5th row of pascal's triangle in expanded form

Graph y > -1/3x+5 <img src="https://tex.z-dn.net/?f=y%20%3E%20%20-%20%20%5Cfrac%7B1%7D%7B%203%20%7D%20x%20%2B%205" id="Tex

ad-work [718]

Explanation:

The function is $y>-\frac{1}{3} x+5$

To graph the function, let us find the x and y intercepts.

To find x-intercept, let us substitute y=0 in the function $y>-\frac{1}{3} x+5$

$\begin{aligned}0 &=-\frac{1}{3} x+5 \\-5 &=-\frac{1}{3} x \\x &=15\end{aligned}$

Thus, the x-intercept is $(15,0)$

To find the y-intercept, let us substitute x=0, we get,

$\begin{aligned}&y=-\frac{1}{3}(0)+5\\&y=5\end{aligned}$

Thus, the y-intercept is $(0,5)$

The graph has no asymptotes.

To plot the points in the graph, we need to substitute the values for x in the function $y>-\frac{1}{3} x+5$ , to find the y-values.

The points are $(-2,5.667),(-1,5.333),(1,4.667),(2,4.333),(3,4)$ . The image of the graph and table is attached below:

6 0

3 years ago

What type of number can be written as a fraction p%q where p and q aré integers and q is not equal to zero

MatroZZZ [7]

Hi there!

The correct answer is Rational Number.

$\bf{EXPLANATION}$ :-

Rational Number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator " p " and a non-zero denominator " q ".

~ Hope it helps!

7 0

3 years ago

3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie

allsm [11]

Answer:

The building is 61.5 m tall

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

$\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 53^\circ=\frac{150-x}{h}$

$\displaystyle \tan 48^\circ=\frac{x}{h}$

From the last equation:

$x=h.\tan 48^\circ$

Substituting into the first equation:

$\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}$

Operating on the right side:

$\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ$

Rearranging:

$\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}$

Solving for h:

$\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}$

Calculating:

h = 61.5 m

The building is 61.5 m tall

5 0

3 years ago

Michael and Lindsey are saving money. Michael begins with $20 and saves $5 per week. Lindsey begins with no money, but saves $10

True [87]

Let
x----------> number of weeks
y----------> saved money

we now that

Michael begins with $20 and saves $5 per week
so
y=20+5x------> equation 1

and
Lindsey begins with no money, but saves $10 per week
y=10x-------> equation 2

the number of weeks it will take for Lindsey and Michael to save the same amount of money is when equation 1 is equals to equation 2

therefore
20+5x=10x------> 10x-5x=20------> 5x=20-----> x=20/5-----> x=4 weeks

the answer is
4 weeks

3 0

3 years ago

The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s

sweet [91]

Answer:

<h2>Below, Hope this helps :)</h2>

Step-by-step explanation:

The variable t represents the amount of gas in mom's truck. Since we need to find a number that is 50% more than 12, we use 1.5 (we would use 2 if we want 100% more, so it makes sense that we use 1.5, since we want to add 1/2 of 12 to 12. The answer is 18.)

6 0

3 years ago