According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 29x2 – 66x 27. select all that are actual roots.

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

Given the equation;

x² + y² + 14x + 2y + 14 = 0

We subtract 14 from both sides

x² + y² + 14x + 2y + 14 - 14 = 0 -14

x² + y² + 14x + 2y = -14

Next, we complete the square for x² + 14

We have, ( x + 7 )² - 49

Next, we complete the square for y² + 2y

We have, ( y + 1)² - 1

We substitute these squares into the given equation

x² + y² + 14x + 2y = -14

( x + 7 )² - 49 + ( y + 1)² - 1 = -14

Collect like terms

( x + 7 )² + ( y + 1)² = -14 + 49 + 1

( x + 7 )² + ( y + 1)² = 36

( x + 7 )² + ( y + 1)² = 6²

Note that, the form of a circle is given as;

( x-h )² + ( y-k)² = r²

Hence, we match the values into the form and determine our center and radius.

( x-(+7) )² + ( y-(+1))² = 6²

( x-7 )² + ( y-1 )² = 6²

Hence Center = ( -7, -1 ) and radius = 6

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

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The true statements about the synthetic division are

The synthetic division is given as:

3)2 -2 -12

       6 12

    2 4 0

In the above representation of the synthetic division, we have:

Because the remainder is 0, then

(2x^2 - 2x - 12) ÷ (x - 3) = (2x + 4) --- option C

Set the divisor to 0

x - 3 = 0

Solve for x

x = 3

This means that 3 is a root of 2x^2 - 2x - 12 --- option (D) and x - 3 is a factor of 2x^2 - 2x - 12 --- option (E)

Hence, the true statements are (C), (D) and (E)

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Answer:

20 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 10000=5000e^{0.035t}[/tex]

[tex]\sf \implies \dfrac{10000}{5000}=e^{0.035t}[/tex]

[tex]\sf \implies 2=e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=\ln e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=0.035t\ln e[/tex]

[tex]\sf \implies \ln 2=0.035t(1)[/tex]

[tex]\sf \implies \ln 2=0.035t[/tex]

[tex]\sf \implies t=\dfrac{\ln 2}{0.035}[/tex]

[tex]\implies \sf t=19.80420516...[/tex]

Therefore, it will take 20 years (to the nearest year) for the initial investment to double.

The solution to the division of the given surd is: [tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]

The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.

Given that:

[tex]\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}[/tex]

i.e.

[tex]\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }[/tex]

Using the fraction rule:

[tex]\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}[/tex]

[tex]\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }[/tex]

By simplification, we have:

[tex]\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }[/tex]

[tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]

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The shape of a data flow diagramming process is a  open box.

Given nothing and we have to tell the shape of a data flow diagramming process.

A data flow diagram expresses  the flow of information for any process or system. It uses symbols like rectangles, circles and arrows to show data inputs, outputs, storage points and the routes between each destination.

In this diagram the information is presented in rectangles and circles which are then joined through arrows.

It can present a process of coordination between departments.

Because there is no shape in which these rectangles , circles and arrows are present. That's why we have said that it is a open box.

Hence the shape of a data flow diagramming process is a open box.

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Answer:

25

Step-by-step explanation:

We can calculate for a using sine rule.

For angle A,

A + 27° + 82° = 180 ( sum of angles in a triangle).

A + 109 = 180

A = 180 - 109 = 71°

Therefore,

A = 71°

calculating for side a

[tex] \frac{sin \: 27}{12} = \frac{sin71}{a} \\ a = \frac{12 \times sin71}{sin27} \\ a \: = \frac{11.346}{0.454} \\ a = 25[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the value of a in the equation 3a+b=54, if b=9?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Put in 9 for b.

[tex]\bf{3a+9=54}[/tex] | subtract 9 on both sides

[tex]\bf{3a=45}[/tex] | divide the entire equation by 3

[tex]\bf{a=15}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

       [tex]\bf{\bigcirc 15}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

a = 15

Step-by-step explanation:

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

Answer:

The second graph

Step-by-step explanation:

Let's start with the top equation, 4y+3x=0

Isolate the y by moving the 3x to the other side. 4y=-3x

Divide both sides by 4 to fully isolate the y which will give you y=-3/4x

There's your first equation.

Then take 4y-x=16 and do the same thing

4y=16+x

y=4+x/4

y=x/4+4

Now you know that one equation is going to go left, or the negative direction, while the other will go right, or positive, meaning there will be a point where they intersect. So just basically look for the one where x/4+4 is rising while going right. Leaving you with either the 1st or 2nd graph.

