In the rectangle below, FH = 4x – 2, EG= 5x-12, and m ZIGF = 53º.Find El and m ZIFE.EFBEI =Хm LIFE =HG
Answers
Answer:
The length EI is;
[tex]EI=19[/tex]The measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]Explanation:
Given the rectangle in the attached image.
Given;
[tex]\begin{gathered} FH=4x-2 \\ EG=5x-12 \\ m\angle IGF=53^{\circ} \end{gathered}[/tex]Recall that the length of the diagonals of a rectangle are equal so;
[tex]\begin{gathered} FH=EG \\ 4x-2=5x-12 \end{gathered}[/tex]solving for x, we have;
[tex]\begin{gathered} 4x-2=5x-12 \\ 12-2=5x-4x \\ x=10 \end{gathered}[/tex]Since we have the value of x, let us substitute to get the length of diagonal EG;
[tex]\begin{gathered} EG=5x-12 \\ EG=5(10)-12=50-12 \\ EG=38\text{ units} \end{gathered}[/tex]Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;
[tex]\begin{gathered} EI=\frac{EG}{2}=\frac{38}{2} \\ EI=19 \end{gathered}[/tex]Therefore, the length EI is;
[tex]EI=19[/tex]To get the measure of angle IFE;
[tex]m\angle IGF=m\angle IFG=53^{\circ}[/tex]Reason: base angles of an isosceles triangle are equal.
So;
[tex]m\angle IFE+m\angle IFG=90^{\circ}[/tex]Reason: Complementary angles.
Substituting the value of angle IFG;
[tex]\begin{gathered} m\angle IFE+53^{\circ}=90^{\circ} \\ m\angle IFE=90^{\circ}-53^{\circ} \\ m\angle IFE=37^{\circ} \end{gathered}[/tex]Therefore, the measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]Related Questions
Which of the following statements about the graph of f (x)=(0.5)^x shown above are true? Select all that apply.
Answers
From the graph, the following are true
[tex]1)Thefunctionf(x)=(0.5)^xis\text{ a decay function.}[/tex][tex]2)\text{The range of the function is the set of all real numbers }>0[/tex][tex]3)\text{ The graph of the function intersects the x-axis at x = 5}[/tex]Hello I need help on question number 12 and number 14 if possible please
Answers
N 12
Remember that
In any triangle, the sum of the interior angles must be equal to 180 degrees
so
In the triangle EBF
mso
mm
step 2
we have that
m by form a linear pair
substitute given values
52+mmm
Write an equation to represent the sum modeled in the following number line. H H H -4 -3 -2 -1 0 1 2 3 4
Answers
The number line shows numbers graded into three parts each such that each point between numbers represent 0.33 units.
This means the red line moving towards the left is a negative because it falls to the left of point 0, where the division between positive and negative numbers take place.
Hence the red line indicates -3.33
The blue line is movin towards the right which means its a positive value. Note that it begins from -3.33 and ends at -1.33. Hence the blue line is a positive value and it covers two units.
The equation that models this number line can be written out as
[tex]x=-3.33+2[/tex]the table below shoes the number of white and yellow flowers Cara used in five different arrangements.a. Are the numbers of white and yellow flowers in Cara's arrangements proportional?b. If it is a proportional relationship, which equations related the number of white flowers, x, to the number of yellow flowers, y?
Answers
to find if it is proportional all the data must fulfill the constant of proportionality.
in this case we can see a pattern in which the yellow flowers tend to be the double of the white flowers.
however this is not fulfilled when there are 7 white flowers, indicating that the arragements are not proportional
[tex]y=kx[/tex][tex]\begin{gathered} 6=k\cdot(3) \\ \frac{6}{3}=k \\ 2=k \end{gathered}[/tex]the constant of proportionality is 2
[tex]\begin{gathered} 12=k\cdot7 \\ k=\frac{12}{7} \end{gathered}[/tex]18. Light Bulbs: The mean lifespan of a standard 60 watt incandescent light bulb is 875 hours with a standard deviation of 80 hours. The mean lifespan of a standard 14 watt compact fluorescent light bulb (CFL) is 10,000 hours with a standard deviation of 1,500 hours. These two bulbs put out about the same amount of light. Assume the lifespan’s of both types of bulbs are normally distributed to answer the following questions. (a) I select one incandescent light bulb and put it in my barn. It seems to last forever and I estimate that it has lasted more than 2000 hours. What is the probability of selecting a random incandescent light bulb and having it last 2000 hours or more. Did something unusual happen here? (b) I select one CFL bulb and put it in the bathroom. It doesn’t seem to last very long and I estimate that it has lasted less than 5,000 hours. What is the probability of selecting a random CFL and having it last less than 5,000 hours. Did something unusual happen here? (c) Compare the the lifespan of the middle 99% of all incandescent and CFL light bulbs. (d) Is there much of a chance that I happen to buy an incandescent light bulb that lasts longer than a randomly selected CFL?
