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3 years ago

Task 1:

Mathematics

1 answer:

laiz [17]3 years ago

4 0

Answer:

The toy's maximum height is $10.12\ \text{feet}$ .

Step-by-step explanation:

The equation that models the toy's height in feet from the ground at t seconds after he threw it is given by :

$h = -2t^2 + 7t + 4$ .....(1)

It is required to find the toy's maximum height. For maxima or minima, put

$\dfrac{dh}{dt}=0$

Plugging the value of t in above equation,

$\dfrac{d(-2t^2 + 7t + 4)}{dt}=0\\\\-4t+7=0\\\\t=\dfrac{7}{4}\\\\t=1.75\ s$

Now put t = 1.75 s in equation (1) such that,

$h = -2(1.75)^2 + 7(1.75) + 4\\\\h=10.12\ \text{feet}$

So, the toy's maximum height is $10.12\ \text{feet}$ .

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m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°. If ∠WYX and ∠WYZ are complementary, what is the measure of each angle?

Neko [114]

We are given : m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°.

∠WYX and ∠WYZ are complementary.

We know, sum of complementary angles is = 90°.

So, we need to add ∠WYX and ∠WYZ and set it equal to 90°.

m∠WYX + m∠WYZ = 90°.

Plugging values of ∠WYX and ∠WYZ in the above equation, we get

(2x−1)° + (4x+1)° = 90°.

Removing parentheses from both sides,

2x-1 + 4x+1 =90.

Combining like terms,

2x+4x= 6x and -1+1 =0

6x +0 =90.

6x=90.

Dividing both sides by 6.

6x/6 =90/6

x= 15.

Plugging value of x=15.

m∠WYX=(2x−1)° = 2*15 -1 = 30 -1 =29

m∠WYZ=(4x+1)° = 4*15 +1 = 60+1 = 61.

Therefore, ∠WYX=29° and ∠WYZ=61°.

5 0

3 years ago

In the picture down below

Setler [38]

Answer:

The answer is option A.

The first graph

Hope this helps you

4 0

2 years ago

Read 2 more answers

X + 3 - 3=-6 show all work

docker41 [41]

Answer:

x = -6

Step-by-step explanation:

$x+3-3=-6~(Given)\\x=-6~(Combine~like~terms)$

5 0

2 years ago

one third of the people at a banquet ordered ice cream for dessert. the rest ordered pie. one forth of those requesting pie orde

Vaselesa [24]

Answer:

30 people ordered apple pie

Step-by-step explanation:

one third of the total people:

180/3 = 60

subtract the people who ordered ice cream, so that we have the total people who ordered pie:

180-60= 120

divide the total people by 4 to find the people who ordered apple pie

120/4 = 30

30 people ordered apple pie

6 0

2 years ago

Please help me, thank you

Alenkinab [10]

Problem 1

Answer: C) No solution

---------------------------

Explanation:

We have z = -4 and 4z = -4 at the same time. Solving 4z = -4 leads to z = -1

So in effect we have z = -4 and z = -1 at the same time, but this is a contradiction. A variable can only hold one number at a time.

======================================================

Problem 2

Answer: C) Infinitely many solutions

---------------------------

Explanation:

The two equations are equivalent. You can prove as such by isolating 2y in the first equation.

5x = 8-2y

5x+2y = 8

2y = 8-5x

2y = -5x+8

-5x+8 = 2y

This shows the first equation is equivalent to the second, and vice versa. They both graph the same line. Any point along the line is a solution. So that's why there are infinitely many of them.

======================================================

Problem 3

Answer: Choice A) $-6 < y \le 3$

---------------------------

Explanation:

The range is the set of the possible y values. We're concerned with every y coordinate of each (x,y) solution. So we only focus on the shaded region.

The dashed line means we exclude the boundary. It's an electric fence we cannot touch. So y > -6 or -6 < y describes part of the range

The other part is $y \le 3$ since y = 3 is the when the highest point occurs.

So writing $-6 < y \le 3$ describes all possible y values of each (x,y) solution in the shaded region.

6 0

3 years ago