The diagram shows a quadrilateral ABCD with each of its sides extended.
AB = AD
Show that ABCD is a kite. Give a reason for each stage of your working
(The diagram is attached)
Thanks, by neve124

Answer:

See below

Step-by-step explanation:

From 5 to 10 mugs is 5 mugs  

   These cost  110 - 67.50 = 42.50

        So each mug costs 42.50 / 5 = 8.50 each  

              With a 'base cost' of 25 dollars

   (Base cost might be artwork, design, order processing, shipping or whatever.....but this amount is added to each order)

(As a check    20 mugs would be   25 + 20 (8.50) = 195   <====yep

150 mugs will then be 25   +  150 ( 8.50) = 1300 dollars

In these linear expressions one is equivalent which is  3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.

Alternatively pluging; we will see that none of the exponents can be greater than 1.

2x - 3(1.3x - 2.5) = 5.9x + 7.5

2x -3.9x + 7.5 = 5.9 + 7.5

-1.9x + 7.5 ≠  5.9 + 7.5

thus linear expression is not equivalent.

3- 2( - 2.6x + 2.1) = 5.2x - 1.2

3 + 5.2x -  4.2 = 5.2x - 1.2

5.2x - 1.2 = 5.2x - 1.2

thus, linear expression is equivalent.

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The function is given below

What is a function?

The value of a function f at an element x of its domain is indicated by f(x); the numerical value resulting from the function evaluation at a given input value is expressed by substituting x with this value; for example, the value of f at x = 4 is denoted by f(x) (4). When the function is not named and is represented by an expression E, the function's value at, say, x = 4 can be expressed by E|x=4. In science, engineering, and the bulk of the mathematical disciplines, functions are commonly used. Functions are claimed to be "the central objects of research" in most branches of mathematics.

The given function is

f(x) = x - 6/2

The function in gf is

g{f(x)} = √(x - 6/2) - 4

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The value of the required composite function is [tex]g(f(x))=\sqrt{x-\frac{6}{2} } -4[/tex].

What is a composite function?

When the result of one function is utilized as the input for another, a composite function is created.

Given that:

[tex]f(x)=x-\frac{6}{2}[/tex] and [tex]g(x)=\sqrt{x}-4[/tex]

To find the composite function [tex]g(f(x))[/tex], it is required to use the output of the first function as the input of the second function. It means that replace [tex]x[/tex] by  [tex]f(x)[/tex]  in the second function as:

[tex]g(x)=\sqrt{x}-4\\g(f(x))=\sqrt{f(x)}-4[/tex]

Now, substitute the value of  [tex]f(x)[/tex] on the right side of the above equation as:

[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]

Hence, the required answer is:

[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]

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Answer:

B' (-3,11)

Step-by-step explanation:

B(2,3)  The rule is saying subtract 5 from x and 8 add to y

(2 -5, 3 + 8)

(-3,11)

The number of cups of bananas is represented by x

The number of cups of strawberries is represented by y

Note that:

27/5 cups of strawberry is used for 27/25 cups of banana

1 cup of strawberry is used for x cups of banana

x = 27/25 ÷ 27/5

x = 27/25 x 5/27

x = 1/5

1/5 cups of banana is used for 1 cup of strawberry

Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:

y = 5x

where k = 5

The constant of proportionality = 5

Answer:

14

Explanation:

To evaluate the expression, we need to replace x by 4. So, the expression is equal to:

3x + 2

3(4) + 2

12 + 2

14

Therefore, the value of the expression is 14

Answer:

total distance = 654.5

Total gas used = 27.5

Distance per gallon = 654.5 ÷ 27.5 = 23.8

We drove 23.8 miles for each gallon of gas

Answer: 2/3

Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.

Answer: 2/3

Step-by-step explanation:

total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)

Given:

The number sentence for 4 and n

Required:

We have to find the given sentence

Explanation:

4 and N, simply means you mixed them up, you sum them up

your result is 9, 4+N=9

Required solution :

4+N=9

The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively

The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.

mean= sum of data in the collection/ number of data

= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)

standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data

finding (x- mean)^2 for each value of x

(20-59.125)^2=848.266

(33-59.125)^2=682.516

(44-59.125)^2=228.766

(53-59.125)^2=37.516

(69-59.125)^2=102.516

(75-59.125)^2= 260.016

(89-59.125)^2= 907.516

(90-59.125)^2= 968.766

S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =

√504.484

Therefore S.D =22.461 ( to the nearest thousandth)

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Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.

