Find the arc length, x, when
r= 8 and 0 = 5 radians.

The system of equations representing the amounts of Drink A and B made by the company is 1) a = b + 30 and 2) 0.20a + 0.15b = 100.5, where a is the amount in liters of Drink A and b is the amount in liters of Drink B.

Let's denote the number of liters of Drink A by the variable a and the number of liters of Drink B by the variable b. Based on the information given, we can establish a system of two equations in two variables that express the relationships between a and b. The first equation is a = b + 30, expressing the fact that the company makes 30 more liters of Drink A than Drink B.

The second equation is 0.20a + 0.15b = 100.5, which expresses the fact that the sum of 20% of a (the amount of real fruit juice in Drink A) and 15% of b (the amount of real fruit juice in Drink B) equals the total amount of real fruit juice used by the company, which is 100.5 liters.

So the system of equations is:

1) a = b + 30

2) 0.20a + 0.15b = 100.5

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To determine the number of liters of Drink A and Drink B made, we can set up a system of equations using the given information.

To write a system of equations, we need to define the variables that represent the number of liters of Drink A and Drink B. Let's use:

A = number of liters of Drink A made

B = number of liters of Drink B made

From the given information, we can create the following equations:

A = B + 30 (since there are 30 more liters of Drink A than Drink B)

0.20A + 0.15B = 100.5 (since the company used 100.5 liters of real fruit juice)

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Answer:

1 13/32

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Answer:

Option A.) is correct  [tex]\triangle XYZ \sim \triangle WVZ[/tex]  by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].

This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.

Step-by-step explanation:

From the given figure we can say that

i) Option A.) is correct  [tex]\triangle XYZ \sim \triangle WVZ[/tex]  by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].

This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.

Answer:

85%

135%

Step-by-step explanation:

34/40=.85

.85 times 100= 85%

54/40=1.35

1.35 times 100=135%

sorry if its wrong!

Answer:

y=3

Step-by-step explanation:

Step 1: Subtract from both sides

3y+39-16y=16y-16y

-13y+39=0

Step 2: Subtract 39 from both sides

-13y+39-39=0-39

-13y=-39

Step 3: Divide Both sides by -13

-13y/-13=-39/-13

y=3

Subtract 3x on both sides: 6x-3x-9=3x-3x+4 which is 3x-9=4

Add 9 to both sides: 3x+9-9=4+9 which is 3x=13

Divide both sides by 3 to get x=13/3 or 4 1/3

Hope this helped!

Answer:

 x = 13/3 = 4.333

Step-by-step explanation:

   6*x-9-(3*x+4)=0  

Step  1  :

Solving a Single Variable Equation :

  Solve  :    3x-13 = 0  

Add  13  to both sides of the equation :  

                     3x = 13

Divide both sides of the equation by 3:

                    x = 13/3 = 4.333

Answer:

The problem does not work.

Step-by-step explanation:

The plane with speed of 31 mph will cover 640 miles in [tex]\frac{640}{31} = 20.64[/tex] hours.

Now, it burns 5 gallons of gas every 3 minutes i.e. 0.05 hours.

So, it will burn in 20.64 hours [tex]\frac{5 \times 20.64}{0.05} = 2064[/tex] gallons.

Now, the helicopter with speed of 45 mph will cover 640 miles in [tex]\frac{640}{45} = 14.22[/tex] hours.

Now, it burns 7 gallons of gas every 5 minutes i.e. 0.083 hours.

So, it will burn in 14.22 hours [tex]\frac{7 \times 14.22}{0.083} = 1194.48[/tex] gallons.

But both of them starts with only 80 gallons of fuel.

Therefore, the problem does not work. (Answer)

Answer:

Option B, y = 4.6x + 5.2

Step-by-step explanation:

Slope-intercept form:  y = mx + b

Step 1:  Use those two points to get slope

m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

m = [tex]\frac{42 - 19}{8 -3}[/tex]

m = [tex]\frac{23}{5}[/tex]

m = 4.6

Step 2:  Find the y - intercept

Use point slope formula:  (y - y1) = m(x - x1)

(y - 19) = 4.6(x - 3)

y - 19 + 19 = 4.6x - 13.8 + 19

y  = 4.6x + 5.2

Answer:  Option B, y = 4.6x + 5.2

Answer :after four years the price of car depreciate

Final answer:

It will take approximately 4 years for the car to depreciate to $4520 using the declining-balance method of depreciation with a depreciation rate of 30%.

Explanation:

To calculate the number of years it would take for the car to depreciate to $4520, we can use the declining-balance method of depreciation. The declining-balance method is based on a fixed percentage of the remaining value of the asset. In this case, the rate of depreciation is 30%, so the car's value will decrease by 30% each year.

Let's start by finding the value of the car after one year. We can use the formula:

Value after one year = Initial value - (Rate of depreciation * Initial value)

Plugging in the values, we get:

Value after one year = $18820 - (0.3 * $18820) = $18820 - $5646 = $13174

Now, let's find the value after the second year:

Value after two years = $13174 - (0.3 * $13174) = $13174 - $3952.2 = $9221.8

We continue this process until we reach a value of $4520. By the time the car's value reaches $4520, it will have taken approximately 4 years.

Answer: If you want mx + b= y form and you want the y intercept, then the answer would be 2x/7 - 12/7 = y. The y intercept is b, so it is 12/7.

Step-by-step explanation: 2x - 7y = 12

Move -7y to the other side: 2x= 12 + 7y

Subtract 12 to the left side: 2x - 12 = 7y

Then divide 7 into everything: 2x/7 - 12/7 = 7y/7

The 7s in the right side cancel out, so the equation is now: 2x/7 - 12/7 = y

The y intercept is b, which is the second term in the equation, so the

Y Equals : 12/7

I hope this is what you are looking for!  

Answer:

y =  − 12 /7  +  2 x /7

Step-by-step explanation:

Answer:

The graph in option 3 will be the correct one.

Step-by-step explanation:

We have to choose the graph from the given options that shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes.

Now, the graph in option 3 will be the correct one.

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16). (Answer)

Answer:

C

Step-by-step explanation:

It will take 3 hours 6 minutes 40 seconds for the cars to be 420 miles apart.

Step-by-step explanation:

Step 1; The cars are traveling in the opposite direction at different speeds. One is going north at a speed of 75 mph while the other is going 60 mph. So for every hour, the cars are traveling they increase the distance between in between themselves by 75 miles + 60 miles = 135 miles.

Step 2; Assume that in x hours the distance between them is 420 miles. To calculate x we divide the distance to be traveled by the distance being traveled every hour.

x = distance to be covered / distance being traveled every hour

= 420 / 135 = 3.11 hours

We multiply the 0.11 hours with 60 to convert it into minutes. 0.11 × 60 = 6.66 minutes and if we do the same for seconds, 0.66 minutes × 60 = 40 seconds.

Answer:

(-1/2,2)

Step-by-step explanation:

2(4x+y=0)=8x+2y=0

8x+2y=0

-(8x-y=6)

3y=6

Divide both sides y=2

4x+2=0

4x=-2

divide both sides x=-1/2

To solve the system of equations, we can use the matrix tool. The solution to the system of equations is (1, 1.5) as an ordered pair.

To solve the system of equations using matrices, you can represent the coefficients and constants as matrices and then use matrix operations. The system of equations can be represented in matrix form as:

[A] [X] = [B],

Where:

[A] is the coefficient matrix,

[X] is the variable matrix (containing x and y),

[B] is the constant matrix.

