Do these coordinate pairs represent a function?: *{(2, 4), (2,5), (3,6), (3, 7) }

A trinomial square has two possible forms:

So, for us to check if

Is a trinomial square, we first check if the first and thrid terms are positive, because both options has positive first and thrid terms, even if a or b are negative, because they are squared in the process.

Both are positive, x² and 64.

Now, by comparison, we see that, in thi case we would have:

If it is a trinomial square, than the middle term has to be:

We use the negative form because we have a negative middle term.

So, let's see if it checks out:

We got -16x, but the middle term is -8x, they don't match.

Since they don't match, the given expression is not a trinomial square. The answer is No.

We can find the point with help of the end points and the ratio so:

now for y:

So now we can graph it so:

We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.

Now we need to solve for N, to do that we add like terms:

Now we multiply both sides by 100:

Now we divide by 107.5:

Solving the operations:

Therefore, the maximum amount to spend is $74

The equation given is,

Since the boundary line is thick bold line and from the graph we can observe that the line (shaded portion) moves from the right to the left hand side.

Then the inequality of the shaded region is,

Find the 0.125% of 7.92x10^10: Multiply the amount by 0.125 and then divide into 100 or multiply the amount by 0.125/100

Hello there. To solve this question, we have to remember some properties about triangles.

Given a triangle ABC as follows:

We can show for each point what it is on this triangle.

1. Midsegment. This is the segment that is parallel to the base, in this case BC and has half its length. Another property: it divides the sides AB and AC into proportional parts. See the drawing.

2. Circumcenter. Take the triangle and inscribe it in a circumference (all its vertices are in the circumference. Now take the perpendicular bisector of each sides. The point in which at least two of them intersects is the circumcenter. See the drawing.

3. Incenter. Take the bisectors of the angles of ABC. The point in which they intersect is the incenter. Another property: It is the center of the inscribed circumference that is tangent to all sides of the triangle.

From a total of 400 students ,

120 votes for Lindsey

280 votes for Sharif

then 200 students = 50%

. 100 students= 25%

. 20 students = (50%)/10 = 5%

then 120 students (100+20) belows to 25%+5%= 30%

30% students voted for Lindsey

EXPLANATION:

Given;

We are told that a forest covers an area of 2300 square kilometers.

Next we are told that this forest area decreases by 7.75% each year.

Required:

We are required to calculate the area remaining after 8 years.

Step-by-step solution:

To solve this math problem, take note that what we have is an exponential decay problem. The initial size decreases (decays) at a constant rate every year.

The formula for an exponential growth/decay is given as shown below;

Where the variables are as follows;

With the values given, we can substitute and we'll have the following;

Rounded to the nearest square kilometer, we would now have;

ANSWER:

Given:

EF = 2

m∠FEG = 144 degrees.

Let's fid the length of arc FG.

To find the length of arc FG, apply the formula:

Where:

r is the radius = 2

θ is the central angle = 144 degrees.

Thus, we have:

Therefore, the length of arc FG as a fraction times pi is:

ANSWER:

The value of 'w' for the two parallel lines are cut by the transversal is 52.

For the given question

Two parallel lines are cut by the transversal.

Then,

w + (3w -28) = 180 (same side exterior angle of the traversal are supplementary)

Solve the equation;

4w - 28 = 180

4w = 208

w = 208/4

w = 52

Thus, the value of 'w' for the two parallel lines are cut by the transversal is 52.

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ANSWER

Subtraction property of equality

EXPLANATION

In this problem they subtracted 14 from both sides of the equation. On the left side we can see that subtraction clearly, but on the right side, we have (19-5). If we solve this: 19 - 5 = 14, we can see that 14 has been subtracted from the right side too.

Answer

From the image attached, we can see that the regions in set B include

II

III

V

VI

Explanation

We are provided with the Venn Diagram for this question and asked to list the region spanned by set B.

For that, we will look at the circle representing the set B and easily list out the regions that exist in this circle.

From the image attached, we can see that the regions in set B include

II

III

V

VI

Hope this Helps!!!

The simple interest after 2, 5 and 8 years on a principal of $3400 at 0.2% are $3413.6, $3434 and $3454.4 respectively

Simple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r(%) and is to be written as r/100.

Using the data given;

S.I = P × R × T

When T = 2 years

S.I = 3400 * 0.002 * 2

S.I = 13.6

The amount after 2 years = 3400 + 13. 6 = $3413.6

When T = 5 years

S.I = 3400 * 0.002 * 5

S.I = 34

The amount after 5 years = 34 + 3400 = $3434

When T = 8 years

S.I = $3454.4

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ANSWER

9

EXPLANATION

A perfect square is a number that can be expressed as the product of two equal integers.

For example, 9 is a perfect square because it can be expressed as the product 3 x 3 = 3² - which are two equal integers.

