Given the function y = 3x^2 - 12x + 9. place a point on the coordinate grid to show each x-intercept of the function. Place a point on the coordinate grid to show the minimum value of the function.

Answer:

∠ A ≈ 75.96°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then

∠ A = [tex]tan^{-1}[/tex] ( 4 ) ≈ 75.96° ( to the nearest hundredth )

The pair of equivalent expressions that represent the sale price for any one item is  0.75m and m-1/4m. Option C

The sale price of an item is the regular price minus 1/4 of the regular price. This can be represented as:

sale price = regular price - (1/4)regular price

Simplifying this expression, we get:

sale price = (3/4)regular price

Therefore, the sale price for any one item can be represented as 0.75m, which is equivalent to option C.

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Answer:I’m not so sure but I’m pretty sure it’s the 4th one?

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

For x=1, y=-0.5

For x=0, y=2

For x=1, y=-7/2

Graphing the equation on the coordinate plane we get the second graph.

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

The volume of the composite solid is 980.2 cm³.

A composite solid is a solid made of two or more well-defined solid objects.

To calculate the volume of the composite solid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The equations are classified as follows

System A

consistent and independent this means that the system as a unique  solution at (3, 3)

System B

inconsistent this means that the system as a no  solution

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

System C

consistent and dependent this means that the system as infinitely many solution

A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.

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The probability of spinning an even number on the spinner is 40%.

The probability of picking a diamond from a standard deck of playing cards is 25%.

P(even) = number of even sections / total number of sections

= 2/5

= 0.4

= 40%

Therefore, the probability of spinning an even number on the spinner is 40%.

P(diamond) = number of diamonds / total number of cards

= 13/52

= 1/4

= 0.25

= 25%

Therefore, the probability of picking a diamond from a standard deck of playing cards is 25%.

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a) The principal of the account is given as follows: 1238.27 euros.

b) The interest rate of the account is given as follows: 4.3%.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

We can take the ratio between the balances two consecutive years to obtain the interest rate as follows:

r = 1569.4/1504.5 - 1

r = 1.0431 - 1

r = 0.043

r = 4.3%.

After 5 years, the balance was of 1504.50, hence the principal is obtained as follows:

1504.5 = P(1 + 0.043 x 5)

P = 1504.5/(1 + 0.043 x 5)

P = 1238.27 euros.

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The coordinates of the solution that lies in quadrant I are

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x² + 4y² = 100    ......equation 1.

4y - x² = -20  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (6, 4).

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The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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The amount of tax and deductions from the income is $229.21

From the question, we have the following parameters that can be used in our computation:

Gross income = $1,568

Net income = 1,338.79

Using the above as a guide, we have the following:

Deductions = Gross income - net income

Substitute the known values in the above equation, so, we have the following representation

Deductions = $1,568 - 1,338.79

Evaluate the expression

So, we have

Deductions = $229.21

Hence, the amount of tax and deductions from the income is $229.21

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The rectangular shaped array with 3 rows and 4 columns is drawn

X X X X

X X X X

X X X X

Given data ,

Let the number of rows for the rectangle be r = 3

Let the number of columns for the rectangle be c = 4

So , when r = 3 and c = 4

X X X X

X X X X

X X X X

Hence , the rectangle shaped array is solved

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 8^2 - 2^2}\implies x=\sqrt{ 64 - 4 } \implies x=\sqrt{ 60 }[/tex]

Answer:

Step-by-step explanation:

Quadratic form:

ax²+bx+c

>We are going to work backwards from getting an equation and then solving for the x's.

>From a graph, you are given your x's.

>Put those x's (x-intercepts)  into factored form.

Red:

x  = -7            >add 7 to both sides

x+7 = 0

x = -5            >add  5 to both sides

x+5=0

x+5   and x+7    are your factors

y= (x+5)(x+7)   >FOIL

y=x²+7x+5x+35

y=x²+12x+35     for RED

Blue:   follow same pattern as RED

x= -4               and                x=-2

(x+4)=0                                (x+2)=0

-(x+4)(x+2)              There is a negative in front because this one is facing

                               down

-(x²+6x+8)               FOILED and simplified, now distribut negative

y= -x²-6x-8       BLUE

Green:

x=-1      x=1

y=(x+1)(x-1)               FOIL and simplify

y=x²-1    GREEN

Orange:

x= 2   x=4

-(x-2)(x-4)

-(x²-6x+8)

y= -x²+6x-8      ORANGE

Purple:

x=5    x=7

(x-5)(x-7)

y=x²-12x+35    PURPLE

Answer:2.7

Step-by-step explanation:

Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters

So 270 centimeters = 270/100 = 2.7

The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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B.

B, is the true comparison

Answer:

B' ( -1,-4)

C' (-6,-5)

Step-by-step explanation:

Take each point and move it one unit left and then 3 units up.

Helping in the name of Jesus.

The requried shading would appear above the solid line of the slope.

To graph the inequality 9x + 5y > 1, we first require to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.

