A line passes through the points (-1, -1)
and (5,8). Which points lie on the same
line? Select all that apply.
(-3, -4)
(9, 14)
(1, 2)
(4, 7)
(3,5)
(-2,-2)

Answers

Answer 1

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]

[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]

[tex]y+1=\dfrac{9}{6}(x+1)[/tex]

[tex]y+1=\dfrac{3}{2}(x+1)[/tex]

Multiply both sides by 2.

[tex]2(y+1)=3(x+1)[/tex]

[tex]2y+2=3x+3[/tex]

[tex]2y=3x+3-2[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].

Now, check each point for this equation.

Putting [tex]x=-3[/tex], we get

[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]

[tex]y=\dfrac{-9+1}{2}[/tex]

[tex]y=\dfrac{-8}{2}[/tex]

[tex]y=-4[/tex]

Similarly,

For [tex]x=9,y=15[/tex].

For [tex]x=1,y=2[/tex].

For [tex]x=4,y=6.5[/tex].

For [tex]x=3,y=5[/tex].

For [tex]x=-2,y=-2.5[/tex].

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.


Related Questions

which inequality represents all values of x for which the quotient below is defined? √15(x-1) ÷ √2^2

Answers

Answer:

Option D: x ≥ 1.

Step-by-step explanation:

Here we have the quotient:

[tex]\frac{\sqrt{15*(x - 1)} }{\sqrt{2*x^2} }[/tex]

Here we have two restrictions for the domain.

first, the denominator can never be zero, so x must be different than zero.

Second, the arguments of the square roots can not be negative.

The one in the denominator is always positive because we have the square of x.

So let's look at the values of x, such that:

15*(x - 1) ≥ 0

(x - 1) ≥ 0

x ≥  1

Note that when x ≥ 1, we are also removing the problem in the denominator, then we can conclude that the fraction is defined when:

x ≥ 1.

The correct option is D

Which statement describes the relationship between x and y?

As x increases, y decreases.
As x increases, y increases.
As x increases, y increases and then decreases.
As x increases, y decreases and then increases.

Answers

Answer:

as x increases, y increases

Step-by-step explanation:

Answer:

B. as x increases, y increases

Step-by-step explanation:

Find the measure of the missing angle using the exterior angle sum theorm

Answers

Answer:

160=130+x

x=160-130

x=30

Help! What is the equation of the line shown in the graph?

Answers

Answer:

y = -x -2

Step-by-step explanation:

Slope = -1

y intercept is -2

Slope = [tex]\frac{-4-1}{2-(-3) }[/tex] = [tex]\frac{-5}{5}[/tex] = -1

What is the product?
(7x^2y^3)(3x^5y^8)
10x^7+y^11
10X^10y^24
21x^7y^11
21x^10y^24

Answers

Answer:

21x^7y^11.

Step-by-step explanation:

:D

Help please guys if you don’t mind

Answers

Answer:

slope = -2

equation y= -2x -1

y - intercept (0,-1)

Answer:

y-int: -1

Slope: -2/1

Equation: Y=-2/1x-1

Step-by-step explanation:

One national survey found that 86 percent of those who were unhappily married, but who stayed with the marriage, were when reinterviewed five years later:

Answers

Comolete question is;

One national survey found that 86 percent of those who were unhappily married but who stayed with the marriage were, when re-interviewed five years later,

A) preparing to divorce

B) resigned to the situation

C) mostly "very" or "quite" happy

D) mostly "very" happy

Answer:

C) mostly "very" or "quite" happy

Step-by-step explanation:

From social psychology, we know that;

Sometimes people could be happy about something but later on as things progress they become satisfied and are happy about that same thing or person.

The same is the case here with marriage and more importantly in this research.

It says they were unhappily married but they stayed in the marriage and were interviewed 5 years after that. Thus, for them to stay that long even after being unhappy, it means that they began to become a bit happy along the line.

Thus, they would gradually become happy or mostly happy.

Let be the set of permutations of whose first term is a prime. If we choose a permutation at random from , what is the probability that the third term is equal to

Answers

Answer:

[tex]Pr = \frac{1}{6}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5\}[/tex]

[tex]n = 5[/tex]

Required

Probability the third term is 3

First, we calculate the possible set.

The first must be prime (i.e. 2, 3 and 5) --- 3 numbers

[tex]2nd \to 4\ numbers[/tex]

[tex]3rd \to 3\ numbers[/tex]

[tex]4th \to 2\ numbers[/tex]

[tex]5th \to 1\ number[/tex]

So, the number of set is:

[tex]S = 3 * 4 * 3 * 2 * 1[/tex]

[tex]S = 72[/tex]

Next, the number of sets if the third term must be 2

[tex]1st \to 2[/tex] i.e. 1 or 5

[tex]2nd \to 3\ numbers[/tex] ---- i.e. remove the already selected first term and the 3rd the compulsory third term

[tex]3rd \to 1\ number[/tex] i.e. the digit 2

[tex]4th \to 2\ numbers[/tex]

[tex]5th \to 1\ number[/tex]

So

[tex]r = 2 * 3 * 1 * 2 * 1[/tex]

