You are opening boxes of cereal one at a time looking for your favorite prize, a Captain America decoder ring, which is in 15% of the boxes. How many boxes would you expect to open, on average, until you find your favorite prize

Therefore, using the completing the square technique, the answers to the equation  2x²-10x-3=0 are x = 5/2 + (1/2)37 or x = 5/2 - (1/2)37.

A polynomial equation of the second degree, or one with at least one squared component, is a quadratic equation. A cubic equation can typically be expressed in the following way: ax² + bx + c = 0 where x is the variable being solved for, a, b, and c are integers. The quadratic term is denoted as ax2, the linear term is denoted as bx, and the constant term is denoted as c. A quadratic equation has a graph that is a parabola, and its greatest power of a variable is 2. Depending on the values of a, b, and c, quadratic equations can have one, two real solutions, or two complicated solutions. Factoring a quadratic problem is one method of solving it.

given

Following these steps, we can use the completing the square technique to find the solution to the quadratic equation 2x2 - 10x - 3 = 0.

Step 1: To obtain a coefficient of 1, divide both parts by the coefficient of x2.

2x² - 10x - 3 = 0 \sx² - 5x - 3/2 = 0

Step 2: Square the x-half coefficient's and add it to both parts of the equation.

x² - 5x + (5/2)² - (5/2)² - 3/2 = 0

(x - 5/2)² - 37/4 = 0

Step 3: Increase both sides of the equation by 37/4.

(x - 5/2)² = 37/4

Take the square root of each half of the equation in step four.

x - 5/2 = ±√(37/4)

5. Find the value of x.

x = 5/2 ± (1/2)√37

Therefore, using the completing the square technique, the answers to the equation  2x²-10x-3=0 are x = 5/2 + (1/2)37 or x = 5/2 - (1/2)37.

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Answer:

x = -3

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

55 + 54 + x + 74 = 180

x + 183 = 180

x = -3

9514 1404 393

Answer:

Step-by-step explanation:

The model scale tells you ...

  (model dimension) / (actual dimension) = 7/48

Multiplying by the actual dimension, we get ...

  model dimension = (actual dimension)×7/48

Then ...

  model length = (97 in)(7/48) = 14 7/48 in ≈ 14 in

  model width = (54 in)(7/48) = 7 7/8 in ≈ 8 in

  model height = (72 in)(7/48) = 10 1/2 in ≈ 11 in

Answer:

469

Step-by-step explanation:

Substitute -5 and -3 into the equation:

-7(8 (-5) + 9 (-3)

-7(-40 - 27)

-7(-67)

+469

Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

Answer:

j =12 you have to combine like terms which is all and then it will give u 12

Answer:

Step-by-step explanation:

14x - 49 - 3 + 3x = 9 - 6 + 9x

17x - 52 = 9x + 3

8x - 52 = 3

8x = 55

x = 55/8

Answer:

100 steps per minute

Step-by-step explanation:

Answer:100 steps per minute

Step-by-step explanation:

The area of the polygon is 696

A polygon is any closed curve consisting of a set of line segments connected such that no two segments cross.

The area of a polygon is is expressed as

A = 1/2 × p × a

where p is the perimeter and a is the apothem

perimeter = n × s

where n is the number of side and s is the side length.

P = 8 × 12 = 96

A = 1/2 × 96 × 14.5

A = 1392/2

A = 696

Therefore the area of the polygon is 696

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1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

I believe the answer is D

Step-by-step explanation:

Inverse proportion occurs when one value increases and the other decreases

D is the answer because as each cat eats the same amount of dry cat food, there is less dry cat food in the bag; so this is why D best answers the question.

Hope this helps!

Answer:

a is false, B is true,

Step-by-step explanation:A is false because the more hours you work, the more money you get.

B is true because if the volume is constant, the bigger the length, the smaller the width, or vice versa.

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Answer:

1/3

Step-by-step explanation:

Every third multiple of 20 is a multiple of 15.

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Answer:

Step-by-step explanation:

\(v =( 7 \times 6 \times 1) + (3 \times 2 \times 1) \\ v = 42 + 6 \\ v = 48 \: {cm}^{3} \)

I hope that is useful for you :)

The position of  √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.

A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.

Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.

The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.

If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:

To begin, determine the approximate square root values:

√17 is between 4 and 5, since 4² = 16 and 5² = 25.

√6 is between 2 and 3, since 2² = 4 and 3² = 9.

Place the number √17 closer to 5, between 4 and 5.

Place the number √6 between the numbers 2 and 3, closer to 2.

Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.

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Number line attached below,

Answer:

Radius=9

Diameter=18

Step-by-step explanation:

Answer:

y = 3x + 41

Step-by-step explanation:

First, lets set up the slope-intercept form equation, that is...

y = mx + b

m = slope

b = y-intercept

because the y-intercept is a positive value, it cannot be y=-3x-41 or y= 3x-41

now, we know that b = 41, but what is the slope?

Well, here are tips for doing slope

if the line is gradually increasing upwards, then it is a positive slope

if the line is gradually decreasing downwards, then it is a negative slope

because the line in the picture is positive, this proves y=-3x+41 wrong, therefore making y = 3x + 41 the only correct answer

Therefore, your correct answer is y = 3x + 41

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

Let's gather some information:

             ⇒ Angle B is shared by both triangles

             ⇒ Angle A' and A are the same, as they are both on parallel

                   lines, A'C' and AC, and both angles are formed with the

                   same line AB

                 ⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

   ⇒ their side lengths are proportional to each other

          ⇒ let's set up a proportion

                 \(\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143\)

          ⇒ let's set up a proportion

                 \(\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25\)

Answer:

Hope that helps!

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Answer:

False

Step-by-step explanation:

8x2=16

16-63=-47

-47=-40

The numbers do not match.

Hence, the equation is false.

Answer:

the perimeter of cube is

28×4=112 ft

Answer:112

Step-by-step explanation: 28•4=112ft

There are about 460 pages left for Quinn to read

The given parameters are

Pages = 788

Pages read = 329

The number of pages does Quinn have left to read is

Pages left = Pages - Pages read

So, we have

Pages left = 788 - 329

Evaluate

Pages left = 459

Hence, there are about 460 pages left for Quinn to read

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Answer:

I think the answer you're looking for is 16807

Answer:

it can be 100 because percentages are out of 100

Step-by-step explanation:

Find the factors of x that makes it zero.. Equate the equation to y and use it to find the value of y. Then get your values for x and y and plot the graph

Answer:

75 dollars

Step-by-step explanation:

real price= 4.95*15= 74.25

estimated cost of purchasing 15 tickets is 74 dollars

75 dollars if 4.95 rounded to the nearest dollar

5*15=75 dollars.