Rectangle JKLM is rotated 90° clockwise about the origin.

What are the coordinates of J’?
J’(–1, –4)
J’(4, –1)
J’(1, 4)
J’(4, 1)

Answer:

[tex]x=1\,,\,y=-1[/tex]

Step-by-step explanation:

Given: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]

To solve: the given linear equations

Solution:

Consider the equations:

[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]

By method of cross multiplication:

[tex]\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}[/tex]

For equations: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]

[tex]ax+by-(a-b)=0\\bx-ay-(a+b)=0[/tex]

Take [tex]A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)[/tex]

So,

[tex]\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1[/tex]

Answer:

2a(5a+3b)(5a−3b)

Step-by-step explanation:

Both terms have 2a, so take out the 2a and you will get your answer.

Answer:

2a(5a - 3b)(5a + 3b)

Step-by-step explanation:

50a³ - 18ab² = 2a(25a² - 9b²) = 2a(5a - 3b)(5a + 3b)

Answer:

No

Mean diameter = 44, which is in the 40 - 44 cm group

Step-by-step explanation:

Given the data:

Diameter (cm) - mid point(X) - frequency(F) - - FX

35-39 - - - - 37 - - - - 8 - - 296

40-44 - - - 42 - - - 10 - - - 420

45-49 - - - 47 - - - 13 - - - 611

50-54 - - - 52 - - - 3 - - - 156

55-59 - - - 57 - - - 1 - - - 57

Mean of grouped data:

Sum of (F × X) / sum of F

1540 / 35 = 44

Answer: 34 cm

Step-by-step explanation:

Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem (to one triangle)

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the distance between corners) and a and b are the other sides.  

Replacing with the values given:  

c^2 = 12^2 + 12^2  

c^2 =144+144  

c^2 = 288

c = √288

c = 16.97 cm = 17 cm (rounded)

The other diagonal has the exact same lenght (because the flag is a square)

So, we have to multiply the length of the ribbon by 2:

17 x2 = 34 cm

Feel free to ask for more if needed or if you did not understand something.  

Answer:

34

Step-by-step explanation:

I did it on Khan

Answer:

3/2

Step-by-step explanation:

Divide by 4 to get 6x/4 = 3x/2

Answer:

52 degree

Step-by-step explanation:

So using cos again again :v

AC^2 = AB^2 +BC^2 - 2ABBCcosB

AC = 31.796cm

then

BC^2=AB^2 + AC^2 -2ABACcosA

Cos A = 0.61

A=52.17degree

Answer:

Area for sector = arc measure/360 degrees times pir^2

145 degrees/360 degrees times pi3.7^2 =

0.40277 times 13.69pi =

17.314in.^2 or B.

Answer:

150 mg

Step-by-step explanation:

This is an addition problem. Simply add the mg of the antibiotic that the patient takes each day.

So  you would do:

60+45+30+15 = 150

Since you get a result of 150, 150 mg is the answer.

The addition is one of the four fundamental mathematical operations. The patient will take a total of 150 mg of antibiotics.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

The total amount of antibiotics the patient will take is,

Total Antibiotic = 60mg + 45mg + 30mg + 15mg = 150 mg

Hence, the patient will take a total of 150 mg of antibiotics.

Learn more about Addition:

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Answer:

Step-by-step explanation:

A kite is a quadrilateral made up of two isosceles triangles. A kite does not have any parallel side, but has two pairs of equal adjacent sides. All four sides are not congruent, only two pairs of consecutive sides are congruent.

The vertices of a kite are right angles. The diagonals bisect each other at right angles ( that is they are perpendicular). Therefore the following are true:

1) two pairs of consecutive sides are congruent

2) The diagonals are perpendicular

3) The diagonals bisect each other.

Point A= (3,6), B = (5,0), C= (-2,-4) D = (-3,4)

[tex]AB=\sqrt{(0-6)^2+(5-3)^2}=\sqrt{40} \\AD=\sqrt{(4-2)^2+(-3-3)^2}=\sqrt{40}\\ BC=\sqrt{(-4-0)^2+(-2-5)^2}=\sqrt{65}\\ DC=\sqrt{(4-(-4)^2)+(-3-(-2))^2}=\sqrt{65}[/tex]

AB=AD, BC = BC.

