Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?

Answer:

The correct option is (A) i.e. cylinder.

Step-by-step explanation:NET BANGERZ

Answer:

never

Step-by-step explanation:

In a 30 - 60 - 90 degree triangle , the common ratio is

1  : [tex]\sqrt{3}[/tex] : 2

Shorter leg that is opposite to 30 degree = 1

Longer leg that is opposite to 60 degree = [tex]\sqrt{3}[/tex]

Hypotenuse is opposite to 90 degree = 2

Shorter leg is half the length of the hypotenuse as per the ratio

Long leg is never the half of the hypotenuse

Final answer:

To solve an equation by factoring, find the factors, set them equal to zero, and solve for the variable.

Explanation:

To solve an equation by factoring, you need to find the factors of the equation and set each factor equal to zero. Then, solve each equation separately to find the values of the unknown variable. Let's take an example:

If we have the equation [tex]x^2 - 5x + 6 = 0[/tex]:

This method of factoring and setting each factor equal to zero is a systematic approach to solving quadratic equations, providing a structured way to identify the solutions for the unknown variable. The application of this technique is fundamental in algebra, enabling the efficient determination of roots in quadratic expressions and contributing to a comprehensive understanding of solving equations.

4.2 Adding up the two equivalent fractions 

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5) - (10 * 7) / 7 = x - 65 / 7

Equation at the end of step 4:

x - 65 / 7 > 0

Step 5: 5.1 Multiply both sides by 7

All equation has always even numbers of imaginary roots because they always come in pairs. Therefore there must be either 2 imaginary roots, or zero. 

To determine the types of roots, we could try synthetic division by some of the factors of the number -32. The simplest factors are +1 or -1. Using this, we can quickly show that (x + 1) is a factor, and leaving (x² + 4x - 32) as the remainder. This remainder equation then factorises to (x - 4) (x + 8). 

So to conclude there are three real zeros which are:

x = -1

x = 4

x = -8

Answer:

The area of BEA is 200 square units.

Step-by-step explanation:

Given information: AB||CD and CD:BA = 6:5.

Let the length of sides CD and BA are 6x and 5x respectively.

If a transversal line intersect two parallel lines, then the alternative interior angles are equal.

[tex]\angle EAB=\angle EDC[/tex]             (Alternate interior angles)

[tex]\angle EBA=\angle ECD[/tex]             (Alternate interior angles)

[tex]\angle AEB=\angle DEC[/tex]             (Vertically opposite angles)

By AAA property of similarity,

[tex]\triangle ABE\sim \triangle DEC[/tex]

The area of two similar triangles is proportional to the square of their corresponding sides.

[tex]\frac{Area(CED)}{Area(BEA)}=\frac{CD^2}{BA^2}[/tex]

[tex]\frac{288}{Area(BEA)}=\frac{(6x)^2}{(5x)^2}[/tex]

[tex]\frac{288}{Area(BEA)}=\frac{36x^2}{25x^2}[/tex]

[tex]\frac{288}{Area(BEA)}=\frac{36}{25}[/tex]

[tex]288\times 25=36\times Area(BEA)[/tex]

[tex]7200=36\times Area(BEA)[/tex]

Divide both sides by 36.

[tex]200=Area(BEA)[/tex]

Therefore the area of BEA is 200 square units.

Answer:

Option (c) is correct.

(x-4) is a factor of given trinomial.

Step-by-step explanation:

Consider the give trinomial [tex]x^2-10x+24[/tex]

We have to find the factors of given binomial and choose the correct one from the given options.

Consider the given polynomial [tex]x^2-10x+24[/tex]

We will simplify the given quadratic equation using middle term split method,

-10x can be written as -4x-6x

Such that the product of term will give the product of the remaning terms,

Thus, the given trinomial becomes,

[tex]x^2-4x-6x+24[/tex]

Taking x common from first two terms and -6 common from last two terms, we have,

[tex]x(x-4)-6(x-4)[/tex]

Thus,  take (x-4) common , we have,

[tex](x-4)(x-6)[/tex]

Thus, out of given factors (x-4) is a factor of given trinomial.

Answer:

[tex]\frac{3}{10}\times 60\text{ or }\frac{30}{100}\times 60[/tex]

Step-by-step explanation:

Given expression,

30% of 60,

We know that,

Convert percentage to fraction :

[tex]a\% =\frac{a}{100}[/tex]

Thus,

[tex]30\% = \frac{30}{100}=\frac{3}{10}[/tex]

So, 30% of 60 = [tex]\frac{3}{10}\times 60[/tex]

Which is the required expression.

parallelogram

DH = FH

3x -3 = x + 7

2x = 10

 x = 5

Answer

To solve this problem, we use the z statistic with formula:

z = (x – u) / s

or

x = s z + u

First we find the value of z at P = top 20%

z = 0.84

So the cut-off is:

x = 5 * 0.84 + 78

x = 82.2                 (ANSWER)

Answer:

So, if coach Stevens places as sprinkler of maximum distance 50 ft, he won't be able to cover the entire infield.

Step-by-step explanation:

Consider the infield as a polygon ABCDE.

It is given that each side AB, BC, CD, and DA is of length 90ft. It is also given that the infield is a perfect square.

Thus, the area of the square ABCD = 8100 ft.

Now consider the triangle BCD. Because of symmetry, the area of this triangle equals half the area of the square. Again, because of symmetry, the length of the base BD equals twice the length of the height EC.  

Thus from to the formula of area of the triangle:

base × height = 4050 base × height = 8100 2(height) × height= 8100 height63.64 ft

Answer:

Throw Blanket : $20

Embroidered Letter: $1.50

Step-by-step explanation:

Create a set of equations to solve this problem, where x is cost of throw blanket and y is cost of single embroidered letter.

My name:

[tex]x+6y=29\\x=29-6y[/tex]

Friend's name:

[tex]x+3y=24[/tex]

Substituting x into friend's name equation:

[tex](29-6y)+3y=24.5\\3y-6y=24.5-29\\-3y=-4.5\\y=1.5[/tex]

Substituting y into equation for x:

[tex]x=29-6(1.5)\\x=29-9\\x=20[/tex]