Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

The Algebraic expression that cannot be factorized is [tex]x^{2}[/tex] + 1

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

[tex]x^{2}[/tex] + -3x -18  can be expressed as  [tex]x^{2}[/tex] -6x +3x -18 which can be factored as (x -6)(x +3)

Also  [tex]x^{2}[/tex] + 7x + 6, (x+6)(x+1)

[tex]x^{2}[/tex] + 5x + 6 , (x+3)(x+1)

But  [tex]x^{2}[/tex] + 1 cannot be factored because since it does not have a variable of x.

In conclusion,  [tex]x^{2}[/tex] + 1 cannot be factored.

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Using the proportion rule, the ratios 1/3 and 2/5 does not form a proportion.

In the given equation,

We have to check the ratios 1/3 and 2/5 form a proportion or not.

As we know that proportion is a ratio in which both ratios are equal to each other.

So to check whether the given statement is proportion or not we put both equation equal to each other.

So the ratios are 1/3 and 2/5.

Now checking the proportion.

1/3=2/5

Multiply by 15 on both side.

1/3 ×15=2/5 ×15

Simplifying

1×5=2×3

5=6

As we can see that both side is not equal so the given ratio is not proportion.

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The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3

Linear sequence is a sequence of number in order with same difference .or same ratio.

when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.

The sequence in the given question

-5 , -2 , 1 , 4 , 7, . . . .

The first term of sequence : a₁ = -5

The second term : a₂ = -2

Common difference : d = a₂ - a₁

=> d = -2 - (-5)

=> d = -2 + 5

=> d = 3

The nth rule of linear sequence is aₙ = aₙ₋₁ + d

replacing the value of d

aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.

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Answer:

BC = 7.9 cm

Step-by-step explanation:

To construct triangle ABC:

Answer:

50m/s = (50 ÷ 1000 × 60 × 60)km/h

           = 180km/h

The equation of a line is written as [tex]y=mx+c[/tex].

What is the equation of a line?

The equation [tex]y = mx + c[/tex] is the general equation of any straight line where [tex]m[/tex] is the gradient of the line and [tex]c[/tex] is the [tex]y -intercept[/tex] .

Here the given equation is

[tex]y=1.5x+20[/tex]       ........[tex](1)[/tex]

when [tex]x=0[/tex]

[tex]y=1.5(0)+20\\y=20[/tex]

when [tex]x=1[/tex]

[tex]y=1.5(1)+20\\y=1.5+20\\y=21.5[/tex]

when [tex]x=-1[/tex]

[tex]y=1.5(-1)+20\\y=-1.5+20\\y=18.5[/tex]

Draw the graph

Hence, by using the values of [tex]x[/tex] and [tex]y[/tex] we formed a straight-line graph.

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Answer: 2 < x < 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Since YP is an angle bisector, Angle 1 and 2 are equal.

We know WYX is 17x+4 so

2 times Angle 1 is 17x+4

[tex]2(8x + 4) =17x + 4[/tex]

[tex]16x + 8 = 17x + 4[/tex]

[tex]4 = x[/tex]

Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

The ingredients Rose needs to make 5 short bread fingers are;

Recipe for 30 shortbread fingers.

To determine the recipe needed for 5 short bread fingers ; divide 30 by 5

= 30/5

= 6

This means, each recipe needed for 30 short bread fingers will be divided by 6 to achieve recipe needed for 5 short bread fingers.

Therefore,

Recipe needed for 5 short bread fingers:

Butter = 120 g / 6

= 20 g

Sugar = 60 g / 6

= 10 g

Flour = 180 g / 6

= 30 g

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Answer:

D. 4 5/13

Step-by-step explanation:

For every time we divide by 13, we consider that a whole number. The whole number is the number on the outside of the fraction. It is equal to 13/13 in this case. So, we can divide 57 by 13, 4 times and have 5/13 left over. Therefore, the answer is D. 4 5/13! :)

24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

Let x ounces of 15% alcohol must be mixed with the 16 ounces of 20% alcohol.

The amount of alcohol in 16 ounces solution is = (20/100) * 16 ounces

                                                                              = 3.2 ounces

The amount of alcohol in x ounces  solution is = (15/100) * x

                                                                              = 0.15x ounces

Total amount of alcohol is = (16 + x) ounces

According to the problem we get an equation,

(3.2 + 0.15x)/(16 + x) = 17/100

100(3.2 + 0.15x) = 17(16 + x)

320 + 15x = 272 + 17x

320 - 272 = 17x - 15x

48 = 2x

x = 48/2

x = 24

Therefore, 24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

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Step-by-step explanation:

We know rhat

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 - \cos(x) }{2} } [/tex]

whenever x lies from 90 to 180.

