
The value of a that makes ∠2 and ∠3 perpendicular is 20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
From the image, HL is perpendicular to HJ, hence:
m∠2 + m∠3 = 90° (Definition of perpendicular)
Substituting gives:
(a + 15) + (a + 35) = 90
2a + 50 = 90
a = 20
value of a = 20
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Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Answers
The way she can use the number line to model the division is; Maria should start at 0 and then make “bounces” of 4 to the right until landing at 12. She will make 3 bounces of 4 because 12 divided by 4 is 3.
How to Model a Number Line?She is using a number line to model division, 12 ÷ 4 = 3
To carry out a division operation using a number line, follow the steps below:
Select the origin (point 0) as the starting pointIdentify the dividend and the divisorUse the divisor as the gap between 0 and subsequent consecutive numbersCount the number of gaps between 0 and the dividendFor the division operation 12 ÷ 4, Maria should:
Make 0 as the starting point on the number lineIdentify the dividend (12) and the divisor(4)Make the gap between 0 and subsequent numbers to be 4(the divisor)Therefore, the points on the number line will be 0, 4, 8, and 12
Count the number of gaps between these points
That is, 0 to 4, 4 to 8, and 8 to 12.
Since there are three gaps between 0 and 12 on the number line, using a gap difference of 4, then 12 ÷ 4 = 3
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Use the four-step procedure for solving the following variation problem
The height that a ball bounces varies directly as the height from which it was dropped. A tennis ball dropped from 14 inches bounces 8.4 inches. From what height was the tennis ball dropped if it bounces
42 inches?
The tennis ball needs to be dropped from the height of
(Type an integer or a decimal)
so that it bounces 42 inches.
9
Answers
Height was the tennis ball dropped if it bounces 42 inches is 0.7 inch.
What do you understand by direct proportionality?
If two quantities are directly proportional, it means that when one quantity increases at a certain rate, the other quantity also increases at the same rate up to a constant value. It is represented by the proportional symbol ∝.
Let the height of the ball bounces be h
The height of the ball drobbed from be y
It is given that the height that a ball bounces varies directly as the height from which it was dropped.
⇒ h ∝ y
⇒ h = ky where k is the constant of proportionality.
It is given that a tennis ball dropped from 14 inches.
⇒ y = 14 inches
Tennis ball bounces back to 8.4 inches.
⇒ h = 8.4 inches
⇒ 8.4 = k × 14
⇒ k = 8.4/14 = 0.6
Now, tennis ball dropped from 42 inches
y = 42
⇒ h = 42 × 0.6 = 0.7
Therefore, height was the tennis ball dropped if it bounces
42 inches is 0.7 inch.
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While the flight some humming birds can flap Thor wings about 500 times in 10 seconds. At this speed how many times might a hummingbird flap it wings in 60 seconds complete the table
Answers
Answer:
I don't see a table :/
Step-by-step explanation:
if a humming bird flaps his/her wings 500 times in 10 seconds you just have to do 500 x 6
humming birds flap their wings about 3000 times per minute
answer: 3,000
"Don't have a good day, have a great day"
-Guy
Which two situations result in a solution of 0?
Responses
On Tuesday morning, the temperature outside is −5∘F. On Tuesday night, the temperature outside is 5∘F. How much does the temperature change from Tuesday morning to Tuesday night?
On Tuesday morning, the temperature outside is − − 5 ∘ ∘ F. On Tuesday night, the temperature outside is 5 ∘ ∘ F. How much does the temperature change from Tuesday morning to Tuesday night?
On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
On Friday morning, a student earns $ 35 mowing lawns. On Friday night, the student spends the $ 35 while out with friends. How much of the money that the student earns from mowing lawns is left?
A vacationer goes scuba diving and is at a depth of −30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A vacationer goes scuba diving and is at a depth of − − 30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
A student owes a friend $ 7.50 . If the student pays the friend $ 7.50 , how much does the student owe the friend?
Answers
The two situations which would result in a solution of 0 include the following:
B. On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
D. A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
For this exercise, the expression which represents the first situation is given by:
Amount of money left = $35 - $35
Amount of money left = 0
For this exercise, the expression which represents the second situation is given by:
Amount of money owed = $7.50 - $7.50
Amount of money owed = 0.
