Solve the system of inequalities by graphing.
y ≥ 2
y < 4
Select a line to change it between solid and dotted. Select a region to shade it.

Answer:

(a)Adult:10.99+0.99x, Kid: 5.99+0.99x

(b)Adult's Total cost = $15.94, Kid's Total cost =$10.94

Explanation:

Cost of a ride = $0.99

Let x be the number of rides.

Cost of an Adult Ticket = $10.99

An equation for adult tickets will therefore be: 10.99+0.99x

Similarly, the cost of a kid ticket =$5.99

An equation for adult tickets will therefore be: 5.99+0.99x

(b)If they ride 5 tickets each, the amount of money spent will be:

x=5 rides

Total cost for an adult=10.99+0.99(5)

=10.99+4.95

=$15.94

Total cost for a kid = 5.99+0.99(5)

=5.99+4.95

=$10.94

Using the area of a triangle, the area of Mr. Knox's garden is: 58 square feet.

The area of any triangular shape can be calculated using the formula for the area of a triangle.

The area of a triangle = 1/2(base)(height).

The shape of Mr. Knox's garden is triangular. The parameters of his triangular garden are:

Length of the base of the triangular garden = 24½ ft

Height of the triangular garden = 8 ft.

Area of the garden = 1/2(24½)(8)

Area of the garden = 1/2(29/2)(8)

Area of the garden = 1/2(232/2)

Area of the garden = 232/4

Area of the garden = 58 square feet.

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For the given values the equation of new line is  y = -3x - 17

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.

Given,

The equation of line is y= -3x+4

as the lines are parallel,

slope of lines will be same,

∴ Slope of new line = -3

The equation of line is:

y - y1 = m(x - x1)

Where x1, y1 are the given coordinates and m is the slope

⇒ y -(-5) = -3 (x - (-4))

⇒ y + 5 = -3 (x + 4)

⇒ y + 5 = -3x - 12

⇒ y = -3x - 17

∴  The equation of the line is y = -3x - 17

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ANSWER:

1616 ft³

STEP-BY-STEP EXPLANATION:

We have that the formula to determine the volume of the cylinder is as follows:

The radius is equivalent to half the diameter, therefore the radius is equal to 3.5 ft (7/2) while the height, in this case, is equivalent to the length, so it is equal to 42 ft. Therefore, we replace each value and calculate the volume, like this:

The volume of the cylindrical pipe is 1616 ft³.

Answer: The answer is 570.

Step-by-step explanation:

So, if you know what numbers are, when you round, this question is easy. If you take a number line and put 570 on the left side and 580 on the right side, and 575 in the middle, you almost got it. Since the number we want to round is 573, we put it in the middle of 570 and 575. And since the number is closer to 570 than 580, the answer is 570. Your welcome!

The minimum value of the parabola is y = -6

An equation of a parabola is given as

y = x²-6

We will find its minimum value using the differentiation method.

For this first we will find the derivative with respect to x and find the value of x at which the derivative becomes zero. The derivative becomes zero only when the parabola has either a maximum or minimum value. We further check whether the parabola has a minimum or maximum at that x by finding the second derivative of the parabola at that x.

So first derivative of y with respect to x is 2x.

So 2x = 0

⇒ x =0

Now take the second derivative of y with respect to x at x = 0,

Second derivative = 2 > 0 at x = 0

Here the second derivative is greater than zero at x = 0. So y has a minimum value at x = 0

The minimum value of the parabola is,

y = 0² - 6

⇒ y = -6

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Letter A doesn't show rotational symmetry of 180 degrees.

The letter 'A' has just one vertical line of symmetry.A vertical line of symmetry is that line which runs down a picture thus dividing it into two identical halves. In other words, it's a straight standing line that divides an image or shape into two identical halves.

The rotational symmetry of a shape explains that when an object is rotated on its own axis, the form of the object looks the same. Many geometrical shapes appear to be symmetrical once they are rotated 180 degrees or with some angles, clockwise or anticlockwise. A number of the examples are square, circle, hexagon, etc.

Complete Question-  A rotation of 180 degrees maps figure A onto itself. It has transformation or not?

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Step-by-step explanation:

You are in charge of planning your mother's surprise party. You have found a hall that rents for $225 and a caterer that will charge you $15 per guest. Write an inequality to calculate your total cost (T) based on the number of guests (g).

T = 15g + 225

If you have a total budget of $1000 how many guests can you

invite?

1,000 = 15g + 225

subtract 225 from both sides:

1,000 -225 = 15g + 225 - 225

775 = 15g

divide both sides by 15:

775/15 = 15g/15

g = 51.66

Because you cannot invite part of a guest round down to inviting 51 guests

3) Alex had 20 video games at the beginning.

2) The strategy to solve the problem backward is:

The number of games Alex has now is 16 games.

The number of games he gave to his brother is 2, so add 2 to the current number of video games, 16 + 2 = 18

Now add the games he sold, which are given as 3

18 + 3 = 21

Subtract the games he traded with Hector,i.e. 6 video games

21 - 6 = 15

This obtained number is 3/4 of his games,

3/4 of the total video games = 15

Therefore, the total video games were = (15×4)/3 = 20

4) Yes the answer makes sense.

Operations in reverse order are:

The number of video games given by Alex to hector is = 1/4 of 20 = 5

Remaining video games = 20 - 5 = 15

Number of games after adding exchanged 6 video games = 15+6 = 21

Number of games after Alex sold 3 video games = 21 -3 = 18

Number of games after Alex gave 2 to his brother = 18 - 2 = 16 video games

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Using distribute property on 41×8 is 328.

What is the Distributive Property?

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.

We know that,

Distributive property is  A × (B + C) = AB + AC.

So, 41 × 8 is  41 × (5 + 3 ) = 41×5 + 41×3

                    41 × (5 + 3 ) = 205 + 123

                    41 × (5 + 3 ) = 328

Hence, using distribute property on 41×8 is 328.

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The diagram of the problem is:

S is the length of the shorter side of the fence. L is the length of the longest side of the field.

We know that the perimeter of the rectangle is 800ft. This means:

And the area:

The smaller rectangles will have dimensions:

The area is:

As we can see, if we maximize the area of the bigger rectangle "A", we are also maximizing the area of the smaller rectangles "a".

Then, we have two equations:

We can solve for L in the first equation:

Then substitute in the second:

Simplify:

This is a function of the area depending on the length of the shorter side of the rectangle:

We can find the maximum of this function if we find the value where the derivative of this function is 0.

Let's differentiate:

And now we find where A'(S) = 0:

We have found that the shorter side must have a length of 200ft to maximize the area. Let's find the length of the larger side:

As expected, the quadrilateral which maximizes the area is the square. Thus, the dimensions of the field are 200ft x 200ft

Solution

Population of the town = 3000

Rate = 4%

Amount = 4700

Find log of both side

Therefore the number of years it will take population to reach 4700 = 11.5yrs

There is a 0.765 percent chance that the flight will leave on time when it is not raining.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.

Given a 0.1 delay probability, the probability of the airplane departing on time is 1-0.1 = 0.9.

The likelihood that it won't rain is 1-0.15 = 0.85.

If it weren't raining, there is a 0.9 (0.85) = 0.765 percent chance that a flight would leave on time.

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The answer is D

To solve this, we can use similar values of the ones in the problems and compare it:

With a just add one to each side:

The slope (rate of change) of the graph shown is 31.3 miles per gallon.

An equation is an expression that shows the relationship between two variables and expressions.

Slope is the ratio of vertical rise to horizontal run. It is given by:

Slope = rise / run

The point passes through (10, 313) and (20, 626), hence:

Slope = rise/run

Slope = (626 - 313) / (20 - 10) = 31.3

The graph's slope is 31.3 miles per gallon.

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The coordinates of B after the translation is ( 3 , -2)

What is coordinates in maths?

Transformation involves changing the position of a shape.

The coordinates of B after the translation is (-4,-2)

A = ( 1, 1)

B = ( 3 , 4)

C = ( -1 , 8 )

The translation rule is given as ( x , y-6)

So, the coordinates of B' is calculated using

( x , y ) ⇒   ( x , y-6)

This gives

B = ( 3 , 4) ⇒  ( 3 , 4 - 6 )

( 3 , 4) ⇒ ( 3, -2 )

Rewrite as

B' = ( 3, -2 )

Hence, the coordinates of B after the translation is ( 3 , -2)

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SOLUTION:

The average is given by the formula;

Thus, the average number of realtors who have a degree attending the course is 848

Based on the angle relationships formed by the parallel lines, the statements that are true are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

Some of the angle relationship that applies when two parallel lines are crossed by a transversal are:

Given the image attached below, where m and n are parallel lines, we can deduce the following measures of the numbered angles based on the angle relationships:

Measure of angle 1 = 60° [vertical angles]

Measure of angle 2 = 20° [corresponding angles]

Using the triangle sum theorem, we also have:

Measure of angle 3 = 180 - m∠CAB - m∠1

Measure of angle 3 = 180 - 20 - 60 = 100°

m∠4 = 60° [corresponding angles]

m∠2 + m∠4 = 20 + 60 = 80°

From the above, we can conclude that the statements are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

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Parallel lines are those straight lines that are always the same distance apart from each other.

