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2 years ago

A 12-m ladder is leaning against a wall.

Mathematics

1 answer:

Len [333]2 years ago

7 0

Answer:

Step-by-step explanation:

Use Pythagorean's Theorem for a right triangle. Your best bet when learning/visualizing word problems is to draw a picture, then learn how to visualize in your head over time.

$3^2+x^2=12^2\\9+x^2=144\\x=\sqrt{135}$

The radical can be further simplified because 135 is the product of 9 and 15. 9 has a perfect root of 3.

$x=3\sqrt{15}$ meters or 11.62 meters

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Please can I have an explanation also, I am terrible at these kinds of questions!

wlad13 [49]

Answer:

<em>The fraction of the beads that are red is</em>

Step-by-step explanation:

<u>Algebraic Expressions</u>

A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:

r:y = 2:3

y:b = 5:4

We are required to find r:s, where s is the total of beads in the bag, or

s = r + y + b

Thus, we need to calculate:

$\displaystyle \frac{r}{r+y+b} \qquad\qquad [1]$

Knowing that:

$\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2]$

$\displaystyle \frac{y}{b}=\frac{5}{4}$

Multiplying the equations above:

$\displaystyle \frac{r}{y}\frac{y}{b}=\frac{2}{3}\frac{5}{4}$

Simplifying:

$\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3]$

Dividing [1] by r:

$\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+y/r+b/r}$

Substituting from [2] and [3]:

$\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+3/2+6/5}$

Operating:

$\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{\frac{10+3*5+6*2}{10}}$

$\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{10+15+12}$

$\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{37}$

The fraction of the beads that are red is $\mathbf{\frac{10}{37}}$

8 0

2 years ago

A student ticket for a high school basketball game costs $3.00. A monthly game pass costs $20.00. Which inequality represents th

Nana76 [90]

3x greater than or equal to 20
3x = 20
X= 7 games for the pass to be better
3(7)=21

4 0

2 years ago

Read 2 more answers

Jackson played a video game for 1/6 for hour. Hailey played a video game for 1/3 hour. Who played the video game for a greater a

viva [34]

Answer:

hailey played the game longer (1/3 hour).

Step-by-step explanation:

You are deciding which is greater: 1/6 or 1/3.in this case, a smaller denominator (such as 3) produces a greater value.1/3 has a smaller denom. than does 1/6, so 1/3 is greater than 1/6.hailey played the game longer (1/3 hour).

5 0

2 years ago

Viktor earns $15.75 per hour cleaning pools. How much money will Viktor earn if he cleans 22 pools? Round your answer to the nea

Bingel [31]

$347

15.75×22=346.5=347

4 0

2 years ago

Simplify:2 1/3(4 1/4÷2)

kondor19780726 [428]

Answer:

$4\frac{23}{24}$