Describe a relationship that the graph may represent

The polynomial would be p(x) = x⁴ - 12x³ + 55x² -116x + 102

How to write the polynomial with these roots?

We know that the roots must be:

2± √2i and 4 ± i

Then we can write the polynomial as:

p(x) = (x - 2- √2i)*(x - 2+√2i)*(x - 4+i)*(x - 4 - i)

Notice that when x equals any of the roots, the polynomial becomes zero, now just expand the products, we will get:

p(x) = (x - 2- √2i)*(x - 2+√2i)*(x - 4+i)*(x - 4 - i)

p(x) = ((x-2)² + 2 )*( (x - 4)² + 1)

p(x) = (x² - 4x + 4 + 2)*(x² - 8x + 16 + 1)

p(x) = (x² - 4x + 6)*(x² - 8x + 17)

p(x) = x⁴ - 12x³ + 55x² -116x + 102

Hello There!

The Y-intercept Of this line is -4 because it’s subtracting 4 that’s me as it’s going down on y axis

Answer:

D $1050

Got that on Apex

Final answer:

Mariana can spend a maximum of $1,050.00 per month on credit cards and loans to avoid credit overload, which is 20% of her annual take-home pay divided by 12 months.

Explanation:

Mariana's annual take-home pay is $63,000. To avoid credit overload, financial advisors often recommend that no more than 20% of your annual take-home pay should go towards servicing debt. To determine the monthly amount Mariana can safely allocate to pay off credit cards and loans, we first calculate 20% of her annual take-home pay, and then divide that number by 12 to get the monthly amount.

First, calculate the annual amount: 20% of $63,000 = 0.20 \(*\) $63,000 = $12,600.

Next, calculate the monthly amount: $12,600 / 12 months = $1,050.00 per month.

Therefore, the maximum amount Mariana can spend per month on debt repayment to avoid credit overload is $1,050.00.

Answer:

B, C, E

Step-by-step explanation:

trust me ;)

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

σ ² = 7²

σ ² = 49

The variance of the data set is, 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

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Answer:

C) Rolling an even number is female and an odd number is male.

Step-by-step explanation:

because it would be an even chance for each sex (Male and female)

Hope this helps

Make sure to mark Brainliest!☺

Answer:

C

Step-by-step explanation:

Answer:

The probability is 2/5.

Step-by-step explanation:

4/5 is the probability of not getting a 5

1/2 is the probability of flipping heads

4/5x1/2 = 4/10 = 2/5

You appear to be missing side A. Here is the equation for that:

a = √(c² - b²)

So do c squared (13 squared) - b squared (12 squared)

= 25

However, the answer is not c squared - b squared, but the SQUARE ROOT of c squared - b squared.

In other words, we want the square root of 25, so your answer is...

Answer:

Step-by-step explanation:

d. 1/4

width of clip is 1/4 to the 1 inch

The width of the paper clip to the nearest eighth of an inch is 1/2 inch.

The smallest subdivision or unit that a scale's digital display can display is a scale division. It's a phrase that's frequently used synonymously with readability or resolution. The scale's capacity can be calculated by dividing it by its readability.

We have to find the width paper clip.

Here, the scale is having 4 division each of marked as 1/4.

So, the paper clip covers

= 1/4 + 1/4

= 2/4

= 1/2

Thus, the width of paper clip in 1/2 inch.

