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leonid [27]
2 years ago
8

After her raise, Shannon earned 3/4 more than she previously made. If Shannon's weekly wages totaled $2100 after her raise, what

was Shannon's original weekly wage?
Mathematics
1 answer:
topjm [15]2 years ago
8 0
So $2100 = 1+3/4 of her original raise.

Remember that 1 = 4/4, so in total it is 7/4 of her original pay (4/4+3/4). Let's find out what 1/4 is equal to.

If $2100=7/4 then 1/4=$300. Therefore 4/4 (or 1, her original pay) is 4 times $300, which is $1200.
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The students in Mr. Wilson's Physics class are making golf ball catapults. The
Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is 0 \leq x \leq 48.6\ ft and the range is 0 \leq y \leq 8.3\ ft

Step-by-step explanation:

we have

y=-0.014x^{2} +0.68x

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's  distance from the catapult in feet

y is the flight of the balls in feet

Part a)  How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-0.014x^{2} +0.68x=0

so

a=-0.014\\b=0.68\\c=0

substitute in the formula

x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}

x=\frac{-0.68(+/-)0.68} {(-0.028)}

x=\frac{-0.68(+)0.68} {(-0.028)}=0

x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

y=-0.014x^{2} +0.68x

Find out the derivative and equate to zero

0=-0.028x +0.68

Solve for x

0.028x=0.68

x=24.3

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint  between the x-intercepts

x=(0+48.6)/2=24.3\ ft

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

y=-0.014(24.3)^{2} +0.68(24.3)

y=8.3\ ft

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A  reasonable domain is the distance between the two x-intercepts

so

0 \leq x \leq 48.6\ ft

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A  reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

0 \leq y \leq 8.3\ ft

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0
2 years ago
How do you know if two lines segments are perpendicular
Greeley [361]

Answer:

when they are intersecting at a 90 degree angle.

Step-by-step explanation:

when lines intersect, they just cross over one another at any point. but with perpendicular lines, they have to be at a right angle. an example of this is a square. all of its corners are perpendicular

6 0
3 years ago
1.3.33 Question Help A certain triangle has a perimeter of 3078 mi. The shortest side measures 71 mi less than the middle side,
maksim [4K]

Answer:

the shortest side is 855 miles long.

Step-by-step explanation:

a + b + c = 3078 miles

a = b - 71

c = b + 371

=>

(b-71) + b + (b+371) = 3078

3b + 300 = 3078

3b = 2778

b = 926 miles

a = 926 - 71 = 855 miles

c = 926 + 371 = 1297 miles

8 0
3 years ago
last week 24% of the campers at a state park were visiting from out of state this weekend additional 12% are from out of state i
lesya692 [45]
Work: x/175=12%/100
multiply 175 by 2 and then you divide it by 100
answer: 21 are visiting from out of state.
5 0
3 years ago
4.5872 _____ √14. A.Greater than, B. Less than, C. equal
Kryger [21]
"A" is the correct answer
8 0
3 years ago
Read 2 more answers
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