In a video game green gems are worth 5 points and blue gems are worth 10 points. Eric collects 25 gems and earned 160?points form his gems. Find how many green gems and how many blue gems Eric collected.

Answer:

[tex]\displaystyle 6x + y = 4[/tex]

Step-by-step explanation:

In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.

I am joyous to assist you anytime.

Answer:

[tex]0.5a[/tex]

Step-by-step explanation:

We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.

We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.

Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.

Answer:

The prepaid phone plan will have a steeper line and lower y-intercept.

I hope this is right

Step-by-step explanation:

prepaid phone plan y = .20x

contracted phone plan y = .02x + 50

The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.

We have:

Prepaid

[tex]Rate = 0.20[/tex]

[tex]Monthly = 0[/tex]

Contracted

[tex]Monthly = 50[/tex]

[tex]Rate = 0.02[/tex]

For both plans, the cost function (y) is:

[tex]y =Monthly + Rate \times x[/tex]

Where:

[tex]x \to[/tex] Number of minutes

[tex]Rate \to[/tex] Steepness

So, we have:

Prepaid

[tex]y =0 + 0.20 \times x[/tex]

[tex]y =0.20x[/tex]

The y intercept (i.e. when x = 0) is

[tex]y = 0.20 \times 0 = 0[/tex]

Contracted

[tex]y = 50 + 0.02 \times x[/tex]

[tex]y = 50 + 0.02x[/tex]

The y intercept is:

[tex]y = 50 + 0.02 \times 0 = 50[/tex]

By comparing the steepness and the y-intercepts,

Hence, (a) is correct

See attachment for the graphs of both plans

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Answer:

For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.

Step-by-step explanation:

1. Let's find the range for the set of numbers given:

Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.

Range = 193 - 111

Range = 82

2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:

Mean = Sum of all the terms / Number of the terms of the set

Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7

Mean = 1,015/7

Mean = 145

Now, we proceed to calculate the variance this way:

Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample

Let's calculate the squared distances of each term in the set from the mean:

111 - 145 = - 34 ⇒ - 34² = 1,156

122 - 145 = - 23 ⇒ - 23² = 529

134 - 145 = - 11 ⇒ - 11² = 121

146 - 145 = 1 ⇒ 1² = 1

150 - 145 = 5 ⇒ 5² = 25

159 - 145 = 14 ⇒ 14² = 196

193 - 145 = 48 ⇒ 48² = 2,304

Now replacing with the real values:

Variance = (1,156 + 529 + 121  1+ 25 + 196 + 2,304)/7

Variance = 4,332/7

Variance = 618.86 (Rounding to two decimal places)

Finally, we can calculate easily the standard deviation:

Standard deviation = √Variance

Standard deviation = √ 618.86

Standard deviation = 24.88 (Rounding to two decimal places)

Answer:

343

Step-by-step explanation:

-(-7^3)=-(-7*-7*-7)=-(-343)=343

Answer:

Step-by-step explanation:

-(-7 to the power 3)

=-(-7×-7×-7)= -(-343)

=343

Answer:

the object would weigh 18.36

since it is 1.2 times as much you multiply the weight of the object on earth by 1.2 and that's the answer

Step-by-step explanation:

Answer:

23,490

Step-by-step explanation:

10% = 0.1

234900 x 0.1 = 23490

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

                 [tex]500=x^2y[/tex]

Therefore, [tex]y=\dfrac{500}{x^2}[/tex]

It is open box. The surface area of box, S .

[tex]S=x^2+4xy[/tex]

Put  [tex]y=\dfrac{500}{x^2}[/tex]

[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]

For critical point, S'(x)=0

[tex]2x-\dfrac{2000}{x^2}=0[/tex]

[tex]x^3=1000[/tex]

[tex]x=10[/tex]

Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]

y = 5

Double derivative of S(x)

[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10

[tex]S''(10) > 0[/tex]

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

The solution to the system of equations is (3,1)

Step-by-step explanation:

The system of equations represented by graph are:

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

Solving the system of equations

Let:

[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]

Putting value of y from eq(2) into eq(1):

[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]

So, Value of x = 3

Putting value of x into eq(2)

[tex]y=x-2\\y=3-2\\y=1[/tex]

So, value of y= 1

So, The solution to the system of equations is (3,1)

Keywords: System of equations

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Answer:

Train b is moving faster than a by 45 units an hour

Step-by-step explanation:

Answer:

=3

Step-by-step explanation:

