Evaluate the expression 4a^2 - 2b ÷ 4 for a = 2 and b = 4.

A. 2

B. 8

C. 14

D. 16

To divide 2 and 5/14 by (2 and 5/8 times 1 and 3/7), convert the mixed numbers to improper fractions, multiply the fractions in the denominator and numerator separately, and then divide by multiplying by the reciprocal of the second fraction. The final answer is 44/5.

To divide 2 and 5/14 by (2 and 5/8 times 1 and 3/7), we first need to convert the mixed numbers into improper fractions. 2 and 5/14 can be written as 33/14, 2 and 5/8 can be written as 21/8, and 1 and 3/7 can be written as 10/7. Next, we can multiply the fractions in the denominator and the fractions in the numerator separately. So (2 and 5/8 times 1 and 3/7) becomes (21/8 times 10/7). This can be simplified to (105/8 times 10/7). We then multiply the numerators (105 * 10) and the denominators (8 * 7) resulting in 1050/56.

Now we can divide 33/14 by 1050/56. Division is the same as multiplying by the reciprocal of the second fraction. So 33/14 divided by 1050/56 is the same as 33/14 times 56/1050. We can simplify this by canceling common factors. After canceling, we are left with (33 * 8) / (2 * 15), which becomes 264/30. Finally, we can reduce this fraction to its simplest form by dividing the numerator and denominator by their greatest common factor, which is 6. So the final answer is 44/5.

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Final answer:

To solve for x in the equation X + 6y = 29, subtract 6y from both sides to isolate x, resulting in x = 29 - 6y. The solution for [tex]\( x \)[/tex] in the first equation is [tex]\( x = \frac{19}{2} \).[/tex]

Explanation:

To solve for [tex]\( x \)[/tex] in the first equation [tex]\( x + 6y = 29 \)[/tex], we can isolate [tex]\( x \)[/tex] by subtracting [tex]\( 6y \)[/tex] from both sides of the equation:

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

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

Now, we can substitute this expression for [tex]\( x \)[/tex] into the second equation [tex]\( 2x - 4y = -6 \):[/tex]

[tex]\[ 2(29 - 6y) - 4y = -6 \][/tex]

First, distribute the 2:

[tex]\[ 58 - 12y - 4y = -6 \][/tex]

Combine like terms:

[tex]\[ 58 - 16y = -6 \][/tex]

Next, isolate the term with [tex]\( y \)[/tex] by adding [tex]\( 16y \)[/tex] to both sides:

[tex]\[ 58 - 16y + 16y = -6 + 16y \][/tex]

[tex]\[ 58 = -6 + 16y \][/tex]

Now, isolate [tex]\( y \)[/tex]by subtracting 6 from both sides:

[tex]\[ 58 - 6 = 16y \][/tex]

[tex]\[ 52 = 16y \][/tex]

Finally, solve for [tex]\( y \)[/tex] by dividing both sides by 16:

[tex]\[ \frac{52}{16} = y \][/tex]

[tex]\[ y = \frac{13}{4} \][/tex]

Now that we have found the value of [tex]\( y \)[/tex], we can substitute it back into the expression we found for[tex]\( x \)[/tex]:

[tex]\[ x = 29 - 6\left(\frac{13}{4}\right) \][/tex]

[tex]\[ x = 29 - \frac{39}{2} \][/tex]

[tex]\[ x = \frac{58}{2} - \frac{39}{2} \][/tex]

[tex]\[ x = \frac{19}{2} \][/tex]

Therefore, the solution for [tex]\( x \)[/tex] in the first equation is [tex]\( x = \frac{19}{2} \).[/tex]

Answer:

The answer is FALSE

Step-by-step explanation:

APEX

To find the length of pole C, we can set up a system of equations using the given information. Solving the system of equations will give us the values of the lengths of poles A, B, and C. The length of pole C is found to be 14.5 inches.

We can solve this problem by setting up a system of equations. Let's represent the length of pole A as 'a', the length of pole B as 'b', and the length of pole C as 'c'. We are given that pole B is 1 3/4 times as long as pole A, so we can write the equation b = 1.75a. We are also given that pole C is 2 1/2 inches longer than pole A, so we can write the equation c = a + 2.5.

Since the total combined length of the three poles is 47 1/2 inches long, we can write the equation a + b + c = 47.5. Now we have a system of three equations:

We can solve this system of equations to find the length of pole C. Substituting equation 1 and equation 2 into equation 3, we get:

a + 1.75a + (a + 2.5) = 47.5

Combining like terms, we get:

3.75a + 2.5 = 47.5

Subtracting 2.5 from both sides, we get:

3.75a = 45

Dividing both sides by 3.75, we get:

a = 12

Now that we know the length of pole A, we can substitute it into equation 1 to find the length of pole B:

b = 1.75 * 12 = 21

Finally, we can substitute the length of pole A and pole B into equation 2 to find the length of pole C:

c = 12 + 2.5 = 14.5

Therefore, the length of pole C is 14.5 inches.

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The measure of the angle 6 is 33°.

Given that, ∠5 and ∠6 are vertical angles and m∠5=33°.

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.

As we know, the vertical angles are congruent.

So, ∠5 = ∠6

⇒ ∠6 = 33°

Therefore, the measure of the angle 6 is 33°.

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1 kilogram = 100 grams

3500 / 1000 = 3.5 kilograms

65.5 - 3.5 = 62

she weighs 62 kilograms

Final answer:

Tom was able to cut 7.5 pieces of ribbon that were 1/12 yard long from a total length of 5/8 yard, which normally rounds down to 7 full pieces.

Explanation:

Tom cut his 5/8 yard ribbon into pieces that were 1/12 yard long. To find out how many such pieces Tom could cut, you divide the total length of ribbon by the length of each piece:

Calculate how many 1/12 yard pieces are in one yard by dividing 1 by 1/12. This equals 12, which means there are 12 pieces of 1/12 yard in one yard.

Multiply 5/8 by 12 to find out how many 1/12 yard pieces are in 5/8 of a yard. (5/8) * 12 = 7.5

Therefore, Tom was able to cut 7.5 pieces of ribbon, each measuring 1/12 yard. Since you can't have half a piece of ribbon, we would round down to 7 pieces (the question remains if the leftover could form a full piece, but based on the initial information, it's assumed to not be a full piece).

Laura will need to subtract the volume from this shape in order to reveal a cone.

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

Since Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of base.

Here, Laura has found the volume of a cylinder. which means, she will need to subtract volume from this shape in order to reveal a cone.

Then proceed to find the area of half the base multiplied by the height and then multiply this quantity,

 where r is length of half the base. She will take this quantity and subract it from her previous quantity.

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