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show which of the following polygons are similar, write the similar polygons in order of their corresponding vertices and determine the scale factor of similarity
Answers
Answer:
see explanation
Step-by-step explanation:
starting with the polygon on the left at vertex Z ( marked with x ) and going clockwise.
Similarly polygon on right starting with vertex D ( marked with x ) and going clockwise.
ZLXY ≅ DABC
the scale factor of ZLXY → DABC
is the ratio of corresponding sides
scale factor = [tex]\frac{DA}{ZL}[/tex] = [tex]\frac{9}{7.2}[/tex] = [tex]\frac{5}{4}[/tex]
A physics student walks 100 meters in 80 seconds. The student stops for 30 seconds, and then walks 200 meters farther in 90 seconds. What is the average speed of the entire walk?.
Answers
The average speed of the student for his entire walk is equal to 1.5 m/s. Therefore, option (b) is correct.
What is the average speed?
The average speed of a body is calculated as the total distance traveled in a fixed interval of time. The average speed can be determined by dividing the total distance traveled by a body by the total time.
The average velocity is a single value if the object moves uniformly. Speed is a scalar quantity, it has no specified direction. The average speed has the S.I. unit the same as velocity i.e. m/s.
Given the distance covered by a student in first 80 sec = 100m
After stooping for 30sec again cover a distance of 200m in 90sec.
The total distance traveled by the student = 100 + 200 = 300m
The time taken by student to cover distance = 80 + 30 +90 = 200 sec
The average speed of the student = total distance/ total time taken
= 300/200 = 1.5 m/s
Therefore, the average speed of the student is equal to 1.5m/s.
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Find hcf
a) x³-1, x^4 + x² + 1, x³ + 2x² + 2x + 1
Answers
Answer:
Hope the picture will help you
Triangle STU with vertices S(- 1, - 6); T(0, - 3) and U(3, - 4) in the line y = - x
Answers
Triangle STU have vertices S'(6,1); T'(3,0) and U'(4,-3) after reflection across y = -x.
The triangles is reflected across the line y = -x.
If any point A(a,b) is reflected across y = -x then the coordinates of x and y axes will be interchanged and the coordinates will become negative,
So the reflected point A' will be (-a,-b).
So, after reflection,
S(-1,-6) will become S'(6,1) after reflection across y = -x.
T(0,-3) will become T'(3,0) after reflection across y = -x.
U(3,-4) will become U'(4,-3) after reflection across y = -x.
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If f(x) = 1/x which equation describes the graphed function? Apex ...
Answers
1) horizontal translation 2 units left (x+2)
2) vertical translation 1 unit down (-1)
The equation that describes the graphed function [tex]f(x) = \frac{1}{x}[/tex] is option A:[tex]y = (x + 2) - 1.[/tex] This is shown in the graph given below, and transformation is translation.
To mathematically derive this equation, start with the original function [tex]f(x) = \frac{1}{x}[/tex].
The given function [tex]f(x) = \frac{1}{x}[/tex] has a reciprocal relationship between x and y.
To perform a horizontal translation 2 units left, substitute (x + 2) for x. This gives:[tex]f(x + 2) = \frac{1}{x + 2}[/tex].
Next, to achieve a vertical translation 1 unit down, subtract 1 from the function.
Thus, [tex]f(x + 2) - 1 = \frac{1}{x + 2}- 1[/tex].
Simplifying further, combine the terms gives:
[tex]y = (x + 2) - 1.[/tex]
This equation represents the original function :
[tex]f(x) = \frac{1}{x}[/tex]
After a horizontal translation of 2 units left and a vertical translation of 1 unit down.
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Need answer now!! Pls help! Will give brainliest to the best/correct answer! 40 points
A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?
A. The line represents a direct variation because -4/3 = 4/3.
B. The line represents a direct variation because it is horizontal.
C. The line does not represent a direct variation because it does not go through the origin.
D. The lines does not represent a direct variation because -4 (3) ≠ 4 (3).
Answers
Answer:
Answer: The line does not represent a direct variation because it does not go through the origin.
