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Gekata [30.6K]
3 years ago
13

The equation y = 5 represents the graph of a line perpendicular to the y-axis and passing through the point (1,5).

Mathematics
2 answers:
DedPeter [7]3 years ago
7 0

Answer:

False

Step-by-step explanation:

A perpendicular line parallel to the y- axis has equation

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (1, 5) with x- coordinate 1, thus

x = 1 ← equation of perpendicular line

MrRa [10]3 years ago
3 0

Answer:

B. False

Step-by-step explanation:

I hope this helps!

Short version of the answer.

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ASAP PLEASE HELP ME !!!!
anygoal [31]

Answer:

90 mallards

Step-by-step explanation:

No. of ducks = 200

Mallards = 45%

45% of 200 = 45/100 × 200

=90

4 0
2 years ago
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Find a factorization of x² + 2x³ + 7x² - 6x + 44, given that<br> −2+i√√7 and 1 - i√/3 are roots.
Levart [38]

A factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

<h3>What are the properties of roots of a polynomial?</h3>
  • The maximum number of roots of a polynomial of degree n is n.
  • For a polynomial with real coefficients, the roots can be real or complex.
  • The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if a+ib is a root, then a-ib is also a root.

If the roots of the polynomial p(x)=ax^4+bx^3+cx^2+dx+e are r_1,r_2,r_3,r_4, then it can be factorized as p(x)=(x-r_1)(x-r_2)(x-r_3)(x-r_4).

Here, we are to find a factorization of p(x)=x^4+2x^3+7x^2-6x+44. Also, given that -2+i\sqrt{7} and 1-i\sqrt{3} are roots of the polynomial.

Since p(x)=x^4+2x^3+7x^2-6x+44 is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.

Hence, -2-i\sqrt{7} and 1+i\sqrt{3} are also roots of the given polynomial.

Thus, all the four roots of the polynomial p(x)=x^4+2x^3+7x^2-6x+44, are: r_1=-2+i\sqrt{7}, r_2=-2-i\sqrt{7}, r_3=1-i\sqrt{3}, r_4=1+i\sqrt{3}.

So, the polynomial p(x)=x^4+2x^3+7x^2-6x+44 can be factorized as follows:

\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)

Therefore, a factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

To know more about factorization, refer: brainly.com/question/25829061

#SPJ9

3 0
1 year ago
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Find the surface area
timofeeve [1]

Answer: 196 m

Step-by-step explanation:

6 0
2 years ago
In 1960, the population of a town was 14 thousand people. Over the course of the next 50 years, the town grew at a rate of 30 pe
andre [41]

SOLUTIONS

Given: Assume y is the population

\begin{gathered} t=0=1960,y=14030 \\ t=1=1961,y=14060 \\ so\text{ b = 14000} \\ so\text{ k = 30} \end{gathered}

The town grow at the rate of 30 people per year.

y=kt+14000y=30t+14000

(A) The population predicted to be in 2030 will be

\begin{gathered} 2030-1960=70 \\ y=30k+14000 \\ y=30(70)+14000 \\ y=2100+14000 \\ y=16100people \end{gathered}

(B) so when y = 15000, find t

\begin{gathered} y=15000 \\ y=30t+14000 \\ 15000=30t+14000 \\ 15000-14000=30t \\ 1000=30t \\ t=\frac{1000}{30} \\ t\approx33 \\ t=1960+33 \\ t=1993 \end{gathered}

3 0
9 months ago
10. What is the solution to the proportion?<br> 3<br> 7<br> 42
cupoosta [38]
Answer: w=18

Explanation: 7×6 = 42 so to get W you have to multiply 3 by 6. 3×6 = 18.
4 0
2 years ago
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