Sorry for the writing around the problem but I really need help ASAP!

The statement that is true is that when p(x) is divided by x-n, the remainder is 7.

This statement can be confirmed by solving the equation

p(x)/x-n = q(x) + 7, where q(x) is the quotient. Solving this equation yields the result that q(x) = 2x - 5. This means that when p(x) is divided by x-n, the remainder is 7 and the quotient is 2x - 5.

This statement can also be verified by using synthetic division. By using synthetic division with 2x2 - 5x + 10 as the dividend and x - n as the divisor, the remainder after the division is 7. This confirms that when p(x) is divided by x-n, the remainder is 7.

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The method of simplification of the radical trinomial is described below.

Particularly those polynomials that are persistent under the influence of the perpendicular group are referred to as radical polynomials. A rated subalgebra of the circle of all polynomials is the circle of radical polynomials.

Utilize the Product Property to condense a radical phrase.

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The coordinates of the midpoint of PQ is (5/8, 1/8)

i. To find the slope of the line l1, you can rearrange the equation 4x - 3y + 5 = 0 to the standard form of y = mx+ b, where m is the slope and b is the y-intercept.

4x - 3y + 5 = 0

3y = -4x + 5

y = (-4/3)x + (5/3)

So the slope of the line l1 is m = -4/3.

ii. To find an equation of the line l2, which passes through the point (1, 2) and is perpendicular to the line l1, you can use the slope-intercept form of a line y = mx + b, where m is the slope and b is the y-intercept. Since line l2 is perpendicular to line l1, the slope of l2 is the negative reciprocal of the slope of l1.

m = -1/(-4/3) = 3/4

We can substitute point (1, 2) into the equation

2 = 3/4 * 1 + b

b = 2 - 3/4

So the equation of the line l2 is y = 3/4 x + (2 - 3/4) = 3/4 x + 1/4

iii. To find the coordinates of the point where line l1 crosses the x-axis, we can set y to 0 and solve for x.

y = (-4/3)x + (5/3)

0 = (-4/3)x + (5/3)

x = 5/4

The point where line l1 crosses the x-axis is (5/4, 0)

Similarly, to find the point where line l2 crosses the y-axis, we can set x to 0 and solve for y.

y = 3/4 x + 1/4

y = 3/4 * 0 + 1/4

y = 1/4

The point where line l2 crosses the y-axis is (0, 1/4)

The midpoint of two points can be found by taking the average of the x and y coordinates.

Midpoint of P and Q = ( (5/4 + 0) / 2, (0 + 1/4) / 2) = (5/8, 1/8)

So the coordinate of the midpoint of PQ is (5/8, 1/8).

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Answer: 3c + r + 2.5s + 5

Step-by-step explanation:

Im not gonna explain it thats too much.

The equation 2x + 3y = 13 has infinitely many solutions.

We know that a linear equation in two variables is of the form ax + by + c = 0, where a, b, c are non-zero real numbers.

Here we have been given a linear equation in two variables 2x + 3y = 13

To find the solution of equation 2x+3y=13, first we solve equation for x and then for any real value of y we find value of x.

We solve this equation for x,

Consider 2x + 3y = 13

2x + 3y - 3y = 13 - 3y            .........(subtract 3y from each side of equation)

2x/2 = (13 - 3y)/2                   .........(divide each side by 2)

x = (13 - 3y)/2

for any real value of y we can find value of x.

This means, an equation 2x + 3y = 13 has infintely many solutions.

The graph of 2x + 3y = 13 is shown below.

From the graph, the y-intercept of line 2x + 3y = 13 is (0, 4.333)

and the x-intercept of line 2x + 3y = 13 is (8, 0)

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The complete question is:

What is the solution of 2x + 3y =13?.

After answering the provided question, we can conclude that The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

"Scatter plots are graphs that show the relationship between two variables in a data set. Data points are represented by a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are also known as scatter graphs or scatter diagrams."

The y-intercept of the line of fit is approximately 80 based on the scatter plot and line of fit.

