how many positive integers are there less than 1000 that are relatively prime to 100, i.e., have no common factor with 100?

The quotient is 2x^2 + 4x + 5.

The given polynomial is 2x^3 - 3x -10.

As we can see that the given polynomial is a three-degree polynomial but the second degree term is missing, so we can write the polynomial as 2x^3 + 0x^2 - 3x -10.

The divisor is (x-2).

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x) (2x^2) = 2x^3

Thus, we multiply the divisor (x-2) by 2x^2 which gives 2x^3 - 4x^2

Now we subtract this from the polynomial which gives 4x^2 -3x -10.

Repeating the same we multiply the divisor by 4x which gives 4x^2 - 8x. Subtracting the same from 4x^2 -3x -10, we get 5x - 10.

Now we multiply the divisor with 5 to get 5x - 10. Subtracting it from the remaining polynomial 5x -10 leaves the remainder 0.

Thus, we get the quotient as  2x^2 + 4x +5.

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Answer:

4

Step-by-step explanation:

6n - n = 5n

13 + 7 = 20

5n = 20

20/5 = 4

n = 4

Answer:

n = 4

Step-by-step explanation:

To solve this, we first have to get the n's on one side:

[tex]6n - 7 = n + 13[/tex]

↓ add 7 to both sides

[tex]6n = n + 20[/tex]

↓ subtract n from both sides

[tex]5n = 20[/tex]

Then, we can divide by 5 on both sides to solve for n.

[tex]n = 4[/tex]

The probability of the spinner is P(not yellow) = 37.5%.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If the spinner is spun once, the probability of not landing on yellow (sections 2 and 3) is equal to the probability of landing on purple (sections 1 and 8), blue (sections 4, 5, and 6), or orange (section 7).

The total probability of these sections is 1- (2/8) = 1-(1/4) = 3/4.

So P(not yellow) = 3/4 = 37.5%.

Hence, the probability of the spinner is P(not yellow) = 37.5%.

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A system of linear equations has infinite solutions when the graphs are the exact same line.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We know that;

Let the system of equations of two lines.

So, When the graphs are the exact same line, then a system of linear equations has infinite solutions.

Thus, A system of linear equations has infinite solutions when the graphs are the exact same line.

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Answer:

Step-by-step explanation:

blb

Answer and Explanation:

Congruent line segments have the same length.

Therefore, to construct a segment congruent to EF that has an endpoint on point G, we simply have to draw a line that is the same length as EF that ends on G.

See the attached image for a sample answer.

Answer:

y = -24

Step-by-step explanation:

Solve for y:

y/8 + 38 = 35

Put each term in y/8 + 38 over the common denominator 8: y/8 + 38 = y/8 + 304/8:

(y/8 + 304/8) = 35

y/8 + 304/8 = (y + 304)/8:

((y + 304)/8) = 35

Multiply both sides of (y + 304)/8 = 35 by 8:

(8 (y + 304))/8 = 8×35

(8 (y + 304))/8 = 8/8×(y + 304) = y + 304:

y + 304 = 8×35

8×35 = 280:

y + 304 = 280

Subtract 304 from both sides:

y + (304 - 304) = 280 - 304

304 - 304 = 0:

y = 280 - 304

280 - 304 = -24:

Answer: y = -24

Answer:

-49.5

Step-by-step explanation:

3x + 96 = x - 3

2x + 96 = -3 (-x both sides)

2x = -99 (-96 both sides)

x = -49.5 (/2 both sides)

Answer:

13

Step-by-step explanation:

the girl will be scoring a total of 30 goals.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Given, the goal scored

3 times 2

4 times 1

and 5 times 4.

So the total goal scored will be 3*2=6

4*1=4

and 5*4=20

Score = 6+4+20=30

Hence the girl will be scoring a total of 30 goals.

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Given condition will be represented by linear equation 5x+10y=90.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Total trail hiked=90miles

mountain trail=5mile

canal-trail=10mile

x represent the number of times Maria hiked the mountain trail, and  y represent the number of times Maria hiked the canal trail

Therefore,

Linear equation will be 5x+10y=90

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Answer:

5/6

Step-by-step explanation:

Alr, so slope of this line is -6/5.

Two lines, which are perpendicular to each other, their slopes' products' is equal to -1.

So, m₁m₂ = -1

or -6/5 m₂ = -1

m₂ = 5/6

Therefore, the slope of that line is 5/6.

Thanks and Cheers!

The replacement approach refers to determining any variable's value from one equation in terms of another variable. Considering that, the point where the function crosses = (0, 7). The correct answer is c. (3,3).