Okay so you 1/2 divided by 1/6

Answer:

3

Step-by-step explanation:

1/2÷ 1/6

=  

1/2×6/1

=  

1 × 6

2 × 1

=  

6/2

=  

6 ÷ 2

2 ÷ 2

=  3

Just Divide 1/6 by 1/2

Answer:

Infinitely many solutions

Step-by-step explanation:

-6(4x+3)=6(-4x-3)

-24x-18=-24x-18

infinitely many solutions

Answer:

[tex]1000-40x>400[/tex]

Step-by-step explanation:

Let's call B the balance of Jacob's checking account. Each week he withdraws $40 from his actual balance of $1000, so if x is the number of weeks, the account's balance is

B=1000-40x

The balance must be more than $400, which means

[tex]1000-40x>400[/tex]

That is the inequality to model the situation. If we wanted to know the limit for x, we can solve the inequality. Operating:

[tex]1000-400>40x[/tex]

600>40X

[tex]x<\frac{600}{40}[/tex]

Or x<15

Which means Jacob can withdraw $40 14 times at most to maintain the minimum balance requirement

Answer:

8/27  is the solution and the alternative form is 0.296 or 2/3 to the power of 3

Answer:

Step-by-step explanation:

The answer is 16

Answer:

Step-by-step explanation:

2 • (xy - 4cs)

Answer:

y = c/z²  

Step-by-step explanation:

(1) y ∝ 1/x²or

   y = a/x² where a is a constant

   x ∝ z or x = bz, where b is a constant

Substitute x into (1)

y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²

a is a constant and b is a constant, so a/b² is a constant.

Let c = a/b². Then

y = c/z²

Final answer:

The probability of rolling an even number on a 9-sided die is 4/9.

Explanation:

To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.

In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).

Therefore, the probability of rolling an even number is 4/9.

Answer:M=24

Step-by-step explanation:

There are 2 ways to do this

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

Method 1) Divide both sides by 25, then add 2 to both sides

25(M-2) = 650

M-2 = 650/25

M-2 = 26

M = 26+2

M = 28

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

Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.

25(M-2) = 650

25M - 50 = 650

25M = 650+50

25M = 700

M = 700/25

M = 28

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

Answer:

5/6

Step-by-step explanation:

Add the fractions by finding the common denominator.

1/2 + 1/3

3/6 + 2/6

5/6

Answer: 1/3

Step-by-step explanation:

5/15 divided both by 5 is 1/3

Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1

Answer:

b

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

0.30 * x = 240

x = 240/0.30 = 800

0.50 * 800 = 400

Answer:

The value of 50 % of number is 400  .

Step-by-step explanation:

Given as :

Let The number be x

According to statement

30 percent of a number is 240

I.e 30 % of x = 240

Or, [tex]\frac{30}{100}[/tex] × x = 240

Or, 0.3 × x = 240

So.  x = [tex]\frac{240}{0.3}[/tex]

∴     x = 800

SO, The number is 800 .

Now again 50 percent of that number = y

I.e y = 50 % of x

or, y =  50 % of 800

Or, y =  [tex]\frac{50}{100}[/tex] × 800

Or, y = 0.5 × 800

∴    y = 400

Hence The value of 50 % of number is 400  . Answer

Answer:

The correct answer is A. f(x)= 2(3^x)

Step-by-step explanation:

The exponential function y = 2(3)ˣ, has an initial value of 2

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplicative rate of change

Given the exponential function y = 2(3)ˣ, has an initial value of 2

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Answer:

33

Step-by-step explanation:

9+2=1/3x

11=1/3x

x=11/(1/3)=(11/1)(3/1)=33/1=33

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

in this problem

For x=-14, y=-7

Find the value of the constant of proportionality k

[tex]k=y/x[/tex]

substitute

[tex]k=-7/-14=0.5[/tex]

so

The linear equation is

[tex]y=0.5x[/tex]

Find x when the value of y=10

substitute the value of y in the equation

[tex]10=0.5x[/tex]

solve for x

Multiply by 2 both sides

[tex]x=20[/tex]

Final answer:

In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.

Explanation:

The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.

Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.

Answer:

40%

Step-by-step explanation:

125 - 75= 50

50 ÷ 125 = 0.4

0.4 = 40%

Answer:

Step-by-step explanation:

[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]

Answer:

exact form x=5/2 decimal form2.5 mixed number form 2 1/2

Step-by-step explanation: