in the figure shown Sigma MN is parallel to y z what is the length of segment MX
Answers
We will solve for MX using similar angles theorem
Let line MX be= y
we have to find the ratio of the small triangle to that of the big triangle
Therefore we will have,
[tex]\begin{gathered} \frac{\text{xcm}}{(x+12)cm}=\frac{3.5\operatorname{cm}}{17.5\operatorname{cm}} \\ \text{when we cross multiply we wil have,} \\ 17.5\times x=3.5(x+12) \\ 17.5x=3.5x+42 \\ by\text{ collecting like terms we wll have} \\ 17.5x-3.5x=42 \\ 14x=42 \end{gathered}[/tex]to get x we divide both sides by the coefficient of x which is 14
[tex]\begin{gathered} \frac{14x}{14}=\frac{42}{14} \\ x=3.0\operatorname{cm} \end{gathered}[/tex]Hence ,
[tex]\vec{MX}=3.0\operatorname{cm}[/tex]Therefore,
The correct option will be OPTION A
Related Questions
A pyramid has a square base with sides 8 ft long and a height of 16.8 ft. Select the correct formula for the volume.
Answers
The volume of the pyramid with square base with sides 8 ft long and a height of 16.8 ft is 358.4 ft.
Given,
A pyramid has a square base with sides 8 ft long and a height of 16.8 ft.
we are asked to find out the volume of the pyramid = ?
we have:
side length (s) = 8 ft
height (h) = 16.8 ft
we know the formula of volume as:
v = 1/3 × s² × h
v = 1/3 × (8)² × 16.8
v = 1/3 × 64 × 16.8
v = 64 × 5.6
v = 358.4 ft
Hence we get the volume as 358.4 ft
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Manuel is planting grass seed in a rectangular lot that is 156 inches long and 228 inches wide. How wide is the deck in feet?
Answers
1 foot = 12 inches
The width of the rectangular lot = 228 inches
To change it to feet divide it by 12
The wide of the deck = 228/12 = 19 feet
The answer is 19 feet
What is the meaning of the x-intercept? A) Olivia's maximum distance from the pool was about 10.5 meters. B) It takes Olivia about 3.2 seconds to enter the pool. C) Olivia's dive was from a 10-meter platform. D) Olivia's speed was not constant.
Answers
Explanation:
X- intercept is the value of x when y is equal to zero.
On the graph, we have distance(meters) over time (secs).
The time is in the x axis. The value of x when y is equal to zero is a bit above 3.
This means when Olivia's distance is at point 0 meters, the seconds it takes to enter to pool is a bit over 3 secs (around 3,
From the options, the correct answer is It takes Olivia about 3.2 seconds to enter the pool (option B)
need help answering the question step by step explanation please
Answers
Given that:
- Lucy must have the construction job done within 30 days.
- The bid of the first engineer is $2050 per hour, 8 hours per day.
- The bid of the second engineer is 1¢ per day which will double each day.
Let be "x" the number of days of work and "y" the total cost (in dollars)
• Using the data given, you can set up this equation to represent the bid of the first engineer:
[tex]\begin{gathered} y=(2050)(8)x \\ \\ y=16400x \end{gathered}[/tex]And you can set up this equation to represent the bid of the second engineer:
[tex]y=0.01(2)^{x-1}[/tex]• In order to graph them, you can give values to the variable "x" and evaluate, in order to get the corresponding y-values.
By substituting this value into the first equation:
[tex]\begin{gathered} \\ x=5 \\ \\ x=10 \end{gathered}[/tex]You get:
[tex]y=16400(5)=82000[/tex][tex]y=16400(10)=164000[/tex]- For the second equation, substitute this value:
[tex]x=20[/tex]And evaluate:
[tex]y=0.01(2)^{20-1}=5242.88[/tex]Now you can graph them:
You can identify in the graph that the total cost is greater in the first line than the cost in the second line. Therefore, the cost of the bid given for the first engineer will be greater.
