1. Consider this system of linear equations: -
y=4/5 x-3
y=4/5 x+1
a. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning.


b. Try solving the system of equations algebraically and describe the result that you get. Does it match your prediction

Answer:

58 teams

Step-by-step explanation:

This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.

Answer: 57.9

Step-by-step explanation:

Based on the given conditions, formulate: 1043 / 18

Evaluate the equation/expression: 57.9444

get the result: 57.9444

After rounding: 57.9

Answer: 57.9

The probability that a student chosen at random studies physics and chemistry or both is  35/41 = 0.85

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.

The Venn diagram shows:

There are 2 students studying both biology and physics.

Six students study biology and chemistry together.

There are 4 students who study physics and chemistry.

There are 5 students who just study physics.

There are 7 students who just study biology.

There are 8 students who just study chemistry.

There are 6 students that study none.

As a result, there are a total of 41 students, which is equal to 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 students.

There are 21 students who study chemistry, which is equal to 8 + 6 + 3 + 4 students.

The number of students that studies physics is = 14

The number of students that studies chemistry is =  21

Probability  = number of favorable outcomes / total number of outcomes

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The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.

To determine the material used to make the ball, we need to first calculate the volume of the ball.

The volume of a sphere with radius r is given by:

V = (4/3) * π * r^3

Plugging in the given values, we get:

V = (4/3) * π * (2 cm)^3

= (4/3) * π * 8 cm^3

= (4/3) * 8π cm^3

= 32π cm^3

We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:

Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g

Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g

Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g

Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.

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Answer: 30 meters

Step-by-step explanation:

A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.

Answer:

11, 13, 17, and 19!

Step-by-step explanation:

Answer:

11, 13,17 and 19

Step-by-step explanation:

prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c

The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.

In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:

Logarithm of a product

㏒ (a · b) = ㏒ a + ㏒ b

Logarithm of a division

㏒ (a / b) = ㏒ a - ㏒ b

Logarithm of a power

㏒ aⁿ = n · ㏒ a

Now we proceed to determine the exact value of the expression:

12 · ㏒₃ [z⁷ / (y⁵ · t²)]

12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]

12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)

12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)

12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)

-711 / 5

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Answer:  d/ 30x +200 <= 1400

Step-by-step explanation:

It can't be the first two answers because the truck can only hold 1400

So it must be < or = 1400

It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.

So the equation is 30x + 200 <=1400

Answer:

The width of the parking is 69 meters

Step-by-step explanation:

Rectangle area = L*W

6279 = 91*W

Widht = 6279/91

W = 69 m

a%2Bb=12 [1]

.75a%2B1.05b=10.20 [2]

Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):

.75a%2B.75b=9

.75a%2B1.05b=10.2

.3b=1.2

3b=12

b=4

ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.

CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20

The required competition mark is given as 60, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60

Thus, the competition mark is  60.

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The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

What is a linear equation in one variable?

The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For the first case:

If 2 movies are streamed, the cost is $14 per month

So the cost = number of movies * cost per movie

            y = 2*x

           14 = 2x

For the second case:

If 6 movies are streamed, the cost is $20 per month

So the cost = number of movies * cost per movie

            y = 6*x

           20 = 6x

Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

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Answer:

1 minute, Because per minute is $2, 12 cents

Using the formula of simple interest, the time period it takes to double the principal is approximately 14.29 years

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The formula is given as

S.I = P(1 + rt)

Substituting the values into the simple interest formula

S.I = 1000(1 + 0.07 * t)

However, we are to calculate the time it takes to double the money

2000 = 1000(1 + 0.07 * t)

2 = 1 + 0.07t

0.07t = 2 - 1

t = 1 / 0.07

t = 14.29 years

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The graph for the linear equation y = -2x + 5 is plotted and shown in the image attached below.

If we are given an equation of a line that is expressed in slope-intercept form as y = mx + b, it means that the graph will have a slope = rise / run = the value of m, while it would cut across the y-axis at b, that is the y-intercept.

Given the equation in slope-intercept form as y = -2x + 5, it means that the graph will have a slope that has a ratio of the rise to the run as -2, while the line will intercept the y-axis at y = 5.

Therefore, the graph in the image attached below shows the equation, y = -2x + 5.

