Each Sophomore and Junior at a high school collected aluminum cans and plastic bottles. The table shows the average number of cans and bottles collected per student by grade level during a 2-week recycling drive.

a. Write a system of equations to represent the situation. Let x represent the number of sophomores, and let y represent the number of juniors. The equation for week 1 is (Type an equation.)​

Answer:

its option C: x = 3

Step-by-step explanation:

The distance between the cars, x = 3 miles

The equation representing two cars traveling in opposite directions is given by, 8x-12 = 4x,

where 'x' is the distance (in miles) between the cars.

We need to find 'x'.

The equation given is a linear equation in x. So we will solve for 'x'.

8x-12 = 4x

⇒ 8x-4x = 12

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

So the distance between the cars = 3 miles

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The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

According to the given question.

We have an expression 3[2(x - 3) + 2] + 5(x - 3).

To simplify the above expression we will use the distributive law and add and subtract the like terms.

Therefore,

3[2(x - 3) + 2] + 5(x - 3)        

= 3[2x - 6 + 5x - 15]      (distributive rule)

= 3[7x - 21]             (adding the like terms)

= 21x - 63

Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

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[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]

Answer:

2

Since the numbers after the decimal are above 500 , thereby rounding it to nearest whole number is 2.

Answer:

40 psi

Step-by-step explanation:

We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth

The data is given from depth of 40 feet

At 40 feet, pressure = 10 psi  

At 55 feet, pressure = 15 psi

At 70 feet pressure = 20 psi

We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure  per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]

But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi

So the equation that connects depth (d) and pressure (p) is:

[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]

If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3

Hope that helps

An angle is a figure formed by two rays with a common initial point called a of the angle.

What does a math angle mean?

What is type of angle ?

What is acute angle?

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Answer:

dbc

Step-by-step explanation:

thats the only one that is obtuse

Answer: x=2/3

Step-by-step explanation:

Answer:

Yes OFC

Step-by-step explanation:

As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height

Using substitution method, the solution of the given system of equations is (-3,0)

A system of equation can be solved using:

The given system of equations:

4y - 6 = 2x   ............   (1)

y - 3x = 9  .............. (2)

We need to find the solution using substitution method.

In equation (2), add 3x to both sides:

y - 3x + 3x = 9 + 3x

y =  9 + 3x   ........ (3)

Substitute y =  9 + 3x into equation (1):

4y - 6 = 2x

4.(9 + 3x) - 6 = 2x

36 + 12x - 6 = 2x

12x - 2x = 6 - 36

10x = -30

   x = -3

Substitute back x = -3 into equation (3)

y =  9 + 3x

  = 9 + 3.(-3)

  = 9 + (-9) = 0

Hence, the solution is (-3, 0)

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Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.

Solution:

To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X

So,

X+1 = 0

X = -1

X-4 = 0

X = 4

When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables

= (x2+4x+3)/(x2-3x-4)

= (x+1) (x+3)/(x+1) (x-4)

Now cancel the common factor (x+1)

= x+3x-4

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Answer:

473085 is the answer

Step-by-step explanation:

Hope it helps you

The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

The given arithmetic series is 10+7+4+ . . .

The summation notion of given series is ∑10-3n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=5, [tex]a_{1}[/tex] = 10

To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .

[tex]a_{5} = a_{1} + (n-1)d[/tex]

d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{5}[/tex] = 10 + (5-1)(-3)

[tex]a_{5}[/tex] = 10-12 =-2

On substituting values in sum of arithmetic series formula, we get

[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20

The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

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Answer:

49π in²

Step-by-step explanation:

Formula for Area of a Circle: A = πr²

The image shows the radius (r) = 7in

A = πr² → A = π(7)²→ A = π(49)

A = 153.94 in²

Step-by-step explanation:

Area of circle with radius of r is given by:

[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]

Answer:

10.63

Step-by-step explanation:

In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term multiplied by the denominator is also non-zero.

