Answers
For this problem, I will be using the equal sign instead of the congruent sign for segments.
1) AC = AB, CD = DE, m∠ABC = 70°, m∠ECB = 35° (given)
2) ∠ACB is congruent to ∠ABC (base angles theorem)
3) m∠ACB = 70° (congruent angles have equal measure)
4) m∠DCE = 35° (angle subtraction postulate)
5) ∠DCE and ∠DEC are congruent (base angles theorem)
6) m∠DEC = 35° (congruent angles have equal measure)
7) ∠DEC is congruent to ∠ECB (angles with the same measure are congruent)
8) DE is parallel to BC (if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel)
Related Questions
The diagram shows the cross-section of a wall of a cinema. It is to be painted. Paint cost £6 for a tin which covers 25m^2. How much will it cost to paint?
Answers
Answer:
53.04 pounds
Step-by-step explanation:
We find the area of the shape:
10*13=130 is the rectangle
(10+6)*8/2=16*8/2=16*4=64 (area of the right trapezoid)
(10+8)*3/2=18*3/2=9*3=27 (area of the left)
130+27+64=221 is the total area
221/25*6=53.04 pounds
The playing time X of classical CDs has the normal distribution with mean 54 and standard
deviation 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with playing
time X between 49 and 69 minutes?
Answers
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 54, \sigma = 5[/tex]
The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:
X = 69:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 54}{5}[/tex]
Z = 3
Z = 3 has a p-value of 0.9987.
X = 49:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 54}{5}[/tex]
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8403.
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Which is equivalent to 16^3/4 x?
Answers
Answer:
The answer is A
9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.
Answers
Answer:
$6.40
Step-by-step explanation:
let d be the cost of 1 doughnut and b the cost of 1 burger.
set up 2 equations and solve for b
9b + d = 31.3 → (1)
6b + 3d = 26.7 → (2)
multiplying (1) by - 3 and adding to (2) will eliminate d
- 27b - 3d = - 93.9 → (3)
add (2) and (3) term by term to eliminate d
- 21b + 0 = - 67.2
- 21b = - 67.2 ( divide both sides by - 21 )
b = 3.2
then
cost of 2 burgers = 2 × $3.20 = $6.40
When you are determining the probability of an event, why must the probablilty be between 0 and 1? explain your answer.
Answers
Probability is the ratio of the desired outcomes to all possible outcomes.
If there are no desired outcomes, the ratio is 0 over all possible outcomes, thus 0.
If the event is all possible outcomes, the ratio is all possible outcomes over all possible outcomes, thus 1.
Probability can never be below zero or negative because desired outcomes can never be negative. If an event is impossible that means there are no desired outcomes meaning that probability is zero, thus couldn't fall below
Probability can never exceed 1 as desired outcomes can never be greater than total outcomes.
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Enter the correct answer in the box. Divide f(x) = | x + 20| by g(x) = x + 1.
Answers
the quotient will be:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
with x ≠ -1
How to get the quotient of functions?
For two functions f(x) and g(x), the quotient:
(f/g)(x) is equal to f(x)/g(x).
Here we have:
[tex]f(x) = |x + 20|\\\\g(x) = x + 1[/tex]
Taking the quotient, we get:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
Where we also need to add the restriction that x must be different than -1, as we can divide by zero.
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Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
Answers
Answer:
parallel lines a and b
parallel lines l and m
Step-by-step explanation:
25 A.
Angles 3 and 7 are alternate interior angles of lines a and b cut by transversal l.
Since angles 3 and 7 are congruent, lines a and b are parallel by the theorem:
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
25 B.
Angles 5 and 12 are same side interior angles of lines l and m and transversal b.
Since the sum of the measures of the angles 5 and 12 is 180, then angles 5 and 12 are supplementary angles making lines l and m parallel by the theorem:
If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.
A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour ? There are 5,289 feet in one mile
Answers
We will see that the bison is faster, by 9.9 miles per hour.
Which animal is faster?
We know that the deer's speed is:
D = 30 mi/h
The bison's speed is:
B = 3,520 ft/min.
We want to convert the second speed to miles per hour, then we can use:
1 hour = 60 min
1 mile = 5289 ft
So, to get the speed in miles per hour, we need to multiply by 60 and divide by 5289, we will get:
B = 3,520 ft/min = 3,520*(60/5289) mi/h = 39.9 mi/h
So we can see that the bison is faster, by 9.9 miles per hour.
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Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
Answers
The functions that have complex roots are b and d.
What is complex root?Complex roots are the imaginary root of polynomial functions. The complex roots are represented as α = a + ib, and β = c + id.
When the quadratic equation has a discriminant value less than zero will have imaginary roots.
Out of the given functions, a ,b, c, and d, the function with complex roots are b and d.
