In trapezoid ABCD, Line AB is parallel to CD. If AE=5.2, AC=11.7 and CD=10.5, what is the length of AB to the nearest tenth?
Answers
In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
What is trapezoid?" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."
According to the question,
Given
Length of AE=5.2
Length of AC=11.7
Length of CD=10.5
As shown in figure
In trapezoid ABCD,
AB is parallel to CD, AC is the transversal.
AC and BD intersect at point E.
In ΔABE and ΔCDE,
∠BAE ≅∠ECD
∠ABE ≅∠EDC
By AA theorem,
ΔABE ~ ΔCDE
Therefore,
[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]
AE + EC = AC
⇒ 5.2 + EC = 11.7
⇒ EC = 11.7 - 5.2
⇒ EC = 6.5units
Substitute the value in the given proportion we get,
[tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]
⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]
⇒[tex]AB = 8.4[/tex] units
Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
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Related Questions
Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54.
what is the first term of the sequence?
to get to the next term, you would_____
this is a _____ sequence
there are 27 weeks left in this school year for monique. if she continues getting coffee at this rate how much money will she have spent on coffee by the end of the year?
Answers
If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
Tₙ = a + (n-1)d
(for all positive integer values of n)
Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,
4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........
Therefore,
The first term of the sequence is 4.54, To get the next term you need to add 4.54. This is an arithmetic sequence.Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,
a₃₆ = 4.54 + (36-1)4.54
a₃₆ = 163.44
Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
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How many solutions does the equation below have? 1/(-6-8x) = -3- 1x
Answers
Answer:
This equation has 2 solutions.
1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]
2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]
1. Trig Function
2. Coordinate value (x, y)
3. Value in terms of sinθ and/or cosθ
sinθ = _________________
cosθ = _________________
secθ = _________________
cscθ = _________________
tanθ = _________________
cotθ = _________________
Answers
The values of the given trig functions in terms of sinθ and/or cosθ are:
sinθ = tanθ.cosθ
cosθ = sinθ/tanθ
secθ = 1/cosθ
cscθ = 1/sinθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
Trigonometric functionsFrom the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ
sinθNOTE: tanθ = sinθ / cosθ
∴ sinθ = tanθ.cosθ
cosθFrom above, we can write that
cosθ = sinθ/tanθ
secθSecant is the inverse of cosine
∴ secθ = 1/cosθ
cscθ (cosecθ)Cosecant is the inverse of sine
∴ cscθ = 1/sinθ
tanθtanθ = sinθ/cosθ
cotθCotangent is the inverse of tangent
∴ cotθ = 1/tanθ
But, tanθ = sinθ/cosθ
∴ cotθ = cosθ/sinθ
Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:
sinθ = tanθ.cosθ
cosθ = sinθ/tanθ
secθ = 1/cosθ
cscθ = 1/sinθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
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|2x -8| < 2
a. 3
b. -5
c. x>5 or x<3
d. x>-3 or x<-5
Answers
Answer:
[tex]3 < x < 5[/tex]
Step-by-step explanation:
Given inequality:
[tex]|2x - 8| < 2[/tex]
[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]
[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]
[tex]\implies -2 < 2x-8 < 2[/tex]
Therefore:
[tex]\implies -2 < 2x-8[/tex]
[tex]\implies 6 < 2x[/tex]
[tex]\implies 3 < x[/tex]
And:
[tex]\implies 2x-8 < 2[/tex]
[tex]\implies 2x < 10[/tex]
[tex]\implies x < 5[/tex]
Merge the overlapping intervals: [tex]3 < x < 5[/tex]
Proof
Graph: [tex]y=|2x-8|[/tex]
Add a line at [tex]y=2[/tex]
The interval that satisfies [tex]|2x - 8| < 2[/tex] is the area under the points of intersection (shaded area on the attached graph).
The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.
So
Case-1
2x-8<22x<2+82x<10x<5Case-2
2x-8>-22x>6x>3So solution is
3<x<5find the solutions(s) to 9x^2-54x+0
Answers
Answer:
x = 6
x = 0
As shown, there are 2 values for x. The question is why, which we will go over in the explanation part.Step-by-step explanation:
identify the coefficients
[tex]9x^2-54x=0\\a=9\\b=-54\\c=0[/tex]
coefficient a = 1
[tex]9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0[/tex]
complete the square
[tex]b=-6\\(\frac{b}{2})^2=(\frac{-6}{2})^2\\(\frac{x}{y})^2=\frac{x^2}{y^2}\\=(\frac{-6}{2})^2=\frac{-6^2}{2^2}\\\frac{-6^2}{2^2}=\frac{36}{4}\\36 \div 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\\frac{b}{2}\\\frac{b}{2}=\frac{-6}{2}\\\frac{b}{2}=\frac{\left(-3\cdot 2\right)}{\left(1\cdot 2\right)}\\\frac{b}{2}=-3\\x^2-6x+9=9\\(x-3)^2=9\\[/tex]
solve for x
[tex](x-3)^2=9\\\sqrt{(x-3)^2}=\sqrt{9}\\x-3=+-\sqrt{9}\\x-3+3=3+-\sqrt{9}\\x=3+-\sqrt{9}\\x=3+-3\\x_1=6\\x_2=0[/tex]
≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.
please answer! this is my final question
Answers
Answer:
C. 103,748
Step-by-step explanation:
The one in the first number is worth 10,000
The one in the Second number is worth 100,000
Daniel has read 10% of a book. He has 45 more pages to finish. How many pages are there in the book?
Answers
Answer:
He read 10% of the book, so 90% remains to be read. That 90% consists of 45 pages, so
45=0.90n
n= 45/0.90
n=50
There are 50 pages total in the book
Step-by-step explanation:
The 45 pages left is 90 percent of it.
If the 10% is _ pages then whatever that number is times 9 (bc of 90%) should be 45.
If u do the math 5 pages is 10%. 45+5=50 pages in total
Select the correct answer from each drop-down menu.
veronica wants to cut a sheet of paper into squares with an area of 12 square inches. for the best approximation, the length of each side o
the square pieces of paper must be approximately equal to
inches. if each side were exactly this length, the area of each square
would be _____
square inches
Answers
Answer:3.46
Step-by-step explanation:i dont know the other one
In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen to the number of sophomores (F:S), and what ratio compares the number of sophomores to the number of freshmen (S:F)
Answers
Answer:
Freshmen to sophomores - (17:19)
Sophomores to freshmen - (19:17)
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
what fraction is at point M?
Answers
Answer:
D
Step-by-step explanation:
because 3/10 is 0.3
Hope this helps!
The type of data that contains results from other people that are of similar age and gender is known as
Answers
The type of data that contains results from other people that are of similar age and gender is known as normative data.
What is normative data?
Normative data is a type of data that is observed that contains information about the characteristics of a population of interest. For example, normative data about students in a class would contain information such as age, gender, height.
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how do i do this could you show step by step please?
Answers
Answer:
x = 2
Step-by-step explanation:
This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.
One leg is x, the second leg is x and hypotenuse x√2.
[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]
somebody please help me
Answers
Answer:
66°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in a triangle is 180°.
__
79° +x +35° = 180°
x = 180° -114° . . . . . . . . subtract 114° from both sides
x = 66° . . . . . simplify
Craig went bowling with $25 to spend. he rented shoes for $5.00 and paid $4.00 for each game. What was the greatest number of games he could have played?
A. 5
B. 7
C. 6
D. 4
Answers
Answer: A
Step-by-step explanation:
Given:
Budget = $25
Shoes rental = $5.00
Price per game = $4.00
To find the greatest number of games he played...
↓
First, subtract the rent for the shoes from the budget.
25 - 5 = 20
Second, divide the remaining money or budget by the price per game.
20 ÷ 4 = 5 (greatest number of games played)
Lastly, check if the expense is the same as the original amount of money.
5 (shoes) + 4(5) (number of games played)
5 + 20 = 25 (original amount of money)
Hope it helps!!! Please mark as brainliest. Thank you :D
m=p-2b/2
p=57.4
b=8.7
Answers
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
What is the value of m?Given that;
m = ( p-2b ) / 2p = 57.4b = 8.7Value of m = ?First, we substitute the value of p and b into the equation.
m = ( p-2b ) / 2
m = ( 57.4 - 2(8.7) ) / 2
m = ( 57.4 - 17.4 ) / 2
m = 40 / 2
m = 20
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
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Can anybody help me with this?
Answers
Answer:
A
Step-by-step explanation:
The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.
__
tableThe slope formula tells us the rate of change is ...
m = (y2 -y1)/(x2 -x1)
m = (-9 -(-10))/(-1 -(-4)) = 1/3
equationThe coefficient of x in the equations of the offered answer choices are 1/4 and 6.
comparisonThe relations between the various slopes are ...