Hence, the answer is:
• Equation 1st:
[tex]y=16400x[/tex]• Equation 2nd:
[tex]y=0.01(2)^{x-1}[/tex]• Graph:
• Better deal: The bid of the second engineer (the graph shows that the total cost using this deal will be less than the total cost using the first deal).
The angle of elevation to the top of a 10-story skyscraper ismeasured to be 3° from a point on the ground 2000 feet fromthe building. What is the height of the skyscraper to thenearest hundredth of a foot?
Answers
ANSWER :
The height is 104.82 feet
EXPLANATION :
The angle of elevation to the top of the building is 3 degrees from a point that is 2000 feet away from the building.
Using tangent function :
[tex]\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]The opposide side to the angle is H and the adjacent side is 2000 feet.
Then :
[tex]\begin{gathered} \tan3=\frac{H}{2000} \\ \\ H=2000\tan3 \\ H=104.816\sim104.82\text{ }ft \end{gathered}[/tex]what is the H3O of a solution with a pH of 1.90
Answers
Given that
pH = 1.90
[tex]\begin{gathered} pH=-log(H^+_3O) \\ pH\text{ = 1.90} \\ \text{Take the log of both sides} \\ 1.90=-log(H^+_3O) \\ 10^{-1.9}=H^+_3O \\ H^+_3O\text{ = }1.26\cdot10^{-2}molL^{-1} \end{gathered}[/tex]Carlos fills an aquarium to a depth of 4/5 meters in 8 minutes. What is the unit rate in minutes per meter?write the answer in the simplest form
Answers
Step 1. The information that we have is:
The aquarium is filled to a depth of 4/5 meters in 8 minutes.
Required: Find the unit rate in minutes per meter.
Step 2. First, we convert 4/5 meters to a decimal number:
[tex]\frac{4}{5}\text{ meters }=0.8\text{ meters}[/tex]Step 3. To find the unit rate, we need to divide the number of minutes by the number of meters:
[tex]\frac{8minutes}{0.8\text{ meters}}[/tex]The result is:
[tex]10\text{ minutes per meter}[/tex]The unit rate is 10 minutes per meter.
Answer: 10
3. Monthly Car Payment: The Mills' purchased a new car for $29,575. The tax on thevehicle was 3.25% and title and license fees were $210. They were able to get a trade-in of$4,500 on Jackson's old car. If they financed the remainder at 5.25% for 5 years, what wasthe monthly payment on the car loan?Select the correct answer for each dropdown menu.A. Total Purchase Price (including taxes and fees): [Select]B. Loan Amount (with down payment): (Select]C. Interest on Loan: [Select]D. Amount to be repaid: [Select]Select)E. Amount of each payment:
Answers
From the question;
Purchase price = $29,575
Tax = 3.25%
License fee = $210
A. We are to calculate the total purchase price
[tex]\begin{gathered} \text{Total Purchase price = \$29,575 + 3.25\% 0f \$29,575 + \$210} \\ \text{Total purchase price = \$29,575 + \$961.19 + \$210} \\ \text{Total purchase price = \$30,746.19} \end{gathered}[/tex]Therefore,
Total Purchase price = $30,746.19
B. Loan amount
[tex]\text{Loan amount = Total purchase - trade-in payment}[/tex]Trade-in payment = $4,500
Therefore,
[tex]\begin{gathered} \text{Loan amount = \$30,746.19 - \$4,500} \\ \text{Loan amount = \$26,246.19} \end{gathered}[/tex]Therefore,
Loan Amount = $26,246.19
C. Interest on loan
[tex]\text{Interest = }\frac{P\times R\times T}{100}[/tex]From the question
P = Loan amount =$26,246.19
R = 5.25
T = 5years
Therefore,
[tex]\begin{gathered} \text{Interest = }\frac{\text{\$26,264.19 }\times\text{5.25 }\times5}{100} \\ \text{Interest =}\frac{\text{\$688,957.5}}{100} \\ \text{Interest = \$6,889.6} \end{gathered}[/tex]Therefore,
Interest on loan = $6,889.6
D. Amount to be repaid