Answers
Set
[tex]\begin{gathered} \mu_1=875,\sigma_1=80 \\ \text{and} \\ \mu_2=10000,\sigma=1500 \end{gathered}[/tex]a) The Z-score formula is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Therefore, in our case, if x=2000
[tex]\Rightarrow Z=\frac{2000-875}{80}=\frac{1125}{80}=14.0625[/tex]Using a Z-score table,
[tex]\begin{gathered} P(z\ge2000)=1-P(z<2000)\approx1-1=0 \\ \Rightarrow P(z\ge2000)=0 \end{gathered}[/tex]A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.
b) Similarly, set x=5000; then,
[tex]Z=\frac{5000-10000}{1500}=-\frac{5000}{1500}=-3.333\ldots[/tex]Thus, using a z-score table
[tex]P(z\le5000)=0.0004[/tex]The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.
c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,
[tex]\begin{gathered} Incandescent \\ \mu_1\pm3\sigma_1=\lbrack875-240,875+240\rbrack=\lbrack635,1115\rbrack \\ \text{CFL} \\ \mu_2\pm3\sigma_2=\lbrack10000-4500,10000+4500\rbrack=\lbrack5500,14500\rbrack \end{gathered}[/tex]The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.
d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.
The probability of an incandescent bulb lasting 10000 hrs is
[tex]\begin{gathered} Z=\frac{10000-875}{80}=114.0625 \\ \Rightarrow P(z\ge10000)=1-P(z<10000)=0 \end{gathered}[/tex]The event is practically impossible.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3628 grams and a variance of 408,321. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4330 grams. Round your answer to four decimal places.
Answers
Answer:
0.13597 = 0.136
Step-by-step explanation:
using normal cd in calculator
Lower- 4330 (since we want weight above this)
Upper- 100000 (any large number will still be valid)
std deviation- [tex]\sqrt{408,321}[/tex]
mean- 3628
p- 0.13597
Hope this helps!
Which function is nonlinear?Which equation represents a nonlinear function? (Let me know if you can’t read the possible answers for the equation and I will send them)
Answers
Given:
There are 4 equation representations are given.
To find:
The nonlinear equation.
Explanation:
A)
[tex]\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}[/tex]Which is of the linear form,
[tex]ax+by+c=0[/tex]B)
[tex]y=\frac{2}{3}x+8[/tex]Which is of the linear form,
[tex]y=mx+c[/tex]C)
Let us consider the two points.
[tex](5,0),(6,2)[/tex]Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{2-0}=\frac{x-5}{6-5} \\ \frac{y}{2}=\frac{x-5}{1} \\ y=2x-10 \end{gathered}[/tex]Substituting the first point to verify the linear equation,
[tex]\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}[/tex]Therefore, the linear equation is satisfied for all 4 points.
Thus, options A, B, and C are linear equation.
So, the nonlinear equation must be given options D.
Final answer:
The correct option is D.
The local seven-digit telephone numbers in city A have 1,8,0, as the first three digits. How many different telephone numbers are possible in city A?
Answers
ANSWER
10,000
EXPLANATION
Given:
The first-three digits to be 1, 8, 0 out of seven-digit telephone numbers.
Desired outcome:
Total number of possible different telephone numbers
Determine the possibilities of the 4th, 5th, 6th and the 7th digits
The 4th digit has 10 possibilities (i.e: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The 5th also has 10 possibilities,
likewise the 6th and the 7th digits.
Now, we have:
10 x 10 x 10 x 10 = 10^4 = 10,000
Hence, the number of possible different telephone numbers is 10,000.
In triangle EFG, m∠E = 91.6° and m∠F = 30.7°. Determine the measure of the exterior angle to ∠G.
