If the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]
Recall:
Area of a rectangle = length x widthGiven the algebraic expressions for the dimension of the rectangular court as:
length = (7x + 8) ft
width = (3x + 6) ft
Therefore,Area = [tex](7x + 8) \times (3x + 6)[/tex]
Apply the distributive property[tex]Area =7x(3x + 6) +8(3x + 6)\\\\Area = 21x^2 + 42x + 24x + 48\\\\[/tex]
Add like terms[tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]
Therefore, if the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]
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Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!
The proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
The given figure showing ΔABE ≅ ΔDCE is in the image attached below.
We know that:
E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.
E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.
∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.
This means that ΔAEB and ΔDEC have:
two pairs of congruent sides - AE ≅ ED and BE ≅ EC
one pair of congruent included side - ∠AEB ≅ ∠CED
Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.
If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.
Therefore, AB∥CD by the CPCTC Theorem.
Thus, the proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
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PLEASE HELPP!! What is the slope and Y intercept of this equation?
Answer:
The slope is 10
The y - intercept is 20
Step-by-step explanation:
The equations are written as:
y = ?x + ?
The first ? is the slope of the equation, every time y increases by that amount, x increases by one, the slope here is 10
The second ? is the y-intercept, or the place where x is 0. Here, when x is 0, y is 20, so it is the y-intercept
Iro drives 50 miles/hour for 0.6 hours. Kalini drives 65
miles/hour for 0.5 hours.
Who drove farther, and how far did that person drive?
Answer:
iro 50*.6 gives us 30 miles
andkalini drives 65 for .5 65*.5= 32.5 miles
so kalini drove further
6 less than the quotient of 4 and a number
Answer:
4/n subtracted by 6 or the third option
Step-by-step explanation:
Which of the following is an arithmetic sequence with common difference 2?
O A. 1, -3, 5, -7, 9, ...
O B. 2, 4, 8, 16, 32, ...
O C. 10, 8, 6, 4, 2, ...
-
D. 13, 15, 17, 19, 21, ...
, ,
Answer:
B
Step-by-step explanation:
You can find the nth term of the arithmetic sequence calculator to find the common difference of the arithmetic sequence. The approach of those arithmetic calculator may differ along with their UI but the concepts and the formula remains the same. You need to find out the best arithmetic sequence solver having good speed and accurate results.
Answer:
iaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
What is the slope of this line?
−12
12
2
2 is the answer!!
MARK ME BRAINLIEST PLSSSSIvanna and her husband are each starting a saving plan. Ivanna will initially set aside $50 and then add $50.85 every week to the savings. The amount A (in dollars) saved this way is given by the function A=50 +50.85N, where N is the number of weeks she has been saving. Her husband will not set an initial amount aside but will add $65.95 to the savings every week. The amount B (In dollars) saved using this plan is given by the function B=65.95N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Answer:
N=0.019666a-0.983284 or
A = 50.85n + 50
Step-by-step explanation:
Let's solve for n.
a = 50 + 50.85n
Step 1: Flip the equation.
50.85n + 50 = a
Step 2: Add -50 to both sides.
50.85n+50+-50=a+-50
50.85n n = a - 50
Step 3: Divide both sides by 50.85.
50.85n
50.85
=
a-50
50.85
n=0.019666a-0.983284
Let's solve for a.
a = 50 + 50.85n
how many 3/5s are in 9/10
Answer:they are only 2
Step-by-step explanation:
3/5 + 3/5 = 6/10 so you need a 6/5 + 3/5 and it will equal 9/10
Answer:
1
Step-by-step explanation:
3/5's = 6/10 and 6/10 plus 6/10 would be 12/10 so only 1 3/5's can fit.
Simplify the following surd expressions
a) 9V3 -4V3 + V5 + 2V5
b) 10V2 + 4V7 - 6V2
a.9v3-4v3+v5+2v5
=5v3+v3+2v5
=5v3+3v5
b.10v2+4v2+6v2
=4v2+4v7
this got me confused but can somebody please tell me what the answer is to: 7(2x - 3) = 14x + 7
Answer:
14x-21=14x +7
x cancels all out which leaves with just
28
Answer:
There is no x that satisfies the condition.
Step-by-step explanation:
7(2x - 3) = 14x + 7
14x - 21 = 14x + 7
-21 = 7
contradiction
the value of /14-15/ is
The volume of one serving of fruit punch
is 3.5 fluid Ounces. How many servings
are there in 29.75 fluid Ounces of
fruit punch?
A. 8.25 Servings
B. 8.5 Servings
C. 9.25 Servings
D. 9.5 Servings
Please help and please no links or just answering for points ¯\_(ツ)_/¯
Answer:
8c + 6 = 3
Step-by-step explanation:
six more than the product of a number and 8 is 3
the product of 8 and c is 8•c, which can also be written as 8c. 6 more than that means you are adding 6, and getting 3... so your equation is,
8c + 6 = 3
hope this helped!
mark me brainliest :D
HELP NEEDED ASAP
Order the numbers from least to greatest
Answer:
-31/6, -/26, -5, -5/6
first choice is the answer
Use cross multiplication to solve this equation. Steps must be shown pls. (Get T alone and on the other side of the equation.)
t/4 = 1/5
Answer:
T = 4/5
Step-by-step explanation:
t/4 = 1/5
x4 x4
t = 4/5
Hope this works.