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Answer:

The volume of the figure is [tex]320\ units^{3}[/tex]

Step-by-step explanation:

we know that

The figure is a pyramid

The volume of a pyramid is equal to

[tex]V=(1/3)BH[/tex]

where

B is the area of the rectangular base of pyramid

H is the height of pyramid

Find the area of the base B

The area of the base B is equal to

[tex]B=AB*AC[/tex]

we have that

[tex]AB=8\ units[/tex] ---> see the graph

[tex]AC=10\ units[/tex] ---> see the graph

substitute

[tex]B=8*10=80\ units^{2}[/tex]

we have

[tex]H=EF=12\ units[/tex] ---> see the graph

Find the volume

[tex]V=(1/3)(80*12)=320\ units^{3}[/tex]

Answer:

Step-by-step explanation:

She makes $325 a week, so go to the 8th row, for weekly income of $300 to $400.  She claims 2 exemptions, so go to the third column labeled 2.  The value is 2.  That means the $2 is withheld from her paycheck on top of the 6.25% for FICA.  The total is therefore:

$2 + (0.0625) ($325)

$22.3125

Rounded to the nearest cent, that's $22.31.

Answer:

286.48°

Step-by-step explanation:

Given in the question that we have to convert 5 rad to degree.

we know that,

π = 180°

1rad = 180°/π

5rad = 180°(5)/π

         = 286.4788°

         ≈ 286.48° (nearest to hundredth)

So 5 rad is 286.48°

[tex]5 \times \frac{180}{\pi} = 286.479[/tex]

if we round it: ans= 286.48

Answer:

<2 =66

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles.

58 + <2 = <4

58 + <2 = 124

Subtract 58 from each side

58-58 + <2 = 124-58

<2 =66

Jack incorrect plotted the third quartile.

Explanation:

A box plot has 5 data descriptions. The option that Jack marked incorrectly is Median.

A box plot has 5 data descriptions:

In the given box plot, the median is plotted wrongly, because the median of the box plot is not 3.9.

Hence, the option that Jack marked incorrectly is Median.

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Answer:

3. 2000 pounds to 600 pounds and 5. 250 cents to 75 cents

Step-by-step explanation:

The ratio is 10:3 so just multiply the first number by ten and the and the second by 3 to see if it matches

ex. 10 x 200= 2000    3 x 200= 600

10 x 25=250   3 x 25= 75

I hope this makes sense, this is kinda hard to physically explain.

The ratio 2000 pounds to 600 pounds and 250 cents to 75 cents are equivalent to 10:3.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b.

To find the ratio equivalent to the ratio 10:3.

Solve with the help of options,

1.

28 days to 6 days

Write in ratio form,

28 : 6 = 14 : 3

2.

120 meters to 8000 meters

Write in ratio form,

120 : 8000 = 3 : 200

3.

2000 pounds to 600 pounds

Write in ratio form,

2000 : 600 = 10 : 3

4.

300 seconds to 20 seconds

Write in ratio form,

300 : 20 = 15 : 1

5.

250 cents to 75 cents

Write in ratio form,

10 : 3

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Answer:

3y² -2y -1 =0

Step-by-step explanation:

X= y²+1    .....(1)

3x - 2y = 4.....(2)

put x in (2) :   3(y²+1 )-2y =4

3y² +3 -2y -4 = 0

3y² -2y -1 =0

Answer:

(5,4)

Step-by-step explanation:

We have that the longer base of an isosceles trapezoid joins points (-3, -2) and (7, -2), and one endpoint of the shorter base is (-1, 4).

The best way to find the coordinates of the other endpoint is to draw or sketch the figure on a coordinate grid.

From the graph in the attachment the coordinates of the other endpoints is (5,4).

ANSWER

a=-32

EXPLANATION

If C(a,1) is on the line that passes through A(3, 7), and B(-4, 9), then the three points are collinear.

This implies that, when we find the slope using any two points, we should get the same result.

