Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.

Answer:

a₁ = 37

Step-by-step explanation:

In an arithmetic progression the common difference d is

d = a₂ - a₁ = a₃ - a₂ , that is

2x - 18 - (x + 1) = 2x - 1 - (2x - 18) ← distribute and simplify both sides

2x - 18 - x - 1 = 2x - 1 - 2x + 18

x - 19 = 17 ( add 19 to both sides )

x = 36

Thus

a₁ = x + 1 = 36 + 1 = 37

Answer:

Value of x = 5

Step-by-step explanation:

Given:

x + 4 = 3(x - 2)

Find:

Value of x

Computation:

x + 4 = 3(x - 2)

⇒ x + 4 = 3x - 6

⇒ x = 3x -6 - 4

⇒ x - 3x = -10

⇒-2x = - 10

⇒ x = -10 / - 2

Value of x = 5

Answer:

y = 2x + 11

Step-by-step explanation:

y - 3 = 2(x + 4)      

y - 3 = 2*x + 2*4

y -3 = 2x + 8

y     = 2x + 8 +3

  y = 2x + 11

Answer:

Probability

Step-by-step explanation:

Answer:

Probability.

Step-by-step explanation: This is the chance of an event or something happening. Like one green, blue, yellow, and a red square have a1/4 chance of happening since there are four. This can go to 1/6 if we add white and purple to the spinner.

Answer:

Center of circle: (1, -2)

Radius: √6

Step-by-step explanation:

First, we need to isolate the constant:

Then, we can divide the whole equation by 4:

Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)

Now that we got the standard equation of the circle, we can find the center and radius by using the equation , where (h, k) is the coordinate of the center, and r is the radius.

Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.

Step-by-step explanation:

The center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and  2 respectively.

To solve the question, we need to know the standard equation of a circle.

The standard equation of a circle with center (h,k) and radius, r is

(x - h)² + (y - k)² = r²  (1)

Now, to find the center and radius of 4x² + 4y² - 4x + 16y + 1 = 0, we convert it to standard form by completing the square method.

This is a mathematical operation in which we convert a mathematical expression into a perfect square.

So, 4x² + 4y² - 4x + 16y + 1 = 0

Subtracting 1 from both sides, we have

4x² + 4y² - 4x + 16y + 1 - 1 = 0 - 1

4x² + 4y² - 4x + 16y = - 1

Divding through by 4, we have

x² + y² - x + 4y = -1/4

Adding half the square of the coefficient of x and y to both sides, we have

x² + y² - x + 4y + (-1/2)² + 2² = -1/4 + (-1/2)² + 2²

x² - x + (-1/2)² + y² + 4y + 2² = -1/4 + 1/4 + 2²

(x - 1/2)² + (y + 2)² = 0 + 2²

(x - 1/2)² + (y + 2)² = 2²  (2)

Comparing equations (1) and (2), we have h = 1/2, k = -2 and r = 2.

So, the center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and  2 respectively.

Learn more about standard equation of a circle here:

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Answer:

b =4

Step-by-step explanation:

         [tex]b * -3 =-12[/tex]

    2. Regroup terms

          [tex]-3b=-12[/tex]

    3. Divide both sides by -3.

         [tex]b=\frac{-12}{-3}[/tex]

   4. Two negatives make a positive.

       [tex]b=\frac{12}{3}[/tex]

  5. Simplify [tex]\frac{12}{3}[/tex] to 4.

      b = 4

Answer:

4 lateral faces

1 base

8 edges

5 vertices

Answer:

The coordinates of point y after the transformation is (-6,5)

Step-by-step explanation:

Firstly , we need to get the coordinates of the point y before the transformation

The coordinates are

(-6,-5)

By reflecting over the y-axis, we have the following change;

(x,y) becomes (-x,y)

So we have;

(6,-5)

Then we are to rotate at an angle of 180 degrees counterclockwise

The operation here will be;

(x,y) to (-x,-y)

So we have;

(6,-5) to (-6,5)

Answer:

answer b

step - by - step explanation

Answer:

Step-by-step explanation:

[tex]\text{Did you mean}\\ \\ \sqrt[3]{15-7}\\ \\ \sqrt[3]{8}=2\text{ which IS a rational number}[/tex]

Answer:

90 Percent of 20 is 18

Step-by-step explanation:

multiply 90 x 100 then divide by 20

Answer:

trapezoid

Step-by-step explanation:

Answer:

The final mean is higher

Step-by-step explanation:

The mean of all the scores = [tex]\frac{90 + 85 + 98 + 60 + 84 + 78}{6\\} = \frac{495}{6} = 82.5\\[/tex]

The mean of the scores with the 60 dropped = [tex]\frac{435}{5} = 87[/tex]

The final mean is higher

That will always happen when you drop the lowest score.  I worked it out for you so that you would see that it happened in your case.

Answer:

lol i have this question too

Step-by-step explanation:

btw is yall really in highschool, cuz this is a middle school question......

Answer:

Step-by-step explanation:

1. is y= 3 x +8

-3 x +  y - 8= 0

y = 3x+ 8

2. is in the pictures

3.

3 X + 5 y - 10 = 0

Real solution:

y = 2 - (3 X)/5

Solution:

y = 2 - (3 X)/5

Integer solution:

X = 5 n, y = 2 - 3 n, n element Z

Solution for the variable y:

y = 1/5 (10 - 3 X)

Answer:

Step-by-step explanation:

log 31.3= 1.49554433755 (round to 1.496)

ln square root of 7= 0.97295507452 (round to .973)

The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

It is given that:

The heights of a large population of ostriches are normally distributed.

The percentage of these heights that is within 3 standard deviations of the mean

As we know from the empirical rule:

It is the rule of 68-95-99.7.

From the data given in the question:

The height of a large population of ostriches is normally distributed.

So,

X ~ (u, б²)

Normal distribution.

P{u - 3б < X < u + 3б}

From the distribution table:

P{u - 3б < X < u + 3б} = 99.7%

Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

Learn more about the empirical rule here:

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Answer:

(1 2 ÷ 3) (2 1 ÷ 2) = x

Step-by-step explanation:

The equation is

Let us assume x be the amount of flour she will need in cups.

Now

1 2 ÷ 3 becomes 5 ÷ 3

2 1 ÷ 3 becomes 5 ÷ 2

Now multiply each number  

(5 ÷ 3)(5 ÷ 2) = x  

25 ÷ 6 = x

Hence, (1 2 ÷ 3) (2 1 ÷ 2) = x this would be the equation

Answer:

7

Step-by-step explanation:

First put them in order.  I got 3, 4, 5, 5, 6, 7, 7, 8, 10, 10, 10. The middle is the sixth, because (1+11)/2 is 6. So the median is 7.

Answer:

X>3

Step-by-step explanation:

Answer:

90 is the answers for the question

Answer:

the value of f is -9

Step-by-step explanation:

Answer:

the answer is B. 150

Answer:

30 degrees

Step-by-step explanation:

Good luck fam

Answer:

7/25

Step-by-step explanation:

Answer:

no it is not a right triangle because the lengths add up to 176 and a right triangle should add up to 190.

Step-by-step explanation:

The side measures of the triangle does not form a right triangle.

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

The side lengths of the triangle are 44 meters, 55 meters, 77 meters.

For the triangle to be a right triangle, one interior angle should be 90°.

Based on the sides, by Pythagoras theorem,

Square of long side = sum of square of other two sides

⇒ [tex]77^{2}=44^{2} +55^{2}[/tex]

⇒ [tex]5929=1936+3025[/tex]

⇒ [tex]5929\neq 4961[/tex]

Hence we can conclude that the side measures of the triangle does not form a right triangle.

Learn more about triangles here

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Answer:

2:3:5

Step-by-step explanation:

24:36:60

1) Find the greatest common factor

24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24

36 ⇒ 1, 2, 3, 4, 6, 9, 12, 18, 36

60 ⇒ 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the greatest common factor is 12.

2) Divide all values by 12

24 ÷ 12 = 2

36 ÷ 12 = 3

60 ÷ 12 = 5

Therefore, the simplified form of the ratio is 2:3:5.

I hope this helps!