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3 years ago

C. In (MN) = In M + In N, for M> 0 and N> 0 True or false

Mathematics

1 answer:

melisa1 [442]3 years ago

8 0

That statement is true

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HELP ASAP (Geometry)

Andrei [34K]

1) Parallel line: $y=-2x-3$

2) Rectangle

3) Perpendicular line: $y = 0.5x + 2.5$

4) x-coordinate: 2.7

5) Distance: $d=\sqrt{(4-3)^2+(7-1)^2}$

6) 3/8

7) Perimeter: 12.4 units

8) Area: 8 square units

9) Two slopes of triangle ABC are opposite reciprocals

10) Perpendicular line: $y-5=-4(x-(-1))$

Step-by-step explanation:

The equation of a line is in the form

$y=mx+q$

where m is the slope and q is the y-intercept.

Two lines are parallel to each other if they have same slope m.

The line given in this problem is

$y=-2x+7$

So its slope is $m=-2$ . Therefore, the only line parallel to this one is the line which have the same slope, which is:

$y=-2x-3$

Since it also has $m=-2$

We can verify that this is a rectangle by checking that the two diagonals are congruent. We have:

- First diagonal: $d_1 = \sqrt{(-3-(-1))^2+(4-(-2))^2}=\sqrt{(-2)^2+(6)^2}=6.32$

- Second diagonal: $d_2 = \sqrt{(1-(-5))^2+(0-2)^2}=\sqrt{6^2+(-2)^2}=6.32$

The diagonals are congruent, so this is a rectangle.

Given points A (0,1) and B (-2,5), the slope of the line is:

$m=\frac{5-1}{-2-0}=-2$

The slope of a line perpendicular to AB is equal to the inverse reciprocal of the slope of AB, so:

$m'=\frac{1}{2}$

And using the slope-intercept for,

$y-y_0 = m(x-x_0)$

Using the point $(x_0,y_0)=(7,1)$ we find:

$y-1=\frac{1}{2}(x-7)$

And re-arranging,

$y-1 = \frac{1}{2}x-\frac{7}{2}\\y=\frac{1}{2}x-\frac{5}{2}\\y=0.5x-2.5$

The endpoints of the segment are X(1,2) and Y(6,7).

We have to divide the sgment into 1/3 and 2/3 parts from X to Y, so for the x-coordinate we get:

$x' = x_0 + \frac{1}{3}(x_1 - x_0) = 1+\frac{1}{3}(6-1)=2.7$

The distance between two points $A(x_A,y_A)$ and $B(x_B,y_B)$ is given by

$d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

In this problem, the two points are

E(3,1)

F(4,7)

So the distance is given by

$d=\sqrt{(4-3)^2+(7-1)^2}$

We have:

A(3,4)

B(11,3)

Point C divides the segment into two parts with 3:5 ratio.

The distance between the x-coordinates of A and B is 8 units: this means that the x-coordinate of C falls 3 units to the right of the x-coordinate of A and 5 units to the left of the x-coordinate of B, so overall, the x-coordinate of C falls at

$\frac{3}{3+5}=\frac{3}{8}$

of the distance between A and B.

To find the perimeter, we have to calculate the length of each side:

$d_{EF}=\sqrt{(x_E-x_F)^2+(y_E-y_F)^2}=\sqrt{(-1-2)^2+(6-4)^2}=3.6$

$d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}=\sqrt{(-1-2)^2+(3-4)^2}=3.2$

$d_{GH}=\sqrt{(x_G-x_H)^2+(y_G-y_H)^2}=\sqrt{(-1-(-3))^2+(3-3)^2}=2$

$d_{EH}=\sqrt{(x_E-x_H)^2+(y_E-y_H)^2}=\sqrt{(-1-(-3))^2+(6-3)^2}=3.6$

So the perimeter is

p = 3.6 + 3.2 + 2 + 3.6 = 12.4

The area of a triangle is

$A=\frac{1}{2}(base)(height)$

For this triangle,

Base = XW

Height = YZ

We calculate the length of the base and of the height:

$Base =XW=\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}=\sqrt{(6-2)^2+(3-(-1))^2}=5.7$