[tex]\begin{gathered} \text{Amount = Loan amount + Interest} \\ \text{Amount = \$26,246.19 + \$6,889.6} \\ \text{Amount = \$33,135.8} \end{gathered}[/tex]Therefore,
Amount to be repaid = $33,135.8
E. Amount of each repayment
since the repayment is on a monthly basis
[tex]\begin{gathered} \text{The loan is for 5 years} \\ \text{Hence, } \\ T\text{otal months = 5 }\times12\text{ months} \\ T\text{otal months = 60 months} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Amount of each payment = }\frac{Amount\text{ to be repaid }}{Total\text{ months}} \\ \text{Amount of each payment = }\frac{\text{\$33,135.8}}{60} \\ \text{Amount of each payment = \$552.3} \end{gathered}[/tex]Therefore,
Amount of each payment = $552.3
Madison says that 579.8 x 0.001 is the same as 579.8 : 10? Is she correct? Explain your answer in 3-5 sentences
Answers
Step 1:
First, write the expression for each value
[tex]\begin{gathered} 579.8\text{ }\times\text{ 0.001 = 0.5798} \\ \\ 579.8\text{ }\times\text{ 10 = 5798} \end{gathered}[/tex]Final answer
The two are not the same because the value of 579.8 x 0.001 is less than the value of 579.8 x 10.
it f (x) = √ which equation describes the graphed function? y = f(-x+4)
y = -f(x+4)
y= -f(x-4) y=f(-x-4)
Answers
For the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
As given in the question,
Given equation is equal to :
f(x) = √x
Equation which help us to defined the graphed function is as follow:
From the graph we have different values of x we get,
When x = 4, x=3 x=2
a. y = f(-x +4) y = f(-x+4) y = f(-x+4)
= √-x +4 = √-3+4 = √-2+4
= √-4 +4 = 1 = 1.414
= 0
Correct. Correct Correct
b. y = -f(x+4)
= -√x+4
= -√4+4
≠ 0
Incorrect.
c. y = -f(x-4) y = -f(x-4)
= -√x-4 = -√3-4
= -√4-4 = -√-1
= 0
Correct Incorrect
d. y = f(-x-4)
= √-x-4
=√-4-4
≠0
Incorrect
Therefore, for the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
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Do these coordinate pairs represent a function?: *{(2, 4), (2,5), (3,6), (3, 7) }
Answers
Given,
The coordinate pairs are
{(2, 4), (2,5), (3,6), (3, 7) }
Here the argument 2 returns to both 4 and 5 while 3 returns to both 6 and 7.
This violates the defination of function.
Thus the coordinate pairs doesnot represent a function.
The answer is No.
What is the coordinate for Pafter reflecting PFEL across the line y = -x?
Answers
The coordinate of P is (-4,4).
A reflection across the line y=-x is given by
[tex](x,y)\rightarrow(-y,-x)[/tex]In this case we have:
[tex](-4,4)\rightarrow(-4,-(-4))=(-4,4)[/tex]Therefore, the image is (-4,4) and the asnwer is third option.
jamie needs to find the height of the parallelogram. the base is three inches long and the area is 30 square inches. what is the height. step one of 2:choose the correct formula
Answers
10 inches
Explanation:Given:
base of parallelogram = 3 in
Area pf the paralllelogram = 30 square inches
height = ?
To find the height, we apply the formula for area of parallelogram:
[tex]\begin{gathered} \text{Area of parallelogram = Base }\times\text{ height} \\ \end{gathered}[/tex][tex]\begin{gathered} 30\text{ = 3 }\times\text{ height} \\ \text{divide both sides by 3:} \\ \frac{30}{3}\text{ = }\frac{\text{3height}}{3} \\ \text{height = 10 } \\ \\ \text{The hright of parallelogram is 10 in} \end{gathered}[/tex]I have two answers for the simplified quotient, I'm not sure which one it is
Answers
factor 2 on the denominator od the second one
Find the Cardinal number of setC = {x |25 < x < 40, x E Z}, where Z denotes the set containing all integers.
