The value of x is 5
Question is based on the Pythagorean theorem :
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
X is the side opposite to the right angle, hence it is a hypotenuse.
Now, by the theorem we know;
Hypotenuse2 = Base2 + Perpendicular2
x2 =[tex]4^{2} +3^{2}[/tex]
x2 = 16+9
x = [tex]\sqrt{25}[/tex]
Therefore, the value of x is 5
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Suppose there is a 1.1 degree drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature o the ground is 59.7 degrees F, what will be the temperature at an altitude of 11,000 ft?
The temperature at an altitude of 11,000 ft is found to be 47.6 Degree Fahrenheit.
What is defined as the temperature?Temperature is a measure of how hot or cold something is demonstrated in terms of one of several scales, such as Fahrenheit and Celsius. Temperature signifies the direction wherein heat energy will instantaneously flow—that is, from a hotter (higher) body to a colder body (at a lower temperature).The plane is at ground level, with a temperature of 59.7 degrees Fahrenheit. The temperature drops by 1.1 degrees Fahrenheit for every 1,000 feet.
Initial Temp = 59.7 Fahrenheit
Distance Covered = 11,000 Ft
As the plane stands there, the ground level is zero feet.
Later, it soars into the sky at 11,000 feet.
= 11×1,000
Temperature drops by 1.1 degrees Fahrenheit for every 1,000.
As a result, at 11,000 feet, the temperature will drop 11 times,
= 11×1.1
or 12.1 degrees.
Therefore, at 11,000 feet, the temperature will be Fahrenheit,
= 59.7 - 12.1
= 47.6 degree Fahrenheit
Thus, the temperature at an altitude of 11,000 ft is computed as 47.6 degree Fahrenheit.
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The points Q, R, S and T all lie on the same line segment, in that order, such that the
ratio of QR RS: ST is equal to 6:3:1. If QT = 10, find RS.
The RS line segment will be 16 units long.
What exactly are collinear points?An axis is a line on which points are located, especially if that line is connected to a triangle or other geometric shape. Because a line is determined by two factors, two points are transparently collinear. If the points are in a straight line, they are collinear points.The collinear points are Q, R, S, and T.
The collinear's condition will then be determined:
QR + RS + ST = QTThe points Q, R, S, and T all lie on the same line segment in that order, so the QR:RS:ST ratio is 1:4:5. If QT = 40.
Let QR / 1 = RS / 4 = ST / 5 = xQR = xRS = 4xST = 5xThe value of the variable x will then be:
QR + RS + ST = QTx + 4x + 5x = 4010x = 40x = 4The length of the line segment RS will then become:
RS = 4xRS = 4 (4)RS = 16Therefore, the RS line segment will be 16 units long.
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The correct question is given below:
The points Q, R, S, and T all lie on the same line segment, in that order, such that the
ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.
6.3 = 2x - 4.5 solve for x
Answer:
x = 5.4
Step-by-step explanation:
6.3 = 2x-4.5
2x = 6.3 + 4.5 = 10.8
x= 5.4
Answer:
5.4is the value if x
Step-by-step explanation:
6.3=2x-4.5
6.3+4.5=2x
10.8=2x
10.8/2=x
5.4=x
So,x=5.4
How far away is Akis house from the pizza place?
11. Lucretia, who works part-time as a substance abuse counselor, earns $18.15
per hour and works 20 hours per week. She is single and claims one withholding
allowance. She lives in a state with no state income tax. (2.1)
Using proportions, it is found that the weekly amounts are given as follows:
Federal Withholding: $33Social Security Tax: $22.51.Medicare Tax: $10.53.State income tax: $134.31.What is the missing information?We have to determine for Lucretia these following weekly amounts:
Federal Withholding.Social Security Tax.Medicare Tax.State income tax.The rates are given as follows:
Withholding allowance: $33 (for someone earning $363 a week).Medicare tax: 2.9%.Social Security: 6.2%.State tax: 37%, as she lives on a state with no tax, hence pays only the Federal rate.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Lucretia's weekly salary is given as follows:
20 x 18.15 = $363.
The withholding allowance is fixed at $33 for a person earning her amount, while the tax rate is of 37%, as she lives in a state with no income tax, hence she only pays the federal tax rate.
