Answers
The value of "x" in the given figure and question is 20 units.
As per the question statement, We are given a figure in which we are supposed to find the value of x.
Before solving the question, if we observe the figure, we can conclude that this question will include the concepts of right angled triangle or specifically Pythagoras Theorem, which states that
[tex]Perpendicular^{2} + base^{2} = hypotenuse^{2}[/tex] where perpendicular, base and hypotenuse are the three sides of the right angled triangle.
In Triangle RTQ
using Pythagoras Theorem
[tex]RQ^{2} = TQ^{2} +TR^{2} \\RQ=x\\x^{2} = 16^{2} + TR^{2} \\TR^{2} = x^{2} -16^{2}[/tex]
Now considering triangle SRT
using Pythagoras Theorem
[tex]SR^{2} = RT^{2} + ST^{2} \\SR^{2} = (x^{2} -16^{2}) +9^{2}\\[/tex]
Now considering triangle RSQ
using Pythagoras Theorem
[tex]SQ^{2} = SR^{2} +RQ^{2} \\(9+16)^{2} = SR^{2} + RQ^{2} \\(9+16)^{2} = x^{2} -7^{2}+x^{2} \\ (9+16)^{2} =2x^{2} -7^{2} \\25^{2}+7^{2} = 2x^{2}[/tex]
[tex]2x^{2} =674[/tex]
[tex]x^{2} =337\\x=\sqrt{337} \\x=18.357[/tex]
Therefore x = 18.357 approx 20 units.
Pythagoras Theorem: The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.To learn more about Pythagoras Theorem, click on the link given below:
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Related Questions
are this functions
i don’t know so i asked
Answers
Answer:
1 is a function
2 and 3 is not
Step-by-step explanation:
the first one doesn't have anything repeating but 2 and 3 both do
Answer:
1. Yes, it's a function.
2. No, it's not a function.
3. No, it's not a function.
Step-by-step explanation:
A function is a relation in which each element of the domain (input) corresponds with exactly one element of the range (output).
Hope this helps.
What is the product of −2 1/4 and −4 1/2?
Answers
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Answers
The height of the base and the perimeter length are respectively; 12 cm and 840 cm
How to find the volume of a Prism?
We are told that;
Volume of Triangular Prism = 1200 m³
Base length = 10 cm
Side length of triangle = 13
Length of box = 20
Now, formula for volume of a triangular prism is;
V = ¹/₄h√(-a⁴ + 2(ab)² + 2(ac)² - b⁴ + 2(bc)² - c⁴)
where;
a is side length of triangle
b is base side length
c is also side length of other triangle
h is length of box
Thus;
Using Pythagoras theorem, we can find the height of the base as;
D = √(13² - 5²)
D = √144
D = 12 cm
B) Formula for perimeter length of triangular prism is;
P = (S1 + S2 + S3)L + BH
P = (13 + 13 + 10)20 + 10(12)
P = 720 + 120
P = 840 cm
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Janelle won 27 tickets at the fair. She traded the tickets for 9 prizes. Each prize was worth the same number of tickets was each prize worth?
Answers
Answer:
3
Step-by-step explanation:
27 tickets = 9 prizes
Since they are all equal, it would be 27 divided by 9 = 3
What’s 8(x + 4) =32? Full answer please
Answers
Answer:
x = 0
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x8(x + 4) = 32 Distribute by multiplying 8 to x and 48(x) + 8(4) = 328x + 32 = 32 Subtract 32 from both sides8x = 0 Divide by 8 on both sidesx = 0The value of x should be 0, as any number multiplied by 0 is 0.
Toby found their mean was \bar x=7
x
ˉ
=7x, with, \bar, on top, equals, 7 years. He thinks the standard deviation is
Answers
The standard deviation is approximately 1.825
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be near to the established mean, whereas a large standard deviation shows that the values are distributed throughout a broader range.
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is equal to the square root of that variable's variance. It is more algebraically straightforward than the average absolute deviation, but being less reliable in actual use.
The standard deviation is calculated by the formula :
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
where N= n-1(n=size of sample) , [tex]\mu[/tex]= mean of the data , [tex]x_i[/tex]= each data value.
Now the given data for the question are {6,5,9,8}
mean of the data ([tex]\mu[/tex])=(6+5+9+8)÷4=28÷4=7
Standard deviation:
[tex]{\displaystyle \sigma ={\sqrt{{\frac {(6-7 )^{2}+(5-7 )^{2}+(9-7 )^{2}+(8-7 )^{2}}{N}}}}[/tex]
[tex]{\displaystyle \sigma ={\sqrt{{\frac {(-1 )^{2}+(-2)^{2}+(2)^{2}+(1 )^{2}}{N}}}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{\frac{1+4+4+1}{4-1}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{\frac{10}{3}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{1.333}[/tex]
[tex]{\displaystyle \sigma =1.825[/tex]
The standard deviation is approximately 1.825.
