Assume the four intersecting lines are parallel. In this figure, A = 36, B = 24, and C = 60 . If D = 33,
what are the measurements of E and F?
Answers
Using the proportionality theorem, the measurements are: c. E = 22 and F = 55.
What is the Proportionality Theorem?If two transversals intersect three or more parallel lines, they divide the lines in such a way that the smaller segments are proportional to each other or have ratios that are equal to each other.
Given the following:
A = 36,
B = 24,
C = 60
D = 33.
Since all lines are parallel, then:
A/D = B/E = C/F
Find the measure of E using the ratio, A/D = B/E:
36/33 = 24/E
Cross multiply
E = (24 × 33)/36
E = 22
Find the measure of F using the ratio, A/D = C/F:
36/33 = 60/F
Cross multiply
F = (60 × 33)/36
F = 55
The answer is: c. E = 22 and F = 55.
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Related Questions
Calculate the value of the expression
1.) 18/3+2(12-5)
a) 33 1/3
b)10 2/3
c) 40
d)56
e)20
2.) 30+4(4+1)/2 -2(3+1)
a)77
b)46
c)92
d)21
e)17
Answers
Answer:
1. e
Step-by-step explanation:
18/3 +2(12-5)
=6+2(7)
=6+14
=20
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]
Divide 18 by 3 to get 6.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2(12-5) \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2\times7 \ \to \ \ [Multiply] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+14 \ \to \ \ [Add] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 20 \end{gathered}$} }[/tex]Therefore, the correct option is "E".
================================================================
===> Exercise 2[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4\times5}{2}-(3+1) \ \to \ \ [Multiply \ 4 \ by \ 5] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{20}{2}-(3+1) \ \to \ \ [Divide \ 20 \ by \ 2] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+10-2(3+1) \ \to \ [Add \ 30 \ and \ 10] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 4-2(3+1) \ \to \ [Add \ 3 \ and \ 1] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-2\times4 \ \ \to \ \ [Multiply \ 2 \ and \ 4.] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-8 \ \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 32 \end{gathered}$} }[/tex]It seems that none of the options is correct.
How to solve this problem
x + 7 = -8
Answers
x + 7 = -8
(x + 7) - (7) = -8 - (7)
x = -8 - 7 = -15
The correct answer is -15
❄ Hi there,
let us first consider this: What should we do to get x all alone, on one side of the equation?
Since
7 is added to xwe should
subtract 7 from x (and from the other side too!)[tex]\ \sf{x=-8-7}[/tex]
[tex]\triangleright \ \sf{x=-15}[/tex]
That's it!
❄
HELP FAST PLEASE!!! Find the sample space of the situation using a table or tree diagram on
paper, and then type your sample space below.
tossing a coin (Heads or Tails) AND spinning the spinner (1-5)
Answers
Answer:
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
Step-by-step explanation:
Tossing a coin has two possible outcomes, heads (H) and tails (T).
Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.
Table:
First spin H H H H H T T T T T
Second spin 1 2 3 4 5 1 2 3 4 5
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
The table lists the speeds of the fastest roller coasters in North America and Asia.
Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .
Answers
The difference of the means of the two data sets is = 4.57
The mean absolute deviation of the roller coaster speeds in North America is 13.3
The mean absolute deviation of the roller coaster speeds in Asia is 16.8
How to solve for the meansFirst we have to start with the data for North America
128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77
To get the mean you have to sum up the values and divide through by the total number 10
937.8/10
Mean = 93.78
Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10
133.32/10 = 13.3
For Asia, we have the data as
149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4
Mean for Asia = 892.1/10
= 89.21
Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10
= 168.32/10
16.8
The difference in the means = 93.78 -89.21
= 4.57
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Select the correct answer from each drop-down menu. Consider circle C with diameter DE. Diameter shows a circle centered at C. Points D and E lies on the circumference of the circle. Point E is labeled (13, 11) and point D is labeled (minus 3, 3). The equation of circle C is
Answers
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard equation of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the circle center and r is the radius of the circle.
