Li keeps track of the time he spends working out each week. The table shows the number of cardio workouts and the number of weighted workouts for 3 recent weeks. The total time in minutes for weeks 1 and 2 are given. Each cardio workout is the same length of time, and each weighted workout is the same length of time. The system of equations can be used to represent this situation. Use the drop-down menus to complete each statement.

There will be 231 handshakes in total

Solution:

There are 22 people in a room

Everyone shakes everyone else’s hand exactly one time

To find: Total number of handshakes in total

Let,

n = total number of people that will shake hands

but since all (total) can't shake hands with themselves, hence we subtract one individual to start the handshaking

(n - 1) = people would each shake hands

hence we multiply both total number persons with people that will shake hands;

n(n - 1)

but that counts every handshake twice, so we have to divide by 2

Therefore;

[tex]\frac{n(n-1)}{2}[/tex]

Here, n = 22

[tex]\frac{n(n-1)}{2} = \frac{22(22-1)}{2} = 11 \times 21 = 231[/tex]

Thus there will be 231 handshakes in total

Answer:

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The radius of grape is 1 cm

Solution:

Given that,

The volume of an object is equal to the ratio of its mass to density

[tex]Volume = \frac{mass}{density}[/tex]

From given,

Mass = 8.4 grams

Density = 2 grams per cubic centimeter

Substituting in above formula,

[tex]Volume = \frac{8.4}{2} = 4.2\ cm^3[/tex]

Given is a spherical grape

The formula for volume of sphere is given as:

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

Where, "r" is the radius of sphere

[tex]4.2 = \frac{4}{3} \times 3.14 \times r^3\\\\4.2 = 4.187 \times r^3\\\\r^3 = \frac{4.2}{4.187}\\\\r^3 = 1.003\\\\\text{Take cube root on both sides}\\\\r = 1.000999 \approx 1[/tex]

Thus the radius of grape is 1 cm

Answer:

1.0 cm

Step-by-step explanation:

Answer:

{(-34/7, -16/7)}

Step-by-step explanation:

Rearrange values, multiply to solve for x.

(5) 2y = 3x + 10

(-2) 5y = 4x + 8

Solve for x.

10y = 15x + 50 ↓

-10y = -8x -16

Combine and evaluate.

0 = 7x + 34

Subtract 34 from both sides.

7x = -34

Divide both sides by 7.

x = [tex]\frac{-34}{7}[/tex]

Plugin x value into either equation to solve for y.

2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10

2y =  [tex]\frac{-106}{7}[/tex] + 10

2y = [tex]\frac{-32}{7}[/tex]

y = [tex]\frac{-16}{7}[/tex]

Final answer:

By rewriting one equation to isolate y and substituting it into the other, the solution to the system of equations is determined to be {(-34/7, 16/7)}.

Explanation:

The solution to the system of equations provided is found by solving the equations simultaneously. We begin by expressing the second equation in terms of y:

Rewrite the second equation:

5y = 4x + 8

y = (4/5)x + 8/5.

Substitute y in the first equation:

3x - 2((4/5)x + 8/5) + 10 = 0.

Simplify and solve for x:

(3 - 8/5)x + (10 - 16/5) = 0

which gives us-

x = -34/7

Substitute x back into y = (4/5)x + 8/5 to find

y = 16/7

Thus, the solution to the system of equations is {(-34/7, 16/7)}.

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

Step-by-step explanation:

Let us revise some rules of logarithm

∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]

- By using the 1st rule in the first term

∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]

∵ 2³ = 8

∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]

- By using the second rule

∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]

∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]

- Add the two answers

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

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Answer:

angle 3 is 84 degree

Step-by-step explanation:

because angle 3 and angle 6 are equal

Answer:

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

Step-by-step explanation:

We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).

Now, the exponential function in the option III will be the answer.

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)

The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.  

The function that has a simplified base of (4∛4) is;

Option C; 4(∛16)^(2x)

From the general formula of an exponential function, we know that;

f(x) = a(b)^(x)

Now, we have;

f(x) = (4∛4)^(x)

Thus, looking at the options, option C is correct because;

In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;

(∛16)² = √(16^(⅔))

>> 256^(⅓)

>> 4∛4

This is the same as our initial value.