Answers
So, given
25 < x < 40
So, the numbers will be
26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39
These numbers are the numbers belongs to Z and achieve the inequality
Note: A Cardinal Number is a number that says how many of something there are.
Find the quotient and write it in rectangular form using exact values: 8 ( cos pi/2 + i sin pi/2 ) /3 ( cos pi/6 + i sin pi/6 )
Answers
Answer:
[tex]\frac{4}{3}+\frac{4\sqrt{3}}{3}i[/tex]Explanation:
Given:
[tex]\frac{8(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2})}{3(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6})}[/tex]To find:
The quotient and write it in rectangular form using exact values
Recall the below;
[tex]\cos\theta+i\sin\theta=e^{i\theta}[/tex]So we can go ahead and rewrite the given expression and simplify as shown below;
[tex]\begin{gathered} \frac{8(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2})}{3(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6})} \\ =\frac{8(e^{\frac{i\pi}{2}})}{3(e^{\frac{i\pi}{6}})} \\ =\frac{8}{3}(e^{\frac{i\pi}{2}-\frac{i\pi}{6}}) \\ =\frac{8}{3}(e^{i\pi(\frac{1}{2}-\frac{1}{6})} \\ =\frac{8}{3}e^{\frac{i\pi}{3}} \end{gathered}[/tex]So we'll have;
[tex]\begin{gathered} \frac{8}{3}(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}) \\ =\frac{8}{3}(\frac{1}{2}+i\frac{\sqrt{3}}{2}) \\ =\frac{8}{6}+i\frac{8\sqrt{3}}{6} \\ =\frac{4}{3}+\frac{i4\sqrt{3}}{3} \end{gathered}[/tex]Carol Wynne bought a silver tray that originally cost $150 and was advertised at 30% off. What was the sale price of the tray?The sale price was $(Type an integer or a decimal.)
Answers
The original price was $150
the discount was 30%
therefore, the final price is the following:
[tex]\begin{gathered} P_{final}=150*(1-0.3) \\ =150*0.7 \\ =105 \end{gathered}[/tex]Thus, the final price of the tray was $105
Answer To this question so that we can move on to the next question so we can get all this homework done
Answers
The values of bills for the last 12 months 338.28 328.93 341.03331.29356.01329.03328.46586.34401.23386.37388.43367.31A) Find the sample mean and sample standard deviation of your data.B) Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?C) Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
Answers
step 1
Find out the mean
we have the data set
Mean=(338.28+328.93+341.03+331.29+356.01+329.03+328.46+586.34+401.23+386.37+388.43+367.31)/12
Mean=(4,482.71)/12
Mean=373.56
step 2
Find out the sample standard deviation
Subtract the mean from each data point and square it
(338.28-373.56)^2=1244.6784
(328.93-373.56)^2=1991.8369
(341.03-373.56)^2=1058.2009
(331.29-373.56)^2=1786.7529
(356.01-373.56)^2=308.0025
(329.03-373.56)^2=1982.9209
(328.46-373.56)^2=2034.01
(586.34-373.56)^2=45275.3284
(401.23-373.56)^2=765.6289
(386.37-373.56)^2=164.0961
(388.43-373.56)^2=221.1169
(367.31-373.56)^2=39.0625
Add the squared deviations
S=56,871.6353
Divide by the number of data sets minus 1
S/(n-1)
where
n=12
56,871.6353/(12-1)=5,170.14866
Take the square root
sample standard deviation=√(5,170.14866)
sample standard deviation=71.90
Part B
Remember that
z =(x - μ)/s
where
μ=373.56
s=71.90
I take the bills
What else would need to be congruent to show that AABC=AXYZ by SAS?BGiven:ZBYAB=XYZO A. ZB=LYB. BC = YZC. AC = XZO D. C= _Z
Answers
We were given two triangles, ABC and XYZ. The problem also states that the angles B and Y are congruent, and the sides AB and XY are also congruent. We need to point out which information is missing so that we can prove the triangles are congruent by SAS.
