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irinina [24]
2 years ago
10

Write an equation in point-slope form that describes the line with a slope of -3 that contains the point (1,2)

Mathematics
1 answer:
Stella [2.4K]2 years ago
8 0

Answer:

<h2>         y - 2 = -3(x - 1)</h2>

Step-by-step explanation:

The point-slope form of the equation that describes the line with a slope of <em>m</em> that contains the point (x₀, y₀) is: y - y₀ = m(x - x₀)

m = - 3

(1, 2)  ⇒    x₀ = 1,  y₀ = 2

Therefore:

y - 2 = -3(x - 1)

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A circle with radius of 1 cm sits inside a 3 cm x 3 cm rectangle.
alina1380 [7]

Answer:

6.14

Step-by-step explanation:

Find area of shaded region:

regtangle area - circle area = shaded area

Regtangle area:

3x3=9

Circle area:

Pi (3.14) x radius x radius= 3.14

area all together if shaded region

9-3.14=6.14

4 0
3 years ago
f(x) = 4x^2+2x+6f(x)=4x 2 +2x+6f, left parenthesis, x, right parenthesis, equals, 4, x, squared, plus, 2, x, plus, 6 What is the
vladimir2022 [97]

<u>Given</u>:

The given function is f(x)=4x^2+2x+6

We need to determine the value of the discriminant f and also to determine the distinct real number zeros of f.

<u>Discriminant</u>:

The discriminant can be determined using the formula,

\Delta = b^2-4ac

Now, we shall determine the discriminant of the function f(x)=4x^2+2x+6

Substituting the values in the formula, we have;

\Delta=(2)^2-4(4)(6)

\Delta=4-96

\Delta=-92

Thus, the value of the discriminant of f is -92.

<u>Distinct roots:</u>

The distinct zeros of the function f can be determined by

(1) If \Delta>0, then the function has 2 real roots.

(2) If \Delta=0, then the function has 2 real roots ( or one repeated root).

(3) If \Delta, then the function has 2 imaginary roots (or no real roots).

Since, the discriminant is \Delta=-92 \ < \ 0 , then the function has no real roots  or 2 imaginary roots.

Thus, the function has 2 imaginary roots.

4 0
3 years ago
Find the missing factor 4x^2+19x-5=(x+5)( )<br><br> NEED HELP PLEASE
S_A_V [24]

Answer:

4x^2+19x-5=(x+5)(4x -1)

Step-by-step explanation:

The given expression is 4x^2 + 19x - 5

The leading coefficient is 4 and last term is -5

Multiply them, we get -20

Now find the factors of -20 such that when you add the factors we have to get 19.

-1*20 = -20

20+ (-1) = 19

The right factors are -5 and 9.

4x^2 + 19x - 5 =4x^2 + 20x -1x - 5

= 4x(x + 5) -1(x + 5)

= (x + 5)(4x -1)

The missing factor is (4x -1)

Thank you.


4 0
3 years ago
Please find the area
DENIUS [597]
Answer: 55

Explanation:
Find the area of the entire shape: 7x9=63
Find the area of the missing piece: 8
7-3=4 9-5=4 4x4=16 16/2=8
Find the area: 63-8=55
3 0
3 years ago
The function f(t) = t2 + 4t − 14 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Sh
Cloud [144]

Answer:

A)  The vertex ( h , k) = ( -2 , -18)

B) The minimum value of the given function = - 18

C) The Axis of the symmetry for f(t) is y -axis

Step-by-step explanation:

A)

Given a parabola   f(t) = t² + 4 t − 14

                               f(t) =  t² + 2(2) t + (2)²-4− 14

                           f(t) = (t +2)² - 18

Let comparing  y = (x +2)² -18

                   (x +2)² = y + 18

                   (x-h))² = 4 a ( y - k))²

<em>The vertex ( h , k) = ( -2 , -18)</em>

B)

  Given a parabola   f(t) = t² + 4 t − 14

  Differentiating with respective to 't'

                                 f¹(t) = 2 t + 4

                                  f¹(t) = 2 t + 4 = 0

now                      t = \frac{-4}{2} = -2

Again Differentiating with respective to 't'

                    f^{ll} (t) = 2 (1) >0

f(x) has a minimum value at t = -2

Given f(t) = t² + 4 t − 14

         f( -2) = 4 + 4(-2) -14 = 4 -8 -14 = -18

The minimum value of the given function = - 18

C)

f(t) = (t +2)² - 18

Let comparing  y = (x +2)² -18

                   (x +2)² = y + 18

                   (x-h))² = 4 a ( y - k))²

The vertex ( h , k) = ( -2 , -18)

The Axis of the symmetry for f(t) is y -axis

8 0
3 years ago
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