A hockey stick costs $67.06. Which equation represents the cost, c, of n sticks?

There were 45 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 3

Helen [10]

45/3=15 45-15=30 30/5=6 3x6=18 30-18=12 the answer is 12

5 0

2 years ago

Alex scored 98,72, and 87 on his first three math test. What must he score on the next test to have an average of at least 86 (P

ss7ja [257]

Answer:

$\huge\boxed{\text{At least an } 87\%}$

Step-by-step explanation:

In order to find what score Alex must earn to have an average of 86 on all his tests, we need to first note what the formula to find the average of a data set is.

$\displaystyle \frac{x_1+x_2+...x_n}{n}$

What the formula means is that we have to add up all the values then divide by the total number of values.

Let's represent our unknown number as $x$ .

$\displaystyle \frac{98+72+87+x}{4} \geq 86$ (since we want AT LEAST an 86).

Let's solve this inequality for x.

$\frac{98+72+87+x}{4} \cdot 4 \geq 86 \cdot 4$
$98+72+87+x \geq 344$
$257 + x \geq 344$
$257 + x - 257 \geq 344 - 257$
$x \geq 87$

So, Alex must score at least an 87% on his next quiz to have an average of 86%.

Hope this helped!

8 0

2 years ago

Solve 3(x+2)+5(x+2)=64

valkas [14]

Answer:

6

Step-by-step explanation:

3x+6+5x+10=64

3x+5x+6+10=64

8x+16=64

8x=64-16

8x=48

divide both sides by 8

x=6

6 0

3 years ago

Help me please<br>help me please

Nikolay [14]

Answer:

1 second

Step-by-step explanation:

$s=-5\\u=0\\v=\\a=-10\\t=t$

$\begin{aligned}\textsf{Using} \quad s & =ut+\dfrac12at^2\\ \implies -5 & =(0)t+\dfrac12(-10)t^2\\ -5 & = -5t^2\\ t^2& = 1\\ t & = \pm\sqrt{1}\\ t & = 1\: \sf s\end{aligned}$

7 0

2 years ago

For how many real values of x is <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B120-%5Csqrt%7Bx%7D%7D%20" id="TexFormula1" title

leva [86]

A good place to start is to set $\sqrt{x}$ to y. That would mean we are looking for $\sqrt{120-y}$ to be an integer. Clearly, $y\leq 120$ , because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since $\sqrt{x}$ is a radical, it only outputs values from $[0,\infty]$ , which means y is on the closed interval: $[0,120]$ .

With that, we don't really have to consider y anymore, since we know the interval that $\sqrt{x}$ is on.

Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval $[0,120]$ , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

$\sqrt{120-\sqrt{x}}=k \implies \\ \sqrt{x}=k^2-120 \implies\\ x=(k^2-120)^2$

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.

5 0

2 years ago