To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.

Now, total distance in race

8/18 + 16/18

= (8+16)/18

= 24/18

= 4/3

= [tex]1\frac{1}{3}[/tex] kilometers

Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

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The blue graph is represented by the equation g(x) = (x - 5)²

The possible graph that completes the question is added as an attachment

From the attached graph, we have the following parameters

Also from the graph, we have the equation of the function f(x) to be

f(x) = x²

Solving further, we can see that:

The only difference is that, f(x) is shifted to the right by 5 units

This means that

g(x) = f(x - 5)

So, we have

g(x) = (x - 5)²

Hence, the blue graph equation is g(x) = (x - 5)²

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The absolute value expressions of the echo sounder are |r - w| and |w - r|

The statement in the question is represented as

The accuracy of an echo sounder is the positive difference between ...

To solve further, we use the following representations

Depth of water reading = r

Actual depth = w

So, the statement becomes

The accuracy of an echo sounder is the positive difference between r and w

The difference can be represented as

Difference = r - w or Difference = w - r

Represented as absolute value expressions

Difference = |r - w| or Difference = |w - r|

Hence, the expressions are |r - w| and |w - r|

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Answer:

y=.25x+6

Step-by-step explanation:

Answer:

Mexico to the United States in 1947

Step-by-step explanation:

Using concept of Linear equation in two variables, we got 23 is  denomination count of 5$ bills and 21 is denomination count of 20$ bills.

Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.

The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).

It is given that 5$ bills are 2 more than 20$ bills,

so let suppose 20$ bills denomination count is x,

then 5$ bills denomination count=x+2;

It is also given that 535$ worth is summation of 5$ bills and 20$ bills

Therefore,[5×(x+2)+(20×x)]=535

On solving for x, we get x=21

Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.

Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21

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Answer:

b= -1, -6

Step-by-step explanation:

divide by common factor

then use x=- b+- sqrt b^2-4ac/2a

separate the equations and solve them

Answer:

15/8 for exact form

1.875 for decimal form

And

1 and 7/8 for mixed number form

hope this helps you!

(also already in the simplest form :)

Answer:

154 feet squared

Step-by-step explanation:

1. Divide 14 by 2

2. Use the equation pie times radius squared

3. Answer is 153 foot squared

Answer:0.0008994

Step-by-step explanation:

The given triangle is a right angled triangle having the follwoing sides;

Hypotenuse = x (longest side)

Opposite = 14 (side facing the given acute angle)

Theta = 15 degrees

Using the SOH trigonometry identity;

sin 15 = opposite/hypotenuse

sin15 = 14/x

x = 14/sin15

x = 14/0.2588

x = 54.09

x is approximately equal to 54.1. Option B is coorect

We are given that the length of a rectangle is 3 inches greater than the width.

Let us draw a rectangle and label the width and length.

Part A:

Let the width of the rectangle is x inches.

Then the length of the rectangle is (x + 3) inches.

Now recall that the area of a rectangle is given by

Where L is the length and W is the width of the rectangle.

Therefore, the above polynomial represents the area of the rectangle.

Part B:

We are given that the width is 4 inches.

Substitute the width (x = 4) into the equation of the area that we found in part A.

Therefore, the area of the rectangle is 28 square inches.

Answer:

brand A. The bag weights for brand A have less variability than the bag weights for brand B

The number and type of roots of each quadratic function are:

The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.

The types of roots of a quadratic equation are;

The roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}[/tex]

Where:

b² - 4·a·c is known as the discriminant of the quadratic equation.

The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:

The given functions are:

Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;

a = 1, b = -9, and c = 21

The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0

The quadratic equation therefore, has complex roots.

The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;

The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;

[tex]x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}[/tex]

x = -8 + 8·√2 or x = -8 - 8·√2

The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;[tex]x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}[/tex]

[tex]x = \dfrac{28 }{-8}= -3.5[/tex] and [tex]x = \dfrac{-48 }{-8}= 6[/tex]

The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0

Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots

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Answer:

Brainliest Answer?

