D =√(x2-x1)^2 + (y2-y1)^2
......._____________
5 =√(3-0)^2 + (k-1)^2
.......__________
5 =√3^2 + (k-1)^2

25 = 9 + (k-1)^2

16 = k^2 - 2k + 1

k^2 -2k - 15 = 0

(k - 5)(k + 3) = 0

k - 5 = 0.....or.......(k + 3) = 0

k = 5.........or.......k = -3

7 0

3 years ago

The student population of a school consist of 300 girls and 500 boys. If 53% of the girls play sports, and 39% of the boys play

Ymorist [56]

Hello!

Convert the percentages to decimals by dividing them by 100, and then multiply them by the amount of boys and girls.

53 ÷ 100 = 0.53 as a decimal

0.53 × 300 girls = 159

This means that 159 of the 300 girls play sports.

Repeat this to calculate how many boys play sports.

39 ÷ 100 = 0.39

0.39 × 500 = 195

This means that 195 out of the 500 boys play sports.

Final Answer:

More boys play sports than girls.

8 0

3 years ago

Which of the following inequalities is not true? |-9| ≠ |9| -2 ^2 < 3 -7 ≤ -5 |-1| ≥ 0

guajiro [1.7K]

Answer:

(a) |-9| ≠ |9| is NOT TRUE.

(b) $-2 ^2< 3$ is TRUE

(c) -7 ≤ -5 is TRUE

(d) |-1| ≥ 0 is TRUE.

Step-by-step explanation:

Solving each expression separably:

(a) |-9| ≠ |9|

By the definition of <u>MODULUS FUNCTION</u>: IxI = x, if x > 0

= (-x) if x <, 0

⇒ I-9I = -(-9) = 9, and I9I = 9

So, I-9I = I9I . Hence, |-9| ≠ |9| is NOT TRUE.

(b) $-2 ^2< 3$

⇒ $-2 ^2 = (-2) \times (-2) \times (-2) = -8$

and (-8) < 3.

Hence, $-2 ^2< 3$ is TRUE

-7 < -5 on the number line of integers.

Hence, -7 ≤ -5 is TRUE

(d) |-1| ≥ 0

I(-1)I = -(-1) = 1

and 1 > 0

Hence, |-1| ≥ 0 is TRUE.

6 0

3 years ago

Read 2 more answers

Bill was able to walk 2 more than twice as many dogs as his friend Steve. Write an algebraic expression to represent the number

Olin [163]

X= Bill
y=Steve

x=2y+2

8 0

3 years ago

What are the two numbers whose some is 1 and the product is -12​

What are the two numbers whose some is 1 and the product is -12