If y = 7x, what happens to x when y is increased by 5 times its original value?
A) x decreases 5 times its original value

B) x increases to 11/5 its original value

C) x also increases 5 times its original value

D) x decrease to 4/5 of its original value

Let

x---------> the number of child tickets

y--------> the number of adult tickets

we know that

the equation that describes the relationship between the number of child tickets and the number of adult tickets  is a linear equation

If the point[tex](4,2)[/tex] is the solution

then

the number of child tickets is [tex]4[/tex]

the number of adult tickets is [tex]2[/tex]

therefore

the answer is

the  solution [tex](4,2)[/tex] represent that

the number of child tickets is [tex]4[/tex]

the number of adult tickets is [tex]2[/tex]

The solution (4, 2) means Olivia purchased 4 child tickets and 2 adult tickets at the movies for a total of $46.

The student's question involves interpreting the solution to a linear equation in the context of purchasing movie tickets. The specific solution given is the ordered pair (4, 2). In the context of the problem described, the number '4' represents the quantity 'x', which is the number of child tickets purchased, and the number '2' represents the quantity 'y', which is the number of adult tickets purchased. Therefore, the solution (4, 2) means that Olivia purchased 4 child tickets and 2 adult tickets at the movies for a total expenditure of $46.

n = -4/9 hope this helps

n-2=10n+4/2

We move all terms to the left:

n-2-(10n+4/2)=0

We add all the numbers together, and all the variables

n-(10n+2)-2=0

We get rid of parentheses

n-10n-2-2=0

We add all the numbers together, and all the variables

-9n-4=0

We move all terms containing n to the left, all other terms to the right

-9n=4

n=4/-9

n=-4/9

Calculate f(3) by replacing X with 3:

f(x) = x^2 -1

f(3) = 3^2 -1

F(3) = 9-1

f(3) = 8

Now calculate f(-4) by replacing x with -4:

f(x) = x^2 -1

f(-4) = (-4)^2 - 1

f(-4) = 16 -1

f(-4) = 15

Now add f(3) to f(-4)

8 + 15 = 23

The answer is a) 23

This problem can be solved using proprtions.  Once you set up the proportion, the calculations are easy.

Let x = number of pens made in 1 second.

[tex]\frac{9pen}{3sec} = \frac{xpen}{1 second}[/tex]

Now, you just cross multiply and solve.

9 = 3x

x = 3

The rate is 3 pens per second.

15 * 28 = 420. Should be your answer.

Answer:

Step-by-step explanation:

Kendra buys  x pounds lettuce.

If lettuce costs $2.25 per pound.

Then for x pounds of lettuce,

cost=2.25x

Kendra buys  y pounds tomatoes.

If tomatoes costs $2.65 per pound.

Then for y pounds of tomatoes,

cost=2.65y

So, total cost=2.25x+2.65y

Now, this total cost will be at least  $8

So, the inequality is-

[tex]2.25x+2.65y\geq8[/tex]

The problem can be represented by the inequality [tex]2.25x + 2.65y \geq 8[/tex] where x is the number of pounds of lettuce Kendra buys and y is the number of pounds of tomatoes she buys. The total cost of the vegetables equals or exceeds $8.

In this situation of buying lettuce and tomatoes, the cost of lettuce per pound is $2.25 and the cost of tomatoes per pound is $2.65. Kendra spends at least $8 on lettuce and tomatoes. Let x represent the number of pounds of lettuce that Kendra buys and let y represent the number of pounds of tomatoes that she buys. Understanding the problem, the inequality that represents this situation is

[tex]2.25x + 2.65y \geq 8[/tex]. This is because each pound of lettuce ('x') is multiplied by its cost, and each pound of tomatoes ('y') is multiplied by its cost. If Kendra spends at least $8, then the total cost equals or exceeds $8.

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We can find the maximum number of CDs she can buy by dividing 153 by 18. The answer ends up being 8.5. Since she can't buy 0.5 of a CD, she can buy a maximum of 8 CDs. Written as an inequality, I think it should be x is less than or equal to 8. I hope this helps!

GIVEN: y = 3x + 5

--> slope of given line = 3

--> This means that your equation must have the same slope, or "m"

FORMULA OF A LINE: y = mx + b

--> Use point-slope form to find "b"

POINT SLOPE FORM: y - y₁ = m ( x - x₁ )

--> Plug in your given point AND the slope of the given line

y - 5 = 3 ( x - 4 )

y - 5 = 3x - 12

y = 3x - 7

Answer: 1/2.