The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

It should be noted that this prediction is based on the linear relationship observed in the sample data and may not be applicable to the entire population. This prediction also assumes that all other factors influencing test performance (such as natural ability, prior knowledge, and test-taking skills) are constant, which may not be the case in real-world situations.

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Answer:

60; a student who studies for 0 hours is predicted to earn 60% on the test

Step-by-step explanation:

The length in centimeters of the side of the square is 8 cm.

The area of a rectangle and a square are -

A{R} = Length x Breadth

A{S} = Side x Side

Given is that a square and a rectangle have the same area. The length of the rectangle is 32 cm and the width of the rectangle is 2 cm.

It is given that -

A{R} = A{S}

Length x Breadth = Side x Side

32 x 2 = (Side)²

(Side)² = 64

Side = 8

Therefore, the length in centimeters of the side of the square is 8 cm.

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The amount of money that the farmer will make after the deduction of percentage of service fees would be = $783.75

A contract earning is defined as the amount of money an individual or company earns for a period of time which only lasts till the end of the contract.

FROM the question,

1 acre /year = 0.11 metric tons

50 acre/year = 0.11 × 50

= 5.5 metric tons

For ten years contract = 5.5 × 10 = 55 metric tons

The amount earned per metric ton = $15

Therefore, 55 metric tons = 15×55 = $825

Deductions of service charge;

5% of 825 = 5/100 × 825

= 4125/100

= $41.25

The balance after deduction of service fees = 825 - 41.25 = $783.75

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Answer: 10

Hope this helps :)

Step-by-step explanation:

29b = 290

/29     /29

b = 10

Answer:

b = 10

Step-by-step explanation:

29b = 290

-----     ------

29        29

b = 10

we can conclude that the probability for the first apple than the peach fruit is 10/39.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Given that there are 8 apples and 5 peaches in a basket.

Total Fruits = 13

For the first event, the probability of getting an apple is,

P(A) = 8/13

Now, Total Fruits = 12

For the second event, the probability of getting peach is,

P(B) = 5/12

The probability for both events is given below.

P = P(A)×P(B)

P = 8/13 ×  5/12

P = 40/156 = 10/39

Hence we can conclude that the probability for the first apple than the peach fruit is 10/39.

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Answer:

6 and 2

Step-by-step explanation:

(a)

the y- intercept is the point on the y- axis where the line crosses.

the line crosses at (0, 6 ) , then y- intercept = 6

(b)

the gradient m ( slope) of the line is calculated using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 6) ← 2 points on the line

m = [tex]\frac{6-0}{0-(-3)}[/tex] = [tex]\frac{6}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

From the adjacent image we can identify the points of the graph.

From the points we can easily find y-intercept and gradient.

How can we identify the points.

Line where cut the x-axis and y-axis. Take that location as point.

For writing point observe the distance of x-axis and y-axis

Let say point A=(0,6) and point B=(-3,0)

For find y-intercept we must know gradient first

Gradient formula for two points m=[tex]\frac{y_{2} -y_{1 }}{x_{2} -x_{1 }}[/tex]

Submit Point A and Point B    m=[tex]\frac{0 -6}{-3 -0\\}[/tex]

                                                m=[tex]\frac{-6}{-3 \\}[/tex]

                                                 m=2

Therefore, Gradient of slope m=2

To find y-intercept, we must solve lin equation

Line equation y=mx+b

m = gradient and b=y-intercept

Submit m in line equation y=2x+b

Submit any one point in the line equation

Take pointA=(0,6)

           6=2(0)+b

           b=6-2

           b=4

Therefore ,y-intercept equals to 4

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The inequality which represents the possible additional amounts Dan will spend is; c ≤ 17.

As evident in the task content; the possible additional amounts Dan will spend is to be determined from the information given in the task content.

Since it is stated that Dan can spend at most $32 in which case, he has spent $15 already.

Let c be the additional amount Dan would spend.

Therefore the inequality which represents the situation is;

c + 15 ≤ 32

Ultimately, the solution set which represents the possible additional amounts he will spend is;

c ≤ 17.

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The value of x from the given triangle is 20 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure,

In ΔABT,

AB²=AT²+BT²

AB²=100+25

AB²=125

AB=√125

In ΔANT,

AN²=AT²+TN²

AN²=100+x²

AN=√100+x²

In ΔABN,

BN²=AB²+AN²

(5+x)²=125+100+x²

25+10x+x²=125+100+x²

10x=200

x=20 units

Therefore, the value of x from the given triangle is 20 units.

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Answer:

70.80

Step-by-step explanation:

40.00 increased by 77% is 70.80. The increase is 30.80.

Carton A has more juice than Carton B, by approximately 0.554 Litres (L).

Carton A: 6.789 L

Carton B: 6.235 L

Difference between Carton A and Carton B:

6.789 L - 6.235 L = 0.554 L

Carton A contains 6.789 Litres (L) of juice, while Carton B contains 6.235 L of juice. To calculate the difference between the two cartons, we subtract the amount of juice in Carton B from the amount of juice in Carton A. We do this by subtracting 6.235 L from 6.789 L, which gives us 0.554 L. This means that Carton A contains more juice than Carton B, by approximately 0.554 L. This difference may seem small, but it can still make a significant difference in the amount of juice one carton can provide compared to the other.

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Answer:

Step-by-step explanation: Since both the numerator and the denominator have a minus (-), they even each other out and the minus signs can be removed. Then we are left with this:

13

23

Now that both the dividend and divisor are positive numbers, we can simply divide 13 by 23 as follows:

13 ÷ 23 = 0.565217391304348

Which means that this is the answer to "What is negative 13 divided by negative 23?":

(-13) ÷ (-23) = 0.565217391304348

Answer:

t = -299

Step-by-step explanation:

[tex]\frac{t}{-13} = 23\\\\ t = 23 * -13\\\\t = -299\\\\Check:\\-\frac{-299}{-13} = 23[/tex]

The angle 360 degree is called as complete angle.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

A form of angle that measures 360° is known as a full angle. When two lines meet at a point, an angle is created, and the angle is the width of the space created.

The angle generated in this case is referred to be the complete angle if, after one complete revolution, the final ray corresponds with the incident or initial ray. A round angle and a complete angle are the alternate names. The angle, which corresponds to the center of a circle, is 2 radians, or 360 degrees. A complete angle is made up of four right angles or two straight angles. The amount of rotation makes the angle different from a zero angle.

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A pair of right triangles are said to be congruent if the lengths of their respective sides and angles are the same.

If the size and shape of two right triangles match, they are said to be congruent. Alternatively said, two right triangles are said to be congruent if the length of their respective sides and angles are equal. Fig. 1 shows that ABC = RPQ since A = R, C = Q, and B = P.

No, not every right triangle has a congruent angle. If the hypotenuse and the leg of one right-angled triangle match the hypotenuse and the corresponding leg of the other triangle, the two triangles are said to be congruent. This circumstance, known as RHS congruence of two triangles, only applies to right angled triangles. An isosceles triangle is one that possesses two congruent sides.

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The product of radicals is C) x[tex]\sqrt[12]{x^5}[/tex]

What is product of radical form?

The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. It indicates that we should multiply the radicals when they are placed next to one another in this manner. Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Here the given form is

=> [tex]\sqrt[3]{x^2} \sqrt[4]{x^3}[/tex]

Now use [tex]\sqrt[n]{a}= \sqrt[mn]{a^m}[/tex] to expand the expression then

=> [tex]\sqrt[12]{x^8} .\sqrt[12]{x^9}[/tex]

Now the product of roots with the same index is equal to the root of the product then

=> [tex]\sqrt[12]{x^8x^9}[/tex]

=> [tex]\sqrt[12]{x^{17}}[/tex]

=> x[tex]\sqrt[12]{x^5}[/tex]

Hence the correct option is C) x[tex]\sqrt[12]{x^5}[/tex]

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Of the two methods for area calculation, the preferred method is the second method because the objects around the polygon are smaller, and easier to calculate their area.

