All categories

3 years ago

15a-25=35

1 answer:

3 0

15a-25=35
3.333

Leah needs to buy some apples from the grocery store. She places fifteen apples in her cart and proceeds to the checkout. Lucky for her, there happens to be a discount on apples for the day. She saves $25 on her purchase. The total money she ends up spending was only $35 (excluding tax). How much did each apple cost?

You might be interested in

Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

$k=0$

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

3 0

2 years ago

The perimeter of the rectangle below is 166 units. Find the length of side RS.

Wittaler [7]

The length of RS is 45 units if the perimeter of the rectangle below is 166 units.

<h3>What is the area of the rectangle?</h3>

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The question is incomplete.

The complete question is:

The perimeter of the rectangle below is 166 units. Find the length of the side RS. Write your answer without variables.

The figure is in the picture please refer to the picture.

The perimeter of the rectangle = 166 units

2(4x + 2 + 5x) = 166

9x + 2 = 83

9x = 81

x = 9

The length of RS = 5x = 5(9) = 45 units

Thus, the length of RS is 45 units if the perimeter of the rectangle below is 166 units

Learn more about the rectangle here:

brainly.com/question/15019502

#SPJ1

3 0

2 years ago

Someone Help me please??

11Alexandr11 [23.1K]

It will be identical, this will explain it https://www.wyzant.com/resources/answers/165599/how_many_degrees_can_a_regular_pentagon_be_rotated_a...

8 0

3 years ago

Read 2 more answers

What is the area of this triangle 8m and 6m

mr_godi [17]

Area for triangles is 1/2b * h.

If 8m were the height, then the area is 24 sq m.

If 6m were the height, then the area is still 24 sq m.

The area is 24 sq m.

Hope this helps! Have a great day :)

4 0

3 years ago

Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!

zaharov [31]

Question 1:

The area of the triangle is $9\frac{5}{8}$ cm², if you want it rounded to the nearest whole number it will be 10 cm²

Question 2:

The area of the parallelogram is 304.5 m²

Question 3:

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

5 tons is equal to 10,000 pounds

Question 6:

A table measures 3 feet across is 36 inches across

Step-by-step explanation:

Question 1:

The formula of the area of a triangle is $A=\frac{1}{2}bh$ , where

b is the base of the triangle
h is the height of the triangle

∵ The base of the triangle = $5\frac{1}{2}$ cm

∵ The height of the triangle = $3\frac{1}{2}$ cm

- Change the mixed numbers to improper fractions

∵ $5\frac{1}{2}$ = $\frac{(5*2)+1}{2}=\frac{11}{2}$

∵ $3\frac{1}{2}$ = $\frac{(3*2)+1}{2}=\frac{7}{2}$

∴ $A=\frac{1}{2}(\frac{11}{2})(\frac{7}{2})=\frac{77}{8}$ cm²

- To change the improper fraction to mixed number divide 77 by 8

∵ 77 ÷ 8 = 9 and remainder 5 (8 × 9 = 72 , 77 - 72 = 5)

∴ 77 ÷ 8 = $9\frac{5}{8}$

∴ $A=9\frac{5}{8}$ cm²

The area of the triangle is $9\frac{5}{8}$ cm²

If you want to round it to the nearest whole number the area will

be 10 cm²

Question 2:

The formula of the area of a parallelogram is A = b h , where

b is the base of the parallelogram
h is the height of this base of the parallelogram

∵ The base of the parallelogram = 14.5 m

∵ Its height = 21 m

∵ A = b h

∴ A = 14.5 × 21 = 304.5 m²

The area of the parallelogram is 304.5 m²

Question 3:

∵ The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and

150 grilled chicken salads

∴ The cafeteria sold = 200 + 100 + 150 = 450 lunches

- To find the ratio between the grilled chicken salads sold to the total

number of lunches sold divide them and simplify the answer to the

lowest term

→ G.C.S : Lunches

→ 150 : 450 ⇒ divide both by 10

→ 15 : 45 ⇒ divide both by 5

→ 3 : 9 ⇒ divide both by 3

→ 1 : 3

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The even numbers are the numbers whose one digit is 0 , 2 , 4 , 6 , 8

The odd numbers are the numbers whose one digit is 1 , 3 , 5 , 7 , 9

∵ The number is 7,208,631

∵ The odd digits are 7 , 3 , 1

∴ There are 3 odd digits

∵ The even numbers are 2 , 0 , 8 , 6

∴ there are 4 even digits

∴ The ratio of odd to even digits is 3 : 4

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

∵ One ton is equal to 2000 pounds

∵ There are 5 tons

→ Ton : Pound

→ 1 : 2000

→ 5 : x

Use the cross multiplication

∵ 1 × x = 5 × 2000

∴ x = 10,000 pounds

5 tons is equal to 10,000 pounds

Question 6:

∵ A table measures 3 feet across

∵ 1 foot = 12 inches

∴ 3 × 12 = 36 inches

A table measures 3 feet across is 36 inches across

Learn more:

You can learn more about ratio in brainly.com/question/10781917

#LearnwithBrainly

6 0

3 years ago