Answers
Apply Thales theorem
[tex]\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}[/tex]
[tex]\\ \rm\rightarrowtail 8RN=50[/tex]
[tex]\\ \rm\rightarrowtail RN=50/8[/tex]
[tex]\\ \rm\rightarrowtail RN=6.25[/tex]
Answer:
RN = 6.25
Step-by-step explanation:
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Therefore,
MQ : MP = MR : MN
⇒ 8 : (8 + 5) = 10 : (10 + RN)
⇒ 8 : 13 = 10 : (10 + RN)
⇒ [tex]\sf\dfrac{8}{13}=\dfrac{10}{10+RN}[/tex]
Cross multiply and solve:
⇒ 8(10 + RN) = 10 × 13
⇒ 80 + 8RN = 130
⇒ 8RN = 130 - 80
⇒ 8RN = 50
⇒ RN = 50 ÷ 8
⇒ RN = 6.25
Related Questions
Kerry cut an 8 foot long board in 3 pieces that are equal in length. How long was each board?
Answers
Answer:
2 2/3 foot
Step-by-step explanation:
3x=8
x=8÷3
=2 2/3 foot
Pls help me
Question 4 Part A (5 points):
Carlos started a business growing palm trees in South Florida.
The function t(s) = 3s + 20 represents the
number of palm trees that grew, where s is the
number of seeds he planted.
The function s(d) = 20d represents the number
of seeds he plants per day, where d represents
the number of days.
Write a composite function that represents
how many palm trees Carlos can expect to
grow over a certain number of days.
Answers
The composite function combines the palm tree and the seed functions
The composite function is t(d) = 60d + 20
How to determine the composite functionsThe functions are given as:
Number of palm trees: t(s) = 3s + 20
Number of seeds: s(d) = 20d
The composite function that represents the number of palm trees Carlos can expect to grow over a certain number of days is represented as:
t(s(d))
This is calculated as:
t(s(d)) = 3s(d) + 20
Substitute s(d) = 20d
t(s(d)) = 3 * 20d + 20
Evaluate the product
t(s(d)) = 60d + 20
Rewrite as:
t(d) = 60d + 20
Hence, the composite function is t(d) = 60d + 20
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Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers?
Answers
Answer:
23
Step-by-step explanation:
Compatible numbers : numbers that are easy to add, subtract, multiply, or divide mentally. They are close in value to the actual numbers, although they do not necessary need to be rounded numbers.
-138 is close to -137.56
-6 is close to -6.12
[tex]\implies \dfrac{-138}{-6}[/tex]
Divide the top and bottom by -2:
[tex]\implies \dfrac{69}{3}[/tex]
Divide the top and bottom by 3
[tex]\implies 23[/tex]
If this is too difficult to divide mentally, you could use -140 and -7:
[tex]\implies \dfrac{-140}{-7}[/tex]
As 2 x 7 = 14, then 20 x 7 = 140, so the answer is 20.
Are the ratios 3:4 and 4:3 equivalent??
Answers
Answer:
Those ratios are not equivalent
Step-by-step explanation:
3:4 is not the same as 4:3 because 3:4 means 3 out of 4 but 4:3 means 4 out of 3 which means it is more than one while 3:4 is less than one
Please help asap! :)
Answers
Answer:
x= 11.57017697
x= 41.2
x=16.50849765
Step-by-step explanation:
sin40=x/18
=> x= sin40 *18
tan x = 14/16
=> x= 41.2
cos 32 = 14/x
=> x= 14/ cos32
a bag contains coins of rupees 2 Rupees 1 and 50 paise, in ratio of 1 is to 2 is to 4. if the total amount is rupees 72 find how many 50 paise coins are there?
