Solve the quadratic equation using the factoring method.

2^x2 - 5x - 3 = 0

Answer:

a. x²-1

b. x²+x-6

c. x²-4x+4

Step-by-step explanation:

a. (x+1)(x-1)

   x²-x+x-1

   x²-1

b. (x-2)(x+3)

   x²+3x-2x-6

   x²+x-6

c. (x-2)²

   (x-2)(x-2)

   x²-2x-2x+4

   x²-4x+4

The lateral surface area and volume of the shape will be 2405.4 square feet and 10,324.6 cubic feet, respectively.

Given information:

Base length, a = 34 ft and b = 10 ft

Height, h = 24.7 ft

Slant height, l = 27 ft

Width, w = 19 ft

The volume of the shape is calculated as,

V = 1/2 x (34 + 10) x 24.7 x 19

V = 10,324.6 cubic feet

The surface area is calculated as,

SA = 2(19 x 27) + 1/2 x (34 + 10) x 24.7 + 10 x 19 + 34 x 19

SA = 1026 + 543.4 + 190 + 646

SA = 2405.4 square feet

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Answer:

= Divide the 26 feet by 3.25 feet

26 ÷ 3.25 = 8

= then Multiply the 8 by 1.7 degrees

8 × 1.7 = 13.6

= Subtract 13.6 from 26 feet

26 - 13.6 = 12.4

= Round 12.4 to the nearest tenth

12.4 = 12

Answer: 12

Answer:

Convert both numbers to improper fractions:

−1 5 3 ​ = -(160 + 53 + 3)/60 = - 68/60

−6 5 = -(6*60 + 5)/60 = -365/60

68/60 ÷ (-365/60) = -68/60 * (-60/365)

-68/60 * (-60/365) = 4080/21900

4080/21900 = 68/365

Therefore the answer is 68/365

The area of the yellow shape will be 5000 m sq.

We know that area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The parameters are given as;

Length = 95 meters

Width = 60 meter

For a triangle we have the dimension of height is 35 meter

the base = 95 - 55 = 40 meter

First we need to find the area of the triangle;

Area =1/2 x base x height

Area =1/2 x 40 x 35

Area = 700 meter sq.

Then area of the rectangle = length × Width

= 95 x 60

=5700 m sq.

Therefore, the area of the yellow shape is;

= Area of rectangle -  area of triangle

= 5700 - 700

= 5000 m sq.

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Answer:

The Correct answer is 381

Step-by-step explanation:

5334÷14

=381

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16.


To find the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen, you need to subtract the sample mean of underclassmen from the sample mean of upperclassmen.

Sample mean of upperclassmen = 0.76
Sample mean of underclassmen = 0.60

Point estimate = Sample mean of upperclassmen - Sample mean of underclassmen
Point estimate = 0.76 - 0.60
Point estimate = 0.16


The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16, which indicates that on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours.

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Answer:

The half-life formula is given as:

t(1/2) = (ln 2) / k

where k is the decay constant.

Given:

mass of substance = 22 g

k = 0.138

We need to find t(1/2) in days.

First, we need to find the decay rate, λ, which is related to k as follows:

λ = k / ln 2

λ = 0.138 / ln 2

λ ≈ 0.199

Now we can substitute λ into the half-life formula to get:

t(1/2) = (ln 2) / λ

t(1/2) = (ln 2) / 0.199

t(1/2) ≈ 3.5 days (rounded to the nearest tenth)

Therefore, the substance's half-life is approximately 3.5 days.

The perimeter of TAP is approximately 12.1 units.

A two-dimensional shape's perimeter is the space surrounding its outer edge. It is the total length of the object's sides. For instance, the perimeter of a rectangle is equal to the total length of its four sides.

The circumference of a circle, also known as its perimeter, is the distance that separates it from the center.

