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umka2103 [35]
3 years ago
14

A baseball is hit upward from a height of

Mathematics
1 answer:
jeyben [28]3 years ago
4 0

Answer:

99

Step-by-step explanation:

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On a certain hot summer's day, 538 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for a
Artist 52 [7]

Answer:

The number of children was 170 and adults was 368.

Step-by-step explanation:

To clarify we'll call children by 'c' and adults by 'a'. The amount of people in the pool should be the sum of adults and children, so:

a + c = 538

The receipts for the adimission should total the amount of tickets from children and adults multiplied by the price of each ticket, so:

1.75*c + 2.25*a = 1125.5

We now have two equations and two variables. Using the first equation we can isolate the 'a' variable and use it on the second equation to find an answer. We then have:

a + c = 538

a = 538 - c

Using it on the second equation:

1.75*c + 2.25*(538-c) = 1125.5

1.75*c + 1210.5 - 2.25*c = 1125.5

1.75*c - 2.25*c = 1125.5 - 1210.5

-0.5*c = -85

c = -85/(-0.5) = 170

Using this value on the first equation:

a = 538 - 170 = 368

7 0
3 years ago
Read 2 more answers
Which could be a possible value of x for the<br> expression below to be a rational number?
notsponge [240]
The answer should be B
4 0
3 years ago
A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is lo
adelina 88 [10]

Answer:

y=-\frac{8}{15}x^2+8x

Step-by-step explanation:

Consider the equation that shows flea's motion is y=ax^2+bx+c.

Since the origin is located at the point from where the flea jumped,

So, y=ax^2+bx+c  passes through (0,0).

That is, (0,0) must satisfy y=ax^2+bx+c,

0=a(0)^2+b(0)+c

\implies c =0

Now, it travels 15 cm horizontally from where it started.

That is, y=ax^2+bx+c  passes through (15,0).

0=a(15)^2+b(15)+c

0=a(225)+b(15)   (Because c=0)

225a+15b=0  ...... (1)

Again, it jumps from the ground to a height of 30 cm,

So, the y-coordinate of vertex of y=ax^2+bx+c is 30.

Now, the x-coordinate of vertex of the quadratic function must be half of the distance from its starting point to final point.

That is, x-coordinate of the vertex = \frac{15}{2} = 7.5,

Thus, vertex = (7.5, 30)

(7.5, 30) must satisfy y=ax^2+bx+c

That is, 30=a(7.5)^2+b(7.5)+c

30=56.25a+7.5b

56.25a+7.5b=30                ...... (2)

Equation (1) - 2 × equation (2),

225a - 112.5a = -60

112.5a = -60

\implies a = -\frac{60}{112.5}=-\frac{8}{15}

From equation (1),

225(-\frac{8}{15})+15b = 0

-120+15b=0

15b=120

b=8

Substitute the values of a, b and c in the quadratic equation y=ax^2+bx+c,

y=-\frac{8}{15}x^2+8x

Which is the required quadratic equation.

6 0
3 years ago
Geometry: Use this illustration to calculate these values, ASAP!!!
Mazyrski [523]

Applying the same-side interior angles theorem,

7. m∠4 = 50°; m∠5 = 130°

8. m∠2 = 15°; m∠8 = 15°.

<h3>What is the Same-Side Interior Angles Theorem?</h3>

The same-side interior angles theorem holds that, two interior angles on a side of a transversal are supplementary, that is they add up to 180 degrees.

<h3>What is the Alternate Exterior Angles Theorem?</h3>

According to the alternate exterior angles theorem, exterior angles that alternate each other along a transversal are congruent, that is they have equal measures.

7. m∠4 + m∠5 = 180 [same-side interior angles theorem]

Substitute

y + 2y + 30 = 180

3y + 30 = 180

3y = 180 - 30

3y = 150

y = 50

m∠4 = y = 50°

m∠5 = 2y + 30 = 2(50) + 30

m∠5 = 130°

8. m∠2 = m∠8 [alternate exterior angles theorem]

Substitute

x - 30 = 3x - 120

x - 3x = 30 - 120

-2x = -90

x = 45

m∠2 = x - 30 = 45 - 30 = 15°

m∠8 = 3x - 120 = 3(45) - 120 = 15°

Learn more about the same-side interior angles theorem on:

brainly.com/question/16976757

#SPJ1

5 0
2 years ago
The quadratic equation x^{2}-6x=12 is rewritten in the form (x+p)^2=q, where q is a constant. What is the value of p ?
Free_Kalibri [48]

Answer:

p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3

8 0
4 years ago
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