Use Distributive Property to simplify the following expression: 10(m + 5)

Answer:

Step-by-step explanation: Bro honestly math is some bull

Answer:

109 it is the answer

Step-by-step explanation:

02947 029377393

According to the lengths of their sides, triangles can be classified into three types which are: Scalene, Isosceles. Equilateral.

Triangles come in six different types and are divided into two groups, namely sides and angles. The three triangles are categorised as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed.

Triangles are divided into three sorts based on their sides.

Equilateral triangle: A triangle is deemed to be an equilateral triangle if its three sides are all the same length.

Isosceles triangle: An isosceles triangle is one in which each of its sides are equal.

A triangle is said to be a scalene triangle if each of its three sides is a different length.

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The definite integral is [tex]& \frac{243}{5}(\ln 3)^2-\frac{2}{5}\left[\ln 3\left(\frac{243}{5}\right)-\frac{243}{25}\right]-\frac{2}{125}[/tex].

The integral is [tex]$\int_1^3 x^4(\ln x)^2 d x$[/tex]

First evaluate indefinite integral, [tex]$\int x^4(\ln x)^2 d x$[/tex]

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as [tex]\int_a^b f(x) d x=F(b)-F(a)[/tex]

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

Use integration by parts:

[tex]$\int u d v=u v-\int v d u$[/tex]

Let [tex]$u=(\ln x)^2$[/tex] and [tex]$a v=x^4 d x$[/tex]

This implies [tex]$d u=\frac{2(\ln x)}{x} d x$[/tex] and [tex]$v=\int x^4 d x=\frac{x^5}{5}$[/tex]

Equation (1) becomes,

[tex]$$\begin{aligned}& \int x^4(\ln x)^2 d x=(\ln x)^2 \frac{x^5}{5}-\int \frac{x^5}{5} \times \frac{2(\ln x)}{x} d x \\& \int x^4(\ln x)^2 d x=(\ln x)^2 \frac{x^5}{5}-\frac{2}{5} \int x^4 \ln x d x\end{aligned}$$[/tex]

Again, use integration by parts to evaluate [tex]$\int x^4 \ln x d x$[/tex]

Let [tex]$u=\ln x, d v=x^4 d x$[/tex]

This implies [tex]$d u=\frac{1}{x}$[/tex] and  [tex]$v=\int x^4 d x=\frac{x^5}{5}$[/tex]

Let [tex]$u=\ln x, d v=x^4 d x$[/tex]

This implies [tex]d u=\frac{1}{x}$[/tex] and [tex]$v=\int x^4 d x=\frac{x^5}{5}$[/tex]

[tex]$$\begin{aligned}\int x^4 \ln x d x & =\ln x\left(\frac{x^5}{5}\right)-\int\left(\frac{x^5}{5}\right) \frac{1}{x} d x \quad \text { since } \int u d v=u v-\int u d u \\& =\ln x\left(\frac{x^5}{5}\right)-\frac{1}{5} \int x^4 d x \\& =\ln x\left(\frac{x^5}{5}\right)-\frac{x^5}{25}\end{aligned}$$[/tex]

From equation (2),

[tex]$$\int x^4(\ln x)^2 d x=(\ln x)^2 \frac{x^5}{5}-\frac{2}{5}\left[\ln x\left(\frac{x^5}{5}\right)-\frac{x^5}{25}\right]$$[/tex]

The required definite integral is,

[tex]$$\begin{aligned}\int_1^3 x^4(\ln x)^2 d x & =\left[(\ln x)^2 \frac{x^5}{5}-\frac{2}{5}\left[\ln x\left(\frac{x^5}{5}\right)-\frac{x^5}{25}\right]\right]^3 \\& =\left[(\ln 3)^2 \frac{3^5}{5}-\frac{2}{5}\left[\ln 3\left(\frac{3^5}{5}\right)-\frac{3^5}{25}\right]\right]-\left[(\ln 1)^2 \frac{1^5}{5}-\frac{2}{5}\left[\ln 1\left(\frac{1^5}{5}\right)-\frac{1^5}{25}\right]\right] \\& =\frac{243}{5}(\ln 3)^2-\frac{2}{5}\left[\ln 3\left(\frac{243}{5}\right)-\frac{243}{25}\right]-\frac{2}{125}\end{aligned}$$[/tex]

Therefore, the required definite integral is [tex]& =\frac{243}{5}(\ln 3)^2-\frac{2}{5}\left[\ln 3\left(\frac{243}{5}\right)-\frac{243}{25}\right]-\frac{2}{125}[/tex].