The other amounts are given as follows:
Medicare Tax: 0.029 x 363 = $10.53.Social Security Tax: 0.062 x 363 = $22.51.State tax: 0.37 x 363 = $134.31.More can be learned about proportions at https://brainly.com/question/24372153
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. A caterer in Florida is making fresh
orange juice, the official state beverage.
Four oranges make 1 cup of juice. How
many oranges will the caterer need to
use to make 58 cups of juice? HELPPP
Step-by-step explanation:
58 multiple 4
..................
4) Mary had some candy to give to her five
children. She first took seven pieces for
herself and then evenly divided the rest
among her children. Each child received
four pieces. With how many pieces did
she start?
Answer: 27 4 peices for 5 children
Step-by-step explanation: 4 peices for 5 children 4×5=20 then she ate 7 so 20 plus 7 is 27
Full equation 4×5+7=27
Convert the given measurement to the unit indicated
using the table to the right.
0.13 m³ to kg
Converting the given measurement 0.13m^3 into kg using the given table. We get the answer as 130 kg.
Measurement of 0.13m^3 to be converted to kg using the table.
To convert cubic meters to kilograms, multiply the value in cubic meters by the density of the ingredient and then multiply the result by 1000.
You can use the conversion formula :
kilograms = cubic meters × density of the ingredient × 1000
According to the table given 1 m^3 = 1 KL = 1000 kg
Here, we are given 0.13m^3,
which means it equals = 0.13 KL
and hence it equals 0.13 * 1000 = 130kg
So, 0.13m^3 = 130 kg.
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in order to construct the perpendicular bisector of ab which statement describes the compass settings and the number of arc intersections needed
Answer:
The compass is placed at point a and point b, then two arcs are drawn respectively.
A line is drawn from the arcs passing through element being bisected.
[tex]{}[/tex]
IM TIMED PLEASE HELP
Find the value of x if U is between T and V, TU=7x+35,UV=4(x+7),and TU≅UV .
Multiple choice questions.
A)
−3
B)
−7/3
C)7/3
D)
3
The value of x if U is between T and V is -7/3
How to determine the value of x?The given parameters are:
U is between T and V,
TU = 7x + 35
UV = 4(x + 7)
TU ≅ UV
The above means that
7x + 35 = 4(x + 7)
Open the brackets
7x + 35 = 4x + 28
Evaluate the like terms
3x = -7
Divide both sides by 3
x = -7/3
Hence, the value of x if U is between T and V is -7/3
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There question I need help on is “What is the ratio of the number of bananas to the total number of pieces of fruit?”
Answer: 3:12 math is power
Answer:
3:12
Step-by-step explanation:
not sure if you have to reduce but if you have simplify it it would be 1/4
A number is divided by four, and then the quotient is added to seventeen. The result is 25. Find the number. Write and solve the equation
Answer:
32
Step-by-step explanation:
32 divided by 4 is 8
8 + 17 = 25
There's your answer!
Answer:16
Step-by-step explanation:First you would have to subtract 17 from 25 and you'd get 8. Then you multiply 8 by 4 and you'll get 16 as your answer.
Simplify (34)−1. I need to know this plsssss
Answer:
Step-by-step explanation:
A model rocket is launched with an initial upward velocity of 126. The rocket's height (in feet) after seconds is given by the following. Find all values of for which the rocket's height is 50 feet.
At time t = 0.4191 and t = 7.456, rocket was at the height of 50 feet;
Given equation; h = 126t - 16t²;
when rocket's height is 50 feet;
126t - 16t² = 50
16t² - 126t + 50 = 0
Using quadratic formula;
t = {126 ±√(-126)² - (4)(16)(50)}/2(16)
After solving; t =0.4191 and t = 7.456
Therefore, at time t = 0.4191 and t = 7.456, rocket was at the height of 50 feet;
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the general solution to
Sin2x = Cosx+l
Answer:
Step-by-step explanation:
sin2x = cosx + l
This can be written as:
2 sinxcosx = cosx + 1
One way would be to draw graphs of sin2x and cosx + 1 and see where they intersect.