[tex] \frac{9 - 1}{ - 4 - a} = \frac{9 - 7}{ - 4 - 3} [/tex]

We simplify to obtain;

[tex] \frac{8}{ - 4 - a} = \frac{ - 2}{ - 7 } [/tex]

[tex]\frac{8}{ - 4 - a} = \frac{ 2}{ 7 } [/tex]

We cross multiply to get;

[tex]8 \times 7 = 2( - 4 - a)[/tex]

This implies that,

[tex]56 = - 8 - 2a[/tex]

[tex]56 + 8= - 2a[/tex]

[tex]64 = - 2a[/tex]

Divide both sides by -2

[tex]a = \frac{64}{ - 2} [/tex]

[tex]a = - 32[/tex]

Answer:

a=-32

Step-by-step explanation:

a. addition

b. multiplication

c. division

d. distributive property

Answer:

six plus y

five times j

h divided by eight / h over eight

x plus seven times four

Step-by-step explanation:

Answer:

Part 1) Option A. The axis of symmetry is x=4

Part 2) Option C. minimum

Part 3) Option A. (4,-4)

Part 4) Option B. (2,0) and (6,0)

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-8x+12[/tex]

Part 1) What is the axis of symmetry of the parabola described by the equation above?

we know that

The equation above is a vertical parabola open upward

The axis of symmetry is the x-coordinate of the vertex

Find the vertex of the parabola (convert the equation in vertex form)

[tex]f(x)-12=x^{2}-8x[/tex]

[tex]f(x)-12+16=x^{2}-8x+16[/tex]

[tex]f(x)+4=x^{2}-8x+16[/tex]

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

[tex]f(x)=(x-4)^{2}-4[/tex] ----> equation in vertex form

The vertex of the parabola is (4,-4)

so

The axis of symmetry is x=4

Part 2) The vertex of the equation above is also

we know that

The equation above is a vertical parabola open upward

therefore

The vertex is a minimum

Part 3) What is the vertex of the parabola described by the equation above

we know that

The equation of the parabola into vertex form is equal to

[tex]f(x)=(x-4)^{2}-4[/tex]

therefore

The vertex of the parabola is (4,-4)

Part 4) What are the  x-intercepts of the parabola described by the equation above

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

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

f)x)=0

so

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

take square root both sides

[tex](x-4)=(+/-)2[/tex]

[tex]x=4(+/-)2[/tex]

[tex]x=4(+)2=6[/tex]

[tex]x=4(-)2=2[/tex]

therefore

The x-intercepts are

(2,0) and (6,0)

answer: 1/4

Answer A I just did this

Answer: 24x3y3

Step-by-step explanation:

Answer:

Option 1 - [tex](8x^2y^2)(3xy)=24x^3y^3[/tex]    

Step-by-step explanation:

Given : A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

[tex](8x^2y^2)(3xy)[/tex] where y represents the number of white tiles.

To find : Which simplified expression represents the number of colored tiles used for a path of length x feet?

Solution :

The number of colored tiles needed to make is [tex](8x^2y^2)(3xy)[/tex]

Where, y represents the number of white tiles.

x represents the length of path in feet.

Simplifying the expression,

[tex](8x^2y^2)(3xy)[/tex]

[tex]=8\times 3\times x^2\times x\times y^2\times y[/tex]

We know, [tex]a^m\times a^n=a^{m+n}[/tex]

[tex]=24x^3y^3[/tex]

Therefore, Option 1 is correct.

Answer:

-5 because the number is before zero which irrational number

Answer:

Step-by-step explanation:

[tex]\text{Let}\ s\ -\ \text{side length of a square. Therefore the diameter d = 2r has }\\\text{length d=s}\to 2r=s\to r=\dfrac{s}{2}.\\r-\text{radius}\\\\\text{The formula of an area of a square:}\\\\A_{\square}=(side\ length)^2\\\\\text{Therefore:}\ A_{\square}=s^2.\\\\\text{The formula of an area of a circle:}\\\\A_O=\pi r^2\\\\\text{Substitute}\ r=\dfrac{s}{2}:\\\\A_O=\pi\left(\dfrac{s}{2}\right)^2=\dfrac{s^2\pi}{4}[/tex]

