The cubic polynomial | f(x) = 6x ^ 3 - 7x ^ 2 - 11x + d has a 2 factor (x-1)
(a)Find the value of d
( b )Find the remainder when the polynomial is divided by (x + 2)​

The two column proof is written as follows

Statement                                                           Reason

AD ≅ BD ≅ CD                                         given

ΔADB and ΔCDB are isosceles             Base angles are equal

< A =  < C = < ABD = < CBD = x              Definition of isosceles triangle.

< ABC =  < ABD + < CBD                         Adjacent angles

< ABC = x + x = 2x                                   Substitution property of equality

< ABC + < A + < C = 180                          Sum of angels of a triangle

2x + x + x = 180                                       Substitution property of equality

4x = 180                                                   Addition property of equality

x = 45 degrees                                        Division property of equality

< ABC = 2x = 2 * 45                                Substitution property of equality

< ABC = 90                                              Definition of right triangle

A triangle is said to be a right triangle if one of the angles is 90 degrees. Right angles are angles that are 90 degrees.

The proof required to proof that < B is 90

With the isosceles triangle giving and the equal sides the equation is written as

4x = 180

x = 45

< B has 2x (< ABD + < CBD) these are adjacent angles

< B = 2 * 45

< B = 90

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Step-by-step explanation:

As given in question that Skyler buys 8 T-shirts and 5 hats for $220.

The next day, he buys 5 T-shirts and 1 hat for $112.

We have to find the cost of T-shirt and hat each.

Let the cost of T-shirt and hat is x and y respectively.

According to the question,

8x + 5y = 220          ............(i)

5x + 1y = 112             ............(ii)

Multiply by 5 in eq. (ii)

25x + 5y = 560        ............(iii)

Now subtract eq. (iii) - eq. (i)

25x + 5y = 560

- 8x + 5y = 220

17x = 340

[tex]x = \frac{340}{17}[/tex]

∴ x = 20

Put the value of x in eq. (ii)

5 x 20 + y = 112

100 + y = 112

y = 112 - 100

∴ y = 12

Answer: (x-1) 3

Step-by-step explanation:

This is equation you want

x is unknown -1 in the mark and then times 3!

Answer:

(x/4)+10

Step-by-step explanation:

Quotient=division, so x/4

Increased by 10, so (x/4)+10

Answer:

567.06 in.²

Step-by-step explanation:

The mat is a semicircle.

The straight side is a diameter.

d = 38 in.

r = d/2 = 19 in.

Area of circle = πr²

Area of semicircle = πr²/2

A = 3.14159 × (19 in.)² / 2

A = 567.06 in.²

Answer:

The terms in Sequence 2 are four times as large as the terms in Sequence 1.

Step-by-step explanation:

If we take a look at the numbers,

Sequence 1: 0, 1, 2, 3, 4, 5

Sequence 2: 0, 4, 8, 12, 16, 20

We can see that 0 × 4 = 0,

1 × 4 = 4,

2 × 4 = 8,

And so on.

We can also see in sequence 2 that 4 is added to each of the numbers every time, whereas the first sequence is simply counting up.

Therefore, we can conclude that the terms in Sequence 2 are four times as large as the terms in Sequence 1.

The measure of m∠x is 110°

What is the Isosceles Triangle?

Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides.

We have,

given the triangle Δwxy,

m∠y = 35°, and

there are two similar sides to the triangle wx ≅ xy,

Properties of an Isosceles Triangle are:

The two sides are congruent with each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

The two angles opposite to the equal sides are congruent with each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.

The angle which is not congruent to the two congruent base angles is called an apex angle.

The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles.

The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles.

The two angles opposite to the equal sides are congruent with each other.

so, m∠w = m∠y = 35°

The sum of measure of the angles of the isosceles triangles is 180.

so,

m∠w + m∠x + m∠y = 180

35 + 35 + m∠x = 180

m∠x = 180 - 70

m∠x = 110°

Hence, the measure of m∠x is 110°.

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Using the Central Limit Theorem for proportions, the correct option is:

E. The statistic is biased.

What is Central Limit Theorem?

The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their properly normalised sum tends toward a normal distribution.

The central limit theorem states that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

- The expected value is[tex]$\mu=p$[/tex].

