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3 years ago

14

Arnie is mixing red and yellow paint to make two different shades of orange. To make 1 cup of dark orange paint, he needs 7 ounc

es of red paint and 1 ounce of yellow paint. To make 2 cup of light orange paint, he needs 13 ounces of yellow paint. Answer part a and b.

1 answer:

nordsb [41]3 years ago

4 0

Answer:

If this is how many ounces of yellow: 14oz

If this is how many ounses of red: 8oz

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

In-s [12.5K]

Answer:

<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

Step-by-step explanation:

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

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

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

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

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

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3 years ago

What is this expression in simplified form 5/2 times 9/6? A.90 B.90/3 C.45/2 D. 45/3

alekssr [168]

5√2 · 9√6

Simplify.

5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.

5 × 9 √12

Simplify √12 to 2√3.

5 × 9 × 2√3 ⇔ Multiply

90√3

Therefore, the <u>correct alternative</u> is <u>option "B".</u>

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2 years ago

Reffect shape A in the line y=-x<br> th<br> 6<br> 2<br><br> A<br> --5-32-10 12345<br> 2 6<br> M

s344n2d4d5 [400]

The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

<h3>What is a transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>translation, rotation, reflection and dilation.</em>

Dilation is the increase or decrease in the size of a figure.

The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

Find out more on transformation at: brainly.com/question/4289712

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2 years ago

A fancy dinner for two cost $69.06 before a 1% tox

N76 [4]

132.40 should be the answer

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3 years ago

Help!!!! Quick and easy!

ELEN [110]

Make an equation
6p + p = 28
Combine like terms
7p = 28
Divide
p = 4

Solution: p = 4

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2 years ago