There are several ways to calculate the area of a polygon. Two of them were carried out by the two students in the problem:

Of the two methods for the area of a polygon calculation, the preferred method is the second method because the objects around the polygon are smaller and easier to calculate their area.

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Sum is an aggregation of the numbers, quantities etc. It is write as 4 + 4 = 8 ( plus symbol (+ ) represent the sum). Similarly, ∑ (sigma) also represents the sum of numbers.

Addition is an important topic in Mathematics. When we add two or more numbers, the result is defined as the SUM. The added numbers are called addends. The sum of two or more numbers make a new number say total. A plus symbol (+) is used when we add the numbers. Summation (or) sum formula is the sum of consecutive terms of a sequence. To write the sum of more terms, say n terms, of a sequence {an} , we use the summation notation instead of writing the whole sum manually. That is summation symbol which represent the sum is ∑ (sigma). For example, Sum of two numbers say 6 and 7 is equals to 6 + 7 = 13. But in case of "n" numbers the sum is determined as following way. Consider the first n even numbers, i.e., 2,4,6,....,n and we have to calculate the sum of it. As we see the above sequence is in AP with first term, a = 2 and common difference, d= 2. Then the sum formula in AP is S = n/2[ 2a + (n -1)d ]

=> S = n/2 [ 4 + (n-1)2 ]

=> S = n/2 [ 4 + 2n - 2 ]

=> S = n(n+1) or ∑n( n+1,) ; n = 1,2,.......

Hence, the sum of first n even numbers can be written as ∑n( n+1,) ; n = 1,2,.......

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Answer:

32

Step-by-step explanation:

22+22+7+7+x=90

44 + 14 + x = 90

58 + x = 90

x = 90 - 58

x = 32

When it comes to static characteristics, there are many desirable attributes that can make a product or service stand out from the competition.

Quality and reliability are essential and desirable, as these are the main factors customers will consider when making a purchasing decision.

Durability is also important, as it ensures that a product will continue to perform to its highest standards over time.

Additionally, value for money is key, as customers want to be sure that they are getting a product or service that is worth the cost.

Furthermore, flexibility is highly desirable, as customers often need the ability to customize products or services according to their specific needs.

Finally, a good customer service experience is an essential static characteristic, as a positive customer experience can increase customer satisfaction and loyalty.

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The number of zeros and nature of zeros for the functions,

g(x) =  8x⁶ - 9x² - 6x⁵        ⇒ 6 Roots and 4 real & 2 imaginary roots

h(x) = -4x² - 3x - 1              ⇒  2 Roots and both are imaginary

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

Functions,

g(x) =  8x⁶ - 9x² - 6x⁵

h(x) = -4x² - 3x - 1

Number of roots and nature of roots = ?

First take,

g(x) =  8x⁶ - 9x² - 6x⁵

8x⁶ - 9x² - 6x⁵  = 0

x² = 0

its two of the zeros are 0, 0

After plotting graph for the given function

It can be say that,

It is intersecting x axis at 3 places

So it will have total 6 roots, 4 real roots and two imaginary roots

h(x) = -4x² - 3x - 1

D  = b² - 4ac

   =  9  - 4 × -4 × -1

   =  9  - 16

D =  -7

D is  negative so it will have 2 roots and nature will be imaginary

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

Solutions 1 and 2.

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

Since we are given what y is, we can plug in y into the first equation.

[tex]3x-2(\frac{3}{2} x-\frac{5}{4} )=8[/tex]                    [distribute]

[tex]3x-3x+\frac{5}{2} =8[/tex]                         [subtract]

[tex]\frac{5}{2}\neq8[/tex]

Since this is false, then the only option is that we have no solution.

Answer:

4/

Step-by-step explanation:

gradient=y2-y1/x2-x1

-2-2/-5-2=

-4/-7

=4/

Answer:

the answer is (-3)

Step-by-step explanation:

its to make it work