help a sister out with a polynomial and quadratic functions question

For the linear function y = 2/3x + 1 given in this problem, we have that:

a) The slope is of 2/3 and the intercept is of 1.

b) The y-intercept is marked at y = 1 on the y-axis.

c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.

d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

In slope-intercept format, a linear function is defined as follows:

y = mx + b.

For this problem, the function is:

y = 2/3x + b.

Hence:

From the intercept, we know that point (0,1), which has x = 0 and y = 1, is part of the graph of the function.

Considering the concept of the slope, of change in y divided by change in x, we have that:

Hence point (3,3) also belongs to the graph of the given function. Given two points, we can graph a line passing through them, hence the graph is given at the end of the answer, and represents the function y = 2/3x + 1.

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An expression for the amount of money (in nickels) in n dollars is 20n nickels.

A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.

To write an expression for the amount of money (in nickels) in n dollars,

Convert the n dollars to nickels.

1 dollar = 20 nickels

So, n dollars = 20n nickels

The required expression for the amount of money (in nickels) in n dollars is 20n nickels.

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Answer: 9 - 5x

Step-by-step explanation:

6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x

Answer:

Step-by-step explanation:

You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.

An equation through points (x1, y1) and (x2, y2) can be written as ...

  (y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1

Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.

For points (-2, 1) and (1, 7), the equation of the line can be ...

  (7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)

  6x -3y = -15 . . . simplify

  2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)

For points (1, 7) and (4, -2), the equation of the line can be ...

  (-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)

  -9x -3y = -30 . . . simplify

  3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)

For points (4, -2) and (-2, 1), the equation of the line can be ...

  (1 -(-2))x -(-2 -4)y = (4)(1) -(-2)(-2)

  3x +6y = 0 . . . simplify

  x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)

In each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.

There will be an "or equal to" symbol when the line is solid.

This means our inequalities are ...

The ratio of blue paint to the total paint in the mixture is 5:8.

Given:

In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.

Total paint in the mixture = 10+6 = 16

Ratio of blue paint to total paint = 10/16 = 5/8

Therefore, the required ratio is 5:8.

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Answer:

Hi

Step-by-step explanation: how are you doing

Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

27x - 5 = 130 ( add 5 to both sides )

27x = 135 ( divide both sides by 27 )

x = 5

(d)

then

27x - 5 = 27(5) - 5 = 135 - 5 = 130

Answer:

24

Step-by-step explanation:

We can see that the value of k is -3, then the line is:

y = -3*x + 4

By finding two points of the line, we can graph the line like in the image you can see below.

Here we have the following linear equation:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.

-2 = k*2 + 4

Solving this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

So the value of k, the slope of the line, is k = -3.

Then the line is:

y = -3*x + 4

If we evaluate in x = 1, we get:

y = -3*1 + 4 = 1

So, at this point we know that the line passes through points (1, 1) and (2, -2).

Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.

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Answer:

Step-by-step explanation:

4 x - 5 y + z = 9z = - 27 + 6 x + 8 y3 x

We solve as follows:

The solution is 36.

Answer: 1yd 2ft

Explanation

s we have a subtraction, we have to have the same units. Thus, in order to do so we have to consider that 1 yd = 3ft:

Then, converting 2yf to ft:

Now, we can make the subtraction:

Finally, we can convert 3 ft to one yd:

and we have 2 ft left.

Answer:

500

Step-by-step explanition

12-children

20-adults

400 sold for 6000

c-children were

500

Angles and lines

We are given the following information

Angle 1 is congruent with angle 2. They have equal measures

Angle CFB measures 124°

Note that angles 4 and F are linear because they are formed by the intersection of two lines.

Linear angles add up to 180°

This means that the measure of angle 4 is:

m angle 4 = 180° - m CFB

m angle 4 = 180° - 124°

m angle 4 = 56°

now note angle 4, 1, and 2 form a straight angle of 180°. This means that

m angle 4 + m angle 1 + m angle 2 = 180°

Since angles 1 and 2 are congruent:

m angle 4 + 2* m angle 1 = 180°

Knowing that m angle 4 = 56°:

56° + 2* m angle 1 = 180°

Subtracting 56°:

2* m angle 1 = 124°

Solving:

m angle 1 = 124° / 2 = 62°

Thus, both angles 1 and 2 measure 62°

Finally, being angles 3 and 4 vertical angles (opposed by a vertex), they are congruent, thus

m angle 3 = m angle 4 = 56°

The solution is given below:

Answer:

-1/5 is the slope

Step-by-step explanation:

the equation

y2-y1 over x2-x1

what is volume answer the volume is your topic for to day

The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.

Given that,

The linear equation is 3x+4y=7

Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.

