Find the Volume and Surface area

A trapezoid is a quadrilateral that has two parallel sides with a height.

From the diagram, AK = 1/2(AD-BC)

The combination of the bases of the equilateral triangle and the parallelogram is = the base of the trapezoid.

Therefore, BC = AD - 2AK

Make AK the subject of formula,

AK= 1/2 (AD -BC)

KD = 1/2(AD - BC). This is wrong because of the following,

BC is parallel to KD.

Therefore length of KD = BC - AK and not KD = 1/2(AD - BC).

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Answer: 23

6*6=36 total area

3*3=9

2*2=4

9+4=13

36-13=23 shaded area

First image -Pentagon(Five sides).

Second image-Equilateral triangle(All sides are equal).

Answer:

Given:

To construct the Venn diagram:

As 2 students study neither subject, place the number 2 in the box outside the circles.

Calculate the number of students who study both subjects (central overlapping section):

Physics students + Chemistry students + neither students - Total students

= 20 + 18 + 2 - 35 = 5

Place the number 5 in the central overlapping section.

⇒ Left section = Physics students - both subjects

                        = 20 - 5

                        = 15

⇒ Right section = Chemistry students - both students

                          = 18 - 5

                          = 13

i) See attachment

ii) Physics and Chemistry = 5 students

iii) Physics only = 15 students

iv) One subject only = 15 + 13 = 28 students

Answer: x = ±5i

Step-by-step explanation:

√x2 = √−25

x = √−1 ∗ 25

x = i√25

x = ±i5

If the length of the side AB is 39.21 then the length of the side AD will be 21.61. Then the correct option is B.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The length AD is given as

AD = AB - BD

AD = AB - 17.6

Then the value of AB will be given by the Pythagoras theorem.

AB² = BC² + CA²

AB² = 26.5² + 28.9²

AB² = 1537.46

AB = 39.21

Then the value of AD will be

AD = 39.21 - 17.6

AD = 21.61

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Answer:

n = 60°

Step-by-step explanation:

60° + n + 60° = 180° ( straight line angles)

-> n + 120° = 180°

-> n = 180° - 120°

-> n = 60°

The measure of the missing angle can be found using the equation 120 + n = 180 and the value of n is 60°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given is a line on which some shapes are drawn.

Clearly, it can be seen that,

The three angles 60°, n and 60° forms a linear angles since all are formed on a line.

So the sum is 180°.

60 + 60 + n = 180

120 + n = 180. is the required equation.

Solving,

n = 180 - 120 = 60°

Hence the value of n is 60 degrees.

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Answer:

2.75

Explain
1 3/5 = 8/5
3 7/16 = 55/16

8/5 x 55/ 16 = 440/80
440/80 : 2 = 5.5

5.5 / 2 = 2.75
Simple as that
You can check the calculator

Answer:

2.72

Step-by-step explanation:

1 3/5 is 1.6 and 3 7/16 is 3.4 so 1.6 x 3.4=5.44 and 5.44/2 is 2.72 sq u

Answer:

width = 7 and length = 9

Step-by-step explanation:

Let's assume width = w, and length = 2 + w

So area of a rectangle = width * length

63 ft² = w (2 + w)

63 = 2w + w²

w² + 2w - 63 = 0

Use the quadratic formula to solve this

here, a = 1, b = 2 and c = -63

w = 7 or -9

The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.

Width = 7 and Length = 7+2 = 9

Answer:

1 - 4/9

2 - 1/9

3 - 5/9

Step-by-step explanation:

1 - Look on the left side for all two-letter combinations with only one R. We can see four. (YR, GR, RG, RY). Divide by the total number of outcomes (9).

2 - There is only one with two yellows, so divide 1 by 9.

3 - Same as before, we find 4 with 1 green and 1 with 2 green. We have to include the new one since it says atleast one. Add 1 and 4 and then divide by 9.

Answer:

50

Step-by-step explanation:

3*50=150. 150/5=30 pounds

Answer:

Step-by-step explanation:

Circumference = 2(pi)r

Radius = Circumference/2(pi)

Circumference = 37.68

Radius = 37.68/2(pi)

Radius = about 59.18760559

Answer:

so you can know how long an objects size on the outside

Answer:

1/8

Step-by-step explanation:

I'd start by rearranging the terms for y:

11x-8y=-1

-8y=-1-11x

y=[tex]\frac{-1-11x}{-8}[/tex]

The x-intercept is found when x equals 0, so substitute 0 for x in this new equation to find the y-intercept:

