MATHEMATICS HIGH SCHOOL

Use cross products to demonstrate whether the two ratios are equivalent in this problem: 4 over 6 times 14 over 21

Answers

Answer 1

Answer:

Determine if the two ratios are equivalent in this problem

The two ratios are equivalent

Given:

4 over 6 times 14 over 21

Times mean multiplication (×) in mathematics

Over means division (÷ or /) in mathematics

So,

4 over 6 times 14 over 21

= 4/6 × 14 / 21

Equate both ratio

4/6 = 14/21

cross product

(4 × 21) = (6 × 14)

84 = 84

Therefore, the two ratios are equivalent

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Answer 2

Answer: 4/6 = 14/21When using cross product always multiply the left fractions numerator times the right side fractions denominator and the left side fractions denominator times the right side fractions numerator4×21 = 6×1484=84They are equivalent because they both equal 84

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State the next term of each sequence
a) 1, 16, 81, 256....
b) 1, 1, 2, 4, 7, 13, 24....

Answers

a) 1, 16, 81, and 256 are all perfect squares. Find their squares:
1, 4, 9, 14.
In this sequence, you first at 3, then 5, then 7. So, logically, you would add 9 next. 14 + 9 is 23, and 23 squared is 529.
b) I'm not sure the data points for this sequence are correct. I'd have to guess 42 based on this difference chart:
1 1 2 4 7 13   24   42
+0 +1 +2 +3 +6 +11 +18
+1 +1 +1 +3 +5   +9
+0 +0 +2 +2   +4
  +0 +2 +0 +2

a)
$1,16,81,256,\underline{625}\n\text{The general formula is } n^4 \text{ where } n\in \mathbb{N}$

b)
$1,1,2,4,7,13,24,\underline{44}\n\text{Each number is the sum of three preceding numbers.}$

Round number to the nearest hundreds 748

Answers

700 because 48 is under 50 which makes it have to round down to the nearest hundred

Choose the equation below that represents the line that passes through the point (7, −2) and has a slope of −3.y − 2 = −3(x + 7)
y + 7 = −3(x − 2)
y + 2 = −3(x − 7)
y − 7 = −3(x + 2)

Answers

Answer:

Therefore, Option 3rd is correct that is $y+2=-3(x-7)$ which is required equation of a line.

Step-by-step explanation:

We have given a point through which line is passing that is (7,-2) and slope is also given which is -3

We have a general equation of line which is

$(y-y_1)=m(x-x_1)$

Here, $m=-3$

And $y_1=-2,x_1=7$ on substituting the values in the given formula for equation of a line we will get

$y-(-2)=-3(x-7)$

$\Rightarrow y+2=-3(x-7)$

Therefore, Option 3rd is correct that is $y+2=-3(x-7)$ which is required equation of a line.

Hello,

y+2=-3*(x-7)

Answer C

How many grams are in 40 hectograms?

Answers

In this case, 40 hectograms is equal to 4000 grams.

To convert hectograms to grams, we need to know that 1 hectogram (hg) is equal to 100 grams (g).

Now, let's calculate the number of grams in 40 hectograms:

1 hectogram = 100 grams

Therefore, 40 hectograms will be:

40 hectograms = 40 * 100 grams

40 hectograms = 4000 grams

So, there are 4000 grams in 40 hectograms.

In summary, to convert hectograms to grams, we use the conversion factor of 1 hectogram = 100 grams. By multiplying the number of hectograms by 100, we get the equivalent weight in grams. In this case, 40 hectograms is equal to 4000 grams. This conversion is based on the metric system, where prefixes like hecto- and kilo- represent multiples of 100 and 1000, respectively, making it easy to convert between different units of weight.

To know more about hectograms:

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#SPJ6

Something i use to convert metric units is: King Henry Died By Drinking Chocolate Milk. This is an acronym for:
K: Kilos
H: Hecto
D: Deka
B: Base (liters or grams etc.)
D: Deci
C: Centi
M: Milli

Now, since you are going from hectograms (hecto) to grams (base) you will move the decimal to the right 2 times (since base is 2 bellow hecto) So that means: There are 4,000 grams in 40 hectograms.

1. Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a month? (assume 4 weeks per month)

Answers

$40 per hour
15 students per week
Each hourly student earns them $40 and there are 15 students, so this is multiplication.
40 * 15 = 600 per week
There are 4 weeks per month to earn 600 each week, this is again multiplication.
600 * 4 weeks = 2400 per month
Out of their earned 2400 they must pay for their overhead, the building rent
2400 - 400 = 2000 profit
They are left with $2000 between them.

Answer:

$4400

Step-by-step explanation:

$40 per hour

15 x 40 = 600

Because 'each' of them had 15 students, 600 x 2 = 1200

There are 4 weeks per month to earn 1200 each week, this is again multiplication.

1200 * 4 weeks = 4800 per month

Out of their earned 4800 they must pay for their overhead, the building rent

4800 - 400 = 4400 profit

They are left with $4400 between them.

Which number produces a rationale number when added to 0.5