Help please! I don’t understand

The lines that are parallel continuously have equal distances from each

other and perpendicular lines form 90° angle at their intersection.

The correct responses are;

Reasons:

Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel where; Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex]

[tex]\displaystyle \overline{AB} \ and \ \overline{CD} \ are \ perpendicular\ where; \ Slope \ of \ \overline{AB} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex]

[tex]1. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{13 - 3}{-2 - 0}} = \frac{10}{-2} = -5[/tex]

[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{3 - 0}{10 - (-5)} = \frac{1}{5}[/tex]

[tex]\displaystyle \mathbf{Slope \ of \ \overline{AB}} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]2. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{7- 1}{3 - (-6)}} = \frac{6}{9} =\frac{2}{3}[/tex]

[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{-5 - (-1)}{-6 - 0} = \frac{-4}{-6}=\frac{2}{3}[/tex]

Slope of [tex]\mathbf{\overline{AB}}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel

[tex]3. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{ \frac{2- 4}{-6 - (-2)} = \frac{-2}{-4}} =\frac{1}{2}[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{11 - (-7)}{-1 - 5} = \frac{18}{-6}=-3[/tex]

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

[tex]4. \ \displaystyle Slope \ of \ \overline{AB} = \frac{8- 3}{-3 - 2} = \frac{5}{-5} =-1[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{6 - 2}{-4 - (-8)} = \frac{4}{4}=1[/tex]

[tex]\displaystyle Slope \ of \ \overline{AB} = \mathbf{-\frac{1}{Slope \ of \ \overline{CD}}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]5. \ \displaystyle Slope \ of \ \overline{AB} = \frac{-1 - 2}{-8 - (-4)} = \frac{-3}{-4} =\frac{3}{4}[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-3 - 6}{0 - 12}} = \frac{-9}{-12}=\frac{3}{4}[/tex]

Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel

[tex]6. \ \displaystyle Slope \ of \ \overline{AB} = \frac{5 - (-1)}{6 - 3} = \frac{6}{3} =2[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-5 - 7}{2 - (-4)}} = \frac{-12}{6}=-2[/tex]

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

Directions: To determine if the equations are parallel or perpendicular

Solution:

The equations are parallel if when expressed in the form, y = m·x  + c, the value of m are equal

The equations are perpendicular, when we have;

[tex]\displaystyle The \ value \ of \ \mathbf{m} \ in \ one \ equation = -\frac{1}{The \ value \ of \ \mathbf{m} \ in \ the \ other\ equation }[/tex]

7. First equation

3·x + 2·y = 6

Therefore; [tex]\displaystyle y = -\frac{3}{2} \cdot x + 3[/tex]

Second equation; [tex]\displaystyle y = \mathbf{-\frac{3}{2} \cdot x + 5}[/tex]

The value of m which is the coefficient of x are both equal to [tex]\displaystyle -\frac{3}{2}[/tex]

Therefore, the equations are parallel

8.  Equation 1; 3·y = 4·x + 15

Therefore;

[tex]\displaystyle y = \frac{4}{3} \cdot x + 5[/tex]

Equation 2; 9·x + 12·y = 12

[tex]\displaystyle y = -\frac{9}{12} \cdot x + 1 = 1 - \frac{3}{4} \cdot x[/tex]

The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular

9. Equation 1: 8·x - 2·y = 4

Therefore;

y = 4·x - 2

Equation 2: x + 4·y = -12

Therefore;

[tex]\displaystyle y = -\frac{1}{4} \cdot x - 3[/tex]

The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular.

10. Equation 1: 3·x + 2·y = 10

Therefore;

[tex]\displaystyle y = -\frac{3}{2} \cdot x - 5[/tex]

Equation 2: 2·x + 3·y = -3

[tex]\displaystyle y = -\frac{2}{3} \cdot x -1[/tex]

The slopes of the equation 1 and 2 are not equal, and are not  the negative inverse of each other, therefore, the equations are neither parallel nor perpendicular.

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Answer:

true

Step-by-step explanation:

0.8 is out of 1.0 so 0.8 + 0.2 = 1.0 and same for 8/10

Answer: True

Step-by-step explanation:

In order to see if the two given numbers are equal to each other, you need to turn one of them into either a fraction or a decimal so both of them are the same and you are able to compare.

In order to turn [tex]\frac{8}{10}[/tex] into a decimal, you divide 10 by 8.

8 ÷ 10 = 0.8

Both of the decimals are the same therefore the numbers are equal to each other and the statement is true.

We must write and solve a system of equations to see how many of each type of coin Carlos has.

The answer is:

We start by defining the variables:

We know there are 46 coins in total, thus:

x + y + z= 46

The number of pennies and dimes is the same, thus:

x = y

The total value of the coins in the box is $4.09, then:

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

So we can write the system of equations:

x + y + z= 46

x = y

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

First, we can replace x by y in the first and third equations (by using the second one) to get:

2y + z =  46

y*$0.11 + z*$0.25 = $4.09

Now we can isolate z in the first equation to get:

z = 46 - 2y

And replace that in the other equation:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

Now we can solve the equation for y:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

y*$0.11 + $11.50 - y*$0.50 = $4.09

y*($0.11 - $0.50) = $4.09 - $11.50

y*(-$0.39) = -$7.41

y = (-$7.41)/(-$0.39) = 19

if y = 19, then x = 19

By using the first equation:

x + y + z = 46

19 + 19 + z = 46

z = 46 - 19 - 19  = 8

We can conclude that:

If you want to learn more about systems of equations, you can read:

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Answer:

positive

Step-by-step explanation:

negative times negative is positive

positive times positive is positive

positive times negative is negative

negative times positive is negative

Answer:

13.5

Step-by-step explanation:

[tex]56-8(\frac{\frac{1}{4}+2 }{1-\frac{3}{5} })= 56-8(\frac{2,25}{0,4 })= 56-8.(5,625)=56-45= 11[/tex]

ok done. Thank to me :>

Answer:

Below.

