In quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units

Answer:

e because the answer would be -4

Answer:

The simplified expression is 498,400÷7. The value is 71,200.

Step-by-step explanation:

712×25×14×2= 498,400.

498,400÷7 becomes our expression. And that answer is 71,200. I hope this helps

Answer:

Step-by-step explanation:

substitute

a + 2p = 4

x − 2y = 6

Answer:

187

Step-by-step explanation:

Answer: 6 foot

Step-by-step explanation:

You want to use the equation

5(n)

n will be 0.20 since the tree grew by 20% of its original height

5(0.20)=1

Now add 1 with 5

1+5

6

Answer:

6.0 ft

Step-by-step explanation:

20% of 5.0 ft is 1.0 so you add,   1.0ft+5.0ft=6.0ft

Answer:

Won't it just be 60, because it's an equilateral triangle.

Step-by-step explanation:

60 + 60 = 120

180 - 120 = 60

11x - 6 = 60

11x = 66

x = 66/11

x = 6

Let's substitute.

11(6) - 6 = 66 - 6 = 60

Answer:

d

Step-by-step explanation:

^u^

The amount of units that must be sold to a number yields a maximum profit is 600. Hence 600 units will be the correct option.

To find the maxima of any function it needs to differentiate with respect to the dependent variable and equate with zero to get stationary points.

After achieving the stationary points it needs to put on the double derivative of that function to check whether it's maxima or minima.

If the double derivative got negative then it will be maxima.

Given that function

f(x) = -0.001(x-600)² + 90

By differentiation

[tex]$f'(x)$[/tex] = -0.002(x - 600) + 90

Now equate with zero

-0.002(x - 600) + 90 = 0

x - 600 = 0

x = 600

Now checking the x at double derivative

[tex]$f''(x)$[/tex] at x = 600 it is coming out to -0.002 which is negative Hence, the 600 units will be the correct answer.

For more about maxima

https://brainly.com/question/13995084

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Answer:

12 years later.

Step-by-step explanation:

Let assume in X years, the table will be twice as old as the sofa.

36+X=2(12+X), X=12

Or think it the other way. The difference of ages between two things never change. So they must have a difference(of age) of 24 forever. When will this difference(24) be as same as the younger's age so that the older one is exactly twice as old as the younger? 12 years later when the sofa is 24.

Answer:

x=4

Step-by-step explanation:

5x-7=13

5x=13+7

5x=20

x=20/5

x=4

Answer:

x = 4

Step-by-step explanation:

5x - 7 = 13

add 7 to both sides:

5x - 7 + 7 = 13 + 7

5x = 20

divide both sides by 5

[tex]\frac{5x}{5} = \frac{20}{5}[/tex]

x = 4

Answer:

(x - 4)(x + 4)

Step-by-step explanation:

x² - 16 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 16

= x² - 4²

= (x - 4)(x + 4)

Answer:The ratio of the number of children who can swim to the number of children who cannot swim=2:1

Step-by-step explanation:

Number of children that can swim  = N umber of boys and girls that can swim =23+17  =40

Number of children that cannot  swim  = N umber of boys and girls that cannot swim=9+11=20

=40:20

=2:1

Answer:

Step-by-step explanation:

Solution:

Rewriting input as fractions if necessary:

9/10, 1/4

For the denominators (10, 4) the least common multiple (LCM) is 20.

LCM(10, 4)

Therefore, the least common denominator (LCD) is 20.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

9/10 = 9/10 × 2/2 = 18/20

1/4 = 1/4 × 5/5 = 5/20

Answer:

117

Step-by-step explanation:

Required number

[tex] = 65 \times \frac{9}{5} \\ \\ = 13 \times 9 \\ \\ = 117[/tex]

Answer:

Step-by-step explanation:

Short Answer: No

2(12 - y) = 23- (2y - 1)                    Remove the Brackets on both sides

24 - 2y = 23 - 2y + 1                     Combine like terms on the right

24 - 2y = 24 - 2y                          No matter what you do, the 2ys are going to cancel. When they do, the question goes with them.

You get 24 = 24 Which is true but not relevant.

The other answer you could use is there are an infinite number of answers.

Equality will be maintained, but there is no single answer that works.

Answer:

This equation is an identity, all real numbers are solutions.

Step-by-step explanation:

Simplifying

2(12 + -1y) = 23 + -1(2y + -1)

(12 * 2 + -1y * 2) = 23 + -1(2y + -1)

(24 + -2y) = 23 + -1(2y + -1)

Reorder the terms:

24 + -2y = 23 + -1(-1 + 2y)

24 + -2y = 23 + (-1 * -1 + 2y * -1)

24 + -2y = 23 + (1 + -2y)

Combine like terms: 23 + 1 = 24

24 + -2y = 24 + -2y

Add '-24' to each side of the equation.

24 + -24 + -2y = 24 + -24 + -2y

Combine like terms: 24 + -24 = 0

0 + -2y = 24 + -24 + -2y

-2y = 24 + -24 + -2y

Combine like terms: 24 + -24 = 0

-2y = 0 + -2y

-2y = -2y

Add '2y' to each side of the equation.

-2y + 2y = -2y + 2y

Combine like terms: -2y + 2y = 0

0 = -2y + 2y

Combine like terms: -2y + 2y = 0

0 = 0

Solving

0 = 0

Answer:

840.89+928= 1768.89

74.4 / 0.8= 93

Step-by-step explanation:

I hope this helps <3

Answer:

The difference:

The product:

The sum:

The quotient:

Answer:

$108

Step-by-step explanation:

The computation of the total profit is shown below:

Given that

1 box = $12

18 boxes = 12×18 = $216

So

Total = 18×65 = 1170 pens

Now Cost price, Cp = $216

Also,

3 = $1

So,

= 378 ÷ 3

= $126

Now

= 1170-378

= 792 pens remaining

4 = $1

So,

792

= 792 ÷ 4

= $198

Now

Total selling price, sp = 126+198 = $324

So finally

Profit = Sp - Cp

= $324 - $216

= $108

Answer: See explanation

Step-by-step explanation:

1. Complementary (adds up to 90°)

2. Neither

3. Supplementary (ads up to 180°)

4. Adds up to 90° since its complementary

22 + 4x = 90

Subtract 22 from both sides

4x = 68

Divide both sides by 4

x = 17

5. Adds up to 90° since its complementary

65 + x + 2 = 90

x + 67 = 90

Subtract both sides 67

x = 23

6. Adds up to 90° since its complementary

43 + x - 7 = 90

x + 36 = 90

Subtract both sides by 36

x = 54

7. Adds up to 180° since its supplementary

29 + x - 5 = 180

x + 24 = 180

Subtract both sides by 24

x = 156

8. Adds up to 180° since its supplementary

110 + 7x = 180

Subtract both sides by 110

7x = 70

Divide both sides by 7

x = 10

9. Adds up to 180° since its supplementary

72 + x + 4 = 180

x + 76 = 180

Subtract both sides by 76

x = 104

10. Adds up to 90° since its complementary

49 + x + 3 = 90

x + 52 = 90

Subtract both sides by 52

x = 38

11. Adds up to 180° since its supplementary

92 + x + 78 = 180

x + 170 = 180

Subtract both sides by 170

x = 10

12. Adds up to 180° since its supplementary

19 + x - 50 = 180

x - 31 = 180

Add 31 to both sides

x = 211

13. Supplementary angles add up to 180°

∠C + ∠D = 180

∠C + 45 = 180

Subtract both sides by 45

∠C = 135°

Hope I helped!

