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3 years ago

What is the equation of the line graphed below?

Mathematics

1 answer:

andrew-mc [135]3 years ago

4 0

Answer: $y=-\frac{1}{3}x$

Step-by-step explanation:

From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope $\frac{-1}{3}$

These are in the form of y=mx+b

b is the y-intercept and m is the slope

since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx

We can put our slope into the equation giving us the answer in C

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A recipe for banana bread requires 3 cups of bananas for every 1 1/2 cups of sugar used. At this rate how many cups of sugar sho

mr Goodwill [35]

Answer:

The answer is 1 cup of sugar

Step-by-step explanation:

x = 2 x 1.5/3

x = 3/3

x = 1 cup of sugar

hope it helps!

4 0

4 years ago

Seven and fifty-one thousands in numbers

mihalych1998 [28]

51,007.

If you want it is thousandths,

7.051.

Bye!

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4 years ago

Read 2 more answers

Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.

katen-ka-za [31]

Answer:

128 if it wants the whole thing than 192

Step-by-step explanation:

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3 years ago

Log(x-2)+log2=2logy<br>log(x-3y+3)=0

In-s [12.5K]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right$

$===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}$

$\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac$

$y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D$

$\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D$

4 0

3 years ago

at the city museum child admission is $5.10 and adult admission is $9.60. on thursday 132 tickets were sold for a total sale of

Bad White [126]

C + a = 132.....a = 132 - c
5.10c + 9.60a = 898.20

5.10c + 9.60(132 - c) = 898.20
5.10c + 1267.20 - 9.60c = 898.20
5.10c - 9.60c = 898.20 - 1267.20
-4.50c = - 369
c = -369/-4.50
c = 82 <=== child tickets sold

5 0

4 years ago