For the given system of equations:

4x + y = 0

8x - y = 6

The coefficient matrix [A], variable matrix [X], and constant matrix [B] are:

[A] = [[4, 1],

[8, -1]]

[B] = [[0],

[6]]

Now, to solve for [X], you can use matrix multiplication:

[A] [X] = [B]

[X] = [A]⁻¹ [B]

First, calculate the inverse of [A]:

[A]⁻¹ = [[-1/12, -1/12],

[1/4, 1/4]]

Now, multiply [A]⁻¹ by [B]:

[X] = [[-1/12, -1/12],

[1/4, 1/4]] [0, 6]

[tex][X] = [(-1/12 \times 0 + -1/12 \times 6),[/tex]

[tex](1/4 \times 0 + 1/4 \times 6)][/tex]

Simplify:

[X] = [-(-1), 1.5)]

[X] = [1, 1.5]

So, the solution to the system of equations is (1, 1.5) as an ordered pair.

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Numbers are 4 and 8

Step-by-step explanation:

Step 1:

Let the numbers be x and y. Given that their sum is 12 and difference is 4. Form equations for this data.

⇒ x + y = 12 ------ (1)

⇒ x - y = 4 -------- (2)

Subtract eq (2) from (1)

⇒ 2x = 8

⇒ x = 4

Step 2:

Find y.

⇒ y = 12 - x = 12 - 4 = 8

Answer:

The length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Step-by-step explanation:

i.) A cube has a volume of 1000 cubic feet.

ii) A cube has edges which are all the same length, let us say that the length of an edge of the cube = x feet.

iii) therefore the volume of the cube is = [tex]x^{3}[/tex] = 1000 cubic feet

iv) therefore the length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Final answer:

The length of an edge of a cube with a volume of 1000 cubic feet is 10 feet. If each smaller cube has linear dimensions one tenth those of the larger cube, then the volume of each smaller cube is 1 cubic foot.

Explanation:

The volume of a cube is calculated by raising the length of one of its edges to the power of three (cubing it). Since we know the volume of the cube is 1000 cubic feet, we can determine the length of an edge by finding the cube root of the volume. The cube root of 1000 cubic feet is 10 feet, so the length of an edge of the cube is 10 feet.

To find the volume of the smaller cubes mentioned, we note that if their dimensions are one tenth of the larger cube, then each side of a smaller cube will be 10 feet divided by 10, which is 1 foot. The volume of each small cube is then 1 foot cubed, which is 1 cubic foot.

For a visual reference, imagine a larger cube divided evenly into smaller cubes, where the length of each side of the big cube is ten times that of the smaller ones. The result is that each smaller cube's volume is the original volume divided by the cube of 10 (since there are 10 layers of small cubes along each dimension of the big cube).

Answer:

391

Step-by-step explanation:

product of 49and 13= 49x13

sum of 92 and 164 =92+164

the difference of them =

49x13-(92+164)

=49x13-256

=637-256

=381

Answer:

78

Step-by-step explanation:

40 x 76 is the equation by 4x4 of 86 and the 36

Answer:28×5=$140.00

Step-by-step explanation:

A system of equations to represent the situation with Sparkles the Clown is: 2p + 2g = 12 for Jenny's party and 4p + 5g = 27 for Roger's party. We can use substitution or elimination methods to solve for 'p' and 'g' to determine the number of balloons needed for each animal.

To write a system of equations based on the given situation with Sparkles the Clown, we will let 'p' represent the number of balloons needed for a poodle and 'g' represent the number of balloons needed for a giraffe. From Jenny's party, we know that 2 poodles plus 2 giraffes used a total of 12 balloons. From Roger’s party, we learn that 4 poodles plus 5 giraffes used a total of 27 balloons. Therefore, our system of equations to represent this situation is:

To solve this system of equations, we could use methods such as substitution or elimination to find the values of 'p' and 'g' which would tell us how many balloons are required for each balloon animal.

Final answer:

To find out how many balloons are required for each balloon animal, we set up a system of equations with p representing the number of balloons for a poodle, and g for a giraffe. The system is based on the balloon usage at two parties, resulting in the equations 2p + 2g = 12 and 4p + 5g = 27.

Explanation:

To solve the problem of how many balloons Sparkles the Clown needs for each type of balloon animal, we need to set up a system of linear equations based on the given information. We will let p represent the number of balloons needed for a poodle, and g represent the number for a giraffe.