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Answer:
b &d is correct. i just took the test. :)
Step-by-step explanation:
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
333. (4 − 6y)(4 + 6y)
Answers
Answer:
The product is the difference of squares is[tex]$$\left(4-6y\right)\left(4+6y\right)=16-36{{y}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4-6 y)(4+6y).We have to multiply the given expression.Square the first term 4. Square the last term 6y.[tex]$$\begin{aligned}&(4-6 y)(4+6 y)=(4)^{2}-(6 y)^{2} \\&(4-6 y)(4+6 y)=16-36 y^{2}\end{aligned}$$[/tex]
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
557. 0.00000103
Answers
Answer:
Hence, 0.00000103 can be expressed as [tex]$1.03 \times 10^{-6}$[/tex].
Step-by-step explanation:
- Given 0.00000103
- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .
- Then count n and write no. as a product with a power of 10 .
Step 1 of 1
Consider 0.00000103,
1.03
Decimal has moved 6 places to right.
The power will be negative as the original no. is less than 1 .
[tex]$$\begin{array}{r}1.03 \times 10^{-6} \\0.00000103=1.03 \times 10^{-6}\end{array}$$[/tex]
What is the answer to the question down below
Answers
Answer:
I'm pretty sure the answer is 4
Step-by-step explanation:
Because SQ is 4 and it looks like QT is the same length
In the interval 0 to the power 0360 find x in which the sin is 0.6691. give your answer to the nearest degree
Answers
The angle for which the sine value is 0.6691 is found to be 42°.
What is the sine value?
A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.
When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.
[tex]sin^{-1}(0.6691)[/tex]=41.99°≈42°
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sharon is participating in basketball practice with her basketball team. She knows that running 40 laps around the rectangular basketball court is equal to running a kilometer (3,280 feet). In addition, the court has an area of 408 square feet. If Sharon's coach tells her to run the length of the longer edge of the basketball court, how many feet must Sharon run
Answers
Answer:
Sharon would have to run 24 ft.
Step-by-step explanation:
Begin by finding the perimeter by dividing 3,280 by 40.
Then eliminate D and E because they are larger than the total perimeter, and then plug in the remaining values into the perimeter and then see which also gives you the area.
This is how you get the answer 24 ft.
Hope this helped :D
f(x) = sin(x² + 2x - 1)²
f'(x) = ?
Need Best Answer? Give the explanation!
ok thx.
Answers
It depends if you mean
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]
i.e. the sine part is getting squared, or
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]
i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].
Now if
[tex]f(x) = \sin^2(x^2+2x-1)[/tex]
• by the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]
• using the derivative of sine and the chain rule again we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]
• with the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]
Recalling the double angle identity for sine,
[tex]\sin(2x) = \sin(x) \cos(x)[/tex]
we can rewrite the derivative among several other ways as
[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]
The graph of a linear function is shown,
Which word describes the slope of the line?
O positive
O negative
O zero
undefined
Answers
Answer:
postive
Step-by-step explanation:
im asian
For the graph of a linear function the slope of the line is positive, option A is correct.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let the line is passing through points (-4, -1) and (0, 0)
m=1/4
The slope value is positive
Hence, for the graph of a linear function the slope of the line is positive, option A is correct.
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A given line passes through the points (2,3) and (2,−3). Determine the equation of the line that is perpendicular to the given line and passes through the point (−1,5).
could someone break this down for me? multiple choice in attachment
Answers
The required equation of the line is y = 5
Equation of a lineThe equation of a perpendicular line to a line in point-slope form is expressed as:
y-y1 = -1/m(x-x1)
m is the slope
(x1, y1) is any point on the line
Determine the slope
Slope = -3-3/2-2
y = ∞
Since there is no slope, hence the equation of the line will be in the form y = b
where b is the y-coordinate of the point. Hence the required equation of the line is y = 5
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Find the distance CD rounded
to the nearest tenth.
C = (4,7) D= (7,11)
CD= [?]
HINT: Use the distance formula:
d = √(x₂-x₁)² + (Y2 − 1)²
Enter
Answers
√(x₂-x₁)² + (Y2 − 1)²
√(7-4)² + (11− 7)²
√(3)² + (4)²
√(9)+ (16)
√(25) = 5
Thus, CD = 5
Hope this helps!
3/8-2/7=2/7-3/8 is the statement true
Answers
Answer:
The statement is not true.
Step-by-step explanation:
[tex]\frac{3}{8} -\frac{2}{7} =\frac{2}{7} -\frac{3}{8}[/tex]
First, let us solve the left side.
[tex]\frac{3}{8} -\frac{2}{7} \\\\\frac{3*7}{8*7} -\frac{2*8}{7*8}\\\\\frac{21}{56} -\frac{16}{56}\\\\\frac{21-16}{56} \\\\\frac{5}{56}[/tex]
And now let us solve the right side.
[tex]\frac{2}{7}-\frac{3}{8} \\\\ \frac{2*8}{7*8}-\frac{3*7}{8*7} \\\\\frac{16}{56}-\frac{21}{56}\\\\\frac{16-21}{56}\\\\\frac{-5}{56}[/tex]
Therefore, it is clear that the left side is not equal to the right side.
∴ Left side ≠ Right side
∴ [tex]\frac{5}{56}[/tex] ≠ [tex]\frac{-5}{56}[/tex]
Someone help please!?!
Answers
Answer: a≈6,1.