[tex]\text{Calculate what fraction of the area of the square is the area of ​​the circle}\\\\\dfrac{A_O}{A_{\square}}=\dfrac{\frac{s^2\pi}{4}}{s^2}=\dfrac{s^2\pi}{4}\cdot\dfrac{1}{s^2}\qquad\text{cancel}\ s^2\\\\\dfrac{A_O}{A_{\squera}}=\dfrac{\pi}{4}\\\\\text{Convert to the percent:}\\\\\dfrac{\pi}{4}\cdot100\%=25\pi\%\\\\\pi\approx3.14\to25\pi\%\approx(25)(3.14)\%=78,5\%[/tex]

Answer:

900 sq ft

Step-by-step explanation:

The area of a trapezoid is (Base 1 + Base 2) * height/2. So to plug the numbers in...

(30+60)20/2

90*20/2

1800/2

900 sq ft

The correct answer is: 708 square feet

the area of the full shape is 900^2 feet and the area of the door is 192^2 feet therefore 900 - 192 = 708.

(230•3)+(.25•600)=?

690+125=?

815=?

Answer:

25°

Step-by-step explanation:

The angle shown in a right angle, which is 90°. Let's start with 3x-10. We want to get rid of the 10 so we add 10 as positive and negative cancel each other out. So when we add 10 to 90 we have 100. Now we have x+3x=100. Simplify that to 4x=100. Divide both sides by 4 to isolate the x and the answer is 25. To double check,

• 25×3=75

•75-10=65

•65+25=90

The whole angle is equal to 90 degrees therefore you can make an equation using the two angle values and set it equal to 90 like so...

x + 3x - 10 = 90

Combine like terms ( x and 3x)

(x + 3x) - 10 = 90

4x - 10 = 90

Bring the 10 to the other side by adding it to both sides

4x + (-10 + 10) = 90 + 10

4x + 0 = 100

4x = 100

To further isolate x divide 4 to both sides

4x/4 = 100/4

x = 25

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The measure of angle y is 90°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠y=(1/2)[180°] -----> because the diameter divide the circle into two equal parts

so

m∠y=90°

m∠x=(1/2)[148°]

m∠x=74°

Answer:

Y = 90

Step-by-step explanation:

Step-by-step explanation:

Firstly to facilitate the conversion we need to convert mph to km/h.

50 m= 0.05 km

1 mph= 0.001 km/h

2 mph= 0.002 km/h

For the girl

D=0.05 km

S= 0.002 Km/h

T= 25 h

For the Boy

D=0.05

S= 0.001

T= 50 h

Now to find after how many time they will meet each other, we simply have to add the two times.

So,

25 h + 50 h= 75 h

ANS: 75 h

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\bold{DOMAIN:}\\\\2x-3\neq0\ \wedge\ 4x^2-9\neq0\\\\2x-3\neq0\qquad\text{add 3 to both sides}\\2x\neq3\qquad\text{divide both sides by 2}\\\boxed{x\neq1.5}\\\\4x^2-9\neq0\qquad\text{add 9 to both sides}\\4x^2\neq9\qquad\text{divide both sides by 4}\\x^2\neq2.25\\x\neq\pm\sqrt{2.25}\\\boxed{x\neq-1.5\ \wedge\ x\neq1.5}[/tex]

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x)^2-3^2}=0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)}{(2x-3)(2x+3)}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0[/tex]

[tex]\text{The fraction is equal to 0 if the numerator is equal to 0. Therefore}\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0\iff x(2x-3)-(8-3x)=0\\\\\text{use the distributive property}\\\\(x)(2x)+(x)(3)-8-(-3x)=0\\\\2x^2+3x-8+3x=0\qquad\text{combine like terms}\\\\2x^2+(3x+3x)-8=0\\\\2x^2+6x-8=0\qquad\text{divide both sides by 2}\\\\x^2+3x-4=0\\\\x^2+4x-1x-4=0\\\\x(x+4)-1(x+4)=0\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\x=-4\in D\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

Answer:

22

Step-by-step explanation: