Answer:
x = 3
y = 2
Step-by-step explanation:
4x + 3(3x - 7) = 18 <em>Substitute</em><em> </em><em>y</em>
4x + 9x - 21 = 18 <em>Simply</em>
13x - 21 = 18 <em>Add</em><em> </em><em>like</em><em> </em><em>terms</em>
13x = 39 <em>Add</em><em> </em><em>2</em><em>1</em>
x = 3 <em>Divide</em><em> </em><em>by</em><em> </em><em>1</em><em>3</em>
y = 3(3) - 7 <em>Substitute</em><em> </em><em>x</em>
y = 9 - 7 <em>Simply</em>
y = 2 <em>Subtract</em>
Let's check:
4(3) + 3(2) = 18
12 + 6 = 18
18 = 18
It works!
Answer:
$116.53
Step-by-step explanation:
Bryan earn's 11.80 per hour. He is paid time and a half for hours worked over 8hrs in a day. So if you divide 11.80 by 2, you get 5.90.
11.80+5.90=17.70. This is the amount he gets paid if he works overtime.
If Bryan worked 9.25 hrs yesterday, we already know that he made $94.40 in 8 hours. We have to find the amount he got paid for working over time.
The remaining hours are 1.25. We can add $17.70 to 94.40 to get 112.10. Now we have to figure out the remainder which is a quarter of an hour. Multiply 17.70 by .25 and you will get 4.43.
The total amount he got paid for working over time was $116.53.
Answer:
No, the two sets are not disjoint.
Step-by-step explanation:
Set of triangular numbers to 50: 1, 3, 6, 10, 15, 21, 28, 36, 45
Set of square numbers to 50: 1, 4, 9, 16, 25, 36, 49
They have 1 and 36 in common, so they are not disjoint, or in other words, they have some of the same numbers.
Answer:
Measure of angle 2 and angle 4 is 42°.
Step-by-step explanation:
From the figure attached,
m∠ABC = 42°
m(∠ABD) = 90°
m(∠ABD) = m(∠ABC) + m(∠DBC)
90° = 43° + m(∠DBC)
m(∠DBC) = 90 - 43 = 47°
Since ∠ABC ≅ ∠4 [Vertical angles]
m∠ABC = m∠4 = 42°
Since, m∠3 + m∠4 = 90° [Complimentary angles]
m∠3 + 42° = 90°
m∠3 = 90° - 42°
= 48°
Since, ∠5 ≅ ∠3 [Vertical angles]
m∠5 = m∠3 = 48°
m∠3 + m∠2 = 90° [given that m∠2 + m∠3 = 90°]
m∠2 + 48° = 90°
m∠2 = 90 - 48 = 42°
m∠3+ m∠4 = 90° [Since, ∠3 and ∠4 are the complimentary angles]
48° + m∠4 = 90°
m∠4 = 90 - 48 = 42°
Therefore, ∠2 and ∠4 measure 42°.
