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3 years ago

Now group the terms in the expression in part c using the associative property

Mathematics

1 answer:

Tom [10]3 years ago

7 0

Answer:

70 + (-30) + 2 + (-9) + 0.3 + (-0.1) = [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.1)]

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If you place a 17 foot ladder against the top of a 8 foot building how many feet will be bottom of the ladder be from the bottom

Marat540 [252]

Answer:

The distance of the bottom of the ladder be from the bottom of the building is = 15 feet

Step-by-step explanation:

Given:

Length of the ladder =17 ft

Height of the building = 8 ft

To find the length between the bottom of the ladder and the bottom of the building.

Solution:

On drawing out the situation, we find out that a right triangle is formed with the ladder being the hypotenuse and the building being a leg of the right triangle.

<em>We need to find the length of the other leg of the triangle which is the distance from the bottom of the ladder to the bottom of the building.</em>

Applying Pythagorean theorem:

$Hypotenuse^2=Leg1^2+Leg2^2$

Plugging in values in feet from the given data.

$17^2=Leg1^2+8^2$

Simplifying.

$289=Leg1^2+64$

Subtracting both sides by 64.

$289-64=Leg1^2+64-64$

$225=Leg1^2$

Taking square root both sides.

$\sqrt{225}=\sqrt{Leg1^2}$

$15=Leg1$

∴ $Leg1=15\ ft$

Thus, distance of the bottom of the ladder be from the bottom of the building is = 15 feet

8 0

3 years ago

Help me plz math (picture)

skad [1K]

For 34, since each diameter is in scientific notation , meaning that we have one number (1-9) followed by a decimal, we simply see which has the smallest power, which is cell C.

For 35, we multiply them out to get 0.83*10^2 (we subtract exponents when dividing). Since scientific notation is one integer from 1-9 followed by a decimal, we move 0.83 one place to the right and therefore remove one power from 10^2, getting 8.3*10

6 0

3 years ago

Estimate the sum or difference.

dangina [55]

1) $\frac{4}{6}+\frac{1}{8}=\frac{19}{24}$

2) $\frac{2}{6}+\frac{7}{8}=\frac{29}{24}$

3) $\frac{5}{6}-\frac{3}{8}=\frac{11}{24}$

4) $\frac{4}{6}+\frac{3}{8}=\frac{25}{24}$

5) $\frac{7}{8}-\frac{5}{6}=\frac{1}{24}$

6) $\frac{1}{6}+\frac{7}{8}=\frac{25}{24}$

Step-by-step explanation:

In order to calculate the sum of two fractions, we first have to find the lowest common denominator of the two fractions, then multiply the numerator of each fraction by the ratio between the lowest common denominator and the original denominator, and then add/subtract the two new numerators.

$\frac{4}{6}+\frac{1}{8}=$

Here the lowest common denominator between 6 and 8 is 24,

So we have to rewrite each fraction as having denominator 24: this means that we have to multiply both numerator and denominator of the 1st fraction by 4 (because 24/6=4), and both numerator and denominator of the 2nd fraction by 3 (because 24/8=3).

So the new numerators of the two fractions are:

$4\cdot 4 = 16\\1\cdot 3 = 3$

The expression then becomes:

$\frac{4}{6}+\frac{1}{8}=\frac{16}{24}+\frac{3}{24}=\frac{16+3}{24}=\frac{19}{24}$

$\frac{2}{6}+\frac{7}{8}=$

Here the lowest common denominator between 6 and 8 is again 24,

so we have again to multiply both numerator and denominator of the 1st fraction by 4, and both numerator and denominator of the 2nd fraction by 3.

So the new numerators of the two fractions are:

$2\cdot 4 = 8\\7\cdot 3 = 21$

And we get:

$\frac{2}{6}+\frac{7}{8}=\frac{8}{24}+\frac{21}{24}=\frac{8+21}{24}=\frac{29}{24}$

$\frac{5}{6}-\frac{3}{8}$

The denominators are the same, so the lowest common denominator is always 24. So we can adopt the same procedure, and new numerators are:

$5\cdot 4 = 20\\3\cdot 3 = 9$

And so:

$\frac{5}{6}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24}=\frac{20-9}{24}=\frac{11}{24}$

$\frac{4}{6}+\frac{3}{8}=$

Using the same lowest common denominator, 24, the new numerators are:

$4\cdot 4 = 16\\3\cdot 3 = 9$

And so we can rewrite the expression as

$\frac{4}{6}+\frac{3}{8}=\frac{16}{24}+\frac{9}{24}=\frac{16+9}{24}=\frac{25}{24}$

$\frac{7}{8}-\frac{5}{6}=$

Again, the lowest common denominator is 24. This time the denominator of the 1st fraction is 8 while the denominator of the 2nd fraction is 6, so we have to multiply the numerator of the 1st fraction by 3 and the numerator of the 2nd fraction by 4.

We get:

$7\cdot 3 = 21\\5\cdot 4 = 20$

So the expression will be rewritten as:

$\frac{7}{8}-\frac{5}{6}=\frac{21}{24}-\frac{20}{24}=\frac{21-20}{24}=\frac{1}{24}$

$\frac{1}{6}+\frac{7}{8}=$

Here the situation is similar to the first 4 exercises: using 24 as lowest common denominator, the numerators become

$1\cdot 4 = 4\\7\cdot 3 = 21$

So the expression becomes

$\frac{1}{6}+\frac{7}{8}=\frac{4}{24}+\frac{21}{24}=\frac{4+21}{24}=\frac{25}{24}$

Learn more about fractions:

brainly.com/question/605571

brainly.com/question/1312102

#LearnwithBrainly

8 0

3 years ago

What is 10and 1 half divided by 7 eights

Lunna [17]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Rectangle KLMN is graphed on the coordinate plane below. On a coordinate plane, rectangle K L M N has points (2, negative 2), (5

gladu [14]

Answer: The correct option is (A) (2, -2).

Step-by-step explanation: Given that rectangle with vertices at K, L, M and N is graphed on the coordinate plane as shown in the figure.The figure is rotated 360° counterclockwise using the origin as the center of rotation.

We are to find the location of the image of point K after the rotation.

We know that

a rotation of 360° in counterclockwise direction about the origin map a point to itself. That is, the co-ordinates of the image point will be same as the original one.

From the figure, we see that the co-ordinates of point K are (2, -2).

Therefore, after rotation of 360° counterclockwise using the origin as the center of rotation,

the co-ordinates of the image of point K will also be (2, -2).

Thus, the location of the image of point K is (2, -2).

Option (A) is CORRECT.

8 0

2 years ago