Why lim x to -3 (x^2) is 9 and not -9???? if when a negative odd number is squared the answer is negative? i don't understand factoring cases. here's the whole exercise lim x to -3 (x^2-2x+4)

Answer:

379.5

Step-by-step explanation:

Answer:

6:1

is the right answer

Step-by-step explanation:

Answer:

45:9 or 49 to 9

Step-by-step explanation:

If you subtract 54-9 because the question is asking what is the the ration from what he KEPT after he deleted 9 so you would subtract so the answer wouls be 45:9 or 49 to 9

Answer: we can make 15,504 different math tests

Step-by-step explanation:

Ok, we have a bank with 20 questions (Q1, Q2........ , Q20)

and we want to make a test with 15 of those 20 questions.

As the order of the questions does not matter in the thest ( is the same if the order is Q1, Q2, ...., Q15 than if the order is Q15, Q14, ....., Q1 )

So we only want the number of combinations.

When we have N elements and we want to create groups of K elements, the total number of combinations is:

\(C = \frac{N!}{(N - K)!*K!}\)

Here N = 20 and K = 15

\(C = \frac{20!}{5!*15!} = \frac{20*19*18*17*16}{5*4*3*2*1} = 15,504\)

So we can make 15,504 different math tests

The anchor was released from a height of 72.5 meters above the water's surface

We are given the rate at which the anchor is dropping (2.5 meters per second), the time it took to reach 40 meters below the water (45 seconds), and we need to find the initial height of the anchor above the water's surface.

Step 1: Calculate the distance the anchor traveled during the 45 seconds.
Distance = Rate × Time
Distance = 2.5 meters/second × 45 seconds
Distance = 112.5 meters

Step 2: The anchor is now 40 meters below the water, so it has traveled 40 meters below the water's surface plus the initial height above the water's surface.
Total Distance = 112.5 meters = Distance below water + Initial height above water
112.5 meters = 40 meters + Initial height above water

Step 3: Solve for the initial height above the water's surface.
Initial height above water = 112.5 meters - 40 meters
Initial height above water = 72.5 meters

So, the anchor was released from a height of 72.5 meters above the water's surface.

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56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$

Properties of triangles are:

A triangle has three sides and three angles.

The sum of the angles of a triangle is always 180 degrees.

The exterior angles of a triangle always add up to 360 degrees.

The sum of consecutive interior and exterior angle is supplementary.

Given:

Height: ha = 7

Height: hb = 24

Height: hc = 25

Sum to sides is:

25 +7 + 24 =56 units.

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The information that is needed to write the equation of a line in point-slope form is the location of one ordered pair that lies on the line and the line's slope. The correct option is the first option

From the question, we are to determine the information that is needed to write the equation of a line in point-slope form.

The point-slope form of a line is given as

y - y₁ = m(x - x₁)

Where, (x₁, y₁) is a point on the line

and m is the slope of the line

Thus, in order to write the equation of a line in the point-slope form, the information that are needed are:

1. An ordered pair on the line

2. The slope of the line

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Answer:

625 seconds. Or 10.4 minutes

Step-by-step explanation:

Well 5000÷8 is 625

Hope this helps

Answer:

Step-by-step explanation:

1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.

2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.

So 5/4 x 1/2 is 5/8.

3. Lila will need 5/8 cups of raisins.

The measure of the missing side length of the right triangle is approximately 32.1.

The figure in the image is a right triangle.

From the image:

Angle θ = 0.646 rad

Opposite to angle θ = 19.3

Hypotenuse =?

To solve for the missing side length, we use the trigonometric ratio.

Note that: sine = opposite / hypotensue

Plug the given values into the above formula and solve for the hypotenuse.

sin( θ ) = opposite / hypotenuse

sin( 0.646 rad  ) = 19.3 / hypotenuse

Hypotenuse = 19.3 / sin( 0.646 rad  )

Hypotenuse = 32.1

Therefore, the hypotenuse measures 32.1 units.

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These complex roots can be represented as points on the Argand diagram, where w₁ is at an angle of π/12 from the positive real axis in the counterclockwise direction and w₂ is at an angle of π/12 from the negative real axis in the counterclockwise direction.

i. Expressing z in polar form:

To express z = 1 + i√3 in polar form, we need to find the magnitude (r) and argument (θ) of the complex number. The magnitude r can be found using the formula |z| = √(Re(z)² + Im(z)²), and the argument θ can be found using the formula θ = tan⁻¹(Im(z)/Re(z)).

