What is the equation of the verticl line through (5,2)?

Write and solve an equation to find the unknown angle.

Julli [10]

There's many properties you can use to find an unknown angle.

There are too many to lists but one core example would be an isosceles triangle that has two adjacent sides and angles.

Let's say that the sides of an isosceles triangle are any number "x"

now since two sides of the triangle are the same we can add these two x's together.

x+x = 2x

now the other side of the triangle can be anything you like. We can call it 4x for this example.

now if we add them all together we'll get 4x+2x=6x

Now since the angles of a triangle add up to 180 degrees
we can equate 6x=180 leaving x to be 30.

Now since x belongs to both sides of the triangle we can say that both angles are congruent as well because the two sides of the triangle are congruent. This is a known triangle law.

Since both angles are now 30 degrees this will leave us with 2(30) = 60

now if we subtract 180 - 60 we'll get 120 which is the remainder of the 3rd angle of the side that corresponds with 4x.
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5 0

4 years ago

I WILL GIVE 15 POINTS!!!!

Archy [21]

Idk I’m not that very smart

7 0

3 years ago

Read 2 more answers

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating <em>11 units to the left:</em>

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating<em> 5 units down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>

SECOND.

Translating <em>8 units to the right:</em>

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating<em> 1 unit down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

7 0

3 years ago

Luke has two summer jobs. During the week he works in the grocery store, and on the

TiliK225 [7]

Hello! First, let's get some important information:

Luke works in the:

week → grocery store → $16/hour
weekend → nursery → $22/hour

Now, let's analyze the questions:

<h3>a) How much does he earn if he works 5 hours at the grocery store and 8 hours at the nursery? </h3>

To find the amount he will receive, you must multiply the amount of 1 hour by the number of hours worked. Look:

$\mathrm{Grocery\:Store}\\\\\$16 \cdot 5 \:\mathrm{hours}= \$80\\\$22 \cdot 8\:\mathrm{hours}=\$176$

<h3>b) How much does he earn if he works g hours at the grocery store and n hours at the nursery?</h3>

$\$16 \cdot \mathrm{g} \:\mathrm{hours}= \$16\cdot\mathrm{g}\\\$22 \cdot \mathrm{n}\:\mathrm{hours}=\$22\cdot\mathrm{n}$

<h3>c) Total pay, 5 hours at the grocery store and 8 hours at the nursery:</h3>

You'll just have to just add the value in each of the jobs:

$80 + $176 = $256

<h3>d) Total pay, g hours at the grocery store and n hours at the nursery:</h3>

Adding the values of each job:

$16g + $22n

Hope this helps!

8 0

3 years ago

I NEED HELP ASAP!!!! PLZZ HELP MEEEE!!!!! Which of the following lists is ordered from least to greatest?

mario62 [17]

Answer: D. -5, 0, 0.8, 1, 1 1/2

<em>Hope this helps!</em>

8 0

3 years ago