57.7°
60.9°
119.1°
122.3°
Answers
Answer:
122.3
Step-by-step explanation:
91.6 + 30.7 = 122.3
180 - 122.3 = 57.7 (angles in a triangle = 180)
180 - 57.7 = 122.3 (angles on a straight line = 180)
Answer: 122.3
Step-by-step explanation: did the practice test
How would you solve this question or similar questions? It is solving for x.
Answers
Given the initial expression
[tex]\sqrt[]{2x+3}=\sqrt[]{2x}+3[/tex]Then,
[tex]\begin{gathered} \sqrt[]{2x+3}=\sqrt[]{2x}+3 \\ \Rightarrow(\sqrt[]{2x+3})^2=(\sqrt[]{2x}+3)^2 \\ \Rightarrow2x+3=2x+6\sqrt[]{2x}+9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow3=6\sqrt[]{2x}+9 \\ \Rightarrow-6=6\sqrt[]{2x} \\ \Rightarrow\sqrt[]{2x}=-\frac{6}{6}=-1 \\ \Rightarrow\sqrt[]{2x}=-1 \\ \Rightarrow\sqrt[]{2}\sqrt[]{x}=-1 \\ \Rightarrow\sqrt[]{x}=-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]And sqrt(x)>=0 for any real number.
Therefore, there is no real solution to the equation.
The system of equations y= -x - 1 is graphed. what is the solution to the system of equations ?
Answers
We solve as follows:
*First: Given one function, we corroborate and find the second one.
*We have that the first function passes by the points (0, -1) & (1, 0); we find its function:
[tex]m=[/tex]A building has two sizes of apartments, small and regular. The ratio of small apartments to regular apartments is 6 to 18. What percent of apartments in the building are small?
Answers
3. Write the tangent of angle Mas a fraction. Then write it as a decimal rounded to the nearest hundredth. tan M=
Answers
solution
For this case we can do the following:
[tex]\tan M=\frac{\sin M}{\cos M}=\frac{\text{opposite}}{\text{adjacent}}[/tex]For this case the opposite side is 8 and the adjacent is 6 so we got:
[tex]\tan M=\frac{8}{6}=\frac{4}{3}[/tex]Hi! I've tried this problem a couple times but am still stumped :( Can you help?!
Answers
ANSWER:
[tex]X\text{ = }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix}[/tex]EXPLANATION:
Given:
[tex]U\text{ = }\begin{bmatrix}{1} & {3} & {-5} \\ {2} & {14} & {11} \\ {-8} & {0} & {5}\end{bmatrix}\text{ V =}\begin{bmatrix}{13} & {1} & {-7} \\ {-6} & {1} & {9} \\ {0} & {15} & {23}\end{bmatrix}[/tex]Since U and V are Matrices with equal dimensions(3 x 3 matrix), and
X + U = V.
To solve for X, we have:
X = V - U
[tex]\begin{gathered} X\text{ = V - U} \\ X\text{ = }\begin{bmatrix}{13-1} & {-1-3} & {-7-(-5)} \\ {-6-2} & {1-14} & {19-11} \\ {0-(-8)} & {15-0} & {23-5}\end{bmatrix}=\text{ }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix} \end{gathered}[/tex][tex]X\text{ = }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix}[/tex]Convert 59°F to degrees Celsius.If necessary, round your answer to the nearest tenth of a degree.Here are the formulas.C= (5/9) (F -32).
Answers
15 ° C
Explanation
to convert form Farenheit to Celcius degree we need to use the formula
[tex]C=\frac{5}{9}(F-32)[/tex]then
Let
F=59
now, replace and evaluate
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ C=\frac{5}{9}(59-32) \\ C=\frac{5}{9}(27) \\ C=15 \end{gathered}[/tex]therefore, the answer is
15 ° C
I hope this helps you
Given is a parallelogram ABCD. Verify each measure is correct. AE = 10EC = 10 DE = 10EB = 10
Answers
AE = 10 and EC = 10
1) Let's find out the measure of each section of those diagonals. Since in a parallelogram their diagonals are bisected. So we can write:
2y = y+5 Subtract y from both sides
2y -y = 5
y= 5
x+1 = 3x -13
x-3x = -13 -1
-2x =-14
2x = 14
x = 7
2) As we now know the measure of each half of those diagonals we can write:
AE = 2y
AE = 2(5)
AE = 10
EC = y+5,
EC =10
DE = x +1
DE = 8
EB = 3(7) -13 = 8
3) Hence, the correct measures are AE = 10 and EC = 10
Some of the tallest crystals in a cave in Mexico are 85 feet tall. Lin is 6 feet tall. About how many times as tall as Lin are the tallest crystals?
