How many solutions does the system formed by x - y = 9 and
ay - ax + 90 = 0 have for a nonzero number a ? Give your answer and
complete the explanation.
a
The system has (select) solution(s). Rearranging the left side of the
2nd equation and subtracting 9a from both sides gives -ax + ay =
Dividing both sides by -a gives x - y = So, the equations describe
the same line.

Answer:

x= y+3/2 -3

Step-by-step explanation:

y+3/2=x+3

y+3/2-3=x

The line y = 2x + 3 on plotted graph.

Given that,
To determine whether the graph matches the equation y+3=2(x+3)

The line is a curve showing the shortest distance between 2 points.
The standard form of the equation of the line can be given as y = mx +c

Here,
y+3=2(x+3)
Simplifying the equation
y = 2x + 6 - 3
y = 2x + 3
The above-simplified equation represents the equation of line with slope and y-intercept as 2 and (0,3) respectively.

Thus, the line y = 2x + 3 on plotted graph.

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We have been given that in a right triangle, the measure of [tex]\theta = 43^{\circ}[/tex] and the side opposite to the measure of theta is 6.5 cm long. We are asked to find the length of adjacent side to the angle theta.

We know that tangent relates opposite side of right triangle adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(43^{\circ})=\frac{6.5}{\text{Adjacent}}[/tex]

[tex]\text{Adjacent}=\frac{6.5}{\text{tan}(43^{\circ})}[/tex]

[tex]\text{Adjacent}=\frac{6.5}{0.932515086138}[/tex]

[tex]\text{Adjacent}=6.9703966[/tex]

[tex]\text{Adjacent}\approx 6.97[/tex]

Therefore, the length of adjacent side to angle theta is approximately 6.97 units.

Answer:

8400

Step-by-step explanation:

Round them to their nearest whole:

23.8 x 349

24 x 350

We then use what we rounded and answer...

24 x 350 estimated to 8400

Answer:

6000

Step-by-step explanation:

23.8 - 20

349 - 300

20 times 300 = 6000

Answer:

M

Step-by-step explanation:

1 and 7/8 is between 1 and 2

Answer:

Point M.

Step-by-step explanation:

Each number is divided into fourths. 7/8 is in the middle of a fourth, and it is 1/2 of a fourth, or 1/8, away from 2. Therefore, Point M is the correct answer.

Answer:

a) the co-ordinates of the center are (-3,4) and the length of the radius is 10 units

Center (h,k) = (-3 ,4) and radius 'r' = 10

Step-by-step explanation:

Step(i):-

Given circle equation is

  [tex]2 x^{2} +12 x+2 y^{2} -16 y-150 =0[/tex]

Dividing "2' on both sides, we get

[tex]x^{2} +6 x+ y^{2} -8 y-75 =0[/tex]

Step(ii):-

now

[tex]x^{2} +2(3x) + (3)^{2}-(3)^{2} +y^{2} -2 (4 y)+(4)^{2}-(4)^2 -75 =0[/tex]

by using (a+b)² =a²+2 a b+b²

              (a-b)² =a²-2 a b+b²

[tex](x+3)^{2}-(3)^{2} +(y-4)^{2}-(4)^2 -75 =0[/tex]

[tex](x+3)^{2}-9 +(y-4)^{2}-16 -75 =0[/tex]

[tex](x+3)^{2} +(y-4)^{2}-100 =0[/tex]

[tex](x+3)^{2} +(y-4)^{2}=100[/tex]

[tex](x+3)^{2} +(y-4)^{2}=(10^2)[/tex]

by comparing

[tex](x-h)^{2} +(y-k)^{2}=(r^2)[/tex]

Final answer:-

Center (h,k) = (-3 ,4) and radius 'r' = 10

Answer:

Range: 40

Mean: 75.5

Median (a.k.a. media): 75

Mode: 75

Step-by-step explanation:

1) Put the numbers in order

60 , 60 , 65 , 75 , 75 , 75 , 75 , 75 , 95 , 100

2) Find the range

To find the range, you subtract the largest number from the smallest number. In this case, it those are 100 and 60 respectively.

100-60 = 40 which means the range is 40.

3) Find the mean

To find the mean, you add all the numbers together and then divide that by the number of numbers. So...

60 + 60 + 65 + 75 + 75 + 75 +75 + 75 + 95 + 100 = 755

755/10 = 75.5

*You divide by 10 because there are 10 numbers*

That means your mean in 75.5.

4) Find the median (a.k.a. media)

To find the median, you must find the number that is in the middle when the numbers are in order.

In this case, we have two numbers in the middle 75 and 75. To find the median we must add these two numbers together and then divide by 2.

75 + 75 = 150

150/2 = 75

That means the median is 75.

5) Find the mode.

To find the mode, you must find the number(s) that appear the most. In this case, that would be 75 as it appears five times in this number set.

That means the mode is 75.

I hope this helps!

Answer:

[tex]XY=2YZ\\XY=2\times4\\XY=8[/tex]

The value of XY is given by the trigonometric relation and the measure of side of the triangle is XY = 8

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as XYZ

Let the measure of the side XY of the triangle be A

The measure of side YZ = 4

Now , from the trigonometric relations , we get

sin θ = opposite / hypotenuse

when θ = 30°

Substitute the value of θ in the equation , we get

sin θ = YZ / XY

On simplifying the equation , we get

sin 30° = 4 / XY

Multiply by XY on both sides of the equation , we get

XY ( sin 30° ) = 4

The value of sin 30° = 1/2

So , XY / 2 = 4

Multiply by 2 on both sides of the equation , we get

XY = 8

Hence , the measure of side XY of triangle is XY =8

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Answer:

parllelogram

Step-by-step explanation:

............