1/4 < 1/3 < 6
That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:
y = 1/4x +4 because ... table of values is 1/3
12. Round 2,870 to the nearest hundred.
Answers
Answer:
2900
Step-by-step explanation:
2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.
Question 9 of 9
Which of the expressions are equivalent to the one below? Check all that
apply.
(15.3)-20
A. (3.15)-20
B. 20-(3.15)
C. 6 (15-20)
D. (3-20) (15-20)
Answers
Simplify the expression |1/12 - 5/6| - (2/5 + 1/10)
Answers
Answer:
x+2
Step-by-step explanation:
x^2+x-7 = x+2
Answer:
The answer is 1/4!!
<3 love
find the nature of the roots of the roots of the equation (x-705)(x-795)+800(x-750)(x-835)=0.
(A) Imaginary roots.
(B) Real and distinct.
(C) Real and equal.
(D) None.
Answers
Answer:
B
Step-by-step explanation:
If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.
These roots are real and distinct, or choice B.
If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.
I hope that helps!
Bottles of water come in packages of 6. Cheese sticks come in packages of 10.
What is the least number of packages of each a person has to buy to have the same number of bottles of water and cheese sticks?
Drag and drop a number into each box to complete the statement.
That person needs to buy Response area packages of bottles water and Response area packages of cheese sticks.
Answers
Answer:
water: 5 packagescheese sticks: 3 packagesStep-by-step explanation:
The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.
__
The LCM can be found by factoring out the greatest common divisor of each of the numbers:
6 = 2 × 3
10 = 2 × 5
The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.
The number of packages of bottles of water will be 30/6 = 5 packages.
The number of packages of cheese sticks will be 30/10 = 3 packages.
_____
Additional comment
You may notice that the number of packages of each kind is the unique factor in the other number.
Given the table, write an equation in slope-intercept form.
Answers
Answer:
If you plot points accordingly to the points on the table, Option A. is correct.
if f(x)= 3x -2, find f-1(x)
Answers
Answer: 1/3x + 2/3
Step-by-step explanation:
f(x)= 3x - 2 =>
y= 3x - 2 =>
x= 3y - 2 =>
3y - 2= x =>
3y= x + 2 =>
y= 1/3x + 2/3 =>
f-1(x)=1/3x + 2/3
Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4. Is she correct? Explain why or why not.
Answers
Answer:
She is wrong.
Step-by-step explanation:
The mean score is
7 + 8 + 3 + 0 + 2= 20
We then divide it by the number which is 5
20/5= 4.
Therefore, Maria is wrong.
This is because she divided by 4 instead of 5, as she didn't include the rational number 0.
Find ∠ if ∠=+49, ∠=+63, and ∠=106∘.
Answers
The vslue of the angle based on the information given will be 142°.
How to calculate the angle?From the information given, it can be deduced that the shape has four sides. The total angles will be:
= (n - 2) × 180
= (4 - 2) × 180°
= 360°
The value of the last angle will be:
= 360° - (49° + 63° + 106°)
= 360° - 218°
= 142°
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Answers
Answer:
-2
Step-by-step explanation:
For a straight-line graph, pick two points on the graph.
The gradient of the line = (change in y-coordinate)/(change in x-coordinate)
(x, y)
Point 1: (2, 0)
Point 2: (3, 2)
Gradient = (change in y)/(change in x)
= (2 - 0) / (3 - 2)
= 2 / 1
= 2
Note: gradient is basically slope where slope = rise / run
Answer:
help has arrived its -2
Step-by-step explanation:
How many inches are in 12 feet?
Answers
Answer:
144 inches in 12 feet.
Step-by-step explanation:
There are 12 inches in 1 foot.
Find inches when you have 12 ft.
[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]
Feet cancel out leaving inches.
There are 144 inches in 12 feet.
Given that m∠TSU = m∠SUQ, why is RT || UQ?
Answers
jeremy spends 3/4 of his check on paying bills and 15% on food if jeremy makes 500 $ how much money will he save
answer choices:
A. 375$
B. 50$
C. 125$
D. 85$
Answers
I got it by taking 15% off of 500 which is 75.
After i took off 75% and got 375. Add 375 and 75 to get 450. 500 - 450 = 50.
Therefore our answer is b, :) good luck
what is the mean of, 50, 30, 40, 10, 20, 80, 60, 90, 10, 30, 110, 70?
Answers
Answer:
50
Step-by-step explanation:
Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.
600 / 12 = 50.