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MaRussiya [10]
3 years ago
13

Fill in the blanks with the correct words:

Mathematics
1 answer:
Natali [406]3 years ago
5 0
An expression must contain a variable


The equation y-4=1 has many solution(s).
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Please Help!!! WILL GIVE BRAINLIEST!!!
kompoz [17]

Answer:

The correct statements are:

A) This polynomial has a degree of 2, so the equation x^{2}  + 4x + 4has exactly two roots.

B: The quadratic equation x^{2}  + 4x + 4 has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

Step-by-step explanation:

Here, the given polynomial is  f(x) = x^{2}  + 4x + 4

FUNDAMENTAL THEOREM OF ALGEBRA:

If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

Now, here the given polynomial is a quadratic polynomial with degree 2.

So, by the fundamental theorem, f(x) has EXACTLY 2 roots including multiple and complex roots.

Now, solving the equation , we get that the only possible roots of the polynomial p(x) is x = -2 and x = -2

So, f(x) has only one distinct root x = -2 with a multiplicity 2.

Hence, the correct statements are:

A) This polynomial has a degree of 2, so the equation x^{2}  + 4x + 4has exactly two roots.

B: The quadratic equation x^{2}  + 4x + 4 has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

4 0
3 years ago
A factory made 4250
vodomira [7]

Step-by-step explanation:

Total amount of cookies = 4250

butter cookies, b

Almond cookies, a

Chocolate cookies, c

It made 715 more butter cookies than

almond cookies

b = a + 715

It made 5 times as many chocolate cookies as almond

5a = c

Total amount of cookies

= a + b + c

= a + (a+715) + (5a)

= 7a + 715

7a + 715 = 4250

7a = 4250-715

a = 3535 / 7

a = 505

c = 5a

= 5 (505)

= 2525

The factory make 2525 chocolate cookies.

5 0
2 years ago
On a test of 80 problems, Bill got 75% of the problems correct
AysviL [449]
The correct answer is c, 60!
8 0
3 years ago
Read 2 more answers
Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.
nirvana33 [79]

Answer:

-56/9

Step-by-step explanation:

By Vieta's formulas,

$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get

$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,

$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$

5 0
3 years ago
Write an equation of the line that passes through a pair of points (-5, -2), (4, 5)
PIT_PIT [208]
To find the equation of a line knowing two points it passes through, we must first find the slope and then substitute the x and y values to figure out the y intercept. 

First thing is to find the slope using the formula m = Δy ÷ Δx
m = 5 - (-2) ÷ 4 - (-5)

Now we simplify 
m = 7 ÷ 9 

Our equation so far is y = 7/9x + b. Now we can substitute the values of x and y from a point to figure out the answer. The equation here uses the point (4,5)

5 = 7/9 · 4 + b

Get b on one side
5 - 28/9 = b

Simplify
b = 1 + 8/9

That makes the equation of the line y = 7/9x + (1 + 8/9)
8 0
3 years ago
Read 2 more answers
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