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3 years ago

Choose the equation below that represents the line that passes through the point (7,2) and has a slope of -3

Mathematics

2 answers:

denis23 [38]3 years ago

7 0

The equation of the line that passes through the point (7,2) with a slope of -3 is y = -3x + 23

Solution:

We need to find the equation for a line that passes through the point (7,2) and has a slope of -3.

Let us use slope-intercept form to find equation of line

The equation of line in slope intercept form is given as:

y = mx + b --- eqn 1

where "m" is the slope of line and "b" is the y-intercept

Here in this sum, given that slope "m" = -3

Given point is (x, y) = (7, 2)

Plug the given values in eqn 1 to find "b" :

2 = -3(7) + b

2 = -21 + b

b = 23

Now plug "b" and "m" values in eqn 1 to get the equation of line

y = -3x + 23

This is the required equation of line found using slope intercept form

True [87]3 years ago

4 0

Answer: y = - 3 + 2x

Step-by-step explanation:

You might be interested in

Triangle ABC had a perimeter 18 cm

Anna007 [38]

Answer:

Use pythagoreum theorem to determine whether it is or isn't since I'm not really sure myself but here's my calculations.

Step-by-step explanation:

We need to find AC.

Picture a triangle called ABC. AB is one side and BC the other while AC is the hypotenuse.

AC=

$ac = \sqrt{ab ^{2} + {bc}^{2} } \\ ac = \sqrt{ {7}^{2} } + {3}^{2} \\ ac = \sqrt{49 + 9} \\ ac = \sqrt{58 } \\ ac = 7.6$

Round up the 7.6 to a whole number and you get AC=8. To get perimeter of a triangle simply add the sides together to get 18.

Not really sure about my answer but hope this helped.

5 0

3 years ago

The vertex of the parabola below is at the point (2, 4), and the point (3, 6) is on the parabola. what is the equation of the pa

Paraphin [41]

Given:

Vertex ===> (h, k) (2, 4)

The parabola passes through the point: (x, y) ==> (3, 6)

Let's find the equation of a parabola.

To find the equation, use the general equation of a parabola with vertex (h, k):

$y=a(x-h)^2+k_{}$

Where:

(h, k) ==> (2, 4)

(x, y) ==> (3, 6)

Substitute values into the general equation:

$\begin{gathered} 6=a(3-2)^2+4 \\ \\ 6=a(1)^2+4 \\ \\ 6=a+4 \end{gathered}$

Subtract 4 from both sides:

$\begin{gathered} 6-4=a+4-4 \\ \\ 2=a \\ \\ a=2 \end{gathered}$

Substitute 2 for a, and input the values of the vertex (h, k) in the general vertex equation:

$y=2(x-2)^2+4$

Therefore, the equation of the parabola is:

$y=2(x-2)^2+4$

ANSWER:

$y=2(x-2)^2+4$

3 0

1 year ago

Which equation describes the sum of the vectors plotted below?

Alex787 [66]

Answer: $A) \ 3\vec{x} -2\vec{y}$

Step-by-step explanation:

The resultant can be calculated using triangular law of vector addition as :

$\rm \vec{r}=\vec{AB} +\vec{AC}=2x+y+x-3y=\boxed{3x-2y }$

8 0

3 years ago

F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,

svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

$g(x)=2x^2+8x+6$

Find the vertex

Factor the leading coefficient

$g(x)=2(x^2+4x)+6$

Complete the square

$g(x)=2(x^2+4x+4)+6-8$

$g(x)=2(x^2+4x+4)-2$

Rewrite as perfect squares

$g(x)=2(x+2)^2-2$

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

$0=2(x+2)^2-2$

$2(x+2)^2=2$

$(x+2)^2=1\\x+2=\pm1\\x=-2\pm1$

The roots or x-intercepts are

x=-1 and x=-3

Verify each statement

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

7 0

3 years ago

Read 2 more answers

Please give answers for all

aivan3 [116]

Answer:

Step-by-step explanation:

5x+20 = 0

5X= -20

X= -20/5 = -4

8(4n+3) = 32n+24 =0

32n = -24

n = -24/32 = -3/4

12n-6=0

12n =6

n = 6/12 = 1/2

9(2x+9)

18x+81 =0

18x= -81

x= -81/18 = -9/2= -4.5

36+9y=0

36=-9y

36/-9 = y = -4

7(n-3) = 0

7n-21=0

7n = 21

n = 21/7

n=3

21+15a = 0

21= -15a

a= 21/-15 = 7/-5 = -1.4

32x-12x=0

20x=0

x=0/20 = 0

n-4-9=0

n-13=0

n=13

-3x-9+15x=0

-3x+15x-9 =0

12x-9=0

12x=9

x=9/12 = 3/4 = 0.75

-16N-14N=0

-30n=0

n=0/-30 =0

-10-90x-6x-10x²-2

-10-2-96x-10x²

-12-96x-10x²

10x²+96x+12

x= -b±√b²-4(a)(c)/2a

{-96±√96²-4(10)(12)}/2(10)

{-96±√(9216-480)}/20

-96±√8736/20

-96±(93.4665715644)/20

-96+93.4665715644/20 -96-93.4665715644/20

-2.5334284356/20 -189.466571564/20

-0.12667142178≅ -0.13 -9.4733285782≅ -9.47

-0.13 -9.47

-5(9n+9) =0

-45n-45 =0

-45n = 45

n = 45/-45 =-1

-5n+3(6+7n)

-5n+18+21n=0

-5n+21n+18 =0

16n+18 =0

16n = -18

n = -18/16 = -9/8 = -1.125

-4+7(1-3n)=0

-4+7-21n=0

3-21n=0

3=21n

3/21=n = 1/7

3n-(2n-8)

3n-2n+8=0

n+8=0

n=-8

5 0

3 years ago