0
Given that the triangles are similar, find the value of x. Find the length of NR.
S
T
40
60
R
2x-2
8
N
M
X=
NR =
Answers
Answer:
NR = 12
Step-by-step explanation:
Given that both trjangles are similar, therefore, it follows that their corresponding side lengths would be proportional to each other. Thus:
\( \frac{40}{8} = \frac{60}{2x - 2} \)
\( 5 = \frac{60}{2x - 2} \)
Cross multiply
\( 5(2x - 2) = 60 \)
\( 10x - 10 = 60 \)
\( 10x = 60 + 10 \) (addition property of equality)
\( 10x = 70 \)
Divide both sides by 10
x = 7
✔️NR = 2x - 2
Plug in the value of x
NR = 2(7) - 2 = 14 - 2
NR = 12
Related Questions
-4h+7=-1 what does h stand for?
Answers
Given the equation:
\(-4h+7=-1\)Solve for h:
\(\begin{gathered} -4h+7=-1 \\ -4h+7-7=-1-7 \\ -4h=-8 \\ \\ \frac{-4h}{-4}=\frac{-8}{-4} \\ \\ h=2 \end{gathered}\)so, the answer is h = 2
Help me solve this problems please
Answers
Answer:
a) 2.5 km
b) 1836 m ≈ 1.8 km (rounded)
Step-by-step explanation:
a) just add the two distances of the vertical and horizontal road. 900m + 1600m = 2500m = 2.5 km
b) Apply Pythagoras (a²+b²=c², where a and b are the vertical and horizontal roads, and c is the diagonal road).
c = √(1600²+900²) ≈ 1836m (rounded)
Boba cost $4.00 and left a tip. The total was $4.36. What % did you tip?
Answers
4.36 - 4 = 0.36
for finding tip percentage=
0.36/4 x 100
= 9%
Hope this helps and please mark me as brainliest.
Vladimir buys 1.20 pounds of Skittles, 7/2 pounds of M&Ms, and 5.2 pounds of pretzels. If the candy cost $1.20 a pound and the pretzels cost $1.10 a pound, how much did Vladimir spend?
Answers
Answer:
$11.36
Step-by-step explanation:
1.20 x 1.20= 1.44
7/2 x 1.20= 4.2
1.44 + 4.2= 5.64
5.2 x 1.10= 5.72
5.64 + 5.72= 11.36
To determine the number of trout in a lake a conservationist catches 94 trout tags them and throws them back into the lake. later 36 trout are caught 12 of them are tagged. how many trout would the conservationist expect to be in the lake?
Answers
As per the unitary method, the conservationist would expect there to be 282 trout in the lake.
From the problem, we know that 36 fish were caught in the sample and 12 of them were tagged, so:
Proportion of tagged fish in the sample = 12 / 36 = 1/3
Let's call the total number of fish in the lake "x". We know that 94 fish were tagged and released back into the lake, so the proportion of tagged fish in the lake is:
Proportion of tagged fish in the lake = (number of tagged fish in the lake) / (total number of fish in the lake)
We can set up an equation using the proportions we've found:
1/3 = 94 / x
To solve for x, we can use a unitary method. We want to isolate x on one side of the equation, so we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 3:
1/3 x 3 = (94 / x) x 3
1 = 282 / x
Now, we can isolate x by multiplying both sides of the equation by x:
1 x x = 282 / 1
x = 282
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Original price: $32; Markup: 12.5%; Retail price
Answers
12.5% = .125
32 x .125 = 4
32 + 4 = $36
The equation of the line tangent to the graph of f(x)= (4x³ + 3) (6x-5) at the point (1,7) is (Type an equation using x and y as the variables.)
Answers
The equation of the tangent line to the graph of f(x) = (4x³ + 3)(6x - 5) at the point (1,7) is y = 54x - 47.
