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katovenus [111]

3 years ago

11

Solve equation

3} = 3" alt="\frac{k-4}{3} = 3" align="absmiddle" class="latex-formula">

1 answer:

3241004551 [841]3 years ago

6 0

k-4/3= 3

Mutiply both sides by 3 .

(3)(k-4/3)= (3)(3)

Cross out 3 and 3 , divide by 3 and then becomes k-4= 9

Move -4 to the other side

Sign changes from -4 to +4

k-4+4= 9+4

k= 13

Answer: k= 13

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What type of angles are ∠4 and∠6? Question 2 options: adjacent angles alternate exterior angles alternate interior angles corres

lianna [129]

Angles 4 and 6 are called Alternate Exterior Angles

Step-by-step explanation:

Alternate Exterior Angles are a pair of angles on the outer side of the each of two lines but on opposite sides of the transversal.

When we take two parallel lines they will create 8 angles, such as 1,2,3,4,5,6,7 & 8.

In that angle 6 is 65 degrees.

Angles 1,2,3 & $ are in one line and remaining four angles on other line.

So Angles 4 and 6 are alternate exterior angles.

5 0

3 years ago

Rewrite the equation by completing the square 4x^2-4x+1=0

oee [108]

Answer:

4(x - $\frac{1}{2}$ )² = 0

Step-by-step explanation:

Given

4x² - 4x + 1 = 0

To complete the square the coefficient of the x² term must be 1

Factor out 4 from 4x² - 4x

= 4(x² - x) + 1 = 0

add/subtract ( half the coefficient of the x- term )² to x² - x

4(x² + 2(- $\frac{1}{2}$ )x + $\frac{1}{4}$ - $\frac{1}{4}$ ) + 1 = 0

4(x - $\frac{1}{2}$ )² - 1 + 1 = 0

4(x - $\frac{1}{2}$ )² = 0

8 0

3 years ago

Read 2 more answers

A store sells three types of note cards. There are three sizes of each type. Show two ways to find the total number of notecards

bonufazy [111]

Answer: There are 9 different types of note cards that the store sells.

We can use the Fundamental Counting Principle to determine the total number of options.

There are two different events in this problem. First, there are 3 kinds of cards. Second, there are 3 sizes for each kind.

Simply, multiply the 3 by the other 3 and you have 9 different options.

Just think, each card would have a small, medium and larger option. So there are 3 groups of 3 or 9 total options.

8 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

3 friends are sharing 1/2 of a blueberry ....how much pie would each friend get

melisa1 [442]

Answer:

each friend would get 1/6 when you divide 1/2 by 3

Step-by-step explanation:

3 0

3 years ago