−3(2−0.4y)+5.6=0.4(3y+1)

Answer:

250

75

40

Step-by-step explanation:

The pattern is 25

4*25= 100

10*25= 250

3*25= 75

40*25=1000

Answer:

1. [tex]R_{90} (x,y)=(-y,x)[/tex]

2. [tex]R_{180} (x,y)=(-x,-y)[/tex]

3. [tex]R_{270} (x,y)=(y,-x)[/tex].

Step-by-step explanation:

Let us assume a point (x,y) in the co-ordinate plane on which the transformations will be applied.

Now, we know that 'rotation' is a transformation that turns that image to a certain degree about a point.

So, the given transformations gives us the forms as:

1. When we rotate an ( x,y ) by 90° about origin counter-clockwise, the resultant co-ordinate is ( -y,x ).

So, the function form is [tex]R_{90} (x,y)=(-y,x)[/tex].

2. When we rotate an ( x,y ) by 180° about origin counter-clockwise, the resultant co-ordinate is ( -x,-y ).

So, the function form is [tex]R_{180} (x,y)=(-x,-y)[/tex].

3. When we rotate an ( x,y ) by 270° about origin counter-clockwise, the resultant co-ordinate is ( y,-x ).

So, the function form is [tex]R_{270} (x,y)=(y,-x)[/tex].

Final answer:

To write functions for rotations around the origin, one can use the standard rotation matrices. For 90 degrees counterclockwise, the point (x, y) goes to (-y, x); for 180 degrees, it goes to (-x, -y); and for 270 degrees, it goes to (y, -x), keeping the distance to the origin invariant.

Explanation:

To solve the problem of finding a function for a rotation about the origin, O, in a counterclockwise direction, we need to consider the standard rotation matrices. The coordinate system rotates counterclockwise, while a point x, y remains fixed but its coordinates change relative to the new axes.

For a rotation of 90 degrees counterclockwise, the coordinates of a point (x, y) change to (-y, x).

For a rotation of 180 degrees counterclockwise, the coordinates of a point (x, y) change to (-x, -y).

For a rotation of 270 degrees counterclockwise (equivalently 90 degrees clockwise), the coordinates of a point (x, y) change to (y, -x).

These transformations ensure that the distance of point P to the origin remains invariant under the rotations, as can be verified through the Pythagorean theorem showing that the sum of the squares of the coordinates remains unchanged: x² + y².

Answer:

min = 67, Q1 = 68, median = 70,

Q3 = 76, max = 78

We have 9 observations.

The correct set of data is:

67, 74, 78, 69, 78, 70, 67, 72, 69

When we rearrange this set of data in numerical order, we have:

67, 67, 69, 69, 70, 72, 74, 78, 78

Answer:

$3.60

Step-by-step explanation:

Answer:

$41.40

Step-by-step explanation:

You just have to do $45.00-8%

11. Answer: cats = $7.33 or less, dogs = $11 or less

Step-by-step explanation:

Let c represent cats and d represent dogs, then

3c + 2d ≤ $22

If he spends $0 on the dogs, then 3c ≤ $22  ⇒  [tex]c\leq \dfrac{22}{3}[/tex]  ⇒ c ≤ $7.33

If he spends $0 on the cats, then 2d ≤ $22 ⇒ [tex]d\leq \dfrac{22}{2}[/tex]  ⇒ d ≤ $11

Therefore, he can spend a maximum of $7.33 on each cat and a maximum of $11 on each dog.

12. Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

2 pounds of trail mix divided by 5 friends

= 2 pounds trail mix ÷ 5 friends

[tex]= \dfrac{2\text{ pounds trail mix}}{5\text{ friends}}[/tex]

[tex]= \dfrac{2}{5} \text{ pounds trail mix per friend}[/tex]

Answer:

37.5

Step-by-step explanation

Th ratio is 2.5 to 1. So then I just multiplied 2.5 to 15 and got the answer!

Hope it helps, if it is right please tell me!

Answer: $37.50

Step-by-step explanation:

$25.00 / 10 = $2.50

$2.50 * 15 = $12.50

$12.50 + $25.00 = $37.50

Answer:

the solution os 3p+2≥-10 is p≥-4

Step-by-step explanation:

So.... 3p+2≥-10

            -2   -2

             3p≥-12

and then you divide...... 3p≥-12

                                       3      3

                                       p≥-4

Answer: 180, 185, & 190

Step-by-step explanation:

1st #: 5x

2nd #: 5(x + 1)

3rd #: 5(x + 2)

1st # + 2nd # + 3rd # = sum

5x + 5(x + 1) + 5(x + 2) = 555

15x + 15 = 555

15x = 540

x = 36

1st #: 5x  = 5(36)  = 180

2nd #: 5(x + 1)  = 5(36 + 1) = 185

3rd #: 5(x + 2)   = 5(36 + 2)  = 190

The answer is D. ∠FVI and ∠GVE. An obtuse angle must be wider than 90° (like the corners of a square or rectangle) and less than 180° (literally a straight line).