What is 85 / 6
/= divided by
Answers
14.16 ≈ 14 times as tall as Lin are the tallest crystals.
Given:
Some of the tallest crystals in a cave in Mexico are 85 feet tall.
Lin is 6 feet tall.
Number of times = tallest crystals height / lin height.
= 85 feet / 6 feet
= 14. 16 ≈ 14 times
14.16 is not represented in times so we take the nearest number which is 14.
Therefore 14 times as tall as Lin are the tallest crystals.
Learn more about the times and tallest crystals here:
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2 Quadrilateral A'B'CD is the result of dilating quadrilateral ABCD about point D by a scale factor of 3 1 ita -4 -3 -2 B Determine whether each claim about the properties of ABCD and A'B'C'D' is true or false. AB and A' B' are on distinct parallel lines. True/false v AD and A'D' are on the same line. True/false v
Answers
Solution
AB and A' B' are on distinct parallel lines. TRUE
Since when we apply the scale factor the new A'B' is on a different line but parallel
AD and A'D' are on the same line. FALSE
The new triangle with the scale factor produce an A'D' line different
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answers
Python is 1.01 times as long as Vortex.
What is division ?
In mathematics, division is the process of dividing a given sum into equal pieces. As an illustration, we could divide a group of 20 people into 4 groups of 5, 5 groups of 4, and so on. The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
Here the given ,
length of Python = 212 feet
length of Vortex = 210 feet
Here to find the length we need to divide python length by vortex length
=> [tex]\frac{212}{210}[/tex]
=> 1.01 times.
Therefore Python is 1.01 times as long as Vortex.
To learn more about division
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how many square inches of wrapping paper are needed to wrap a present that is 12 inches wide, 5 inches deep and 12 inches tall
Answers
ok
Area of a rectangular prism: 2(wide x deep) + 2(wide x tall) + 2(tall x deep)
Substitution
Area = 2(12 x 5) + 2(12 x 12) + 2(5 x 12)
Simplification
Area = 2(60) + 2(144) + 2(60)
Area = 120 + 288 + 120
Result
Area = 528 in^2
Describe the transformation from triangle DEF to triangle D′E′F′ in the figure.Question options:A) Rotation 90° clockwise about the originB) Reflection about the originC) Rotation 90° counterclockwise about the originD) Transformation down 8 units and right 6 units
Answers
The transformation from triangle DEF to triangle D'E'F' is a reflection about the origin.
since,The corrdinates of the traingle DEF is,
point D is (-5,6) , E is (-1,5) , F (-4,2) and The corrdinates of the traingle D'E'F' is,
D' (5,-6) , E' (1,-5) and F' (4,-2).
x/6 -7 = -4 what value of x makes this equation true
Answers
Answer:
x=18
Explanation:
Given the equation:
[tex]\frac{x}{6}-7=-4[/tex]To solve for x, follow the steps below.
Step 1: Add 7 to both sides of the equation.
[tex]\begin{gathered} \frac{x}{6}-7+7=-4+7 \\ \implies\frac{x}{6}=3 \end{gathered}[/tex]Step 2: Multiply both sides of the equation by 6.
[tex]\begin{gathered} \frac{x}{6}\times6=3\times6 \\ x=18 \end{gathered}[/tex]The value of x that makes the equation true is 18.
13. Rose's probability of successfully shooting a basketball is 2/5. What is the probability of hershooting in at least 1 if she makes 4 shots?
Answers
Answer:
0.8704
Explanation:
The probability of successfully shooting a basketball is 2/5, so the probability t3/o fail will be equal to:
[tex]P=1-\frac{2}{5}=\frac{3}{5}[/tex]Then, we will calculate the probability of failing the 4 shots. So, we need to multiply 3/5 by itself 4 times.