Another way is to use y = tan(x/2), then sinx = 2y/(y^2+1) and cos x
= (-y^2 + 1) / (y^2 + 1) to substitute into the given equation and solve for y.
The algebra will be pretty challenging in this method.
The height of a clocktower is 44 meters. Max, who is standing near the clocktower, casts a 7 meter shadow and is 2 meters tall. How long is the shadow of the clocktower? Round your answer to the nearest tenth, if necessary
Answer:
the answer is 220 i calculated
A ball is thrown up in the air from the top of a building. The function h(t) = -5t²+10t + 80 models the height of the ball, in feet, after t seconds. Graph this function.
What is the maximum height reached by the ball?
Answer:
Step-by-step explanation:
h(t)=-5t²+10t+80=-5(t²-2t+1-1)+80
=-5(t²+2t+1)+5+80
=-5(t-1)²+85
maximum height reached=85 ft
I need help to find the perimeter of this triangle
Answer:
3(x+1)
Step-by-step explanation:
The perimeter of triangle is equal to sum of all side of triangle.
perimeter of triangle=(x-3)+x+(x+6)
on simplify
=3x+3
=3(x+1)
so, perimeter of triangle is equal to
=3(x+1)
I need help 3(1+3)*x(4+3)
5 + 7x + 10 = −41 what is the answer I don’t understand
answer:
[tex]15 + 7 \times = - 41 \\ 7 \times = - 41 - 15 \\ 7 \times = - 56 \\ \times = - 8[/tex]
Answer:
Step-by-step explanation:
I believe you need to just combine like terms:
5 + 7x +10 = -41
Try to get the 7x alone:
7x + 15= -41
To get 7x alone completely have it alone on the side move the 15 to the other side of the =.
7x +15 = -41
-15 -15
you'll get
7x= -55
then you need to get x all alone so divide the 7from both sides
7x=-55
/7 /7
Your solution will be:
x=-7.857 round to whichever place you need
Student Name: davidmontague
Distributive Property Using Area
You have just used the distributive property to write these products as a sum. If drawing rectangles
helps you, feel free to use that visual aid to rewrite the following expressions as a sum. 2 points each
5
14. 8(y + 2)
16. a(a + 3)
18. 2m(m + 4)
13. 5(m-2);
15.-3(m + 4)
17. h(h-2).
19.-2(z-8)
20. -4x(x - 10)
Following expressions are represented as a sum
14. 8y +16
16. a² +3a
18. 2m² + 8m
13. 5m - 10
15. -3m -12
17. h² - 2h
19. -2z + 16
20. -4x² + 40x
The distributive property is also known as the distribution law of multiplication in addition and subtraction. The name itself means the activity that involves dividing or distributing something. The distribution law applies to addition and subtraction.The distributive property shows that an expression given in the form A(B + C) can be solved as A × (B + C) = AB + AC. This distribution law also applies to subtraction and is expressed as A(B - C) = AB - AC. This means operand A is split between the other two operands. The distributive property of multiplication on addition is applied when we need to multiply a number by the sum of two numbers. For example, let's multiply 7 by the sum of 20 + 3. Mathematically we can represent this as 7 (20 + 3).
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3. The cost of mass production of cars is partly constant and partly varies as the number of cars produced. The total cost of making 400 cars is sh 3,740,000 and that of making 1000 cars is sh 7,100,000. Find the cost of making 2500cars.
Step-by-step explanation:
since the process is defined by a constant term plus a variants term, the equation looks like
costs(c) = k + a×c
3,740,000 = k + 400a
7,000,000 = k + 1000a
let's simply subtract the guys from the second equation
7,000,000 = k + 1000a
- 3,740,000 = -k - 400a
------------------------------------
3,260,000 = 0 + 600a
600a = 3,260,000
a = 5,433.333333... 5,433 1/3
3,740,000 = k + 400×5,433.333333...
k = 3740000 - (400×5,433.333333...) =
= 1,566,666.66666...
so, the function is
costs(c) = 1,566,666.66666... + 5,433.333333... × c
therefore,
costs(2500) =
= 1,566,666.66666... + 5,433.333333... × 2500 =
= sh 15,150,000
What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?
Answer:
1
Step-by-step explanation:
What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?
