What is the domain of this function?(–10,3)(3,2)(0,–8)(8,–4)(7,6)

If the slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, If the slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary.

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Solution of x is  1± 5√2  for the given quadratic equation.

What is quadratic equation?

Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.

Main body;

11)

x² = 2x +48

The given is an quadratic equation:

solution of this can be found out using quadratic formula:

x =(-b ±[tex]\sqrt{b^{2} -4ac}[/tex])/2a

for this ,

x² -2x -48 = 0

a = 1

b= -2

c = -48

x =( 2±√ (4- 4*1*-48))/2

x = (2±√200)/2

x = 1± 5√2

Hence solution of x is  1± 5√2.

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Answer:

Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.

The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:

$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$

$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$

Substituting this expression for $h$ into the formula for the area of the triangle, we get

$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$

Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.

Step-by-step explanation:

The standard height of the television is 12 inches.

What are ratios?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other.

The given ratio is 4:3. Let us take a variable 'x' such that 4x=16 and 3x=height.

We find x from 4x=16

x=4

Now putting the value of x in 3x, we get 12 inches.

Therefore, the height of the television is 12 inches.

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The standard height of the television is 12 inches.

The aspect ratio of a screen is the ratio of the width to the height. In the case of a television screen with a 4:3 aspect ratio, the width is 4 units and the height is 3 units.

If we let "h" represent the height of the television screen, we can set up the following equation:

4:3 = 16:h

To solve for "h", we can cross-multiply to get:

4h = 48

Dividing both sides by 4, we get:

h = 12

So the height of a television screen that is 16 inches wide and has a 4:3 aspect ratio is 12 inches.

what is aspect ratio?

The aspect ratio of a screen is the ratio of the width to the height of the viewable area of the screen. It is usually expressed as two numbers separated by a colon, such as 16:9 or 4:3.

Aspect ratios are used in a variety of applications, including television screens, computer monitors, and movie theaters. Different aspect ratios are used for different types of content, and some screens can be adjusted to display content in different aspect ratios.

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y = | x + 5 | - 4

You subtract 4 outside the abs val to move the graph down.

You add 5 inside the abs val to move the graph left.  (Inside translations are the opposite of what you'd expect.)

Answer:

Length of the rectangle is 18 ft when its width is 4ft

Step-by-step explanation:

Let us assume that the length is represented by l.

Let us assume that the width is represented by w.

As given

The length of the rectangle varies inversely with its width.

Thus

L x 1/w

l=k/w

Where k is the constant of proportionality .

As given

If the

length of the rectangle is 6 feet when the width is 12 feet,

l=6, w=12

putting the values in l = k/w

6 = k/12

k = 12 x 6

k=72

As given

width is 4ft

k= 72, w = 4

Putting the values in, L = k/w

                                   L= 72/4

                                    L=18 ft

Therefore the  length of the rectangle is 18 ft when its width is 4ft

Hope this helps You

Answer:

Step-by-step explanation: By using the verticle line test, because the line has passed more than one point, it is NOT A FUNCTION.

Answer:

C) is 20

Step-by-step explanation:

3 inches x 5= 15

so we do the same with 4 minutes

4 minutes x 5= 20

Answer:

x^3-2x^2+6x+1

Step-by-step explanation:

x^3+2x-1-2x^2-4x+2

collect like terms

x^3-2x^2+2x+4x-1+2

x^3-2x^2+6x+1

Answer:

48 buckets of gravel

15 buckets of gravel

Step-by-step explanation:

The required diameter of the dilated graphic is 8 inches.

Scale factor is the  ratio  of comparing sides on two comparative figures. In math, scale factor is utilized to decide how often bigger or more modest one item or figure is to another.

We have,

diameter of circular banner = 4 feet

scale factor = 1/6

Then, the diameter of circular sticker = 4(1/6) = 4/6 feet.