For z = 1 + i√3, the magnitude is |z| = √(1² + (√3)²) = 2, and the argument is θ = tan⁻¹(√3/1) = π/3.

Therefore, z can be expressed in polar form as z = 2(cos(π/3) + isin(π/3)).

ii. Finding complex roots of w = z¹/²:

To find the complex roots of w = z¹/², we need to take the square root of z and consider both the positive and negative square roots.

Taking the square root of z, we get:

√z = ±√2(cos(π/6) + isin(π/6)).

Therefore, the complex roots of w = z¹/² are:

w₁ = √2(cos(π/12) + isin(π/12)),

w₂ = -√2(cos(π/12) + isin(π/12)).

These complex roots can be represented as points on the Argand diagram, where w₁ is at an angle of π/12 from the positive real axis in the counterclockwise direction and w₂ is at an angle of π/12 from the negative real axis in the counterclockwise direction.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

So, approximately 7.71 grams of radium will be present after 100 years.

To calculate the remaining amount of radium after 100 years, we will use the half-life formula:
Remaining Amount = Initial Amount * (1/2)^(time passed / half-life)
Here, the initial amount is 8 grams, the half-life is 1690 years, and the time passed is 100 years.
Step 1: Plug in the values
Remaining Amount = 8 * (1/2)^(100 / 1690)
Step 2: Calculate the exponent
Exponent = 100 / 1690 ≈ 0.05917
Step 3: Calculate the base raised to the exponent
(1/2)^0.05917 ≈ 0.9634
Step 4: Multiply the initial amount by the base raised to the exponent
Remaining Amount = 8 * 0.9634 ≈ 7.7072
So, approximately 7.71 grams of radium will be present after 100 years.
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The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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Answer:

Step-by-step explanation:

Equation are true:

C.

(3⁴)·(3⁵) = 3⁽⁴⁺⁵⁾ = 3⁹

D.

\(( 8^6 = \frac{1}{8^{-6}} )\)

Answer:

C and D

Step-by-step explanation:

Steps for C:

Step 1: Combine exponent terms on left side
\(4+5=9\)

Leave the base the same.

\(3^9=3^9\)

\(True\)

Steps for D:

Step 1: Simplify left side

\(\frac{1}{8^{-6} }=\frac{1/1}{262144} =262144\)

Step 2: Simplify right side

\(8^6=262144\)

\(262144=262144\)

\(True\)

Hope this helps :)

15 Kilocalorie (international) (kcal) = 15000 Calorie (cal)

The kilocalorie, sometimes call kilogram calorie is a measurement unit of energy. It is defined as the amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius. The symbol of kilocalorie is kcal. The kilocalorie is commonly used in measuring the calorific, heating, or metabolizing value of foods. It is equal to 1000 calories, or approximately 4.2 kilojoules.

The calorie is a pre-SI metric unit of energy. Its symbol is cal, and first defined as a unit of heat by Nicolas Clément in 1824. The calorie is commonly used in the field of chemistry, and in many countries it is commonly used as a unit of food energy. There are two defined for the calorie, gram calorie (approximately equals 4.2 joules) and kilogram calorie (approximately equals 4.2 kilojoules).

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Answer:

5,809 m^2

Step-by-step explanation:

50/2=25 m

25^2 times 3.14=1,962.5 m^2

70/2=35 m

35^2 times 3.14=3,846.5 m^2

1,962.5+3,846.5=5,809 m^2

Answer:

Step-by-step explanation:

m<1 = 50

m<2 = 22

m<3 = 108

m<4 = 50

m<5 = 65

m<6 = 50

m<7 = 43

m<8 = 65

m<9 = 75

m<10 = 18

m<11 = 25

m<12 = 40

m<13 = 115

m<14 = 65

m15 = 115

Although increasing the sample size can improve the accuracy of the estimate, there are some problems that may arise with very large samples.

The following are the problems that can occur:

Difficulty in obtaining a very large sample: It may be difficult to obtain a large sample that is representative of the population and has a low bias.

Cost of sampling: Collecting data from a very large sample can be time-consuming and expensive.

None of these: This is not a problem that can arise with very large samples.

Increase in standard error: As the sample size increases, the standard error of the estimate tends to decrease, but after a certain point, increasing the sample size further may not lead to a significant reduction in the standard error, and may even increase it due to other factors such as measurement errors or non-random sampling. This is called the "law of diminishing returns".

