Answer:
Part A: x^2 + 5x - 8
Part B: 5x^3 + 3x^2 - 6x + 5
Step-by-step explanation:
Part A:
To find the total of side 1 and 2, add the two expressions which represent each side. Combine like terms to simplify.
3x^2 − 2x − 5 + (7x - 2x^2 − 3)
3x^2 - 2x^2 -2x + 7x -5 + -3
x^2 + 5x - 8
Part B:
To solve for the third side of a triangle using its perimeter, subtract the lengths of two of its sides from its perimeter. The perimeter is 5x^3 + 4x^2 − x − 3. Subtract 3x^2 − 2x − 5 and 7x - 2x^2 − 3. The remaining expression is the third side. Combine like terms to simplify.
5x^3 + 4x^2 − x − 3 - (3x^2 − 2x − 5) - (7x - 2x^2 − 3)
5x^3 + 4x^2 - x - 3 - 3x^2 + 2x + 5 - 7x + 2x^2 + 3
5x^3 + (4x^2 -3x^2 + 2x^2) + (-x + 2x - 7x) + (-3 + 5 + 3)
5x^3 + 3x^2 - 6x + 5
Answer :
x = 53.85
Step by step explanation:
If 78% of x (some numbers) is equal to 42, then we must set this as an equation to find it.
1) Rewriting 78% as a fraction and considering that when we say 78% of some number (x) we mean a product.
78% = 78/100 ➡️ 78/100x = 42
2) Then we can go on :
100 * 78/100x = 42 * 100
78x = 4200
78x/78 = 4200/78 ➡️ x = 53.85
3) Alternatively, simply dividing 42 by 0.78 (78%) would come to the same result :
42/0.78 = 53.85
Firstly,we need to understand the properties of a parallelogram:
-Opposite sides are parallel by .
-Opposite sides are congruent.
-Opposite angles are congruent.
-The diagonals bisect each other.
Therefore in this case:
XW must be congruent to YZ.
WZ must be congruent to XY.
Hope it helps!
Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step explanation:
equation of a parabola in vertex form: y = a(x - h)² + k
where (h, k) is the vertex
Substituting the given vertex (-3, -18) into the equation:
y = a(x + 3)² - 18
If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:
0 = a(0 + 3)² - 18
⇒ 0 = a(3)² - 18
⇒ 0 = 9a - 18
⇒ 9a = 18
⇒ a = 2
Therefore, y = 2(x + 3)² - 18
To find the x-intercepts, set the equation to 0 and solve for x:
2(x + 3)² - 18 = 0
Add 18 to both sides: 2(x + 3)² = 18
Divide both sides by 2: (x + 3)² = 9
Square root both sides: x + 3 = ±3
Subtract 3 from both sides: x = ±3 - 3
so x = 3 - 3 = 0
and x = -3 - 3 = -6
So x-intercepts are (0, 0) and (-6, 0)
Answer:
1/9
Step-by-step explanation:
For these questions, you have to first find the probability of each event individually occuring then multiply these two probabilities together. So, lets first find the probability of Event 1 occuring (rolling a number higher than 1). On a dice, we know that there are 6 numbers (1, 2, 3, 4, 5, 6) of which the numbers 5 and 6 are higher than 4. Therefore, the proability of Event 1 occuring is 2/6 = 1/3. Now, we find the probability of event 2 occuring.
We know that there are 3 options on the spinner that the arrow can land on. It is also evident that they all have the same chance of landing on it. Therefore, the possibility is 1/3.
Now that we have both of our probabilities, we multiply the answer together.
Therefore, our answer will be:
1/3 x 1/3, which gives 1/9.