Then,

Graph both using the rise/run method or just look for an answer choice where one of the equations is positive and intersects at y=4 (since the second equation is x/4+4) which makes it the second graph.

Let me know if you need any extra explanation

Answer:

(-4,3)

Step-by-step explanation:

To solve a system of equations by graphing, we'll need to graph both equations, and find their points of intersection.

Note that both equations are linear (no exponents, no radicals, no variables in a denominator, no variables multiplied to other variables, etc -- just numbers multiplied to a variable and added to other numbers multiplied to a variable).

To graph linear equations, often they are graphed by putting the equation in slope-intercept form.  Alternatively, since it is a line, two points can be found on the line, and then the line can be graphed.

Slope intercept form is [tex]y=mx+b[/tex], where "m" is the slope of the line, and "b" is the y-intercept (the place where the line crosses the y-axis).

To convert to slope intercept form, isolate "y".

First equation:

[tex]4y+3x=0[/tex]

[tex](4y+3x)-3x=(0)-3x[/tex]

[tex]4y=-3x[/tex]

[tex]\dfrac{4y}{4}=\dfrac{-3x}{4}[/tex]

[tex]y=\frac{-3}{4}x[/tex]

Second equation:

[tex]4y-x=16[/tex]

[tex](4y-x)+x=(16)+x[/tex]

[tex]4y=x+16[/tex]

[tex]\frac{1}{4}*(4y)=\frac{1}{4}*(x+16)[/tex]

[tex]y=\frac{1}{4}*x+\frac{1}{4}*16[/tex]

[tex]y=\frac{1}{4}x+4[/tex]

To graph the lines, plot their y-intercepts first, then use their slopes to determine the rest of the line.

Recall that the slope is [tex]\frac{rise}{run}[/tex].

Once the equations are graphed, find the intersection from the diagram, (-4,3).

The equations currently are in an implicit form (a form where the variables aren't isolated, so neither variable is written in terms of the other).  To graph any line, find and plot two points, then draw the line between them.

To find points on the line, recall that the equation for a line relates the x-coordinate and y-coordinate through the equation.  So, if you want to find the y-coordinate for the line when the x-coordinate is 0, substitute 0 for x, and solve for y.  Often zero is used, because multiplying by zero cancel out the term, and makes the calculations easier.

Equation 1 - finding a point where x=0

[tex]4y+3x=0[/tex]

[tex]4y+3(0)=0[/tex]

[tex]4y+0=0[/tex]

[tex]4y=0[/tex]

[tex]\dfrac{4y}{4}=\dfrac{0}{4}[/tex]

[tex]y=0[/tex]

So, if x=0, then y=0.  So, the point (0,0) is on line 1.

To find another point, we need to choose another number.  As mentioned previously, often zero is used, and we could find a point on the line where the y-coordinate is zero.  However, since we just found that the point (0,0) is on the line, x=0 when y=0, and so y=0 when x=0.  We'll need a new number.

Another number that it often an easy choice mathematically is to choose the coefficient of the other variable.  So, for instance, in equation 1, the coefficient of the y term is "4", so let's choose the x-coordinate to be 4, and find the y-coordinate that goes with it:

Equation 1 - finding a second point, where x=4

[tex]4y+3x=0[/tex]

[tex]4y+3(4)=0[/tex]

[tex]4y+12=0[/tex]

[tex](4y+12)-12=(0)-12[/tex]

[tex]4y=-12[/tex]

[tex]\dfrac{4y}{4}=\dfrac{-12}{4}[/tex]

[tex]y=-3[/tex]

So, if x=4, then y=-3.  So, the point (4,-3) is also on line 1.

Those two points can be plotted, and the line drawn.

Equation 2 - finding a point where x=0

[tex]4y-x=16[/tex]

[tex]4y-(0)=16[/tex]

[tex]4y=16[/tex]

[tex]\dfrac{4y}{4}=\dfrac{16}{4}[/tex]

[tex]y=4[/tex]

So, if x=0, then y=4.  So, the point (0,4) is on line 2.

To find another point, this time, we can choose the y-coordinate to be zero, because we don't already know the x-coordinate that is associated with it.

Equation 2 - finding a second point, where y=0

[tex]4y-x=16[/tex]

[tex]4(0)-x=16[/tex]

[tex]0-x=16[/tex]

[tex]-x=16[/tex]

[tex]-1*(-x)=-1*(16)[/tex]

[tex]x=-16[/tex]

So, if y = 0, then x = -16.  So, the point (-16,0) is also on line 2.

