(x+3)(3x² - 5x - 10) multiply polynomial

Answer:

slope= 3/2

Step-by-step explanation:

Answer:

Exact Form:

x = ln ( 64 )/ ln ( 5 )

Decimal Form:

x = 2.58405934 …

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

Start by dividing both sides by 3

5^x = 192/3

5^x = 64

Now take the log of both sides

log(5^x) = log(64)

Bring down the power

x log(5) = log(64)

Find the logs

x * 0.69897 = 1.8062

Divide

x = 1.8062 / 0.69897

x = 2.5841

Answer:

factors are 5, 6, a, 11, b

Step-by-step explanation:

3)   5 + 6a + 11b

Algebraic expressions: 5 + 6a + 11b

Are combinations of numbers, variables, and at least one arithmetic.

Term are: 5, 6a, 11b

Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable(s).

Factors are: 5, 6, a, 11, b

Something which is multiplied by something else. A factor can be a variable, number,  a term, or a longer expression.

Coefficient: 6, 11

The numerical factor of a multiplication expression that contains a variable.

Constant: 5

A number that cannot change its value.

4).  13m-2n​ (note: it applies as above)

Answer:

0.89417

Step-by-step explanation:

Using the relation to obtain the Zscore :

Z = (x - mean) ÷ standard deviation / sqrt(n)

x = 0.8535

Mean = 0.8565

Standard deviation = 0.0518

Sample size, n = 465

P(x ≤ 0.8535) = (0.8535 - 0.8565) ÷ 0.0518/sqrt(465)

P(x ≥ 0.8535) = - 0.003 / 0.0024021

P(x ≥ 0.8535) = - 1.249

P(Z ≥ - 1.249) = 0.89417

Answer:

2√5

Step-by-step explanation:

Distance = √(x1-x2)² + (y1-y2)²

Distance = √(-1-3)² + (4-2)²

Distance = 2√5

Answer:

\(\displaystyle d = 2\sqrt{5}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (-1, 4)

Point (3, 2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

D. He should survey all the students in all the history classes to make sure he collects enough data.

Step-by-step explanation:

correct on edge 2021

If you are putting a quadratic function in the form of \(ax^2 + bx + c\) into the quadratic formula \(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\) and the b value in the function is negative, then you still write it as negative in the quadratic formula.

The reason is that the b term in the quadratic formula is being added or subtracted, depending on whether it is positive or negative.The quadratic formula is used to solve quadratic equations that are difficult to solve using factoring or other methods. The formula gives the values of x that are the roots of the quadratic equation.

The quadratic formula \(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\) can be used for any quadratic equation in the form of \(ax^2 + bx + c = 0\).

In the formula, a, b, and c are coefficients of the quadratic equation. The value of a cannot be zero, otherwise, the equation would not be quadratic.

The discriminant \(b^2-4ac\) determines the nature of the roots of the quadratic equation. If the discriminant is positive, then there are two real roots, if it is zero, then there is one real root, and if it is negative, then there are two complex roots.

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Answer:

Step-by-step explanation:

{m}, {a} , {t} ,{h} ,{m,a}, {m,t} ,{m,h} ,{a,t} ,{a,h} ,{t,h} ,{m,a,t} ,{m,a,h} ,{m,t,h} ,{a,t,h} ,{ m,a,t,h} , {} are the subsets of the given question.

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Answer:

x=-24

Step-by-step explanation:

Value of cos(x+π) = \(\bold{\frac{\sqrt{3} }{2}}\)

Given cosine of x = \(-\frac{\sqrt{3} }{2}\)

i.e., cos(x) =  \(-\frac{\sqrt{3} }{2}\)

Also cos(\(\frac{\pi}{6}\)) =  \(\frac{\sqrt{3} }{2}\). So x = \(\frac{\pi}{6}\).

We need to find cos(x+π) = cos(\(\frac{7\pi}{6}\)).

But its value is not easy to find. So we use trigonometric formulas.

We have the trigonometric formula, cos (x+π) = - cos(x) = -  \(-\frac{\sqrt{3} }{2}\) =  \(\bold{\frac{\sqrt{3} }{2}}\)

Cos(x+π) lies in the 3rd quadrant. So there cosine has negative values. That is why, cos (x+π) = - cos(x).

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mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.