Answers
Answer:
Final answer -
[tex]number \: of \: 50 \: paise \: coins \: in \: the \: bag = 4x \\ \dashrightarrow{4 \times 12 = 48 \: coins}[/tex]
hope helpful :D
The number of 50 paise coins that we have in the bag with the respective other coins is; 48 coins
How to solve currency conversions?Since the respective coins are in ratio of 1:2:4. Then, we can deduce the following;
Let number of 2 rupees coins in the bag = 1x
Let number of 1 rupees coins in the bag = 2x
Let number of 50 paise coins in the bag = 4x
Total amount of money = 72 rupees. Thus;
(2 * 1x) + (1 * 2x) + (0.5 * 4x) = 72
2x + 2x + 2x = 72
6x = 72
x = 72/6
x = 12
Thus, number of 50 paise coins = 4x = 4 * 12 = 48 coins
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Let x and b be positive real numbers so that log_b(x^2) = 10. Find log_3sqrtb (1/x)
Answers
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.
How to analyze and solve logarithmic expressionsLogarithms are trascendental functions, that is, functions that cannot be described algebraically.
In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:
[tex]\log_{b} x^{2} = 10[/tex]
[tex]2\cdot \log_{b} x = 10[/tex]
[tex]\log_{b} x = 5[/tex]
x = b⁵
Then, the value of the latter logarithm is:
log₃ (x⁻¹)[tex]^{1/b}[/tex]
- b⁻¹ · log₃ x
- b⁻¹ · log₃ b⁵
- 5 · b⁻¹ · log₃ b
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]
RemarkThe statement is poorly formated, correct form is described below:
Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].
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Seven times a number is between – 28 and 28.
Answers
Answer:
four and negative four
Step-by-step explanation:
7*4 =28 7 *-4 = -28
The sales tax on a table saw is $8.25.
a. What is the purchase price of the table saw (before tax) if the sales tax rate is 5.5%?
b. Find the total price of the table saw.
Answers
Answer:
a. $150
b. $158.25
Step-by-step explanation:
a.The amount of tax is the product of the tax rate and the price being taxed. This relation can let us solve for the price.
tax = tax rate × price
price = tax/(tax rate) = $8.25/0.055 = $150.00
The purchase price of the table saw is $150.00.
__
b.The total price is the sum of the purchase price and the tax.
total price = price + tax
total price = $150.00 +8.25 = $158.25
The total price of the table saw is $158.25.
Help please! How many cups for white paint on 1 then white paint on 10!
Answers
Answer:
1 is .83 or .80 if your rounding and 10 is 8.3 but if your rounding its just 8
Step-by-step explanation:
Its because 5/6 is .83 so for every 1 white there .83 red
draw a model of 1/2 ÷ 4 pls don't say I cant draw it or something I DONT GET IT THEN BUT IF YOU CANT DRAW IT PLS EXPLAIN GOOD! URGENT!!!
Answers
Answer:
try using a pie chart and split the division up in the pie, look to internet for images for an example
Step-by-step explanation:
Answer:
The answer is 3.1
Step-by-step explanation: 1/2 ÷ 4 would go like 4-1/2=2.8 then do it again 2.5-1/2=1.3 then do it once more 1.3 ÷ 1/2= 0.1 so the overall answer is 3.1. Your welcome!
You want to know the average height of your three closest friends.
Should you survey the population or a sample?
Answers
Answer:
population
Step-by-step explanation:
An orchard has 700 pear trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row?
Answers
Answer:
25
Step-by-step explanation:
Number of rows: x
Number of trees per row: y
So x rows multiplied by y trees per row = 700
x × y = 700
xy = 700
This is our first equation
x rows = y trees per row plus three (or x rows minus three = y trees)
x = y + 3
So if x = y + 3,
In xy = 700, we can substitute the x because we have it's value
(y + 3)y = 700
y² + 3y = 700
Divide 3 by 2 then square the answer = 2.25
y² + 3y + 2.25 = 700 + 2.25
Simplify
(y + 1.5)² = 702.25
Get the square root of both sides
(y + 1.5) = ±26.5
y = 26.5 - 1.5 or -26.5 - 1.5
So y is either 25 or -28 (A negative number of trees doesn't make sense so we'll stick with 25
Triangle ABC is similar to triangle WYZ.
Select all angles whose cosine equals 3/5.
Angle A
Angle C
Angle Z
Angle B
Angle W
Angle Y
Answers
Answer:
Angles A and W.
Explanation:
Cosine = Adjacent side/Hypotenuse
Consider a right triangle with a side of length x opposite angle A, a side of length y opposite angle B, and a hypotenuse of length z opposite the right angle. If [tex]sinB=1/sqrt(3)[/tex] and x=8, find the length of the other side (y) and the length of the hypotenuse (z).