Considering that the function's intersection point is now = (0, 7) As a result, the point must fulfil the function. We have to check whether these pairs satisfy equation 2x + y = 7 or not.. So, we will put these pairs one by one.

A) (0,7) x=0 & y=7

Than

2×0+7=7

7=7 so, it satisfies.

B) (1,5) x=1 & y=5

Than

2×1+5=7

2+5=7

7=7 so, it satisfies

C) (3,3) x=3 & y= 3

Than

2x3+3= 7

6+3 = 7

9= 7 so, it does not satisfies.

D) (2,3) x=2 & y= 3

Than

2x2+3 = 7

4+3= 7

7=7 so, it satisfies.

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Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

A linear equation in two variables is an equation of the form ax + by = c, where a, b, and c are constants, and x and y are variables. These equations represent a straight line in a two-dimensional coordinate system, and the slope-intercept form of the equation is y = mx + b, where m = -a/b is the slope of the line, and b = -c/b is the y-intercept.

1. (x-1)(y+2)=0: This equation is not a linear equation in two variables as it is a product of two linear equations in one variable, therefore this is not a linear equation in two variables.

2. 2x-3y+7=0: This equation is a linear equation in two variables. The equation is in the form of ax + by + c = 0 where a, b, and c are constants and x and y are variables. This equation is a straight line in a 2D coordinate system and the slope and y-intercept can be calculated using a and b.

7x-3y+2z=0: This equation is not a linear equation in two variables as it has three variables (x, y and z) and it is not possible to graph this equation in a 2D coordinate system as it has three variables.

(y+x)^2-2=0: This equation is not a linear equation in two variables because it is a square of a linear equation. The equation is in the form of (y+x)^2 and we know that any equation in the form of (y+x)^n where n>1 is not a linear equation.

So the correct answer is option 2) 2x-3y+7=0.

Therefore, Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

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The area of the given triangle is 130.7 cm^2.

What are Triangles?

Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorized into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorized into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now,

Area of a right angle triangle =1/2*base*height

here a=base and let h=height

h^2=b^2-a^2

=23^2-15^2

h^2=304

h=17.43cm

therefore

area=1/2*15*17.43

Area of the triangle=130.7cm^2

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The value 120 in the linear function represents the y - intercept

In this problem, the 120 in the equation y = 120 - 15x represents the initial amount of money that Ahmed starts with from his summer job.

It is the y-intercept of the linear equation, which means that when x = 0, y = 120. This means that if Ahmed does not subscribe to the PlayStation Plus Extra subscription for any months, he will have $120 left from his summer job.

It can be interpreted as the starting point or the base point of Ahmed's savings.

It's important to note that the y-intercept of a linear function is the point where the function crosses the y-axis, it gives the value of the dependent variable (y) when the independent variable (x) is equal to zero.

It also indicates that the amount of money Ahmed has is decreasing by 15 dollars per month of subscription, since the coefficient of x is -15.

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The price per pound that was paid for the apples is $0.85 per pound

An equation shows the relationship between numbers and variables in an expression.

Unit rate is the ratio of two quantities. The denominator of a unit rate is always equal to one.

The apples are 3.4 lbs and their total price is $2.89. hence:

The price per pound is gotten by dividing the total price of apples by the weight of the apple

Price per pound = $2.89 / 3.4 lbs = $0.85 per pound

The price per pound is $0.85 per pound

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The graph for the given piecewise function is as provided in image.

What is piecewise function?

A piecewise function is a function f(x) which has different definitions in different intervals of x. The graph of a piecewise function has different pieces corresponding to each of its definitions. The absolute value function is a very good example of a piecewise function. Let us see why is it called so. We know that an absolute value function is f(x) = |x| and it is defined as:

f(x)=(x if x≥0 ,

     -x  if x><0)

We should read this piecewise function as

f(x) is equal to x when x is greater than or equal to 0 and

f(x) is equal to -x when x is lesser than 0.

Given piecewise function

f(x)=(3x-5  if x<=-1

       -2x+3 if -1<x<4

        2      if x>=4)

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All real numbers except {x = 4} denote the solution set.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = (4⁢x + 8/6⁢x − 24)

The given function is -

y = (4⁢x + 8/6⁢x − 24)

Domain is the set of values for which the given function is defined. The given function is not defined for -

6x - 24 = 0

6x = 24

x = 4

So, all real numbers except {x = 4} denote the solution set.

Therefore, all real numbers except {x = 4} denote the solution set.

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The value of f is 0.6.

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Given that,

0.25(4f-3) = 0.05(10f - 9)

=> f - 0.75 = 0.5f -0.45

Rearranging the equation and combining like terms we get

f - 0.5f =  -0.45 + 0.75

=> 0.5f = 0.30

=> f = 0.30/0.5

=> f = 3/5

=> f= 0.6

Therefore, the value of f is 0.6.

Correct question: Simplify and solve the following linear equation: 0.25(4f-3) = 0.05(10f - 9)

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Answer: the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2) is y = (1/2)x + 5.

Step-by-step explanation:

The slope of the line that is perpendicular to y = -2x + 5 is the negative reciprocal of the slope of y = -2x + 5, which is -2. The negative reciprocal of -2 is 1/2.

To find the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2), we can use the Point-Slope Form: y - y₁ = m(x - X1)

y - 2 = (1/2)(x + 4)

Simplifying, we get:

y = (1/2)x + 5

So the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2) is y = (1/2)x + 5.

The missing term is "zero" for the given equation.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

As per the given figure, the required solution would be as:

8x - 3 + 4x + 3 = 180

Rearrange the likewise terms and apply the arithmetics operation,

12x + 0 = 180

We know that the sum of 3 and -3 is 0.

Compared to the given equation, we get the missing term as zero.

Thus, the required value is 0.

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Answer:b,c

Step-by-step explanation:i got it correct

The number of downloads that make site A the better deal is 31 downloads

An equation shows the relationship between numbers and variables in an expression.

Let y represent the total cost of download for x downloads.

For site A, there is a flat rate of $29 per month plus $0.80 per download, hence:

y = 0.8x + 29

For site B, there is a flat rate of $17 per month plus $1.19 per download, hence:

y = 1.19x + 17

For site A to be better then the total cost should be lower:

0.8x + 29 < 1.19x + 17

-0.39x < -12

x > 30.8

It would take 31 downloads for site A to be the better deal

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The ratio of the midpoint of any given line segment is equal to 1 : 1.

As given in the question,

Therefore, the ratio of the midpoint for any given line segment is always equal to 1 : 1.

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Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.

Here,

Given :

Let Rosa age = x

Rosa's father age =  3x

and

=> 3x -x < 35

=> 2x < 35

=> x <35/2

=> x < 17.5

Thus , Rosa's age is 17 .5 and her fathers age is 3*17.5 = 52.5 years

Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

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A 95% confidence interval for the mean is (3193, 2607).

Confidence interval in simple words is the range of values that the specific parameter lies within.

Confidence interval for mean is found by the formula,

CI = Х ± t [tex]\frac{s}{\sqrt{n} }[/tex]

where X is sample mean, s is the standard deviation and n is the sample size.

Sample mean = 2900

s = 1300

n = 55

Degree of freedom = n - 1 = 54

t value of degree of freedom 54 with the probability of exceeding the critical value as 1 - 95% = 5% = 0.05 is 1.674.

CI = 2900 ± (1.674)[tex]\frac{1300}{\sqrt{55} }[/tex]

   = 2900 ± 293.44

   = (3193.44, 2606.56)

   = (3193, 2607)

Hence the confidence interval is (3193, 2607).

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The quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) is 3x^3 + 6x^2 + 8x + 24.

To find the quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) we can use polynomial long division method.

First, divide 3x^4 by x and write down the quotient (3x^3)

Now, we multiply (x - 2) by 3x^3 and subtract it from 3x^4 - 4x^2 + 8x - 1

(3x^4 - 4x^2 + 8x - 1) - 3x^3(x - 2)

= 3x^4 - 4x^2 + 8x - 1 - 3x^4 + 6x^3

= 6x^3 - 4x^2 + 8x - 1

Now, we divide 6x^3 by x and write down the quotient (6x^2)

Now, we multiply (x - 2) by 6x^2 and subtract it from 6x^3 - 4x^2 + 8x - 1

(6x^3 - 4x^2 + 8x - 1) - 6x^2(x - 2)

= 6x^3 - 4x^2 + 8x - 1 - 6x^3 + 12x^2

= 8x^2 + 8x - 1

Now, we divide 8x^2 by x and write down the quotient (8x)

Now, we multiply (x - 2) by 8x and subtract it from 8x^2 + 8x - 1

(8x^2 + 8x - 1) - 8x(x - 2)

= 8x^2 + 8x - 1 - 8x^2 + 16x

= 24x - 1

Now, we divide 24x by (x - 2) and write down the quotient (24)

Remainder is

24x - 1 - 24(x - 2) = 47

Finally, we have found that the quotient of the polynomial division is 3x^3 + 6x^2 + 8x + 24 and the remainder is 47. So the final answer is

(3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) = (3x^3 + 6x^2 + 8x + 24)(x - 2) + 47

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