insert parentheses to make the equality a true statement.
12+3*8-8÷4=16

Answer:

[tex]y = - \frac{1}{4} {(x + 2)}^{2} + 5[/tex]

Step-by-step explanation:

The vertex of this parabola is the midpoint of the focus (-2,4) and where the directrix intersects the axis of symmetry of the parabola (-2,6)

This parabola must open downwards due to the position of the directrix and has equation of the form:

[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]

where (h,k) is the vertex.

This implies that:

[tex]h = - 2[/tex]

and

[tex]k = \frac{4 + 6}{2} = 5[/tex]

The value of p is the distance from the vertex to the focus:

[tex]p = |6 - 5| = 1[/tex]

We substitute all the values into the formula to get:

[tex](x - - 2)^{2} = - 4(1){(y - 5)}[/tex]

[tex] {(x + 2)}^{2} = - 4(y - 5)[/tex]

Or

[tex]y = - \frac{1}{4} {(x - 5)}^{2} + 5[/tex]

Answer:

a. The approximated salary cap in 2009 is $136.0 millions

b. The salary cap reached 65 million dollars in 2000

Step-by-step explanation:

* Lets explain how to solve the problem

- The quadratic model of the salary cap in million is

 y = 0.2313 x² + 2.600 x + 35.17

- The approximation of this cap in millions of dollars for the years

  1993-2013 where x = 0 represents 1993, x = 1 represents 1994,

  and so on

a. Lets calculate the approximated sports league salary cap in 2009

∵ x at 2009 = 2009 - 1993 = 16

∵ y = 0.2313 x² + 2.600 x + 35.17

∴ y = 0.2313 (16)² + 2.600 (16) + 35.17

∴ y = 135.98 ≅ 136.0 millions

* The approximated salary cap in 2009 is $136.0 millions

b. Lets calculate in what year did the salary cap reach 65 million dollars

∵ y = 65

∵ y = 0.2313 x² + 2.600 x + 35.17

∴ 65 = 0.2313 x² + 2.600 x + 35.17

- Subtract 65 from both sides

∴ 0.2313 x² + 2.600 x - 29.83 = 0

- Use the calculator to find the value of x by solving the quadratic

 equation

∴ x = 7.05 and x = -18.29 (we will reject this value)

∴ x ≅ 7 years

∴ The salary cap reached 65 million dollars in (1993 + 7) = 2000

* The salary cap reached 65 million dollars in 2000

Final answer:

To approximate the sports league salary cap in 2009, plug in 2009 for x in the given quadratic model equation. The salary cap in 2009 is approximately $942.9 million. If we set the salary cap to $65 million and solve for x using the quadratic model, we find that the cap reached $65 million in the year 2004.

Explanation:

To approximate the sports league salary cap in 2009, plug in 2009 for x in the quadratic model given. The equation becomes:

y = 0.2313(2009)^2 + 2.600(2009) + 35.17

Simplifying the equation gives:

y ≈ 942.85

Therefore, the approximate sports league salary cap in 2009 is $942.9 million (rounded to the nearest tenth).

To determine the year when the salary cap reached $65 million, set y = 65 in the quadratic model and solve for x:

65 = 0.2313x^2 + 2.600x + 35.17

By rearranging the equation and solving for x using the quadratic formula, we find that:

x ≈ 4.56

Rounding down to the nearest year, we can conclude that the salary cap reached $65 million in the year 2004.

Answer:

(0,3)

Step-by-step explanation:

The x-intercept is the point in the graph where x=0.  On the graph you can see that when x=0, y=3.  Therefore our coordinate is (0,3)

Our coordinate pair in the graph is (0,3)

The x-intercept of a line occurs where the line intersects the x-axis, meaning the y-coordinate is zero. In the provided graph, when x equals zero, the corresponding y-value is three. Thus, the coordinate pair (0,3) represents the point where the line intersects the x-axis. This result indicates that when x equals zero, the line crosses the y-axis at a height of three units.

To find the x-intercept, one sets y equal to zero and solves for x. In this case, when y equals zero, there is no such point on the line, so the x-intercept does not exist. Therefore, the coordinate (0,3) accurately identifies the x-intercept of the given line, demonstrating the point where it intersects the x-axis on the graph.

