Answer:
Larger number:
16
Smaller number
3
Step-by-step explanation:
Larger number: 16
Smaller number: 3
Explanation:
Suppose the larger number is
a
and the smaller number is
b
.
You solve the following system of equations:
a⋅b=48
a−13=b
Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48
a 2−13a=48
a2−13a−48=0
Factor the polynomial:
(a−16)(a+3)=0
a=16 or a=−3a is positive so a=16.
We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.
Out of the four options,
A. 99 cm B. 105.98 cm C. 90 cm D. 104.5 cm,
option A is the correct answer.
Because 1 m = 100 cm and this is the nearest approximation. Thus, the<span>A student used A tape measures to estimate the length of a meterstick manufactured to he exactly 1 meter. </span>
That is the definition of a irrational number, A rational number must be able to be written as a ratio of 2 integers. The denominator cannot be 0, because that would make the number undefined
Answer:
0
Step-by-step explanation:
<h3>Given</h3>
- (x +
)(y + 
) = 1 - (x+y)² = ?
<h3>Solution</h3>
<u>Let's make substitution as:</u>
- (x + ) = m
then
- (y + ) = 1/m
<u>Solving the first equation for x and the second one for y:</u>
- (x + ) = m
- = m - x
- 1 + x² = (m - x)²
- 1 + x² = m² - 2mx + x²
- 2mx = m² - 1
- x = (m² - 1)/2m
And
- (y + ) = 1/m
- = 1/m - y
- 1 + y² = 1/m² -2y/m + y²
- 1 = 1/m² - 2y/m
- m² = 1 - 2my
- 2my = 1 - m²
- y = (1 - m²)/2m
- y = - (m² - 1)/2m
<u>Now, sum of x and y:</u>
- x + y = (m² - 1)/2m - (m² - 1)/2m = 0
<u>Therefore:</u>
Answer is zero
Answer:
18°
Step-by-step explanation:
The law of cosines tells you ...
a² = b² + c² -2bc·cos(A)
Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.
cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140
A = arccos(133/140) ≈ 18.2° ≈ 18°