Answers
Answer:
y = 4√2 ≈ 5.66z = 4√6 ≈ 9.80Step-by-step explanation:
From the sine of the angle, the other trig function values can be determined:
cos(B) = √(1 -sin²(B)) = √(1 -(1/√3)²) = √(2/3) = (√6)/3
tan(B) = sin(B)/cos(B) = (1/√3)/(√2/√3) = 1/√2 = (√2)/2
__
Then the unknown side can be found from ...
Tan = Opposite/Adjacent
tan(B) = y/x
y = x·tan(B) = 8·√2/2 = 4√2 ≈ 5.66
__
And the hypotenuse is ...
Cos = Adjacent/Hypotenuse
cos(B) = x/z
z = x/cos(B) = 8/√(2/3) = 8√(3/2) = 4√6 ≈ 9.80
a) Solve for x.
b) Then determine the angle measurement.
Answers
Answer:
a)x=12
b)64 degress
Step-by-step explanation: 1.Due to the law of opposite adjacent angles (or whatever its called) you can set both equations equal to each other- 4x+16=7x-20 2. Use algebra and get 3x=36 3. Divide both sides by 3 to get x=12 (first answer) 4. Now plug 12 in for x in either equations. I chose the bottom to get 4(12)+16 which is equal to 64 (second answer).
Given that g(x) = f(x) + k, identify a value of k that transforms f into g
Answers
Answer:
7
Step-by-step explanation:
The value of k will translate the graph up k units if k is positive and down k units if k is negative. To transform f into g line f would translate up 7 units.
Apply
7. Mr. Miller is tiling his shower floor. The blueprint of the shower
floor shown uses a scale of 1 inch 3 feet. If the tile costs
$5.99 per square foot, how much will it cost to tile the
bathroom? Round to the nearest cent if necessary. The bathrooms height is 1.25 inches in the blueprint. The bathrooms width is 1.5 inches in the blueprint
Answers
$. 101.08
Step-by-step explanation:[tex]SUPERFACE=(4.5)(3.75)ft^2[/tex]
[tex]=16.875ft^2X[/tex]
[tex]Cos:\$5.99\times \frac{1}{At^2}\times16.875{\rm ft}^2[/tex]
[tex]Cost=\$101.08y.[/tex]
I hope this helps you
:)
Rounded to the nearest cent, the cost to tile the bathroom would be $100.86.
How to calculate area of the shower floor?In that case we use the concept of area of rectangle.
The area of a rectangle is the measure of the size of the surface enclosed by a rectangle in a two-dimensional plane. It is calculated by multiplying the length of the rectangle by its width.
In mathematical terms, the formula for calculating the area of a rectangle is:
Area = Length x Width
To find the area of the shower floor, we need to convert the blueprint measurements to actual measurements.
1 inch on the blueprint represents 3 feet, so:
Height of shower floor = 1.25 inches * 3 feet/inch
Height of shower floor = 3.75 feet
Width of shower floor = 1.5 inches * 3 feet/inch
Width of shower floor = 4.5 feet
The area of the shower floor is then:
Area = Height * Width
Area = 3.75 feet * 4.5 feet
Area = 16.875 square feet
So the cost of tiling the bathroom would be:
Cost = Area * Cost per square foot
Cost = 16.875 square feet * $5.99/square foot
Cost = $100.86
Rounded to the nearest cent, the cost to tile the bathroom would be $100.86.
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Simplify Sinx + cosx/ cos²x - sin²x
Answers
[tex]\dfrac{\sin x + \cos x}{\cos^2 x - \sin^2 x}\\ \\\\=\dfrac{\sin x + \cos x}{(\cos x + \sin x )\\\\(\cos x - \sin x)}\\\\\\=\dfrac{1}{\cos x - \sin x}[/tex]
1.
3 ft
2 ft
6 ft
what is the surface area of the rectangular prism?
Answers
S = 2(lw + lh + wh)
l = length
w = width
h = height
Just plug in the values of the length, width, and height into that formula for the answer.
pls help
Letf(x)=(x+2)2.
Letg(x)=3(x+2)2.
Which statement describes the graph of g(x) with respect to the graph of f(x)?
It is compressed horizontally by a factor of 3.
It is translated up 3 units.
It is stretched vertically by a factor of 3.
It is translated right 3 units.
Answers
g(x) is the same as saying y, so…
y=3(x+2)2
Because it is multiplying all of the terms by 3, y will be 3 times larger than it would be in f(x). Y is the vertical variable, so it will be stretched vertically by 3.
Alternatively, depending on how your teacher teaches it, 3 is in the location of the “a” value. A is a number that stretches an equation vertically by a factor of itself. Since a=3, the equation is stretched by a factor of 3.
Does x/x+11 simplify to 1/11? Why or why not ?
Answers
Answer:
No.
Step-by-step explanation:
Because only x / 11x simplifies to 1 / 11
X and 11 are not the same, therefore you cannot simplify them
1). 15workers can dig a well in 16 days.how long will it take to dig the well by 20 workers?
2). 24 men can do a piece of work in 15 days. in how many days can 45 men do another piece of work 2 times as great
Answers
Answer:
a)12days
b)8days
Step-by-step explanation:
15x16
=240
240÷20
=12days
24x15
=360
360÷45
=8 days
Find an equation of the vertical line through (-4,-3)
Answers
Answer:
x = -4
Step-by-step explanation:
Vertical lines are up and down, which means the x coordinate stays the same.
This means the line is in the form
x=
x = -4
Answer:
Step-by-step explanation:
A vertical line has the general equation of x = a. y can be anything.
The x value that you will use is -4. Every point must have -4 as its value for a.
Answer: x = -4
Click and drag like terms onto each other to simplify fully. 1+7+3y
Answers
Answer:
8+3y
Step-by-step explanation:
Combine like terms; 1+7=8. That is the only like term in this expression.
What is the exact value of tan(67.5°)?
StartRoot 3 EndRoot
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
StartStartRoot StartFraction 2 minus StartRoot 2 EndRoot Over 2 + StartRoot 2 EndRoot EndFraction EndEndRoot
StartStartRoot StartFraction 2 + StartRoot 2 EndRoot Over 2 minus StartRoot 2 EndRoot EndFraction EndEndRoot
Answers
Answer:
the answer is shown below
I truly hope this helps you -TJ
Step-by-step explanation:
here you go
Answer:
D
Step-by-step explanation:
Edge
___________________cm
Answers
Answer:
10 cm
Step-by-step explanation:
mostly guess and check, 15 is 5 more than 10, and both added together is 25.
Need some help 54 pts
Answers
Step-by-step explanation:
as shown in the picture.
you can comment if there is a problem
 Find the equation of the line that is perpendicular to 4 x + 3 y = 5 and goes through the point (3, –3)
Answers
Step-by-step explanation:
the line equation
y = ax + b
gives us slope (a) and y-interception (b).
4x + 3y = 5
3y = -4x + 5
y = -4/3 × x + 5/3
the slope of the original line is therefore -4/3.
a perpendicular slope flips x and y upside-down and flips the sign.
so, the perpendicular slope of -4/3 is 3/4.
the desired line looks like
y = 3/4 × x + b
b we get by using the given point and its coordinates :
-3 = 3/4 × 3 + b = 9/4 + b
-12/4 = 9/4 + b
b = -21/4
so our full line equation is
y = 3/4 × x - 21/4
or
4y = 3x - 21
-3x + 4y = -21
What is the area of the parallelogram shown? A) 60in B) 120in C) 140in D) 180in. + What is the area of a parallelogram that has a base 5 inches longer and the height 5 inches taller than a parallelogram shown? A) 230in B) 260in C) 290in D) 310in.
Answers
Answer:
B and B
Step-by-step explanation:
A = bh
A = 15 × 8
A = 120 in²
A = bh
A = 20 × 13
A = 260 in²
The area of the parallelogram shown are 120 in² and 260 in².
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
We are given that parallelogram that has a base 5 inches longer and the height 5 inches taller than a parallelogram
A = bh
A = 15 × 8
A = 120 in²
Now,
A = bh
A = 20 × 13
A = 260 in²
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