In the diagram shown,
CDEF is a trapezium,
ABCF is a rectangle,
BD = 9 cm,
AB = 6 cm,
EF = 3 cm,
Perimeter of ABCF = 20 cm.
6 cm
Calculate the area of trapezium CDEF.
You must show all your working.

Answer:

The translation is (5, -6)

Step-by-step explanation:

Let us solve the question

∵ The coordinates of point Q are (4, 5)

∴ x = 4 and y = 5

∵ The coordinates of point Q' are (9, -1)

∴ x' = 9 and y' = -1

→ That means x increased and y decreased ⇒ 3rd case above

∴ The point Q is moved to the right and down

→ By using the 3rd rule above ⇒ (x + h, y - k)

∵ x + h = 9

∵ x = 4

→ Substitute x by 4

∴ 4 + h = 9

→ Subtract 4 from both sides

∵ 4 - 4 + h = 9 - 4

∴ h = 5

∵ y - k = -1

∵ y = 5

→ Substitute y by 5

∴ 5 - k = -1

→ Subtract 5 from both sides

∵ 5 - 5 - k = -1 - 5

∴ -k = -6

→ Divide both sides by -1

∴ k = 6

∵ The translation is (h, -k) in the 3rd case

∵ h = 5 and k = 6

∴ The translation is (5, -6)

We can check the rule by finding D' the image of the point D

∵ D = (-5, -2)

∵ D' = (x + h, y - k)

∵ D' = (-5 + 5, -2 - 6)

∴ D' = (0, -8) as the given point D'

∴ The translation is correct

Answer:

$54.16

Step-by-step explanation:

Answer:

This is only one that includes 12 in its quotient, other quotients are 11 and 13 so I didn't add them :)

47.6/3.9

Step-by-step explanation:

so it is a estimate to 12 not 12 exact

Step-by-step explanation:

sorry

Answer:

13 inches ; 2 inches per hour ; 48 inches

Step-by-step explanation:

Given that :

Inches of snow after 2 hours = 4 inches

Since, snow is falling steadily ;

We can infer that:

Inches of snow per hour : (4 in / 2 hrs) = 2 in / hr

Hence, rate of snow fall = 2in /hr

Inches of snow after 6.5 hours

Rate per hour * Numbee of hours

2 * 6.5

= 13 inches

Amount of snow after x hours :

Rate * x

2 * x

= 2x

Inches of snow after 24 hours

2 * 24 hrs = 48 inches

Answer:

the answer is B

Step-by-step explanation:

Step-by-step explanation:

Basically the question is asking how many multiples of 5 there are in the range 1000\leq x \leq 9999

Answer: 400000 numbers

the number we need is abcdef (a ≠ 0)

becauuse abcdef > 199999 and it is a multiple of 2.

=> 200000 ≤ abcdef ≤ 999998

=> there are: (999998 - 200000)/2 + 1 = 400000 (numbers)

Step-by-step explanation:

Answer:

The value of the entry represented by [tex]c_{41}[/tex] is 12.

Step-by-step explanation:

Let [tex]A = \left[\begin{array}{ccc}-5&3&8\\3&6&-5\\5&-9&0\\7&3&4\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}-7&-8&-5\\7&9&2\\2&5&-7\\2&8&-7\end{array}\right][/tex]. The sum of equal-sized matrices consist in the sum of each pair of corresponding elements. If [tex]C = (A-B)+A[/tex], then:

[tex]C = 2\cdot A -B[/tex] (1)

Then, [tex]c_{41}[/tex] is the element of matrix C located in the fourth row and first column and is defined by the following expression:

[tex]c_{41} = 2\cdot a_{41}-b_{41}[/tex] (2)

If we know that [tex]a_{41} = 7[/tex] and [tex]b_{41} = 2[/tex], then [tex]c_{41}[/tex] is:

[tex]c_{41} = 2\cdot (7)-2[/tex]

[tex]c_{41} = 12[/tex]

The value of the entry represented by [tex]c_{41}[/tex] is 12.