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find a sequence of rigid motions to take each vertex of triangle ABC onto the corresponding vertex of triangle A’B’C’
Answers
Using translation concepts, the sequence of rigid motions to take each vertex of triangle ABC onto the corresponding vertex of triangle A’B’C' are:
Rotation over a vertical line.Shift down and right.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For the motions in this problem, we have that:
There was a rotation over a vertical line, due to the changes in the orientation of A and C.Then, only the position changed, not the orientation, meaning that there was a shift down and right.More can be learned about translations at https://brainly.com/question/4521517
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
2m+4 is the answer
Step-by-step explanation:
Khadija asked Muhammad, "How many text messages have you sent today?" Is this a statistical question?
Answers
regina has five brothers who are 4, 6, 6, 9, and 15 years of age. the mean age of regina's brothers is .
Answers
The calculated mean age of Regina's brothers is 7. This is being attained by using the concept of measure of central tendency i.e. mean.
What is a mean?
Mean is interpreted as the total of all values divided by the total number of values. It is also called a mathematical average. There are three types of mean namely, arithmetic, geometric and harmonic mean.
Calculation of the mean age of Regina's brothers
Total number of Regina's brothers = 5
Sum of their ages = 4 + 6 + 6 + 9 + 10
= 35
Mean age = sum of their ages / total number
= 35 / 5
= 7
Hence, the calculated mean ages of Regina's brothers is 7
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Eli, Freda and Geoff were given 800 pounds to share in the ratio of there age. Eli is 9 years old Freda is 13 years old and Geoff is 18 years old. How much should they each have?
Answers
I NEED HELP WITH THIS ANSWER ASAP!!!!!!
A sequence is defined by the formula U(subscript 1)=4/27, u(subscript n+1)=3 x u(subscript n), n>1.
A) Show the sequence is geometric and find the common ratio
Answers
From the recursive definition, the next term of a sequence is the previous term multiplied by 3, hence it is a geometric sequence with a common ratio of 3.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The recursive definition of a geometric sequence is:
[tex]a_{n+1} = qa_n[/tex]
In this problem, the sequence is given by:
[tex]u_{n+1} = 3u_n[/tex]
With first term [tex]u_1 = \frac{4}{27}[/tex].
Hence it is a geometric sequence with a common ratio of 3.
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An equilateral triangle with side length 13 cm is shown in the diagram, work out the height of the triangle. Give your answer rounded to 1 DP.
Answers
the answer to the given question is 11.3 cm
A triangle having equally length sides is referred to as an equilateral triangle in geometry.The measurements of the three opposite angles are equal because the three sides are congruent.It is also referred to as a triangle that is comparable since each measured angle is 60 degrees. Equilateral triangles have formulas for their area, perimeter, and height just like other triangles do.Equal on all three sides. The sum of the three congruent angles is 60 degrees. It is a three-sided, equilateral polygon.Side = 13 cm
Height of triangle = root3/2 * 13
= 11.25 cm
Therefore, the Height of the triangle is 11.3 cm
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if the length of a rectangular field is 2 feet less than four times its width, and the perimeter is 106 feet.
Answers
The length and width of the rectangle are: 42 feet and 11 feet.
What is a rectangle?Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Given:
Perimeter of the rectangular field = 106 feetLength of the field is 2 feet less than 4 times the width.To find: the length and width of the rectangular field.
Finding:
Let the width of the rectangular field be 'x'
Then the length of the field = 4x - 2
Perimeter of rectangle = 2 (width + length)
=> 106 = 2 ( x + 4x -2)
=> 53 = 5x - 2
=> 55 = 5x
=> 11 = x, i.e., the width of the field = 11 feet
The length of the field = 11(4) - 2 = 42 feet.
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the sum of two numbers is 80 .One of the numbers is 4 times the other number.Find the two numbers.
Answers
Find the lengths of line segment
GJ.
Answers
Add the two parts (G,H) + (H,J) to get the length of the whole line
pls help marking brainly 8 × 0 pls help
0 × 3
5 × 1
1 × 9
Answers
The equation 8 * 0 is similar to 0 * 3, the correct option is the first.
How to find solution for 8 * 0In mathematics, zero has unique properties, one of the properties is seen in multiplication. The unique property of zero in multiplication is that, zero has the power to return itself to any number that multiplies it, or when zero multiplies the number. The order does not matter.
For instance, as used in the equation 8 multiplying zero will return zero as the solution. Bearing in mind this unique feature zero multiplying any number gives zero too hence 0 * 3 = 0.
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After a 80% reduction, you purchase a new DVD player on sale for $160. What was the original price of the DVD player?
The original price was $
Answers
Answer: $800
Step-by-step explanation: 80% of 800 is 640. So you would do 800-640=160. Hope this helps :)
Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
Answers
Domain: {x-9 ≤x ≤9}, Range:{x-9 ≤x ≤9}, Intercepts points : (-9, 0), (0, -9), (0, 9), (9, 0) and Symmetry: x-axis and y-axis the correct answer would be option (C).
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
We have been given that the graph is that of a function.
To determine its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin
The domain of the given function would be {x-9 ≤x ≤9}
The range of the given function would be : (y-9 y ≤9)
The intercepts points of the given function would be : (-9, 0), (0, -9), (0, 9), (9, 0)
And the graph is symmetric about the x-axis and y-axis.