Total mean score = 40

\(mean \: = \frac{sum \: of \: observation}{number \: of \: observations} \)

sum of observations

= mean × no of observations

= 40×100

= 4000

After the replacement, sum of new observation will be

=4000-83+53

= 3970

mean of new the observation will be

\( = \frac{3970}{100} \)

\( = 39.7\)

[Hence, the actual mean is 39.7]

Bayesian regression with undirected network predictors offers a powerful framework for analyzing brain connectome data and gaining a deeper understanding of the relationships between brain connectivity and various outcomes of interest.

Bayesian regression with undirected network predictors refers to a statistical modeling approach that combines Bayesian inference principles with regression analysis when the predictors are represented as an undirected network. This approach is particularly useful when dealing with data that has a network structure, such as brain connectome data.

In the context of brain connectome data, a connectome represents the structural or functional connectivity between different regions or nodes of the brain. Each node can be seen as a predictor variable, and the relationships between nodes are represented by edges in the network.

Bayesian regression allows for flexible modeling of the relationships between predictors and the response variable, taking into account uncertainty in the parameter estimates. By incorporating the network structure of the predictors, Bayesian regression with undirected network predictors can capture complex dependencies and interactions among brain regions, providing insights into the relationships between brain connectivity and the outcome of interest.

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Answer: $126.00, the difference is 54.00

Step-by-step explanation:

126 ∛·÷÷∈∈πΔ≈∨∨⊃∪∡∠∉∉⇔βββ

Answer:

C and D

Step-by-step explanation:

Hope this Helped! Please tell me if I'm wrong!

The situations that describe a quantity that changes in an exponential manner relative to the other quantity are,

A. The value of a printer decreases in value by 15% each year.

E. The amount of money in Devonte's savings account in it he earns 3.5% interest each year.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The situations that describe a quantity that changes in an exponential manner relative to the other quantity are,

The value of a printer decreases in value by 15% each year,

It is an exponentially decaying function.

Suppose the first year it decayed to 85% of it's original value, next year it will decay 15% of 85% of its value.

The amount of money in Devonte's savings account it he earns 3.5% interest each year.

Suppose he earned 3.5% for $100, which is 103.5, next year he will earn

3.5% on $103.5, an exponentially growing function.

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Given,

At x=-2, f(x) is,

At x=4, f(x) has value,

The rate of change of f(x) on the interval [-2,4] is,

Therefore, the rate of change of f(x) on the interval [-2,4] is 2.

it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.

The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:

\(diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)\)

Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.

The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm

To find the space diagonal (d), we can use the following formula:

\(d = \sqrt{r^2 + r^2 + h^2}\)
Plug in the values:

\(d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}\)
d ≈ 9.06 cm

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The longest segment that can fit inside the cylinder is. \($\sqrt{73}$ cm\).

The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.

The length of this diagonal by using the Pythagorean theorem.

Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]

\({\displaystyle a^{2}+b^{2}=c^{2}.}\)

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

Consider a right triangle with legs equal to the radius.

\($r$\) and the height \($h$\) of the cylinder, and with the diagonal as the hypotenuse.

Then, by the Pythagorean theorem, the length of the diagonal is:

\($\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$\)

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Answer:

0.9082

Step-by-step explanation:

z=(63-67)/3=-1.3333

using a calculator we can find the probability is 0.9082 rounded to four decimal places

Answer:

c = 9

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

Answer:

they can all be mesures of a triangle

Answer:

Circumference! it's the major arc whose starting and ending point coincide.

 The distance of B from the boat is 8.99 miles

To calculate  the distance of the the boat from B we use cosine rule.

Cosine rule is a formula use to find one side of a triangle if two sides and an angle is given.

Cosine rule formula can be stated as

From the question,

⇒ Given:

⇒ Substitute these values into equation 1 and solve for R

Hence, the distance of B from the boat is 8.99 miles.

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Answer: Length = 10cm

Width = 6cm

Step-by-step explanation:

First and foremost, we should note that

1 meter = 100 cm.

Therefore,

Length = 5m = 500 cm

Breadth = 3m = 300 cm.

Since Elena wants to make a scale drawing of 1 to 50, then

Length = 500 cm / 50 = 10 cm

Breadth = 300 cm / 50 = 6 cm.

Therefore, the length of the scale drawing will be 10 cm and the width of the scale drawing will be 6cm.

The measure of angle A, B, C are 60°,60°,60°

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angle in a polygon is 180°. i.e

A+B + C = 180°

therefore we can say that;

2x+2x + 3x-30 = 180

7x -30 = 180

7x = 180+30

7x = 210

divide both sides by 7

x = 210/7 = 30

therefore ;

angle A = 2× 30 = 60°

angle B = 2×30 = 60°

angle C = 3×30-30 = 90-30 = 60°

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