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2 years ago

Given that f(x) = x^2 - 5x - 24 and g(x) = x - 8, find (f-g)(x) and express the result in standard form

Mathematics

1 answer:

maxonik [38]2 years ago

6 0

Answer: x^2 - 6x - 18

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)=(x^2 - 5x - 24)-(x-8) = x^2 - 5x - 24 - x + 8 = x^2 - 6x - 18

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What are the possible steps involved in solving the equation shown? Select three options. 3.5 + 1.2(6.3 – 7x) = 9.38 Add 3.5 and

motikmotik

Answer:

1) Distribute 1.2 to 6.3 and -7x

2)Combine 3.5 and 7.56

3)Subtract 11.06 from both sides

Step-by-step explanation:

3.5 + 1.2(6.3 - 7x) = 9.38

Distribute 1.2 to 6.3 and -7x

3.5 + 1.2* 6.3 - 1.2 * 7x = 9.38

3.5 + 7.56 - 8.4x = 9.38

Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Subtract 11.06 from both sides

11.06 - 8.4x -11.06 = 9.38 - 11.06

-8.4x = -1.68

To find solution:

Divide both sides by (-8.4)

-8.4x/-8.4 = -1.68/-8.4

x = 0.02

8 0

3 years ago

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Evaluate 725+ 41092 -5688

Mazyrski [523]

Answer:

36129

Step-by-step explanation:

6 0

2 years ago

A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

In (circle)A, m∠BAD = 110. Find mDE.

Veseljchak [2.6K]

Answer:

Line BE = 180 degrees

Therefore, angle BAD + angle DAE = 180 degrees

Angle DAE = 180 -110 = 70 degrees

Step-by-step explanation:

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2 years ago

Can someone explain rational and irrational numbers to me? Odysseyware sucks at teaching.

umka2103 [35]

I'm doing geometry for credit advancement in Odysseyware. Brainly and Openstudy are saviors. Anyways. So, and irrational number can't be written as a fraction, but can be written as a decimal. An irrational number has endless non repeating number to the right of the decimal point. A rational number is a number that can be written in a ratio. Which in turn means it can be written as a fraction. Both number of the fraction (numerator and denominator) are whole numbers. Any whole number is a rational number. <span />

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3 years ago

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