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2 years ago

Find the missing length indicated

Mathematics

2 answers:

faltersainse [42]2 years ago

6 0

Answer:

D) 20

Step-by-step explanation:

Len [333]2 years ago

4 0

Answer:

D) 20

Step-by-step explanation:

they are asking for the longest length of the triangle. as you can see, 20 is just over 15, and from the diagram, the missing length is just over 15 so we can apply our knowledge to come to the answer of 20.

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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

2 years ago

Last month 4,861 books were checked out from the Library.this month 3,278 books were checked out.how many more books were checke

ludmilkaskok [199]

Answer:

1,583

Step-by-step explanation:

4,861 - 3278 = 1,583. All you have to do is subtract each amount of books from both months.

6 0

2 years ago

With which information can you construct a unique rhombus?

Yakvenalex [24]

It has 4 equal sides, but it can be "squished" so all 4 angles are not equal

8 0

3 years ago

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Malcolm ran the 440-yard and the 220-yard dash at a track meet.There are 3 in one yard. How many total feet did Malcolm run?Esti

Tresset [83]

For this case we have the following conversions:

1 yard = 3 feet

The estimate distance Is:

400yd = 1200feet

200yd=600 feet

Ten, the estimate Is:

1200 + 600 = 1800 feet

The real distance Is:

The total distance in yards is given by:

440 + 220 = 660 yd

Then, let's transform this distance to feet, with the given conversion:

660 * 3 = 1980 feet

The distance traveled is reasonable for a person

Comparing the estimate and the actual answer, the distance malcom Ran Is reasonable.

Answer:

Malcolm ran 1980 feet.

The distance is reasonable.

5 0

2 years ago

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Trapezoid problem pls help

lakkis [162]

Do Area = (base 1 + base2) × H

7 0

3 years ago