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Yes, there is a correlation between these measures. The higher the placement exam score, the higher the student's score on their first exam tends to be. For example, students with placement exam scores of 11 and 49 had first exam scores of 27 and 71 respectively, indicating that the higher the placement exam score, the higher the first exam score.

A measure in mathematics is a generalization of the ideas of length, area, and volume. Measures are sometimes referred to as "mass distributions" informally. A measure, in more exact terms, is a function that gives numbers to particular subsets of a given set. This quantity is described as the set's measure.

To measure length or distance, this system employs inches, feet, yards, and miles. Volume or capacity are expressed in fluid ounces, cups, pints, quarts, or gallons. In ounces, pounds, and tons, weight or mass is expressed.

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Answer:

there are no signs between the x and y and constant

it could be

2x+5y=15

2x+5y=-15

-2x+5y=15

2x-5y=15

for ax+by=c, the equation of a line paralell to that is

ax+by=d where a=a, b=b, and c and d are constants

(for this answer, I'm going to use 2x+5y=15)

given 2x+5y=15, the equation of a line paralell to that is 2x+5y=d

to find d, subsitute the point (4,-2), basically put 4 in for x and -2 for y to get the constant

2x+5y=d

2(4)+5(-2)=d

8-10=d

-2=d

the eqaution is 2x+5y=-2 (Only if the original equation is 2x+5y=-15

pls mark me brainlest

Answer:

2x+ 5y= -2

Step-by-step explanation:

Arnav needs to sell more than 8 boxes of cookies to reach his goal of making more than $30. Since the number of boxes must be a whole number, Arnav would need to sell at least 9 boxes of cookies to achieve his goal.

To determine how many boxes of cookies Arnav needs to sell to reach his goal of making more than $30, we can set up an inequality based on the selling price of each box.

Let's represent the number of boxes he sells as "x". Since each box is sold for $3.75, the total amount of money he will earn from selling "x" boxes is 3.75x.

To reach his goal of making more than $30, we can write the following inequality:

3.75x > 30

To solve for "x", we divide both sides of the inequality by 3.75:

x > 30 / 3.75

Simplifying the right side of the inequality, we get:

x > 8

To fulfil his objective of earning more than $30, Arnav must sell more than 8 boxes of cookies. Arnav would need to sell at least 9 boxes of cookies in order to reach his objective because the number of boxes must be a whole number.

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the inequality model. 5x-6y <0 is attached below.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2x + 3y > 7x-3y ​

5x-6y <0

So we have to plot this inequality.

Hence, the inequality model. 5x-6y <0 is attached below.

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Answer:

5

Step-by-step explanation:

17+8+17+17+17+17=93

8.50+50.50+8.50+8.50+8.50+8.50=93

The mean hourly snowfall is 10/3 cm/hour or 3.33 cm/hr.

What do you mean by snowfall?

Snowfall is the term for precipitation that takes the shape of snow-like solid particulates. Snowfall happens at mean sea level in high-latitude, temperate locations while it happens higher than the snowline height in equatorial areas.

Given,

At 4 P.M the total snowfall is 3 centimetres.

AT 7 P.M, the total snowfall is 13 centimetres.

Duration of time = (7-4) = 3 hours

Snowfall changes= (13-3)= 10 centimeters

We know that,

Mean hourly snowfall= Snowfall changes/ duration of time

= 10/3 cm/hour

≅3.33 cm/hr

The mean hourly snowfall is 10/3 cm/hour or 3.33 cm/hr

Hence the correct answer is 10/3 cm/hour or 3.33 cm/hr

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Using a system of equations, the amounts in grams of each mix that should be used are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows:

The mix has 23g of protein, hence, from the table:

0.2a + 0.1b + 0.15c = 23.

The mix has 6.2g of fat, hence:

0.02a + 0.06b + 0.05c = 6.2.

The mix has 16g of moisture, hence:

0.15a + 0.1b + 0.05c = 16.

Hence the system is given by:

Using a calculator, the solution for the system is given as follows:

a = 60, b = 50, c = 40.

Which are the amounts in grams of each substance.

The table containing the compositions of the mix is missing, and is given at the end of the answer.

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Based on the information, it can be inferred that the volume of the figure is 6,786 ft³.

To calculate the volume of the figure we must perform the following procedure:

Find the volume of the lower part, the cubic part. For this we must multiply all the sides as shown below:

Then we must calculate the volume of the upper part, for this we must perform the following procedure:

we calculate as if it were a completely square or cubic figure and then we divide it in two.

Finally we must add both values to find the total volume

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