- The standard error is [tex]$s=\sqrt{\frac{p(1-p)}{n}}$[/tex]

In this problem, the expected value is different of the expected of [tex]$\mu=p$[/tex], hence, the statistic is biased, and the correct option is [tex]$\mathbf{E}$[/tex].

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The equation of a line is y = 2x - 4. If the equation is changed to y = 2x - 2, how will the graph of the line change?

A The line will become less steep.

B The line will shift right 2 units.

C The line will shift up 2 units.

D The line will shift left 2 units.

E The line will shift down 2 units.

Answer:

y = 1.3x + 10

Step-by-step explanation:

as, y = 1.3 * 5 + 10

= 16.5

Answer: y = 1.3x + 10

Step-by-step explanation: 1.3 x 0 = 0→ 0 + 10 = 10

1.3 x 5 = 6.5→ 6.5 + 10 = 16.5
1.3 x 10 = 13→ 13 + 10 = 23

1.3 x 15 = 19.5→ 19.5 + 10 = 29.5

1.3 x 20 = 26→ 26 + 10 = 36

Hope this helps.

Classification of given triangle is right angle triangle.

Let's suppose a, b and c are the sides of a triangle.

then we know that sum of 2 sides is always greater than third side.

a + b>c

b + c>a

c + a>b

a = 4.35, b = 5.8 , c = 7.25

a + b>c 4.35+5.8 = 10.15>7.25

b + c>a  5.8 + 7.25 =  13.05>4.35

c + a>b 7.25+4.35 = 11.60>5.8

So now we can say given side lengths are representing sides of a triangle.

It generalizes the Pythagorean Theorem, which states that for a right-angled triangle square of the hypotenuse is equal to the sum of squares of the base and height of the triangle, which is [tex]c^2 = a^2 + b^2[/tex]      

Similarly, It can be observed that

For acute-angled triangle

[tex]c^2 < a^2 + b^2[/tex]    

For Obtuse-angled triangle

[tex]c^2 > a^2 + b^2[/tex]

[tex]a^2 + b^2[/tex] = 18.9225 + 33.64 = 52.5625

[tex]c^2[/tex] = 52.5625

clearly we can see that [tex]a^2+b^2 = c^2[/tex]

So given triangle is Right-angled triangle.

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Answer: $28.79

Find 20% of $35.99.

Then subtract that answer (7.2) from $35.99

your answer is

The shoes where on sale for $28.79

Using the equations 2x+2.5y=26 and x=y+4, Jordan also brought 4 beverages and 8 tacos.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical sentence with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let x be the tacos and y be the drinks,

cost of each drink=$2.5

cost of each tacos=$2

2x+2.5y=26

x=y+4

2(y+4)+2.5y=26

2y+8+2.5y=26

4.5y=18

y=18/4.5

y=4

x=y+4

x=8

Jordan brought 8 tacos using the system of equation as 2x+2.5y=26 and x=y+4 as well as 4 drinks.

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Answer:

(0, 2 )

Step-by-step explanation:

If the dilatation is centred at the origin then the original coordinates are multiplied by the scale factor , that is

B (0, 4 ) → ( [tex]\frac{1}{2}[/tex] (0), [tex]\frac{1}{2}[/tex] (4) ) → (0, 2 )

Answer:

x        0     1     2    3    4

f(x)     4     5    6    7    8

Step-by-step explanation:

f(x) = x + 4

f(0) = 0 + 4 = 4

f(1) = 1 + 4 = 5

f(2) = 2 + 4 = 6

f(3) = 3 + 4 = 7

f(4) = 4 + 4 = 8

x        0     1     2    3    4

f(x)     4     5    6    7    8

Answer:

81.5%

Step-by-step explanation:

Note that 90 is 2 standard deviations away from 144, which accounted for 47.5% area

171 8 is 1 standard deviations away from the mean is which is 34% area.

So the total area is 81.5%

Answer:

Base is 5/2

Step-by-step explanation:

lets say that 2x = the base.

25/24 = 2( [tex]\frac{1}{2}[/tex]([tex]\frac{5}{6}[/tex])x)

[tex]\frac{25}{24}[/tex] = 2( [tex]\frac{5}{12}[/tex]x)

[tex]\frac{25}{24}[/tex] = [tex]\frac{5}{6}[/tex]x

[tex]\frac{25}{24}[/tex] times [tex]\frac{6}{5}[/tex]= x

5/4 =x

2x = 10/4

2x = 5/2

The y-intercepts for the models are equal to 13.2.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, The y-intercepts for the models are equal to 13.2.

