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3 years ago

Gretchen made 189 cookies in 4.5 hours what was her rate in cookies per hour

Mathematics

1 answer:

jasenka [17]3 years ago

3 0

Answer: 42 cookies/1 hour

Step-by-step explanation: Since Gretchen made 189 cookies in 4.5 hours, we set the equation up as 189/4.5. To get cookies per hour, we divide 189 by 4.5, which is 42/1. This means that Gretchen can make 42 cookies in 1 hour.

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A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

3 years ago

Calculate the gradient of the line using rise/run method.

Lapatulllka [165]

Given:

The graph of line.

To find:

The gradient of the line using rise/run method.

Solution:

We know that the gradient of a line is also known as slope.

$Slope=\dfrac{Rise}{Run}$

Consider the two intercepts, then rise is distance between origin and y-intercept and run is the distance between origin and the x-intercept. But rise must be negative because the value of y decreased from 3 to 0.

$Rise=-3$

$Run=2$

Now,

$Slope=\dfrac{Rise}{Run}$

$Slope=\dfrac{-3}{2}$

The gradient of the line is $-\dfrac{3}{2}$ .

Therefore, the correct option is C.

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3 years ago