1/2 - 1/7 =
3/5 - 1/2

The area of the trapezium will be = 90[tex]mm^{2}[/tex]

According to the figure of the trapezium =

Let us consider the length of base a = 5mm

length of base b = 13mm

height h of the trapezium = 10mm

According to the formula of the area of trapezium

= (1/2) x h x (a + b)

= (1/2) x 10 x (13 + 5)

= 5 x 18

= 90[tex]mm^{2}[/tex]

Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]

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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm

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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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:

11) KF = DB

12) DC=YZ

13) <C = <W

14) <S and <K

Step-by-step explanation:

11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.

12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.

13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.

14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.

Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.

The point of intersection of f(x) and [tex]f^{-1}[/tex](x)   is (3, 3)

"It defines a relation between input and output values."

"In function, for each input there is exactly one output."

"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"

For given question,

A function  f(x) and its inverse function [tex]f^{-1}(x)[/tex],  are both plotted on the same coordinate plane.

We know that the inverse function [tex]f^{-1}(x)[/tex]   is the mirror image of the function f(x.)

This means, both the functions must be symmetric about the line y = x.

The curve of inverse function [tex]f^{-1} (x)[/tex]  would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)

And both the functions intersect each other only on y = x

The point which satisfy the line y = x is (3, 3)

Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)

The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).

A.(0, –2)

B.(1, –1)

C.(2, 0)

D.(3, 3)

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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

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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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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Answer:

Step-by-step explanation:

3x+23/54

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:

£115

Step-by-step explanation:

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: x=-3

Step-by-step explanation:

Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].

What is the slope of line?

The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.

The slope is usually represented by the letter [tex]m[/tex].

Here given that,

The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].

Let the linear function is

[tex]y=mx+b[/tex]

[tex]x=2,y=0[/tex]

Then

[tex]0=m(2)+b\\\\2m+b=0[/tex]      .......[tex](1)[/tex]

And for

[tex]f(4)=-6\\x=4,y=-6[/tex]

[tex]-6=m(4)+b\\\\4m+b=-6[/tex]       ......[tex](2)[/tex]

Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get

In equation [tex](1)[/tex]

[tex]b=-2m[/tex]      ........[tex](*)[/tex]

Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]

[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]

Put [tex]m=-3[/tex] in [tex](*)[/tex] equation

[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]

Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].

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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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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.)

The probability their average salary is less than $33,200 is = 0.6554

Given that,

Mean = $32,000

Standard deviation = $3,000

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Standard deviation (SD) is a widely used measurement of variability used in statistics. It shows how much variation there is from the average (mean). A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.

The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from,

z = (x- μ) / σ           (Equation-1)

Where,

x=raw score,

μ=mean,

σ=standard deviation

μ=32,000,

σ=3,000

Average salary is less than $33,200

x < 33,200

We can substitute values in Equation-1,

z = (33,200-32,000)/3000

z = 1200/3000

z = 0.4

Using the normal distribution table as a guide,

P(x < 33,200) = P(z < 0.4)

P(x < 33,200) = 1-P(z>0.4)

P(x < 33,200) = 0.6554

Therefore,

The probability their average salary is less than $33,200 is = 0.6554

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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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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.

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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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 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

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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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 correlation of the scatterplots are defined as;

The math and English scores show; A positive correlation.

The math and chemistry scores show; A negative correlation

In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.

A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.

A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.

No correlation means there is no relationship between the two variables.

Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.

Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.

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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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If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees

The length of the blood stain = 3 cm

The width of the blood stain = 1.5 cm

The equation for measuring the angle of impact is

sin (angle of impact) = The width of the blood stain / The length of the blood stain

Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)

Substitute the values in the equation

Angle of impact = sin^-1(1.5 / 3)

= sin^-1(0.5)

= 30 degrees

Therefore, the angle of impact is 30 degrees

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After solving the equation the linear equation is x = 27/5 , y = 7/5.

What do you mean by linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".

Given system of equation:

7x - 7y = 28 ..........(1)

2x - 7y = 1 .............(2)

Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)

7x - 7y = 28

7x - 28 =7y .............(3)

Substitute this value in equation (2)

2x - (7x - 28) = 1

2x - 7x + 28 = 1

-5x + 28 = 1

5x = 28 - 1

5x = 27

x = 27/5

Substitute this value in equation (3)

7y = 7(27/5) - 28

7y = 189/5 - 28

7y = 49/5

y = 7/5

Therefore, x = 27/5 , y = 7/5

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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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