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3 years ago

choose the point-slope form of the equation below that represents the line that passes through the points (-3,2) and (2,1)

Mathematics

2 answers:

algol [13]3 years ago

5 0

Answer:

Equation of line in point slope form is:

$y=-\dfrac{1}{5}(x+3)+2$

Step-by-step explanation:

The point-slope form of the equation is:

y= mx + c

The equation of line passing through (a,b) and (c,d) is given by:

$y-b=\dfrac{d-b}{c-a}(x-a)$

firstly we find equation of line passing through (-3,2) and (2,1) and then convert it to point-slope form.

$y-2=\dfrac{1-2}{2+3}(x+3)$

$y-2=-\dfrac{1}{5}(x+3)$

$y=-\dfrac{1}{5}(x+3)+2$

Hence, Equation of line in point slope form is:

$y=-\dfrac{1}{5}(x+3)+2$

UkoKoshka [18]3 years ago

4 0

The answer should be: (2 - 1) = m(-3 - 2)

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Fit a quadratic function to these three points:<br> (-2,8), (0, -4), and (4, 68)<br> Respuesta

zloy xaker [14]

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8) ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8 For (0, -4) we have:

0 + 0 + c = -4 so c = -4. For (4, 68) we have:

16a + 4b + c = 68

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

3 0

3 years ago

Help please -19 + 2z = -21

777dan777 [17]

Answer:

z = -1

Step-by-step explanation:

You must first start out by adding 19 to both sides to isolate the variable z, which results in:

2z = -2

Now, you can just divide by two on both sides to get z completely on its own, which gives you:

z = -1

Hope this helped somewhat! :D

6 0

2 years ago

Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sig

Fed [463]

Answer: PART A : $\frac{4.4}{x}$ = $\frac{3}{4}$

PART B : 5.9 FEET

Step-by-step explanation:

Length of the first sign = 4.4 feet

height of the first sign = 3 feet

Length of the second sign = x feet

height of the second sign = 4 feet

If two shapes are similar , then the ratio of their sides are equal,

That is ;

$\frac{h_{1}}{h_{2} }$ = $\frac{L_{1}}{L_{2} }$

PART A

$\frac{4.4}{x}$ = $\frac{3}{4}$

PART B

$\frac{4.4}{x}$ = $\frac{3}{4}$

cross multiplying , we have

3x = 4.4 x 4

3x = 17.6

Divide through by 3

x = 17.6/3

x = 5.86666666666667

x≈ 5.9 feet

Therefore , the length of the new sign is 5.9 feet

6 0

3 years ago

H(x) = x2 1 k(x) = x – 2 (h k)(2) = (h – k)(3) = Evaluate 3h(2) 2k(3) =.

natima [27]

Quadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.The value of the given functions are,

$(h+k)(x)=5$

$(h-k)(x)=9$

$3h(2)+2k(3)=17$

<h3>Given information-</h3>

The given function is,

$h(x)=x^2+1$

$k(x)=x-2$

<h3>Quadratic equation</h3>

Quadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.

1) The value of the function (h+k)(2),

$(h+k)(x)=h(x)+k(x)$

$(h+k)(x)=x^2+1+x-2$

$(h+k)(2)=2^2+1+2-2$

$(h+k)(x)=5$

2)The value of the function (h-k)(3),

$(h-k)(x)=h(x)-k(x)$

$(h-k)(x)=x^2+1-x+2$

$(h-k)(3)=3^2+1-3+2$

$(h-k)(x)=9$

3) The value of the function 3h(2)+2k(3)

$3h(x)+2k(x)=3x^2+3+2x-2\times 2$

$3h(2)+2k(3)=3\times2^2+3+2\times2-2\times 2$

$3h(2)+2k(3)=17$

Hence the value of the given functions are,

$(h+k)(x)=5$

$(h-k)(x)=9$

$3h(2)+2k(3)=17$

Learn more about the quadratic equation here;

brainly.com/question/2263981

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3 years ago

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Jobisdone [24]

The answer is a. $11 bc you divide the amount made by the hours worked

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3 years ago