Which set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20?

A. (2, -7)
B. (1, -6)
C. (5, 0)
D. (0, -7.5)

Answer:

one solution, i.e x = 1 and y = -2

Step-by-step explanation:

Given two equations :

x+3y = -5   -------(1)

4x - y =6   ---------(2)

Using elimination method,

Multiply equation (2) by 3 and add it to equation (1)

We get,

x + 3y + {(4x - y)×3} = -5 +(6×3)

x + 12x + 3y - 3y = -5 + 18

13x = 13

x = 13/13  = 1

And corresponding y will be:

x + 3y = -5   , Plug x =1  to get y

1 + 3y = -5

3y = -5 - 1

y = -6/3 = -2

Hence we got only one solution, i.e x =1 and y = -2

Answer:

4.8

Step-by-step explanation:

b to c is 3.6

b to d is 8.4

if c is in the middle , you would subtract 8.4 and 3.6

Answer:

see explanation

Step-by-step explanation:

(a)

Since lines AB and CD are parallel then their slopes are equal

y = - [tex]\frac{1}{2}[/tex] x + 14 is in slope- intercept form ( y = mx + c )

with slope m = - [tex]\frac{1}{2}[/tex]

Hence slope of CD = - [tex]\frac{1}{2}[/tex]

D is the point (0, 7) ⇒ c = 7

y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of CD

(b)

to find the x- intercept let y = 0, in the equation and solve for x

- [tex]\frac{1}{2}[/tex] x + 7 = 0 ( multiply through by 2 )

- x + 14 = 0 ⇒ - x = - 14 ⇒ x = 14 ← x- intercept of CD

Answer:

Step-by-step explanation:

4x=2z+5/y

X= 1/4(2z+5/y)

Answer:

60 degrees.

Step-by-step explanation:

The total measure of the exterior angles of all polygons is 360 degrees,

A regular hexagon has 6 equal exterior angles so the measure of each angle is 360 / 6 = 60 degrees.

Answer:

Measure of each exterior angle for regular hexagon = 60°

Step-by-step explanation:

We have sum of interior angles of a polygon with n sides = (n-2) x 180

Sum of exterior angles =  n x 180 - (n-2) x 180 = 2 x 180 = 360 degree.

So whatever be the number of sides the sum of exterior angles of a polygon is 360°.

Here we are asked to find the measure of each exterior angle for regular hexagon.

We know sum of exterior angles = 360°

Number of exterior angles = 6

Measure of each exterior angle for regular hexagon = 360/6 = 60°

Measure of each exterior angle for regular hexagon = 60°

It takes 11 seconds to scan one person. So we have this ratio to start with

11 seconds: 1 person

Divide both sides by 11 to get this new ratio

1 second: 1/11 person

1 second: 0.0909 person

So in 1 second, 0.0909 of a person can be scanned. This statement seems silly because we can't have a fraction of a person, but it helps with the next part as shown below. The next step is to multiply both sides by 1800 to get....

1 second: 0.0909 person

1800*1 second: 1800*0.0909 person

1800 seconds: 163.62 persons

In a span of 1800 seconds (equivalent to 30 minutes), about 163 people's lunches can be scanned. Unfortunately, none of the answer choices are 163. The closest thing is 180, but that is an overestimate. So I would ask your teacher if there is a typo somewhere.

Note: if it took exactly 10 seconds for each student (instead of 11), then the answer would be 1800*(1/10) = 1800*0.10 = 180.

Answer:

12 hours

Step-by-step explanation:

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

The parallel lines have the same slope.

We have y = -3x + 7 → m = -3. Therefore y = -3x + b.

Put the coordinates of the point (2, -4) to the equation of a line:

[tex]-4=-3(2)+b[/tex]

[tex]-4=-6+b[/tex]            add 6 to both sides

[tex]2=b\to b=2[/tex]

Answer: .0459

Step-by-step explanation:

Answer:

-79/20 < x< -17/20

Step-by-step explanation:

-4| 5x+12| -13> -44

The first step is to add 13 to each side

-4| 5x+12| -13+13> -44+13

-4| 5x+12| > -31

Divide each side by -4.  Remember when dividing by a negative to flip the inequality

-4/-4| 5x+12| < -31/-4

| 5x+12| < 31/4

Now we will have 2 equations, one positive and one negative.  Remember to flip the inequality for the negative

5x+12 < 31/4   and 5x+12 >-31/4

Subtract 12 from each side

5x+12-12 < 31/4-12   and 5x+12-12 >-31/4-12

5x < 31/4-12   and 5x >-31/4-12

Get a common denominator of 4

5x < 31/4-48/4   and 5x >-31/4-48/4

5x < -17/4       and   5x > -79/4

Divide each side by 5

x < -17/20    and x >-79/20

-79/20 < x< -17/20

Answer:

He could use 104 pages in the photo books .

Step-by-step explanation:

Given :

A photographer has 591 photos of animals and 234 photos of plants.

Each page of the photo books holds 8 photos.

To Find : Fewest number of pages he could use in the photo books.

Solution :

A photographer has 591 photos of animals and 234 photos of plants.