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The measure of central tendency that would most likely give the best representation for the data would be Median.

The mean (average) would be greatly skewed by the presence of 0's and would not accurately represent the scores of the students who took the test. Since the scores were all above 75, the mean would be much lower than the actual scores due to the presence of 0's.

The mode (most common value) would be 0 and it would not be a good representation of the scores of the students who took the test.

The median can be calculated by ordering the scores and finding the middle value. Since 5 students were absent and their scores were listed as 0, it would be the middle value of the test scores that were above 75. This is therefore the best measure of central tendency.

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The number that satisfies the given condition is x= 64.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Let the number be x.

Then one eight of the number can be represented as follows: [tex]\frac{1}{8}x[/tex]

The number 17 exceeds by 9, this is written as [tex]\frac{1}{8}x + 9 =17[/tex]

Using the equation, we find the value of x by isolating the variable:

[tex]\frac{1}{8}x + 9 =17\\\\x+ (8)(9) = (17)(8) \\\\x = 136 - 72\\\\x=64[/tex]

Hence the number x that satisfies the given condition is 64.

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Answer:

-10/7 or -1.429

Step-by-step explanation:

-5/7 ÷ 2/4

Fractions can't be divided, so you reciprocate and replace the division sign with a multiplication sign.

-5/7 × 4/2

-20/14

= -10/7 or -1.429

The result of the given multiplication of the mixed fraction is found as 78/3.

A number that combines an integer as well as a legal fraction is referred to as a mixed fraction.

The given expression:

= 4 1/3 x 6

Solving the mixed fraction.

= (4*3 + 1)/3 x 6

= (12 + 1)/3 x 6

= 13/3 x 6

= 78/3

Thus, the result of the given multiplication of the mixed fraction is found as 78/3.

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The area of triangle whose sides are 9 cm 12 cm and 15 cm is 54 cm².

The formula to be used for calculating of the area of triangle is -

A = ✓s(s-a) (s-b) (s-c), where a, b and c are sides of triangle. S is (a+b+c)/2.

Let us assume side a to be 9 cm, side b to be 12 cm and side c to be 15 cm. Calculating the value of s.

s = 9 + 12 + 15/2

Adding values on Right Hand Side of the equation

S = 36/2

Performing division

S = 18

Keep the values in formula of area -

A = ✓18 × (18 - 9) × (18 - 12) × (18 - 15)

Performing subtraction

A = ✓18 × 9 × 6 × 3

Performing multiplication

A = ✓2916

Taking square root

A = 54 cm²

Thus, the area of triangle is 54 cm².

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Answer:0.3

Step-by-step explanation:

The total area of kite LMNP with diagonal length of 6.4 m and 12.4m in square meters is 39.68 square meters.

Therefore the answer is 39.68 square meter.

To find the area of a kite, you need to know the lengths of its diagonals. The formula for finding the area of a kite is

(d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here diagonals d1 = 6.4m and d2 = 12.4m, so

area = (d1 × d2) / 2

area = (6.4 × 12.4) / 2

area = 39.68 square meters

So area of the kite LMNP is 39.68 square meters.

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The cosine function will be equal to f(x) = 3cos(π(6/7)x) + 4

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A generic cosine function is written as:

f(x) = Acos(wx + p) + M

where:

A = amplitude

w = angular frequency

p = phase

M = midline.

We know that:

The midline is 4, then  M = 4

The amplitude is 3, then A  = 3

There is no information about the phase, so p = 0.

And we know that the period is 7/3.

The period is written as T, and the relation between the period and the angular frequency is:

T = 2π/w

Then we have:

7/3 = 2π/w

w = (2π)*(3/7) = π  x (6/7)

where π= 3.14

Then we have:

w =  π  x (6/7)

A = 3

M = 4

p = 0

Hence, the cosine function is: f(x) = 3cos(π(6/7)x) + 4

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The option that is not a possible way to evaluate that function and find the correct answer is given as follows:

Answer 1: See what x is when y=-5.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² - 2x + 5.