An obtuse angle in Mathematics is an angle that is greater than 90 degrees but less than 180 degrees. To identify obtuse angles in a figure, you measure the angles with a protractor. An example of an obtuse angle is one that measures 95 degrees.

In the field of Mathematics, specifically geometry, an obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. To determine which angles in your figure are obtuse, you would need to measure them. You typically do this with a protractor. If the angle measures more than 90 degrees, it is obtuse. For example, if an angle measures 95 degrees, it is considered obtuse. However, providing specifics without an actual figure to reference is difficult.

https://brainly.com/question/29077542

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Answer:

The sum is 4 i√2

Step-by-step explanation:

Both the numbers √-2 and √-18 are imaginary number and thus can be presented as  

i√2 and i√18  

On simplifying, the i√18  can be written as i√( 9 x 2)

Taking out square root of 9 we get-  

3i√2  

Thus the summation of i√2 and i√18  can be written as  

i√2 + 3i√2  

= 4 i√2

Answer:

The correct answer is  (4 √2) i

Step-by-step explanation:

The sum we are looking is "x"

x= √-2+ √-18

By the Radical Properties of Multiplication ,

x=√-2 +√(-2*9)

x=√-2 +√-2* √9

Considering √-2= √((-1)*2)= √-1 *√2

According to the propriety of complex numbers , we can say

i=√-1

Replacing

x= i √2 + 3 i√2  

The answer is x= (4 √2) i

Answer:

 -31 = F

Step-by-step explanation:

We need to convert Celsius to Fahrenheit

(C * 9/5) + 32 = F

C= -35

Lets substitute this in

(-35 *9/5) +32 = F

-63 + 32 = F

 -31 = F

Answer:

718 cubic inches

Step-by-step explanation:

The formula for a sphere is [tex]V=\frac{4}{3} \pi r^{3}[/tex]. A hemisphere is half this value. We will find the volume and then divide it in half. We substitute r=7 inches.

[tex]V=\frac{4}{3} \pi r^{3}\\V=\frac{4}{3} \pi (7^{3})\\V=\frac{4}{3} \pi (343)\\V=1,436 inches^3[/tex]

We divide 1,436 by 2 for the volume of a hemisphere. V= 718 cubic inches

Answer: -1

Step-by-step explanation:

I think because if u graph it you can count the boxes down and to the side and you get -1

Answer: D) -1

Step-by-step explanation: Use the slope formula and plug in two points form tha table.

I chose the first two (3, -5) and (6, -8)

Y2-y1/x2-x1

-8--5/6-3

Hope it helps!

[tex]ax^2+bx+c=0\\\\x_1,\ x_2-the\ roots\\\\x_1+x_2=\dfrac{-b}{a}\\-------------------------\\\text{We have}\ 3x^2+11x-4=0\\\\a=3,\ b=11,\ c=-4\\\\\text{Substitute:}\\\\x_1+x_2=\dfrac{-11}{2(3)}=-\dfrac{11}{6}\\\\Answer:\ \boxed{-\dfrac{11}{6}}[/tex]

Answer:

0.783

Step-by-step explanation:

To find first r and then r square for the data

n statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

correlation coefficient of x and y = Cov (x,y)/std dev x * std dev Y

Cov (x,y) = E(xy) -E(x)E(y)

Hence calculations would be as follows:

x y xy

1 2 2

2 10 20

5 5 25

7 18 126

10 25 250

Mean 5 12 84.6

Cov E(xy)-E(x)E(y)  24.6

r 0.884640297

r^2 0.782588454

so answre is 0.783 after rounding off.

Answer:

0.783

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Divide the numerator by the denominator.

2. Write down the whole number answer.

3. Write down any remainder above the denominator.

Answer:

A. 180°+z−w

Step-by-step explanation:

We know that x  + w = 180  because they are same side exterior angles and a and b are parallel.

z=y  because they are alternate interior angles and a and b are parallel.

x  + w = 180

Solve for x by subtracting w from each side

x = 180-w

y =z

Lets find x+y

x+y

(180-w) +z

Rewriting

180+z-w

Answer:

A. 180º + z - w

Step-by-step explanation:

x + w = 180, because they are same side exterior angles, and are on opposite sides.

z = y, because if you move z down, then you will see that they overlap.

From x + w = 180, you can get x = 180 - w.

We are trying to find x + y in terms of w and z, so:

x = 180 - w

y = z

With that, you can assemble the expression, 180 - w + z.

If you re-arrange, you will get 180 + z - w.

Therefore, A is the answer.

