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3 years ago

The diagram shows a 5 cm x 5 cm x 5 cm cube.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

8.7 cm

Step-by-step explanation:

The question is a 2-two-step Pythagoras theorem. (c^2 = a^2 + b^2)

Consider as such, If I were to draw a diagonal line along the base of the cube what is the length of the diagonal line. To find out that we use the theorem. We can substitute a for 5 and b for 5 as well. So

a^2 +b^2 = c^2

5^2 + 5^2 = c^2

25 + 25 = c^2

√50 = c

Then since the line side of the cube is on a 3d angle we need to do the same process again but now using the imaginary diagonal line that we just calculated and the height (5).

a^2 +b^2 = c^2

√50^2 + 5^2 = c^2

50 + 25 = c^2

√75 = c

c = 8.6602...

when rounded to 1 d.p.

c = 8.7

Line AB is 8.7 cm long.

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Ann, Chang, and Kareem sent a total of

Gnoma [55]

It is given in the question that

Ann, Chang, and Kareem sent a total of 89 text messages over their cell phones during the weekend. Ann sent 9 fewer messages than Chang. Kareem sent 3 times as many messages as Ann.

Let number of messages Chang sent be x. And Ann sent 9 fewer than Chang, so Ann sent (x-9) messages. And Kareem sent 3 times as many messages as Ann, so Kareem sent 3(x-9) messages.

And the total messages are 89. That is

$x+x-9+3(x-9)=89$

Combining like terms

$x + x - 9 + 3x-27 =89
\\
5x -36=89
\\
5x = 125
\\
x =25$

So Chang sent 25 messages, Ann sent

$25-9=16 messages$

And Kareem sent

$3*16 = 48 messages$

8 0

2 years ago

Work out the value of angle x 24 degrees

stich3 [128]

Answer:

180=2x+ 24( angles opposite to equal sides)

156/2=x

x=78

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

X^4 − 3x^2 − 90 x= -3

Ahat [919]

Answer:

-36

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Step-by-step explanation:

Step 1: Define

x⁴ - 3x² - 90

x = -3

Step 2: Evaluate

Substitute in x: (-3)⁴ - 3(-3)² - 90
Exponents: 81 - 3(9) - 90
Multiply: 81 - 27 - 90
Subtract: 54 - 90
Subtract: -36

8 0

2 years ago

For f(x) = 4x+1 and g(x) = x2 - 5, find (f - g)(x).

Lostsunrise [7]

Answer:

Step-by-step explanation:

Simply substitute the equations f(x) and g(x) for f and g.

(4x+1)-( $x^{2}$ -5)

4x+1- $x^{2}$ +5

Do some rearranging and:

$-x^{2}$ +4x+6

Hope this helped!

3 0

2 years ago

Find the distance that the earth travels in eight days in its path around the sun. assume that a year has 365 days and that the

lora16 [44]

The speed of earth will be found as follows:
speed=distance/time
distance=93 million
time=365
speed=(93)/365=254, 794.5205 mi/day
thus distance moved for 8 days will be:
distance=speed*time
=(254794.5205)×8
=2,038,356.164 miles

5 0

3 years ago