Step-by-step explanation:

f) (a + b)^3 - 4(a + b)^2  

The (a+ b)^2 can be taken out to give:

= (a + b)^2(a + b - 4)

= (a + b)(a + b)(a + b - 4).

g)  3x(x - y) - 6(-x + y)

=  3x( x - y) + 6(x - y)

= (3x + 6)(x - y)

= 3(x + 2)(x - y).

h) (6a - 5b)(c - d) + (3a + 4b)(d - c)

=  (6a - 5b)(c - d) + (-3a - 4b)(c - d)

= -(c - d)(6a - 5b)(3a + 4b).

i)  -3d(-9a - 2b) + 2c (9a + 2b)

= 3d(9a + 2b) + 2c (9a + 2b)

=  3d(9a + 2b) + 2c (9a + 2b).

= (3d + 2c)(9a + 2b).

j)  a^2b^3(2a + 1) - 6ab^2(-1 - 2a)

=  a^2b^3(2a + 1) + 6ab^2(2a + 1)

= (2a + 1)( a^2b^3 + 6ab^2)

The GCF of a^2b^3 and  6ab^2 is ab^2, so we have:

(2a + 1)ab^2(ab + 6)

= ab^2(ab + 6)(2a + 1).

Answer:

Neither

Step-by-step explanation:

Since line a and b have different slope, it isnt parallel, and since the slopes both negative, its not an opposite reciprocal, so that isnt perpendicular, thus leading to neither

Answer:

The answer is 6.5

Step-by-step explanation:

It was a long process, but overall if you look at how long the segment x looks, it has to be less than half of the segment that is 30 units long so the only one that makes sense is 6.5

Answer:

pretty sure 60, 5 x 12

Step-by-step explanation:

just do 5 x 12 if there's 12 tiles and their measurement is 5 inches each

Answer:

x=79 degrees y=22degrees

Step-by-step explanation:

you see it has 2 equal sides, so the triangle is an isosceles triangle. If the triangle is isosceles, then its 2 base angles are equal, that is, x = 79 according to the triangle property, the 3 angles add up to 180 degrees, so you take 180 degrees minus 2 * 79 degrees you get a y angle equal to 22 degrees

Answer:

18 square feet

Step-by-step explanation:

hope this helps :)

Answer:

18 ft might be the answer

Answer:

x = 40

y = 8

Step-by-step explanation:

3x-9 = 2x+31

3x-2x = 31+9

x = 40

4y+5 = 2y+21

4y-2y = 21-5

2y=16

y=8

Answer:

The first and third are functions.

Step-by-step explanation:

Functions must have only one y-value for an x-value.

Answer:

3 2/5

Step-by-step explanation:

17/5= 3 2/5

Answer:

First find the nearest number divisible by 5 to get a whole number returned

that number is 15

15/5 = 3 (no decimals)

so the ‘big’ (as I like to call it) number or the integer that isn’t part of the fraction would be 3.

now what is left?

subtract 15 from the numerator

17 - 15 = 2

replace 17 with 2 in the fraction to get 2/5

The result is [tex]3\frac{2}{5}[/tex]

to prove this is the same

multiply the ‘big number’ by the denominator

3*5 = 15

and add the numerator

15+2 = 17

now just insert the denominator below it, and you get 17/5

[tex]4 \times + 5 \times + 135 = 180[/tex]

[tex]9 \times + 135 = 180 \\ 9 \times = 45 \\ \times = 45[/tex]

O centroid

Step-by-step explanation:

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

Answer:

The measure of <CAO = 21°

Answer:

Collect as many ants as you can with the container you have provided. A excellent approach to do this is to sprinkle some sugar or bread crumbs in a container and position it near the ant nest, where the ants will gather. A reasonable starting point is about 100.

Step-by-step explanation:

Hope it helps:)

Answer:

x=4

Step-by-step explanation:

Step 2 and 3 are incorrect,

4x+8 = 24

24-8 = 16

it should then be 4x=16

you then divide by 4 on each side

x=4

The true statement is

The survey results are most at risk for under coverage.

Survey methodology is an area of applied statistics that focuses on human-research surveys. It examines the sampling of discrete groups from a population and related methods for gathering survey data, such as creating questionnaires and techniques for boosting response rates and accuracy.

We have,

A school board is interested in whether high school students would like to shift the school day forward by 30 minutes.

As, It would be biassed to just survey kids who participate in extracurricular activities because they would be excluding the opinions of many other students.

Thus, the survey results are most at risk for under coverage.

Learn more about Survey here:

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#SPJ2

Answer:

1.6 x 10^-6.

Step-by-step explanation:

a) Work out (8 x 10^-3)(2 x 10^-4)

= 8 x 2 x 10^(-3 + -4)

= 16 x 10^-7

Convert this to standard form by dividing the first part by 10 and multiplying the second by 10.

= 1.6 x 10^-6.

Answer:

7/21=3/9

Step-by-step explanation:

7/21=3/9=1/3 - Ratios are basically the same as fractions

Answer:

[tex] \\ 7 \ratio21 = 3 \ratio9[/tex]

[tex] \\ \frac{7}{21} = \frac{3}{9} [/tex]

Answer:

Angles 7 and 8 are supplementary because they are a pair of adjacent angles that form a straight line.

Supplementary angles add up to 180°

Answer:

24

Step-by-step explanation:

-3(1(-8))

1x(-8) = -8

-3 x -8 =24

Answer:

His answer was correct:

(200*0.09)=18

18*16=288

200+288=488