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3 years ago

A shelf takes 3 1 /2 ft. of lumber. How many shelves can be made from 24 1 /2

Mathematics

2 answers:

soldier1979 [14.2K]3 years ago

5 0

Answer:

The answer is 7.

Step-by-step explanation:

3 1/2= 3.5

24 1/2= 24.5

Now you divide them.

24.5/3.5= 7

levacccp [35]3 years ago

3 0

Answer is 7

hope it helps

24 1/2 = 24.5
3 1/2 = 3.5

24.5/3.5 = 7

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I need the answer to all 4 questions

andreev551 [17]

Answer:

The answer to your question is:

Step-by-step explanation:

a) There is no figure 0.

b) From one figure to the other there are 2 more cubes

c) Number of cubes = 3 + 2(n- 1)

where n is the number of figure

Number of cubes in figure 100 = 3 + 2(100 - 1)

= 3 + 2(99)

= 3 + 198

= 201

5 0

3 years ago

A police helicopter flying at a height of 85 feet shines a light on a speeding vehicle below. If the angle of depression is 62 d

Naily [24]

Answer: 96 feet i believe

8 0

3 years ago

Secants AC and DB intersect at point E inside the circle. Given that the measure of arc CD = 40o, arc AB = 60o, and arc BC = 160

s344n2d4d5 [400]

Answer:

C. $130^{\circ}$

Step-by-step explanation:

Please find the attachment.

We have been given that secants AC and DB intersect at point E inside the circle. Given that the measure of arc $CD = 40^o$ , arc $AB = 60^o$ , and arc $BC = 160^o$ . We are asked to find the measure of angle AED.

We know that the measure of angle formed by two intersecting secants is half the sum of measure of the arcs by intercepted by the angle and its vertical angle.

$\angle AED=\frac{\widehat{BC}+\widehat{AD}}{2}$

Let us find measure of arc AD by subtracting measure of given arcs from 360 degrees as:

$\widehat{AD}=360^{\circ}-(60^{\circ}+40^{\circ}+160^{\circ})$

$\widehat{AD}=360^{\circ}-(260^{\circ})$

$\widehat{AD}=100^{\circ}$

$\angle AED=\frac{160^{\circ}+100^{\circ}}{2}$

$\angle AED=\frac{260^{\circ}}{2}$

$\angle AED=130^{\circ}$

Therefore, measure of angle AED is 130 degrees and option C is the correct choice.

6 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

18 is ( blank ) % of 30

meriva

Make an equation.

'is' is an equal sign

The blank can be 'x'

'of' = multiplication

18 = x * 30

Multiply:

18 = 30x

Divide 30 to both sides:

x = 0.6

Multiply by 100:

0.6 * 100 = 60%

4 0

3 years ago

Read 2 more answers