To graph this line, we can solve for y in terms of x:

9x + 5y = 1

y = (-9/5)x + 1/5

Although the slope of the line is negative, the shading should occur above the line, which means the correct answer is, the shading would occur above the solid line of the slope.

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The true population proportion of people with kids is between 0.0565 and 0.1835.

We are given that;

Number of people= 100

Percent= 95%

Now,

To construct a 95% confidence interval for the true population proportion of people with kids. Here are the steps to do so:

Find the sample proportion p. This is the ratio of the number of successes (people with kids) to the sample size. In this case, p = 12 / 100 = 0.12.

Find the z-value that corresponds to the 95% confidence level. You can use a table or a calculator to find this value. The z-value for a 95% confidence level is 1.96.

Find the standard error of the sample proportion. This is the standard deviation of the sampling distribution of p. You can use the formula √p (1-p) / n to find this value. In this case, the standard error is √0.12 (1-0.12) / 100 = 0.0324.

Plug these values into the formula for the confidence interval and simplify. You get:

Confidence interval = 0.12 +/- 1.96*0.0324 Confidence interval = 0.12 +/- 0.0635 Confidence interval = [0.0565, 0.1835]

Therefore, by proportions the answer will be 0.0565 and 0.1835.

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Тhе sum оf thе first 6 tеrms оf thе given sеquеncе is аpproximаtely 14.56.

First detеrmine thе common rаtio (r) аnd thе first tеrm (а1).

Eаch tеrm is obtаined by multiрlying thе prеvious tеrm by 1/3. Тherefоre, thе common rаtio is r = 1/3.

Тhe first tеrm is а1 = 12.

Now wе cаn use thе fоrmulа fоr thе sum оf а finite geоmetric series:

Sn = а1(1 - r^n) / (1 - r)

whеrе n is thе number оf tеrms.

Plugging in thе vаlues, wе gеt:

Sn = 12(1 - (1/3)^6) / (1 - 1/3) ≈ 14.55

Rounding to thе neаrest hundredth, wе gеt:

Sn ≈ 14.55 ≈ 14.56

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Answer: A

Step-by-step explanation: complementary is 180 that’s the angle is A. Supplementary is 90 so that’s incorrect.

Answer:

N′(−5, −6), M′(−2, −5), O′(−3, −7)

Step-by-step explanation:

To reflect a point over a line, we can use the following steps:

Find the distance between the point and the line.

Construct a perpendicular line from the point to the given line.

Extend this perpendicular line to the same distance on the other side of the given line.

The intersection of the extended perpendicular line with the given line is the reflected point.

Alternatively, we can use the fact that reflecting a point over a line is equivalent to reflecting the coordinates of the point across the line. In this case, we are reflecting over the line y = -2, so we can simply negate the y-coordinate of each point to find its reflection.

Using this method, the reflected vertices are:

N'(-5, -4)

M'(-2, -3)

O'(-3, -1)

′(Therefore, the correct answer is option D: N−5, −6), M′(−2, −5), O′(−3,-7)

The length of each side of the tile with an area of 790 cm² correct to 3 significant figures is 28.1 cm.

Significant figures are the digits in a number that give a reliable accuracy of the quantity of a measurement.

The significant figures do not include the zeros immediately after the decimal place but those that occur between other numbers are regarded as significant.

The area of a square tile = Length x Length

= 790 cm²

The length of each side = √790 = 28.1069

= 28.1 cm

Thus, we can conclude that the length of each side of the square tile is 28.1 cm.

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The system of equations are t = 22.28 years , number of nickles and dimes are solved

Given data ,

a)

Let the number of years be represented as t

For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck A = 20345 + 1230t

For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck B = 16000 + 1425t

when the total costs are equal , we get

20345 + 1230t = 16000 + 1425t

On simplifying , we get

195t = 4,345

t = 22.28 years

b)

Let the number of nickels be n and number of dimes be d

The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)

The total value of the coins = $ 2.05

And , the total number of coins = 56

0.05n + 0.10d = 2.05

And , n + d = 56

Hence , the system of equations are solved

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The two lines will intersect after 3 months.

We can set the two expressions for y equal to each other:

400x + 700 = 300x + 1,000

100x + 700 = 1,000

100x = 300

x = 3

So the two lines will intersect after 3 months. In this case, to find the corresponding value of y, we can substitute x = 3 into either of the equations:

y = 400x + 700

y = 400(3) + 700

y = 1,500

Therefore, the two lines will intersect after 3 months, at a point with coordinates (3, 1,500).

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The statement that explains the validity of the sampling procedure used by the company is the company applied the same procedure to all three locations and used random sampling to select the times to collect data. The Option A is correct.

The procedure used is valid because they applied the same procedure to all three locations and used random sampling to select the times to collect data.

By using the random sampling, they ensured that they were selecting a representative sample of the entire population of mall visitors.

Also, by applying same procedure to all three locations, they ensured that they were collecting comparable data and this helps to increase the generalizability of their findings and make their decision-making process more reliable.

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Answer:

-4/3

Step-by-step explanation:

-1.33333333333 or -1 1/3