Two pupils each drew a triangle with one side of 6 cm , one side of 10 cm and one side of 7 cm. Must their triangles be congruent? (Answer ‘yes’ or ‘no’).

Answer:

a) [tex]x = 10^{18}\,\mu m^{2}[/tex], b) [tex]x = 10^{18}[/tex], c) [tex]x = 10^{21}\,\mu m^{2}[/tex], d) [tex]x = 10^{21}[/tex], e) [tex]x = \frac{1}{10^{21}}[/tex],  f) [tex]x = 10^{3}\,nm^{2}[/tex], g) [tex]x = 10^{3}\,nm^{2}[/tex]

Step-by-step explanation:

a) The product of one terameter and one micrometer is:

[tex]x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{6}\,\frac{\mu m}{m} ) \cdot (1\,\mu m)[/tex]

[tex]x = (10^{18}\,\mu m)\cdot (1\,\mu m)[/tex]

[tex]x = 10^{18}\,\mu m^{2}[/tex]

b) The quotient of one terameter and one micrometer is:

[tex]x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{6}\,\frac{\mu m}{m} )}{1\,\mu m}[/tex]

[tex]x = \frac{10^{18}\,\mu m}{1\,\mu m}[/tex]

[tex]x = 10^{18}[/tex]

c) The product of terameter and one nanometer is:

[tex]x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{9}\,\frac{nm}{m} ) \cdot (1\,nm)[/tex]

[tex]x = (10^{21}\,nm)\cdot (1\,nm)[/tex]

[tex]x = 10^{21}\,\mu m^{2}[/tex]

d) The quotient of one terameter and one nanometer is:

[tex]x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}{1\,nm}[/tex]

[tex]x = \frac{10^{21}\,nm}{1\,nm}[/tex]

[tex]x = 10^{21}[/tex]

e) The quotient of one nanometer and one terameter is:

[tex]x = \frac{1\,nm}{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}[/tex]

[tex]x = \frac{1\,nm}{10^{21}\,nm}[/tex]

[tex]x = \frac{1}{10^{21}}[/tex]

f) The quotient of one nanometer and one micrometer is:

[tex]x = \frac{1\,nm}{(1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )}[/tex]

[tex]x = \frac{1\,nm}{10^{3}\,nm}[/tex]

[tex]x = \frac{1}{10^{3}}[/tex]

g) The product of one nanometer and one micrometer is:

[tex]x = (1\,nm)\cdot (1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )[/tex]

[tex]x = 10^{3}\,nm^{2}[/tex]

Answer:

Quadrant 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The denominators are 4, 5, and 8.

Write the prime factorizations:

4 = 2²

5 = 5

8 = 2³

To find the least common denominator, multiply the prime numbers with the highest exponents.

2³ × 5 = 40

Answer:

LCD=40

EXPLANATION= To find the least common denominator first convert all integers and mixed numbers (mixed fractions) into fractions. Then find the lowest common multiple (LCM) of the denominators.

Answer:

(1/6)^2

Step-by-step explanation:

We want to find the fraction that is equivalent to 1/36.

Let us look at each of them individually:

a. [tex](\frac{1}{108})^3 = \frac{1}{1259712}[/tex]

b. [tex](\frac{1}{9})^4 = \frac{1}{6561}[/tex]

c. [tex](\frac{1}{6})^2 = \frac{1}{36}[/tex]

d. [tex](\frac{1}{5})^2 = \frac{1}{25}[/tex]

Therefore, the correct answer is c.

Answer:

1/6 to the second power, which is the third option.

Step-by-step explanation:

I took the test.

Answer:

Function 2.

Step-by-step explanation:

For the first equation, the y-intercept is the 'b' value in the equation

y = mx + b.

In the equation given, b = 5. This is the y-intercept for the equation.

To find the y-intercept, you need to look for the 'y' value at x = 0. Therefore:

In the table, notice that when t = 0, r = 5.25. This is the same as x = 0, y = 5.25. This means that the y-intercept of the table is y = 5.25.

Since 5.25 > 5, function 2 has a greater y intercept.

Answer:

Option C

Step-by-step explanation:

A "tessellation" is a flat covering of 2D geometric shapes. A shape in a tessellation is called a "tile".  

Tessellations can be in a pattern that goes 'forever', and they cannot overlap. This eliminates A and D, since they are true.

A "tessellation" cannot have any spaces. This eliminates option B, since this is true. Since a circle and an eclipse have curved sides, they can not tessellate on their own. Regular pentagons and octagons will also not tessellate on it's own. Any shape that are put together and leave a gap will not tessellate.  

I have attached a picture showing why circles and pentagons will not tessellate.

So, not any 2D shape would tessellate. Option C's statement is false.

Option C should be the correct answer.

Answer:

It can't be solved - there are no real roots

Answer:

37.7

Step-by-step explanation:

C=2(pi.)r

2×3.14=6.28

6.28×6=37.6

37.68 rounded is 37.

Answer:

10/8 pounds

Step-by-step explanation:

Answer:

5/4 or 1.25 pounds of choclate chips

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

b = number of blue bikes

9 = 9 red bikes

1. "The sum of," this tells us that the answer will be addition based. Based on this information we can solve the question as there is only one answer with an addition symbol (B)

Answer: I don't know the options but from this situation it is 3x+2 or x=3/2

Step-by-step explanation:

You add all the x together and that's the first option second divide it so x us all by itself

Answer:

C. 22.28

Step-by-step explanation:

area of square is 4*4 =16

area of half of circle is

(Pi*r²)/2 = 3.14*4/2 = 6.28

16+6.28 = 22.28

Answer:

C. 22.28

Step-by-step explanation:

 4 x 4 = 16 (Pi x r²)/2 = 3.14 x 4/2 = 6.28

16 + 6.28 = 22.28

Answer:

the solution is (0,2) to the problem

Answer: 37/40

Step-by-step explanation: 17+8+12 out of 40 total

Answer:

d = [tex]\frac{C}{3.14}[/tex]

Step-by-step explanation:

Given

C = 3.14d ( isolate d by dividing both sides by 3.14 )

[tex]\frac{C}{3.14}[/tex] = d

Answer: 30 white  and 20 yellow

the aswer is c and can u place mack it clear

Step-by-step explanation:

Answer: 55°

Step-by-step explanation: Let me know if you need an explanation.

