What is the area of rectangle CDEF?<br> Area= ...square units

yuko is volunteering at the food bank. He is creating thanksgiving food baskets to give to local families. He has 192 cornbread

Deffense [45]

Answer:

32 baskets
2 boxes of stuffing mix, 3 cans of vegetables, 6 cornbread muffins

Step-by-step explanation:

The greatest common factor (GCF) will be the greatest number of baskets yuko can create. We can examine the factoring of these numbers to see what it might be.

64 = 2^6

96 = 2^5 × 3

192 = 2^6 × 3

The unique factors are 2 and 3, and the lowest powers of each are 5 and 0, respectively. Then the GCF is ...

2^5 × 3^0 = 32 × 1 = 32

After the factor of 32 is removed from each of these numbers, we have ...

64 = 32·2 boxes of stuffing mix

96 = 32·3 cans of vegetables

192 = 32·6 cornbread muffins

These other factors are the numbers of the corresponding item that will be in each of the 32 baskets:

2 boxes of stuffing mix
3 cans of vegetables
6 cornbread muffins

6 0

3 years ago

Given Δ ABD ≅ ΔEBD, what can you conclude?

Anna71 [15]

You can conclude that AE = DE because the triangles are about equal

8 0

3 years ago

Read 2 more answers

Whats the answer? <br> and how did I get my answer?

Kamila [148]

Answer:

40°

Step-by-step explanation:

Angle 1 and Angle 2 are corresponding angles.

Corresponding angles are congruent, so 3x + 4 = 5x - 20

Solving 3x + 4 = 5x - 20

3x = 5x - 24

2x = 24

x = 12

Substitute angle 1

3x + 4 = 36 + 4 = 40

7 0

2 years ago

Find , , and if and terminates in quadrant .

ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

$\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}$ $\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}$

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

$\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})$ $=\frac{12}{13}$

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

$\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}$

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

$\tan 2x=\frac{2\tan x}{1-\tan ^2x}$ $=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}$ $=\frac{\frac{4}{3}}{1-\frac{4}{9}}$ $=\frac{\frac{4}{3}}{\frac{9-4}{9}}$ $=\frac{\frac{4}{3}}{\frac{5}{9}}$ $=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}$

OR

$\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago

Find the equation of the line passing through the given points. Express the equation in standard form.

Artyom0805 [142]

We want to write the equation of the line passing through these two points in standard form.

First, we are going to do this in slope intercept form and then change the form to standard form, which is Ax + By = C

We will use the equation y = mx + b, and since we are given two points on the line we are going to determine the slope of the line by determining the change in the y coordinates

m = y sub2 - y sub1 divided by the change in the X coordinates x sub2 – x sub1

We will start by determining the slope

(1, -6) the 1 is x sub 1 and the 6 is y sub 1

(-7, 2) the -7 is x sub 2 and the 2 is y sub 2

2 - (-6) = 8

-7 -1 = -8

so equation now is m = -1

So now again referring back to the slope intercept of the line we now know y = -1 + b. We still have to determine b and the y intercept, and we can do this by using one of the given points and substituting in the value for y and x, and then solve for b. Since these points are on the line, they must satisfy this equation. If we use the first coordinates, we would substitute 1 for x and -6 for y.

-6 = -1 times x, which is 1 + b

b = -5

construct the line equation y = mx + b where m = -1 & b = -5

In slope intercept form the equation would be y = -x - 5

Now we want to write this in standard form now. We have to deal with two things. The x and y terms have to be on the left side and A and B and C have to be integers.

The standard form of a linear equation is Ax + By=CA x + By = C . Move all terms containing variables to the left side of the equation.

Add x to both sides of the equation.

y + x = -5

Reorder y & x

x + y = -5

3 0

3 years ago

What is the area of rectangle CDEF? Area= ...square units