The term SAS stands for Side-Angle-Side, it means that two triangles are similar when they have two congruent Sides and one congruent Angle. Since the problem already said that one side and one angle are congruent, then we only need one more side. From this, we can conclude that the correct option is B.
What is the exact volume of the figure?5 om12 cm(The figure is not to scale.)cm3V=(Type an exact answer in terms of A.)
Answers
Explanation
The volume of a cone is one third the area of the base multiplied by the height of the cone:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]This cone has a radius of 5cm and a height of 12cm. The volume is
[tex]\begin{gathered} V=\frac{1}{3}\pi(5\operatorname{cm})^2(12\operatorname{cm}) \\ V=\frac{1}{3}\cdot\pi\cdot5^2\cdot12\cdot cm^{2}cm \\ V=\pi\cdot\frac{1}{3}\cdot25\cdot12\operatorname{cm}^{3} \\ V=\pi\cdot\frac{300}{3}cm^{3} \end{gathered}[/tex]Answer
The volume of the figure is:
[tex]V=100\pi cm^{3}[/tex]Which of the following expressions is equal to5 - 2(x + 2)?O -2x+1O 3x+6O -2x+2O 3x+2
Answers
Given:
an expression is given as 5 - 2(x + 2)
Find:
we have to simplify the expression and find correct expression from the options, which is equal to the given expression.
Explanation:
Now
5 - 2(x + 2) = 5 - 2x - 4 = - 2x + 1
Therefore, 5 - 2(x + 2) = - 2x + 1
help meeeeeee ok will you
Answers
∠ BCD has the same measure as ∠ CFG and ∠ FIJ.
If ∠ GFI measures x degrees, then the measure of HIK is (180 - x) degrees.
The sum of the measures of ∠ CFE and ∠ ACF is 180 degrees.
Given that:-
AD II EG II HJ and BK is the transversal.
As AD II EG
∠ BCD = ∠ CFG
As EG II HJ
∠ CFG = ∠ FIJ
Hence,
∠ BCD has the same measure as ∠ CFG and ∠ FIJ.
As ∠ GFI = x degrees
Hence, ∠ FIJ = (180 - x) degrees (Sum of internal angles is 180 degrees)
∠ FIJ = ∠ HIK (Vertically Opposite angles)
Hence,
∠ HIK = (180 - x) degrees.
As ∠ CFE and ∠ ACF are internal angles, hence their sum will be 180 degrees.
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raina is jogging from her house to school her school is 4 3/4 miles from her house she has gone 1 1/3 miles so far how many miles does raina have left
Answers
Solution
For this case we have the following:
[tex]4\cdot\frac{3}{4}=\frac{19}{4}mi[/tex][tex]1\cdot\frac{1}{3}=\frac{4}{3}mi[/tex]then we can find the difference on this way:
[tex]\frac{19}{4}-\frac{4}{3}=\frac{41}{12}[/tex]Then she has 41/12 miles left
Finding the multiplier to give a final amount after a percentage increase or decrease
Answers
(a) The function with which the new price can be found in terms of the original price is; New price = 0.86 × Original price
(b) New price: $34, 056
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of another set B, such that each element of A is mapped to only one element of the set B.
The original price of the car = $39,600
The percentage by which the price of the car is decreased = 14%
The equation that can be used to find the new price in terms of the original price is therefore;
New price = (1 - 0.14) × Original price = 0.86 × Original price
Therefore;
New price = 0.86 × Original price(b) The value of the new price is obtained by plugging in the value of the original price in the equation above, as follows;
New price = 0.86 × 39,600 = 34,056
The new price is; $34,056
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Dona paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. She uses one bottle of paint to paint 202 cm2. How many bottles of paint does she need in order to paint 70 ornaments? Use 3.14 for pi.1. The surface area of one ornament is about ___cm2.2. She needs ___ bottles.