[tex]P(\text{fail all times) = }\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}=0.1296[/tex]Finally, the probability of her shooting in at least 1 if the complement of the probability to fail all times, so, the answer is:
[tex]P(at\text{ least 1) = 1 - 0.1296 = 0.8704}[/tex]Therefore, the answer is 0.8704
Zach wanted to prove that the arcs on a railroad crossing symbol did not each equal90°. He drew an inscribed angle A with arc BC as the intercepted arc. Angle Ameasured 35°. Fill in the blank with the measure of the intercepted arc.BmBC =RXR35°A
Answers
The given problem can be exemplified in the following diagram:
In this case the value of angle "x" is 35 degrees, therefore, the measure of arc BC is double this angle, that is:
[tex]\begin{gathered} \text{mBC}=35\times2 \\ mBC=70 \end{gathered}[/tex]A supermarket is holding a raffle for a new wrist watch. Out of the 500 tickets sold, David buys ticketsnumbered 5, 6, 7, and 8. What are the odds in favor of David's winning the raffle?O 1:500O 500:1O 1:124O124:1
Answers
Explanation:
Total tickets = 500
Tickets number bought by David = 5, 6, 7 and 8
Number of tickets bought by David = 4
Remaining ticket = 500 - Number of tickets bought by David
Remaining ticket = 500 - 4
Remaining ticket = 496
Odds in favour of an event = success for the event/ failures for the event
success for winning the raffle = Number of tickets bought by David = 4
failures for winning the raffle = Remaining ticket = 496
[tex]\begin{gathered} \text{odds in favour of David winning = }\frac{4}{496} \\ \text{odds in favour of David winning = }\frac{1}{124} \\ \\ \text{odds in favour of David winning = }1\text{ : 124 (option C)} \end{gathered}[/tex]a spinner with 10 equally sized slices has four yellow slices, three red slices, and three blue slices. Martina spun the dial 500 times and got the following results. (refer to pic)answer the following. Round your answers to the nearest thousand.a) from Martinas results, compute the experimental probability of landing on red.b) assuming that the spinner is fair, compute the theoretical probability of landing on red.c) assuming that the spinner is fair, choose the statement below that is true. 1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 2. the smaller the number spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 3. the experimental probability will never be close to the theoretical probability, no matter the number of spins.
Answers
Given the experimental results of spinning the spinner:
Yellow: 212
Red: 144
Blue: 144
The sum of times = 500
a) from Martina's results, compute the experimental probability of landing on red.
So, the answer will be probability = 144/500 = 0.288
b) assuming that the spinner is fair, compute the theoretical probability of landing on red.
As shown: the spinner has 10 equally sized slices.
The number of red slices = 3
So, the probability of red = 3/10 = 0.3
c) assuming that the spinner is fair, choose the statement below that is true.
The true statement will be:
1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
10 pointsThe cafeteria manager at a middleschool asked 90 randomly selectedstudents to name their favorite schooldessert. The table below shows theresults of the manager's survey.Favorite School DessertDessertFrequencyCakeTHL THE 1941CookiesTULMAL 18 41Ice Cream MIL MHL MSL 1971CobblerTHEMAFruitPHI HI |||Based on the results of the survey,how many of the school's 1,200students would the manager expoato choose fruit as their favorite schooldessert?A 120C 300B 240D600
Answers
From the table , we can see that:
Cake ------------ -16
cookies - 20
Ice cream - 26
Cobbler - 10
Fruit - 18
Total - 90
Out of 1900 students, the manager is expected to choose fruits as their favourite school desert?
Ice cream - 26/90 x 1900 = 548 .89 = 600 ------- option D
does the point (2,0) satisfy the equation y=9×
Answers
No, it does not.
[tex]0\ne18[/tex]A property owner paid $960 for the tiles to cover a 800 sq. ft yard. Then he decided to tile an additional 260 sq. ft. How much will be paid for the additional tiles?
Answers
Answer:
$312 will be paid for the addditional tile
Explanation:
Given that the property owner paid $960 for tiles to cover a 800 sq. ft yard
Since he decided to tile an additional 260 sq. ft, to know how much will be paid for the additional tiles, we need to know how much he paid for each of the last set of tiles.
The amount is
960/800 = 1.2
He paid $1.2 per tile.
For 260 sq. ft, he will pay:
$1.2 * 260
= $312
In which type of composition does a soloist or a small group of instruments interact wi
dance suite
sonata
concerto
chamber music
Answers
Step-by-step explanation:
Hey! The correct answer is Chamber Music.