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3 years ago

Choose an equivalent expression for 123 • 129 • 124 • 122. 124 1218 1235 12216

Mathematics

1 answer:

mihalych1998 [28]3 years ago

3 0

Question:

Choose an equivalent expression for 12^3 • 12^9 • 12^4 • 12^2

A. 12^4 B. 12^18 C. 12^35 D. 12^216

Answer:

$12^{18}$

Step-by-step explanation:

Given

$12^3 . 12^9 . 12^4 . 12^2$

Required

Determine the equivalent

Applying law of indices, we have:

$12^{3 + 9 + 4 + 2}$

$12^{18}$

Hence:

$12^3 . 12^9 . 12^4 . 12^2 = 12^{18$

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pamela claims that if you multiply a fraction that is negative by another fraction that is negative, the product will also be ne

svetoff [14.1K]

Pamela is incorrect. When you multiply anything negative by a negative, the product will always be a positive. Because the two negative signs cancel each other out.

5 0

3 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

3 years ago

A textbook store sold a combined total of 477 sociology and math textbooks in a week. The number of sociology textbois sold was

denpristay [2]

Answer:

The correct answer is 218 math textbooks and 259 sociology textbooks.

Step-by-step explanation:

To solve this problem, we can make a system of equations. Let the number of sociology textbooks sold be represented by the variable "s" and the number of math textbooks sold be represented by the variable "m". Using these variables, we can make two equations:

s + m = 477

m + 41 = s

There are many ways to solve this system of equations. One approach we can take is substituting the value for s given by the second equation into the first equation. This is modeled below.

s + m = 477

(m + 41) + m = 477

Combining like terms on the left side of the equation yields:

2m + 41 = 477

Subtracting 41 from both sides of the equation gives us:

2m = 436

Finally, dividing both sides of the equation by 2 gives us:

m = 218

To solve for the number of sociology textbooks, we can substitute into either of our original equations.

m + 41 = s

(218) + 41 = s

s = 259

Therefore, your answer is m = 218 and s = 259, or 218 math textbooks and 259 sociology textbooks were sold.

Hope this helps!

6 0

2 years ago

Help!<br><br> If a sphere has a radius of 8mm, what is its volume? (Show work)

babymother [125]

The formula for the volume of a sphere is V = (4/3) * π * r³. Knowing this, we can plug in the radius:

$V = \frac{4}{3} \pi *8^{3} \\ V = \frac{4}{3} \pi*512 \\ V = 2144.66$

The sphere's volume is approximately 2144.66 mm^3.

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3 years ago

Will a 7/32 inch diameter pin fit into a reamed hole with a diameter of 0.215 inches?

lana [24]

Answer:

no ... the pin will not fit the reamed hole

Step-by-step explanation:

The decimal equivalent of 7/32 is 0.21875. This is larger than the reamed

hole: 0.215

and so the answer is no ... the pin will not fit the reamed hole.

6 0

3 years ago