The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:
h = (13 + (-3))/2 = 5
k = (3 + 11)/2 = 7
(h, k) = (5, 7)
[tex]Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}[/tex]
Radius = diameter / 2 = 8√5 ÷ 2 = 4√5
The equation of the circle is:
(x - 5)² + (y - 7)² = (4√5)²
(x - 5)² + (y - 7)² = 80
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
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Help me pls this is very hard for me and plus i gotta turn this in tomorrow
Answers
Answer: [tex]\Large\boxed{x=40^\circ}[/tex]
Step-by-step explanation:
Given information
∡ 1 = 90°
∡ 2 = 50°
∡ 3 = x°
Total Angle = 180° (Triangle angle sum theorem)
Given formula
∡ 1 + ∡ 2 + ∡ 3 = Total Angle
Substitute values into the formula
(90) + (50) + (x) = (180)
Combine like terms
140 + x = 180
Subtract 140 on both sides
140 + x - 140 = 180 - 140
[tex]\Large\boxed{x=40^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
answer 1: meters
answer 2: meters
HELP PLS
Answers
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the length and y represent the width. Hence:
x + 2y = 50
x = 50 - 2y
Also:
xy = 288
(50 - 2y)y = 288
y = 9; and y = 16
x = 32; and x = 18
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
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Select the order in which the operations should be performed
12-4/4
Divide 12 by 4, then subtract 4 from that number.
Divide 4 by 4, then subtract that number from 12.
Subtract 4 from 12, then divide that number by 4.
Subtract 4 from 12, then multiply that number by 4.
None of the above
Answers
Answer: Divide the 4/4 then subtract that from 12.
Step-by-step explanation:
Use PEMDAS. The Division comes first, then the subtraction.
A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.
Answers
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
Data obtained from the questionFrom the question given above, the following data were obtained:
Force (F) = 3 poundsExtension (e) = 0.6 feetWork done (Wd) =?How to determine the spring constantForce (F) = 3 poundsExtension (e) = 0.6 feetSpring constant (K) =?F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
How to determine the work doneSpring constant (K) = 5 pound/footExtention (e) = 0.7 feetWork done (Wd) =?Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
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Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x³
a=0
b=3
3 Intervals
Answers
Split up the interval [0, 3] into 3 equally spaced subintervals of length [tex]\Delta x = \frac{3-0}3 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3]
The left endpoint of the [tex]i[/tex]-th subinterval is
[tex]\ell_i = i - 1[/tex]
where [tex]i\in\{1,2,3\}[/tex].
Then the area is given by the definite integral and approximated by the left-hand Riemann sum
[tex]\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}[/tex]
The number of pennies on square 64 is the total number of pennies on the first 63 squares.
Answers
Answer:The number of pennies on square 64 is greater than the pennies on 63 squares since 64 is already greater 63 that when 63 gets bigger 64 will also get bigger so it will always be greater than 63
Step-by-step explanation:
Answer:
Step-by-step explanation:
greater than
The sum of fice consecutive positive intergers is 2020. Find the largets of these numbers.
Answers
Answer:
3, 7, 14
Step-by-step explanation:
If f(x)=x²-3x - 4 and g(x) = x² + x, what is (f + g)(x)?
Answers
Answer: (f+g)(x)=2(x-2)(x+1).
Step-by-step explanation:
[tex]f(x)=x^2-3x-4\ \ \ \ \ g(x)=x^2+x\\(f+g)(x)=(x^2-3x-4)+(x^2+x)\\(f+g)(x)=x^2-3x-4+x^2+x\\(f+g)(x)=2x^2-2x-4\\(f+g)(x)=2*(x^2-x-2)\\(f+g)(x)=2*(x^2-2x+x-2)\\(f+g)(x)=2*(x*(x-2)+(x-2))\\(f+g)(x)=2*(x-2)*(x+1).[/tex]
What is the result of subtracting the second equation from the first?
- 2x + y = 0
-7x + 3y = 2
Answers
The result is [tex]5x-2y=-2[/tex].
On the day after my birthday this year, I can truthfully say: "The day after tomoroow is Monday". ON which day is my birthday?
Answers
Answer:
Saturday
Step-by-step explanation:
2 days before (starting from Monday) is Saturday
Which of the following is the domain and range of the ellipse with equation 4x2 + 25y2 – 8x + 100y + 4 = 0?
Answers
The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
How to determine the domain and the range of the ellipse?The equation of the ellipse is given as:
4x^2 + 25y^2 – 8x + 100y + 4 = 0
Next, we plot the graph of the ellipse
See attachment for the graph of the ellipse
The domain
From the attached graph the minimum and the maximum values of x are:
Minimum = -4
Maximum = 6
So, the domain of the ellipse is [-4. 6]
The range
From the attached graph the minimum and the maximum values of y are:
Minimum = -4
Maximum = 0
So, the range of the ellipse is [-4. 0]
Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
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Find the smallest number by which 35280 must be multiplied so that the product is a perfect square.
Answers
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
What number must be an integer multiplied by to find a perfect square?
A number is a perfect square if the following property is satisfied:
a = b², where is a natural number.
Please notice that b can be either a prime number or a product of prime numbers.
Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of prime numbers:
35280 = 2⁴ × 3² × 5 × 7²
35280 = (2²)² × 3² × 5 × 7²
35280 = 4² × 3² × 5 × 7²
Then, we must add a 5 to find a product that is a perfect square:
4² × 3² × 5² × 7² = 176400
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
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Two 6-sided dice, one red and one green, are rolled. What is the probability that the red die shows a 2 and the green die shows a 5
Answers
The probability that the red die shows a 2 and the green die shows a 5 is 1/36
How to determine the probability that the red die shows a 2 and the green die shows a 5?The sample space of a die is
S = {1, 2, 3, 4, 5, 6}
This means that
Red die = {1, 2, 3, 4, 5, 6}
Green die = {1, 2, 3, 4, 5, 6}
On the dice, we have
P(Red = 2) = 1/6
P(Green = 5) = 1/6
The probability that the red die shows a 2 and the green die shows a 5 is
P = P(Red = 2) * P(Green = 5)
Substitute the known values in the above equation
P = 1/6 *1/6
Evaluate the product
P = 1/36
Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36
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Which expression is equal to
CSC X
- cOs x cot x
using identities?
Answers
Step-by-step explanation:
Because the two sides have been shown to be equivalent, the equation is an identity.
on a unit circle, the terminal point of theta is (0, - 1) what is tan theta?
A. 1
B. Undefined
C. -1
D. 0
Answers
The answer is B.
If the terminal point of θ is at (0, -1), then tanθ is equal to :
Δy/Δx-1/0UndefinedThe tangent of the given angle is undefined, so the correct option is B.
What is a tangent function?The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.
Given that on a unit circle, the terminal point of θ is (0, - 1) we need to determine tan θ,
We know that the terminal point of θ is (0, -1).
Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:
tan(θ) = =1/0
And we can't divide by zero, so it is undefined, then the correct option is B.
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A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number.
Answers
The smaller number that we can take is x = 14, and in that case, the value of the other number is y = 34
How to write the inequality?First, we have two numbers, x and y, such that:
y = 6 + 2*x
"the first number is 6 more than 2 times another number".
Now we know that the sum of these two numbers is smaller than 50, then we can write:
x + y < 50
Replacing y by the above equation we get:
x + 6 + 2x < 50
3x + 6 < 50
Now we can solve that inequality for x:
3x < 50 - 6 = 44
x < 44/3 = 14.6
And x can only be a whole number, then:
x ≤ 14
The smaller number that we can take is x = 14, and in that case, the value of the other number is:
y = 6 + 2*14 = 34
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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
Answers
The probability that the person is over 40 and prefers cola exists at 1.3725.
What is probability?The probability of an event exists in the ratio of the size of the event space to the size of the sample space.
The size of the sample space exists the entire number of possible outcomes.
The event space exists the number of outcomes in the event you exists interested in.
So, P = size of the event space/size of the sample space
To estimate the probability that the person exists over 40 years.
Size of the sample size = 255
Size of the event space = 85
P = 85/255
P = 1/3
To estimate the probability that they drink cola.
Size of the sample size = 255
Size of the event space = 95
P = 95/255
P = 19/51
To estimate the probability that the person exists over 40 years of age or that they drink cola
So, P = (1/3) + (19/51)
[tex]$P = (51*3+3*19)/153[/tex]
P = 1.3725
Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.
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(ASAP PLEASE) Peter had some triangular tiles with sides 3 cm long. He placed them side by side to make a trapezium. If the perimeter of the trapezium was 27 cm, how many tiles did Peter use?
Answers
Answer:
She used 9 tiles which are 3 cm long
Step-by-step explanation:
cuz 3x9=27 and yea
Mrs. kelley asked her students to plot the number of books they read over the summer. a dot blot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots. using the dot plot, what was the total number of students that plotted the number of books they read? 3 6 17 18
Answers
The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.
In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.
We are asked to find the total number of students that plotted the number of books they read using the dot plot.
The dot plot is attached to the solution.
The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.
Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
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Write an equation for the
function graphed above
Answers
Answer:
g(x) = (x + 1)² + 1
Step-by-step explanation:
the original function
f(x) = x²
for the new function g(x)
it is shifted 1 unit to the left and 1 unit up.
the shift to the left is done by adding these units to the input variable x :
g(x) = f(x+1) = (x+1)²
that way we get the function value for x+1 already at x :
1 unit "earlier" than in the original.
and the shift up is easy.
whatever the function calculates, we simply add 1 to everything.
the whole curve stays as it is, just one unit higher. g
so, the final g(x) = f(x+1) + 1 = (x + 1)² + 1
How do I write a comment on the data following the completion of the scatterplot
Answers
Hope this helps!
The question is down below.
Answers
The correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875
SOH CAH TOA identityThe given figure is a right triangle with legs 12.0 and 22.5cm and the hypotenuse 25.5cm
For sinA, <A is the reference angle, hence the opposite side will be 22.5cm
sin A = opp/hyp
sinA = 22.5/25.5
For cos C, the adjacent side will be 22.5cm, hence the measure of cos C is 22.5/25.5
cosC = 22.5/25.5
Similarly, sinC = 12/25.5 = 24/51
<A = 180-(90 +38)
<A =180 - 128
<A = 62 degrees
tan A = opp/adj
tan A = 22.5/12 = 1.875
tan C = 12/22.5
tan C = 0.533
Hence the correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875
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Please do it fast as possible
Answers
The factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).
The given expression is 20m²/n²- 30n²/m² +1.
We need to factorise the given expression.
How to factorise the trinomial?To factor, a trinomial in the form x²+ bx + c, find two integers, r and s, whose product is c and whose sum is b.
Rewrite the trinomial as x²+ rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).
Now, we can rewrite 20m²/n² +1 - 30n²/m² as 20m²/n² +25mn/mn- 24mn/mn- 30n²/m².
=(20m²/n² +25mn/mn)- (24mn/mn- 30n²/m²)
=5m/n(4m/n + 5m/n)-6n/m(4m/n+5n/m)
=(4m/n + 5m/n)(5m/n-6n/m)
Therefore, the factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).
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help pls with math lotsss of points!!!
Answers
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
The odds in favor of a horse winning a race are 9:5. find the probability that the horse will win the race.
Answers
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.
