Writing Exercises
352. How do you decide which pattern to use?

The solutions to the quadratic equations are:

a) [tex]x = \frac{3 \pm \sqrt{19}}{5}[/tex]

b) x = -8, x = 5.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

Item a:

The coefficients are a = 5, b = -6, c = -2, hence:

Item b:

The equation is:

x² + 3x = 40

x² + 3x - 40 = 0.

It can be simplified as follows:

(x - 5)(x + 8) = 0.

Hence the solutions are:

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The expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

Given the expression below;

-0.5 (1.7 + 1.7)

According to the distributive law;

A(B+C) = AB + AC

Expand

-0.5(1.7) + (-0.5)(1.7)

-0.5(1.7) - 0.5(1.7)

2(-0.5(1.7))

Hence the expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

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Answer:

-4

Step-by-step explanation:

Answer:

try 4

Step-by-step explanation:

8x4= 32

32-7=25

Based on the calculations, the scale factor for this dilation is equal to 1/3.

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

its 1/3

The game is profitable since the payout is always less than what you earn.

Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the  so cost of the 10 points will make the game profitable.

Let's discuss the Lucky 7 game

The game is played with the two fair dice rolls.

You put your money on either of 3 things: Above 7, Lucky 7 or below 7

The game below is designed in Excel:

Each cell formula to generate the game:

They are 36 possible outcomes.

7 is the most likely number coming up

6/36=1/6

of the time.

Thus the expected value of the bet is:

(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12

Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:

(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1

Which is a perfectly fair game.

Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.

Then the 7 returns the money

4/36 = 1/9.

The new case then yields:

(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18

This says that for every $18 handled in bets the bank expects to pay out $17.

Hence we can say that the game is profitable since the payout is always less than what you earn.

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Answer:

Step-by-step explanation:

Hi!

A is congruent to angle C. Because angle FCE is on the other side of the angle C which is equal to A, angle FCE has to equal A

Answer:

my ans will be wrong also and right also 50%5$chances it is an opposite angle so it is in out manner so iys sum is 180 so we have to subbtract

Step-by-step explanation:

65०to 180०(180०-65०=115०) i think ans is 115०the missing angle measurement is 115०in my opinion

Answer:

the Slope: 11

the y-intercept: (0, - 8) x        y

                                     0       -8

                                     1         3

Step-by-step explanation:

Answer:

[tex]y=\frac{11}{8}x+\frac{1}{2}[/tex]

Answer:

==============

Let the cost price is x.

We have:

Solve it for x:

The cost is 22500, find selling price with 20% profit:

Answer:

Step-by-step explanation:

I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5

Answer:

The product is the difference of squares is [tex]$$\left(c-5\right)\left(c+5\right)={{c}^2}-25$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(c-5)(c+5)=(c)^{2}-(5)^{2} \\&(c-5)(c+5)=c^{2}-25\end{aligned}$$[/tex]

Work Shown:

| x-1 | < 2

-2 < x-1 < 2 ... see note1 below

-2+1 < x-1+1 < 2+1 ... see note2

-1 < x < 3

The system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal is;

x + y ≥ 8

x + y ≥ 84x + 2y ≤ 25

let

x + y ≥ 8

4x + 2y ≤ 25

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Answer:

this question is not clear i have read it twice an still dont understand it. Sorry

h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.

We are asked to find h(2.5) and explain its meaning.

To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.

Thus,

h(2.5) = - 16(2.5)² + 58(2.5) + 2,

or, h(2.5) = - 16(6.25) + 145 + 2,

or, h(2.5) = -100 + 147,

or, h(2.5) = 47.

Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

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Answer:

2 parts

Step-by-step explanation:

The rectangle has a 1/2 ratio, because there are 4 parts of the circle, you will shade 2. This is because 2/4 ratio is simplified to 1/2.

The data is modeling a geometric sequence because they have a common ratio of 2.

The recursive formula to determine the time she will complete station 5

Part C:

The explicit formula to find the time she will complete the 9th station.

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Answer:

18+62=80x

12+18=30x

x=80÷30=2

x>2

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

An equation is an expression that shows the relationship between two or more variables and numbers.

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

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Answer:

Step-by-step explanation:

Since the sum of all exterior angles in a polygon is 360°, we have to divide 360 by 6 to find the number of sides.

360/6 = 60.

So, the polygon has 60 sides.

Hope this helps! (:

Answer:

14

Step-by-step explanation:

because it is a small angle that will indooor more sides

Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

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Answer:

the chance is 1.5 out of 5

Hello,

[tex]Speed = \frac{Distance}{Time} = \frac{15 km}{3 h} = \boxed{5 km/h}[/tex]

Stan walked at 5 km/h

Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]

And

[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]

Since, both slopes are reciprocal of each other.

Therefore, the lines are perpendicular.

The probability of not winning of united is [tex]\frac{2}{5}[/tex] .

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that the probability of winning of united is [tex]P(A)=\frac{3}{5}[/tex] .

Usually, we take the total probability is 1

So, the probability of not winning of united is [tex]1-\frac{3}{5}[/tex]

                                                                        [tex]=\frac{5-3}{5}\\=\frac{2}{5}[/tex]

Therefore, the probability of not winning of united is [tex]\frac{2}{5}[/tex] .

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Answer:

The required linear equation satisfying the given conditions f(-5)=-4 and f(5)=2 is

[tex]$$y=\frac{3}{5} x-1$$[/tex]

Step-by-step explanation:

It is given that f(-5)=-4 and f(5)=2. It is required to find out a linear equation satisfying the conditions f(-5)=-4 and f(5)=2. To find it out, first, represent the given conditions in the form of points and then find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the form [tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]

Step 1 of 4

Observe, f(-5)=-4 gives the point (5,-4)

And f(5)=2 gives the point (5,2)

This means that the function f(x) satisfies the points (-5,-4) and (5,2).

Step 2 of 4

Now find out the slope of a line passing through the points (-5,-4) and (5,2).

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{2-(-4)}{5-(-5)} \\m &=\frac{2+4}{5+5} \\m &=\frac{6}{10} \\m &=\frac{3}{5}\end{aligned}$$[/tex]

Step 3 of 4

Now use the slope [tex]$m=\frac{3}{5}$[/tex] and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-2)=\frac{3}{5}(x-5)$$[/tex]

Distribute [tex]$\frac{3}{5}$[/tex],

[tex]$$\begin{aligned}&y-2=\frac{3}{5} x-\frac{3}{5} \times 5 \\&y-2=\frac{3}{5} x-3\end{aligned}$$[/tex]

Step 4 of 4

This linear function can be written in the slope-intercept form by adding 2 on both sides, [tex]$y-2+2=\frac{3}{5} x-3+2$[/tex]

[tex]$$y=\frac{3}{5} x-1$$[/tex]

So, this is the required linear equation.

Answer:

b is not a polynomial

Step-by-step explanation:

b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial

A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

In this question we have two rigid transformations to be defined: (i) Rotation, (ii) Translation. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Herein we must describe the characteristic of a rotation and a translation.

A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

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Answer:

A rotation is a transformation where an object-

moves in a circular arc around a point

A translation is a transformation where an object-

moves a specified distance along a line parallel to a specified line

Step-by-step explanation:

Plato answer