Answer:

2(x-8)=2

Step-by-step explanation:

Answer: 0.6 (choice B)

x = number of days the book has been checked out

Check out the attached image below. I've marked 3 boxes in red to represent the bars that span from x = 9 to x = 18. The heights of these bars add up to 0.15+0.30+0.15 = 0.45+0.15 = 0.60

So if we randomly pull out a book, then the chances of picking a book that has a x value between 9 and 18 (including 9; excluding 18) is 0.60

Given : The Total Bill at the Restaurant is $84.99

Given : The Additional Tax is $5.10

⇒ Total Bill Including the Tax is : (84.99 + 5.10) = $90.09

Given : Three Friends decide to evenly split their Bill

⇒ $90.09 should be Divided into 3 Equal Parts

[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = (\frac{90.09}{3})}[/tex]

[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = 30.03\;Dollars}[/tex]

His Friend Calculation is not Reasonable

The friend's calculation of each person owing $45.04 is not reasonable as the correct amount should be $30.03 per person when evenly splitting a bill of $84.99 with an additional $5.10 tax.

To determine whether the friend's calculation of $45.04 each for splitting a bill of $84.99 with an additional $5.10 tax is reasonable, let's calculate the correct amount each person should owe. First, we combine the total bill and tax: $84.99 + $5.10 = $90.09. Then, we divide this total by three, as there are three friends: $90.09 / 3 = $30.03 per person.

The friend's calculation is not reasonable because each person should owe about $30.03, not $45.04. The estimate of $45.04 is significantly higher than the accurate calculation.

Answer:

First box:  A straight line measures 180 degrees

Second box: Alternate interior angles theorem

Step-by-step explanation:

All lines are straight, and therefore measure 180 degrees

You can see that the red line is parallel to the line with angles 2 and 3. Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Which justifies step 2

Answer:

1.A straight line measures 180 degrees

2.Alternate interior angles theorem

Step-by-step explanation:

We have to prove that

Sum of interior angles of any triangle =180 degrees

Proof:

1.[tex]m\angle 1+m\angle 4+m\angle 5=180^{\circ}[/tex]

Reason: A straight line measures 180 degrees

2.[tex]\angle 4\cong\angle 2[/tex]

[tex]\angle 5\cong \angle 3[/tex]

Reason:Alternate interior angles theorem

3.[tex]m\angle 4=m\angle 2,m\angle 3=m\angle 5[/tex]

Reason: by definition of congruent angles.

4.[tex]m\angle 1+m\angle 1+m\angle 3=180^{\circ}[/tex]

Reason: By substitution

Hence, proved.

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have

[tex]y-6=-3(x+2)\to y-6=-3(x-(-2))[/tex]

Therefore

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

2x - y = 4    it's standard form Ax + By = C

y = 2x - 4     it's slope-intercept form y = mx + b

y - x = 4 → x - y = -4  t's standard form Ax + By = C

Answer:

[tex](\frac{-8}{9}) /  (\frac{-2}{3}) * (\frac{-4}{1} )\\\\= (\frac{-8}{9}) *  (\frac{3}{-2}) * (\frac{-4}{1} )\\\\= (\frac{4}{3}) *  (\frac{1}{1}) * (\frac{-4}{1} )\\\\= \frac{-16}{3}[/tex]

What we know here is that the pattern subtracts 6 every nth value progression.

We can create a explicit formula for this sequence.

let the output be f(n)

let term # = n

so the formula would be...

[tex]f(n)=10-6(n-1)[/tex]

If we plug in the value 41 for n

[tex]f(n)=10-6(41-1)\\f(n)=10-6(40)\\f(n)=10-240\\f(n)=-230[/tex]

41st term of the sequence is -230

Answer:

There are 4 quarts in a gallon. 3x4=12. He bought 12 quarts of milk.

Step-by-step explanation:

Answer:

$26,195.

Step-by-step explanation:

total of new members(1942) - age group 18-24 (587)= new members(1355) to pay $15 each in fees.

1942-587=1355 x$15=20,325

next: take age group 18-24 (587)and multiple by $10 fee

587 x$10=5,870

last add both numbers together:

$20,325+ $5870=$26,195

Answer:

3. 9n + 6 = 78

5. see below

Step-by-step explanation:

3.

Let the number of adults be n. Each adult ticket costs $9, so the cost of n adult tickets is 9n. There is only one child, and a child's ticket is $6, so the cost of the child's ticket is 6. Adding the costs, you get 9n + 6. The total cost is $78, but the expression representing the total cost is 9n + 6, so 9n + 6 must equal 78. That is the equation.

9n + 6 = 78

5.

Sam bought equal gifts for his two children. The two gifts had the same price, x. He received a discount of $125. How much did each of the two gifts cost before the discount?

Answer:

Step-by-step explanation:

If answer A works then so will Answer A. The reason is because 1/4 and 0.25 are equal to one another. The only comment you should recognize is that

5/0.25 is a whole lot easier to do than 5/(1/4)

B is the same thing as C when you apply the division by fractions rule.

D is the odd method out. Instead of 20 games (5 * 4) she will only get to play 4. That because she has 5 dollars and if you multiply by 0.25 you get 1.25 games