5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.

A quadratic equation is an equation whose leading coefficient is of the second degree. The correct options are A, B, and E.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Roots of the quadratic equation:

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The complete question is:

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot

8(x2 + 2x + 1) = 3 + 1

8(x2 + 2x) = –3

If we simplify the given options, then the option that is correct is,

A.) 8(x² + 2x + 1) = –3 + 8

     8x² + 16x + 3 = 0

B.) 8x² + 16x + 3 = 0

[tex]x = \dfrac{-16\pm\sqrt{16^2-4(8)(3)}}{2(8)}\\\\x = -1 \pm \dfrac{\sqrt{10}}{4}\\\\x = -1 \pm \sqrt{\dfrac{10}{16}}\\\\x= -1 \pm \sqrt{\dfrac{5}{8}}[/tex]

E.) 8(x² + 2x) = –3

8x² + 16x + 3 = 0

Hence, the correct options are A, B, and E.

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The value of x in the given expression x² = 50 is 5√2

x² = 50

Thake the square root of both sides

x = √50

Recall

√50 = √(25 × 2) = 5√2

Thus,

x = √50

x = 5√2

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The rotations that will carry the equilateral triangle in discuss onto itself are;

It follows from the task content that the rotation which produces the desired output in which case, the rotation maps exactly unto the equilateral triangle is required.

On this note, when the rotation is 90° and 270° about the center P in which case, the rotation can be clockwise or anticlockwise, the desired result is obtained.

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Answer: 240 and 120

Step-by-step explanation:

Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.

The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.

Hence, as per the Cavaleri's principle the volume of both the figures will be the same.

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Answer:

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

B) The slopes of EF and GH are both 5/8

Step-by-step explanation:

The following inference can be made about each answer choices:

For option A

A) The slope of EH is 3/2 and not -8/5

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

For option B

B) The slopes of EF and GH are both 5/8

slope of a graph can be determined by change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For option C

C) FG is perpendicular to GH, its can't be determined since it is concluded that the quadrilateral is a parallelogram, therefore this option is wrong.

For option D

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

Slope of a graph can be determined by rise divided by run change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

for FG, slope =  (7-1)/(8-4) = 6/4 =3/2

EF and GH give the same slope, likewise EH and FG and they are opposite to each other, this make them parallel. Therefore, EFGH is a parallelogram.

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The relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know for every single value of x there should be only one image in y set.

If there are multiple images are there for a single value of x then the relation is not a function.

In a set of relations:

D. {(1,4), (2,5) (1,7)}

There is two mirror image of y for a single value of x:

Thus, the relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.

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Answer: C

Step-by-step explanation:

[tex]50 < 5x-10\\\\60 < 5x\\\\x < 12[/tex]

However, the angle has to have positive measure, so:

[tex]5x-10 > 0\\ \\ 5x > 10\\\\x > 2\\\\\therefore \boxed{2 < x < 12}[/tex]

Answer:

4 inches

Step-by-step explanation:

In a regular pentagon, all sides are equal in length

In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.

When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.

If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.

When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.

If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.

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The area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have three point A(-1,1) B(-3,2) and C (-1,2) in a cartesian plan.

After plotting the points on the cartesian plane.

We will get a right-angle triangle,

The area of the right angle triangle = (1/2)height×base

Base length from the graph = 1 units

The height of the triangle = 2 units

= (1/2)(2)(1)

= 1 square units

Thus, the area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.

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Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

Step-by-step explanation:

There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.

To find a, we can substitute the coordinates of the y-intercept, (0, -50).

[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]

So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

Answer:

Step-by-step explanation:

Comment

If you know this formula

tn = t1 + (n - 1)*d then you don't even have  to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.

Givens

1 = t1

25 = tn

d = 2

Solution

25 = 1 + (n - 1)*2                 Subtract 1 from both sides?

25-1 = 1-1 + (n - 1)*2            Combine

24 = (n  -  1) * 2                   Divide by 2

24/2 = (n - 1)*2/2                

12 = n - 1                               Add 1 to both sides

12 + 1 = n - 1 + 1                     Combine

13 = n

Answer

So you have 13 cards that  will bring success.

Answer:

x = -1/2 = -0.5

Step-by-step explanation:

4.5x + 9 -1/2x = -3.75 +5 1/2 + 5.25

⇔ (4 1/2 - 1/2)x + 9 = (5 1/2 + 5 1/4) - 3 3/4

⇔ 4x + 9 = 10 3/4  - 3 3/4

⇔ 4x + 9 = 10 - 3

⇔ 4x + 9 = 7

⇔ 4x = 7 - 9

⇔ 4x = -2

⇔ x = -2/4

⇔ x = -1/2

⇔ x = -0.5

Answer:

C

Step-by-step explanation:

The slope of a horizontal line, such as that of y= 3, is equal to 0.

This can be proved using the slope formula.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Let's choose 2 points on the line y= 3:

(0, 3) and (2, 3)

Slope

[tex] = \frac{3 - 3}{2 - 0} [/tex]

[tex] = \frac{0}{2} [/tex]

= 0

Thus, the line has a slope of zero.

On the other hand, vertical lines have an undefined slope.

Additional:

To learn more about horizontal lines and their slopes, do check out the following!

6/7 converted to a decimal is 0.8571

From the question, we are to convert the given fraction to a decimal

The given fraction is

6/7

6/7 = 0.8571

Thus,

6/7 expressed as a decimal is 0.8571

Hence, 6/7 converted to a decimal is 0.8571

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The image is attached with the answer.

A magic square is a 3*3 , 4*4 ,5*5 square in which the magic sum is constant for all the columns and rows and even diagonally the sum is same.

The empty squares have been filled and the image has been attached.

