In one day annie traveled 5times the sum of the number of hours Brian Traveled and 2. Togther they traveled 20hours. Find the number of hours each person traveled.

Answer:

296

Step-by-step explanation:

111/3 = 37

37 * 8 = 296

Hope this helps :-)

The distance formula is given by:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

We are given two points A and B as

A(1,1) and

B(7,-7)

so we have ,

x1 = 1 , y1=1

x2= 7 and y2=-7

Plugging these in the formula we have:

[tex]d=\sqrt{(7-1)^{2}+(-7-1)^{2} }[/tex]

d=√(36+64)

d=√100

d=10

Answer: The distance between A(1,1) and B(7,-7) is 10

Answer:

d=10 units

Step-by-step explanation:

Hello.

Step 1

the formula of the distance between two points is based on the Pythagorean theorem, which states that in a rectangle :

[tex]side^{2} +side^{2}=hypotenuse^{2}\\[/tex]

Now, suppose we have two points P1(X1,Y1) and P2(X2,Y2), the distance between the two points will be the hypotenuse of our triangle, the difference in x will be the adjacent leg, and the difference in coordinates in y will be our opposite leg.

adjacent side =X2-X1

opposite side=Y2-Y1

hypotenuse=distance between P1 and P2

replacing

[tex]adjacent\ leg^{2} +opposite\ leg^{2}=hypotenuse^{2}\\(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}=(distance between\ P1\ and\ P2)^{2}\\ distance between\ P1\ and\ P2=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\\\[/tex]

we take only the positive root because it is a distance, a negative distance makes no sense

Step 2

find the distance between A(1,1) and B (7,-7) using the formula

Let

P1=A(1,1)

P2=B(7,-7)

put the values into the formula

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\let\\\\x_{1}=1,y_{1}=1,x_{2}=7,y_{2}=-7\\d=\sqrt{(7-1) ^{2} +(-7-(1))^{2}}\\d=\sqrt{(6) ^{2} +(-8)^{2}}\\d=\sqrt{36 +64}\\d=\sqrt{100}\\ d=10[/tex]

d=10 units

Have a good day.

Final answer:

To find the actual distance from Rose Lake to the hiking trail, a proportion is used based on the given information of the map scale, resulting in an actual distance of 7 miles.

Explanation:

The question involves solving for an actual distance on a map scale, which is a proportional relationship problem in mathematics. To find the actual distance between Rose Lake and the hiking trail, we can set up a proportion using the given distances: if 2 inches on the map equal 3.5 miles in reality, then 4 inches would represent the distance from Rose Lake to the hiking trail (since the relationship between inches on the map and actual miles should be consistent).

Set up the proportion as follows:

2 inches (map) / 3.5 miles (real) = 4 inches (map) / X miles (real)

Now, solve for X, which represents the unknown actual distance in miles. By cross-multiplying and solving for X, we get:

X = (4 inches * 3.5 miles) / 2 inches

Therefore, the actual distance between Rose Lake and the hiking trail is 7 miles.

The perimeter is 32m add all sides to find perimeter

*I hope this will help*

(3 x 16) + (2 x 21) + 8

3 people made 16, which is 48

2 made 21, making 42

and 1 made 8, making 8

The answer would be c. because there is 3 players with 16 points (3x16) and 2 with 21 points (2x21) so (3x16)+(2x21) and one player scored 8 points so (3x16)+(2x21)+8

I hope this helps     have a nice day

Answer:

your graph is gonna have a horizontal line crossing the y axis at (0,3)

I don't really under stand what to do but the answer for 7 3/4 divided by 1/3 is 23 1/4.

Let me know what else is needed to figure out your question.

Let x= #1 number

let y= #2 number

We would get xy-3 as the answer

ab-3 is the required expression for the sentence "3 less than a product of two numbers". Here a and b are two numbers.

we need to write expression for 3 less than a product of two numbers

The product is the multiplication of two integers.

Let a be one number

b be second number

Product of two numbers is ab.

as given 3 less than a product of two numbers

we get ab-3.

Therefore ab-3 is the required answer for 3 less than a product of two numbers.

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Given

Angie and Kenny play online video games

Angie buys 1 software package and 3 months of game play

Kenny buys 1 software package and 4 months of game play

Each software package cost $50

total cost is 240

Find out the cost of one month of gameplay.

To proof

let us assume that the cost of one month of game play = x

As given in the question

Angie buys 1 software package and 3 months of game play

Kenny buys 1 software package and 4 months of game play

Each software package cost  = $50

Total cost =$240

Than the equation becomes

( 50 + 3x ) + ( 50 + 4x ) = 240

100 + 7x= 240

7x= 140

x = $20

The cost of one month gameplay  is $ 240.

Hence proved

Hello!

I was going to try to use the slope formula, and solve for the y-intercept, but the given graph is hard to distinguish accurate ordered pairs. So, we will find the equation with the graph instead.

Looking at the graph, we can see that the y-intercept is negative. Also, we can also determine that each square represents one unit. So, the y-intercept has to be -3/2 or -1.5. That removes the choices A and C because the y-intercept is in between the values of -1 and -2.

Secondly, the graph has a positive slope. Why? When the x-values increase, the y-values increase. Also, when the x-values decrease, the y-values also decrease. This tells us that the graph has a positive slope (this doesn't remove any choices, but it helps to distinguish which graph has a positive or negative slope).

Finally, we know that if the slope is greater than one, then it is steeper (m > 1). But, if it's less than one, then it becomes less steep (0 < m < 1). Looking at the graph, the graph looks relatively steep (graphing the equations y = 5/7 x - 3/2 and y = 7/5x - 3/2 can help you see the differences between them).

Therefore, the equation of the line given by the graph is choice D, y = 7/5 x − 3/2.

The equation of the line given by the graph is y = 5/7 x - 2/3 (Option A).

The equation of the line given by the graph is y = 5/7 x - 2/3 (Option A).

To determine the equation, we look at the slope and y-intercept of the line. The slope of the line can be determined by comparing the change in y-coordinates to the change in x-coordinates between any two points on the line. In this case, the slope is 5/7. The y-intercept is the value of y when x = 0, which is -2/3 in this case.

Therefore, the equation of the line is y = 5/7 x - 2/3.

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(0, 0) 0 pages in zero minutes.

(3, 1) 3 pages in one minute.

(6, 2) 6 pages in two minutes.

(9, 3) 9 pages in three minutes.

87 Pounds would be the correct answer I believe.

5x=29x

x=3

87 pounds

Since $5 = 29. You can multiply both 5 and 29 to get 15=87 pounds

[tex]\left(\dfrac{3}{\sqrt5}\right)\left(\dfrac{4}{\sqrt3}\right)=\dfrac{3\cdot4}{\sqrt5\cdot\sqrt3}=\dfrac{12}{\sqrt{5\cdot3}}=\dfrac{12}{\sqrt{15}}\\\\=\dfrac{12\cdot\sqrt{15}}{\sqrt{15}\cdot\sqrt{15}}=\dfrac{12\sqrt{15}}{15}=\dfrac{12\sqrt{15}:3}{15:3}=\dfrac{4\sqrt{15}}{5}[/tex]

[tex]Used:\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\\\\\sqrt{a}\cdot\sqrt{a}=a[/tex]

CE is equal to 58 units.

To find the length of CE, we'll use the fact that D is the midpoint of CE. The midpoint of a line segment divides it into two equal parts.

If CD is one part and DE is the other, then we can set up an equation:

CD=DE

9X−7=3X+17

Now, solve for X:

6X=24

X=4

Now that we have the value of X, substitute it back into either CD or DE to find the length of each part:

CD=9X−7=9(4) −7=36−7=29

DE=3X+17=3(4) +17=12+17=29

Now, since D is the midpoint, CD and DE are equal.

CD=DE=29

Finally, CE, the total length, is the sum of CD and DE:

CE=CD+DE=29+29=58

So, CE is indeed 58

The formula of a midpoint:

[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have:

[tex]A(7,\ 12)\to x_A=7,\ y_A=12\\B(-1,\ 6)\to x_B=-1,\ y_B=6[/tex]

Substitute:

[tex]\dfrac{7+(-1)}{2}=\dfrac{7-1}{2}=\dfrac{6}{2}=3\\\\\dfrac{12+6}{2}=\dfrac{18}{2}=9[/tex]

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount  is invested at 10% simple interest

Interest for first part =  10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest

Final answer:

To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.

Explanation:

Investment Allocation Problem

Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:

x + y = 9500

The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:

0.10x + 0.09y = 914

Now we can solve the system of equations:

x + y = 9500 (Equation 1)

0.10x + 0.09y = 914 (Equation 2)

Multiplying Equation 1 by 0.10 gives us a new equation:

0.10x + 0.10y = 950 (Equation 3)

Now, we subtract Equation 2 from Equation 3:

(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914

0.10y - 0.09y = 36

0.01y = 36

y = 3600

Substitute y = 3600 into Equation 1 to find x:

x + 3600 = 9500

x = 5900

Therefore, $5900 is invested at 10% and $3600 is invested at 9%.

Answer:

1968

Step-by-step explanation:

I use the following method when it comes about products of big numbers

I grab the longer and put on the first line, below I put the smallest number.

492

x 4

Now, it is time to distribute the product, term by term, remember that when performing a product, if the result is greater or equal than 10, you need to carry a number for the following product.

      492

        x 4

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

   19    6    8

(end) (c3) (nc)

nc means: not carrying anything since 4x2=8 and 8 <10

c3 means: carrying 3 since 4x9= 32 and 32 >10

end means: put the whole number and sum it what you were carrying. 4*4+3=19

The product 492*4=1968

The product of 4 multiplied by 492 equals 1968. To find this, we used a step-by-step approach using basic multiplication and the distributive property.

To determine the product of 4 multiplied by 492, you can execute the following steps:

Therefore, 4 × 492 = 1968.

Answer:

B)3x^2 (4*x^2 + 2x + 6)

Step-by-step explanation:

Step 1: Find the Greatest common factor of the given expression.

12x^4 + 6x^3 + 18x^2

The above expression can be written as .

= 2*2*3*x^4 + 2*3*x^3 + 2*3*3*x^2

Here 3x^2 is prime factor

Step 2: Let's take out the 3[tex]x^{2}[/tex] and write the remaining terms in the parenthesis.

= 3x^2 (2*2*x^2 + 2x + 2*3)

= 3x^2 (4x^2 + 2x + 6)

Therefore, the answer is B)3x^2 (4*x^2 + 2x + 6)

Thank you.

Answer:

2 pieces

Step-by-step explanation:

Julie wants to cut 1 and a quarter yard long pieces of a 3 yard string.

1 and a quarter yard =  [tex]1\frac{1}{4}[/tex] yards =  [tex]\frac{5}{4}[/tex] yards

= 1.25 yards

The total length of a piece of string = 3 yards

Julie can cut the number of pieces of 1.25 yards = [tex]\frac{3}{1.25}[/tex]

                                                                                 = 2.4 pieces

She can cut 2 pieces of 1.25 yard = 1.25 × 2 = 2.5 yard

3 yard - 2.5 yard = 0.5 yard would be leftover.

he negative square root of negative 75

= - √-75

= - √(25 * 3 * i^2)          ...............because i^2 = -1

= - 5i√3

The negative square root of -75 simplifies to [tex]5\sqrt{3}i[/tex] in the complex number system. 'i' is the imaginary unit, where i is the square root of -1.

In Mathematics, we cannot take the square root of a negative number in the set of real numbers. However, we use the concept of imaginary numbers where i is the square root of -1. Therefore, to simplify the negative square root of negative 75, we begin to simplify the terms inside the square root. Negative 75 can be factored into -1 and 75. Therefore, the square root of -75 is[tex]\sqrt{75}i[/tex], where the square root of 75 can further simplifies it to[tex]5\sqrt{3}i[/tex] , making the final answer [tex]5\sqrt{3}i[/tex]

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Start with expressions in blue boxes:

1st column) [tex]36x+9;[/tex]

2nd column) [tex]9(4x-1)=36x-9;[/tex]

3rd column) [tex](4\cdot 9x)+(4\cdot 2)=36x+8.[/tex]

You have 6 expressions. Consider all them:

1. [tex]36x+8[/tex] - 3rd column;

2. [tex](9\cdot 4x)+(9\cdot 1)=36x+9[/tex] - 1st column;

3. [tex](3\cdot 12x)-(3\cdot 3)=36x-9[/tex] - 2nd column;

4. [tex]9(4x+1)=36x+9[/tex] - 1st column;

5. [tex]36x-9[/tex] - 2nd column;

6. [tex]4(9x+2)=36x+8[/tex] - 3rd column.

Answer:

The equivalent expressions are:

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]

[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]

Step-by-step explanation:

Consider the provided expressions.

[tex]36x + 9[/tex]

The expression [tex]36x + 9[/tex] can be written as:

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)[/tex]

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]

Consider the expression [tex]9(4x-1)[/tex]

The expression [tex]9(4x-1)[/tex] can be written as:

[tex]9(4x-1)=36x-9[/tex]

Take 3 common.

[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]

Consider the expression [tex](4\cdot 9x)+(4\cdot 2)[/tex]

The expression [tex](4\cdot 9x)+(4\cdot 2)[/tex] can be written as:

Take out 4 common

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)[/tex]

Open the parentheses.

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]

For unit rate, divide the total dollar amounts by the amount of the item you have.

in number 1:

18 golf balls equal $32.99

so divide 32.99 by 18

32.99

 18

This tells us that 1 golf ball costs roughly $1.83

2. Do the same thing except put the ounces of juice under the total cost

2.75

 15

This will tell us that 1 oz of juice costs $0.18.

Since this is in word form, it is a rule in higher math to answer in the same format.

The unit rate for one golf ball is $1.83, and it costs $0.18 per ounce of juice.

Dived the price by the number of ounces and that should be your answer to the questions .

Answer:

 [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

 [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

Explanation:

Ratio between [tex]4*10^{15}[/tex] and [tex]8*10^9[/tex] = [tex]\frac{4*10^{15}}{8*10^9} =5*10^5[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

Ratio between [tex]2*10^{-5}[/tex] and [tex]4*10^{-12}[/tex] = [tex]\frac{2*10^{-5}}{4*10^{-12}} =5*10^6[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

Answer:

[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The wholesale price of the home audio system is = $264

The electronics store had marked up the price of the system by = 60%

So, the additional price becomes= [tex]\frac{60}{100}*264[/tex] = $158.40

Total price of the audio system now becomes = 264+158.40 = $422.40

As Lori was paid commission of = 15% on 422.40, so her commission becomes = [tex]\frac{15}{100}*422.40[/tex]

= $63.36

Hence, option D is correct.

Answer:

Lori was paid a 15 percent commission for the home audio system that she sold. The electronics store had marked up the price of the system by 60 percent over the wholesale price of $264. How much did Lori earn for the sale of the home audio system?

Answer is=$63.36

Step-by-step explanation:

I am doing a unit test on it.

Answer:

It is 8 3 pointers and 13 2 pointers

Step-by-step explanation:

8 x 3 = 24

13 x 2 = 26

24 + 26 = 50

The bulldogs made 13 2-pt shots and 8 3-pt shots.

Let's assume that the bulldogs made x 2-pt shots and y 3-pt shots. Since each 2-pt shot is worth 2 points and each 3-pt shot is worth 3 points, we can set up the following equations: 2x + 3y = 50 (equation 1) and x + y = 21 (equation 2). To solve this system of equations, we can multiply equation 2 by 2 to get 2x + 2y = 42, and then subtract equation 1 from it. This gives us y = 8. Substituting y = 8 into equation 2, we get x + 8 = 21, which means x = 13. Therefore, the bulldogs made 13 2-pt shots and 8 3-pt shots.

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The inequality is

[tex]-32> -5+9x[/tex]

We need to isolate x and for that first we need to get rid of 5 by adding 5 to both sides.

[tex]-32+5 +-5+9x+5\\-27>9x\\[/tex]

Now we need to get rid of 9 and for that we divide both sides by 9 .That is

[tex]-\frac{27}{9}>\frac{9x}{9}[/tex]

[tex]-3>x[/tex]

[tex]x<-3[/tex]

Final answer:

The expanded form of the decimal 24.56 is 20 + 4 + 0.5 + 0.06, which breaks down each digit by its place value.

Explanation:

The expanded form of the decimal 24.56 is an expression that shows the value of each digit in the number. To write it in expanded form, we break down each digit according to its place value. For the number 24.56, the expanded form would look like this:

Combining these values, the expanded form of 24.56 is:

20 + 4 + 0.5 + 0.06