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3 years ago

14

Kathy is baking cakes. Each cake requires 1/12 of a teaspoon of vanilla,and she has 3/4 of a teaspoon,how many cakes can she bak

e?

1 answer:

scZoUnD [109]3 years ago

8 0

Answer:

Step-by-step explanation:

You want to find out how how 1/12 of a tsp go into 3/4 of a tsp so.......

You do 3/4 divided by 1/12 but when dividing fractions you flip over the second fraction and change the division operation to a multiplication operator so....

It will 3/4 x 12/1 and this will give you 36/4

36 divided by 4 is 9

So....

Kathy can bake 9 cakes.

Hope this helps!

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The diagram represents the shape and dimensions of Kayla's garden. A special fertilizer is used for the vegetable garden. Each b

Serjik [45]

Answer:

B. 18 bags

Step-by-step explanation:

First you need to determine the area of the vegetable garden. The vegetable garden is a rectangle with the following dimensions:

L = 24 ft

W = 9 ft

The Formula for the area of a rectangle is:

$A = L\times W$

So let's solve it:

$A = L\timesW\\A = 24 ft\times9ft\\A= 216ft^{2}$

With that, we can figure out how many bags of fertilizer would be needed by dividing the area of the vegetable garden by how much one bag of fertilizer covers:

$\dfrac{214ft^2}{12ft^2/bag}=18\;bags$

3 0

3 years ago

Read 2 more answers

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

topjm [15]

Given:

The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).

To find:

The fourth vertex of the parallelogram.

Solution:

Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).

We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Two diagonals of ABCD are AC and BD.

Midpoint of AC = Midpoint of BD

$\left(\dfrac{-3+2}{2},\dfrac{8-5}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)$

$\left(\dfrac{-1}{2},\dfrac{3}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)$

On comparing both sides, we get

$\dfrac{4+a}{2}=\dfrac{-1}{2}$

$4+a=-1$

$a=-1-4$

$a=-5$

And,

$\dfrac{5+b}{2}=\dfrac{3}{2}$

$5+b=3$

$b=3-5$

$b=-2$

Therefore, the coordinates of fourth vertex are (-5,-2).

3 0

3 years ago

Dan Perkins goat is attached to the corner of the 14-foot-by-7-foot pump house by a 14-foot length of rope. The goat eats the gr

fenix001 [56]

<span>This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat?</span>

We know that the formula for the area of the pitch circle are:
$\pi*r^2*\alpha$ where alpha is the pinch of circle, r is radius, and pi is mathematics constant approximately equal 3,14

$\pi*14^2*\frac{3}{4}+\pi*7^2*\frac{1}{4}=461,58+38,465=500,045(feet^2)$

5 0

3 years ago

A truck's gas tank holds 50 gallons of gas. if one gallon takes 30 seconds to pump, how many minutes will it take to fill the em

umka2103 [35]

To find how long it will take to fill the tank, you can use the idea that every 30 seconds will get you one gallon closer to being full.

This means to fill 50 gallons, you will need 50 groups of 30 seconds.

50 x 30 = 1500 seconds

1500/60 = 25 minutes.

It will take 25 minutes.

You could also think of it as filling 2 gallons every minute. It would take 25 of these.

7 0

3 years ago

Assuming that the equations define x and y implicitly as differentiable functions x=f(t),y=g(t) find the slope of the curve x=f(

Mumz [18]

The given equations are
$x(t+1)-4t \sqrt{x} =9$ (1)
$2y+4y^{3/2}=t^{3}+t$ (2)

When t=0, obtain
$x=9 \\ 2y+4y^{3/2}=0 \,\,=\ \textgreater \ \, y(1+2 \sqrt{y} )=0 \,=\ \textgreater \ \,y=0$

Obtain derivatives of (1) and find x'(0).
x' (t+1) + x - 4√x - 4t*[(1/2)*1/√x = 0
x' (t+1) + x - 4√x -27/√x = 0
When t=0, obtain
x'(0) + x(0) - 4√x(0) = 0
x'(0) + 9 - 4*3 = 0
x'(0) = 3
Here, x' means $\frac{dx}{dt}$ .

Obtain the derivative of (2) and find y'(0).
2y' + 4*(3/2)*(√y)*(y') = 3t² + 1
When t=0, obtain
2y'(0) +6√y(0) * y'(0) = 1
2y'(0) = 1
y'(0) = 1/2.
Here, y' means $\frac{dy}{dt}$ .

Because $\frac{dy}{dx} = \frac{dy}{dt} / \frac{dx}{dt}$ , obtain
$\frac{dy}{dx} |_{t=0}\, = \frac{1/2}{3}= \frac{1}{6}$

Answer:
The slope of the curve at t=0 is 1/6.

3 0

3 years ago