To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.

If x = -2 then (x^2) + 4 is 0.

So, the discontinuities are shown as x = -2

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The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.

Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

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So we are provided with the equation,

x2 + 10x + 40 = 5

To simplify it, we will first reorder the terms,

40 + 10x + x2 = 5

Now we will solve the equation to find the value of the unknown variable that we declared here as x.

40 + 10x + x2 = 5

Solving for variable 'x.'

40 + -5 + 10x + x2 = 5 + -5

We will combine similar terms; the variables and the constants.

40 + -5 = 35

35 + 10x + x2 = 5 + -5

Combine the like terms again:

5 + -5 = 0

35 + 10x + x2 = 0

Adding -35 on both sides

35 + 10x + -35 + x2 = 0 + -35

35 + -35 + 10x + x2 = 0 + -35

35 + -35 = 0

0 + 10x + x2 = 0 + -35

10x + x2 = 0 + -35

0 + -35 = -35

10x + x2 = -35

The x term is 10x.

Take half its coefficient (5) to make it a perfect square.

Square it (25) and add it to both sides.

10x + 25 + x2 = -35 + 25

25 + 10x + x2 = -35 + 25

-35 + 25 = -10

25 + 10x + x2 = -10

Perfect square on the left side:

(x + 5) (x + 5) = -10

We can see that the Square root of the right side can’t be calculated.

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to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]

Answer:

z = 9

Step-by-step explanation:

Divide both sides by 3 to get z by itself

Answers:

14 rides: 52

and

r rides: 3r + 10

Step-by-step explanation:

3(14) + 10

52

The coordinate of another point will be (a/2,y) where y can be any value.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

An isosceles triangle is a triangle whose two sides are equal.

Let's say AB = AC

So,

Distance associate to AB = Distance associate to AC

(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²

x² + y² = (x - a)² + y²

x = a/2

So the coordinate of the third vertex is (a/2,y)

Hence "The coordinate of another point will be (a/2,y) where y can be any value".

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If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot

Given,

The algebraic expression of the distance in feet that an object falls = [tex]16t^{2}[/tex]

Where t is the time in seconds

Here,

time t = 10 seconds

Substitute the value in the expression

[tex]16t^{2}=16(10)^{2}[/tex]

=1600 foot

Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot

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If Mohammad leaves home walks 5 blocks to the library and he then walks 2 blocks toward home to meet up with his friend and then together, he and his friend walk to the library together, then Mohammad walked for 9 blocks.

To calculate how far Mohammad walked we use addition.

Total blocks Mohammad walked = blocks to the library + blocks towards home to meet up with friend + blocks back to the library together

blocks to the library = 5

blocks towards the home to meet up with friend = 2

blocks back to the library together = 2 (As he walked 2 blocks towards home from the library, he will walk the same number of blocks again to reach the library)

Therefore,

total blocks Mohammad walked = 5 + 2 + 2

total blocks Mohammad walked = 9

Hence, the number of blocks Mohammad walked for is calculated to be 9.

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Answer:

The answer is A because both equations are true

[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]

The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2

Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).

The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.

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probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)

=0.14+0.02 = 0.16

Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.

Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.

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Answer:

14ft 8in by 12ft 10in

By finding the positive root of the quadratic equation, we conclude that the rock will hit the ground 7 seconds after it is thrown.

We know that a rock is thrown from a cliff whose height is 224 ft. And the equation that models the height of the rock as is the quadratic equation:

h(t) = -16t² + 80t + 224

The rock will reach the ground when its height is equal to zero, so what we need to find is the positive root of the quadratic equation, so what we need to solve is:

-16t² + 80t + 224 = 0

Solving it we get:

t = (-80 ± √(80² - 4*(-16)*224)/(2*-16)

t = (-80 ± 144)/(-32)

The positive solution is:

t = (-80 - 144)/(-32) = 7

This means that the rock will hit the ground 7 seconds after it is thrown.

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