Answer:  [tex]\bold{B)\quad x = \dfrac{8}{3}}[/tex]

Step-by-step explanation:

[tex]log_2(9x)-log_2(3)=3\\\\\\log_2\bigg(\dfrac{9x}{3}\bigg)=3\qquad\qquad \rightarrow \text{used rule for condensing logs}\\\\\\log_2(3x)=3\qquad\qquad \rightarrow \text{simplified}\\\\\\3x=2^3\qquad\qquad \rightarrow \text{used rule for eliminating log}\\\\\\3x=8\qquad\qquad \rightarrow \text{simplified}\\\\\\\large\boxed{x=\dfrac{8}{3}}[/tex]

Answer:  [tex]\bold{\dfrac{19}{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7b-2}{-a+1}\\\\\\=\dfrac{7(3)-2}{-(-2)+1}\\\\\\=\dfrac{21-2}{2+1}\\\\\\=\dfrac{19}{3}[/tex]

Answer:

x=15

y=5

Step-by-step explanation:

The small looking triangle has 3 angles that are congruent to each other. We know this because they all share that same single marker. That means each of those angles ate 60 degrees. That triangle is known as both a equilateral and equilangular. All that means is all of it's 3 sides are congruent and all of it's 3 angles are congruent.

So that angle that measures 8x forms a linear pair with the angle right next to it in the other triangle. All that means is that is supplementary to and adjacent to that angle that measures 60 degrees.

So we have 8x+60=180.

We need to solve this equation for x:

8x+60=180

Subtract 60 on both sides:

8x. =120

Divide both sides by 8

x. =120/8

x. =15

Now to find y.

The bigger looking triangle is an isosceles. We know this because its two base angles are congruent (they have the same double marker). This means 5y+1=26.

Solving:

5y+1=26

Subtracting 1 on both sides:

5y. =25

Dividing 5 on both sides:

y. =5

The values of [tex]x[/tex] and [tex]y[/tex] are required.

[tex]x=15,y=5[/tex]

In the figure

[tex]\angle BAD=\angle BDA[/tex]

This means the sides opposite to the angles will also be equal.

So, [tex]AB=BD=26[/tex]

In [tex]\Delta BDC[/tex] all angles are equal, so it is an equilateral triangle.

So, all angles are [tex]60^{\circ}[/tex]

[tex]\angle ABD+\angle DBC=180\\\Rightarrow 8x+60=180\\\Rightarrow x=\dfrac{180-60}{8}\\\Rightarrow x=15[/tex]

All sides are equal in [tex]\Delta BDC[/tex]

[tex]26=5y+1\\\Rightarrow y=\dfrac{26-1}{5}\\\Rightarrow y=5[/tex]

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let's firstly convert the mixed fractions to improper fractions and then simply get their difference, our denominators will be 8 and 2, so our LCD will be 8.

[tex]\bf \stackrel{mixed}{27\frac{3}{8}}\implies \cfrac{27\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{219}{8}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{219}{8}-\cfrac{5}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)219~~-~~(4)5}{8}}\implies \cfrac{219-20}{8}\implies \cfrac{199}{8}\implies 24\frac{7}{8}[/tex]

Answer:

The coordinates of the center of this circle are (-5 , -3)

Step-by-step explanation:

* Lets explain how to solve the problem

- The mid-point of the segment whose endpoints are (x1 , y1) , (x2 , y2)

  is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

- AB is the diameter of circle T

∵ The diameter must passing through the center of the circle

∵ The center of the circle is the mid-point of all diameters of the circle

∵ The center of the circle is point T

∴ T is the mid point of the diameter AB

- Lets calculate the coordinates of point T by using the rule above

∵ A = (-9 , -1) and B = (-1 , -5)

∵ T is the mid-point of AB

- Let A = (x1 , y1) , B = (x2 , y2) and T = (x , y)

∴ x1 = -9 , x2 = -1 and y1 = -1 , y2 = -5

∴ [tex]x=\frac{-9+-1}{2}=\frac{-10}{2}=-5[/tex]

∴ [tex]y=\frac{-1+-5}{2}=\frac{-6}{2}=-3[/tex]

∴ The coordinates of point T are (-5 , -3)

* The coordinates of the center of this circle are (-5 , -3)

Answer:

(-5,-3)

Step-by-step explanation:

I got it correct on founders edtell

The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.

Given that;

A number is decreased by five and then the result is multiplied by two.

The result is 26.

Let x represent the unknown know number.

Hence,

The equation is ( x - 5 ) × 2 = 26

We can go further and solve for the value of the unknown number.