Thus total no. of photos he have = 591+234 = 825 photos

Since he wants to put all the photos into photo book  

No. of pages required for 8 photos = 1

No. of pages required for 1 photo = 1/8

No. of pages required for 825 photos:

= [tex]\frac{1}{8} *825[/tex]  

⇒103.125 pages ≈ 104 pages

Hence he could use 104 pages in the photo books .

Final answer:

The quadratic equation 2x² + 18 = 0 is solved by isolating the x² term and taking the square root of both sides, yielding solutions x = 3i and x = -3i.

Explanation:

To solve the quadratic equation 2x² + 18 = 0, you need to first move all terms to one side of the equation to set it equal to zero, which is already done in this case. Next, you would typically factor the quadratic or use the quadratic formula.

However, this equation can be simply factored since it is missing the x term. So, subtract 18 from both sides to isolate the x² term.

2x² = -18

Now, divide both sides by 2 to solve for x².

x² = -9

To solve for x, take the square root of both sides. Remember, when taking the square root of a number, you will have both a positive and negative solution.

x = √{-9} = ±3i

The solutions to the equation are x = 3i and x = -3i, where i is the imaginary unit.

Answer:

30:75:60

Step-by-step explanation:

I'm not sure if this is how you're supposed to solve it, but I'll give it my best shot.

1. Think of the 2:5:4 as "chunks". 2 Chunks:5 Chunks:4 Chunks. 2+5+4 is 11. We obviously have to use all of the 165 perimeter units, and we know the ratio already.

2. We need to take 165, and divide it by 11. This will give us what one "chunk" is. It equals 15.

3. Now that we know what one chunk is equal to, we can simply multiply.

2 Chunks * 15 Per Chunk = 30

5*15=75

4*15=60

So, our final answer is 30:75:60

--

Checking, 30+75+60=165, so we used the whole perimeter.

The measure of sides of the triangle be 30, 75 and 60 unit.

Given,

the ratio of the measures three sides of triangles is 2:5:4.

The perimeter of triangle is 165 units.

Let the sides of triangle be 2x, 5x and 4x respectively.

We know that perimeter of triangle is sum of all sides, So

[tex]\rm P= 2x+5x+4x[/tex]

[tex]165=11x[/tex]

[tex]x=\dfrac{165}{11} \\\\[/tex]

[tex]x=15\\[/tex]

So the sides of triangle will be [tex]2\times15=30[/tex], [tex]5\times 15=75[/tex] and [tex]4\times15=60[/tex] units respectively.

Thus the sides of triangle are 30, 75 and 60 units.

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[tex]Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}<0\iff(x+2)(x-4) < 0\\\\x+2=0\to x=-2\\x-4=0\to x=4\\\\(x+2)(x-4)=x^2-4x+2x-8\\\\\text{parabola op}\text{en up}\\\\\text{Look at the picture}\\\\Answer:\ \dfrac{x+2}{x-4}<0\ for\ x\in(-2,\ 4)\to\boxed{B)\ -2 < x < 4}[/tex]

Other method:

[tex]\dfrac{x+2}{x-4}<0[/tex]

zeros of numerator and denominator are x = -2 and x = 4.

Look at the second picture.

for x < -2 → x + 2 < 0 and x - 4 < 0

therefore [tex]\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0[/tex]

for -2 < x < 4 → x + 2 > 0 and x - 4 < 0

therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0[/tex]

for x > 4 → x + 2 > 0 and x - 4 > 0

therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0[/tex]

Answer:

-2 < x < 4

Step-by-step explanation:

Answer:

The answer would be 20.05 hours per day.

Answer: There are 20.05 kwh that Luke use per day during the month of April.

Step-by-step explanation:

Since we have given that

Amount of electric bill = $84.21

Charges of electric company = $ 0.14 per kWh

We need to find the number of kilowatt hours.

Number of days in the month of April = 30 days

According to question,

[tex]84.21=0.14\times 30\times x\\\\84.21=4.2\times x\\\\\dfrac{84.21}{4.2}=x\\\\x=20.05\ kwh[/tex]

Hence, there are 20.05 kwh that Luke use per day during the month of April.

Answer:

3 3/5 lbs

Step-by-step explanation:

We will multiply the pounds of berries by the faction she used to see how much she used for the pie

4 4/5 * 3/4 = amount used in pie

We need to convert the mixed number to an improper fraction

4 4/5 = (5*4+4)/5 = 24/5

24/5 * 3/4 =

I will change the order to make the math easier

24/4 * 3/5

6 * 3/5 =

18/5

Now we need to change it back to a mixed number

5 goes into 18   3 times with 3 left over

3 3/5 lbs

She used 3 3/5 lbs

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

The statement "Some rectangles are not parallelograms" is false.

Option B is the correct answer.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Some rectangles are not parallelograms.

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

So,

All rectangles are parallelograms.

Thus,

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

The statement "Some rectangles are not parallelograms" is false.

Option B is the correct answer.

Learn more about parallelograms here:

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Answer:

Positive association and nonlinear

Step-by-step explanation:

Answer:

Positive association & Linear Association  

Step-by-step explanation:

Positive charts go up from left to right (which this plot does)

Liner plots are any plots that can form a straight line (which this one does)

Answer:

3n^2

Step-by-step explanation:

3, 12, 27, 48, 75

List the differences between terms:-

9, 15, 21, 27

Now find the second differences:-

6, 6, 6

The sequence in the question is  quadratic and the first coefficient ( that of n^2) = 6/2  = 3.  The first term in the nth term formula is 3n^2.

Now we write out the original sequence and the  3n^2 values  as follows:-

3  12  27  48  75

3  12  27  48  75

They are the same so the formula for the nth term is 3n^2.

The nth term of the given sequence is 3n².

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given the series,

3,12,27,48,75

Since all terms are multiplied of 3

3 × 1 = 3

3 × 4 = 12

3 × 9 = 27

3 × 16 = 48

3 × 25 = 75

It is clear that it is forming a series by 3 and the product of the square root of a natural number.

So, it will be 3n².

Hence "The nth term of the given sequence is 3n²".

For more information about the series,

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Answer

the answer is P=7.8

Step-by-step explanation:

P=14.7e           -0.21x

X=14.7e      (-0.63)

take the natrual log of both sides

1n(P)=1n(14.7e(-.63)

1n(P)=1n(14.7)-.63

(because ln(e^a) = a)

1n(P)=2.688 - .63

1n(P)=2.058

P=e       2.058

P=7.8

Final answer:

To find the average atmospheric pressure at an altitude of 2.3 miles, substitute x = 2.3 into the given formula and solve, resulting in approximately 9.1 pounds per square inch.

Explanation:

The average atmospheric pressure for an altitude of 2.3 miles can be found by substituting x = 2.3 into the given formula: [tex]p = 14.7e^{-0.21x[/tex]

Substitute x = 2.3 into the formula:

p = [tex]14.7e^{-0.21(2.3)[/tex]

p ≈ [tex]14.7e^{-0.483[/tex]

p ≈ 14.7⁩ × 0.617 ≈ 9.1 pounds per square inch (rounded to the nearest tenth)

The probability that the red die shows a number larger than three or the green die shows a number less than three is 0.83 or 83%.

The question relates to the topic of probability in mathematics, which is the measure of the likelihood that an event will occur. In this case, we are looking at the probability of combined events with two standard six-sided dice, one red, and one green.

Firstly, the probability that the red die rolls a number larger than three is 3/6 or 0.5 since, out of 6 possible outcomes (1, 2, 3, 4, 5, 6), 3 (4, 5, 6) are favorable outcomes.

Secondly, the probability that the green die shows a number less than 3 is also 2/6 or approximately 0.33, as there are two favorable outcomes (1 and 2).

To find the probability of the red die showing a number larger than three OR the green die showing a number less than three, we add the two individual probabilities because these are independent events. Hence Probability = 0.5+0.33 = 0.83 or 83%

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The probability of the red die showing a number larger than three or the green die showing a number less than three is 1/9.

To calculate the probability of the red die showing a number larger than three or the green die showing a number less than three, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The favorable outcomes are when the red die shows a number larger than three (i.e., 4, 5, or 6) or when the green die shows a number less than three (i.e., 1 or 2).

Since each die has 6 sides, the total number of possible outcomes for each die is 6. Therefore, the total number of possible outcomes for both dice is 6 * 6 = 36.

The number of favorable outcomes is 3 (for the red die) + 2 (for the green die) - 1 (for the outcome where both dice show a number larger than three and a number less than three) = 4.

Therefore, the probability is 4/36 = 1/9.

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I'll do the first one to get you started.

Start at point A as that is the first letter of the sequence ABC. The second letter is B so we'll record the length of segment AB, which is 4 units long.

Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.

Segment ED is 2 units long. So AB and ED pair up

------------------------------

BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up

I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4

So A pairs up with E, B pairs with D, and C pairs with F

Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.

I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.

The correct solution: 4x^2 -27x +167 - 996/(x+6)

Step-by-step explanation:

36 is 12.5% of 288

I hope this helps!

Answer:

The answer is 8696

Step-by-step explanation:

This answer is obtained by multiplying the speed per second by 8

Answer:

8696 feet

Step-by-step explanation:

We are given that the sound travels at a speed of nearly 1087 feet per second when the temperature is 32 F. And we are supposed to find the distance the sound travels in 8 seconds.

We know the formula of the speed:

[tex]Speed = \frac{distance}{time}[/tex]

Putting in the values to find the distance:

[tex]1087=\frac{distance}{8}[/tex]

[tex]distance = 1087*8\\\\distance=8696[/tex]

Therefore, the speed travels for 8696 feet in 8 seconds.

Answer:

x=1 , y=6

Step-by-step explanation:

7x+3y = 25

-2x-y = -8

Multiply the second equation by 3 so we can eliminate y

3(-2x-y )= -8*3

-6x -3y = -24

Add this equation to the first equation

-6x -3y = -24

7x+3y = 25

----------------------

x = 1

But we still need to find y by substituting x =1

-2x -y = -8

-2(1) -y = -8

-2-y = -8

Add 2 to each side

-2+2 = -8+2

-y = -6

Multiply by  -1

y = 6