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The interval at which the function f(x) = |4(x - 1)| + 2 is decreasing is (- ∞, 1).

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know in an absolute value function y = |x - h| + k, the vertex is (h, k) and it changes its direction from here.

Given, f(x) = |4(x - 1)| + 2 has a vertex at (1, 2).

Therefore the interval where the function is continuously decreasing is

( - ∞, 1).

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Equation for representing energy to the number of days E = P*( 1/d / 1000 )

This formula of energy is used to calculate the use of energy for a given period in a day . The consumption of energy is measured by multiplying the number of power units consumed in a given period.

E = P*(1/d/1000); where E = energy measured in Joules or kilowatt-hours (kWh), P = power units in watts,  and d = time over which the power or energy was consumed in a day  

Thus, whenever someone asks you how to calculate power consumption, you can calculate and answer using the above equation.

Energy consumption can be widely classified based on several factors such as worldwide energy consumption, its impact on the environment, etc.

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The volume of the cylinder is 21.2m³

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. The formula is given as πr²h, where r is the radius of the circular base and h is the height of the cylinder.

V = πr²h

radius = diameter / 2

radius = 3 /2

radius = 1.5m

v = π × 1.5² × 3

v = 21.2m³

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Yes, she is. The exact product of 602 and 341 is 205,282.

In mathematics, an algorithm is a process, a description of a series of steps that can be used to solve a problem; however, they are now far more prevalent than that. Although many areas of research (and daily life) use algorithms, long division's step-by-step process is probably the most prevalent example.

To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.

So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.

Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.

So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.

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The table can be completed as follows x = 0, 2, 4 we get y = 1, 2, 3 for the linear equation [tex]y = \frac{1}{2}x + 1[/tex].

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Basically, there are infinitely many solutions to a linear equation with two variables.

The equation is :

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

So, when x = 0

y = 1,

when x = 2

y = [tex]\frac{1}{2}*2 + 1[/tex] = 1 + 1 = 2

and , when x = 4

y = [tex]\frac{1}{2}*4 + 1[/tex] = 2+ 1 = 3

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Answer:

g= 7-3e / 4 - 9e

Step-by-step explanation:

I assume you need to solve for g. Please let me know if that is not the case

y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

-x+3y=6

3y=6+x

Divide both sides by 3

y=2+1/3x

y=1/3x+2

slope is 1/3

In parallel lines the slope will remain same

We need to find the equation of line passing through (3, 5) and parallel to 3y=6+x

5=1/3(3)+b

5=1+b

b=4

Hence, y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6

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The equation of line parallel to y = -3 passing through (2,6) is y = 6

The slope-intercept form of straight line is used to find the equation of line. It is given as y =mx + b

where m is a slope of line

b is y-intercept

According to the question,

The required line is parallel to line y = -3

Slope of given line : m₁

m₁ = 0

When two lines are parallel to each other then their slopes are equal

Therefore , slope of required line is m₂ =  m₁ = 0

Also , given that the line is passing through the coordinate (2,6)

So , 6 = 0(2) + b

=> b = 6

Substituting the values of slope and intercept

y = 6 is required equation of line

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The values of as shown in the isosceles triangle x is 55°

An isosceles triangle is a type of triangle that have two equal sides.

To calculate the value of x in the isosceles triangle, we use the formula below.

Note: The sum of the angle in a triangle is 180°.

Formula:

Where:

From the image,

Given:

Substitute these values into equation and solve for x

Hence, the values of x is 55°

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The probability that all of them get the same number is 1/36.

Given :

Three people are asked to throw a fair die.

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

In one dice probable outcomes 1, 2, 3, 4, 5 and 6

Total out comes in three dice = ( 6 * 6 * 6 = 216 )

Probability of getting 1 = 1/216

Similarly for 2, 3, 4, 5 and 6

Probability of getting same number = 6 * 1/6 * 1/6 * 1/6

= 6*1/6 * 1 * 1 / 6 * 6

= 6/6 * 1/36

= 1 * 1/36

= 1/36

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