Work out the area of this trapezium.
15m
6m
10m

Answer:

a) V(x) = x ( 60 -2x )( 15-2x )

b) 0.55 inches ≤ x ≤ 6.79 inches

c) x ≥ 6.79 inches

Step-by-step explanation:

Given data:

No top, cardboard dimensions ; 15-in by 60-in

a) A function for the volume of the box as a function of x the Volume can be represented by this function below

= V(x) = x ( 60 -2x )( 15-2x )

where : x = height ,  ( 60 - 2x ) = length , ( 15 -2x ) = width

b) determine x so that the volume of the box ≥ 450 inches

450 = x( 60 - 2x ) ( 15 -2x ) ( solving the equation )

0.55 inches ≤ x ≤ 6.79 inches

c ) The value of x for which volume of the box is maximum

will be x ≥ 6.79 inches

The volume of the box as a function of x V(x) = x ( 60 -2x )( 15-2x )

The volume of the box as a function of x inches 0.55 inches ≤ x ≤ 6.79

The volume of the box is maximum x ≥ 6.79 inches

Given ,

The box with no top that is to be made by removing squares of width x

The corners of a 15-in by 60-in piece of cardboard.

         V(x) = x ( 60 -2x )( 15-2x )

Where : x = height ,  ( 60 - 2x ) = length , ( 15 -2x ) = width

The volume of the box as a function of x is  V(x) = x ( 60 -2x )( 15-2x )

The volume of the box ≥ 450 inches

V(x) = x ( 60 -2x )( 15-2x )

The volume of the box is at least 450 cubic inches.0.55 inches ≤ x ≤ 6.79 inches

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Answer: I think its answer choice b

Step-by-step explanation:

You're dividing so you would be subtracting the exponents

Answer:

x = 63°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ DAB is an exterior angle of the triangle, thus

x + 65 = 128 ( subtract 65 from both sides )

x = 63

Answer:m

Step-by-step explanation:m

The result of five ninths minus two sixths is two - ninths.

Let us first write the words in figures so that we can perform the required calculation;

five ninths = 5/9

two sixths = 2/6

This means that we are simply asked to subtract 5/9  from 2/6

Hence;

5/9 - 2/6, we have to take LCM. The LCM of 5/9 and 2/6 is 18. The term LCM actually means lowest common multiple of 9 and 6.

So;

[tex]\frac{10 - 6}{18} = \frac{4}{18} = \frac{2}{9}[/tex]

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Answer

the answer would be 12/54 i did the test and got 100%

Step-by-step explanation:

.

Answer:

A 7,200 is the answer. I divided 864 by 0.12 and got that answer

Answer:

answer is A

A. 7,200

Step-by-step explanation:

Hope this helps

Answer:

$53.83

Step-by-step explanation:

For David

David invested $340 in an account paying an interest rate of 2\tfrac{1}{8}2 8 1 ​ % compounded continuously.

r = 2 1/8% = 17/8% = 2.125% = 0.02125

t = 17 years

P = $340

For Compounded continuously, the formula =

A = Pe^rt

A = Amount Invested after time t

P = Principal

r = interest rate

t = time

A = $340 × e^0.02125 × 17

A = $ 487.94

For Natalie

Natalie invested $340 in an account paying an interest rate of 2\tfrac{3}{4}2 4 3 ​ % compounded quarterly.

r = 2 3/4 % = 11/4% = 2.75% = 0.0275

t = 17 years

P = $340

n = compounded quarterly = 4 times

Hence,

Compound Interest formula =

A = P(1 + r/n)^nt

A = Amount Invested after time t

P = Principal

r = interest rate

n = compounding frequency

t = time

A = $340 (1 + 0.0275/4) ^17 × 4

A = $ 541.77

After 17 years, how much more money would Natalie have in her account than David, to the nearest dollar?

This is calculated as

$541.77 - $ 487.94

= $53.83

Hence, Natalie would have in her account, $53.83 than David

Answer:

The base –2 is a negative number

Step-by-step explanation:

We need to solve the exponential expression (–2)³.

(–2)³ = -2×-2×-2

= -8

The final answer is -8. It is negative. It is because the base i.e. -2 is an even number. If the base is negative and the power is odd, the answer will be a negative number. Here, base is -2, power is 3. Hence, the correct option is (c) "The base –2 is a negative number".

Answer:

The exponent 3 is an odd number.

Step-by-step explanation:

Since the exponent (3) is an odd number, the answer will be negative. Answer: –8

Sidenote: I got this answer correct on the test :)))

Answer:

&usher jxn xviii h h bxjcu hxhxh ucjcucjj cjdnjxj j uidusijxkd

Answer:

Weight of EACH square = 0.2 pounds

18% oat = 0.36 pounds

Step-by-step explanation:

Given that:

Weight of bag = 2 lb

Percentage of oat in mix = 18%

% of the mix is oats. (a) Use the 10 by 10 grid to represent 2 lb of trail mix. Determine how much weight each square represents and label all the squares. Then, shade in 18% of the grid. (b) What is the weight of the oats in the trail mix? Show your work and label your answer. Answer:

If trail mix is represented by 10 by 10 square grid ;

Each square represents : 2 pounds / 10 = 0.2 pounds

18% of the total weight

0.18 * 2 = 0.36 pounds

Answer:

X< -3

( − ∞ , − 3 )

Answer:

graph two points at the coordinates (-6, 0) and the coordinates (-8, 3), and make a line through them.

Step-by-step explanation:

First simplify. 2x+3y= -18.,   -----------> 3y= -2x -18., ---------> y= -2/3x -6

To graph this you would first go to the coordinates (-6, 0) and put a point there. Next, you would go to the coordinates (-8, 3) and put a point there. Then make a line and you are done. That should be right.

Answer:

6.8

Step-by-step explanation:

Answer:

6.8

Step-by-step explanation:

40 / 100 = 0.4

0.4 · 17 = 6.8

Answer:

28 ft

Step-by-step explanation:

Since the shadows were cast at the same time of the day, both triangular images formed would be similar to each other.

Therefore, the ratio of their corresponding sides would be equal.

That is, the height of the tree / the height of the alien = the shadow of the tree / the shadow of the alien

Height of the tree = x ft

Height of the alien = 7 ft

Shadow of the tree = 48 ft

Shadow of the alien = 12 ft

Plug in the values into the proportional equation stated earlier.

Thus, the ratio of their corresponding sides would be:

[tex] \frac{x}{7} = \frac{48}{12} [/tex]

Cross multiply

[tex] x*12 = 48*7 [/tex]

[tex] 12x = 336 [/tex]

Divide both sides by 12

[tex] x = \frac{336}{12} [/tex]

[tex] x = 28 [/tex]

The height of the tree = 28 ft

Answer:

Is student B because student B data has -2 which is facing the same way the scatter plot is while student A is facing the left while the scatter plot is on the right.

If you don't understand go to desmos graphing calculator and enter y=−2x+24 and y=1.5x+23.

Answer:

When diving in the ocean, you must consider how much pressure you will experience from diving a certain depth.

From the atmosphere, we experience about 14.7 pounds per square inch (psi) and for every foot we dive down into the ocean, we experience another 0.44 psi in pressure.

How far (in feet) can you dive without experiencing more than 58.7 psi of pressure on your body?

:

let d = the depth which gives 58.7 psi

.44d + 14.7 = 58.7

.44d = 58.7 - 14.7

.44d = 44

d = 44/.44

d = 100 ft

Step-by-step explanation:

Answer:

There is no picture but i can help you if you want. :)

Step-by-step explanation:

Answer:

what is the question

Step-by-step explanation:

Answer:

d=rt is basically y=mx+b but with different variables. B is where the line intercepts the y axis and since this line intercepts at 0, 0 b can automatically be deleted from the equation. therefore d=rt is equivilent to y=mx

The slope is 6. I know this by looking at the first point of the line (0, 0) and finding the next point on the line (1, 6). To get from 0, 0 to 1,6 you need to go up 6 and over 1. Since rise/run is the slope of a line 6/1 or 6 is the slope.

At 1, 6 we see that in 1 hour, joseph went 6 miles. Therefore the constant rate is 6 miles per hour (6 mp/h.)

The slope, already found, is 6 and therefore if d=rt is equivilent to y=mx we can write our equation as d=6t

6 mp/h

d=6t

Step-by-step explanation:

Answer:

18 eggs

Step-by-step explanation:

Answer:

38 euros

Step-by-step explanation:

£3=4 euros

28.50=

28.50/3=9.5

4 x 9.5=

Answer:

v=5

Step-by-step explanation:

you are trying to make 4v into v right ?

so simply divide it by 4 - the same if it was 4a or 7a or 9k, always start by dividing by the number

then you need to balance the two sides - so whatever number you divide the letter by (which is the 4 in this case) , you do the same with the other side , so whatever number is after the equal sign , divide it by 4

PART ONE                                      ↓ 4v  =   20  

           DIVIDE BY 4                       →  v   =    20

PART TWO                                          v   =   20 ↓

                                                            v   =     5 ←           DIVIDE BY 4

Answer:

slope is m = 2

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ [/tex]

From the question we have

[tex]m = \frac{ - 5 - 5}{ - 3 - 2} = \frac{ - 10}{ -5 } = \frac{10}{5} = 2\\ [/tex]

We have the final answer as

Hope this helps you

Answer:

110 yards of string

Step-by-step explanation:

Converting the feet of the string of 1 balloon to yard

1 foot = 1/3 yard

6 feet = x

x = 6 × 1/3 yard

x = 2 yard

Hence 1 balloon uses 2 yard of string

Since:

1 balloon = 2 yard of string

55 ballons = x

x = 55 × 2 yard of string

x = 110 yards of string

Hence, for 55 balloons he would need 110 yards of string.

Answer:

i think it is c but i am not for sure hope that helps

Answer:

a). Perimeter = (5r + 9) cm

b). r = 8

Step-by-step explanation:

Property of isosceles triangle:

- Two sides of an isosceles triangle are equal.

- Opposite sides of the equal angles are equal in measure.

  From the figure attached,

  PQ = QR = (2r + 3)

a). Since perimeter of a polygon = sum of all sides of the polygon

                                                 = PQ + QR + PR

                                                 = (2r + 3) + (2r + 3) + (r + 3)

                                                 = 5r + 9

    Perimeter of the given triangle = (5r + 9) cm

b). Perimeter of the given triangle = 49 cm

    (5r + 9) = 49

     5r = 40

      r = 8

Answer:

[tex]a_n=-4n+10[/tex]

Step-by-step explanation:

Let us consider the given terms one by one:

First term, [tex]a[/tex] = 6

Second term, [tex]a_2=2[/tex]

Difference between First and Second term = 2 - 6 = -4

Third term, [tex]a_3[/tex] = -2

Difference between Second and Third term = -2 - 2 = -4

Fourth term, [tex]a_4[/tex] = -6

Difference between Second and Third term = -6 -(-2) = -4

Therefore, the common difference is:

[tex]d[/tex] = -4

Let the use the formula for [tex]n^{th}[/tex] term of an arithmetic sequence:

[tex]a_n=a+(n-1)d[/tex]

Putting the values of [tex]a[/tex] and [tex]d[/tex]:

[tex]a_n=6+(n-1)(-4)\\\Rightarrow a_n=6-4n+4\\\Rightarrow a_n=-4n+10[/tex]

Therefore, the [tex]n^{th}[/tex] term is:

[tex]a_n=-4n+10[/tex]

The  function that generates the sequence 6, 2, -2, -6, ... is: f(n) = 6 - 4(n - 1)

To generate the arithmetic sequence 6, 2, -2, -6, ... , use the general formula for an arithmetic sequence:

an = a1 + (n - 1)d

A) f(n) = 6 - 4n

If we substitute n = 1, we get f(1) = 6 - 4(1) = 2, which matches the second term of the sequence.

However, it doesn't generate the rest of the sequence, so it is not correct.

B) f(n) = 6 - 4(n - 1)

If we substitute n = 1, we get f(1) = 6 - 4(0) = 6, which matches the first term of the sequence.

By substituting other values of n, we can verify that this function generates the entire sequence. It is correct.

C) f(n) = 6 + 4(n - 1)

If we substitute n = 1, we get f(1) = 6 + 4(0) = 6, which matches the first term of the sequence.

However, it doesn't generate the rest of the sequence, so it is not correct.

D) f(n) = 6 - 2n

If we substitute n = 1, we get f(1) = 6 - 2(1) = 4, which does not match the first term of the sequence. It is not correct.

Based on the analysis above, the function that generates the sequence 6, 2, -2, -6, ... is: f(n) = 6 - 4(n - 1)

Learn more about Arithmetic Sequence here:

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The missing options are:

A) f(n) = 6 - 4n

B) f(n) = 6 - 4(n - 1)

C) f(n) = 6 + 4(n - 1)

D) f(n) = 6 - 2n