What is a prime polynomial?

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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Answer:

Yes

Step-by-step explanation:

It is reflective

The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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Answer:

-------------------------------

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence:

Answer:

 in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2.Apr 24, 2017

Answer:

When the negatively charged balloon approaches a wall, the negative charges in the wall are repelled (or pushed away)

Step-by-step explanation:

As the two come in contact, the balloon will stick because of the rule that opposites attract (positive to negative)

Answer:

Hope this helps. If it doesn't then I apologize.

Answer:

In Grade 4, students are introduced to the concept of chance and the idea that different situations have different probabilities of occurring. They learn that for many situations, there are a finite number of different possible outcomes. However, at this stage, students are not expected to calculate the probability of events occurring. In Grade 5, students continue to build on their understanding of probability and may begin to learn more advanced concepts and techniques for calculating probabilities.

Step-by-step explanation:

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The interest that y dollars earn in one day at a rate of 1.75% compounded daily is 0.0175

An equation is an expression that shows the relationship between two or more numbers and variables.

Let I represent the total interest gotten from investing y dollars. Since y dollars is invested at a rate of 1.75% compounded daily, hence:

Interest = y * 0.0175 = 0.0175

The interest that y dollars earn in one day at a rate of 1.75% compounded daily is 0.0175

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The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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\(\cfrac{3}{5}\times\cfrac{3}{5}\times\cfrac{3}{5}\implies \cfrac{3\times 3\times 3}{5\times 5\times 5}\implies \cfrac{27}{125}\)

Answer:27/125

Step-by-step explanation:

Multiply the tops 3x3x3=27

Multiply the bottoms 5x5x5=125

a)

Answer: 3

b)

Answer: 2

c)

Answer: 0

d)

Answer: -2

The expression representing the fraction in the situation is option D: 5 ÷ 6

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To divide 5 same-size blocks of clay equally among 6 artists, divide the total amount of clay by the number of artists.

Let C represent the total amount of clay, then -

C/5 = 56

To solve for C, multiply both sides by 5 -

C = 5 × 56

C = 280

So the total amount of clay is 280 units.

To find how much clay each artist receives, divide 280 by 6 -

280/6 = 46.67

Therefore, each artist receives approximately 46.67 units of clay.

Now let's consider the division expression shown by the fraction.

The fraction is -

56/C

Substituting C = 280, it is obtained -

56/280

Simplifying this fraction, divide both the numerator and denominator by 56 -

56/280 = 1/5

Therefore, the division expression shown by the fraction is -

C/56 = 5/1

C = 5 × 56

This means that the total amount of clay is equal to 5 times the amount that each person received, which is consistent with our earlier calculation.

Therefore, the expression is 5 ÷ 6.

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If you want the answer simplified, its
-36x + 32

The area of the rectangle is 1296 square feet.

Let's denote the width of the rectangle as "w" and its length as "4w" since the length is four times the width.

The formula for the perimeter of a rectangle is given by:

P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Given that the perimeter of the rectangle is 180 ft, we can write the equation as:

180 = 2(4w + w)

Simplifying the equation:

180 = 2(5w)

180 = 10w

w = 18

So, the width of the rectangle is 18 ft.

Now, we can find the length of the rectangle:

Length = 4w = 4(18) = 72 ft

The area of a rectangle is given by the formula:

\(A = l \times w,\)

where A is the area,

l is the length,

and w is the width.

Substituting the values we found:

Area \(= 72 ft \times 18 ft = 1296 ft^2\)

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Answer:

c

Step-by-step explanation:

it just is that's the right book

Answer:

Areas under the curve

Step-by-step explanation:

The area under a curve on an interval [a, b] is the integral of the function computed in this interval :  \(A=\int _a^b|f\left(x\right)|dx\)

(1) For \(f\left(x\right)=3\sqrt{x}\) with \(a=1,\:b=4\)

area \(=\int _1^4\left3\sqrt{x}\;dx\) = \(3\cdot \int _1^4\sqrt{x}dx\) =

\(\int \sqrt{x}\) = \(\frac{2}{3}x^{\frac{3}{2}}\)

\(3\cdot\frac{2}{3}x^{\frac{3}{2}}\) = \(2x^{\frac{3}{2}}\)

At \(x = 4,\) we get \(2\cdot4^{\frac{3}{2}}\) = \(2\cdot8 = 16\)

At \(x = 1,\) we get \(2\cdot1^{\frac{3}{2}}\) = \(2.1 = 2\)

So area under the curve for \(f(x) = \:3\sqrt{x}\) in the interval \([1, 4] = 14\)

(2) \(f\left(x\right)=x-\frac{2}{3}\\\)

\(\int \:x-\frac{2}{3}dx\) = \(\int \:xdx-\int \frac{2}{3}dx\)  \(=\frac{x^2}{2}-\frac{2}{3}x\)

\(\left[\frac{x^2}{2}\right]^{27}_1 = \frac{27^2}{2} - \frac{1}{2} = \frac{729}{2}-\frac{1}{2} = \frac{728}{2} = 364\)

\(\left[\frac{2}{3}x\right]^{27}_1 = \frac{2}{3}\cdot \:27 - \frac{2}{3}\cdot \:1 = 18-\frac{2}{3} = \frac{52}{3}\)

\(\int _1^{27}\left|x-\frac{2}{3}\right|dx = 364-\frac{52}{3} = \frac{1040}{3}\)  (Answer)

The graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

In mathematics, a graph is a visual representation of a set of objects where some pairs of the objects are connected by links. The objects, which are usually represented by points, are called vertices or nodes, and the links, which are usually represented by lines or arcs, are called edges.

The original function y = 5x + 1 has a slope of 5, which means that for every 1 unit increase in x, y increases by 5 units.

The new function y = 2x + 1 has a slope of 2, which is less steep than the slope of the original function.

However, the y-intercept of both functions is the same, which is 1.Therefore, the graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

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On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )

A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.

public static double solve(double a, double b, double c, boolean flag)

{     double d = Math.sqrt(b*b - 4*a*c);     if(flag)

{         return (-b + d) / (2*a);     }

else {         return (-b - d) / (2*a);     } }

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To support her discussion, it would be best for Alex to use Graph A for her presentation. Alex should use this graph for her presentation because the number of faulty products appears to decrease less on this graph.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In order to determine an equation with a declining line, we would have to determine the slope of each line graphically and then taking note of the line with a negative rate of change (slope) because it indicates a decreasing function.

In this context, we can reasonably infer and logically deduce that Graph A is more suited for Alex's presentation because the number of faulty products appears to decrease less on it.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x = 26

Step-by-step explanation:

m<B = m<E = (x + 17)°

180 - (25 + 112) = (x + 17) (sum of ∆)

180 - 137 = x + 17

43 = x + 17

Subtract both sides by 17

43 - 17 = x

x = 26

Answer:

N = 50 +4d

Step-by-step explanation:

Take the original number of stamps and add the stamps per days times the number of days

N = 50 +4d

Answer: -2x-27

Step-by-step explanation:

The sky appears blue because of Rayleigh scattering while water appears blue due to selective absorption and scattering of light.

The blue color of the sky is a result of Rayleigh scattering which occurs when the Earth's atmosphere scatters shorter wavelengths of light (blue and violet) more efficiently than longer wavelengths (red and orange).

When sunlight enters the atmosphere, the blue light is scattered in all directions by the molecules and tiny particles present in the air creating the blue appearance of the sky.

Similarly, water appear blue due to selective absorption and scattering of light. Water molecules selectively absorb colors from the visible light spectrum and absorb longer wavelengths (such as red) more effectively than shorter wavelengths (such as blue).

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Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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Answer:

-5/3

Step-by-step explanation:

trust me bro

Answer:

Use desmos

Step-by-step explanation:

Basically it is a graphing calculator put your points

The equation of the line passing through A and B is y = (4/5)x - (2/5).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.

The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:

y - y1 = m(x - x1) (x - x1)

where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.

To calculate the slope, we can use points A (3, 2) and B (8, 6).

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5

So the equation for the line connecting A and B is:

y - 2 = (4/5)(x - 3) (x - 3)

This equation can be simplified by multiplying both sides by 5:

5y - 10 = 4x - 12

Then we can rearrange it to form the slope-intercept equation, y = mx + b:

5y = 4x - 2

y = (4/5)x - (2/5)

As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).

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