To find the perimeter of TAP, we need to add up the lengths of its three sides. We can use the distance formula to find the lengths of each side:

Distance between T and A:

d(TA) = √((4-1)² + (4-4)²) = √(9 + 0) = 3

Distance between A and P:

d(AP) = √((3-4)² + (0-4)²) = √(1 + 16) = √(17)

Distance between P and T:

d(PT) = √((1-3)² + (4-0)²) = √(4 + 16) = √(20)

Therefore, the perimeter of TAP is:

P = d(TA) + d(AP) + d(PT) ≈ 3 + √(17) + √(20) ≈ 12.1

Rounding to the nearest tenth, the perimeter of TAP is approximately 12.1 units.

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The percentage increase of last year's attendance is 24%

In this year, There are 558 people went to the performance.

Last year, There are 450 theatre-goers attended a performance at St. Lawrence Centre.

We have to find the increase as a percentage of last year's attendance.

Now, According to the question:

Subtract from In this year's people to last year's people.

=> 558 - 450

=> 108 people more attended from the last year.

Now, Find the increment of percentage.

We know that, For calculation in percentage multiply by 100

=> 108 / 450 × 100 = 24

The percentage increase of last year's attendance is 24%

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The number of line segments that will be needed to create step 4 of the sequence is 30.

A line segment is a given straight line which has two terminating points, each at its two ends.

In the given sequence, it can be observed that each end point of the line segment requires two other line segment for extension in the next step.

step 1 = 2

step 2 = 2 + 4

           = 6

step 3 = 6 + 8

          = 14

step 4 = 14 + 16

          = 30

So that comparing the line segments in the steps given, the number of line segments that will be needed to create step 4 of the sequence is 30.

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The mathematical term used to designate a trapezoid (or trapezium in the UK) having its two non-parallel sides of equal length is an isosceles trapezoid.

The mathematical term used to designate a trapezoid having its two non-parallel sides of equal length is called an isosceles trapezoid or isosceles trapezium in the UK.

This shape is also sometimes referred to as a regular trapezoid, but the term "isosceles trapezoid" is more commonly used.

A trapezoid is a four-sided polygon that has two parallel sides and two non-parallel sides. The parallel sides of a trapezoid are called the bases, and the non-parallel sides are called the legs. The distance between the bases is called the height of the trapezoid.

The area of a trapezoid is given by:

Area = ((base1 + base2) x height) / 2

where base1 and base2 are the lengths of the two parallel sides, and height is the distance between the parallel sides.

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It is not recommended to read an LIA (Line Immunoassay) result early because it may lead to inaccurate or false results. LIA tests rely on a specified incubation time for proper reaction between the sample and the test reagents.

It is not recommended to read an LIA (Line Immunoassay) result early. This is because the results of an LIA test may not be accurate until the recommended waiting period has passed, which is typically 20-30 minutes after the test is performed. Reading the result early may lead to incorrect interpretations, false negatives, or false positives, which could cause unnecessary anxiety, confusion, or wrong medical decisions. It is crucial to follow the manufacturer's instructions and guidelines carefully and wait for the appropriate time to read the test result accurately.

We should not read an LIA (Lateral Flow Immunoassay) result early because it may lead to inaccurate or false results. LIA tests rely on a specified incubation time for proper reaction between the sample and the test reagents. Reading the result too early can cause false negatives or false positives, which could impact critical decision-making related to diagnosis or treatment. It is crucial to follow the manufacturer's recommended waiting time to ensure accurate and reliable results.

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Answer:

7:8

Step-by-step explanation:

El número de hombres en la encuesta es:

150 - 80 = 70

Por lo tanto, la razón de hombres a mujeres es:

hombres / mujeres = 70 / 80

Para simplificar esta razón, podemos dividir ambos términos por 10, ya que 10 es un factor común:

hombres / mujeres = (70/10) / (80/10) = 7/8

Por lo tanto, la razón hombres:mujeres en su forma más simple es 7:8

Answer: 7:8

Step-by-step explanation:

80 = women

70 = men

150 = Total

Ratio of Men: Women

= 70:80

= 7:8

A moderately negative correlation between both of them variables is shown by the resultant correlation coefficient of -0.55.

We can construct a correlation matrix to determine the relationship between the number the group visits received and the fructosamine level. This indicates that the fructosamine level typically decreases as the amount of group visits increases.

This could imply that patients can keep better control of glucose, as seen by lower fructosamine levels, by participating in group visits and getting support or education about managing diabetes.

It's crucial to remember that a connection does not necessarily indicate a cause.

Further study is required to show a causal link between the fructosamine level and the number the group visits that participants attended. Overall, the moderately negative correlation points to some potential benefits of group visits for treating diabetes.

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Answer:

x divided by 2 times 2 simplifies to x.

Step-by-step explanation:

Answer:

The expression "x divided by 2 times 2" can be simplified as follows: x / 2 * 2 = x * (2 / 2) = x * 1 = x

Therefore, the answer is x.

Step-by-step explanation:

Answer:

s^45/t^81

Step-by-step explanation:

The answer to the subtraction of the numbers 698000003120006200130 and 299900503811873452 is 39809949918812678.

Subtraction is an arithmetic operation that involves finding the difference between two numbers. It is the process of taking away a quantity from another quantity, or finding the result when one quantity is subtracted from another.

According to the given information:

Let's subtract the numbers step by step.

First, let's align the numbers vertically, lining up the digits by place value:

698000003120006200130

     - 299900503811873452

Now, let's start subtracting from the rightmost digit (the ones place) to the leftmost digit (the highest place value).

Step 1: Subtract the ones place:

0 - 2 = -2. Write -2 in the ones place and borrow 1 from the tens place of the first number.

Step 2: Subtract the tens place:

1 (after borrowing) - 5 = -4. Write -4 in the tens place and borrow 1 from the hundreds place of the first number.

Step 3: Subtract the hundreds place:

2 (after borrowing) - 4 = -2. Write -2 in the hundreds place and borrow 1 from the thousands place of the first number.

Step 4: Continue this process for each place value, borrowing as necessary:

(No borrowing needed for the next few steps)

Step 5: Finally, subtract the numbers in the highest place value:

6 - 2 = 4. Write 4 in the highest place value.

So, the result of the subtraction is 39809949918812678.

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The total length of the three rods is 125cm

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

This statements are interpreted into mathematical equation or expression.

representing length of rod A,B,C by x,y,z respectively

x: y = 3:2

therefore x/y = 3/2

x:z = 2:5= x/z = 2/5

The smallest length will be y and longest will be z

z-y = 55

x/y = 3/2

3y = 2x

y = 2/3( x)

x/z = 2/5

2z = 5x

z = 5/2(x)

we can say;

5/2(x) -2/3(x) = 55

(15x - 4x)/6 = 55

11x = 55×6

x = 5 × 6 = 30 cm

y = 2/3 × 30 = 20cm

z = 5/2 × 30 = 75 cm

Therefore the total length = 30+20+75 = 125cm

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The number of possible outcomes is option (c) 16 when Camila flips a fair coin two times and then spins a four-section spinner.

There are two independent events: flipping a coin twice and spinning a spinner with 4 equal sections.

The number of possible outcomes for flipping a coin twice is 2 x 2 = 4 (HH, HT, TH, TT).

The number of possible outcomes for spinning a 4-section spinner is 4.

To find the total number of possible outcomes, we need to multiply the number of possible outcomes for each event

Total number of possible outcomes = 4 x 4 = 16

Therefore, the correct option is (c) 16

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The number of units manufactured at a cost of $9,500 is approximately 141.75 units.

The sunglasses will hit the ground after 100 seconds

The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.

The width of the floor is 6 feet, and the length is 9 feet.

Now we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -15, and c = -9,450.

Plugging these values in:

x = (-(-15) ± √((-15)² - 4(1)(-9,450))) / 2(1)

x = (15 ± √(15 + 18,960)) / 2

x = (15 ± √19,185) / 2

x ≈ 141.75

In order to find when the sunglasses will hit the ground, we need to find the time t when h(t) = 0.

h(t) = -16t + 1600 = 0

Solving for t:

-16t = -1600

t = 100

Therefore, the sunglasses will hit the ground after 100 seconds.

h(t) = -16t² + 80t

96 = -16t² + 80t

0 = -16t² + 80t - 96

0 = -t² + 5t - 6

0 = (t - 2)(t - 3)

The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.

2w² - 3w - 90 = 0

(2w + 15)(w - 6) = 0

If w - 6 = 0, then w = 6, which is a valid solution.