( x - 5 ) × 2 = 26

2x - 10 = 26

2x = 26 + 10

2x = 36

x = 36 ÷ 2

x = 18

The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.

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Final answer:

The equation based on the given statement is 2(x - 5) = 26. By following the order of operations and solving for the unknown number x, we find that x = 18.

Explanation:

To write an equation for the statement "If a number is decreased by five and then the result is multiplied by two, the result is 26," we start by letting x represent the unknown number. First, we decrease x by five, which is represented mathematically as x - 5. Following this, we then multiply the result by two, which gives us 2(x - 5). The statement concludes by saying that this expression is equal to 26, giving us the final equation:

2(x - 5) = 26

To solve for x, we can follow these steps:

Therefore, the number we are looking for is 18.

Answer:

smallest positive x intercept =Π/2

The sentences based on the graph of the function:

This is the graph of a function.

The y-intercept of the graph is the function value y = 0.

The smallest positive x-intercept of the graph is located at 2.5.

The greatest value of y is y = 7.

For x between 2 and 3, the function value y = 0.

A function is a relation between two sets, where each element in the first set is paired with exactly one element in the second set. In other words, for every input, there is only one output. The graph above shows that for every input value of x, there is only one output value of y. Therefore, the graph represents a function.

The y-intercept of a graph is the point where the graph crosses the y-axis. The y-intercept of the graph above is (0, 0), which means that the function value at x = 0 is y = 0.

The x-intercept of a graph is the point where the graph crosses the x-axis. The smallest positive x-intercept of the graph above is (2.5, 0), which means that the smallest positive input value for which the function value is 0 is 2.5.

The greatest value of y is the highest point on the graph. The highest point on the graph above is (3, 7), which means that the greatest value of y is 7.

For the interval 2 < x < 3, the function value is 0. This means that for all input values in this interval, the output value is 0.

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The following question may be like this:

• This is the graph of a function.

• The y-intercept of the graph is the function value y =

• The smallest positive x-intercept of the graph is located at 25

• The greatest value of y is y =

Answer:

7 boxes

Step-by-step explanation:

Simply divide 42 by 6 to get your answer.

I am joyous to assist you anytime.

Answer:

I think it's:

x(2x^2+4x-1)

Answer:

4 hours and 20 minutes

Step-by-step explanation:

Answer:

4 1/3 hours

Step-by-step explanation:

10:30 to 11:30  1 hour

11:30 to 12:30  1 hour

12:30 to 1:30  1 hour

1:30 to 2:30 1 hour

2:30 to 2:50  20 minutes   20 minutes/60 minutes =  1/3 hour

1+1+1+1 +1/3 = 4 1/3 hours

Answer:

7y - 4x

Step-by-step explanation:

Given

- 3(2x - y) + 2y + 2(x + y) ← distribute both parenthesis

= - 6x + 3y + 2y + 2x + 2y ← collect like terms

= - 4x + 7y

= 7y - 4x

Answer:

8.87

Step-by-step explanation:

The square means "right angle"

[tex] \sin(\alpha ) = \frac{x}{13} \\ \\ \sin(43) = \frac{ x }{13} \\ \\ x = \sin(43) \times 13 \\ x = 8.86597868081 \\ x = 8.87[/tex]

Answer:

5000

Step-by-step explanation:

650 is 13% of the day's production.

650 = 0.13 × n

n = 5000

If N || P and P bisects M then, line N must be perpendicular to line M (N ⊥ M) (option A).

How to determine the relationship between line N and line P?

From the given diagram we are told that line N is parallel to line P and line P is perpendicular to line M.

So line P bisect line M and it is also perpendicular to line M, we can deduce the following;

line N is perpendicular to line M

So based on the information given to us, we can only deduce the relationship between M, N and P.

Hence N must be parallel to P, then line P must be perpendicualr to line M and line N and line M must be perpendicular to each other.

Answer:

Step-by-step explanation:

[tex](-12.7y-3.1x)+5.9y-(4.2y+x)\\\\=-12.7y-3.1x+5.9y-4.2y-x\qquad\text{combine like terms}\\\\=(-12.7y+5.9y-4.2y)+(-3.1x-x)\\\\=-11y-4.1x[/tex]

The simplest form of given expression is  [tex]-11y-4.1x[/tex].

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression

[tex](-12.7y-3.1x)+5.9y-(4.2y+x)[/tex]

= [tex]-12.7y-3.1x+5.9y-4.2y-x[/tex]

Combine like terms

= [tex](-12.7y+5.9y-4.2y)+(-3.1x-x)[/tex]

= [tex]-11y-4.1x[/tex]

The simplest form of given expression is  [tex]-11y-4.1x[/tex].

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Answer:

=22%

Step-by-step explanation:

Since we have given two conditions simultaneously that is windy and not sunny. So we will use the concept of conditional probability.

The probability of sunny day= P(sunny)=10%

P(sunny)=10%=0.1

The probability of windy and not sunny=P(windy|not sun)=20%

P(windy|not sun)=20% = 0.2

Now divide the both probabilities:

P(windy|not sun)/P(sunny)

=0.2/[1-0.1]              

{Hence there are 10% chances of sun tomorrow than there are (1 - 0.1) chances of no sun}

If we subtract 1 from 0.1 than it becomes:

=0.2/0.9

=2/9

=0.2222222222

=22%

Hence the probability that it is windy = 22% ....

The probability that it is windy given that it is not sunny is approximately 22% when rounded to the nearest percent.

To find the probability that it is windy given that it is not sunny, you apply the concept of conditional probability. There's a 10% chance of sun, hence, there is a 90% chance of no sun (100% - 10%). Among this 90%, there is a 20% chance that it's windy without sun. To find the probability of windiness given no sun, you would take the chance of wind and no sun (20%) and divide it by the probability of no sun (90%).

The calculation would be as follows:

(20% chance of wind and no sun) / (90% chance of no sun) = (0.20) / (0.90)
= approximately 0.222

When expressed as a percentage and rounded to the nearest percent, this is approximately 22%.

the sweater costs $15.99 regularly, however today is on sale, 1/4 off the regular price, how much is 1/4 of 15.99? well just their product, 15.99 * (1/4) = 3.9975.

that means that just for today, the sweater costs 15.99 - 3.9975.

so, today you're not really paying $15.99 for the sweater, you're paying 3.9975 less, so you're saving 3.9975.  That's $3.9975 that you won't be spending on it, thus saving it.

Answer:

4 dollars off

Step-by-step explanation:

The cost of the sweater is 15.99

You get 1/4 off

Multiply the cost by the discount

15.99 * 1/4

The questions asks about how much so you can round 15.99 to 16

16*1/4 = 4

You will get about 4 dollars off

Answer:

The intervals on the y-axis are inconsistent.

Step-by-step explanation:

The x- and y-axes start at 0 - this is what graphs normally start with - it is out of the norm to not start at 0.

The intervals on the y-axis are inconsistent - this can cause a problem - we humans tend to judge a graph on height, so changing some of the intervals can mess up a human's actions based on the graph,for example people might think more positively or negatively of a brand or company, and even a totally different view.

The intervals on the y and x-axis are different - they can be different for particular reasons, for example a company might want to put time intervals in months on the x-axis and revenue in dollars on the y-axis - sometimes it is just necessary.

Differing heights are used on a bar graph - this allows us to compare data - without it we would not be able to do much with it.

Misleading graphs can occur due to various reasons such as inconsistent intervals on the axes or the axes not starting at zero. Using different heights on a bar graph can also lead to misleading data representation.

Misleading graphs can occur when certain elements are not accurately represented. Three situations that could lead to a misleading graph are:

Additionally, using differing heights on a bar graph can also lead to a misleading representation of data.

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Answer:

14.21 units

Step-by-step explanation:

We can use distance formula to solve this easily.

Distance Formula is  [tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where

D is the distance

x_1, y_1 is the first points, respectively (let it be -6,-6)

x_2,y_2 is the second pints, respectively (let it be 3,5)

Substituting the values into the formula, we can get the value of D:

[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\D=\sqrt{(5--6)^2+(3--6)^2}\\D=\sqrt{11^2+9^2}\\ D=\sqrt{202} \\D=14.21[/tex]

This is the distance, the first answer choice is right.

Answer:

13

Step-by-step explanation:

The magnitude of a vector < a, b > is

[tex]\sqrt{a^2+b^2}[/tex]

Given < - 12, 5 > then the length of the side is

[tex]\sqrt{(-12)^2+5^2}[/tex]

= [tex]\sqrt{144+25}[/tex]

= [tex]\sqrt{169}[/tex] = 13

Final answer:

The length of the triangle side represented by the vector 〈-12,5〉 is calculated using the Pythagorean theorem and is found to be 13 units.

Explanation:

The student has asked about finding the length of the side of a triangle given a vector from one vertex to another. The vector given is 〈-12,5〉. The length of this side can be calculated using the Pythagorean Theorem for the magnitude of a vector, which states that the magnitude is the square root of the sum of the squares of the vector's components. The formula for the magnitude (or length) of a vector 〉 a, b 〉 is √(a² + b²).

For the vector 〈-12,5〉, the calculation would be:

Which simplifies to:

Therefore, the length of the side of the triangle is 13 units.

For this case we must solve the following equation by completing squares:

[tex]x ^ 2 + 6x-6 = 0[/tex]

We add 6 to both sides of the equation:

[tex]x ^ 2 + 6x = 6[/tex]

We divide the middle term by 2, and square it:

[tex](\frac {6} {2}) ^ 2[/tex]

And we add it to both sides of the equation:

[tex]x ^ 2 + 6x + (\frac {6} {2}) ^ 2 = 6 + (\frac {6} {2}) ^ 2\\x ^ 2 + 6x + (3) ^ 2 = 6 + 9[/tex]

We rewrite the left part of the equation:

[tex](x + 3) ^ 2 = 15[/tex]

We apply root to both sides:

[tex]x + 3 = \pm \sqrt {15}[/tex]

We have two solutions:

[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]

Answer:

[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]

Answer:

[tex]x=-3\±\sqrt{15}[/tex]

Step-by-step explanation:

We have the following equation

[tex]x^2+6x-6=0[/tex]

To use the method of completing squares you must take the coefficient of x and divide it by 2 and square the result.

[tex](\frac{6}{2})^2=9[/tex]

Now add 9 on both sides of equality

[tex](x^2+6x+ 9)-6=9[/tex]

Factor the term in parentheses

[tex](x+3)^2-6=9[/tex]

Add 6 on both sides of the equation

[tex](x+3)^2-6+6=9+6[/tex]

[tex](x+3)^2=15[/tex]

Take square root on both sides of the equation

[tex]\sqrt{(x+3)^2}=\±\sqrt{15}[/tex]

[tex]x+3=\±\sqrt{15}[/tex]

Subtract 3 from both sides of the equation.

[tex]x+3-3=-3\±\sqrt{15}[/tex]

[tex]x=-3\±\sqrt{15}[/tex]

Answer:

that is really confusing.

Step-by-step explanation:

Answer:

800 basic 200 accent tiles

Step-by-step explanation:

The required square feet of basic tile and accent tile is 800 and 200 square feet respectively.

As the data available, 1,000 square feet of tile. He will do most of the floor with a basic tile that costs $1.50 per square foot, but he also wants to use an accent tile that costs $9.00 per square foot.

In mathematics, it deals with numbers of operations according to the statements.

Here,
Let the number of basic tiles be x and the number of accent tiles be y,
According to the question,
x + y = 1000
x = 1000 - y  - - - - - -- - - - - - - (1)
1.5x + 9y = 3000  - - - - -  - -- - - (2)
Put the value of x in equation 2
1.5 (1000 - y ) + 9y = 3000
1500 - 1.5y + 9y = 3000
7.5y = 1500
y = 1500 / 7.5
y = 200
Now, put y in equation 1
x = 800

Thus, the required square feet of basic tile and accent tile is 800 and 200 square feet respectively.

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Answer:

28.57142857% decrease

Step-by-step explanation:

To find the percentage decrease in speed, take the original speed minus the new speed over the original speed.  Then multiply by 100%

original speed = 70   new speed =50

percent decrease = (70-50)/70 *100%

                              = 20/70 *100%

                              =28.57142857%

Answer:

the other factor is (X-4)

Step-by-step explanation:

this is a perfect square trinomial so the two factors should interact the next way:

x2 + 2x – 24

(X+6) * (X-4)     the two numbers added give you the middle       .                                 .                        number  (2)

                        and multiplied give you the final number (24)  so:

1)     +6-4 =  2

and

2)     +6 * - 4  =  -24

Replace x in the equation with -5 and solve.

5(-5) +40 = -25 + 40 = 15

The value of f(x) when x = -5 is f(-5) = 15 by substitution.

Given that a function is defined as:

f(x) = 5x + 40

It is required to find the value of f(x) when the value of x = -5.

Substitute the value of x = -5 in the expression for f(x).

So,

f(-5) = 5(-5) + 40

       = -25 + 40

       = 15

So, the value of f(x) when x = -5 is 15.

Hence f(x) = 15 when x = -5.

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