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daser333 [38]
2 years ago
7

Solve. Log8 (6x) = Log8 2 + Log8 (x-4)

Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
7 0

Write both sides as powers of 8, then simplify:

8^{\log_86x}=8^{\log_82+\log_8(x-4)}=8^{\log_82}8^{\log_8(x-4)}

\implies6x=2(x-4)

\implies6x=2x-8

\implies4x=-8

\implies x=-2

However, on the left hand side, this would mean we'd have, \log_8-12, which is undefined (assuming the real-valued logarithm), so this equation has no real solution.

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Hhhhhhhhhhhhhhhhhhhhhh​
irga5000 [103]

Answer:

13 miles

Step-by-step explanation:

The shortest distance would be a straight line between the two points.  This would be a hypotenuse of a right triangle

We can use the Pythagorean theorem to determine the length

a^2+b^2=c^2

5^2 +12^2 = c^2

25+144= c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 = c

3 0
3 years ago
Read 2 more answers
Unit 4 Test, Part 2: Congruence and Constructions<br> Help with my math please
lakkis [162]

Answer/Step-by-sep explanation:

1. Given:

∆NMK ≅ ∆TRP

\overline{NM} = 20

\overline{MK} = 15

\overline{KN} = 25

\overline{TR} = 3x - 1

a. To complete the congruent statement, thus: ∆MNK ≅ ∆RTP

b. The side that is congruent to \overline{TR} is \overline{NM}. Thus:

\overline{TR} ≅ \overline{NM}

c. Since \overline{TR} ≅ \overline{NM}, therefore:

\overline{TR} = \overline{NM}

3x - 1 = 20 (substitution)

Add 1 to both sides

3x = 20 + 1

3x = 21

Divide both sides by 3

x = \frac{21}{3}

x = 7

2. a. Slope of LK = \frac{rise}{run} = \frac{4}{3}

Slope of LM = \frac{rise}{run} = -\frac{3}{5}

b. ✍️Length of LK is the distance between L(-7, 4) and (-4, 8):

Lk = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Lk = \sqrt{(-4 -(-7))^2 + (8 - 4)^2}

Lk = \sqrt{(3)^2 + (4)^2}

Lk = \sqrt{9 + 16}

Lk = \sqrt{25}

Lk = 5

✍️Length of LM is the distance between L(-7, 4) and (-2, 1):

LM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

LM = \sqrt{(-2 -(-7))^2 + (1 - 4)^2}

LM = \sqrt{(5)^2 + (-3)^2}

LM = \sqrt{25 + 9}

LM = \sqrt{34}

LM = 5.8 (nearest tenth)

∆KLM is not an isosceles ∆ because it does not has two equal side lengths. This we can see because LK and LM are not equal.

Therefore, Anthony is incorrect. Am isosceles ∆ has two equal sides.

8 0
3 years ago
Question 7
serg [7]

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

  • Given - <u>a </u><u>cone</u><u> </u><u>with </u><u>volume</u><u> </u><u>7</u><u>6</u><u>9</u><u>?</u><u>3</u><u> </u><u>ft³</u><u> </u><u>,</u><u> </u><u>having </u><u>a </u><u>height </u><u>of </u><u>1</u><u>5</u><u> </u><u>ft</u>

  • To calculate - <u>radius </u><u>of </u><u>the </u><u>cone</u>

We know that ,

\bold{Volume \: of \: cone =  \frac{1}{3}\pi \: r {}^{2}  h }\\

<u>substituting</u><u> </u><u>the </u><u>values </u><u>in </u><u>the </u><u>formula</u><u> </u><u>stated </u><u>above </u><u>,</u>

\bold{769.3 =  \frac{1}{3}  \times 3.14 \times r {}^{2}  \times 15} \\  \\\bold{\implies r {}^{2}  =  \frac{769.3 \times 3}{3.14 \times 15} } \\  \\\bold{\implies  r {}^{2}  =  \cancel\frac{2307.9}{47.1}}  \\  \\\bold{ \implies \: r {}^{2}  = 49} \\  \\ \bold{\implies \: r = 7 \: ft}

therefore ,

<u>radius </u><u>=</u><u> </u><u>7</u><u> </u><u>cm</u>

hope helpful ~

4 0
2 years ago
5.1.2 Exam: Semester 2 Exam
Nikolay [14]

Answer:

See attached picture to view the graph

Step-by-step explanation:

Start by analyzing how this average idea works:

If only one member goes to the trip, it will cost him/her $1000+$200 = $1200.

If two members go to the trip, then they will share the cost as per the following: ($1000+ $200 + $200 = $1400) which they will be dividing into two people, thus costing each of them $700.

Notice that the general function that represents such average will be given by: f(x) = \frac{1000+200x}{x}

Plot such function in the two dimensional plane, and you will get the asymptotic behavior shown in the attached image.

8 0
2 years ago
Draw a triangle that is both a right triangle and an isosceles triangle. You can use either pencil and paper, or a draw program.
dem82 [27]
2. measurements can be any to complementary angles.
   for example, 60 & 30
3. the 2 sides are equal. Since it is an isosceles triangle.
4.an equi.triangle can never be right angled. Since, all angles are 60° in an             equi.triangle.
5. right triangle can never have an obtuse angle since one angle is already          90°. therefore the other two agles are supposed to be acute angles.[ since        sum of all angles in a triangle is 180°]
6 0
3 years ago
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