This is a kite since two pairs of consecutive sides are congruent

Answer: A. [tex]y = x^{2} + 6x + 8[/tex]

Step-by-step explanation:

You can plug in the know point of (-3, -1) to each equation to see which one fits. The correct one in this case is [tex]y = x^{2} + 6x + 8[/tex]

Answer:

x = -4

y = -21

Step-by-step explanation:

To solve this, we will need to set up a system of equations and get rid of a variable.

-3x - 2y = 54

-6x + 2y = -18

From this, we can see that the 'y' variables can be cancelled out if we add the two together. This means that we must add these equations to each other to cancel out the 'y' variables:

-3x - 2y = 54

-6x + 2y = -18

-------------------- +

-9x = 36

x = -4

Since we have solved for 'x', we can simply plug this value into an equation to find 'y'.

-3(-4) -2y = 54

12 - 2y = 54

-2y = 42

y = -21.

Answer:

4^15

Step-by-step explanation:

(4^3)^5

We know a^b^c = a^(b*c)

(4^3)^5 = 4^(3*5) = 4^15

Answer:

[tex] {4}^{15} [/tex]

Answer B is correct

Step-by-step explanation:

[tex]( { {4}^{3} })^{5} \\ {4}^{3 \times 5} \\ = {4}^{15} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Divide the 5% of Spanish by 40% male:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

The answer is a. 12.5%

The probability of the student studying Spanish, if you know the students male will be 12.5%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that in a certain group of students, the probability of a randomly chosen student being male is 40%, the probability of the students studying Spanish is 18%, and the probability of the student being male who studies Spanish is 5%.

The probability of the student studying Spanish, if you know the student male will be calculated as below:-

Divide the 5% of Spanish by 40% of males:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

Therefore, the probability of the student studying Spanish, if you know the students male will be 12.5%.

To know more about probability follow

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Answer:B

Step-by-step explanation:

Answer: A

Step-by-step explanation:my answer was A and it was correct

Answer:

D. -∞ < y < 5

Step-by-step explanation:

The range are all the possible values for y that the function can take. In the graph we can see that the highest value for y is 5 and there isn't a lowest value for y. It means that the range are values between -∞ and 5.

So the range is:

-∞ < y < 5

Answer:

O AB is a major arc

Step-by-step explanation:

Circle M has the central angle LAMB with a measure of 63º

Which of the following statements does not represent the  circle M?

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

O AB is a minor arc

O mAB=63 º

O The center of the circle is point M.

O AB is a major arc

Answer:

The distance when x = 6km is D = 498 KM

Step-by-step explanation:

Here, given the formula for the distance, we want to find the distance D given the value of x to be 6km

What we do simply here is to substitute the value 6km as x in the equation

The equation is

D = 4x^3 - 10x^2 -6

Substituting x = 6, we have

D = 4(6^3) -10(6^2) -6

D = 864-360-6

D = 498 km

Answer:

Only Noah is correct.

Step-by-step explanation:

Volume of the cube = 10^3 = 1000 units.

Total volume of the cube + the prism = 1000 + 2

= 1020 cubic units.

Answer:

Only Noah is correct.

Step-by-step explanation:

Volume of the cube = 10^3 = 1000 units.

Total volume of the cube + the prism = 1000 + 2

= 1020 cubic units.

Step-by-step explanation:

Answer:

The answer is 88%

After 7 seconds the cup is about 88% filled with water.

Answer:

(5, 1/2)

Step-by-step explanation:

To find the midpoint

Take the sum of the x coordinates and divide by 2

(5+5)/2 = 10/2 = 5

Take the sum of the y coordinates and divide by 2

(4+-3)/2 = 1/2 = 1/2

The midpoint is ( 5, 1/2)

It is answer D

Its is exactly in between these to values

Answer:

30,19

Step-by-step explanation:

let the numbers be x and y,x>y

x+y=49

x-y=11

add

2x=60

x=60/2=30

30+y=49

y=49-30=19

Answer:

x = first number = 30 and y = second number = 19

Step-by-step explanation:

let the first number be x and second number be y.

According to the given information

The sum of the two numbers is 49

Here, we get the equation.

x + y = 49

Now, Similarly second given information

the difference is 11.