Answer:

X = 55°

Step-by-step explanation:

X = 180° - ( 75 + 50)°

X = 180° - 125°

X = 55°

Answer:

$180.00

Step-by-step explanation:

The painting is rectangular and it measures 1 meter by 2 meters. The frame shop charges $30.00 per meter for a wooden frame.

To find the cost, we need to find the perimeter of the painting and then multiply it by the cost of a wooden frame per meter.

The perimeter of a rectangle is:

P = 2(L + B)

P = 2(1 + 2) = 2 * 3 = 6 m

The cost of the frame is therefore:

6 * 30 = $180.00

Answer:

[tex]f(4) = \frac{256}{3}[/tex]

Step-by-step explanation:

To find f(4), '4' will need to be substituted in place of 'x'. Therefore:

[tex]f(x)\frac{1}{3} * 4^{x}[/tex] becomes:

[tex]f(4) = \frac{1}{3}* 4^{4}[/tex]

Simplify:

[tex]f(4) = \frac{1}{3}* 256\\ \\f(4) = \frac{256}{3}[/tex]

Therefore, f(4) equals [tex]\frac{256}{3}[/tex]

Answer:

-8

Step-by-step explanation:

47 = -7x -9

Add 9 to each side

47+9 = -7x-9+9

56 = -7x

divide each side by -7

56/-7 = -7x/-7

-8 = x

Volume of Big Pyramid= 324 cubic feet

Volume of small pyramid= 12

Volume of a pyramid is given as V=⅓xBasexheight

For the big pyramid

324=⅓xbasexheight

But 324= 27x12

Then for the big pyramid,

12=1/3x1/27xbasexheight

For the small pyramid

12=1/3xbasex6

Since both base are similar and from the equations derived so far

1/3x1/27xheight=1/3x6

Height=27x3x1/3x6=162feet

Answer:D. 73 people

Step-by-step explanation:

365 / 5% = 7300

7300÷100=73

Answer:

She catered for 40 people.

Step-by-step explanation:

According to the information given, you can write an equation that indicates that 30 people multiply for its cost that is $10 plus the number of people after 30 for its cost that is $9 is equal to $390. According to this, the equation is:

10(30)+9x= 390, where

x= number of people after 30

Then, you can solve for x:

300+9x= 390

9x=390-300

9x= 90

x=90/9

x=10

The answer is that she catered for 40 people, 30 people at a cost of $10 and 10 people for a cost of $9.

Answer:

median = 80 inches

mean = 79.692 inches

typical height = 80 inches

Step-by-step explanation:

Given height

84, 80, 87, 75, 77, 79, 80, 74, 76, 80, 80, 82, 82

arranging the height in increasing order we have

74,75,76,77,79,80,80,80,80,82,82,84,87

no, of terms in the heights = 13

We know

that median for any data set is the middle number, if data is arranged in increasing order of their occurrence.

If the number of terms is odd, then median is (n+1)/2 th term

If the number of terms is even, then median is taken average of  n/2 th term and( n/2 + 1)th term .

________________________________________

since here number of term is 13.

then median will be (13+1)/2 th term

i.e 7th term

as shown above seventh term is 80.

1. What is the median?

answer: Median is 80

_____________________________________

Mean is calculated average of all the terms

mean = sum of all the terms/ number of terms

mean = 74+75+76+77+79+80+80+80+80+82+82+84+87/13

         = 1036/13 = 79.692

Thus, means is 79.692

2. What is the mean?

Answer: Mean is 79.692

3. What is the typical height of a Knicks basketball player? Explain

Answer: Typical height for basket ball player will the height which  is the most commonly occurring height in the group.

The most commonly occurring data in the data set is also called mode.

Since, in this data group 80 inches occurring most number of times i.e 4 times.

Thus, typical height of group is 80 inches.

Answer: 39.58 cm

Step-by-step explanation:

The circumference of a circle is 2 times  the radius times pi or  pi times the diameter.  so we know the diameter is 12.6 so just multiply it by pie.

12.6 * pi = 39.584

Now rounded to the nearest hundredth is 39.58.

Answer:

V is inside the circle.

Step-by-step explanation:

We work out the radius of the circle which is the distance between K (0,0) and (6, -4).

Radius = √[(6 - 0)^2 + (-4 - 0)^2]

= √(16 + 36)

= √52.

Now find the distance of point V from K(0,0):

= √((√2-0)^2 + (-7-0)^2]

= √(2 + 49)

= √51.

This is less than the radius of the circle, so V lies inside it.

Apply the area formula [tex]A=\frac{bh}{2}[/tex] to get [tex]\frac{8\cdot 14}{2}=\boxed{56\,\text{square units}}.[/tex]

Answer:

Step-by-step explanation:

First we rewrite the expression:

 3sec (x) -2 = 1

 3 (1 / cos (x)) -2 = 1

 3 (1 / cos (x)) = 1 + 2

 3 (1 / cos (x)) = 3

 (1 / cos (x)) = 3/3

 cos (x) = 1

 x = 2 * pi * n

 on the interval [0, 2pi):

 x = 0

 Answer:

 x = 0 on the interval [0, 2pi)