Answer:
(I) (-5) is a zero of P(x)
(II) 5 is a zero of P(x)
(III) (-5/2) is a zero of P(x)
Step-by-step explanation:
<h3>
(I) P(x) = x + 5</h3>
Here, P(x) = x + 5
To find the zeroes of P(x)
let P(x) = 0
∴ x + 5 = 0
∴ x = (-5)
Thus, (-5) is a zero of P(x)
<h3>(II) P(x) = x - 5</h3>
Here, P(x) = x - 5
To find the zeroes of P(x)
let P(x) = 0
∴ x - 5 = 0
∴ x = 5
Thus, 5 is a zero of P(x)
<h3>(III) P(x) = 2x + 5</h3>
Here, P(x) = 2x + 5
To find the zeroes of P(x)
let P(x) = 0
∴ 2x + 5 = 0
∴ 2x = -5
∴ x = (-5/2)
Thus, (-5/2) is a zero of P(x)
<u>-</u><u>TheUnknownScientist</u>
a) Here, sum of two non-adjacent angles: 52 + 25 = 77
Now, ∠3 = 180 - 77 [ sum of all angles in a triangle is 180 ]
so, ∠3 = 103
Now, ∠3 + ∠4 = 180 [ Supplementary angles ]
So, ∠4 = 180 - ∠3
∠4 = 180 - 103 = 77
∠4 = 77 [ which is sum of two non-adjacent angles ]
....Hence proved.
b) m∠4 = 77
[ Solved in previous section ]
Hope this helps!
The given quadrilateral ABCD is a parallelogram since the opposite sides are of same length AB and DC is 4 and AD and BC is 2.
<u>Step-by-step explanation</u>:
ABCD is a quadrilateral with their opposite sides are congruent (equal).
The both pairs of opposite sides are given as AB = 3 + x
, DC = 4x
, AD = y + 1
, BC = 2y.
- AB and DC are opposite sides and have same measure of length.
- AD and BC are opposite sides and have same measure of length.
<u>To find the length of AB and DC :</u>
AB = DC
3 + x = 4x
Keep x terms on one side and constant on other side.
3 = 4x - x
3 = 3x
x = 1
Substiute x=1 in AB and DC,
AB = 3+1 = 4
DC = 4(1) = 4
<u>To find the length of AD and BC :</u>
AD = BC
y + 1 = 2y
Keep y terms on one side and constant on other side.
2y-y = 1
y = 1
Substiute y=1 in AD and BC,
AD = 1+1 = 2
BC = 2(1) = 2
Therefore, the opposite sides are of same length AB and DC is 4 and AD and BC is 2. The given quadrilateral ABCD is a parallelogram.
Answer:
x = ¹⁰⁄₄,⁵⁄₂, or 2.5
Step-by-step explanation:
Given: 13 - 2(2x + 1) = 1
1. Distribute -2 through the parentheses:
⇒ 13 - 2(2x + 1) = 1
⇒ 13 + (-2)(2x) + (-2)(1) = 1
13 - 4x - 2 = 1
2. Combine like terms:
⇒ 13 - 4x - 2 = 1
⟹ 11 - 4x = 1
3. Subtract 11 from both sides:
⇒ 11 - 11 - 4x = 1 - 11
⟹ -4x = -10
4. Divide both sides by -4:
⇒ -4x ÷ -4 = -10 ÷ -4
⟹ x = ¹⁰⁄₄,⁵⁄₂, or 2.5
5. Check your work:
⇒ 13 - 2(2x + 1) = 1
⇒ 13 - 2(2(2.5) + 1) = 1
⇒ 13 - 2(5 + 1) = 1
⇒ 13 - 2(6) = 1
⇒ 13 - 12 = 1
⟹ 1 = 1 ✔
Learn more here:
brainly.com/question/17139226
brainly.com/question/26315061
Answer:
The inequality is;
p≤ 10.53
where 10.53 is the highest value she can spend on other stationery
Step-by-step explanation:
Here, we want to write an inequality
The amount she has to spend is 33
This means she can spend less than or equal to this amount
she has spent 22.47 and still has p to spend
Mathematically;
p + 22.47 ≤ 33
p ≤ 33-22.47
p ≤ 10.53
