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abruzzese [7]
3 years ago
12

The base of a triangle is 7 less than twice its height. if the area of the triangle is 102cm^2 find the length of the base

Mathematics
1 answer:
Gre4nikov [31]3 years ago
7 0
B=2h-7
Area of a triangle: A=1/2 of bh
replace b with 2h-7: A=(1/2)(2h-7)h=102 => (2h-7)h=204
2h^2-7h-204=0
factor or use quadratic function to solve
h=12
b=2*-7=17
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A basketball player shoots a basketball that reaches a height above 15 feet before landing back on the ground exactly after 7 se
Papessa [141]

Answer:

I and IV

Step-by-step explanation:

Since the height of the basketball reaches above 15 feet, hence the maximum of the function should be greater than 15 feet. Also at 7 seconds, the ball is on the ground, hence f(7) = 0 feet

The maximum of a function is at x = -b/2a

i) f(x) = -(x-3)² + 16 = -(x² - 6x + 9) + 16 = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 16 = 16 > 15

Also f(7) = - (7 - 3)² + 16 = 0

Hence this option is correct

ii) f(x) = -x² + 8x - 7

The maximum of a function is at x = -b/2a = -8 / 2(-1) = 4

f(4) = -4² + 8(4) - 7 = 9 < 15   not correct

Also f(7) = - 7² + 8(7) - 7 = 0

Hence this option is not correct since the maximum f(4) = 9 < 15  

iii)  f(x) = -(x-3)² + 14 = -(x² - 6x + 9) + 14 = -x² + 6x + 5

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 14 = 14 < 15

Also f(7) = - (7 - 3)² + 14 = -2

Hence this option is not correct since the maximum f(4) = 9 < 15 and f(7) ≠ 0

iv)f(x)  = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3)² + 6(3) + 7 = 16 > 15

Also f(7) = - (7)² + 6(7) + 7 = 0

Hence this option is correct

3 0
3 years ago
Solve for c in a+b+c=180
AleksAgata [21]

Answer:

c = -a - b + 180

Step-by-step explanation:

Isolate the c. Note the equal sign, what you do to one side, you do to the  other. Subtract a and b from both sides

a (-a) + b (-b) + c = 180 (-a) (-b)

c = 180 - a - b

c = -a - b + 180 is your answer

~

4 0
3 years ago
Write the equation of a line in slope intercept form that passes through the point ( -8, 2) and is parallel to the line y=1/4x−3
mel-nik [20]
Y-2=1/4(x+8) is your answer
Explanation
Desmos
6 0
3 years ago
At a farm, the average number of chickens, ducks, rabbits and sheep is 315 per type of animal. The average number of chickens, d
Greeley [361]

The average number of chickens, ducks, rabbits and sheep = 315 per type of animal.

The average number of chickens, ducks and rabbits = 320 per type of animal.

The number of sheep is 60 more than the number of rabbits.

Let us assume number of rabbits = x.

Number of sheep is 60 more than number of rabbits, that is = x+60.

There are half as many ducks as there are rabbits.

Therefore, number of ducks = x/2.

Let us assume number of chickens = y.

Adding  number of chickens, number of rabbits, number of sheep and number of ducks and dividing by 4 (because those are four types of animal).

\frac{y+x+x+60+x/2}{4}  = 315

Multiplying both sides by 4, we get

y+x+x+60+x/2 = 1260

Subtracting 60 from both sides

y+x+x+60-60+x/2 = 1260-60

y+x+x+x/2 = 1200.

Combining like terms .

y + 5x/2 = 1200

Multiplying both sides by 2, we get

<em>2y +5x = 2400  ------------equation (1)</em>

Adding  number of chickens, number of rabbits and number of ducks and dividing by 3 (because those are three types of animal).

\frac{y+x+60+x/2}{3}  = 320

Multiplying both sides by 3, we get

y+x+60+x/2 = 960

Subtracting 60 from both sides

y+ x+x/2 = 900

Combining like terms .

y+ 3x/2 = 900

Multiplying both sides by 2, we get

<em>2y+3x = 1800 --------------------equation (2)</em>

Multiplying first equation by 3 and second equation by -5, we get

(2y +5x = 2400 ) * 3   => 6y +15x = 7200

(2y+3x = 1800) *-5      =>

Adding

6y +15x = 7200

-10x + -15x = -9000.

_________________

-4y = -1800.

Dividing both sides by -4, we get

y=450.

<h3>Therefore, number of chickens are  450 there at the farm.</h3>


7 0
3 years ago
Turn -6 13/15 as a decimal
barxatty [35]
-6.867
You do 13 divided by 15 the plug in the -6 in the front
7 0
3 years ago
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