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2 years ago

Find the point-slope equation of the line contains (-2,-3) and having slope m=4

Mathematics

1 answer:

vodomira [7]2 years ago

3 0

Answer:

y + 3 = 4 x (x + 2)

Step-by-step explanation:

point slope formula is y-y1 = m(x-x1)

slope intercept form is y = 4x + 5

y=mx +b

m=4

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An algebra test contains 38 problems. Some of the problems are worth 2 points each. The rest of the questions are worth 3 points

Naily [24]

Let 'x' be the problems worth 2 points.

Let 'y' be the problems worth 3 points.

Since, there are 38 total problems.

So, $x+y =38$ (equation 1)

x = 38-y

Since, a perfect score is 100 points.

So, $2x+3y = 100$ (equation 2)

Substituting the value of 'x', we get

$2(38-y)+3y=100$

$76-2y+3y=100$

$76+y = 100$

y = 24

x+y = 38

x = 38-24 = 14

So, 14 problems are worth 2 points and 24 problems are worth 3 points.

5 0

2 years ago

Read 2 more answers

Indira is climbing and starts at 182.5 meters above sea level each hour she descends 36.5 meters the table shows the function re

VLD [36.1K]

The function relating in indira‘s height to the number of hours she mountain climbing is: y = -36.5x + 182.5

A linear equation is given by:

y = mx + b;

where m is the slope(rate of change), b is the initial value of y, y is the dependent variable and x is the independent variable.

Let x represent the number of hours spent climbing the mountain and y represent the distance above see level.

She starts at 182.5 meters above sea level, hence; b = 182.5 meters

She descends 36.5 meters each hour, hence m = -36.5 meter per hour

Therefore the equation becomes:

y = -36.5x + 182.5

Find out more at: brainly.com/question/19586594

5 0

2 years ago

Given: △ABC, AB=5sqrt2 m∠A=45°, m∠C=30° Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago

Which of the following points does Not lie on the graph of y =3x

nalin [4]

Answer:

(2,6)

Step-by-step explanation:

The options of the questions are

(0,1) (1,3) (2,6) (3,27)

and the given function is $y=3^x$

we know that

If a ordered pair lie on the graph of the given equation, then the ordered pair must satisfy the given equation

Verify each ordered pair

case 1) (0,1)

substitute the value of x and the value of y in the linear equation and then compare the results

$1=3^0$

$1=1$ ----> is true

The ordered pair lie on the graph of the given equation

case 2) (1,3)

substitute the value of x and the value of y in the linear equation and then compare the results

$3=3^1$

$3=3$ ----> is true

The ordered pair lie on the graph of the given equation

case 3) (2,6)

substitute the value of x and the value of y in the linear equation and then compare the results

$6=3^2$

$6=9$ ----> is not true

The ordered pair not lie on the graph of the given equation

case 4) (3,27)

substitute the value of x and the value of y in the linear equation and then compare the results

$27=3^3$

$27=27$ ----> is true

The ordered pair lie on the graph of the given equation

8 0

2 years ago

The public library has an approximate length of 1 x 10^5 millimeters and width of 8 x 10^4 millimeters. what is the area, in squ

Wewaii [24]

Area = length*width
.. = (1*10^5 mm)*(8*10^4 mm)
.. = (1*8)*10^(5+4) mm^2
.. = 8*10^9 mm^2

Selection A is appropriate.

3 0

2 years ago