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dsp73
3 years ago
7

In order to burn calories and lose weight, Vera is trying to incorporate more exercise into her busy schedule. She has several s

hort exercise DVDs she can complete at home. Last week, she burned a total of 517 calories by doing 2 body sculpting workouts and 5 yoga sessions. This week, she has completed 2 body sculpting workouts and 1 yoga session and burned a total of 185 calories. How many calories does each workout burn?
Mathematics
1 answer:
mel-nik [20]3 years ago
8 0

Answer:each session of body sculpting workouts burns 51 calories.

Each session of Yoga workouts burns 83 calories.

Step-by-step explanation:

Let x represent the number of calories that she burnt doing one body sculpting workout session.

Let x represent the number of calories that she burnt doing one Yoga session.

Last week, she burned a total of 517 calories by doing 2 body sculpting workouts and 5 yoga sessions. This means that

2x + 5y = 517 - - - - - - - - - -1

This week, she has completed 2 body sculpting workouts and 1 yoga session and burned a total of 185 calories. This means that

2x + y = 185 - - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

4y = 332

y = 332/4 = 83 calories

Substituting y = 83 into equation 2, it becomes

2x + 83 = 185

2x = 185 - 83 = 102

x = 102/2 = 51 calories

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The circumference of the top rim of the cone-shaped paper cup is 8.66 inches. Find the least amount of paper that can form the c
navik [9.2K]

Answer:

15.59 square inches

Step-by-step explanation:

In the required given diagram, the slant height of the cone was given as 3.6 inches.

The least amount of paper required would be equal to the curved surface area of the cone.

curved surface area of a cone = \pirl

where r is the radius and l the slant height.

circumference of the top rim = 8.66 inches

circumference = 2\pir

⇒ 8.66 = 2\pir

4.33 = \pir

r = 4.33/\pi

curved surface area = \pi x  4.33/\pi x 3.6

                                 = 4.33 x 3.6

                                = 15.588 square inches

Thus, the least amount of paper that can form the cone shaped cup is 15.59 square inches.

7 0
3 years ago
What does jury duty mean?
JulijaS [17]

Jury duty is where you have to server your duty being on a jury for a court case. On a jury duty, you vote if you think the person on trial is guilty or not.

-Steel jelly


3 0
3 years ago
What is<br> is 1/4 + 9/10y -3/5y +7/8 written in simplest form?
Leviafan [203]

Answer:

Step-by-step explanation:

\frac{1}{4}+\frac{9}{10}y - \frac{3}{5}y+\frac{7}{8}\\\\=\frac{1}{4}+\frac{7}{8}+\frac{9}{10}y-\frac{3}{5}y\\\\

Combine like terms. 1/4 and 7/8 are like terms and LCD of 4 and 8 is 8

9/10y and -3/5y are like terms and LCD of 10 , 5 is 10

= \frac{1*2}{4*2}+\frac{7}{8}+\frac{9}{10}y-\frac{3*2}{5*2}y\\\\=\frac{2}{8}+\frac{7}{8}+\frac{9}{10}y-\frac{6}{10}y\\\\=\frac{9}{8}+\frac{3}{10}y

5 0
2 years ago
Read 2 more answers
Please someone help me to prove this. ​
morpeh [17]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities:   sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS:                                  2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle:    2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]  

Expand:        2[(1/2)cos²2A  + cos2A·sin2A + (1/2)sin²2A]

Distribute:              cos²2A   + 2cos2A·sin2A + sin²2A  

Pythagorean Identity:    1 + 2cos2A·sin2A

Double Angle:                1 + sin4A

LHS = RHS:  1 + sin4A = 1 + sin4A   \checkmark

6 0
3 years ago
a line is perpendicular to y = 3/7x - 2 and intersects the point (3,3). What is the equation of this perpendicular line?
snow_lady [41]

Answer:

y = -7/3x + 10

Step-by-step explanation:

Step 1: Find the slope of the perpendicular line

Do this by taking the negative inverse of the first line

m = -7/3

Step 2: Find <em>b</em>

y = mx + b

y = -7/3x + b

3 = -7/3(3) + b

3 = -7 + b

b = 10

You should get y = -7/3x + 10 as your final answer.

6 0
2 years ago
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