Answer:

  x-5

Step-by-step explanation:

The middle term has a coefficient that is the sum of the constants in the binomial factors. For that to be zero, the other binomial factor must be ...

  (x -5)

__

  (x +5)(x -5) = x^2 -25 . . . . . middle term is zero

Answer:

dependent-samples t test

Step-by-step explanation:

Here we want to test the effect of game Dance Dance Revolution (DDR) on heart rate.

The hypothesis is

[tex]H_0:\mu_d=0 vs H_a:\mu_d\neq 0[/tex]

where,

[tex]\mu_d=\frac{\sum di}{n} di = Xi-Yi[/tex]

Where Xi =  heart rate before playing the game Dance Dance Revolution (DDR)

Yi = heart rate after playing the game Dance Dance Revolution (DDR)

This test is paired t-test( dependent sample t test).

To measure the effect of experiment. (before - after condition)

Answer:

3 1/2 houses

Step-by-step explanation:

To find the unit rate we must divide 4 by 10

4 hours divided by 10 house = 1/4

1/4 houses per hour

8 hours times 0.4= 3.2 houses

Answer:

20 houses

Step-by-step explanation:

Let’s make a proportion using this setup:

houses/hours=houses/hour

We know that 10 houses can be cleaned in 4 hours. We don’t know how many houses can be cleaned in 8 hours, so we can say x houses can be cleaned in 8 hours.

10 houses/4 hours= x houses/8 hours

10/4=x/8

Now we have to solve for x, by getting x by itself. Perform the opposite of what is being done to both sides.

x is being divided by 8. The opposite of division is multiplication, so multiply both sides by 8

8(10/4)=(x/8)8

8(10/4)=x

8(2.5)=x

20=x

20 houses can be cleaned in 8 hours.

Answer:

320 Student Tickets

180 Adult Tickets

Step-by-step explanation:

You can solve this problem by using system of equations. First, we need to figure out our equations.

Equation 1: x as students and y as adults

[tex]x+y=500[/tex]

We get this equation because the total tickets sold was 500. The x represents the students sold to students, and the y represents the tickets sold to adults.

Equation 2:

[tex]3x+5y=1850[/tex]

We get this equation based on the prices. Each student ticket costs $3, and each adult ticket costs $5. The total amount earned was $1850.

Now that we have out equations, we can use system of equations to find our students and adults.

[tex]x+y=500[/tex]

[tex]3x+5y=1860[/tex]

Typically elimination is the easiest strategy because you are able to cross out variables.

[tex]3(x+y=500)[/tex]

[tex]3x+5y=1860[/tex]

Becomes:

[tex]3x+3y=1500[/tex]

[tex]3x+5y=1860[/tex]

We see that both equations now have 3x. We can cancel out 3x.

[tex]-2y=-360[/tex]

[tex]y=180[/tex]

Now that we know y=180, we can plug it back into one of our equations to find x.

[tex]x+180=500[/tex]

[tex]x=320[/tex]

320 student tickets and 180 adult tickets were sold.

Answer:

k= 5

Equation is: y=5x

Answer:

  58.0 units

Step-by-step explanation:

In order to use the law of sines, we need to know angle C. It will be the angle that brings the total of all angles to 180°.

  C = 180° -A -B = 180° -72° -16°

  C = 92°

The law of sines tells us ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = 61·sin(72°)/sin(92°)

  a ≈ 58.0 . . . . units

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation: It’s C, So you just plug it in basically. y = 4x + 1, for example let’s use the third column y = 4(2) + 1, equals 9. You just repeat it in all the other columns and you equal y. So it’s C, y = 4x + 1

Answer: 3

Step-by-step explanation: edge (other girl is obviously challenged if she didn’t see the possible answers...)

Answer:

3×4 = 12!

TWO WAYS TO LOOK AT IT:

(A) 3 groups of 4!

(B) 4 groups of 3 apples!

Answer:

Step-by-step explanation:

Huh lol ok

Answer:

1 lemon = 2 cups of lemonade

Step-by-step explanation:

Answer: 2/5

Step-by-step explanation:

Answer:

Expanded form

Step-by-step explanation:

Expanded form or expanded notation is a system of writing numbers to see the value of each individual digits. The number are written in the form of tens, hundreds and ones etc. The expanded form of 44 will be 40 +4 where 4 is at ones place and 40 is at tens place.

Answer:

220

Step-by-step explanation:

Answer:

It Is The 3rd Choice, Y = -1/4( 4x - 8)

Step-by-step explanation:

This Is Becuase -1/4 times 4x is -1x which is negative x. Then -1/4 times -8 is 2.

Do not listen to the answer below it is wrong.

Answer:

C

Step-by-step explanation:

I got it right on edge

Answer:

37 7/13

Step-by-step explanation:

there are 13 students

total marks of students is488

therefore we are finding the median

=488/13

=37 7/13

The right answer is <DEF and <GHJ.

EXPLANATION:

if we add 40 degree and 50 degree then it will result to 90 degree .

Right angles are those angles which is exactly 90 degree.

Hope it will help you.....

-pragya~~

Step-by-step explanation:

angles GHJ and DEF

50+40=90

Answer:

the answer will might be A yeah I'm sure the answer is A

Answer:

125 m/min

Step-by-step explanation:

Find the rate (speed) as follows:

 25 meters

--------------------- = (125/1) meters/min = 125 m/min

(1/5) minute

This is equivalent to about 380 ft/min

Answer:

Step-by-step explanation:

the slope perpendicular is 1/2

y - 2 = 1/2(x - 4)

y - 2 = 1/2x - 2

y = 1/2x