$Height =YZ=\sqrt{(x_Y-x_Z)^2+(y_Y-y_Z)^2}=\sqrt{(7-5)^2+(0-2)^2}=2.8$

So the area is

$A=\frac{1}{2}(XW)(YZ)=\frac{1}{2}(5.7)(2.8)=8$

A triangle is a right triangle when there is one right angle. This means that two sides of the triangle are perpendicular to each other: however, two lines are perpendicular when their slopes are opposite reciprocals. Therefore, this means that the true statement is

"Two slopes of triangle ABC are opposite reciprocals"

10)

The initial line is

$y=\frac{1}{4}x-6$

A line perpendicular to this one must have a slope which is the opposite reciprocal, so

$m'=-4$

Using the slope-intercept form,

$y-y_0 = m'(x-x_0)$

And using the point

$(x_0,y_0)=(-1,5)$

we find:

$y-5=-4(x-(-1))$

Learn more about parallel and perpendicular lines:

brainly.com/question/3414323

brainly.com/question/3569195

#LearnwithBrainly

8 0

3 years ago

Please help urgent! Lee uses the graph of the function f(x) to express

icang [17]

Step-by-step explanation:

d the house Lee will work per week

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3 years ago

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2/5 of a class are girls. 3/4 of the boys are called Paul. What fraction of the whole class is not called Paul?

Novay_Z [31]

Answer:

1/4

Step-by-step explanation:

3/4 + 1/4 = 4/4

7 0

3 years ago

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1. What is the probability of getting a number greater than 2 on two rolls of a six-sided die both times?

prisoha [69]

Answer:

For this question, the options are written the wrong way. In each of the answers below, the correct form of the question will be added.

The answers are:

1. e) 4/9

2. a) 1/16

3. 980 girls

4. c) 2/3

5. d) 1/13

6. a) 42 boys

7. d) 1/21

8. b) 1/6

Step-by-step explanation:

1. What is the probability of getting a number greater than 2 on two rolls of a six-sided die both times?

a) 4/3

b) 2/6

c) 4/6

d) 3/6

e) 4/9

The correct answer is e) 4/9 because the probability of getting a number greater than 2 in two rolls is 4/6 * 4/6 =16/36 = 4/9

2. A fair coin is tossed four times. What is the probability that it will be heads every time?

a) 1/16

b) 4/2

c) 2

d) 4/16

e) 1

The correct answer is a) 1/16 because the probability of each time that the coin is tossed is 1/2, and for 4 tosses is 1/2*1/2*1/2*1/2 = 1/16

3. The ratio of the number of girls to the number of boys was 2 to 5. If 2,450 students were present, how many were girls and how many were boys?

The correct answer is 980 girls, because 2450*2/5 = 980

4. A die is rolled twice. What is the probability of rolling a 5 or getting an even number?

a) 3/1

b) 1/12

c) 2/3

d) 1/3

If the die is rolled twice there are 12 possible outcomes and 8 of those outcomes can be 5 or an even number. The probability is 8/12 = 2/3

5. If one card is drawn from a standard deck, what is the probability of getting a jack?

a) 4/13

b) 1/52

c) 52

d) 1/13

e) 4

In a standard deck, there are 13 jack cards, the probability of getting a jack the first time is 1/13

6. There are 210 boys trying out for football. If 20% made the team, how many were chosen?

a) 42

b) 10

c) 4200

d) 105

e) 20

The number of boys that will be picked for the team is 210*20% = 42

7. From 42 boys who made the team, one will be chosen as kicker and one will be chosen as quarterback. What is the probability of being chosen as the kicker or the quarterback?

a) 2/21

b) 1/42

c) 2

d) 1/21

e) 42

The probability of getting picked for one of the 2 positions is 2/42 = 1/21

8. Two dice are rolled. There are 36 possible outcomes of rolling two dice. What is the probability of getting a total of seven on one roll?

a) 7

b) 1/6

c) 0

d) 7/36

e) 1/36

There are 6 ways of getting a sum of 7 tossing 2 dice, 1+6, 6+1, 2+5, 5+2, 3+4, 4+3. The probability is 6/36 = 1/6

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3 years ago

Find the determinant of this matrix:

Bogdan [553]

Answer:

Step-by-step explanation:

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc$

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2 years ago

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