Those two points can be plotted and the line drawn.  Once the lines are drawn, the intersection can be found.  From the diagram, the intersection is (-4,3).

Answer:

108

Step-by-step explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.

Answer: They both run more than 8 miles

Step-by-step explanation:

9/5 * 7 = 12 3/5

1 2/3 * 7 = 11 2/3

They both run more than 8 miles

Answer:

Jess and Gigi run more than 8 miles

Step-by-step explanation:

9/5 times 7 = 12.6

1 2/3 times 7 equals 11.6

The unit rate of 187pounds of food for 1447.38 is 7.74 per pound

Unit rate = Total cost of food ÷ Quantity of food

= 1447.38 ÷ 187

= 7.74 per pound

Therefore, the unit rate of 187pounds of food for 1447.38 is 7.74 per pound

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The factor computed illustrates that the number of cabins that should be occupied will be 20 cabins.

From the information given, there are 40 children and 30 adults. In this case, the common factors are 1, 2, 3, 5, and 10. The highest common factor is 10.

The question depicts that they will have same cabins. Therefore, the total number of cabins will be:

= 10 × 2

= 20 cabins

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The area of wood needed for the frame is 5. 5 + 106 square inches. Option A

The amount of wood needed for the window frame will be equal to area of window frame.

It is important to note that the upper part of window is semicircle

Area of the upper part = π [tex]\frac{R^2 - r^2}{2}[/tex]

where,

R = Outer radius,

r = Inner radius.

Area of upper part = π ×  [tex]\frac{6^2 - 5^2}{2}[/tex]

Area of upper part = 11π/2

Area of upper part = 5. 5π

To find the area of the lower part, it is important to note that the area of lower part of frame will be area of 3 different rectangles. Two are the same rectangles with length 48 inches and width 1 inch and one rectangle with length 10 inches (12-2) and width 1 inch.

Area of lower part = 2 × 48 × 1 + 10 × 1

Area of lower part = 96 + 10

Area of lower part  = 106 inches

Thus, the area of wood needed for the frame is 5. 5 + 106 square inches. Option A

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Answer:

B.) y = x² + 3, x < 4
          x + 4, x ≥ 4

Step-by-step explanation:

Remember, the x-values associated with closed dots are not included in the function. Therefore, only greater than/less than signs can be applied to these points.

The exponential function includes all x-values before x = 4. Therefore, the domain for the parabola is x < 4.

The linear function includes all x-values after and including x = 4. Therefore, the domain for the linear portion of the function is x ≥ 4.

Answer:

The product is the difference of squares is [tex]$$(7w+10x)(7w-10x)=49{{w}^2}-100{{x}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(7 w+10 x)(7 w-10 x)=(7 w)^{2}-(10 x)^{2} \\&(7 w+10 x)(7 w-10 x)=49 w^{2}-100 x^{2}\end{aligned}$$[/tex]

The relationship modeled that has the function of  f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times  of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.

For us to know the relationship modeled by the above function, the best way to do it is for one to factor it.

The function is: f(x) = 4x³ - 72x² + 320x

First. we factor it so as to extract the common factor 4x:

Secondly,  we factor the quadratic trinomial.

This is often done by writing it as a product of two binomials where the two constant terms are said to be sum up - 18 and its product is said to be 80.

The above terms are known to be -10 and - 8; so the two factors are said to be (x - 10) and (x - 8).

Therefore The relationship modeled that has the function of  f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times  of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.

Where it has :

x = the desired  length,

4x = 4 times its desired length,

x - 10 = 10 lower than its desired length,

x - 8 = 8 lower than its desired length,

We can therefore say that the volume of the prism is said to be the product of the three factors which are:

V = (4x)(x-10)(x-8)

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Answer: 1226

Step-by-step explanation:

The classical probability of the given event is 1/4 or 0.25 or 25%.

The classical property of an event is the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.

If we suppose an event A.

The total number of favorable outcomes to event A to be n.

The total number of possible outcomes in the experiment to be S.

Then, the classical probability of event A is given as:

P(A) = n/S.

In the question, we are informed that in a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event.

We are asked to find the classical probability of the event.

As we know, the classical probability of an event is the ratio of the number of favorable outcomes to the event to the total number of possible outcomes in the experiment.

Thus, the classical probability = 2/8 = 1/4 or 0.25 or 25%.

