What is x^2 + 3x - 10 =0
Answers
The final result is: x = 2, -5.
Set both factors equal to 0
x - 5 = 0
x + 2 = 0
Solve for x and the answer is
x = 5
x = -2
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Answers
The product of two binomials is sometimes called FOIL.
It stands for ...
the product of the First terms (3j x 3j)
plus
the product of the Outside terms (3j x 5)
plus
the product of the Inside terms (-5 x 3j)
plus
the product of the Last terms (-5 x 5)
FOIL works for multiplying ANY two binomials (quantities with 2 terms).
Here's another tool that you can use for this particular problem (a).
It'll also be helpful when you get to part-c .
Notice that the terms are the same in both quantities ... 3j and 5 .
The only difference is they're added in the first one, and subtracted
in the other one.
Whenever you have
(the sum of two things) x (the difference of the same things)
the product is going to be
(the first thing)² minus (the second thing)² .
So in (a), that'll be (3j)² - (5)² = 9j² - 25 .
You could find the product with FOIL, or with this easier tool.
______________________________
(b).
This is the square of a binomial ... multiplying it by itself. So it's
another product of 2 binomials, that both happen to be the same:
(4h + 5) x (4h + 5) .
You can do the product with FOIL, or use another little tool:
The square of a binomial (4h + 5)² is ...
the square of the first term (4h)²
plus
the square of the last term (5)²
plus
double the product of the terms 2 · (4h · 5)
________________________________
(c).
Use the tool I gave you in part-a . . . twice .
The product of the first 2 binomials is (g² - 4) .
The product of the last 2 binomials is also (g² - 4) .
Now you can multiply these with FOIL,
or use the squaring tool I gave you in part-b .
3j(3j + 5) - 5(3j + 5)
3j(3j) + 3j(5) - 5(3j) - 5(5)
9j² + 15j - 15j - 25
9j² - 25
b. (4h + 5)²
(4h + 5)(4h + 5)
4h(4h + 5) + 5(4h + 5)
4h(4h) + 4h(5) + 5(4h) + 5(5)
16h² + 20h + 20h + 25
16h² + 40h + 25
c. (g - 2)²(g + 2)²
(g - 2)(g - 2)(g + 2)(g + 2)
(g(g - 2) - 2(g - 2))(g(g + 2) + 2(g + 2))
(g(g) - g(2) - 2(g) + 2(2))(g(g) + g(2) + 2(g) + 2(2))
(g² - 2g - 2g + 4)(g² + 2g + 2g + 4)
(g² - 4g + 4)(g² + 4g + 4)
g²(g² + 4g + 4) - 4g(g² + 4g + 4) + 4(g² + 4g + 4)
g²(g²) + g²(4g) + g²(4) - 4g(g²) - 4g(4g) - 4g(4) + 4(g²) + 4(4g) + 4(4)
g⁴ + 4g³ + 4g² - 4g³ - 16g² - 16g + 4g² + 16g + 16
g⁴ + 4g³ - 4g³ + 4g² - 16g² + 4g² - 16g + 16g + 16
g⁴ - 12g² + 4g² + 16
g⁴ - 8g² + 16
A- Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
B- Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78.
C- Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42.
D- Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.
Answers
A- Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
A is the answer my folks.
Answers
We can conclude that the side of the given square with an area of 8100ft² is 90ft.
What is a square?
- A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.
- It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.
- A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90-degree angles.
So, the area of the square is 8100ft².
- Formula: s²
- So, we know that: 8100 = s²
Now, calculate for s as follows:
- s² = 8100
- s = √8100
- s = 90ft
Therefore, we can conclude that the side of the given square with an area of 8100ft² is 90ft.
Know more about squares here:
#SPJ2
To determine the length of one side use the formula for the area of square. As a square is equal on all four sides, finding one length results in any of the four. Solve using the formula and you receive your answer of 90.
A = s²
8100 ft² = s² (set up formula)
√8100 ft² = s² ( get s alone by squaring both sides)
90 ft = s (answer)
Answers
Answer:
2/3, 3/4, and 4/5.
Step-by-step explanation:
Three fractions that are greater than 1/2 but less than 1 are 2/3, 3/4, and 4/5.
To write three fractions that are greater than 1/2 but less than 1, the following calculation must first be performed:
1/2 = 0.5
Therefore, the fraction must have a value between 0.5 and 1.
2/3 = 0.666
3/4 = 0.75
4/5 = 0.80
Therefore, three fractions that are greater than 1/2 but less than 1 are 2/3, 3/4, and 4/5.
Answer:
2/3, 3/4, and 4/5
Step-by-step explanation:
B. x ≥ -1
C. x ≤ -5 or x ≥ -1
D. x ≥ -5 or x ≥ -1
Answers
4 | x + 3 | ≥ 8 =>
| x + 3 | ≥ 2
Then eliminate the absolute operator like this:
| x + 3 | ≥ 2 =>
-x-3 ≥ 2 or x+3 ≥ 2
Simplify:
-x ≥ 5 or x ≥ -1=>
x ≤ -5 or x ≥ -1
That's answer C
4x + 12 >=8
4x >= =4
x >= -1
or
4x + 12 <= -8
4x <= -20
x <= -5
Answer is C
Answers
Look at the picture.