Therefore, the width of the floor is 6 feet, and the length is 2(6) - 3 = 9 feet.

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Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a and b are the endpoints of the interval.

For the function f(x) = -0.5x^2, we have:

f(-3) = -0.5(-3)^2 = -4.5

f(3) = -0.5(3)^2 = -4.5

So the average rate of change of f(x) over the interval -3 < x < 3 is:

average rate of change = (f(3) - f(-3)) / (3 - (-3))

average rate of change = (-4.5 - (-4.5)) / 6

average rate of change = 0

For the function g(x) = -1.5x^2, we have:

g(-3) = -1.5(-3)^2 = -13.5

g(3) = -1.5(3)^2 = -13.5

So the average rate of change of g(x) over the interval -3 < x < 3 is:

average rate of change = (g(3) - g(-3)) / (3 - (-3))

average rate of change = (-13.5 - (-13.5)) / 6

average rate of change = 0

Therefore, the average rates of change for both f(x) = -0.5x^2 and g(x) = -1.5x^2 over the interval -3 < x < 3 are 0. This means that the functions are constant over this interval, and their slopes are not changing.

Riley has collected approximately 22.7 grams of the trace element in his sample.

To calculate the amount of trace element collected by Riley, we first need to find the volume of the cylinder-shaped container that he used. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

Plugging in the values given in the problem, we get:

V = π(5.7 cm)²(13.6 cm)

V ≈ 1338.6 cubic centimeters

Since the sample contains 0.017 grams of the trace element per cubic centimeter of water, we can find the total amount of trace element collected by multiplying the volume of the sample by the concentration of the trace element:

0.017 grams/cubic centimeter × 1338.6 cubic centimeters ≈ 22.7 grams

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Answer: B

Step-by-step explanation: As slope is "rise over run", and only B has a decreasing rise (y-value), it must be the only one with a negative slope.

In a population of rabbits that has reached carrying capacity, the growth curve would exhibit logistic growth.

Logistic growth is characterized by an S-shaped curve, which represents a rapid initial growth followed by a slowed growth rate as the population approaches its carrying capacity.

The carrying capacity is the maximum number of individuals that an environment can support, taking into account factors such as food availability and habitat space.

In this situation, the rabbit population would experience density-dependent factors, such as competition for resources, which would limit their growth and maintain the population around the carrying capacity.

Eventually, the growth curve would stabilize, with the population size fluctuating slightly around the carrying capacity due to environmental factors or other influences.

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Answer: 45.580

Explanation: x=2279/50=45.580

The quadratic equation is decreasing on the interval (3, ∞).

Here we have the quadratic function:

y = 8 - (x - 3)^2

Remember that the quadratic equation in the vertex form can be written as:

y = a*(x - h)^2 + k

Then in this case the vertex is at (3, 8).

And we can see that the leading coefficient is -1, then the vertex is a maximum and after that the function starts decreasing.

Thus, the function decreases on the interval (3, ∞).

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The rewritten function after completing the square is h(x) = 4(x - 4.5)² - 81

To complete the square and rewrite the function in the desired form, we can follow these steps, Factor out the leading coefficient of the quadratic term (in this case, 4) from the first two terms:

h(x) = 4(x² - 9x) + 81

To complete the square, we need to add and subtract a constant term inside the parentheses that will make the expression a perfect square trinomial. To determine this constant term, we can take half of the coefficient of the x-term, square it, and add it to the expression. Half of -9 is -4.5, so we have,

h(x) = 4(x² - 9x + (-4.5)² - (-4.5)²) + 81

Simplify the expression inside the parentheses by combining like terms and factoring the perfect square trinomial,

h(x) = 4((x - 4.5)² - 20.25) + 81

Distribute the 4 and simplify,

h(x) = 4(x - 4.5)² - 81

Therefore, the function h(x) can be rewritten in the desired form as:

h(x) = 4(x - 4.5)² - 81

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if you assume 2 person in the centre

there are 4! possibilities that other people can ve sorted.

but the 2 person can sit in 2 ways.

so the answer is 4!.4

= 96