Thus, the classical probability of the given event is 1/4 or 0.25 or 25%.

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Answer: non of those numbers

Step-by-step explanation:

all the numbers couldn't form a triangle

The ratio of cups of mixed nuts to cups of granola is 2:11.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

Given:

Rolled oats= 6 cups

Mixed nuts=2 cups

Sesame seeds=1/2 cup

Cranberries= 1 cup

Dried unsweetened coconuts=1

Honey =1/2 cup

As, the ingredients listed

Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey

=6 + 2 + 1/2 + 1 + 1 + 1/2

=11 cups

Hence, the ratio of cups of mixed nuts to cups of granola is 2:11.

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The complete question is

Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberries. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey

22 students study both subjects.

What is Venn diagram in math ?

N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4

Now, number of students who studying only Mathematics

n(M∩P)∩C =n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C)    (by  Venn diagram) diagram=23−9−12+4=6

number of students who studying only Physics

n(P∩M )∩C  =n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)    (by Venn diagram)

                =24−12−7+4=9

Now, number of students  who studying only Chemistry

n(C∩M  )∩P =n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C)    (by Venn diagram)

                    =19−9−7+4=7

So, how many students study only one of the three disciplines in detail                                                            6+9+7=22

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The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

An expression is often seen as a form of mathematical statement about a thing.

Note that from the expression:

[tex]\sqrt{75x^{5} y^{8} }[/tex]

[tex]\sqrt{25 x 3 x x^{4} x x x y^{8} }[/tex]

=   5x² y² [tex]\sqrt{3x}[/tex]

So, The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

See options below

Which describes the error Jamal made?

A. He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

B. He should have written the square root of x Superscript 4 in the answer as x, not x squared.

C. He should have written the 5 inside of the radical in the answer.

D. He should have written the 3 outside of the radical in the answer.

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Answer:

A)

Step-by-step explanation:

Based on the right angle triangle and the given parameters, cos K = 5/13

Given parameters:

Therefore,

cos K = adjacent / hypotenuse

cos K = 5/13

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Answer: 3

Step-by-step explanation:

By the intersecting chords theorem,

[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]

The value of 5284 Ib is expressed as 2000 tons 642 lbs

Given the following parameters

2000lb = 1 ton

5284 Ib = 5284lb/2000 = 2.642 tons

2.642 tons = 2000 tons 642 lbs

Hence the value of 5284 Ib is expressed as 2000 tons 642 lbs

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Answer:

A

Step-by-step explanation:

[f(x) + g(x)]=x²+3x-6+1

=x2+3x-5

The value of the composite function is A: x² + 3x - 5.

Option A is the correct answer.

We have,

To find (f + g)(x), you simply need to add the two functions f(x) and g(x) together.

So, (f + g)(x) = f(x) + g(x).

Given:

f(x) = 3x + 1

g(x) = x² - 6

Now, add the two functions:

(f + g)(x) = (3x + 1) + (x² - 6)

Now, combine like terms:

(f + g)(x) = 3x + 1 + x² - 6

Finally, rearrange the terms in descending order of powers of x:

(f + g)(x) = x² + 3x - 5

Thus,

The value of the composite function is A: x² + 3x - 5.

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Answer:

24

Step-by-step explanation:

The combination of possible outcomes that we get exactly four tails is 1365.

According to the statement

The times for which coin is flipped (n) is 15

The number for which we get exactly the tails (r) is 4

So, use Combination formula which is written below

C(n,r)= n! / r!(n−r)!

Substitute the values in it

C(15,4)= 15! / 4!(15−4)!

C(15,4)= 15! / 4! * 11!

C(15,4)= 15*14*13*12*11! / (4*3*2*1) * 11!

C(15,4)= 32760 / 24

C(15,4)= 1365

So, the combination of possible outcomes that we get exactly four tails is 1365.

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Answer:

x = -1

Step-by-step explanation:

Note: when you send a number across it can change it sign. If it is positive it will turn negative.

5x + 2 = 8x + 5

Send 8x across

5x + 2 - 8x = 5

send 2 across

5x - 8x = 5 - 2

- 3x = 3

Divide both sides by - 3

- 3x/- 3 = 3/- 3

- 3 cancel out - 3

x = 3/ - 3

3 divided by - 3 is - 1

x = -1

The t-test for the two means is appropriate in this situation because women and men are independent samples.

Independent samples are those that are chosen at random, ensuring that their results are independent of other observations' values.

The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.

The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. A parametric test is the Independent Samples t-Test.

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