Joni worked 14 hours more than Dominic last month. If Joni worked 7 hours for every 3 hours that Dominic worked, how many hours did they each work?
Answer:
look at the multiple of 3 and seven and find which number in the 7 multiple equal 14 more.
Evaluate.
Remember Order of Operations!
(PEMDAS)
-5 × (-7+2) - 13
Answer:
the answer is 12 just =12
Consider the line y = 6x-9.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of a parallel line:
Slope of a perpendicular line:
Answer:
Gradient of parallel line: 6
Gradient of perpendicular line: -1/6
Step-by-step explanation:
The gradient is the value of m in the equation format y = mx + c.
Parallel lines share the same gradient, with just the y-axis intercept (c value) changing.
The gradient of a line perpendicular to a line is found by taking the negative reciprocal of the original line's gradient. A reciprocal is a essentially fraction flipped over. For example 3/2 becomes 2/3. 6 can be expressed as 6/1 (as every whole number can be divided by 1), so the reciprocal of that is 1/6. The negative version of 1/6 is -1/6.
Which classification of the real number system describes all of the following numbers listed below? 0.5, −13, 0.62, 3.14, 19%
Rational Numbers
Whole Numbers
Irrational Numbers
Integers
The numbers 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer
How to determine the classification of the real numbers?The numbers are given as:
0.5, −13, 0.62, 3.14, 19%
Numbers that can be represented as a fraction of two integers are rational numbers
The given numbers can be represented as a fraction of two integers
i.e.
0.5 = 5/10
0.62 = 62/100
3.14 = 314/100
19% = 19/100
This means that 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer (because it has no decimal point and it is negative)
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HELP ASSAPP PLSASEEE
Answer:
(-2,-2)
Step-by-step explanation:
For a cartesian plane, the solutions to 2 lines is where the 2 lines intercept.
Where this interception point is put into a coordinate (x,y)
Which in this case, the point of intersection is found to be (-2,-2) (Read from the graph)
18. Callie's cat lost 4 1/2pounds before having
surgery. Two weeks after having surgery, her cat gained 2 7/8pounds. What was the total
change in weight of Callie's cat?
The total change in the weight of Callie's cat will be 1 5/8 pounds.
How to calculate the fraction?It should be noted that weight is a measurement of the force an acceleration field, particularly the gravitational field of the Earth near the surface, exerts on a particle or object.
From the information that was given, it should be noted that Callie's cat lost 4 1/2 pounds before having surgery and two weeks after having surgery, her cat gained 2 7/8 pounds.
Therefore, based on the information that was illustrated, it should be noted that the change in weight will be the difference between the weights given.
The change in weight will be:
= 4 1/2 pounds - 2 7/8 pounds
= 4 4/8 - 2 7/8 pounds.
= 1 5/8 pounds
Therefore, the change in weight of Callie's cat will be 1 5/8 pounds.
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Neuer started a systematic investment program by buying $200.00 with of mutual funds on the first day of every month starting on February 1. When you purchase mutual funds, you purchase units in the fund. Neuer purchased as many units as he could with his $200.00, including fractions of units. Unit prices for the first six months were $10.00, $10.60, $11.25, $9.50, $9.20 and $12.15 respectively.
(a) What is the simple average of the unit prices?
(b) What is the total number of units purchased during the first six months (Correct to three decimals)?
(c) What is the average cost of the units purchased?
(d) What is the value of Neuer's mutual fund holdings on July 31 if the unit price on that date is $11.90?
a) The simple average of the unit prices is $10.45.
b) The total number of units purchased during the first six months is 115.898 units.
c) The average cost of the units purchased is $10.35.
d) The value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19.
What is an average?An average refers to the mean of a data set.
The average is computed as the total value divided by the number of values in the data set.
Data and Calculations:Month Unit Price Total Value Units
February $10.00 $200 20.000
March 10.60 200 18.868
April 11.25 200 17.778
May 9.50 200 21.052
June 9.20 200 21.739
July 12.15 200 16.461
Total prices $62.70 $1,200 115.898
Simple Average = $10.45 ($62.70/6)
The average cost of the purchased units = $10.354 ($1,200/115.898)
Thus, the value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19 (115.898 x $11.90).
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