Here, we get the equation.

x - y = 11

Now,

Step 1:

Name the equations

x + y = 49 ...(1)

x - y = 11 ...(2)

Step 2:

Now,

From equation (1) we get,

x = 49 - y

Substitute the value of x = 49 - y in equation (2) we get,

x - y = 11

i.e.,

49 - y - y = 11

49 - 2y = 11

-2y + 49 = 11

2y - 49 = - 11

2y = 49 - 11

2y = 38

y = 38/2

y = 19

Step 3:

Now,

Put the value of y = 19 in equation (1), we get.

x + y = 49

i.e.,

x + 19 = 49

x = 49 - 19

x = 30

Thus, The value of x = first number = 30 and y = second number = 19

30 + 19 = 49

30 - 19 = 11

Answer:

23/27

Step-by-step explanation:

The square root of 529 is 23

while the square root of 729 is 27

Answer:

23/27

Step-by-step explanation:

529=23^2

729=27^2

sqrt{529/729} =sqrt{[tex]23^{2}[/tex]/[tex]27^{2}[/tex]}

= 23/27

Answer: 3

Step-by-step explanation:

A simple way to calculate the distance between numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. We have to find PQ. TAking the difference we have 94-91= 3.

Answer:

[tex]3[/tex]

Step-by-step explanation:

You can find the length by subtracting.

[tex]Q-P[/tex]

[tex]94-91[/tex]

[tex]=3[/tex]

You can also find the length by counting the units of the distance covered between the points.

Question:

The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour

Answer: 13 dollars per hour

Step-by-step explanation:

The rate of change (ROC) for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :

Point a = (5, 65) = (x2, y2)

Point b = (2, 26) = (x1, y1)

Calculating the gradient or slope :

Rate of change = (y2 - y1) / (x2 - x1)

Rate of change = (65 - 26) / (5 - 2)

Rate of change = 39 / 3

= 13 dollars per hour

Answer:

I think that the answer is D

Answer:

Shirley bought a fax machine and sells to Devi at a profit of 25% on the cost price.

Shirley buy price:: x

Devi buy price:: 1.25x

Devi sells the fax machine to Amirah at a loss of 250 on the price which she buys it from Shirley.

Amirah buy price = 1.25x -250

if Amirah pays $360 for the fax machine,how much did Shirley pay for it?

Equation:

1.25x - 250 = 360

1.25x = 360 + 250

x = 610 / 1.25

x = 488

Ans: x = $488 (Price Shirley paid)

Answer:

$2.70

Step-by-step explanation

Jennifer and Linda both bought one apple, but they bought different numbers of oranges. Looking at the numbers, we see that Linda bought 2 more oranges than Jennifer (they bought the same number of apples, so disregard apples for now, we will look at them later).

Subtracting Jennifer's cost from Linda's cost, 7.50 - 5.10 = 2.40

So, we know that 2 oranges cost $2.40, so 1 orange will then cost $1.20.

Now we know the cost of 1 orange. So, we can find the price of an apple by finding the cost of 3 oranges. 3 x 1.20 = 3.60. So, Jennifer's 3 oranges cost 3.60, and subtract this cost from the total cost and we find that 1 apple costs $1.50.

Add the price of 1 apple and 1 orange. $1.50 + $1.20 = $2.70

Answer:

Yes

Step-by-step explanation:

As long as the input has an output it will always be a function.

Answer:

Yes

Step-by-step explanation:

Because there isn't a number in the input colum that is repeated like:

1

1

2

3

Instead each number is individual and they aren't repeated.

If they were repeated then it would NOT be a function.

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

Answer:

1cm = 320 km?

Step-by-step explanation:

Answer:

[tex]3.2km[/tex]

Step-by-step explanation:

[tex]1 \: : 320000 \\ 1cm = 320000cm[/tex]

[tex]1cm = 100m \\ [/tex]

[tex]1cm = 320000cm \\ 1cm = 3200m[/tex]

[tex]1km \: \: = 1000m[/tex]

[tex]1cm = 3200m \\ 1cm = 3.2km[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Juan conclusion is counterexample

Answer:

1, 2, and 5

Step-by-step explanation:

Answer:

$24000

Step-by-step explanation:

Let the full advertising budget of the company be $x.

Therefore, 30% of x = $7,200

[tex]\frac{30}{100} \times x= 7200 \\\\x = \frac{100}{30} \times 7200\\\\x = 100 \times 240\\\\x = \$24000[/tex]

Hence, full advertising budget of the company is $24000.