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Answer:

9p+8r-7

Step-by-step explanation:

1) subtract like terms: 12p-3p=9p

2) add unlike terms: 8r+9p -7

The given algebraic expression can be simplified as 8r+9p-7.

The given expression is 8r+12p-7-3p.

To simplify algebraic expression, simplify like terms in it.

In the given expression group the like terms, that is

8r+12p-3p-7

=8r+9p-7

Therefore, the given algebraic expression can be simplified as 8r+9p-7.

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Answer:

3

Step-by-step explanation:

(3*2 + 16x +9) + (-16x -12)

6 + 16x + 9 -16x -12

3

Answer: A. M, the number of movies. 

Step-by-step explanation: I put A, and it was the right answer.

Step-by-step explanation:

[tex] \because \triangle \: RSU \sim \: \triangle VST \\ \\ \therefore \: \frac{RS}{VS} = \frac{7}{14} = \frac{1}{2} ....(1) \\ \\ \angle RSU \cong \: \angle VST ....(2) \\ (vertically \: opposite \: angles) \\ \\ \frac{US}{TS} = \frac{4}{8} = \frac{1}{2} ....(3) \\ \\ from \: equations \: (1) \: (2) \: and \: (3) \\ it \: is \: clear \: that: \\ \triangle \: RSU \sim \: \triangle VST\\ ..(by \:SAS\:similarity\:postulate) [/tex]

Thus, given triangles are similar by SAS similarity postulate.

When the triangles RSU and VST are said to be similar, it means the corresponding sides and angles are proportional and equal respectively, which is known as the Angle-Angle criterion for similarity.

If the triangles RSU and VST are similar (RSU ~ VST), it means the corresponding sides and angles of the two triangles are proportional, and the corresponding angles are equal. This is also known as the Angle-Angle (AA) criterion for similarity. The order of the letters signifies the corresponding parts of the triangles. R corresponds to V, S to S, and U to T. So, the angles R and V are congruent, as are the angles U and T. Because we have two pairs of congruent angles, we can say that the triangles are similar by the AA criterion.

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Answer:

125%

Step-by-step explanation:

this is because the difference is 25% so b is 125% more than a

Answer:

4(x-1)units

Step-by-step explanation:

In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.

Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where

L is the length(shorter side) and x is the breadth (longer side).

According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,

L = x-2

Substituting L = x-2 into the formula of perimeter of a rectangle we have,

P = 2(x-2) + 2x

P = 2x-4+2x

P = 4x-4

P = 4(x-1)

The perimeter of the rectangle will be 4(x-1)units

Answer:

3c-28

Step-by-step explanation:

Answer:-28+3c

Step-by-step explanation:

1)combine like factors

1-29=-28

-c+4c=3c

-28+3c

48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

Solution:

Let "x" be the kilograms of 15 % copper

Then, (120 - x) be the kilograms of 75 % copper

Then, according to question,

"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

Thus we frame a equation as:

15 % of x + 75 % of (120 - x) = 51 % of 120

Solve the equation for "x"

[tex]15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48[/tex]

Thus 48 kilograms of 15 % copper used

Then, (120 - x) = (120 - 48) = 72

Thus, 72 kilograms of 75 % copper is used

y=a.(X-x1)(X-x2)

x1 and x2 are x-intercepts

x1=-3

x2=1

other points: (-1,8) and (0,5)

y=a.(x+3).(x-1)

a=-2

f(x)= -2.(x+3)(x-1)

The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

Given the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]

Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]

We are also provided with two other points: (-1, 8) and (0, 5).

We can substitute the point (-1, 8) into the equation to solve for \(a\):

[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]

Therefore, the value of \(a\) is -2.

Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]

[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

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Answer:

Adults: $8

Children: $5

Step-by-step explanation:

First Step:

Let's represent The leas by: 2A + 3C = 31

Let's represent The Smiths Station by: 2A+2C=26

Second step:

Solve The leas expression for A → 2A + 3C = 31

[tex]A =\frac{31-3C}{2}[/tex]

Third step:

Replace A on The Smiths Station and solve for C:

2([tex]\frac{31-3c}{2}[/tex]) + 2C = 26

31-3C+2C = 26

31-C=26

31-26 = C

C= 5

Fourth step:

Replace C=5 in expression [tex]A =\frac{31-3C}{2}[/tex]

A = [tex]\frac{31-3*5}{2}[/tex] →→ A=[tex]\frac{31-15}{2}[/tex]  →→ A=[tex]\frac{16}{2}[/tex]  →→ A= 8

Answer: to get to what answer

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The greatest common factor of 16k - 24 is 8.

The first step to find the greatest common factor (GCF) of 16k - 24 is to factor out any common terms. In this case, both 16k and 24 are divisible by 8, so we can factor out an 8: 8(2k - 3). Now, we need to look at the expression inside the parentheses, 2k - 3, and try to factor out any common terms. However, since 2k - 3 does not have any common factors, the GCF of 16k - 24 is simply 8.

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To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).

The student is asking how to find the solution to a system of linear equations:

x + 5y = 4

3x - 7y = -10

To solve this system, one can use the method of elimination.

Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.

The resulting equations are:

3x + 15y = 12

3x - 7y = -10

Subtract the second equation from the first to eliminate x:

22y = 22

Divide by 22 to find y:

y = 1

Substitute y = 1 into the original first equation:

x + 5(1) = 4

Solve for x:

x = -1

The solution to the system is (x, y) = (-1, 1).

Answer:

7 units  

Step-by-step explanation:

I plotted your points to form the polygon in the diagram below.

The vertical side joins the points (0 ,3) and (0, -4).

The vertical distance between them is

3 - (-4) = 3 + 4 = 7

The length of the vertical side is 7 units.

Answer:

7 units

Step-by-step explanation:

Answer:

[tex]Y = 15x+ 100[/tex]

x = 10 months

Step-by-step explanation:

Given:

Initial deposit = $100

Weakly deposit = $15

Solution:

We need to create an equation where total amount is y is equal to initial deposit plus multiplication of weakly deposit and month x, so the equation is written as.

[tex]Y = 15x+ 100[/tex] ---------(1)

Where:

Y = Total amount

x = Number of months.

Second thing we need to find the month for y = $250

Now, we substitute y = 250 in equation 1.

[tex]250 = 15x+ 100[/tex]

[tex]15x=250-100[/tex]

[tex]15x =150[/tex]

[tex]x=\frac{150}{15}[/tex]

x = 10 months

Therefore, we need to required 10 months for $250.

Answer:

ç

Step-by-step explanation:

fufujphgfhjunkksbkbbdkdbkdldbdjdbdkdjjdkdmdljdbdivdjbdkd

The answer will be number (a).

Yo sup??

This question can only be solved when the power of 10 in both the numbers is same.

therefore we can express the two numbers as

12.04*10^23 and 3.01*10^23

Clearly we can now say that a>b

Hence a is greater

Hope this helps.

Answer:

aaf ducks chicks h.c Khan ffc blackjack wUtah's hands perches yachts

Answer:

39 degrees

Step-by-step explanation:

The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP.  Take 180-141 to get 39 degrees for <PMN

Answer:

A = 4/7

B = 2/3

C = 2/5

Step-by-step explanation:

It's Easy.

Answer:

A is 4/7

B is 2/3

C is 2/5

Step-by-step explanation:

Therefore I earn $50 interest

Therefore I earn $30.88 interest.

I would do the first one.

Step-by-step explanation:

A.

Given , I invested $500 at 5% simple interest for 2 years.

P=$500,  r =5% and t = 2 years

[tex]Interest (I) =\frac{P \times r \times t}{100}[/tex]

                  [tex]=\$\frac{500 \times 5 \times 2}{100}[/tex]

                   =$50

Therefore I earn $50 interest.

B.

Given , I invested $500 at 3% compounded monthly for 2 years.

P=$500,  r =3% = 0.03 and t = 2 years

[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]  

                   [tex]=\$500(1+\frac{0.03}{12})^{ 2\times 12}[/tex]

                   =$530.88

Interest = $(530.88-530) = $30.88

I would do the first one.