[tex]y=\frac{-1-11x}{-8} \\y=\frac{-1-11(0)}{-8}\\ y=\frac{-1-0}{-8} \\y=\frac{-1}{-8}\\ y=\frac{1}{8}[/tex]

The y-intercept is 1/8

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

The equation of the function is given as:

f(x) = -(x + 3)(x -1)

The above function is a quadratic function, and the domain of a quadratic function is the set of all real numbers

Expand the function

f(x) = -(x² + 3x - x - 3)

f(x) = -(x² + 2x - 3)

Expand

f(x) = -x² - 2x + 3

Differentiate

f'(x) = -2x - 2

Set to 0

-2x - 2 = 0

Add 2 to both sides

-2x = 2

Divide through by -2

x = -1

Substitute x = -1 in f(x)

f(-1) = -(-1 + 3)(-1 -1)

Evaluate

f(-1) = 4

This means that the maximum value of the function is 4

Hence, the domain is all real numbers, and the range is all real numbers less than or equal to 4.

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Answer: C: The domain is all real numbers, and the range is all real numbers less than or equal to 4.

Step-by-step explanation: EDGE 2022

Answer:

f(x) = (x + 1)(x - 4)

Step-by-step explanation:

let f be the function

FACTORED FORM of f :

f(x) = a(x - p)(x - q)

Where p and q are the roots/zeros of f

and ‘a’ is a real number.

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

Find p and q :

The roots of f are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: x = -1 and x = 4 ⇒ p = -1 and q = 4.

then f(x) = a(x + 1)(x - 4)

Find ‘a’ :

f(3) = -4  ⇒ a((3) + 1)((3) - 4) = -4 ⇒ a(4)(-1) = -4 ⇒ -4a = -4 ⇒ a = 1

Therefore, f(x) = (x + 1)(x - 4)

1³ + 2³ + 3³

1 + 8 + 27

36

hope it helps..!!!

Answer:

6 weeks

Step-by-step explanation:

Since Reggie has $240 in the account already we first subtract this $240 from the $450. 450 - 240 = 210. Now since he deposits $35 a week and needs to hit at least 210 to reach is goal of $450 for the summer then we need to divide 210/35 to see the amount of weeks.  210/35 = 6. So 6 weeks  is the shortest time.

Answer:

108 minutes

Step-by-step explanation:

because 45/5=9 and 180/20=9 so multiply 12 by 9 12x9=108

Answer:

32

Step-by-step explanation:

With the ratio 8:4 we can assign variables.

8x+4x=96

12x=96

x=8

Subsitute to ratio: 8x:4x

64:32

32 orange packages

Hope this helps

Answer:

A. 288pi in^3

Step-by-step explanation:

s

ee image

Answer:

87

Step-by-step explanation:

common difference = d  = 2

an = a1 + (n-1)*d

a43 = 3 + 42*2  = 87

Answer:

B) [tex]f(x)=(x+5)(x-4i)(x+4i)[/tex]

Step-by-step explanation:

[tex]f(x)=x^3+5x^2+16x+80\\\\f(x)=x^2(x+5)+16(x+5)\\\\f(x)=(x^2+16)(x+5)\\\\f(x)=(x-4i)(x+4i)(x+5)[/tex]

Thus, the second choice is correct.

Answer:

a) Probability is the chance or possibility that an event will occur.

b) No,

just as the question states there is a 25% chance of this event happening in a child, so no matter the number of children they have the chances of them getting cystic fibrosis is 25% for each child and it's never guaranteed.

Answer:

1. 35.476

2. 83.33%

3. 531001

4. 3/4

5. 250%

6. 17.507

7. £29•00

8. 32

Step-by-step explanation:

math is done on calculator :)

Answer:

No.

Step-by-step explanation:

8:3 = 8/3

4:1 = 4/1 = 8/2

8/2 is not = 8/3

Answer:

La respuesta es A

Step-by-step explanation:

simplemente tienes que multiplicar 7 x 3 que te da 21 y luego tienes que sumar el 2 del numerador (siempre multiplica el o los enteros por el denominador y sumale el numerador)

Answer:

A

Step-by-step explanation:

The larger number in a mixed number represents how many "wholes" of the fraction there are. The fraction in a mixed number is sort of like the "leftovers", the amount that doesn't fit into a whole number. In this case, the whole number is 7, meaning there are 7 amounts of 3/3. You would multiply the whole number by the number in the denominator of the fraction, which would equal 21. The improper fraction of the whole number would be 21/3 (21 divided by 3 equals 7). Now you would add that to the fraction 2/3. The answer would be 23/3.

I hope this makes some type of sense, I didn't explain it very well.