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3 years ago

11. All services at the salon are 25% off today. Maria decided to get a haircut that originally costs $22.

Mathematics

1 answer:

laila [671]3 years ago

8 0

22 * (1 - 0.25) = 16.50

16.50 * (0.2) = 3.30

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2 years ago

Write an algebraic expression with the variable x that has a value of 3 when evaluated

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X=23

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3 years ago

Find the point P on the line y=2x that is closest to the point (20,0) .what is the least distance between pans (20,0)?

Vsevolod [243]

The closest point on a line, to another point, will be a point that's on a normal of that line, or a line that is perpendicular to it, notice picture below

so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or $\bf 2\qquad negative\implies -2\qquad reciprocal\implies \cfrac{1}{-2}\implies -\cfrac{1}{2}$

so, we know that line passes through the point 20,0, and has a slope of -1/2

if we plug that in the point-slope form, we get $\bf y-0=-\cfrac{1}{2}(x-20)\implies y=-\cfrac{1}{2}x+10$

now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph

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------------------------------------------------------------

not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ \square }}\quad ,&{{ \square }})\quad 
% (c,d)
&({{ \square }}\quad ,&{{ \square }})
\end{array}\qquad 
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d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

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3 years ago

H(x) = -4x – 4; Find h(3x) please help, I’m confused if it’s -4•3•3 or not

inna [77]

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3 years ago

Show work and explain with formulas.

Juli2301 [7.4K]

20 Answer: a₁ = 4

Step-by-step explanation:

$a_n=324,\ r=3,\ n=5\\\\a_n=a_1 \cdot r^{n-1}\\\\324=a_1\cdot 3^{5-1}\\\\\dfrac{324}{3^4}=a_1\\\\\dfrac{324}{81}=a_1\\\\\large\boxed{4}=a_1$

21 Answer: n = 13

Step-by-step explanation:

$a_n=\dfrac{1}{64},\ a_1=64,\ r=\dfrac{1}{2}\\\\a_n=a_1 \cdot r^{n-1}\\\\\dfrac{1}{64}=64\cdot \bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{64\cdot 64}=\bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{2^6\cdot 2^6}=\dfrac{1}{2^{n-1}}\\\\6+6=n-1\\\\\large\boxed{13}=n$

22 Answer: n = 5

Step-by-step explanation:

$a_n=48,\ a_1=1875\ r=\dfrac{2}{5}\\\\a_n=a_1 \cdot r^{n-1}\\\\48=1875\cdot \bigg(\dfrac{2}{5}\bigg)^{n-1}\\\\\dfrac{48}{1875}=\bigg(\dfrac{2}{5}\bigg)^{n-1}\\\\\dfrac{16}{625}=\bigg(\dfrac{2}{5}\bigg)^{n-1}}\\\\\bigg(\dfrac{2}{5}\bigg)^4=\bigg(\dfrac{2}{5}\bigg)^{n-1}}\\\\4=n-1\\\\\large\boxed{5}=n$

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3 years ago

Read 2 more answers