The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>
The polynomials are given as:
-4w^3 + 5w^2 - 8, w - 3
Set the divisor to 0.
So, we have
w - 3 = 0
Add 3 to both sides
w = 3
Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder
-4(3)^3 + 5(3)^2 - 8
Evaluate the expression
-71
This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71
The quotient (Q) is calculated as follows:
Q = [-4w^3 + 5w^2 - 8]/[w - 3]
The numerator can be expressed as follows:
Numerator = -4w^3 + 5w^2 - 8
Subtract the remainder.
So, we have:
Numerator = -4w^3 + 5w^2 - 8 + 71
This gives
Numerator = -4w^3 + 5w^2 + 61
So, the quotient becomes
Q = [-4w^3 + 5w^2 + 61]/[w - 3]
Expand
Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]
Evaluate
Q = -4w^2 - 7w - 21
Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
Read more about polynomials at:
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The sum is adding
3 times a number is 3x
And 15 is +15
3x+15
400 divided by 10 is 40
Then you multiply 8 by 40 because you ate ate chicken nuggets
You should get 320
Answer:
UV=29
Step-by-step explanation:
In right triangles AQB and AVB,
∠AQB = ∠AVB ...(i) {Right angles}
∠QBA = ∠VBA ...(ii) {Given that they are equal}
We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle
∠AQB+∠QBA+∠BAQ=180 ...(iii)
∠AVB+∠VBA+∠BAV=180 ...(iv)
using (iii) and (iv)
∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV
∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))
∠BAQ=∠BAV...(v)
Now consider triangles AQB and AVB;
∠BAQ=∠BAV {from (v)}
∠QBA = ∠VBA {from (ii)}
AB=AB {common side}
So using ASA, triangles AQB and AVB are congruent.
We know that corresponding sides of congruent triangles are equal.
Hence
AQ=AV
5x+9=7x+1
9-1=7x-5x
8=2x
divide both sides by 2
4=x
Now plug value of x=4 into UV=7x+1
UV=7*4+1=28+1=29
<u>Hence UV=29 is final answer.</u>
Step-by-step explanation:
<h2>Answer:-</h2>
Hope it helps :)