In inches, we know

1 foot = 12 inches

4/6 feet = 12(4/6) = 8 inches

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Answer:

R200

Step-by-step explanation:

R200

a) The probability of selecting three marbles where one is blue and two are green is of: 0.0818 = 8.18%.

b) The probability of selecting one blue marble and then selecting three red marbles is of: 0.0152 = 1.52%.

c) The probabilities were obtained dividing the number of desired outcomes by the number of total outcomes, and all the possible combinations were considered.

The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.

The outcomes with one blue and two green are given as follows:

Hence a multiplication for 3 is used for the probability, as follows:

p = 3 x 3/12 x 4/11 x 3/10 = 0.0818 = 8.18%.

For blue then three red, the outcomes are given as follows:

Thus the probability is of:

p = 3/12 x 5/11 x 4/10 x 3/9 = 0.0152 = 1.52%.

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The line that goes through the point (2,-2) and is perpendicular to the line shown by y=2/5x +2 will have the slope intercept equation 5x+3y=6.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

Here,

Slope of the line given=2/5

Slope of the line perpendicular=-5/2

coordinates=(2,-2)

y=mx+b

-2=-5/2*2+b

b=3

y=-5/2x+3

3y=-5x+6

5x+3y=6

The equation in slope intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2 will be 5x+3y=6.

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In particular, despite the language overlap, a glide reflection is not a reflection and a (ordinary) reflection is not a glide reflection.

There are many intriguing accounts of what occurs when you mix two of them together. Here are a few instances:

Each isometry may be classified as belonging to one of the five classes listed below.

The identity is the combination of two reflections along the same line.

Translation is the combination of two reflections in dissimilar but related directions. Rotation is the result of two reflections in non-parallel lines.

A gliding reflection is made up of a reflection over a line plus a translation along a non-perpendicular line (and not a reflection).

A reflection is made up of a translation along a perpendicular line and a reflection across a line (and not a glide reflection).

There are fascinating things to say about what occurs when you combine two isometries dependent on the types of the isometries that you combine, but it does not change the fact that the five types are all distinct from one another. I could go on, but I think you get the point now.

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Answer:

22

Step-by-step explanation:

we can set this up and make the unknown number X

32-x=10

Subtract 32 from both sides

32-x=10

-32.  -32

-x= -22

Divide both sides by -1

-x=-22

/-1.  /-1

x=22

Hopes this helps

Answer:

Step-by-step explanation:

3x+23/54

The interest rate would be 13%.

What is the simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.

To find the interest rate, we can use the formula for simple interest:

I = Prt

where I is the amount of interest earned, P is the principal (the initial amount of money deposited), r is the interest rate, and t is the time in years.

In this case, we know that I = $3,900, P = $10,000, and t = 3 years. We can use this information to solve for r:

I = Prt

$3,900 = $10,000r3

r = $3,900/($10,000*3)

r = 0.13 or 13%

Hence, the interest rate is 13%.

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Waterworks must produce more than 4 and fewer than 11 paddleboards.

What do you mean by polynomial?

A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and trinomial.

It is given that Waterworks is a company that manufactures and sells paddleboards. Its profit​ P, in hundreds of dollars​ earned, is a function of the number of paddleboards sold​ x, measured in thousands. Profit is modeled by the function ​

[tex]p(x) = -3x^{3}+45x^{2} -132x[/tex]

zeroes of the p(x) will show the quantity at which profit = 0 i.e. breakeven

Let p(x) = 0

[tex]-3x^{3} +45x^{2} -132x =0[/tex]

-3x ([tex]x^{2} -15x+44[/tex]) = 0

-3x ([tex]x^{2} -11x-4x+44[/tex] ) = 0

-3x (x(x-11) - 4(x-11)) = 0

-3x (x-11) (x-4) = 0

-3x = 0 or x-11 = 0 or x-4=0

x = 0,11,4

So,profit is obtained when 4<x<11.

Therefore,  Waterworks must produce more than 4 and fewer than 11 paddleboards.

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By probability ,181753 are  ways are there to distribute the coupons so that at least one woman receives a coupon.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                                        Statistics describes the examination of events subject to probability.

Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:

= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men

         = ( 20 10 ) - ( 15 10 ) = 184756 - 3003

          = 181753

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The complete question is -

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.

(a) If the coupons are identical, how many ways are there to distribute the coupons so that at least one woman receives a coupon?

By probability ,181753 are  ways are there to distribute the coupons so that at least one woman receives a coupon.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

Statistics describes the examination of events subject to probability.

Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:

= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men

        = ( 20 10 ) - ( 15 10 ) = 184756 - 3003

         = 181753

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For the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that the expression is,10of 0.9, and its simplification is obtained as 90.

We have to find out why Juliet is incorrect.

Juliet is incorrect because when any decimal value is multiplied by 10 the obtained value is increased by its one's place,

=10 × 0.9

=9

Thus, for the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.

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Answer:

Statement 2 is a lie

Step-by-step explanation:

Statement 1 = TRUE

[tex]13^{2} * 13^{x} = 13^{6} \\13^{2+x} =13^{6}\\2 + x = 6\\x = 6 - 2\\x = 4[/tex]

x = 4 is True

Statement 3 = TRUE

[tex]5^{y} * 5^{6} =5^{12} \\5^{y+6} = 5^{12} \\y+6 = 12\\y=12 -6\\y =6[/tex]

y = 6 is True

Statement 2 =  LIE

[tex]m^{y} *m^{z} = m^{x} \\m^{6} *m^{z} = m^{4}\\m^{6+z} = m^{4}\\6 + z = 4\\z= 4-6\\z= -2[/tex]

z = -2 is Lie

Answer: x=-3

Step-by-step explanation:

Therefore ,the domain and range of this graph  f(x)=x^5+x^2

Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R

A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.

Here,

The domain is all values of x that make the expression defined.

Interval Notation:

(−∞,0)∪(0,∞)

=>(-∞,∞)

The Range is all values of y that make the expression defined.

Interval Notation:

(−∞,0)∪(0,∞)

=>(-∞,∞)

Therefore ,the domain and range of this graph  f(x)=x^5+x^2 Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R

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15. commulative

16. distributive, distributing the 3 to the 'a' and 'b' within the parentheses.

17. distributive, distributing the w to the variables inside of the parentheses.

The area of the triangle from the vertices is 27 square units

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

$A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .

Represent the vertices properly

So, we have

A = (2, -2)

B = (4, -2)

C = (6, -11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |2 * (-2 + 11) + 4 * (-2 + 11) + 6 * (-2 + 2)|

Evaluate the sum of products

Area = 0.5 * |54|

Remove the absolute bracket

Area = 0.5 * 54

Evaluate

Area = 27

Hence, the area of ABC with vertices is 27 square units

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The required equation of line in slope intercept form is

y = 3x + 4

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

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

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Let the taxi is driven x miles and the total cost is $y

A taxi ride costs $4, plus an additional $3 per mile

Total cost = 4 + 3x

By the problem,

y = 4 + 3x

This is the required equation of line which represents the above situation.

The graph has been attached here.

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Antelope eats 3.5kg of vegetation per day .

What are fractions?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given :

antelope eats 7kg of vegetation in 2 days

Thus ,  vegetation eated  per day = 7 / 2 = 3.5 kg

Hence , antelope eats 3.5kg of vegetation per day .

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Answer: The Commutative Law of Addition states that the order in which numbers are added does not affect the result. This means that for any two numbers a and b, we have a + b = b + a.

We can use the Commutative Law of Addition to rewrite the equation 177 + 563 = 740 as follows:

177 + 563 = 740

563 + 177 = 740

Both of these equations are equivalent to the original equation, because they represent the same mathematical statement.

Note that in the first equation, we simply reordered the terms of the original equation. In the second equation, we added the numbers in a different order, but the result is still the same.

The other equations you provided are not equivalent to the original equation and do not use the Commutative Law of Addition.

In linear equation, 1/5 min far will he travel in 1 hour .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6/8 = 3/4

1/5 min/hr *  1 hr = 1/5 min

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