B m∠3 = 100°

C. m∠2 + m∠4 = 80° are true

Parallel lines are those straight lines that are always the same distance apart from each other. · Parallel lines never meet no matter how much they are extended.

Given that, n||m

Point B is lies on line m.

Point A and C are lies on line n.

There are two lines started from point B and one line passes through point A and one line passes through point B forms a triangle ABC.

∠ACB=1

∠ABC=2

There is an angle with line m and line AB is denoted by 2.

Using the triangle sum theorem, we also have:

Measure of angle 3 = 180 - m∠CAB - m∠1

Measure of angle 3 = 180 - 20 - 60 = 100°

m∠4 = 60° [corresponding angles]

m∠2 + m∠4 = 20 + 60 = 80°

Hence From the above, we can conclude that the statements are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

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In the given figure, Triangle ABC is similar to triangle DEF.

Applying the Similar Triangle Formula, the proportion to be used to find the length of DE is:

Therefore, the answer is A.

The closest number to 6.3 is the number 40, because when we substract 6.3 from 40, we get the smallest number.

40 - 6.3 = 33.7

748 - 6.3 = 741.7

a. G(x) = 1/4x - 5 Since it's similar to the equation f(x)=mx + b, which is a linear

function, g(x) is a linear function.

b. f(x) = 2*(x - 1)^2 - 5 Since the degree of the polynomial is 2, we deduce it is a cuadratic function.

c. f(x) = 7 Since the degree of x is zero ( there is no x) , we deduce it is a constant function.

A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)​. The y-coordinates are different with the negative sign in the given transformations.

Given that,

A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)​

We have to find the difference of the transformations.

So,

First take A(-6, -2)→ A'(-6, 2)

We can see the difference is the A of y-coordinates have negative sign of the A'.

Now,

Take B(-3, -6) →B'(-3, 6)

We can see the difference is the B of y-coordinates have negative sign of the B'.

Now,

Take C(-2,-2)→ C'(-2, 2)​

We can see the difference is the C of y-coordinates have negative sign of the C'.

Therefore, The y-coordinates are different with the negative sign in the given transformations.

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Answer:

Yes, y=0.08x​

Explanation:

The unit price can be calculated as the price divided by the number of ozs, so the unit prices are:

Therefore, the unit prices are equal, so the equation that represents the relationship is:

y = kx

Where k is the unit price, so replacing k by 0.08, we get:

y = 0.08x

So, the answer is:

Yes, y=0.08x​

Given: The square STUV

To Determine: The coordinate of the image after reflection over the y-axis

Solution

The reflection over the y-axis rule is

Locate the coordinates of STUV

Let us apply the rule to get the coordinate of the image

Hence, the coordinate of the image after a reflection over the y-axis is

S'(10, - 10)

T'(0, - 10)

U'(0, 0)

V'(10, 0)

f(1)=1/2 f(2)=(1/2)^2=(1/2)*(1/2)=1/4

1/2>1/4 => f(1)>f(2) => it is decreasing, because with the grow of x the value(y) is decreasing what we have shown

a)The solution of the inequality is 3 < x ≤ 5

c) The solution in interval notation is (3, 5]

Step - by - Step Explanation:

What to find?

• The solution of the inequality.

• The graph of the inequality.

• The solution in interval notation.

Given:

7 < x +4 ≤ 9

Re-write the above inequality.

x + 4 > 7 or x + 4 ≤ 9

Solve for x in each case.

x + 4 > 7

Subtract 4 from both-side of the inequality.

x > 7 - 4

x > 3

x + 4 ≤ 9

Subtract 4 from both-side of the inequality.

x ≤ 9 - 4

x≤ 5

Combine the two solutions.

3Hence, the solution to the inequality is 3 < x ≤ 5

b) We can proceed to graph the inequality.

c) The solution in interval notation is (3, 5]

For this problem, we are given two sides and one angle of a triangle. We need to determine the length of the side that is opposite to the known angle.

To solve this problem, we need to use the law of cosines.

Applying the given data, we have:

The correct answer is 27.4.

The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -  a[n] = 10 - 3n

An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -

a₁ , a₂, a₃ , a₄ ...... aₙ

will be an arithmetic progression if -

a₂ - a₁ = a₃ - a₂ = a₄ -  a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.

Given is the the first term equal to 7 and the common difference equal to

- 3.

We can calculate the nth term of an A.P. using the formula -

a[n] = a + (n - 1)d

a[n] = 7 + (n - 1)(- 3)

a[n] = 7 - 3n + 3

a[n] = 10 - 3n

Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -

a[n] = 10 - 3n

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