The magic sum is 0.81

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The required probabilities are as follows:

a) P(X=5) = 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

Using a binomial random variable, the following is modeled:

There are always ten (10) persons that are being questioned.

From trial to trial, the likelihood of success (i.e., very little faith in newspapers) remains consistent (p=0.68).

The trials are impartial (a reasonable assumption, since the response of 1 of the people should not affect the response of any other)

There are just two possible results for each trial: low faith in newspapers or not.

X counts how many of the 10 trials were successful.

P(X=k) = is the probability mass function for the binomial random variable.

= [tex]^nC_k\times(p^k)\times(1-p)^{n-k}[/tex]

a) P(X=5) =[tex]^{10}C_5\times(0.68)^5\times(0.32)^5[/tex]≈ 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

These may all be calculated individually, then summed together.

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

the same concept as in (b) above.

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The income of the man in discuss as in the task content is; rs 10,200.

Since, it follows that 100 paisas make one rupee. This insinuates that the income tax rate which corresponds to 5 paisa per rupee is; 5%.

Hence, the amount earned by the man in discuss can be evaluated as follows;

(5/100) × Income = 510

Hence, Income = 510/0.05 = rs 10,200.

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Answer:

First simply it as 2x²+3

(a) vertex (0,3)

(b)f(0)=3

(c) no x-intercept

Answer:

y= 4x+8

Step-by-step explanation:

Add 12x to both sides.

3y=24+12x

The equation is in standard form.

3y=12x+24

Divide both sides by 3.

3

3y

​

=

3

12x+24

​

Dividing by 3 undoes the multiplication by 3.

y=

3

12x+24

​

Divide 24+12x by 3.

y=4x+8

The profit is the amount left from you net income after your fixed expenses have been paid.

The amount earned by an individual or corporation after costs, allowances, and taxes is referred to as net income. Net income in company is what remains after all costs, such as salaries and wages, the cost of goods or raw materials, and taxes, have been paid.

Profit is a financial gain, specifically the sum obtained over that which was used to acquire, maintain, or produce the good or service.

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

Hence the profit is the amount left from you net income after your fixed expenses have been paid.

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Answer:

B

Step-by-step explanation:

Comment

Thank you for editing the choices.

The reason the answer is B is because the object begins to move when t = 0. Only - 12 will be left after that.

The acceleration is 3. I don't know how to explain that because I'm using calculus and I don't know if you have taken that or not. I assume not by the right answer you are not in a calculus class. You'll have to ask your instructor about the actual answer. Not A

The same is true of D. The answer is - 5 m/s. It is - 4  Not D

All the minus signs indicate a decrease during that interval. Not C

The time for the ball to pass the top of the building is determined as 4 s.

The time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.

h = -16t² + 128t + 144

v = dh/dt

v = -32t + 128

at maximum height, v = 0

0 = -32t + 128

32t = 128

t = 128/32

t = 4 s

Thus, the time for the ball to pass the top of the building is determined as 4 s.

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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

An object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

When the ball pass the top of the building, h = 144 foot

Plug h = 144 foot in h= -16t² + 128t + 144

144 = -16t² + 128t + 144

[tex]\rm -16t^2+128t=0[/tex]

t = 0 or t = 8 seconds

At t = 0, initially, the ball was thrown upward.

At t = 8 seconds, the ball passes the top of the building

Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

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The linear equation that satisfy the data in the table is: A. y = −4x − 4.

Given the table attached below, find the slope (m) = change in y / change in x using two pairs of values, say, (-1, 0) and (0, -4):

Slope (m) = (-4 - 0)/(0 - (-1)) = -4/1 = -4

Find the y-intercept (b), which is the value of y when x = 0. From the table, when x = 0, y = -4.

b = -4.

Substitute m = -4 and b = -4 into y = mx + b

y = -4x + (-4)

y = -4x - 4

The equation that satisfy the data is: A. y = −4x − 4.

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There are a few possibilities:

The second term refers to the idea of simplifying a claim down to an impossible absurd one.

When decomposing into prime factors, it is when a number is taken out of its half, third, fifth and seventh, and it is also possible for the same number number.

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{10692 }\\ \ 5346\\ \ 2673\\ \ \ \ 891\\ \ \ \ 297\\ \ \ \ \ 99\\ \ \ \ \ 33\\ \ \ \ \ 11\\ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 3\\ 11\\ \: \end{matrix} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were weighed, the total weight of food donated is 65 ounces.

Units are used to measure and express quantities. In the context of the given problem, units are used to indicate the weight of the donated food items.

Pounds (lb) and ounces (oz) are units of weight commonly used in the United States. One pound is equal to 16 ounces.

To add these weights together, we need to make sure they are all in the same units. Let's convert everything to ounces:

- 1 lb 6 oz = 22 oz (since 1 lb = 16 oz, and 6 oz + 16 oz = 22 oz)

- 2 lb 3 oz = 35 oz (since 2 lb = 32 oz, and 3 oz + 32 oz = 35 oz)

- 8 oz = 8 oz

Now we can add the weights:

22 oz + 35 oz + 8 oz = 65 oz

Therefore, the total weight of food donated is 65 ounces.

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Y=x+8

Table

[tex]\boxed{\begin{array}{c|c}\bf x&\bf y\\ \rm 2&\rm 10\\ \rm 0&\rm 8\\ \rm 4&\rm 12\end{array}}[/tex]

How?

x=2

x=0

x=4

Answer:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Given rule:

[tex]y=x+8[/tex]

The rule tells us that to the corresponding y-values, simply substitute the given value of x into the given rule:

[tex]x=2 \implies y=2+8=10[/tex]

[tex]x=0 \implies y=0+8=8[/tex]

[tex]x=4 \implies y=4+8=12[/tex]

Therefore, the completed table is:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]