[tex]r = 12[/tex]

So, the probability is:

[tex]Pr = \frac{r}{S}[/tex]

[tex]Pr = \frac{12}{72}[/tex]

[tex]Pr = \frac{1}{6}[/tex]

HELP QUICKLY PLEASE!! ​

Answers

Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Translations _______ side lengths of the figure. A. alter B. all of these C. change D. preserve

Answers

Answer:

alter I think I am small but also I know these

HELPPP
A. X=20, y=10
B. X=15, y=8
C. X=20, y=12
D. X=15, y=12

Answers

Answer:

Step-by-step explanation:

If this is a parallelogram, then opposite sides are congruent and opposite angles are congruent. That means that

2y + 8 = 3y - 4 and

3x + 25 = 5x - 5

We'll solve that first equation for y:

-y = -12 so

y = 12 Now onto x:

-2x = -30 so

x = 15

Choice d is the one you want.

what is the answer to this?

Answers

The answer would be 90

please help answer these!!!!

Jimmy’s family moved to a tropical climate. For the year that followed, he recorded the number of days that had a temperature above 400C each month. His data contained -

14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13 and 8

1) Find the mean for his data set of days that had a temperature above 400C.

2) Find the median for his data set of days that had a temperature above 400C.

3) Find the mode for his data set of days that had a temperature above 400C.

4) If, instead, there are 5 more days per month that had a temperature above 400C, what will be the mean for the data?

5) If, instead, there are 2 more days per month that had a temperature above 400C, what will be the mode for the data?

Answers

Answer:

1) 11.75

2) 11.5

3) 11 and 14

4) 16.75

5) 13, and 16

Step-by-step explanation:

The given data is 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8

1) The mean, [tex]\overline x[/tex] = (14+14+10+12+11+13+11+11+14+10+13+8)/12 = 11.75

2) The data arranged in increasing order is presented as follows;

8, 10, 10, 11, 11, 11, 12, 13, 13, 14, 14, 14

The count of he data points = 12

The median = The data at the (n + 1)/2 = (12 + 1)/2 = 6.5th position = 11 + (12  11)/2 = 11.5

The median = 11.5

3) The mode of the data set are 11 and 14

4) Where there are 5 more days per month that had a temperature above 40°C, we get;

The mean, [tex]\overline x_1[/tex] = (14+14+10+12+11+13+11+11+14+10+13+8+5×12 )/12 = 16.75 = [tex]\overline x[/tex] + 5

5) Given that there are 2 more days per month that had a temperature above 40°C, we get the days per month with temperatures above 40°C as follows;

8 + 2, 10 + 2, 10 + 2, 11 + 2, 11 + 2, 11 + 2, 12 + 2, 13 + 2, 13 + 2, 14 + 2, 14 + 2, 14 + 2

10, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16

Therefore, the mode are 13, and 16

An angel is formed by A: Parallel lines B: any ray and any line C: Two rays that shares the same end point D: any two rays
plz help me

Answers

Answer:

c

Step-by-step explanation:

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

options are on the picture:)

Answers

Answer:-

The option B is the right answer.

Solution:-

[tex] \sf h = 2d = 2 \: • \: 2r = 4r[/tex]

[tex] \sf = \frac{1}{3} \pi {r}^{2} h[/tex]

[tex] \sf = \frac{1}{3} \pi {r}^{2} \: • \: 4r[/tex]

[tex] \sf = \frac{4}{3} \pi {r}^{3} \: \green✓ [/tex]

Need help with these 3 problems!

Answers

Answer:

1. 25

2. 44

3. 9

Step-by-step explanation:

Answer:

25 students44 cents9 eggs

Step-by-step explanation:

If there are 3 cookies for each student and 75 cookies in total, then the equation would be 75 ÷ 3. that equals 2588 total for 2 cans. Divide 88 by 2 for the unit price. That makes 44 cents. 45 eggs total, 5 layers. Divide 45 by 5. That makes 9 eggs per layer.

The metric system has several advantages that include all of the following except _____.

only need to move the decimal point for conversions
prefixes are the same throughout
based on the numeral ten
only 10 base units to learn

Answers

Answer:

Only 10 base units to learn

Step-by-step explanation:

The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units

During conversion in the metric system, which is decimal based, it is only required to move the decimal point

The prefixes which are used to specify multiples and submultiples are the same through out

The decimal system is based on the powers of ten

The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)

Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn

Find P(5) given P(x) = 4 - 1

Answers

Answer:6

Step-by-step explanation:

sorry if im wrong

Drag each condition to the correct location on the table.
Match each condition to the number of triangles that can be constructed to fit the condition.
condition A: one side
measuring 4 inches,
another side measuring
8 inches, and a third
side measuring 10 inches
condition B: one angle
measuring 60°, another
angle measuring 40°, and
a third angle measuring 90°
condition C: one side
measuring 4 inches,
another side measuring
8 inches, and the angle
between them measuring 70°
condition D: one side
measuring 5 inches,
another side measuring
7 inches, and a third
side measuring 12 inches
condition E: one angle
measuring 30°, another
angle measuring 80°,
and the length of the
included side measuring
8 inches
condition F: one angle
measuring 40°, another
angle measuring 80°, and
a third angle measuring 60° I don't know how to do a pic, but it is no triangle one triangle and many triangle

