Translate the sentence into an inequality

The quotient of c and 5 is at most 18 .

Answer:

b

Step-by-step explanation:

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)

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Answer: 1/3

Step-by-step explanation:

5/15 divided both by 5 is 1/3

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:

[tex]\large\boxed{\dfrac{1}{8}\%=\dfrac{1}{800}}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\\dfrac{1}{8}\%=\dfrac{\frac{1}{8}}{100}=\dfrac{1}{8}\cdot\dfrac{1}{100}=\dfrac{1}{800}\\\\\text{other method}\\\\\text{Convert the fraction to the decimal:}\\\\\dfrac{1}{8}=0.125\to\dfrac{1}{8}\%=0.125\%\\\\0.125\%=\dfrac{0.125}{100}=\dfrac{0.125\cdot1000}{100\cdot1000}=\dfrac{125}{100000}=\dfrac{125:125}{100000:125}=\dfrac{1}{800}[/tex]

it is d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

First find how many bottles Ginger will need.

15 mL x 365 day = 5475 mL for 1 yr

5475 mL / 350mL = 16 bottles

Then find the price for the 16 bottles.

16 bottles x $4.85 = $77.60

Answer:

Infinitely many solutions

Step-by-step explanation:

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

-24x-18=-24x-18

infinitely many solutions

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:

Step-by-step explanation:

10/25=20/50=40/100

6/8=3/4=12/16

3/5=6/10=60/100

1/10=10/100

Answer:

44 quarts of paint

Step-by-step explanation:

Given,

75-foot fence needs = 4 quarts.

We have to use the unitary method to determine how many quarts will be needed for the fencing system. Hence,

75-foot fence needs         = 4 quarts of paint

1-feet fence needs            = (4/75) quarts of paint

825-foot fence needs      = (4 x 825)/75 quarts of paint

                                          = 3,300/75 quarts of paint

                                          = 44 quarts of paint

Therefore, we need 44 quarts of paint for 825-foot fence.

To determine how many quarts of paint are needed for an 825-foot fence, we can set up a proportion and solve for the unknown quantity.

To determine how many quarts of paint are needed for an 825-foot fence, we can use the concept of ratios. Since we know that 4 quarts of paint are needed for a 75-foot fence, we can set up a proportion:

To solve for the unknown quantity, we can cross-multiply and solve for the missing value:

Dividing both sides of the equation by 75, we get:

By performing the calculation, we find that quarts of paint is approximately 44 quarts. Therefore, 44 quarts of paint are needed for an 825-foot fence.

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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

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:

=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:

33

Step-by-step explanation:

9+2=1/3x

11=1/3x

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

Answer:

40%

Step-by-step explanation:

125 - 75= 50

50 ÷ 125 = 0.4

0.4 = 40%

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:

x = 90°

Step-by-step explanation:

We are given a trigonometric function of x from which we have to a solution for x.

The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]

⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]  

{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}

⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]

⇒ [tex](\sin x - 1)^{2} = 0[/tex]

{Since we know the formula (a - b)² = a² - 2ab + b²}

⇒ [tex](\sin x  - 1) = 0[/tex]

⇒ [tex]\sin x = 1 = \sin 90[/tex]

⇒ x = 90° (Answer)

To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.

To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:

Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:

(1 - sin2x) + 2sin x - 2 = 0

Simplifying, we get:

1 - sin2x + 2sin x - 2 = 0

-sin2x + 2sin x - 1 = 0

This is a quadratic equation in terms of sin x. Let's solve it:

sin2x - 2sin x + 1 = 0

We recognize this as a perfect square trinomial:

(sin x - 1)2 = 0

So, we have:

sin x - 1 = 0

Therefore:

sin x = 1

So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.

Answer: 17

================================

How I got that answer:

(2,3) and (3,1) have '3' in common in that the y value of the first pairs with the x value of the second.

If you picture a chain, then you start with x = 2, move to y = 3, then move to x = 3 and then y = 1

2 ---> 3 ---> 3 ---> 1

So f(f(2)) = f(3) = 1

If g(x) = f(f(x)), then we know (2,1) is on the graph of g(x)

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

Repeat for (3,1) and (1,5)

3 ---> 1 ---> 1 ---> 5

f(3) = 1

g(x) = f(f(x)) = f(f(3)) = f(1) = 5

We know that (3,5) is on the graph of g(x)

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

The two points on g(x) are: (2,1) and (3,5)

Comparing that to (a,b) and (c,d) we can see

a = 2, b = 1, c = 3, d = 5

a*b + c*d = 2*1 + 3*5 = 2 + 15 = 17

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

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:

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:

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:

6

Step-by-step explanation:

8-2=6

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:

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

Step-by-step explanation:

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 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:

multiply all together

Step-by-step explanation