Answer:

They both will meet each other when they both have been running for 10 seconds

Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]40\ \text{ft}[/tex]

Step-by-step explanation:

Velocity of Lauren

[tex]v_l=\dfrac{24}{3}\\\Rightarrow v_l=8\ \text{ft/s}[/tex]

Velocity of Clara

[tex]v_c=\dfrac{20}{5}\\\Rightarrow v_c=4\ \text{ft/s}[/tex]

Let distance traveled by Lauren be [tex]x[/tex]

As Clara has a 40 feet head start distance she will travel is [tex]x-40[/tex]

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

The time that will have passed when they both will meet will be the same for both of them so

[tex]\dfrac{x-40}{4}=\dfrac{x}{8}\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=\dfrac{320}{4}\\\Rightarrow x=80\ \text{ft}[/tex]

Time they will meet is [tex]\dfrac{80-40}{4}=\dfrac{80}{8}=10\ \text{s}[/tex].

So, Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]x-40=80-40=40\ \text{ft}[/tex].

Answer:

7^53

Step-by-step explanation:

8x3=24

24x4=96

96/9=10.6

10.6x5=53

Answer:

7^11

Step-by-step explanation:

There is a rule for simplifying exponents: n^a + n^b = n^a+b.

The rule applies here too. 7 is the n and the exponents on top are a and b. Following the rule:

[tex] {7}^{8} \times {7}^{3} = {7}^{8 + 3} = {7}^{11} [/tex]

Then you continue this formula:

11+4-9+5 = 11

Since the end result is 11 the answer is

[tex] {7}^{11} [/tex]

Answer:

(3, -5)

Step-by-step explanation:

Can I please have brainliest?

Answer:

(3,-5)

Step-by-step explanation:

This is given if your chart goes by 1 unit, thus it goes 3 units to the right, and 5 units down (which makes it negative) therefore point c is located at (3,-5)

Answer:

Average number in a month = 46

Average number in a day = 1.5

Step-by-step explanation:

Given that:

Scientific Dr. Sparks has counted the flashes of lightning around his home for a period of 3 months.

Number of sparks counted in June = 25

Number of sparks counted in July = 51

Number of sparks counted in August = 62

To find:

Average number in a month ?

Average number in a day ?

Solution:

Average of observations can be defined as the ratio of total sum of all the observations to the total number of observations.

[tex]Average = \dfrac{\text{Sum of all observations}}{\text{Total number of observations}}[/tex]

Average as per month = [tex]\frac{25+51+62}{3} =\frac{138}{3} = 46[/tex]

To find the average number in a day, we need to first find the number of days.

Number of days in June = 30

Number of days in July = 31

Number of days in August = 31

Total number of days = 92

Average as per month = [tex]\frac{25+51+62}{92} =\frac{138}{92} = 1.5[/tex]

Answer:

10.

Step-by-step explanation:

6+1/3*12=6+4=10

Answer: 10

Step-by-step explanation:

Answer:

the answer is 3 because is you go left it turns it negative

Answer:

1) x=20 degrees

2) x=25 degrees

Step-by-step explanation:

1) there is 9x if you add all of the angles together and there is 180 degrees in a triangle so 180 divided by 9 equals 20 degrees.

2)there is 7x and 5 dgress in total so we can make an equation:

7x+5=180

7x=175

x=25

Answer:

8/s

Step-by-step explanation:

do you really not no  this or are you being sarcastic

Answer:

They frosted the same amount

Step-by-step explanation:

did it on IXL and got it right ("Wonderful!")

Answer:

6 < x < 30

Step-by-step explanation:

The angle of the side AB = 48 degrees

the angle of the side AD = 2x - 12 degrees

If the angle AD is greater than zero;

  2x -12 > 0

= 2x > 12

= x > 12/ 2

= x > 6

if the maximum angle of AD is equal to angle AB, then;

= 2x -12 = 48

 2x = 48 + 12

2x/ 2 = 60 / 2

x = 30

Therefore, the range of x is; 6 < x < 30

Answer:

He would have made 105 shots!

Step-by-step explanation:

8 shots × 21 is 168

5 shots × 21 is 105

So, he scored 105/168

Step-by-step explanation:

By Law of Indices, a^m / a^n = a^(m-n).

Therefore a² / a⁸ = a^(-6).

x = -6.

Answer:

6/7

Step-by-step explanation:

Answer: 6/7

Step-by-step explanation:

Answer:

We have the following function:

f (x) = 3/8 (4) ^ x

The function is of the form:

f (x) = A (b) ^ x

Where,

A: initial amount

b: growth factor (b> 1)

x: time variable.

Answer:

f (x) = 3/8 (4) ^ x

It is an exponential function of the form:

f (x) = A (b) ^ x

Step-by-step explanation:

Answer:

Exponential growth

Step-by-step explanation:

Part (i)

-----------------

Work Shown:

(x+3)(x+2)

y(x+2) ..... Let y = x+3

y*x + y*2 ... distribute

x(y) + 2(y)

x(x+3) + 2(x+3) .... plug in y = x+3

x*x + x*3 + 2*x + 2*3 ... distribute

x^2 + 3x + 2x + 6

x^2 + 5x + 6

=====================================================

Part (ii)

-----------------

Work Shown:

We could follow the same set of steps as shown back in part (i), but I'll show a different approach. Feel free to use the method I used back in part (i) if the visual approach doesn't make sense.

The diagram below is a visual way to organize all the terms. Many textbooks refer to it as "the box method" which helps multiply out any two algebraic expressions.

Each inner cell is found by multiplying the corresponding outer terms. For instance, in the upper left corner we have 2x*2x = 4x^2. The other cells are filled out the same way.

The terms in those four inner cells (gray boxes) are:

The like terms here are -14x and -2x which combine to -16x, since -14+(-2) = -16.

We end up with the answer 4x^2-16x+7

Answer:

x=34

Step-by-step explanation:

a^2 + b^2 = c^2

16^2 + 30^2 = c^2

256 + 900 = c^2

1156 = c^2

sqrt1156 = c

34 = c

34 = x

Checked work with a calculator. Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, be safe and wash your hands. Happy Holidays.

Answer:

x = 34

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to find the missing side.

Step 2: Identify Variables

Leg a = 30

Leg b = 16

Hypotenuse c = x

Step 3: Solve for x

Answer:

undefined

Step-by-step explanation:

square root of a - # does not exist in the set of real numbers

Answer:

Otieno's age in 4 years: [tex]k+4[/tex]

Kidole's age in 4 years: [tex]k-1[/tex]

Step-by-step explanation:

[tex]k[/tex] = Otieno's age

[tex]k-5[/tex] = Kidole's age

Their ages will increase by 4 years when 4 years pass.

[tex]k+4[/tex] = Otieno's age in 4 years

[tex]k-5+4[/tex] = Kidole's age in 4 years

[tex]k-1[/tex] = Kidole's age in 4 years (after simplifying the expression)

I hope this helps!

Answer:

35000/1000 = 35m height

Answer: 35m

Step-by-step explanation: 35000mm -m

1m = 1000mm

therefore, 35000/1000

= 35m

HOPE IT HELPED U,

PLS MARK AS BRAINLIEST

^_^

Answer:

5: 4

Step-by-step explanation:

original ratio: 3:5

new ratio: 5:4

hope it helps!

Answer:

612

Step-by-step explanation:

you multiply 27 x 12 and 24 x 12, and add up the products, and you get 612

Answer: 612 Treats

Work: To find out how many treats he baked, you do 27 x 12 and 24 x 12. After doing so, you get 324 and 288. Add those up, and you get 612.

I hope this helps, and Happy Holidays! :)

Answer:

57.9532

Step-by-step explanation:

Given that:

Wholesale price = 29.95

Markup = 80%

Sales tax = 7.5%

Retail price of the game :

Price before sale tax:

Wholesale price * ( 1 + markup %)

29.95 * (1 + 0.8)

29.95 * (1.8)

$53.91

Sales tax = 7.5%

53.91 * (1 + 0.075)

53.91 * (1.075)

= 57.9532

Hence, $57.9532 will have to be paid