There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.

The x and y are positive integers so it is a unique solution.

Therefore, The solution to the equation 3x+4y=7 is unique.

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Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

Step-by-step explanation:

Each value of x corresponds to only one value of y, making the relation a function.

Answer:

See below

Step-by-step explanation:

Time charge =   2.75 hr * £7.00/hr =  £  1`9.25

Mileage charge =  ( 25423 - 25263) mi * 40p / mile = 6400 p

  (edited: forgot to multiply by 40p)

Now add the two charges together :   19 + (.25 * 240) + 6400/240 =

£ 45.92

  ( I think <===if I correctly did the monetary conversion between pence and pounds!     <=== I used 240 p = 1£ )

Step-by-step explanation:

what we were not told is, if he charges a full hour for a fraction of an hour, or only a corresponding fraction of his hourly rate.

I assume the first : charging a full hour for any fraction of an hour spent.

it took him 2h and 45 minutes, so that is 3 hours charged.

and he was driving

25423 - 25263 miles = 160 miles

so, he charges

3×7 + 160×0.40 = 21 + 64 = £85

if he charges also fractions of his hourly rate, then his hourly charge would be

2 3/4 × 7 = (2×4 + 3)/4 × 7 = 11×7/4 = 77/4 = £19.25

in total that would be

19.25 + 64 = £83.25

20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.

A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.

First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).

We know that there are 30 total pints of the mixture. Thus:

x+y=30

We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.

For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:

.65x+.90y=30 ×0.7

Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:

65x+90y=2100

Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:

65x+65y=1950

Subtract the second equation from the first equation:

25y=250

y=10

Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).

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Given:

1 = 1²

1 + 3 = 2²

1 + 3 + 5 = 3²

1 + 3 + 5 + 7 = 4²

1 + 3 + 5 + 7 + 9 = 5²

1 + 3 + 5 + 7 + 9 + 11 = ___

Let's find the answer and determine the pattern.

Here, we have:

1 + 3 = 4

Now, write the sum as a perfect square:

4 = 2²

For the third equation:

1 + 3 + 5 = 9

Now, write the sum as a perfect square:

9 = 3²

This means the result will be the sum written as a perfect square.

Thus, we have:

1 + 3 + 5 + 7 + 9 + 11 = 36

Now, let's write the sum (36) as a perfect square:

36 = 6²

Therefore, we have:

1 + 3 + 5 + 7 + 9 + 11 = 6²

• ANSWER:

6²

Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).

A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.

You must be able to distinguish between the given expressions in order to do that.

So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.

Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.

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We need to expand the term:

This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'

I'll paste an image of it above

We will use it in this way:

Each one of the rows, represent the n in the term:

So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.

In our case, we need the 6th row.

Now, usually a term of the form

As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!

And we need the term that corresponds to x^2, we need the number e=5!

So, after the expansion, the coefficient of the term x^2 will be equal to 5

We have a quadrilateral inscribed in a circle.

The quadrilateral is a trapezoid.

When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.

Then, we can write:

Answer: x = 21.1

The area of triangle ABC is 17.5 or 35/2

To solve this, we need to know the base and height of the triangle.

In this case, the base is the side AB, and the height is the side BC

Now we can count the units to get the lenght of the sides:

AB is 7 units long

BC is 5 units long.

Now we can use the formula for the area of a triangle:

Where A is the area, b is the base and h is the height.

Putting the values of b and h:

Then the area is 35/2 or 17.5 square units

Answer:

55%

Step-by-step explanation:

Answer:

55%

132 is 55% of 240

Step-by-step explanation:

Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.

Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.

Proportions, like ratios, use fractional values because they show the quantity of one variable in another.

We state proportions in fractions, decimals, or percentages.

The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli

3/4 pound = 0.75 pound

9/8 cups = 1.125 cups

The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)

1.5 cups = 1½ cups

Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.

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Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

The equation of the exponential function that goes through the points (0,3) and (3,375) is y = 5(3)^x

The standard form of an exponential equation is given as y = ab^x

Using the coordinate points on the graph (0,3) and (3,375).

The equivalent equations are;

375 = ab^3

3 = ab^0

From equation2;

a= 3

Substitute into equation 1;

375 = 3b^3

b^3 = 375/3

b^3 = 125
b = 5

Determine the equation

y = 3ab^x

y = 3(5)^x

This gives the required exponential equation

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Answer:

1/216

Step-by-step explanation:

[tex] \frac{1}{6} \div 6 \div 6[/tex]

[tex] \frac{1}{6} \div \frac{6}{1} \div \frac{6}{1} [/tex]

[tex] \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} [/tex]

[tex] \frac{1}{216} [/tex]