Answer:

62/100= 31/50

45/100= 9/20

Step-by-step explanation:

Divide 62 and 100 by two to simplify

Divide 45 and 100 by 5 to simplify

Answer:

62/100 = 31/50

45/100 = 9/20

Step-by-step explanation:

62 and 100 have a greatest common factor of 2. We can use this to break the fraction 62/100 apart:

[tex]\dfrac{62}{100}=\dfrac{2\times31}{2\times50}=\dfrac{2}{2}\times\dfrac{31}{50}=\dfrac{31}{50}[/tex]

We can do the same to simplify 45/100. The greatest common factor of 45 and 100 is 5, so following the same process:

[tex]\dfrac{45}{100}=\dfrac{5\times9}{5\times20}=\dfrac{5}{5}\times\dfrac{9}{20}=\dfrac{9}{20}[/tex]

9514 1404 393

Answer:

  (a) $2.857 million

  (b) vertical compression by 1/3; shift left by 6; shift up by 2

Step-by-step explanation:

(a) Find the year difference (2021-2010=11) and put that value where x is. Then do the arithmetic.

  g(11) = (∛(11+6))/3 +2 = (∛17)/3 +2 ≈ 2.57128/3 +2 ≈ 0.857 +2

  g(11) ≈ 2.857 . . . 2021 revenue in millions of dollars

__

(b) For parent function f(x), the transformation ...

  g(x) = a·f(x -h) +k

represents a vertical scaling by a factor of 'a', right shift by h units, and up shift by k units.

Comparing this form to the given g(x), we see ...

  a = 1/3 . . . vertical compression by a factor of 1/3

  h = -6 . . . .right shift 6 units

  k = 2 . . . . up shift 2 units

_____

Additional comment

The vertical scaling is called "compression" when the scale factor is less than 1, and "stretch" when the scale factor is greater than 1. Here, the scale factor of 1/3 means the graph is vertically compressed.

Answer: (a+a)-10

Step-by-step explanation: I think this works bcuz it's equivalent?

Answer:

B. 36/100 x 400

C. 0.36 ⋅ 400

Step-by-step explanation:

A. 3.6/100 x 400

B. 36/100 x 400

C. 0.36 ⋅ 400

D. 36 ⋅ 400

E. 0.36/100 x 400

36% of 400

= 36/100 × 400

= 0.36 * 400

= 144

Answer:

-3x+5y-3z + 2x-7y+3z

= -x-2y

= x-2y-(-x-2y)

= x + x +2y-2y

= 2x

Answer: 876 feet

Step-by-step explanation:

Given

Carmelit travels 5658 feet horizontally

The slope of trajectory is   [tex]\dfrac{14.6}{94.3}[/tex]

We know, the slope is

[tex]\Rightarrow \text{slope}=\frac{\text{Vertical distance}}{\text{horizontal distance}}\\\\\Rightarrow \dfrac{14.6}{94.3}=\dfrac{Y}{5658}\\\\\Rightarrow Y=876\ feet[/tex]

Hence, the elevation of the top station is 876 feet

Answer:

x = -3

y = -2

Step-by-step explanation:

Answer:

( x,y ) = ( 72/163,-3294/163

Answer:

720

Step-by-step explanation:

in an all year is 8760

Answer:

area is 9

see picture for points

Step-by-step explanation:

base is 6

height is 3

6 * 3 /2 = 9

Imagine cutting this shape into two semi-circles and one rectangle.

------------------------------------------------------------------------------------------------------

--------------------------------------------------------------------

We know the area of a whole circle which is π[tex]r^{2}[/tex]

because a semi-circle is basically half of the whole circle!

However, since we have two equal semi-circles...we can just put them together and solve for the whole circle's area.

for reference:

1/2(π[tex]r^{2}[/tex]) + 1/2(π[tex]r^{2}[/tex]) = 2/2(π[tex]r^{2}[/tex]) = π[tex]r^{2}[/tex]

----------------------------------------------------------

First, the area of rectangle: length times width = 84 x 36 = 3024 square meters

Anyways, since we have to sub in 3.14 for π

Area of a whole circle: (3.14 x [tex]r^{2}[/tex]) = (3.14 x [tex]18^{2}[/tex]) = 1017.36 square meters

-----------------------------------------------------------

3024 + 1017.36 = 4041.36 square meters

Answer:

Step-by-step explanation: