When can we say that a function is continuous?

y = x^2 represents a nonlinear function.

A linear function has the form of y = mx+b where m and b are constants and x is variable, the graph of a linear function is always a straight line. A nonlinear function is any function that is not linear, the graph of a nonlinear function is not a straight line.

y = x^2 is nonlinear because the variable x is squared, a quadratic function and its graph is a parabola.

y=2x is a linear function and its graph is a straight line, increasing linearly with x.

y = x is also a linear function and its graph is also a straight line, increasing linearly with x.

y = x+2 is a linear function and its graph is also a straight line with a y-intercept of 2, increasing linearly with x

So, y = x^2 represents a nonlinear function, and it is the correct answer.

The points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

The Cartesian coordinate system on a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates.

These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph).

The orientation of these two axes is perpendicular.

The graph's exact center is marked by the origin (O).

So, we have the points:

(4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5)

Now, the graph is as follows:

(Refer to the graph attached below)

Therefore, the points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

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Answer:A,D,E,F

Step-by-step explanation:A(x) = x4 - 2x³ - 21x² +22x + 40= A,D,E,F

Comparing the provided equations in the options with the slope-intercept form y = mx + c and with the intercept value given , The answer is option A and B.

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

In a linear equation, the slope (also called the gradient) is a measure of the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis. The slope of a linear equation can be represented as m in the form of y = mx + b, where m is the coefficient of x, and b is y-intercept. The y-intercept is the point where the line crosses the y-axis, which can be represented by the value of b in the form of y = mx + b.

intercept (c) = 3units

option A also has 3 as c

option B also has 3 as c

when compared with y= mx + c

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The time period of fm wave is found to be  1.13 x 10⁻⁸ sec.

The quantity of waves that pass a fixed point in a unit of time is referred to as frequency in physics.

For the given frequency of a fm wave =  8.85 × 10⁷ hertz.

Time period = 1 / frequency

T = 1 / 8.85 × 10⁷

T = 0.112 x 10⁻⁷ sec

T = 1.13 x 10⁻⁸ sec

Thus, the period of the fm wave is found to be  1.13 x 10⁻⁸ sec.

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Dilating a shape with a scale factor is a process of enlarging or shrinking a shape.

Scale factor the research between two corresponding length area of the volumes of two similar figure it is used to compare the size of one figure to another as well as the enlarge of reduced to size of a figure the scale factor is expressed as the ratio searches one it's to one.

It can be done using a compass or a ruler. First, measure the length of the side of the shape and calculate the scale factor. Then, use the compass or ruler to draw a line that is the length of the side multiplied by the scale factor. Finally, join the new line with the other side of the shape to complete the dilation.

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The product of the operation -1.2 x (-1.2) is 1. 44

Multiplication is simply described as one of the four primary mathematical operations of arithmetic, other are;

The result of any multiplication operation is called a product.

Also, to multiply simply means to add equal group of numbers or variables.

It is also important to note the following multiplication of mathematical signs, we have;

From the information given, we have that;

-1.2 x (-1.2)

To find the product, expand the bracket, we get;

- 1.2 × - 1.2

Multiply the values, we get;

1. 44

Hence, the value is 1.44

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The equation of the perpendicular line is y = -7/2(x + 5) + 2

From the question, we have the following parameters that can be used in our computation:

y=2/7x-8

Also, from the question;

We have the following points

Point = (-4, 2) i.e.  (x, y) = (-4, 2)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2/7

This means that the slope is 2/7

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -7/2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -7/2

(x₁, y₁) = (-4, 2)

So, we have

y = -7/2(x + 5) + 2

Hence, the line has an equation of y = -7/2(x + 5) + 2

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Answer:

A and B

Step-by-step explanation:

theres one input for each ouput

The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The linear equations here as y = -x + 2 & y = 3x + 6

For a system of two linear equations and two variables, there can be no solution, exactly one solution, or infinitely many solutions (just like for one linear equation in one variable). An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

But clearly the two equations are not coincident and also not parallel

Thus the system of equations must have exactly one unique solution.

Therefore solving for the equations

y = -x + 2

y = 3x + 6

Substracting the two equations we get -4x-4=0 or x=-1

∴ y=1+2

     =3

Hence, The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.

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Answer:

Step-by-step explanation:

show picture

To multiply two mixed numbers, you can convert them to improper fractions and then multiply the numerators and denominators separately.

2 1/5 can be written as (2 x 5 + 1) / 5 = 11/5

2 2/3 can be written as (2 x 3 + 2) / 3 = 8/3

So the product of 2 1/5 x 2 2/3 is (11/5) * (8/3) = 88/15 which is equivalent to 5 8/15 or 5.533 repeating (if you want to express it as decimal)

You can simplify 88/15 by dividing both numerator and denominator by the greatest common divisor (GCD) which is 1 in this case, so the final result is 88/15.

Let angle D be an acute angle such that  D=0. 33. The measure of angle D is 70.7 degree.

Acute Angle:

An angle is formed when two rays meet at a vertex. If this angle is less than 90°, it is called an acute angle. In the image below, the angle formed between "Ray 1" and "Ray 2" is acute. Bisecting a right angle also creates two acute angles.

Inverse Cosine :

Inverse cosine is the important inverse trigonometric function. Mathematically, it is written cos-1(x) and is the inverse of the trigonometric cosine cos(x). Note that arc cosine is not the reciprocal of cos x. There are six inverse trigonometric functions like sin-1x, cos-1x, tan-1x, csc-1x, sec-1x, cot-1x. The arc cosine is used to determine angular measurements from the trigonometric ratio cos x values.

According to the question:

To approximate the measure of angle D, we will need to use the inverse cosine function on our calculator. All calculators vary, so I am not sure where you would find the button for it on your calculator. However, I know many calculators have it so you click the second button, then cos

 cos(D) = 0.33

⇒ D = cos^-1 (0.33)

⇒ D = 70.7 degrees

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According to our answer to the given question of ratio, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or

$ten (2 x $5).

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equation two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

There is a total of $30.

Gertie shares out $30 in such a 2:4 proportion.

The maximum number of outstanding shares is 6, which is 2 plus 4.

$5 per share is the result of dividing $30 by six.

Two parts, or $ten (2 x $5), go to Jasmine.

Holly will receive four $5 shares, for a totaling of $20.

According to our answer to the given question, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or $ten (2 x $5).

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Answer:

1,107 is your answer

Step-by-step explanation:

Triangle ABC and Triangle DEF are congruent, as stated, of 7:3 with scale factor of isocellus triangle.

Find scale factor?

According to the scale factor, the ratio obtained by dividing the equivalent side lengths of like figures.

Triangle ABC and Triangle DEF are congruent, as stated.

Similar figures have equivalent angles and sides that are equal.

To determine the scale factor,

You must ascertain the ratio between the triangle's corresponding sides.

In order to obtain the sides of the other triangle, multiply each side of the first triangle by the same number.

What we're looking for is the scale factor, which is represented by the number.

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The equation can be used to find the number of pie he need to sell to break event.

c. 5x + 30 = 12x

Given :Mrs. Ramirez is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies. She plans to sell the pies for $12 each.

To Find: Which equation can be used to find the number of pies she needs to sell to break even.

Solution:

Let no. of pies be x

It cost her $5 to make each pie

So, cost of making x pies = 5x

Since there is a one-time cost of $30 for baking supplies.

So, total cost for her is 5x+30

If she sells each pie for $12

Then cost of pies = 12x

Now,

The equation can be used to find the number of pies she needs to sell to break even:

c) 5x+30=12x

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The 3-4-5 rule is a rule that states that in any right triangle, the ratio of the length of the two shorter sides will be 3:4 if the length of the hypotenuse is 5.

To determine if a triangle is a 3-4-5 triangle, you can use the following steps:

Divide the length of the hypotenuse by 5: 10 / 5 = 2

Multiply the result by 4: 2 x 4 = 8

Multiply the result by 3: 2 x 3 = 6

So, the triangle has sides of 6, 8, and 10 units, which is a multiple of 3-4-5 triangle and it is a right triangle.

Note that not all triangles that have sides in the ratio 3:4:5 will be a right triangle, only those that have a 90-degree angle are considered as a right triangle.

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if pp is sufficient for q  is not equivalent to P <-> q for p and q conditional statement

The true statements for the conditional statement p → q are;

If p then q

p, therefore q

q, if p

p is enough condition for q

Reason for the above selection

The conditional statement p → q is read as If p then q

The deductive validity of the conditional statement is; p, therefore q

The conditional statemen, p → q also means;

1) q, if p

2) q, provided p

3) p, only of q

4) p implies q

5) q whenever, p

6) p is enough condition for q

7) q is a necessary condition for p

Therefore, the correct statements are;

If p then q

p, therefore q

q, if p

p is enough condition for q

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In mathematics, an algebraic expression is an assertion built up from integer constants, variables, and algebraic operations. This article is all about to Monomials, Binomials, and Polynomials.

1. Monomial

An algebraic expression that carries only one non-zero term is known as a monomial. A monomial is a just like a type of polynomial, like, binomial and trinomial, which is an algebraic expression having only a one single term, which is a non-zero.

It comprises of only a single term which makes it easy to do the operation of addition, subtraction, and multiplication.

2. Binomial

An algebraic expression that comprises of two non-zero terms is known as a binomial. It is expressed in the form equation ax ^m + bx ^n where a and b number, x is variable, m and n are nonnegative distinct integers.

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A. The radius of the sun in scientific notation is 9.66 x 10^8 kilometers and the radius of Earth is 6.37 x 10^3 kilometers.

B. To find the surface area of a sphere with a given radius, we can use the formula S = 4πr^2.

The surface area of the sun is 4π(9.66 x 10^8)^2 = 1.4 x 10^18 square kilometers.

The surface area of Earth is 4π(6.37 x 10^3)^2 = 5.1 x 10^10 square kilometers.

C. To find the ratio of the surface area of the sun to the surface area of Earth, we can divide the surface area of the sun by the surface area of Earth.

The ratio of the surface area of the sun to the surface area of Earth is: 1.4 x 10^18 / 5.1 x 10^10 = 2.7 x 10^7.

This ratio tells us that the surface area of the sun is 2.7 x 10^7 times larger than the surface area of Earth.

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An expression to find the perimeter of this triangle is P = 3x + 10.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

Given the following parameters:

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

Perimeter of triangle, P = x + 4 + x + 6 + x

Perimeter of triangle, P = 3x + 10

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Answer:34.5

Step-by-step explanation:

Answer: -21x-8

Step-by-step explanation:

Combine the like terms

Answer: 21d^7

Step-by-step explanation:(7x3) x d^(5+2)
= 21 d^7

Answer:

(7d^5)(3d^2)

7*3 = 21

5+2 = 7

21d^7

The approximate annual cost of raising a child born in 2013 at age 17 is 15230.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.

b) (8, 12800) and (14, 14420)

Here, slope m=(14420-12800)/(14-8)

= 1,620/6

= 270

Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get

12800=270(8)+c

12800=2160+c

c=10640

Substitute m=270 and c=10640 in y=mx+c, we get

y=270x+10640

c) Now, substitute x=17 in y=270x+10640, we get

y=270×17+10640

y=15230

Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.

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The number of cubic yards of each component needed are 3.99 cubic yards of cement, 7.97 cubic yards of sand  and 15.94 cubic yards of gravel

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another

Since a total of 18.6 cu yd of concrete is required and the total amount of these components must be 1½ times the volume of concrete needed. We can say:

total amount of these components = 1½ × 18.6 cu yd = 27.9 cu yd

Also, since the ratio of cement to sand to gravel for this application is 1:2:4. We have:

Total share = 1 + 2 + 4 = 7

cement = 1/7  × 27.9 =  3.99 cubic yards

sand  = 2/7  × 27.9 =  7.97 cubic yards

gravel = 4/7  × 27.9 =  15.94 cubic yards

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The distance between the line and the point is 8 units.

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given a line L,

and the equation of a line is y = 1

actual equation of line is ax + by +c = 0

equation of line is 0x + y - 1 = 0

here a = 0, b = 1 and c = -1

and point T(-1, -7)

distance between line and the point is d = [tex]\frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2} }[/tex]

x₁ = -1, y₁ = -7

|ax₁ + by₁ + c| = |0(-1) + 1(-7)  +(-1)|

|ax₁ + by₁ + c| = 8

√(a² + b²) = √(0² + (1)²) = 1

distance between line and the point is d = 8/1 = 8 units

Hence the distance is 8 units.

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