Given the follow:

Root96 - root54 + root24

We are to find the expression that is equivalent.

root96 = root16 x root6

root54 = root9 x root6

root24 = root4 x root6

(root16 x root6) - (root9 x root6) + (root4 x root6)

= 4root6 - 3root6 + 2root6

= (4 - 3 + 2)root6

= (1 + 2)root6

= 3root6

Therefore, the correct option is C which is 3root6

Given:

Find-:

(a) Maximum second after launch will the object reach its maximum height

(b) Find the maximum height that the object reaches.

(c) Find the x-intercept and explain its meaning in the context of the problem.

(d) After how many seconds will the object be 100 feet above the ground

(e) Find the y-intercept and explain its meaning on the context of the problem

Sol:

(a)

Maximum second after launch.

For maximum value derivative should be zero.

After 3-second the object reaches maximum height.

(b)

For maximum height is at t = 3

(c) x-intercept the value of y is zero that means:

The negative value of "t" is not considered so at

x-intercept is 6 and -0.061

(d) Object be 100 feet above grounded is:

So, the time is:

At t= 4.76 and t =1.23

(e)

For y-intercept value of "x" is zero.

So, the y-intercept is 6.

First let us define the theorem that would help us solve the problem

The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

Next, applying the theorem:

Solving for x:

Answer:

x = 6

Answer

3x = 24

Explanation

Let sister Maria's age be represented by x.

Katie is twice as old as her sister Mara

So Katie's age will be 2x.

If the sum of their ages is 24, it implies x + 2x =24

Therefore, a one-variable equation to the situation will be: 3x = 24

The food for both gorilla and grizzly bear in the bucket is 9.972 kg.

Given, at the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears.

The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food.

Let the weight of the grizzly bear food be x,

According to the question,

weight of gorilla food = weight of grizzly bear food + 0.796 kg

5.384 = x + 0.796

x = 5.384 - 0.796

x = 4.588

So, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.

Hence, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.

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To solve this expression we need to solve the parenthesis first:

The median is defined as the sum of all the values divided by the total number of data, then in this case:

To find the median we need to order the data:

The median is the number that divides all the data in half, since we have an even number of data we need to take the mean between the middle data, that is, the median is:

The mode is the number that repeats itself more on the data set, then in this case we the mode is 98.

The range is the difference between the lowest and highest data, then:

Summing up we have:

mean: 90.7

median: 89.5

mode: 98

Range: 16

You have a pentagon. In order to determine the value of x for the given expression, of the measure of the angles, take into account that the sum of the interior angles of a pentagon is 540°.

Then, by using the given expressions you have:

(98) + (149 - x) + (2x + 4) + (114) + (128) = 540

To solve for x, proceed as follow:

(98) + (149 - x) + (2x + 4) + (114) + (128) = 540 eliminate parenthesis

98 + 149 - x + 2x + 4 + 114 + 128 = 540 simplify like terms left side

493 + x = 540 subtract 493 both sides

x = 540 - 493

x = 47

Hence, the value of x is x = 47

Answer:

Explanation:

Here, we want to get the distance the snail can go in the given time

Mathematically, we have it that:

speed = 3/25 mph

Time = 1 2/3 hours = 5/3 hours

Thus, we have it that:

Answer:

(a)The slope of f(x) is greater than the slope of g(x).

(b)g(x) has a greater y-intercept.

Explanation:

Part A

From the table of f(x), we have the pairs:

(-1,-12),(0,-6) and (1,0).

First, we find the slope of f(x).

Given the function g(x) defined as follows:

Comparing g(x) with the slope-intercept form (y=mx+b), the slope of g(x) is m=2.

Sentence: The slope of f(x) is greater than the slope of g(x).

Part B

The y-intercept is the point in a function where x=0.

In f(x), When x=0, f(x)=-6

• The y-intercept of f(x) is -6.

Comparing g(x) with the slope-intercept form (y=mx+b), the y-intercept of g(x), b=6.

Therefore, g(x) has a greater y-intercept.

x=19 * sin(40)

x = 12.21

1) Since we have a right triangle and the opposite leg to angle 40º, then we can write the following trig ratio

2) Then the equation for that is x= 19*sin(40) and the value of that leg is approximately 12.21 units

We know that

• Each ice cream costs $3.

• Sales tax is 6%.

• The total amount of money is $24.

Let's find the unit price including sales tax.

So, each ice cream costs $3.18 with sales tax included. Now, we divide $242 by this price to get the total number of ice creams we can buy

Recall that the y% of x is given by the following expression:

Now, let S be the number of people that were in the survey, then, we know that 39% of S is 351, then we can set the following equation:

Multiplying the above equation by 100/39 we get:

Answer: 900.

plane flies 390 miles with the wind

or 325 miles against the wind

The speed of the wind is 10 miles per hour

find the speed of the plane

In this case, we can see that

hence the answer is