Answers

Answer:

Condition A= 320 inches

Condition B= 190 Degrees F

Condition C= 2240 inches

Condition D= 350 inches

Condition E= 110 Degrees F 8 inches

Condition F= 180 Degrees F

Step-by-step explanation:

4 inches

8 inches

70 inches

60 D

40 D

90 D

4 inches

8 inches

70 D

5 inches

7 inches

12 inches

30 D

80 D

8 inches

40 D

80 D

60 D

Answer:

Condition A= 320 inches

Condition B= 190 Degrees F

Condition C= 2240 inches

Condition D= 350 inches

Condition E= 110 Degrees F 8 inches

Condition F= 180 Degrees F

Step-by-step explanation:

What is the quotient of

Answers

Answer:

x^5+8x^4+17x^3-14x^2-84x-72

Step-by-step explanation:

The first and last term of an A. P are 1 and 121 respectively. Find the number of terms in the A.P and the common difference between them if the sum of the term is 1281​

Answers

Answer:

No.of terms=21

Common difference=6

Il y a 5ans Thomas avait 5 fois l'âge de benoit aujourd'hui Thomas a 3 fois l âge de Benoît quel est l'âge de benoit

Answers

Répondre:

Benoit a 10 ans

Explication étape par étape :

Laisser :

Âge de Thomas = x

Benoit age = y

il y a 5 ans :

x - 5 = 5 (y - 5)

x - 5 = 5y - 25 - - (1)

Aujourd'hui :

x = 3y - - (2)

Mettez x = 3y dans (1)

3 ans - 5 = 5 ans - 25

Recueillir des termes similaires

3 ans - 5 ans = - 25 + 5

-2a = - 20

Diviser les deux côtés par - 2

y = 10

please say me the answer fast with step by step process​

Answers

Yes I’m sorry but I’m sorry I’m texting back to my sister in

Find the equation of the line through point (2,2) and parallel to y=x+4. Use a forward slash (i.e.”/“) for fractions (e.g. 1/2 for

Answers

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

Which of the following is a characteristic of a regular tessellation?​

Answers

Answer: Choice A

Explanation:

For regular tessellations, the types of polygons that we can use are

squares or rectanglesequilateral trianglesregular hexagons

We can only pick one of those shapes.

Shapes like regular octagons or pentagons will not work on their own because there is gap or overlap if we tried to glue them together. Think of tiles on the floor. There cannot be any gap or overlap when forming a tessellation.

If you wanted to use octagons to tessellate the plane, then you'd need squares to fill in the gaps. At this point, it's not considered a regular tessellation.

Helppppp
A. 8/15
B. 8/17
C. 15/8
D. 15/17

Answers

Answer:

D

Step-by-step explanation:

sin theta is equal to perpendicular by hypotenuse

here perpendicular is equal to 15 and base is equal to 8 therefore hypotenuse will be equal to 17

on putting on putting the value of perpendicular by hypotenuse we get 15 by 17 as sin theta

Answer:

Step-by-step explanation:

hypotenuse = √(15²+8²) = √289 = 17

sinθ = (leg opposite θ)/hypotenuse = 15/17

Please help me ASAP!!!

Answers

Answer:

[tex]108 in^{2}[/tex]

Step-by-step explanation:

[tex]===========================================[/tex]

Formulas:

Area of a rectangle/square:

[tex]A=lw[/tex]

Area of a triangle:

[tex]A=bh\frac{1}{2}[/tex]

[tex]===========================================[/tex]

To find the square, length*width. Both the length and width are 6, so the area of the square is 36 in.

The triangles all have a base of 6 and a height of 6. So, 36 divided by 2 or multiplied by [tex]\frac{1}{2}[/tex]

You would get 18 in.

There are 4 triangles, so multiply 18 by 4. 72 in.

Add up 36 and 72.

The answer is 108.

[tex]===========================================[/tex]

[tex]108 in^{2}[/tex]

the question is on the image.​

Answers

Hi there!

[tex]\huge\boxed{\text{22 cm}}[/tex]

We know that:

Area of a rectangle = l × w

The areas are the same, so:

3x · 4 = 6(3x - 2.5)

Simplify:

12x = 18x - 15

Solve for x:

15 = 6x

x = 2.5

Plug in this value of x to find the perimeter of rectangle B:

P = 2l + 2w

l = 6

w = 3(2.5) - 2.5 = 5

P = 2(6) + 2(5) = 22 cm

Can someone help with problems fivethroughseven

Answers

Answer:

5) 15120

6) 11880

7) 336

Step-by-step explanation:

The formula for permutation where mPn is m!/(m-n)!

Applying this to question 5, we get 9!/4!, which is 15120.

For question 6, we get 12!/8!, which is 11880.

For question 7, we get 8!/5!, which is 336.

If Clare earns $75 the next week from delivering newspapers and deposits it in her account, What will her account balance be then?\


answer pls

Answers

Answer: $15

Step-by-step explanation:

-$50 + $75 = $15

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