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raketka [301]
3 years ago
7

a necklace is being made with beads that are 1.25 centimeters in a diameter each. The necklace us 30 centimeters long. How many

beads are needed?
Mathematics
1 answer:
denpristay [2]3 years ago
4 0
<span>Since the beads are exactly 1.25 centimeters long it would then take 24 beads side by side to get to a length of 30 centimeters for the necklace. In order to figure this out in written form you would then start by dividing 30 by 1.25. Your equation should look like this when it is done -- 30/1.25=24.</span>
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3 years ago
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What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
lutik1710 [3]

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}

so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill

7 0
3 years ago
Find sin θ if θ is in Quadrant III and tan θ = . 0.958
Leokris [45]
Use the following identities:
sec^2 = 1  + tan^2 \\  \\ sec = \frac{1}{cos} \\  \\ sin^2 = 1 - cos^2
Also because the angle is in quadrant 3, sin must be negative.
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Subbing in tan = 0.958
sin \theta = -0.69178
7 0
3 years ago
At work, Elon takes a break 1/5​​ of each hour he works. He also takes a lunch break for 1/2​​ of an hour each day he works. Elo
Anton [14]

Answer:

h=50\ hours

Step-by-step explanation:

Let

h -----> the number of hours, Elon works during one 5​-day work week

we know that

12\frac{1}{2}\ h=\frac{12*2+1}{2}=\frac{25}{2}\ h

Elon’s break time must be equal to 1/2​​ of an hour multiplied by 5 days plus  1/5​​ multiplied by the total hours h

so

\frac{25}{2}=5(\frac{1}{2})+\frac{1}{5}h

Solve for h

Multiply by 10 both sides to remove the fraction

125=25+2h

2h=125-25

2h=100

h=50\ hours

8 0
3 years ago
Factor 64v^3 + 192v^2 -56v - 168​
Kaylis [27]

Hello from MrBillDoesMath!

Answer:

8(v+3) ( -1/2 (sqrt(14) - 4 v) (4 v + sqrt(14)) )


Discussion:

Given

64v^3 + 192v^2 - 56 v - 168      

Factor 64v^2 from the first two terms. Factor 56 from the last two terms:

64v^2(v+3) - 56(v  + 3)     => factor (v+3) from both terms

(v+3) (64v^2 - 56)             => factor 8 from both terms in the right ()

8(v+3)(8v^2-7)                   => factor 8y^2-7

8(v+3) ( -1/2 (sqrt(14) - 4 v) (4 v + sqrt(14)) )



Thank you,

MrB

4 0
3 years ago
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