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dimulka [17.4K]
2 years ago
15

Mia has $50 on a gift card to her favorite coffee shop. Each time she visits the coffee shops she spends $3.75 on her favorite d

rink. Choose the equation that represents the relationship between x, the number of times she visits the coffee shop, and y, the total amount on her gift card.
Mathematics
1 answer:
kirza4 [7]2 years ago
5 0

Given:

Value of Gift card = $50

Each time she visits the coffee shops she spends $3.75 on her favorite drink.

To find:

The equation for the given situation.

Solution:

Let x be the number of times she visits the coffee shop, and y be the total amount on her gift card.

Cost of her favorite drink for one time = $3.75

Cost of her favorite drink for x times = $3.75x

Value of gift card is $50. So,

Amount on her gift card = 50 - Cost of her favorite drink for x times

y=50-3.75x

Therefore, the required equation is y=50-3.75x.

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9/16 = x/12<br>x-3/18 = 12/9<br>7/11 = 18/x+1<br>3x-4/14 = 9/10<br>Simplify​
hjlf

Answer:

Step-by-step explanation:

9/16=x/12

cross product

16x=9*12

16x=108

x=108/16

simplify

x=27/4

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

x-3/18=12/9

x=12/9+3/18

x=24/18+3/18

x=27/18

x=3/2

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

7/11=18/x+1

18/x=7/11-1

18/x=7/11-11/11

18/x=-4/11

x=18/(-4/11)=(18/1)(-11/4)=-198/4=-99/2

x=-99/2

4 0
3 years ago
Julio bought several books from the Coming-Around-Again Bookstore. He paid $31.80, including 6% sales tax. He then discovered th
ladessa [460]
C is the answer all you had to do was
31.80-4.00
Which is 27.80
Then add 2.50
Which is 30.3!
5 0
3 years ago
Parabolas. Please help me
olganol [36]
  1. x² = 16 y
  2. x = 0
  3. (x + 4)² = 2/3 (y - 2)
  4. Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
  5. (y - 6)² = 4p (x - 3)

Step-by-step explanation:

1. First figure

We plot the parabola as given in the attached diagram.

As it is facing upwards, the equation goes as x² = 4py

where, p = 4 (refer the attached diagram)

x² = 4py

x² = 4 (4) y

∴, standard form of parabola is x² = 16 y

2. Second figure

(y + 3)² = 4 (x - 1)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

h = 1

p = 1

Directrix is x = (h - p)

So, x = 0

3. Third figure

3x² + 24x - 2y + 52 = 0

3x² + 24x = 2y - 52

3 (x² + 8x) = 2 (y - 26)

(x² + 8x) = 2 (y - 26) / 3

Adding 16 on both sides,

x² + 8x + 16 = 2 (y - 26) / 3 + 16

(x + 4)² = 2/3 y - 52/3 + 16

(x + 4)² = 2/3 y - 4/3

(x + 4)² = 2/3 (y - 2)

4. Fourth figure

(y + 1)² = 12 (x - 3)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

k = -1

h = 3

p = 3

Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>

5. Fifth figure

Focus = (2, 6)

Directrix is x = 4

Therefore, it follows the standard form

(y - k)² = 4p (x - h)

Directrix is given by x = h-p = 4

Focus is given by (h + p, k) = (2, 6)

Solving for (h - p) = 4, (h + p) = 2

2 - p - p = 4

-2p = 2

p = -1

Hence, h = 3

Therefore, the standard form can be written as

(y - 6)² = 4p (x - 3)

7 0
3 years ago
A boy wants to jump onto a carousel that is spinning at a rate of 14 revolutions per minute. If the carousel is 23 feet in diamt
nirvana33 [79]

Answer:

16.86 ft/s

Step-by-step explanation:

Given that

Speed of the carousel, s = 14 rpm

Distance from the carousel, d = 23 ft

To start with, we convert the given speed to revolution per second, so that

s = 14/60 rev/sec

To find the needed speed, we use the formula

v =2πnR, remember that Diameter = 2R, so we substitute D for 2R and get πnD

v = πnD, and we use this to find our needed velocity

v = 3.142 * 14/60 * 23

v = 72.266 * 14/60

v = 16.86 ft/s

Therefore the boy must run at a speed of 16.86 ft/s in order to be able to match the carousel and jump on it

6 0
3 years ago
Find BD.<br> help me pls
Anna [14]

Answer:

16

Step-by-step explanation:

We can see that Ar is the perpendicular bisector of chord BD. Since A is the center of the circle, AR is the radius of the circle, which is 10 (6+4)

Next, we can see that when we connect point A to point D, it is also a radius. Thus, AD is also equal to 10 as the radius of the circle remains the same.

Using Pythagoras theorem, a^2 + b^2 = c^2, we can make a right angled triangle of ACD.

AC = 6 = a

CD = ? = b

AD = 10 = c

10^2 = 6^2 + b^2

b^2 = 10^2 - 6^2 = 64

b = CD = 8

Now, since Ar is the perpendicular bisector of chord BD, BD = CD x 2

BD = 8 x 2 = <u>16</u>

5 0
1 year ago
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