A company makes 140 bags.

Ben is spending his summer driving across the country. He is going to spend the first day

KengaRu [80]

Answer:

The graph of the data presented is shown in the attached image to this solution.

It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t

Step-by-step explanation:

The distance travelled with the corresponding time taken are presented in the table

Note: D - Distance travelled (miles)

t - Time (hours)

D | t

55 | 1

110 | 2

165 | 3

220 | 4

275 | 5

330 | 6

We are then told to plot these distance travelled on a graph with the time taken.

The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.

The image of the graph of this function will be attached to this answer

It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t

Hope this Helps!!!

4 0

3 years ago

In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.

Elena L [17]

Given:

PQRS is a circle, PQT and SRT are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

$m\angle SPQ+m\angle QRS=180^\circ$

$81^\circ+m\angle QRS=180^\circ$

$m\angle QRS=180^\circ-81^\circ$

$m\angle QRS=99^\circ$

Now, SRT is a straight line.

$m\angle QRT+m\angle QRS=180^\circ$ (Linear pair)

$m\angle QRT+99^\circ=180^\circ$

$m\angle QRT=180^\circ-99^\circ$

$m\angle QRT=81^\circ$ ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

$m\angle PQR=m\angle QRT+m\angle QTR$

$x=81^\circ+22^\circ$

$x=103^\circ$

Therefore, the value of x is 103 degrees.

4 0

3 years ago

Given the following functions f(x) and g(x), solve (f + g)(5) and select the correct answer below: f(x)=2x^2-10 g(x)=x+9

steposvetlana [31]

Answer:

$\large\boxed{(f+g)(5)=54}$

Step-by-step explanation:

$f(x)=2x^2-10,\ g(x)=x+9\\\\(f+g)(x)=f(x)+g(x)\\\\\text{Substitute:}\\\\(f+g)(x)=(2x^2-10)+(x+9)=2x^2-10+x+9=2x^2+x+(-10+9)\\\\(f+g)(x)=2x^2+x-1\\\\(f+g)(x)(5)\to\text{put x = 5 to the equation of the function:}\\\\(f+g)(5)=2(5^2)+5-1=2(25)+5-1=50+5-1=54$