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polet [3.4K]
3 years ago
14

The price of a dress is reduced by 25​%.When the dress still does not​ sell, it is reduced by 25​% of the reduced price. If the

price of the dress after both reductions is ​$18​, what was the original​ price?The price of a dress is reduced by 25​%.When the dress still does not​ sell, it is reduced by 25​% of the reduced price. If the price of the dress after both reductions is ​$18​, what was the original​ price?
Mathematics
1 answer:
fredd [130]3 years ago
8 0
18= (d - 0.25d) - 0.25d
18= 0.75d - 0.25d
18= 0.50d
d = 36

the original price was $36
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You invested $27,200 and started a business selling vases. Supplies cost $11 per
AleksAgata [21]
1,600 vases must be produced and sold to break even.

x($28-$11)=$27,200
Simplify to 17x=27,200
Divide 17x by 17 so it cancels out.
What you do to one side of the equation you have to do to the other.
27,200/17=1,600
x=1,600
6 0
2 years ago
Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
stepladder [879]

The length of the curve y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6

Start by differentiating the curve function

y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x

Evaluate

y' = x(9x^2 + 6)^\frac 12

The length of the curve is calculated using:

L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx

This gives

L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx

Expand

L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx

This gives

L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx

Express as a perfect square

L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx

Evaluate the exponent

L =\int\limits^6_3 {3x^2 + 1} \ dx

Differentiate

L = x^3 + x|\limits^6_3

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

brainly.com/question/14015568

#SPJ1

7 0
1 year ago
A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16.
dimulka [17.4K]
That is when h=0
so assuming yo meant
h(t)=-16t²+24t+16
solve for t such that h(t)=0
because when height=0, the gymnast hits the ground

so
0=-16t²+24t+16
using math (imma complete the square
0=-16(t²-3/2t)+16
0=-16(t²-3/2t+9/16-9/16)+16
0=-16((t-3/4)²-9/16)+16
0=-16(t-3/4)²+9+16
0=-16(t-3/4)²+25
-25=-16(t-3/4)²
25/16=(t-3/4)²
sqrt both sides
+/-5/4=t-3/4
3/4+/-5/4=t
if we do plus (because minus would give us negative height)
8/4=t
2=t
it takes 2 seconds
5 0
2 years ago
A ball is thrown into the air from an apartment balcony and falls to the ground. The height of the ball, h metres, t seconds aft
andriy [413]

Answer:

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Step-by-step explanation:

When the ball hits the ground, its height will obviously be 0. Therefore, you can set up the equation the following way:

0=-5t^2+10t+35 \\\\-5(t^2-2t-7)=0

Plugging this into the quadratic equation, you get:

t=\dfrac{2\pm\sqrt{4+28}}{2}= \\\\\dfrac{2\pm4\sqrt{2}}{2}= \\\\1\pm2\sqrt{2}

Since the time must be positive, it takes the ball 1+2\sqrt{2} seconds to hit the ground, or around 3.828. Hope this helps!

7 0
3 years ago
Write and solve the following expression:<br><br>The sum of 7 and twice a number is 15
Nastasia [14]

Answer:

It would be 7 + 2x = 15

8 0
2 years ago
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