Determine the total surface area of the composite shape below
Answers
Answer:
118.558 cm^2
Step-by-step explanation:
Ok, a rectangular cube and a Cylinder.
Let's start with the rectangular cube.
SA= 2(lw + lh + wh)
total surface area = 94 cm^2
Now the Surface Area of the of the Cone.
A=2πrh+2πr^2
A=2πrh+2πr^2=2·π·1·5+2·π·1^2≈37.69911 cm^2
Since the cone is standing on top of the rectangular cube, we need to deduct just the area of the circle.
A=πr2=π·12≈3.14159 cm^2
So, 84 cm^2 + 37.69911 cm^2 - 3.14159 cm^2
Sum the quantities:
84 cm^2 + 37.6991 cm^2 - 3.14159 cm^2
Sum the numbers 84 + 37.7 - 3.142 = 118.558:
Answer: 118.558 cm^2
Algebraic Expression
a is 7 times less than b.
Answers
[tex]7a = b[/tex]
THIS SIMPLY MEANS THAT TO ATTAIN b we have to multiply a by 7.
Question
What numbers are a distance of 23 unit from 12 on a number lineQuestion
What numbers are a distance of 23 unit from 12 on a number line
Answers
The number which is at a distance of 23 unit from 12 on a number line is 11.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
Now, we can determine the distance as follows:
Distance = 23 - 12
Distance = 11.
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What is the quotient of (x³ - 3x² + 5x − 3)÷(x - 1)? x² - 2x - 3
x² + 2x + 7
x² - 3x + 8
x² - 2x + 3
Answers
Select the correct answer.
What is the effect on the graph of f(x)
The au
=
when the function is changed to g(x) = |(x - 1)|?
Answers
Function transformation: Function transformation is the process of changing one function into another.
The f(x) graph will be shifted 1 unit down in the vertical direction.
How to do this function sum?Function transformation: Function transformation is the process of changing one function into another.
changing a function's form from one to another
Transformational rule
The function will move 'a' units higher when f(x)->f(x)+a is used.
f(x)-> f(x)-a The action is going to be 'a' units down.
The function will be relocated 'a' units left if f(x)->f(x+a).
The function will be relocated 'a' units right if f(x)->f(x-a).
The fundamental job is [tex]f(x)=\frac{1}{x}[/tex]
F(x)-1 is used in place of f(x).
It indicates that the graph of f(x) will shift down by one unit.
A unit down will be added to the vertical translation of the f(x) graph.
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help me I can't solve this question
Answers
The constant of proportionality of the given function of the graph would be 3 / 4.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
Let the equation below which is shown in the graph:
y = kx ....(i)
where k is the constant of proportionality.
As per the given graph, take a point x = 4, and y = 3
Substitute the values x = 4, and y = 3 in the equation (i)
3 = k × (4)
4k = 3
k = 3 / 4
Thus, the constant of proportionality of the given function of the graph would be 3 / 4.
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Which statement cannot be assumed based on the diagram?
A) <GBE and <DBC are adjacent
B) <DBC is vertical to <FDE
C) <EDF and <EDC are adjacent
D) <ABG and <GBD are adjacent.
Answers
The statement that cannot be assumed based on the figure is that
<DBC is vertical to <FDE. This makes option B the answer.
Why < DBC is vertical to < FDE cannot be assumed in the given figureThe given data consist of various intersections and line types however the line type used to vertical angles are not among.
The line type responsible for vertical angles or used for vertical angle theorem is the parallel lines and a transversal line. This two lines are used together to prove or get angles that are vertical
We can therefore conclude that <DBC is vertical to <FDE is the the correct option
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Write and solve an equation to solve the problem. lisa is 4 centimeters taller than her friend lan. lan is 8 centimeters taller than jim. every month, their heights increase by 2 centimeters. in 4 months, the sum of lan's and jim's heights will be 170 centimeters more than lisa's height. how tall is lan now? let h be lan's height today in centimeters.
Answers
After solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.
As given ,
Let h be Lan's height today in centimeters.