Explanation:

First, note that since the previous drops have already happened, their result do not modify the occurrence of future results when the toast is dropped again.

In oder to have a total of three time landing butter side up, exactly, there are two possibilities:

Since there are two ways of totaling side up 3 times, you have to sum both chances.

1) Next drop butter side up and second drop butter side down:

     1/2 × 1/2  = 1/4

2) Next drop butter side down and second one butter side up:

     1/2 × 1/2 = 1/4

3) Add both probabilities: 1/4 + 1/4 = 1/2

And that is the answer: 1/2

Answer:

s can take any real value.

Step-by-step explanation:

Given that

-2(6+s)_>-15-2s

Distribute -2 over 6+s

-12-2s >= -15-2s

Simplify both the sides

Add 2s to both the sides.

We get 2s cancel out and -12>=-15 which is true.

Hence the given inequality is valid for all values of s.

This is a special case of inequality which has infinite number of solutions.

s can take any real number and this inequality is valid.

Answer:

Solution of inequality: -12 ≥ -15 Which is true.

Step-by-step explanation:

Given data:

Equation:-2(6+s)_>-15-2s

-2(6+s)_>-15-2s

=-12 - 2s ≥ - 15 -2s

By dividing -2s on both sides:

= -12 - 2s/-2s ≥ - 15 -2s/-2s

= -12 ≥ -15

                                                  -2(6+s)_>-15-2s =  -12 ≥ -15

Final answer:

The distance formula calculates the straight-line distance between two points on a coordinate plane using the Pythagorean theorem, which is applied to the differences in the x and y coordinates of the points to form a right triangle.

Explanation:

Explaining the Distance Formula

The distance formula is a way to calculate the straight-line distance between two points in a coordinate plane. This formula is derived from the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In other words, a² + b² = c².

To understand the distance formula, consider two points (x1, y1) and (x2, y2) on a coordinate plane. The difference in the x values (x2 - x1) and the y values (y2 - y1) represent the lengths of the legs of a right triangle, where the straight-line distance we are trying to find is the hypotenuse. Thus, by the Pythagorean theorem, the distance (d) can be found by taking the square root of the sum of the squares of these differences. The resulting distance formula is d = √((x2 - x1)² + (y2 - y1)²).

The distance formula logically extends the Pythagorean theorem to two-dimensional space, where distances on the plane are calculated irrespective of the orientation or position of the line connecting the two points.

how should anyone know this

Answer:

The independent variable is the time spent petting an animal, and the dependent variable is the stress level.

The independent variable is time, and the dependent variable is the population of field mice.

The independent variable is the number of floors ascended, and the dependent variable is the height of the elevator.

Any fraction that, when dividing the numerator and denominator, it'll give you 4.

For example:

8/2, which, when divided: 8/2 = 4

16/4, which, when divided: 16/4 = 4

hope this helps

~Rise Above the Ordinary

For m it’s 1,1/3and -5/3 you will get different values when plug the different values of n

The angle of cba is 3.408* if you wanna know

cba is 3.408 and just ask if you want to know how

y+6=1/3(x-9)

Moved all terms from left to right that doesn't contain y

Y=-6 +1/3x-3

Simplify

Y=1/3x-9

Your answer is c.

Answer: [tex]y=\dfrac{1}{3}x-9[/tex]

Step-by-step explanation:

The equation of a line in slope -intercept form is written as :-

[tex]y=mx+c[/tex]

The given equation : [tex]y+6=\dfrac{1}{3}(x-9)[/tex]

To write the given equation in slope - intercept form , we need to first solve the right -hand sides in the equation.

[tex]y+6=\dfrac{1}{3}(x-9)\\\\\Rightarrow\  [tex]y+6=\dfrac{1}{3}x-3\\\\\Rightarrow\ y=\dfrac{1}{3}x-3-6\\\\\Rightarrow\ y=\dfrac{1}{3}x-9[/tex]

Hence, the equation written in slope-intercept form :  [tex]y=\dfrac{1}{3}x-9[/tex]

The area of the park is 2.45 acres.

The area of a park is determined to be exactly halfway between 2.4 acres and 2.5 acres. To find this midpoint or average, we add the two values together and then divide by 2.

First, we add 2.4 acres and 2.5 acres:

2.4 acres + 2.5 acres = 4.9 acres

Now, we divide this sum by 2 to find the midpoint:

Midpoint = 4.9 acres / 2 = 2.45 acres

Therefore, the area of the park is 2.45 acres. This means that it is precisely halfway between the two given values.

Understanding the midpoint or average is essential in various contexts, such as real estate, land measurement, and statistical analysis. In this case, it signifies that the park occupies an area that is equidistant from 2.4 acres and 2.5 acres. It can be seen as a balanced point between these two values, serving as a useful concept for situations where precision or fairness is required, such as in property assessments or distributing resources evenly.

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C. <2 is the correct answer

Final answer:

The algebraic expression for 'Double the sum of 2 and x increased by one-half x squared' is 2(2 + x) + (1/2)x².

Explanation:

To translate the phrase 'Double the sum of 2 and x increased by one-half x squared' into an algebraic expression, we break it down into parts:

The sum of 2 and x is given by the expression (2 + x).

Double this sum can be written as 2(2 + x).

One-half x squared is written as (1/2)x².

Increasing the doubled sum by one-half x squared means adding (1/2)x² to it.

Therefore, the complete algebraic expression is 2(2 + x) + (1/2)x².

Regarding the concept of squaring of exponentials, remember that when you square a term like x², you are effectively raising x to the power of 4 because the exponents are multiplied.

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]M(-6,\ 8)\to x_M=-6,\ y_M=8\\A(-2,\ 10)\to x_A=-2,\ y_A=10[/tex]

Substitute:

[tex]\dfrac{-2+x_B}{2}=-6\qquad|\cdot2\\\\-2+x_B=-12\qquad|+2\\\\x_B=-10\\\\\dfrac{10+y_B}{2}=8\qquad|\cdot2\\\\10+y_B=16\qquad|-10\\\\y_B=6[/tex]

[tex]6\frac{2}{3} = \frac{3(6) + 2}{3} = \frac{20}{3} miles[/tex]

[tex]1\frac{1}{3} = \frac{3(1) + 1}{3} = \frac{4}{3} miles/day[/tex]

[tex]\frac{20}{3} miles[/tex] ÷ [tex]\frac{4}{3} miles/day[/tex]

= [tex]\frac{20(miles)}{3}[/tex] * [tex]\frac{3(days)}{4 (miles)}[/tex]

= [tex]\frac{20(3) days}{3(4)} = \frac{20 days}{4} = 5 days[/tex]

Answer: 5 days

63 seconds is 90% of Niki's time for one lap. So, Niki's time for one lap is 63/0.9, which equals 70 seconds or 1 min. 10 seconds.

The eighth grade class at grade school has 15 girls and 14 boys. The different boy-girl dates that can be arranged is 210 boy-girl.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The eighth grade class at grade school has 15 girls and 14 boys.

The different boy-girl dates can be arranged

15 x 14 = 210

210 boy-girl

Hence, The different boy-girl dates that can be arranged is 210 boy-girl.

Learn more about the unitary method;

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To determine how many different boy-girl dates can be arranged from 15 girls and 14 boys, multiply the number of boys by the number of girls, leading to 210 different boy-girl dates.

The question asks how many different boy-girl dates can be arranged if an eighth-grade class has 15 girls and 14 boys. To solve this, we can use the concept of multiplication principle in combinations. Each boy in the class has the option to date any of the 15 girls. This means each of the 14 boys has 15 choices for who to date. Therefore, to calculate the total number of distinct boy-girl date arrangements, we multiply the number of boys by the number of girls they can potentially date.

Calculating: 14 boys × 15 girls = 210 different boy-girl dates can be arranged.

This simple calculation shows how combinations are used to determine possibilities in everyday scenarios, reinforcing the importance of basic arithmetic skills in problem-solving.

Answer:

7/4  or 3

Step-by-step explanation:

To determine the slope of the line , we look at the position of the line

From the given graph , the line goes up

When line goes up , the slope is positive

when a line goes down , the slope is negative

If we have a vertical line then slope is undefined

For horizontal line the slope is 0

Here the line goes up, so slope is positive

We pick the slope from the given option that is positive

7/4  or 3