Forming a Perfect Square Trinomial Form the perfect square trinomial in the process of completing the square. What is the value of c? x2 + 3x + c = + c

Final answer:

To determine when the number of new cars reaches 15,000, the quadratic equation 26t^2 + 168t + 4208 = 15,000 is solved for t and then added to 1958.

Explanation:

To find the year when the number of new cars reaches 15,000, we need to set the equation C = 26t^2 + 168t + 4208 equal to 15,000 and solve for t, where t is the number of years since 1958.

First, set up the equation: 15,000 = 26t^2 + 168t + 4208.

To solve for t, we subtract 15,000 from both sides to get the quadratic equation: 0 = 26t^2 + 168t - 10,792.

Next, we use the quadratic formula [tex]t = (-b \pm \sqrt{b^2 - 4ac}) / (2a)[/tex], where a = 26, b = 168, and c = -10,792.

Plugging the values into the quadratic formula, we get the two possible solutions for t. After calculating the roots, we discard any negative value as it would not make sense in the context of time since 1958. The positive year will give us the answer we need.

Adding the positive value of t to 1958, we obtain the year in which the number of new cars purchased will reach 15,000.

Which best describes the diameter of a circle?

Statements

A. The distance from the center to any point of the circle

This statement describes the radius of the circle

B. The length of a chord that contains the center of the circle

This statement describes the diameter of the circle

C. The distance around the circle

This statement describes the circumference of the circle

D. The length of a chord that does not contain the center of the circle

This statement describes a line segment linking any two points on a circle that does not contain the center of the circle

therefore

the answer is the option

B. The length of a chord that contains the center of the circle

The correct answer is:

B) The length of a chord that contains the center of the circle

Explanation:

A chord is a segment that goes across a circle, with both endpoints on the circle.

A diameter goes through the center of a circle and has both endpoints on the circle; this makes it a chord that goes through the center.

Final answer:

The provided sequence is a geometric sequence that converges to 0 because its common ratio's absolute value is less than 1.

Explanation:

The sequence provided is 48, 12, 3, 3/4, suggesting a pattern where each term is divided by 4 to get the next term (this is a common ratio r = 1/4). This type of sequence is known as a geometric sequence, and to determine if it converges, we can apply the ratio test.

In a geometric sequence, successive terms approach zero if |r| < 1. Since the absolute value of the common ratio here is less than 1, the terms of the sequence will get progressively smaller and approach zero. Therefore, we can conclude that this geometric sequence converges, and the limit is 0.

Answer:

a)the length of each side is [tex]5\sqrt3[/tex] feet

b)In the nearest tenth the length of the side is 8.7 feet.

Step-by-step explanation:

The area of the square garden is 75 square feet.

a) Let x  be the length of each side.

We know that,

[tex]\text{Area of square}=\text{(Side)}^2[/tex]

Hence, we have

[tex]75=x^2\\\\x=\sqrt{75}\\\\x=5\sqrt{3}[/tex]

Thus, the length of each side is [tex]5\sqrt3[/tex] feet

b)

In the nearest tenth the length of the side is 8.7 feet.

Final answer:

Using the formula for combinations with repetition, with 15 different toppings and no limit on the number of toppings per pizza, we find that there can be 32,768 different possible pizzas.

Explanation:

The question you're asking relates to combinations with repetition, a topic in combinatorics, a branch of mathematics. Given 15 different pizza toppings and the possibility of choosing any number of these toppings for a single pizza (including the possibility of a pizza with no toppings at all), we're essentially looking at how many different pizzas can be created.

To calculate the total number of different pizzas that can be ordered, we use the formula for combinations with repetition, which is (n+r-1)C(r), where 'n' is the number of toppings to choose from (15 in this case), 'r' is the number of toppings chosen, and 'C' represents the combination function. Since there's no limit to the number of toppings, 'r' can vary from 0 (a pizza with no toppings) to 15 (a pizza with all the toppings). However, because the question allows any number of toppings and we consider repetitions, the calculation simplifies to 2ⁿ, where n is the number of toppings.

Therefore, calculating this gives us 2¹⁵, which equals 32,768 different possible pizzas. This includes every combination from no toppings at all to a pizza with all 15 toppings.

Answer:  

[tex]\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

Step-by-step explanation:

Number of nurses in the hospital = 12

Number of doctors in the hospital = 4

Number of male nurses = 3

Number of male doctors = 2

Number of male persons = 5

So, Number of female persons = 16 - 5 = 11

Number of female doctors = 4 - 2 = 2

So, Probability that the person is female or a doctor = Probability that a person is female + Probability that a person is doctor - Probability that a person is female doctor

[tex]\implies\text{Probability that the person is female or a doctor = }\frac{11}{16}+\frac{4}{16}-\frac{2}{16}\\\\\implies\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

The given statement is a false statement.            

Collinear Points--

Two or more points are said to be collinear if they lie on a straight line.

Coplanar--

Set of points are said to be coplanar if they lie on the same plane.

If the set of points are collinear then we may get a line such that it will contain all these points and as we know that line always lie in a plane also there may be infinite number of planes which may contain the same line.

So, all the points on the line will also lie in the same plane.

Yes, collinear points are necessarily coplanar.

Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:

f (x) = 2 * x^2 + 1

where the second 2 is a power of x

The average rate of change is also defined as the slope of the equation. Therefore:

average rate of change = slope

Where slope is:

m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)

Calculating for f (0): x2 = 0

f (0) = 2 * 0^2 + 1 = 1

Calculating for f (-1): x1 = -1

f (-1) = 2 * (-1)^2 + 1 = 3

Substituting the known values to the slope equation:

average rate of change = (1 – 3) / (0 – 1)

average rate of change = -2 / -1

average rate of change = 2

Answer: 2

Answer:

I believe the proper form of this question is actually... as I have also come across this question.

"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."

Step-by-step explanation:

the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).

This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.

Next you have 6/-3 which will give you a answer of -2

Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.

44 x 4 = 176

44 x 7 =308

44 x 8 = 352

44 x 28 =1232

 none of those will =432

 are you sure you have the right numbers?

(44)x=432

x=432/44 = 9.8181

Answer:

Step-by-step explanation610:

Answer:

It will cost approximately $71.360.

Step-by-step explanation:

Given,

The dimension of the concrete is 17 ft by 17 ft by 2 in.

1 ft = 12 inches ⇒ 2 inches = 1/12 × 2 = 1/6 ft.

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

Now, the volume of the concrete = 17 × 17 × 1/6

[tex]=\frac{289}{6}\text{ cubic ft}[/tex]

We know that,

1 cubic yard = 27 cubic feet

[tex]\implies 1 \text{ cubic feet}=\frac{1}{27}\text{ cubic yards}[/tex]

[tex]\implies \frac{289}{6}\text{ cubic ft}=\frac{289}{6}\times \frac{1}{27} = \frac{289}{162}\text{ cubic yards}[/tex]

Since,  the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete = [tex]\frac{289}{162}\times 40=\frac{11560}{162}=\$71.3580247\approx \$71.360[/tex]

The total cost of concrete is,

C = $71.4

We have to give that,

Dimensions of the concrete are,

17 ft by 17 ft by 2 in.

And, the concrete costs $40.00 per cubic yard.

Since we know that,

1 feet = 12 inches

Hence,

2 inches = 2/12 = 1/6 feet

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

So, the Volume of the concrete,

V = 17 x 17 x 1/6

V = 48.2 cubic feet

Here, 1 cubic yard = 27 cubic feet

And, the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete is,

C = 48.2 × 40 / 27

C = $71.4

To learn more about the volume visit:

brainly.com/question/24372707

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Sample Response:

Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

1 cup = 0.25 quarts

52 *0.25 = 13 quarts

13 is the answer HOPE THAT HELPS