At x = -5, the numeric value is obtained replacing the two instances of x by -5, hence:

f(-5) = 3(-5)² - 2(-5) + 5 = 90.

Meaning that only answer 1 is incorrect.

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The term 91 is present in sequence S at n = 43, and the term is not a part of the sequence T.

A sequence is an enumerated group of items in mathematics where repetitions are permitted, and order is important. Similar to a set, it has members.

Given that:

a = 91

Substitute the value of a in the given sequence.

Sequence S:

a = 2n+5

91 = 2n + 5

91 - 5 = 2n

n = 43

Sequence T:

a = 3n - 6

91 + 6 = 3n

n = 97/3

As the terms present in a sequence cannot be a fraction we figure that 91 is not present in sequence T.

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Answer: <C = 32, <D = 80, <DEC = 68

Step-by-step explanation:

First, the exterior angle DEF equals the sum of the two other interior angles that are not adjacent to it, meaning that the angle DEF equals the sum of angles DCE and EDC.

Therefore, you get the equation

2y+8+6y+8=112

8y+16=112

8y = 96

y = 12

Since y is 12, let's use this to find the measure of the other angles.

DCE = 2y+8 = 32

EDC = 6y+8 = 80

Angle DEC equals 180 - 112 = 68

Answer:

4

2

3

4

5

3

7

3

4

5

4

3

2

Step-by-step explanation:

Answer:

The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.

Step-by-step explanation:

Hope it helps!

[tex]26 sin 58°[/tex] is the expression that represents the length of segment PR.

The word "length" is used to describe an object's size or the separation between two points. The length of an object or the separation between two points is measured by its length. It is employed to determine an object's size or the separation between two points.

Since triangle JKL and triangle PQR are similar, we can use the similarity ratios to find the length of PR.

We know that the ratio of PR to JK is the same as the ratio of PQ to JL. We know that [tex]PQ = 26 and JL = 26 + 13 = 39[/tex], so the ratio is [tex]26/39[/tex].

So, [tex]PR = (26/39) * 13 = 26sin( JL/2) = 26sin58°[/tex]

So the answer is [tex]26 sin 58°[/tex]

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Answer:

• Two $10 bills

• Four $20 bills

Step-by-step explanation:

We are told that Gerardo received a number of $20 and $10 bills upon changing a $100 bill at the bank. We are also told that he received 2 more $20 bills than $10. Then we are asked to find the number of each kind of bill.

To solve this problem, let's consider the number of $10 bills he received was [tex]x[/tex]. Since he received 2 more $20 bills, he got [tex](2 + x)[/tex] $20 bills. Therefore, in total he received:

[tex]10 \times x + 20 \times (x +2)[/tex]

This should add up to $100 since that is the amount he changed. Solving the resulting equation for [tex]x[/tex] will give us the number of $10 bills he received.

[tex]10 \times x + 20 \times (x +2) = 100[/tex]

⇒ [tex]10x + 20x + 40 = 100[/tex]

⇒ [tex]30x +40 = 100[/tex]

⇒ [tex]30x + 40 - 40 = 100 - 40[/tex] [Subtracting 40 from both sides of equation]

⇒ [tex]30x = 60[/tex]

⇒ [tex]\frac{30}{30}x = \frac{60}{30}[/tex]              [Dividing both sides of the equation by 30]

⇒ [tex]x = \bf 2[/tex]

Therefore, he received 2 $10 bills.

Since the number of $20 bills is 2 more than the number of $10 bills,

no. of $20 bills = 2 + 2

                         = 4

The equation of the line which passes through points (2 3) and (-4 1) is 3y - x = 7.

What is the equation of the line?

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Here, we have

Given: points (2 3) and (-4 1)

We have to find the equation of a line.

we need to determine the slope of the line. The slope can be found by using the formula

m = (y₂ - y₁) /(x₂ - x₁)

Now, we put the given points and get the value of m.

m = (1 - 3) /(-4 - 2)

m = 1/3

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

(y - y₁) = m(x - x₁)

(y - 3) = 1/3 (x-2)

3y - 9 = x - 2

3y - x = 7

Hence,  the equation of the line which passes through points (2 3) and (-4 1) is 3y - x = 7.