Answers
The surface area of a cone is given by the following formula:
[tex]SA=\pi rs+\pi r^2[/tex]Where SA is the surface area, s is the slant and r is the radius. Replace for the given values:
[tex]\begin{gathered} SA=(3.14)\cdot(2.7)\cdot(8.6)+(3.14)\cdot(2.7)^2 \\ SA=72.91+22.89 \\ SA=95.8 \end{gathered}[/tex]Each ornament has 2 cones, it means that each ornament has a surface area of:
[tex]SA=2\cdot95.8=191.6[/tex]If she needs to paint 70 ornaments, she will have to paint:
[tex]SA=191.6\cdot70=13412[/tex]According to the question statement, she uses one bottle of paint to paint 202cm^2. To find how many bottles she needs to paint 70 ornaments, divide the total area of the 70 ornaments by 202:
[tex]\frac{13412}{202}=66.39[/tex]The answers are:
1. The surface area of one ornament is about 191.6 cm^2.
2. She needs 67 bottles.
1. A bank account pays 0.5% monthly interest.a. If $600 is put in the account, what will the balance be at the end of one year, assuming no additionaldeposits or withdrawals are made?b. What is the effective annual interest rate?c. Is the effective annual interest rate more or less than 6% (the nominal interest rate)?
Answers
a. 637.007$
b. 0.5%
c. Less than the nominal interest rate
Explanation & Steps:
a.
[tex]600\cdot(1.005)^{12}\text{ }\cong637.006687\text{ }\cong\text{ 637.007\$}[/tex]b.
[tex]\begin{gathered} (1+(\frac{0.5\%}{12}))^{12}\text{ - 1 = x} \\ (1\text{ + (}\frac{0.005}{12}))^{12}\text{ - 1 = x} \\ (1+0.000417)^{12}-1\text{ = x} \\ (1.000417)^{12}\text{ - 1 = x} \\ 1.000502\text{ - 1 =x} \\ 0.00502\text{ = }0.5\text{ = x} \end{gathered}[/tex]c. 0.5% < 6%
if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<14=?
Answers
According to the diagram, angles 10 and 14 are supplementary, so they sum 180°.
[tex]\begin{gathered} m\angle10+m\angle14=180 \\ 77+m\angle14=180 \\ m\angle14=180-77 \\ m\angle14=103 \end{gathered}[/tex]Hence, angle 14 measures 103°.The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 timesBrooke's age. How old is Darius now?
Answers
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 times
Brooke's age. How old is Darius now?
Let
x ------> darius's age
y -----> Brooke's age
we know that
x+y=78 ------> equation A
(x-7)=3(y-7) -----> equation B
solve the sytem of equations
isolate the variable x in the equation A
x=78-y -------> equation C
substitute equation C in equation B
78-y-7=3(y-7)
slve for y
71-y=3y-21
3y+y=71+21
4y=92
y=23
Find the value of x
x=78-y
x=78-23=55
therefore
Darius now is 55 year old
14. Consider the function / graphed below. For whatvalues of Xo does lim /(x) exist?Sorry if u were last tutor, the app crashed
Answers
The limit exists at all values of x₀ where the function is continuous, i.e. where there is no break in the graph.
So only consider the points where there is a vertical asymptote (x₀=-6), where there are holes and jump discontinuity (x₀=-3,3).
The vertical asymptote is a place where the function is undefined and the limit of the function does not exist.
Hence, the limit does not exist at x₀=-6.
For the point where there is a hole, x₀=-3, notice that the graph approaches the same y-value both from the left and right, hence the limit exists at this point, as this is a removable discontinuity.
For the point, x₀=3 where there is a jump discontinuity, notice that the graph approaches different values from the left and right, respectively. Hence, the left and right limits are not equal and thus the limit does not exist.
So the limit exists over the set of real numbers except {-6,3}.