As per the relation between Lan, Lisa and Jim height we have,
Lan=h cm
Lisa=h + 4
Jim=h -8
After 4 months, every month their heights increase by 2 cm
Lan=h + 8
Lisa=h + 4 +8
Jim=h -8 +8
Required equation for given condition:
Lan + Jim=170 +Lisa
⇒h +8 + h -8 + 8=170 + h + 4+8
⇒2h+8=h+182
⇒h=174cm
Therefore, after solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.
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Need help on question 5 please ASAP I’m going to really appreciate it
Answers
Answer:
x+7
Step-by-step explanation:
to shift the function up, you need to add -4x by 4
and to shift the function to the left you need to add 1 by 6
Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has 120 stamps. Lona joined a stamp club, which sends her 12 new stamps each month. The stamp book holds a maximum of 500 stamps. a. Complete the table at right. b. How many stamps will Lona have in one year from now?zetb c. Write an equation using function notation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by t(n). Month Stamps
0, 120
1 ,132
2
3
4
5
Answers
Using a linear function, it is found that:
a. The table is completed as follows: Month 2, Stamps 144; Month 3, Stamps 156; Month 4, Stamps 168; Month 5, Stamps 180.
b. She will have 264 stamps after one year.
c. The function is given by: t(n) = 120 + 12n.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the function in this problem, we have that:
The intercept is of 120, as the initial value is of 120 stamps.The slope is of 12, as 12 stamps are added each month to the collection.Hence the function is given by:
t(n) = 120 + 12n.
To complete the table, we find the numeric values are follows:
t = 2, t(2) = 120 + 12(2) = 144.t = 3, t(3) = 120 + 12(3) = 156.t = 4, t(4) = 120 + 12(4) = 168.t = 5, t(5) = 120 + 12(5) = 180.One year from now is 12 months, hence:
t(12) = 120 + 12(12) = 264.
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solve the following equation 2x=12
Answers
2
x
=
12
Step 1: Divide both sides by 2.
2
x
2
=
12
2
x
=
6
Answer:
x
=
6
Kareem caught a 4 3/4 pound fish. How much did it weigh in ounces?
Answers
Answer:
76 ounces as ( 1 lb = 16 oz ) 4 3/4 * 16 = 76
Step-by-step explanation:
4 3/4 pounds = 76 ounces or 4 3/4 pounds = 2.15456376 kilograms
The number m and 58 are additive inverses. Drag and drop 58 and m to their correct positions on the number line.
Answers
The value of m which is an additive inverse of 58 is -58.
What numbers are additive inverses?Additive inverse is what you add to a number to make the sum zero. When two numbers are added together to get 0, then we say both the numbers are additive inverses of each other.
Since m is the additive inverse of 58, hence:
m + 58 = 0m = -58
The additive inverse of 58 is -58.
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Justin earns $13.9 per hour at the Rite Aid Pharmacy. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 50 hours. What was his gross pay for the week?
Answers
Based on the amount earned by Justin per hour, and the overtime work rate, Justin's gross pay for the week is $764.50
How to find the gross pay?First, find the amount that Justin earns from Rite Aid Pharmacy for his regular work:
= Number of hours in regular week x Pay per week
= 40 x 13.9
= $556
The overtime hours was:
= 50 - 40
= 10 hours
The overtime pay is:
= 10 x 13.9 x 1.5
= $208.50
The total gross pay for the week is:
= 556 + 208.50
= $764.50
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-3b (2y3 +5y) - 6y3b
Answers
Answer:
-15by
Step-by-step explanation:
distribute
rearrange terms
Find measure of angle g rounded to the nearest degree
Answers
We need to know about trigonometry to solve this problem. The measure of angle G is 27.9°
Trigonometry is related to functions of angles and their applications. There are six main functions of an angle, sine, cosine, secant,cosecant,tangent and cotangent. Here in this question we know the measure of all the sides of the triangle, and the angle T is 90°. We will be using the function tangent(tan) to solve for angle G. The base of the triangle is RG and the height is TR.
RG=8 TR=15
tan G=base/height=RG/TR=8/15=0.533
G=[tex]tan^{-1}[/tex] 0.53=27.9°
Therefore the measure of the angle G is 27.9°.
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c(x) = 0.08x + 9.75
please answer
Answers
Step-by-step explanation:
I hope this will be helpful for you.