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Answer:$231.2

Step-by-step explanation:

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The total cost of farmers' chicks is $231.2

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 5 is an equation.

We have,

Total chicks = 70

4 Rhode Island Red chicks = 3 Buckeye chicks.

Multiply 10 on both sides.

40 Rhode Island Red chicks = 30 Buckeye chicks.

We see that,

40 + 30 = 70

Now,

Rhode Island Red chicks cost = $3.20

Buckeye chicks cost = $3.44

Now,

= 40 x 3.20 + 30 x 3.44

= 128 + 103.2

= $231.2

Thus,

The total cost of farmers' chicks is $231.2

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The transformation is an example of a translation because the figure slides in one direction, but does not flip, turn, or change size.

Now, According to the question:

Type of Transformation:

There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.

The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.

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Answer:

Step-by-step explanation:

remember,

x^(a/b) corresponds to

bth root of x^

7.

x^(2/3) × y^(5/3)

= 3rd root of (x²y⁵)

8.

(a³b⁷/(a²b^-3))

= a¹×b¹⁰

so, the whole expression is

a^(1/5) × b^(10/5) = a^(1/5) × b²

9.

(2^(1/2) × 3^(5/2))^(1/3)

= (2^(1/6) × 3^(5/6))

the whole expression is

6th root of (2 × 3⁵)

The cost of  the two clubs will be the same after 4 sessions

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

Let x represent the number of session

Since One tennis club charges $ 34 per session to play tennis. We can write the cost as:

cost = 34x

And another tennis club charges an annual fee of $ plus $ 22 per session. We can write the cost as:

cost = 48 + 22x

At the same cost, we have:

34x = 48 + 22x

34x - 22x = 48

12x = 48

x = 48/12

x = 4

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Complete Question

One tennis club charges $30 per session to play tennis. Another tennis club charges an annual fee of $48 plus $22 per session. After how many sessions is the cost at the two clubs the same?

No, it is not possible to draw a triangle with side lengths of 2.5 cm, 4.2 cm, and 8 cm.

The triangle inequality theorem states that for any triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.

In other words, for a triangle with sides of lengths a, b, and c, where c is the longest side, the following must be true: a + b > c, b + c > a, and a + c > b.

In the case of the triangle with side lengths of 2.5 cm, 4.2 cm, and 8 cm, the sum of the lengths of the two shorter sides (2.5 cm + 4.2 cm) is 6.7 cm, which is less than the length of the longest side (8 cm).

Therefore, it is not possible to form a triangle with these side lengths, as the triangle inequality theorem is not satisfied.

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Option C is correct. 1 = x/4 is not an expression. It is an equation. An expression is a combination of numbers, variables, and operators (such as +, -, *, /) that can be simplified or evaluated to a single value, while an equation is a statement that asserts the equality of two expressions.

Expression: In order to indicate the value of something, an expression is defined as a grouping of integers (constant), letters (variables), or their combination connected by operators (+, -, *, /). A mathematical, algebraic, polynomial, or analytical expression can be used.

It does not demonstrate any relationship because it lacks the equals (=) sign. As a result, it lacks left and right sides. An expression can be made simpler by grouping related terms together, or it can be evaluated by replacing the variables with values to get a numerical value.

Equation: Equation refers to a claim of equivalence. In this statement, two expressions are positioned on either side of one another. The value of the relevant variable must be known in order for an equation to be satisfied; this is referred to as the solution or root of the equation.

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In mathematics, an inequality is a statement that compares two expressions or values.

The expressions or values being compared are separated by an inequality symbol, such as; > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), or ≠ (not equal to).

For example, the inequality statement "3 < 5" means that 3 is less than 5. The symbol "<" is the inequality symbol, and it shows the relationship between the two values 3 and 5. Another example would be "x + 2 > 5", this inequality states that the value of x + 2 is greater than 5, where x can be any value.

Inequality statements can also be represented graphically on a number line. For example, the inequality x > 3 would be represented by a line on the number line with an open circle at 3, with all the numbers to the right of 3 being included in the solution set.

Inequality statements can also be combined to form a system of inequalities, which can then be solved graphically by finding the common solution set of all the inequalities in the system.

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