Answer:
(10, 4, -3)
Step-by-step explanation:
z = -3
y + z = 1
y - 3 = 1
y = 4
x + y - z = 17
x + 4 - -3 = 17
x + 4 + 3 = 17
x + 7 = 17
x = 10
(10, 4, -3)
Answer:
Option A.
Step-by-step explanation:
Properties of the similarity of two polygons,
1). All angles of one polygon will be equal to the angles of the other polygon.
2). Their corresponding sides will be in the same ratio.
If the measures of corresponding angles of KLMN and ABCD are equal, but the lengths of the corresponding sides of ABCD are half those of KLMN,
Then the polygons ABCD and KLMN will be similar.
Option A will be the answer.
Answer:
16 males and 9 females
Step-by-step explanation:
To solve this we can use a system of equations.
Let's start by naming the number of females x.
The number of males would then be y.
<u>Using these variables, we can set up 2 equations using info provided:</u>
A french class has a total of 25 students, -> x+y=25
The number of males is 7 more than the number of females -> x+7=y
Use substitution to solve.
<u>From the second equation:</u>
x+7=y
Subtract 7 from both sides.
x=y-7
Substitute that into the first equation.
x+y=25
y-7+y=25
Combine like terms.
2y-7=25
Add 7 to both sides.
2y=32
Divide both sides by 2.
y=16
Substitute y=16 into equation 2.
x+7=y
x+7=16
Subtract 7 from both sides.
x=9
Therefore, there are 16 males and 9 females in the french class.
Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