If

[tex] \csc(x) = 9[/tex]

Using Reciprocal Identities

[tex] \sin(x) = \frac{1}{9} [/tex]

Using Pythagorean Identity,

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex]( \frac{1}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = \frac{80}{81} [/tex]

[tex] \cos(x) = \frac{4 \sqrt{5} }{9} [/tex]

Cosine is negative in when x lies between 90 and 180 so

[tex] \cos(x) = - \frac{4 \sqrt{5} }{9} [/tex]

So

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{9 + 4 \sqrt{5} }{18} } [/tex]

For cosine remember

[tex] \cos( \frac{x}{2} ) = \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

Cosine is negative in second quadrant so

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 - \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{9 - 4 \sqrt{5} }{18} } [/tex]

For tangent,

[tex] \tan( \frac{x}{2} ) = \frac{ \sin( \frac{x}{2} ) }{ \cos( \frac{x}{2} ) } [/tex]

[tex] \frac{ \sqrt{ \frac{1 - \cos(x) }{2} } }{ \sqrt{ \frac{1 + \cos(x) }{2} } } [/tex]

[tex] = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

Tangent is negative over 90<x<180 so

[tex] - \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

[tex] - \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{1 - \frac{4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{ \frac{9 + 4 \sqrt{5} }{9} }{ \frac{9 - 4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{9 + 4 \sqrt{5} }{9 - 4 \sqrt{5} } } [/tex]

[tex] - \sqrt{ \frac{1}{(9 - 4 \sqrt{5) {}^{2} } } } [/tex]

[tex] - \frac{1}{9 - 4 \sqrt{5} } [/tex]

so

[tex] \tan( \frac{x}{2} ) = - \frac{1}{ 9 + 4 \sqrt{5} } [/tex]

or

[tex] \tan( \frac{x}{2} ) = - 9 + 4 \sqrt{5} [/tex]

In the scientific notation, the total population of Brazil and Lithuania is 2.02255 x 10⁸

Scientific notation

A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 is known as Scientific notation.

Given,

In 2010, the population of Brazil was about 1.987 x 10⁸ people. The population of Lithuania was about 3.555 x 10⁶ people.

Here we need to find the total population of Brazil and Lithuania and expression the value in scientific terms.

Here we know that,

Population of Brazil = 1.987 x 10⁸

Population of Lithuania = 3.555 x 10⁶

In order to find the total population, first we have to make the exponent of the two value as equal,

For that we have to rewrite the population of Brazil as,

Population of Brazil = 198.7 x 10⁶

Now, we have to add the two population count in order to find the total population,

=> (198.7 x 10⁶) + (3.555 x 10⁶)

Take the exponent term as common,

=> (198.7 + 3.555) x 10⁶

=> 202.255 x 10⁶

Now, we have to move the two decimal point to simplify this one, then we get,

=> 2.02255 x 10⁸

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Answer:

15.62 is the length of the side of the rhombus.

Step-by-step explanation:

Formula:

A = (e x f)/2

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Answer:

[tex]r \geqslant - 16[/tex]

Step-by-step explanation:

[tex] \frac{ - 10 + r}{2} \geqslant - 13[/tex]

multiply both sides by 2:

[tex] - 10 + r \geqslant - 26[/tex]

add 10 on both sides:

[tex]r \geqslant - 16[/tex]

Answer:

[tex]r \ge -16[/tex]

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

[tex]\frac{-10+r}{2} \ge -13[/tex]

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

[tex]\frac{-10+r}{2} *2 \ge -13 *2[/tex]

[tex]-10+r \ge -26[/tex]

Add 10 to both sides, and simplify

[tex](-10+r)+10 \ge (-26)+10[/tex]

[tex]r \ge -16[/tex]

The answer is : p = -4

the following are the steps to solve it::

13 - 3p = -5 (3 + 2p)

calculate the area of the right hand first by multiplying the number 5 by the number in brackets

13 - 3p = -15 - 10p

move everything that contains p to the left side

13 - 3p + 10p = - 15

count all containing p

13 + 7p = -15

move the ones that don't contain p to the right

7p = -15 - 13

count on the right side

7p = - 28

p = -4

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

The value of x is 15.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

(8x + 9)° and 51° are co-interior angles.

So,

8x + 9 + 51 = 180

8x = 180 - 60

8x = 120

x = 120/8

x = 15

Thus,

The value of x is 15.

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Answer:

Step-by-step explanation:

Fraction=2/100

Decimal=0.02

Percent=2%

Answer: 0.02 as a decimal and 2%

Step-by-step explanation:

its correct!

Answer:

$25940

Step-by-step explanation:

Future value of an Investment at r% for n years is given by:

Future Value = Initial Investment (1 + r/100)n

If r = 10% and n = 10 years

Future Value = 10000(1 + 10/100)10

= 10000(1.1)10

= 10000(2.594)

= $ 25940

Hence the required value is $ 25940.

Answer:

b: x=66 degrees

Step-by-step explanation:

132 degrees and 2x are corresponding angles since of the transversal.

So 132=2x and x=66 degrees

Answer: People attended the two performances are 683

What makes something common?

A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10. A factor that everyone whole numbers share is 1, or 1.

What is a greatest common factor?
It is the biggest number that two numbers are divisible by.

For example, if you did 12 and 24

The factors of 12 are:

1, 2, 3, 4, 6, 12

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24

Their greatest common factor would be 12 since, it is the greatest number that each number can be divisible by.

Step-by-step explanation:

Number of people attend Friday event = 728
Number of people attend Saturday event = 728 - 45 = 683
Hence the answer is 683

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Step-by-step explanation:

[tex]1 - (\frac{1}{4} + \frac{2}{3}) \\ = 1 - ( \frac{3 + 8}{12}) \\ = 1 - ( \frac{11}{12} ) \\ = \frac{1}{12} [/tex]

Answer:

[tex]1 \frac{7}{12}\; \sf pounds[/tex]

Step-by-step explanation:

To find the amount of flour Grandma has left over, subtract the amount she used to make rolls from the original amount.

Given calculation:

[tex]3 \frac{1}{4}-1 \frac{2}{3}[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]\implies \dfrac{3 \times 4+1}{4}-\dfrac{1 \times 3+2}{3}[/tex]

[tex]\implies \dfrac{13}{4}-\dfrac{5}{3}[/tex]

Change both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{13 \times 3}{4\times 3}-\dfrac{5 \times 4}{3 \times 4}[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}=\dfrac{39-20}{12}=\dfrac{19}{12}[/tex]

Divide the numerator by the denominator:

[tex]\implies 19 \div 12 = 1 \; \sf remainder \; 7[/tex]

The solution as a mixed number is the whole number and the remainder divided by the denominator:

[tex]\implies 1 \frac{7}{12}[/tex]

Answer: true

Step-by-step explanation:

The value of  ∇r^n = n(r^n-2)r​ is [tex]-n r^{n-2} \bar{r}[/tex]

A quantity in mathematics known as a vector that lacks position but has both magnitude and direction

The movement of an object between two points is described by a vector. The directed line segment can be used to geometrically represent vector math. The magnitude of a vector is the length of the directed line segment, and the vector's direction is indicated by the angle at which it is inclined.

Given ,

[tex]$&\nabla r^n=n r^{n-2} \bar{r} \\[/tex]

[tex]$&\text { let } \bar{r}=x \hat{i}+y \hat{j}+z \hat{k} \\[/tex]

[tex]$&r=|\bar{r}|=\sqrt{x^2+y^2+z^2} \\[/tex]

[tex]$&\frac{\partial r}{\delta x}=\frac{-x}{r} ; \frac{\delta r}{\delta y}=-\frac{y}{r}, \frac{\delta r}{\delta z}=-\frac{z}{r} \\[/tex]

[tex]$&\because \nabla r^n=\frac{\delta}{\delta x}\left(r^n\right) \hat{i}+\frac{\delta}{\delta y}\left(r^n\right) \hat{j}+\frac{\delta}{\delta z}\left(r^n\right) \hat{k} \\[/tex]

[tex]$&\left.=n r^{n-1} \frac{\delta r}{\delta x} \hat{i}+n r^{n-1} \frac{\delta r}{\delta y} \hat{j}+\frac{\delta}{\delta z} x r^n{ } \hat{k} \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[-\frac{x}{r} \hat{i}- \frac{y}{r} \hat{j}-\frac{z}{r} \hat{k}\right] \\[/tex]

[tex]$&=\frac{n r^{n-1}}{r}[-x \hat{i}-y \hat{j}-z \hat{k}]=-n r^{n-2} \bar{r} \\[/tex]

Therefore the value of ∇r^n = n(r^n-2)r is [tex]-n r^{n-2} \bar{r}[/tex]

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Answer:

A ................................

Answer:

75%

Step-by-step explanation:

The third graph passing through the points (-2,4) and (2,-2) represents the equation y = 3/2x + 1.

Given:

y = 3/2 x + 1

m = 3/2

the graph whose m value is equal to 3/2 is correct.

First graph:

Take any two points (-2,-2) and (0,2)

slope m = 2-(-2) / 0-(-2)

= 2+2 / 0+2

= 4/2

= 2

This graph is incorrect

Second graph:

Two points(-2,2) and (2,-4)

slope m = -4-2 / 2-(-2)

= -6/2+2

= -6/4

= -3/2

This graph is incorrect.

Third graph:

Two points (-2,4) and (2,-2)

slope m = -2-4 / 2-4

= -6/-2

= 3/2

This graph is correct.

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Answer: D

Step-by-step explanation:

I dont gotta explain it, here you go bro :) its -10

Answer:

x=12

Step-by-step explanation:

2x+4=6x

x-6=6x

6x=6x

x=6+6