( 7 / 8 ) seconds

( 77 / 4 ) feet

Step-by-step explanation:

The question is a bit confusing but I will do it both ways. I will assume that you made a mistake copying over the function because the graph s( t ) is linear. Linear functions have a maximum value of infinity because it is an odd-degree polynomial.

Assume that s( t ) = - 16t² + 28t + 7;

The equation forms an upside-down parabola which means it has a maximum value.

Complete the square to get the axis of symmetry and the maximum value of the parabola or use my very cool formula. The variables h and k represent the axis and max respectively.

ax² + bx + c = a( x - h )² + k;

ax² + bx + c = a( x - ( - b / 2a ) )² + c - ( b² / 4a );

ax² + bx + c;

Take a as a factor.

a( x² + ( b / a )x + ( c / a ) );

Add and subtract the square of ( 1 / 2 ) of ( b / a ). This is called completing the square because it forms a perfect square trinomial.

a( x² + ( b / a )x + ( b / 2a )²  - ( b / 2a )² + ( c / a ) );

Factorise the trinomial.

a( ( x + ( b / 2a ) )² - ( b / 2a )² + ( c / a ) );

Use the distributive property of multiplication.

a( x + ( b / 2a )² + a( ( c / a ) - ( b / 2a )² );

a( x + ( b / 2a )² +  a( ( c / a ) - ( b² / 4a² ) );

Simplify the fractions.

a( x + ( b / 2a )² + c - ( b² / 4a );

Substitute the values.

- 16( t - ( - 28 / 2( - 16 ) )² + 7 - ( ( 28 )² / 4( - 16 ) );

Time is the x-axis so we need to solve for the axis of symmetry.

h = ( - 28 / 2( - 16 ) );

h = ( - 28 / - 32 );

Simplify the fraction.

h = ( 7 / 8 );

Maximum height is the parabola's y of the vertex.

k = 7 - ( ( 28 )² / 4( - 16 ) );

k = 7 - ( ( 28 )( 28 ) / - 64 );

k = 7 - ( 784 / - 64 );

k = 7 - ( - 49 / 4 );

k = ( 28 / 4 ) + ( 49 / 4 );

k =  77 / 4;

Answer:

1 hour

Step-by-step explanation:

Since the penguin supposedly walks a 1 mile per hour, it would take one hour to achieve 1 mile

Answer: the radius of a cylinder is 4 cm

Step-by-step explanation:

[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]

The total surface area:

[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]

Divide both parts of the equation by 2π:

[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]

Answer:

r ≈ 4 cm

Step-by-step explanation:

Total Surface Area of a cylinder

A = Base Area x 2 + Lateral Surface Area

A = 2(πr²) + 2πrh

where r = radius of base and h = height of cylinder

Solving for r we get

[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]

Given h = 10 cm and A = 325 we get

[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]

[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]

= [tex]\sqrt{324.09}[/tex]

= 18.0025

1/2 x 18.0025 ≈ 9

So r ≈  9 - 10/2 = 9 -5 = 4

r ≈ 4 cm

Answer:

Step-by-step explanation:

Since the population quadruples each day, the population for the subsequent day would be 4*(population of the previous day).

Thus, the evolution of the population value takes the form of a geometric progression, with a common ratio, r = 4

The n-th term of a geometric progression is given by:

[tex]a_{n}[/tex] = [tex]ar^{n-1}[/tex]             (1)

Where a is the 1st term of the progression.

From (1), our population would generally take the form:

[tex]P_{d}[/tex] = [tex]P_0r^{d-1}[/tex]             (2)

In this case, the initial value (1st term) [tex]P_{0}[/tex] = 120.

So putting r and  [tex]P_{0}[/tex] into  (2):

P(d) = 120*([tex]4^{d-1}[/tex])

Noting that 4  = 2²:

P(d) = 120*([tex]2^{2(d-1)}[/tex])

FOR d = 8:

P(d) = 120*([tex]2^{2d-2}[/tex])

becomes:

P(8) = 120*([tex]2^{2(8)-2}[/tex])

P(8) = 120*([tex]2^{16-2}[/tex])

P(8) = 120*([tex]2^{14}[/tex])

P(8) = 120*(16,384)