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3 years ago

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If m<6 = (3x-13)° and m<8 = (2x-5°), what is the value of x

1 answer:

mestny [16]3 years ago

6 0

Answer:

<h2>The value of x is 8.</h2>

Step-by-step explanation:

We know that $m\angle 6 = m \angle 8$

Each angle is defined as

$m\angle 6 = 3x-13$ and $m \angle 8 =2x-5$

Replacing all in the first equation, we have

$3x-13=2x-5\\3x-2x=13-5\\x=8$

Therefore, the value of x is 8.

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Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

4 years ago

Without drawing the lines, state the gradient of the lines with the following equation y=2x+4

777dan777 [17]

Answer:

gradient m is 2

Step-by-step explanation:

the equation is y=mx+c therefore m is 2.

3 0

3 years ago

Louisa ran at an average speed of five miles per hour along an entire circular park path. Calvin ran along the same path in the

docker41 [41]

Answer:

15 miles

Step-by-step explanation:

Let $x$ be the miles in the circular park path, $t_{L}$ the time Louisa takes to finish and $t_{C}$ the time Calvin takes to finish both in hours.

Then $x$ , the longitude is equal to the velocity times the time used to finish. So

$x=5t_{L}$

$x=6t_{C}$

And the difference between Louisa's time and Calvin' time is 30 minutes, half an hour. So:

$t_{C}=t_{L}-0.5$

Three equations, three unknowns, the system can be solved.

Equalizing the equation with x :

$5t_{L}=6t_{C}$

In this last equation replace $t_{C}$ with the other equation and solve:

$5t_{L}=6(t_{L}-0.5)\\ 5t_{L}=6t_{L}-3\\ 3=6t_{L}-5t_{L}\\ 3=t_{L}\\ t_{L}=3$

With Louisa's time find x:

$x=5t_{L}\\ x=5(3)\\ x=15$

7 0

3 years ago

Help me with this please

qwelly [4]

The fraction is written as 3/4.
If you divide 3 by 4 you will get the decimal.

8 0

3 years ago

HELPPPP PLEASE!!!!!!!!

babunello [35]

Answer:

False, since x values cannot have more than one y value.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers