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3 years ago

Given: AM = 8, AB = 5x +1 and M is the midpoint of AB, find x and AB X= AB=

Mathematics

1 answer:

NARA [144]3 years ago

3 0

Answer:

x = 3

AB = 16

Step-by-step explanation:

Given: AM = 8, AB = 5x +1 and M is the midpoint of AB, the AM = MB

AB = 2AM

5x+1 = 2(8)

5x + 1 = 16

x = 16 - 1

5x = 15

x = 15/5

x = 3

Hence the value of x is 3

Since AB = 5x+1

AB = 5(3) + 1

AB = 15 + 1

AB = 16

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STALIN [3.7K]

Answer:

Step-by-step explanation:

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2 years ago

A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 fee

Novay_Z [31]

Answer: The height of the tree is 21 feet.

Step-by-step explanation:

Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.

Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.

Then we will have a relationship like:

Tg(angle) = shadow/height

height = shadow/Tg(angle)

Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K

Tg(angle) = K

Then we have the equation:

Height = Shadow/K

We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:

6ft = 2ft/K

K = 2ft/6ft = (1/3)

Now we know that the shadow of the tree is 7ft long, then the height will be:

height = 7ft/(1/3) = 7ft*3 = 21ft

The tree is 21 ft tall.

6 0

3 years ago

Robert is 10 years older than her brother. In 2 years, Robert will be three times as old as his brother. How old are they now?

valentina_108 [34]

Robert is 13 and his brother is 3 y.o.
X... brother’s age
X+10... Robert’s age
X+10+2... Robert’s age in 2 years
X+2...Brother’s age in 2 years
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X=3
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4 years ago

We have 12 pumpkin pies that need to be shared evenly between 16 people

Artyom0805 [142]

You can divide 16 and 12, which will get you 1 and 1/4 a person left, but rounded will get 2

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4 years ago

3x-10-4

snow_lady [41]

Answer/Step-by-step Explanation:

1. 3x - 10 +4 if x = 3

To evaluate, plug in the value of x in the expression given

3(3) - 10 + 4 = 9 - 10 + 4

= 3

2. $\frac{x}{2} + 6x$

if x = -12

$\frac{(-12)}{2} + 6(-12)$

- 6 - 72 = - 78

3. 8(x - y), if x = 2, y = 6

8(2 - 6) = 8(-4) = -32

4. x + xy, if x = 3, y = -2.5

3 + (3)(-2.5) = 3 + (-7.5)

= 3 - 7.5 = - 4.5

5. (2x)² + 6, if x = -2

(2*-2)² + 6 = (-4)² + 6

= 16 + 6 = 22

6. 3x + 4y - 3x, if x = 2, y = 4

3(2) + 4(4) - 3(2) = 6 + 16 - 6

= 16

7. $-10x + \frac{4}{x}$

If x = -2

$-10(-2) + \frac{4}{-2}$

20 + (-2) = 20 - 2 = 18

8. 3(8x - 10) + 5x, if x = ½

3(8*½ - 10) + 5(½)

3(4 - 10) + 2.5

3(-6) + 2.5 = -18+2.5 = - 20.5 or 20½

9. x + 8y - (x)², if x = -5, y = ¼

-5 + 8(¼) - (-5)² = -5 + 2 - (25)

= -3 - 25 = -28

10. (8x)² + 6x + 2, if x = -3

(8*-3)² + 6(-3) + 2 = (-24)² - 18 + 2

= 576 - 18 + 2 = 560

11. 2x² + 4y² + xy, if x = ½, y = 2

2(½)² + 4(2)² + (½)(2)

= 2(¼) + 4(4) + 1

= ½ + 16 + 1 = ½ + 17 = 17½

12. 8x + 2y, if x = 1.5, y = -2.2

8(1.5) + 2(-2.2)

12 - 4.4 = 7.6

13. $\frac{5}{2}(x - 6) + 4$

if x = 8.

$\frac{5}{2}(8 - 6) + 4$

$\frac{5}{2}(2) + 4$

= 5 + 4 = 9

14. 3x - 8x² + 7, if x = 4.5

3(4.5) - 8(4.5)² + 7

13.5 - 8(20.25) + 7

13.5 - 162 + 7 = -141.5

15. -2x² + 8y, if x = 3, y = -9

-2(3)² + 8(-9)

-2(9) - 72 = - 18 - 72 = 90

16. (-5x)² - 3x + x, if x = -3.5

(-5*-3.5)² - 3(-3.5) +(-3.5)

(17.5)² + 10.5 - 3.5

306.25 + 10.5 - 3.5 = 313.25

8 0

3 years ago