From Jenny's party, we have the first equation:

2p + 2g = 12

From Roger's party, we have the second equation:

4p + 5g = 27

Now, we have established our system of equations:

1) 2p + 2g = 12

2) 4p + 5g = 27

Solving this system will give us the number of balloons needed to make each type of balloon animal.

Answer:

14

Step-by-step explanation:

Answer: Area = 14 [tex]units^{2}[/tex]

Step-by-step explanation:

The formula for calculating the area of Triangle is given by :

Area = [tex]\frac{1}{2}[/tex] x base x height

From the given triangle

base = 4

height = 7

substituting into the formula

Area = [tex]\frac{1}{2}[/tex] x 4 x 7

Area = [tex]\frac{1}{2}[/tex] x 28

Area = 14 [tex]units^{2}[/tex]

Answer:

The ball would be at its peak at 8 feet from the basket.

Step-by-step explanation:

The basketball should be at its maximum height when it is 10 feet away from the player.

We have,

In a standard basketball shot, the path of the ball follows a parabolic arc. The maximum height is reached at the peak of this arc, which occurs halfway between the player and the basket.

The distance at which the basketball should be at its maximum height is half the distance between the player and the basket.

Half of 20 feet is 10 feet.

Therefore,

The basketball should be at its maximum height when it is 10 feet away from the player.

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Answer:

x = 5

Step-by-step explanation:

Given

2x - 2 + 5 = 13, that is

2x + 3 = 13 ( subtract 3 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

D) 0,6,12,18,24

Step-by-step explanation:

[tex]$-\frac{1}{2}\cdot2=-1[/tex]

Slope of the line h is 2.

The equation for line h is y = 2x + 4.

Solution:

General equation of a line is y = mx + c,

where m is the slope of the line and c is the y-intercept.

In the given image, line g and line h are intersecting lines and perpendicular to each other.

Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].

Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]

If two lines are perpendicular, then the product of the slopes is –1.

⇒ [tex]m_1 \cdot m_2=-1[/tex]

To find the slope of the line h:

[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]

[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]

[tex]$\Rightarrow m_2=2[/tex]

Slope of the line h is 2.

To find the equation of a line h:

Line h passing through the point (0, 4) and slope 2.

Point-slope formula:

[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]

[tex]\left(y-4)=2\left(x-0\right)[/tex]

[tex]y-4=2x[/tex]

[tex]y=2x+4[/tex]

The equation for line h is y = 2x + 4.

Answer:

Step-by-step explanation:

y = mx + b....in this form, the slope will be in the m position and the y int will be in the b position

so ur equation is : y = 2/3x - 7

Check the picture below.

well, then we know that (3x-5) + (4x+10) = 180, so

[tex]\bf (3x-5)+(4x+10)=180\implies 7x+5=180\implies 7x=175 \\\\\\ x = \cfrac{175}{7}\implies x = 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \measuredangle BEC}{3x-5\implies 3(25)-5\implies 70} \\\\\\ \stackrel{~\hfill \measuredangle ABE}{180 - (x-5)\implies 180-(25-5)\implies 180-20\implies 160}[/tex]

Final answer:

The product of 5/12 multiplied by 7 is equal to 35/12.

Explanation:

The product of 5/12 multiplied by 7 is equal to 35/12. To multiply fractions, you multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Therefore, (5/12) x 7 = (5 x 7) / (12 x 1) = 35/12.

Answer:

y=(x-2)^2+4

Step-by-step explanation:

The quadratic function that represents the parabola is y = - (x - 4)² + 4.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

From the graph of the function, the parabola intersects the x-axis

at 0 and 4, and we also know when a parabola opens downwards the equation is negative.

So, The required equation is y = - (x - 0)(x - 4).

y = - (x² - 4x).

y = - {x² - 4x + 4 - 4}.

y = - { (x - 2)² - 4}.

y = - (x - 4)² + 4.

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