Step-by-step explanation:
The sine theorem states:
[tex]\boxed {\frac{a}{sinA^0} =\frac{b}{sinB^0}= \frac{c}{sinC^0} }[/tex], ⇒
[tex]a=\frac{c*sinA^0}{sinC^0}[/tex]
m∡A=180°-(m∡B°+m∡C°)
=180°-(68°+76°)
=180°-144°
=36°. ⇒
[tex]a=\frac{c*sin36^0}{sin76^0}\\ =\frac{10*sin36^0}{sin76^0} \\\approx6,1.[/tex]
Good luck an' have a nice day!
The time t required to empty a tank varies inversely as
the rate r of pumping. If a pump can empty a tank in
45 minutes at a rate of 300 gallons per minute, how
long will it take to empty a tank at 500 gallons per
minute?
k
Answers
If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have
[tex]V = tr[/tex]
It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains
[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]
of liquid.
If it's emptied at 500 gal/min, it would take
[tex]13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}[/tex]
What is 72,910 / 10^2
Answers
10^2=100
72,910/100=729.1
Use natural logarithms to solve the equation. Round to the nearest thousandth.
7e^2x + 10 = 29
Answers
Answer:
x ≈ 0.499
Step-by-step explanation:
The value of x can be found by undoing the operations done to it.
SolutionThe operations done to the variable are ...
multiply it by 2use that as the exponent with a base of emultiply the result by 7add 10We undo these operations in reverse order:
7e^(2x) + 10 = 29 . . . . given
7e^(2x) = 19 . . . . . . . . . subtract 10
e^(2x) = 19/7 . . . . . . . . . divide by 7
2x = ln(19/7) . . . . . . . . take the natural logarithm
x = (ln(19/7))/2 . . . . . . divide by 2
The rounded result is ...
x ≈ 0.499
a student
multiplied 4552 by 175 instead of multiplying by 157 how much was his product greater than the correct product
Answers
The student product is 81936 greater than the correct product
How to multiply numbers?The student was suppose to multiply 4552 by 157 but instead he multiplied 4552 by 175.
Therefore, let's find how much his product is greater than the correct product.
incorrect product = 4552 × 175 = 796600
Correct product = 4552 × 157 = 714664
Therefore,
difference = 796600 - 714664 = 81936
Therefore, his product is 81936 greater than the correct product.
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Select the correct answer.
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted left 3 units and up 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted right 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and down 4 units.
Answers
=============================================================
Explanation:
When going from f(x) to f(x-3), we replaced x with x-3.
Doing this shifts the xy axis 3 units to the left since each x input is three units smaller than before. If we had the f(x) curve fixed in place while the axis moves like this, then it gives the illusion of the curve moving 3 units to the right.
The +4 at the end adds 4 to each y coordinate to shift things 4 units up.
Solve for X if possible:
5x -4y = 24
x =_
Answers
The possible values of x be 4.8, 5.6 and 6.4.
What is equation?The statement of equality between two expressions consisting of variables and/or numbers.
Given:
5x -4y = 24
when y=0
5x = 24
x = 4.8
when y=1,
5x= 28
x= 5.6
when y=2,
5x= 32
x= 6.4
Hence, the possible values of x is 4.8, 5.6 and 6.4.
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I need help :(:(:(:(
Answers
The resulting matrix of the row operation is given as follows:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
How to find the resulting matrix?We apply the row operation on the original matrix, given as follows:
[tex]A = \left[\begin{array}{ccc}4&3&0\\-6&-3&12\end{array}\right][/tex]
The operation is given by:
[tex]R_1 = R_1 - 0.5R_2[/tex]
That is, applying to each element, we have that:
4 - 0.5(-6) = 7.3 - 0.5(-3) = 4.5.0 - 0.5(12) = -6.Hence the resulting matrix is:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
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The mean output of a certain type of amplifier is 498 watts with a standard deviation of 12 watts. If 86 amplifiers are sampled, what is the probability that the mean of the sample would be less than 494.7 watts
Answers
Mean (m) = 498
Standard deviation (σ) = 12
Sample size (n) = 86
The probability that the sample mean would differ from Population mean by less than 494.7 watts
P(m - s < Z < m + s)
P(498-494.7 < Z < 498+ 494.7)
Using the Z formula :
Zscore = (x - m) / (σ/√n)
x = 498 - 494.7 = 3.3 , x = 498 + 494.7 = 992.7
Z = (3.3 - 498) / (12/√86) = -383.48
P(Z < -383.48)
Z = (992.7 - 498 ) / (12/√86) = 383.48
P(Z<383.48)
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Can someone help me out on this
Answers
Answer:
Step-by-step explanation:
Which of the following appear in the diagram below?
Check all that apply.
z
A. YX
B. ZXYZ
C. ZYXZ
D. YW
Answers
Answer:
A , B, D
Step-by-step explanation:
YX is the segment joining points Y and X and is defined (A)
∠ XYZ is the angle between XY and YZ and is defined (B)
∠ YXZ is the angle between YX and XZ
However there is no segment joining XZ ← not defined
YW is the segment joining points Y and W and is defined (D)