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VladimirAG [237]
3 years ago
6

The equation y = -4.9x^2 + 9.8x + 2 models the trajectory of a ball thrown in the air by a man, where y = the distance the ball

is from the ground in meters and x = the elapsed time in seconds. What is the greatest distance the ball is from the ground?
a) 2.2 meters
b) 9.8 meters
c) 6.9 meters
d) 4.9 meters
Mathematics
1 answer:
MissTica3 years ago
7 0
The answer should be B!!!
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The difference between the areas of the figures is less than 4.
coldgirl [10]

Answer:

1. |40 – 4x| < 4

2. 9 < x < 11

Step-by-step explanation:

We'll begin by calculating the area of each figure. This can be obtained as follow:

For triangle:

Area = ½ × base × height

Base = 8

Height = 6

Area =?

Area = ½ × 8 × 6

Area = 4 × 6

Area = 24

For Rectangle:

Area = length × breadth

Length = x – 4

Breadth = 4

Area =?

Area = (x – 4) × 4

Area = 4x – 16

Summary:

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

1. Writing an absolute value for the inequality.

From the question given above, we were told that the difference between the areas of the figures is less than 4. This can be written as:

Aₜ – Aᵣ < 4

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

24 – (4x – 16) < 4

Simplify

24 – (4x – 16) < 4

Clear bracket

24 – 4x + 16 < 4

24 + 16 – 4x < 4

40 – 4x < 4

Thus, we can write the absolute value for the above inequality as:

|40 – 4x| < 4

2. Determination of the solution of the inequality.

This is illustrated below:

|40 – 4x| < 4

Thus the above equation can be written as

– 4 < 40 – 4x < 4

Subtract 40 from both side

– 4 – 40 < 40 – 4x – 40 < 4 –40

– 44 < – 4x < – 36

Divide through by –4

– 44/–4 < x < – 36/–4

11 > x > 9

Note: the inequality sign changed because we divided by a negative number

Thus, 11 > x > 9 becomes 9 < x < 11

Therefore, the solution to the inequality is 9 < x < 11

3 0
4 years ago
At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students, and 28 chose social studies as their favorite. He us
Umnica [9.8K]

Answer:

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

Step-by-step explanation:

At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students from each grade level for their favorite subject.

   90 randomly selected students from each grade level for their favorite subject, and 28 chose social studies as their favorite.

so, the percent of students who love social studies is given by:

28/90 x 100=31.11%

   He used this data to draw the inference that out of the 250 middle school students, about 20% prefer social studies.

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

6 0
3 years ago
Write the log equation as an exponential equation. You do not need to solve for x.
Ugo [173]

Answer:

Step-by-step explanation:

(2x) (4x)= 8x = 3x+2

i think but i dont know if this is an exponential equation

5 0
3 years ago
Given the expression: 6x10 − 96x2
Jlenok [28]

The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.

<h3>What is an expression?</h3>

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

Part A)

= 6x¹⁰ - 96x²

= 6x²(x⁸ - 16)

Part B)

\rm =6x^2(\left(x^4\right)^2-4^2)

\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))

\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)

Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

8 0
2 years ago
Bro please help meee
Sidana [21]

Answer:

504 in³

Step-by-step explanation:

First find the volume of the large rectangle, which is 576 in³

Then find the volume of the small rectangle, which is 72 in³

Then subtract 72 from 576 = 504

6 0
3 years ago
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