Answer:
4/5
Step-by-step explanation:
t/4 = 1/5
5t = 4
t = 4/5
yeah-ya.... right?
solve pls brainliest
6. What is the percent of increase from 10 to
12?
A. 20%
B. 25%
C. 30%
D. 33
33%
Answer:
A. 20%
Step-by-step explanation:
% Increase = 12−10/10x100
= 2/10x100
= 20%
Mark me as brilliant
Two trains, Train A and Train B, weigh a total of 557 tons. Train A is heavier than Train B. The difference of their weights is 371 tons. What is the weight of each train?
Answer:
A=464
B=93
Step-by-step explanation:
A+B=557
A-B=371
Solving the two equations simultaneously gives A=464 and B=93
Pleaseeee Helpppp
Point M is located at 1.2 x 10-6. Plot Point M on the number line below
Which expression is equivalent to (-x-16)
-x-16?
X-+16
-X+16
X-16
Answer:
- x - 16
Step-by-step explanation:
. A rectangular trunk has a volume of 28,600 cubic inches. The trunk is 50 inches long by 22 inches wide. What is the trunk’s height
Is 9/12 somehow related to the fractions "4/5","3/4" and "2/3"?
State the connection or how to get 9/12 from those fractions pls
Answer:
3 / 4
Step-by-step explanation:
9 = 3 x 3
12 = 3 x 4
9 / 12
= ( 3 x 3 ) / ( 3 x 4 )
= 3 / 4
Answer:
3/4
Step-by-step explanation:
9= 3×3
12= 3×4
9/12
= (3×3) / (3×4)
= 3/4
An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his 6 nephews and rented five pairs of ice skates.
He was charged $32. Juanita paid admission fees for her seven grandchildren and rented 5 pairs of ice skates. She was charged $35.25. What is the admission fee?
What is the rental fee for a pair of skates?
Answer:
if we let admission fee per child to be a and the rental fee for the skates to be s.
Then john 6a + 5s =32
Juanita 7a + 5s = 35.25
Solving simultaneously we can eliminate s to solve for a first by subtracting one equation from the other.
6a + 5s = 32
7a + 5s = 35.25
we get -a + 0s = -3.25 therefore a= 3.25
Then we can solve for s by substituting a in either of the two equations
6 (3.25) + 5s =32
19.5 + 5s =32
5s = 12.5
s = 12.5/5
s = 2.5
Therefore, the admission fee: $ 3.25 per person and rental fee: $ 2.5 per pair of skates.
Step-by-step explanation:
20 points solve (x-3)(x^2+3x+9)=37
Answer:
the answer is x = 4.
1. use the quadratic formula.
2. use a coordinate plane to check your answer.
hope this helps.
Answer:
x = 4
Step-by-step explanation:
(x - 3)(x² + 3x + 9) = 37 ← distribute left side
x³ + 3x² + 9x - 3x² - 9x - 27 = 37 , simplify left side by collecting like terms
x³ - 27 = 37 ( add 27 to both sides )
x³ = 64 ( take cube root of both sides )
x = [tex]\sqrt[3]{64}[/tex] = 4
is this correct? if not what is the correct answer?
6 soaps comparing to the other 5 = 30 different comparisons:
30 x 2,000 = 60,000
Answer: H. $60,000
Given: x - 5 > -2.
Choose the solution set.
{x | x R, x > 3}
{x | x R, x > -3}
{x | x R, x > -7}
{x | x R, x > 7}
Answer:
{x | x R, x > 3}
Step-by-step explanation:
x - 5 > -2
Add 5 to each side
x - 5+5 > -2+5
x> 3
help 6th grade math im will give brainliest
ok I don't see the thing you need help with
What do you need help with?
NEED ANSWER ASAP!
Write an equation, in the form y = mx + b, that shows the linear relationship between the x and y values in the table.
Table: Below
Answer:
y = -5 + 2
Step-by-step explanation:
We can use change in y over change in x to find slope:
[tex]\frac{y2-y1}{x2-x1} =\frac{-8--3}{2-1} =\frac{-8+3}{1} =-5[/tex]
So, our slope (aka m) is -5.
For our b, or the y-intercept, we will need to find what value y is when x is 0. To do this, we will plug in a point for what we have so far, and then solve for b
y = -5x + b
-8 = -5(2) + b
-8 = -10 + b
2 = b
And there is our equation,
y = -5 + 2
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
If i can get 6 poland spring water 3-liter for $6. How much would it be if i get 3 poland water?
Explain
Answer:
$3
if we wanted to find how much 1 bottle would cost we would do 6/6=1 and from that we now know that 1 bottle of water costs $1 so if we times that by 3 to find out how much 3 bottles will cost we get $3.
Which rational expression does not have any excluded values?
x+2/2x^2
2x+4/3x+3
6x-5/x^2-7
x+2/-x^2-5
Answer:
D.
Step-by-step explanation:
An excluded value often comes from a zero in the denominator.
Set each denominator equal to zero creating an equation in x. If there is a solution to the equation, then there are excluded values. If the equation has no solution, then there are no excluded values.
A.
2x^2 = 0
x = 0
excluded value
B.
3x + 3 = 0
3x = -3
x = -1
excluded value
C.
x² - 7 = 0
x² = 7
x = √7 or x = -√7
excluded values
D.
-x² - 5 = 0
x² = -5
x = √(-5) or x = -√(-5)
There is no real solution for x.
no excluded values
Answer: D