Hence, the correct answer would be option (C).
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7 pens cost 84p, how much
would 11 pens cost?
Answers
Answer:
132p
Step-by-step explanation:
if 7 pens cost 84 total then you need to find the cost of each to know how much 11 pens would cost in total
84/7=12
now you know it's 12 each so just multiply 12 by 11 and you know how much for 11 total!
12*11=132p
Answer:
132 is correct
Step-by-step explanation:
84÷7=12
12×11= 132
what is 14/7 into improper fraction
Answers
Answer: 2 and 0/7
MATH
Solve the following equation
3(1-3x)=2(-4+7)
Answers
Answer:
x=-1/3
Step-by-step explanation:
3(1-3x)=2(-4+7)
Use distributive property.
3-9x=-8+14
Combine like terms.
3-9x=6
Subtract 3 from both sides.
-9x=3
Divide -9 from both sides.
x=-1/3
Hope this helps!
Please mark as brainliest if correct!
Answer:
The value of x is -1/3.
Step-by-step explanation:
Given equation,
→ 3(1 - 3x) = 2(-4 + 7)
Now the value of x will be,
→ 3(1 - 3x) = 2(-4 + 7)
→ 3 - 9x = 2 × 3
→ -9x = 6 - 3
→ x = 3/(-9)
→ [ x = -1/3 ]
Hence, the value of x is -1/3.
Mr. Hazel is a professional plumber. To fix a drain that is clogged, he charges a customer
$50 per hour, plus a fixed fee of $25 for the service call, as represented by the function
f(x)= 50x + 25. In the equation, what is represented by the variable "x"?
Answers
Answer:
The x is how much hours the job takes,
You can see that 25 is a fixed fee which is why there is no x attached to it, and 50 is the variable that can change, hope that made sense!
Step-by-step explanation:
^^^
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
si tardamos 20 minutos en recorrer una distancia a una velocidad de 40 km/h
1)cuanto tardaremos en recorrer dicha distancia si circulamos a 50 km/h
2) si la velocidad maxima en la zona es de 90 km/h a que porcentaje corresponden los 50 km/h?
porfa necesito el paso a paso :(
ya se q son inversas solo necesito el paso a paso
Answers
1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
¿Cómo analizar móviles a rapidez constante?
1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.
[(40 km /h) / (50 km / h)] = t / 20 min
4 / 5 = t / 20
t = 80 / 5
t = 14 min
El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:
r = [(50 km / h) / (90 km / h)] × 100 %
r = 55.556 %
La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
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With explanation please! ASAP
Answers
W/3+8=20 what is W ???
please help fast
Answers
W=60-24
W=36
. . . .
What is the standard deviation of a data set whose values are all the same?
(A) -1
(B) -2
(C) 0
(D) 1
Answers
Answer:
C
Step-by-step explanation:
all the values will equal the mean
Which statement describes the system of equations?
√x+2y=2
x-2y=-2
O It has infinitely many solutions.
OIt has no solution.
O It has one solution (0, 1).
It has one solution (4, -1).
Mark this and return
Answers
For the system of equations √x + 2 y = 2 and x - 2 y = - 2, it has no solutions.
We are given a system of equations:
√x + 2 y = 2 … (1)
x - 2 y = - 2 … (2)
We need to find out which of the given statements if true about this system of equations.
We will do this by first comparing the a₁ / a₂, b₁ / b₂ and c₁ / c₂ with each other.
We have:
a₁ = 1
b₁ = 2
c₁ = 2
a₂ = 1
b₂ = -2
c₂ = -2
Since, b₁ / b₂ = 2 / -2 = -1 and c₁ / c₂ = 2 / - 2 = -1
So,
a₁ / a₂ ≠ b₁ / b₂ = c₁ / c₂
From this, we get that:
It has no solution.
Therefore, for the system of equations √x + 2 y = 2 and x - 2 y = - 2, it has no solutions.
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a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:
Answers
For 450 km, the car need 9.32 liters of gasoline to cover the distance of 450km.
Given,
Car averages 35 miles per gallon of gasoline.
Here we need to find how many liters of gasoline will be needed for a trip of 450 km.
First we have to convert the km into miles in order to solve it.
1 mile = 0.621371 miles
So, 450 km is equal to,
=> 450 x 0.621371 miles
=> 279.617 miles.
Now, we already know that,
1 gallon of gasoline will cover 35 miles.
So, for 279.617 miles, it will need,
Let x be the liters of gasoline will be needed to cover the distance.
So,
=> x = 279.617 / 30
=> x = 9.32
Therefore, we need 9.32 liters of f gasoline will be needed for a trip of 450 km.
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How do I get the answer
Answers
Answer:11
Step-by-step explanation:
Answer:
11 units
Step-by-step explanation:
use the absolute value function to find the difference between A and E
A = - 6 , E = 5 , then
AE = | - 6 - 5 | = | - 11 | = | 11 | = 11
or
AE = | 5 - (- 6) | = | 5 + 6 | = | 11 | = 11