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WITCHER [35]
2 years ago
11

Geometry 1.4 - Segment Addition Postulate & Midpoint

Mathematics
1 answer:
Roman55 [17]2 years ago
4 0

Answer:

28

Step-by-step explanation:

AB + BC = AC

14 + 3x-4 = 4x+4

Combine like terms

10 +3x = 4x+4

Subtract 3x from each side

10+3x-3x = 4x+4-3x

10 = x+4

Subtract 4 from each side

10-4 =x-4+4

6 =x

We want AC

AC = 4x+4 = 4*6+4 = 24+4 = 28

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An instructor wants to write a test with 25 questions where each question is worth 3, 4, or 5 points based on difficulty. He wan
irakobra [83]

ANSWER

Find out the how many 3, 4, and 5 point questions could there be.

To proof

Let us assume that the 3 points based question be = x

Let us assume that the 4 points based question be = y

Let us assume that the 5 points based question be = z

As given

An instructor wants to write a test with 25 questions

than the equation become in the form

x + y + z = 25

he quiz to be worth a total of 100 points.

than the equation is becomes

3x + 4y + 5z =100

As given

He wants the number of 3-point questions to be 4 less than the number of 4-point questions

x = y -4

Than the three equation are

x + y + z = 25 ,3x + 4y + 5z =100 and x = y -4

put  x = y -4 in the x + y + z = 25 ,3x + 4y + 5z =100

than

2y + z = 29, 7y +5z= 112

multiply 2y + z = 29 by 5 and subtracted 7y +5z= 112

10 y -7y + 5y -5y = 145 -112

3y = 33

y = \frac{33}{3}

y =11

put in the  x = y -4

x = 11-4

x= 7

put the value of x ,y in the x + y + z = 25

7 + 11 +z =25

18 +z = 25

z = 25 -18

z=7

therefore

numbers of the 3 point question be = 7

numbers of the 4 point question be = 11

numbers of the 5 point question be = 7

Hence proved



3 0
3 years ago
Determine the factors of x2 − 8x − 12. (x − 6)(x 2) (x 3)(x − 4) prime (x 6)(x − 2)
Ivanshal [37]

The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.

<h3>What is a quadratic equation?</h3>

In a quadratic equation ax² + bx + c = 0

when (b² - 4ac) exists a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12 we have to determine the value of

b² - 4ac

From the equation, we get b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12)

= 64 + 48 = 112

Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.

To learn more about quadratic equation refer to:

brainly.com/question/1214333

#SPJ4

4 0
2 years ago
I NEED HELP PLEASE, THANKS!! :)
Lisa [10]

Answer:

The answer is

\frac{1372}{3} \pi \:  {cm}^{3}

Step-by-step explanation:

First you have to find the radius of sphere by dividing diameter by 2 :

radius = diameter \div 2

Let diameter = 14,

radius = 14 \div 2

radius = 7 \: cm

Next you have to use the volume of sphere formula :

v =  \frac{4}{3}  \times \pi \times  {r}^{3}

Let r = 7,

v =  \frac{4}{3}  \times \pi \times  {7}^{3}

v =  \frac{4}{3}  \times \pi \times 343

v =  \frac{1372}{3} \pi \:  {cm}^{3}

7 0
3 years ago
2/x+3/y=9<br>4/x+9/y=21​
Brrunno [24]

Answer:

ok

Step-by-step explanation:

ok

3 0
3 years ago
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of
sweet-ann [11.9K]

Answer:

G.

Step-by-step explanation:

cards = 2

dollars = 9

to check that the number of cards with the correct amount d;

use the ratio and proportion.

(3 x 18)/9 = 4

(4 x 31.5)/18 = 7

(7 x 45)/31.5 = 10

therefore, option G. table G. is the correct answer

try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount.  (see attached)

6 0
3 years ago
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