To find the equation of the tangent line, we need to determine the slope of the tangent line at the given point. This can be done by finding the derivative of f(x) and evaluating it at x = 1. Taking the derivative of f(x) using the product rule, we get f'(x) = (12x²)(6x - 5) + (4x³ + 3)(6), which simplifies to f'(x) = 72x³ - 60x² + 24x + 18.
Evaluating f'(x) at x = 1, we get f'(1) = 72(1)³ - 60(1)² + 24(1) + 18 = 72 - 60 + 24 + 18 = 54.
The slope of the tangent line is equal to the value of the derivative at the given point, so the slope is 54.
Using the point-slope form of a line, we can write the equation of the tangent line as y - 7 = 54(x - 1), which simplifies to y = 54x - 54 + 7, and further simplifies to y = 54x - 47.
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THIS IS EASY!!! (PLEASE HELP... ILL GIVE BRAINLIST)
Answers
Answer:
-7(9) < -56
Step-by-step explanation:
-7(9) is -63 which is less than -56 so anything above that is less than 56-
Answer:
x=8
Step-by-step explanation:
Hope,it helps it wasn’t that easy (:
Write an algebraic expression for the following verbal description. Use n for your variable.
The quotient of 4 and a number decreased by 8
Answers
Answer:
(4 ÷ n) - 8
Step-by-step explanation:
Quotient means division.
Decreased means subtraction.
Therefore, the expression would be (4 ÷ n) - 8.
Answer:4/n- 8 or n/4 -8
Step-by-step explanation:decreased means subtract .
MATH SUFACE AREA OF PYRAMIDS
WILL GIVE YOU MY LAST 10 POINTS!!!! AND BRAINLYIST!!
Answers
Step-by-step explanation:
the surface areas are always the sum of the areas of the individual sides and base area.
so, all we need to do here is calculating the areas of triangles, rectangles (actually squares) and a hexagon.
the area of a triangle is
baseline × height / 2
or with Heron's formula when we have all sides
s = (a+b+c)/2
area = sqrt(s×(s-a)×(s-b)×(s-c))
the area of a rectangle is
length × width
for a square that is then
side × side = side²
and the area of a regular hexagon can be created again as sum of multiple sub-shapes. but ultimately it is
3 × sqrt(3) × side² / 2
1.
square base area : 10×10 = 100 cm²
lateral areas :
one triangle is 10×13/2 = 65 cm²
4 triangles are then 4×65 = 260 cm²
total surface area :
100 + 260 = 360 cm²
2a.
3 lateral triangles :
3 × 8×10/2 = 120 units²
base area (Heron's, as all 3 sides are 8 units) :
s = 3×8/2 = 12
area = sqrt(12×4×4×4) = sqrt(3×4×4×4×4) = 16×sqrt(3)
total surface area :
120 + 16×sqrt(3) = 147.7128129... units²
2b.
4 lateral triangles :
4 × 8×10/2 = 160 units²
base area : 8×8 = 64 units²
total surface area :
160 + 64 = 224 units²
2c.
6 lateral triangles :
6 × 8×20/2 = 480 units²
base area :
3×sqrt(3)×8²/2 = 96×sqrt(3)
total surface area :
480 + 96×sqrt(3) = 646.2768775... units²
2d.
base area : 16² = 256 units²
4 lateral triangles. but we need to get their height first.
Pythagoras :
(16/2)² + 24² = height²
8² + 24² = height²
64 + 576 = height²
height² = 640
height = sqrt(640) = sqrt(64×10) = 8×sqrt(10)
4 triangles are
4 × 16×8×sqrt(10)/2 = 256×sqrt(10) units²
total surface area :
256 + 256×sqrt(10) = 256×(1 + sqrt(10) = 1,065.543081... units²
Florida has about 66 tornadoes each year, which is approximately 5.7% of all tornadoes in the United States annually. Estimate how many tornadoes occur in the United States each year
Answers
The number of tornadoes that occur in the United States each year is 1158
How to determine the tornadoes each yearLet's call the number of tornadoes in the United States each year "x".
The number of tornadoes in Florida each year is 5.7% of this total
So we can write:
66 = x * 5.7%
Divide both sides by 5.7%
x = 66/5.7%
Evaluate
x = approximately 1158
So, approximately 1162 tornadoes occur in the United States each year.
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The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark
Answers
Answer:
\(5.5\)
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
\(\mu = \frac{{\sum}x}{N}\)
The formula for the mean of a sample is
\(\bar{x} = \frac{{\sum}x}{n}\)
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
\(\frac{55}{10} = 5.5\)
A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows:
F(x) =
0 x < 0
0.06 0 ≤ x < 1
0.16 1 ≤ x < 2
0.33 2 ≤ x < 3
0.69 3 ≤ x < 4
0.92 4 ≤ x < 5
0.99 5 ≤ x < 6
1 6 ≤ x
Calculate the following probabilities directly from the cdf
(a) p(2), that is, P(X = 2) (b) P(X > 3) (c)P(2 ≤ X ≤ 5) (d)P(2 < X < 5)
Answers
(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x
The probability mass function p(x) can be derived from the cdf by taking differences:
p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06 x = 10.1 x = 20.17 x = 30.36 x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)
The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.
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4. From the top of a tower 14m high, the angle of depression of a student is 32° Make a scale drawing and find the distance of the student from the foot of the tower to the nearest 1/2
Answers
The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.
Given that From the top of a tower 14m high
The angle of depression of a student is 32°
we can use trigonometry to find the distance from the foot of the tower to the student:
tan(32°) = opposite/adjacent = 14/distance
Rearranging this equation gives:
distance = 14/tan(32°)
= 25.63m
Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.
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determine whether the variable would best be modeled as continuous or discrete: the weight of a randomly chosen student's backpack.
Answers
Answer:
variable would be best modeled as discrete
Step-by-step explanation:
Since there are finite students and finite backpacks, so the weights will also be finite and hence countable, so the variable would be best modeled as discrete
The figure below is made of 222 rectangles
Answers
The volume of the figure, which is made up of 2 rectangular prisms, would be 276 cm ³.
How to find the volume of the rectangular prism ?The figure shown is made up of two rectangular prisms which means that we can find the volume of the entire figure by finding the volumes of the rectangular prisms and then adding up these volumes to find the total volume.
Volume of the first rectangular prism:
= Length x Width x Height
= 10 x 6 x 3
= 180 cm ³
Volume of the second rectangular prism:
= Length x Width x Height
= 4 x 6 x 4
= 96 cm ³
The total volume of the figure:
= 180 + 96
= 276 cm ³
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graph the line with the slope -1 passing through the point (5,4)
Answers
y - y1 = m(x - x1)
y - 4 = -1(x - 5)
y - 4 = -x + 5
y = -x + 9
(0, 9) is the y-intercept
Basic points on the graph:
(1, 8)
(-1, 10)
(2, 7)
(3, 6)
2(1/3x-5)=5/3x-11
can somebody help me ASAP
Answers
Answer: x=1 my friend
Step-by-step explanation:
Answer:
x=0
Step-by-step explanation:
2/3x-10=5/3x-11
2/3x=5/3x-1
x=3/3-1
x=0
Order equivalent equations of 2(x−3) = 4x to solve for x.
Answers
Answer:
So, to do this we must do distrubition so 2 times x = 2x -3 times 2 = -6 and 4x times 2 equals 6x and subtract the 6x from 6 which equals x so therefore 2 and 2 cancels out so you're left with x=x and there is ur answer and remember to subtract have a good day^_^
Step-by-step explanation:
which is the best estimate for the mass of a rose
Answers
Answer: I think it would be 5 grams
Step-by-step explanation:
A triangle includes one angle that measures 72º. Which pair could be the measures of the other two angles of the triangle
A 9º , 9º C 53º , 55º
B 26º , 46º D 72º , 108º
Answers
Answer:
B
Step-by-step explanation:
180-72 = 108
26+46=72
108+72=180
In a triangle, PR is 12 more than twice PQ and QR is two more than 4 times PQ. If all three sides of the triangle have integer lengths, what is the largest possible value of x?
Answers
Answer:
x = 10
Step-by-step explanation:
In a triangle, PR is 12 more than twice PQ and If all three sides of the triangle have integer lengths, what is the largest possible value of x?
From the attached diagram, x = PQ
We have sides:
PQ, PR and QR
PR is 12 more than twice PQ
PR = 12 + 2PQ
PR = 12 + 2x
QR is two more than 4 times PQ.
QR = 2 + 4(PQ)
QR = 2 + 4x
Hence: we solve using Triangle Inequality
The triangle inequality states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side.
Based on this property, if you know the lengths of two sides of a triangle and are trying to find the range of lengths of the third side, you can add the two known side lengths together and subtract the smaller one from the bigger one. The third side must be greater than the sum of the other two sides and less than their difference.
PQ > PR + QR
PQ < PR - QR
Therefore:
x + 12 + 2x > 2 + 4x
3x + 12 > 2 + 4x
12 - 2 > 4x - 3x
10 = x
Someone please help me!!!
Answers
Answer:
8
Step-by-step explanation:
\( \cos(51) = \frac{5.3}{x} \)
X = 5.3/0.6293
X = 8.4
12 is 2/3 of what number?
Answers
Answer:
18
Step-by-step explanation:
18 ÷ 3 = 6
6 ⋅ 2 = 12
Therefore, 12 is 2/3 of 18.
10x + 8 = 3(x - 2)
10x + 8 = 3x
Answers
Answer:
1) -2
2) 8/7
Step-by-step explanation:
1) 10x+8=3(x-2)
10x+8=3x-6
10x-3x=-6-8
7x=-14
x=-2
2) 10x+8=3x
10x-3x=8
7x=8
x=8/7
Hope it helps
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answers
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
An office manager buys 34 chairs for the new office. Each chair costs $205. What is the total amount the office manager pays for chairs? Enter your answer in the box. $_____________
Answers
Answer:
so each chair will cost 205
205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order
the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered
34*205= 6970
the total cost will be 6970
A group of friends wants to go to the amusement park. They have no more than $345 to spend on parking and admission. Parking is $17.25, and tickets cost $28.75 per person, including tax. Write and solve an inequality which can be used to determine
Answers
x≤11.4 is the solution of the inequality 17.25+28.75x≤345
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that A group of friends wants to go to the amusement park.
They have no more than $345 to spend on parking and admission.
Parking is $17.25, and tickets cost $28.75 per person, including tax.
17.25+28.75x≤345 is the required inequality.
Subtract 28.75 on both sides
28.75x≤345-17.25
28.75x≤327.75
Divide both sides by 28.75
x≤327.75/28.75
x≤11.4
Hence, x≤11.4 is the solution of the inequality 17.25+28.75x≤345
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5. write an equation for the table of values. explain how you got your answer
Answers
Answer:
You forgot to put the table
Step-by-step explanation:
are you given enough information to determine whether the quadrilateral is a parallelogram? explain your reasoning.
Answers
There is a enough information to determine whether the quadrilateral is a parallelogram
As we observe the quadrilateral the pairs of opposite sides in a parallelogram are parallel.
This means that they have the same slope and will never intersect, even if extended indefinitely.
The lengths of the opposite sides in a parallelogram are equal.
This property distinguishes a parallelogram from a general quadrilateral.
The pairs of opposite angles in a parallelogram are congruent.
This means that they have the same measure, making them equal in size.
The given figure is a parallelogram as it satisfies all the properties of parallelogram.
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