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The scale factor of the transformation is 1.5

From the question, we have the following parameters that can be used in our computation:

Point T (6,2) T’ (9,3)

Also, see attachment for the missing graph in the question

This means that

The scale factor of the transformation = T'/T

Substitute the known values in the above equation, so, we have the following representation

Scale factor = (9, 3)/(6, 2)

Evaluate

Scale factor = 1.5

Hence, the scale factor is 1.5

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Answer: 60

Step-by-step explanation:

The square root of 144 is 12.

12 = x/5

You multiply 5 on BOTH sides (make sure when you do something to one side you do it to the other)

60 = x

The intersection region of every solution in the system of inequalities is the system's solution. Inequality y≤x2 should be graphed first. y=x2 serves as the related equation.

Example

Graph the inequalities and solve the system:

y≤x−2y>−3x+5

Inequality yx2 should be graphed first. y=x2 serves as the related equation.

The border line is solid due to the inequality's, which is not a rigid one.

The inequality yx2 should be substituted in for a point that is not on the line, such as (0,0).

0≤0−20≤−2

It's untrue. The point (0,0) is therefore not part of the solution. Subtract from the line's lower half.

To do the same for the second inequality's related equation, y>3x+5, which has a rigorous inequality, draw a dashed line. The half that does not contain the point (0,0) should be shaded because it does not satisfy the inequality at that location.

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Answer: y = 1/12x

Step-by-step explanation:

(24, 2)

(12, 1)

find slope (y2 - y1) / (x2 - x1)

2 - 1 / 24 - 12

1 / 12

find y intercept

y = mx + b

1 = 1/12(12) + b

1 = 1 + b

b = 0

y = 1/12x + 0

y = 1/12x

There is a 7°F difference in temperature between the morning and the afternoon.

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Answer:

68 feet tall

Step-by-step explanation:

Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since  "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".

Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).

Solve for x.

[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]

The proportion is solved and the height of the tree is A = 68 feet

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Now , we can set up the following proportion:

Height of tree / length of tree's shadow = height of person / length of person's shadow

On simplifying , we get

A / 51 = 6 / 4.5

Now we can solve for A by cross-multiplying and simplifying:

A = 51 x 6 / 4.5

A = 68 feet

Therefore, the tree is 68 feet tall

Hence , the proportion is solved

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The range of the function will be;

⇒ Range = (91, 16, - 5)

The set of all inputs of the function is called Domain of set.

Given that;

The function is,

⇒ f (x) = x² - 6x

And, The domain = (- 7, - 2, 1)

Now,

Since, The function is,

⇒ f (x) = x² - 6x

We know that;

The range of the function gives the value of y.

Here, The domain (x) = (- 7, - 2, 1)

Put x = - 7;

⇒ f (-7 ) = (-7)² - 6 × - 7

            = 49 + 42

            = 91

Put x = - 2;

⇒ f (- 2) = (-2)² - 6 × - 2

            = 4 + 12

            = 16

Put x = 1;

⇒ f (1) = (1)² - 6 × 1

         = 1 - 6

         = - 5

Thus, The range = (91, 16, - 5)

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The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.

In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .

Mathematically, sound intensity level or decibel level can be calculated by using this formula:

[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]

Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).

Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:

Decibel level, β = 10 × log(10⁻²/10⁻¹²)

Decibel level, β = 10 × log(10¹⁰)

Decibel level, β = 10 × 10

Decibel level, β = 100 dB.

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Answer:SLOPE

Step-by-step explanation:M in a equation is slope

Triangles MNO and QPO are congruent.

It is given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

Therefore, Triangles MNO and QPO are congruent.

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Using the elimination method, the solution to the system of equations is as follows:

x = 19 / 13  and y = - 74 / 13

System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.

Let's use the elimination method to solve the system of equations as follows:

The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Therefore,

4x - 7y = 10

3x + 2y = -7

multiply equation(ii) by 3.5

4x - 7y = 10

10.5x - 7y = 24.5

subtract equation(i) from equation(ii)

6.5x = 14.5

x = 14.5 / 6.5

x =  145 / 65

x = 19 / 13

Let's find y

3(19 / 13) + 2y = -7

57 / 13 + 2y = -7

2y = - 7 - 57 / 13

2y = -91 - 57  / 13

2y = - 148 / 13

cross multiply

26y = - 148

y = - 148 / 26

y = -  74 / 13

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Answer: 10: 6 is

ration add them 16

Step-by-step explanation: