How many isoceles triangles are there if each of its sides have an integral length and it's perimeter is 144​

The value of f of 2, which means f(2), is 6.

As we know,

f'(x) = [tex]\[ \lim_{h\to0}[/tex] [f(x+h) - f(x)]/h

= [tex]\[ \lim_{h\to0}\\[/tex] [f(3x + 3h)/3 - f(3x + 0)/3]/h

= [tex]\[ \lim_{h\to0}\\[/tex] [{2 + f(3x) + f(3h)}/3 - {2 + f(3x) + f(0)}/3]/h

∴f'(x) = [tex]\[ \lim_{h\to0}\\[/tex] [f(3h) - f(0)]/3h-0 = f'(0)

⇒ f′(2) = f′(0) = 2          [∵f′(2) = 2]

⇒f′(x) = 2

Now, apply integration on the above equation with respect to x

∴f(x) = 2x + c          (1)

Substituting x = 0 = y in f{(x+y​)/3} = {2 + f(x) + f(y)]/3

⇒3f(0) = 2 + f(0) + f(0)

∴f(0) = 2​

By equation (i) f(0) = 2.0 + c

∴c = 2          [∵f(0) = 2]

Now (1) becomes

∴f(x) = 2(x + 1)

Put x = 2

f(2) = 2(2 + 1) = 2 × 3 = 6

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If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. The rules to show this include SSS, SAS, ASA.

Side-Side-Side (SSS) Rule The SSS rule states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent

The SAS rule states that if two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

The ASA rule states that if two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.

An overview was given due to the incomplete information.

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Answer:

The quotient is x^2 + 9x + 6 with a remainder of 6.

Step-by-step explanation:

I used the polynomial long division method to divide the polynomial 2x^3 + 17x^2 + 20x + 6 by 2x + 1.

So the quotient is x^2 + 8.5x + 0.25x which simplifies to x^2 + 9x + 6 and the remainder is 6.

Answer:

[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]

Step-by-step explanation:

[tex] \sf \frac{2x^ 3 +17x^ 2 +20x+6}{ 2 x + 1}[/tex]

2x³/2x = x²

[tex] \sf \frac{x^ 2 +17x^ 2 +20x+6}{ 1}[/tex]

[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]

Rina has been visiting the coffee shop every day for 7 days and he spent an average of $1 each day he visited the coffee shop during the week.

He started on Monday, spending $1, and each day he spent a dollar more than he did the day before. By the end of the week, he had spent $7. To calculate the average amount he spent each day, add up the total amount of money he spent that week and divide it by 7 (the total number of days he visited the shop).

7/7=1

In this case, the total amount of money spent was $7, so when divided by 7, the average amount spent each day is $1. Therefore, Rina spent an average of $1 each day he visited the coffee shop during the week.

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Answer:

Step-by-step explanation:The equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y, is:

y = 50x

This equation shows that the number of words Wyatt types is directly proportional to the number of minutes he types. For every 1 minute he types, he types 50 words.

This equation can also be read as "y is equal to 50 multiplied by x" which means that for any given number of minutes, x, that Wyatt types for, the number of words he types will be 50 times that value.

Answer:

The answer is D the second quadrant.

Step-by-step explanation:

HAVE A GREAT DAY!!!!!

The slope intercept form of a line is,

⇒ y = x - 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The equation is,

⇒ 3x - 3y = 18

Now, We know that;

The slope intercept form of the equation is,

⇒ y = mx + b

Here, The equation of line is,

⇒ 3x - 3y = 18

Take 3 as common,

⇒ 3(x - y) = 18

Divide by 3;

⇒ x - y = 18/3

⇒ x - y = 6

⇒ x - 6 = y

⇒ y = x - 6

Thus, The slope intercept form of a line is,

⇒ y = x - 6

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Step 1: Find some points on the exponential f(x). The more points we plot the better the graph will look.

Step 2: Switch the x and y values to obtain points on the inverse.

Step 3: Determine the asymptote.

Graph the following logarithmic functions. State the domain and range.

A logarithmic scale (or log scale) is a way of displaying numerical facts over a completely extensive range of values in a compact manner—typically the biggest numbers inside the data are loads or even lots of times large than the smallest numbers.

Logarithmic scales are useful for quantifying the relative alternate of a fee in place of its absolute distinction. moreover, because the logarithmic feature log(x) grows very slowly for huge x, logarithmic scales are used to compress massive-scale scientific statistics.

A logarithm is an exponent or power to which a base need to be raised to yield a given quantity. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. for example, 23 = 8; therefore, 3 is the logarithm of eight to base 2, or 3 = log2 eight.

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Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).

Three conditions must be satisfied for a radical expression to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors.

Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.

A radical expression can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.

The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.

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The definition for the function is b.

       So, when x is 2, left ray cannot get the value as 2 .Thus x <2

       So the constant term of the equation is 1

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The domain of a function is not always all real numbers.

We know that the domain of function is the set of all possible input values for which the function is well defined.

And the range of function is the set of all possible output values for given input.

As we know the domain of a function, f(x), is all real numbers when there are no restrictions on what we can take input for x, as all real numbers would make function f(x) true.

But the domain of a function is not always all real numbers.

consider the function f(x) = 1/x

This function is not defined for x = 0

So, the domain of above function f(x) is R - {0}

Also, we know that the domain of a logarithmic function is all non-zero positive real numbers.

Thus, the domain is not always set of all real numbers.

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The numbers for the sequences are 10-n = 9, 8, 7, 6, 0, and 6-2n = 4,2, 0, -2, and -14.

A sequence is a series of numbers that follow the sample principle in terms or order. In this case, the sequence is determined by the equations given, and based on this the numbers are calculated.

10-n:

10 - 1 = 9

10 - 2 = 8

10 - 3 = 7

10 - 4 = 6

And the 10th term is

10- 10 = 0

6-2n:

6 - 2 = 4

6 - 4 = 2

6- 6 = -0

6 - 8 = -2

And the 10th term is

6 - 20 = -14

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Answer: X=9

180 -108=72

72/8=9

Answer:

x = 9° (or) 8x = 72°

Step-by-step explanation:

Now we have to,

→ find the required value of x.

We know that,

→ Straight line is always 180°.

Forming the equation,

→ 8x + 108° = 180°

Then the value of x will be,

→ 8x + 108° = 180°

→ 8x = 180° - 108°

→ 8x = 72°

→ x = 72° ÷ 8

→ [ x = 9° ]

Hence, the value of x is 9°.

The expression that is equivalent to the expression n/4+n/4+n/4+n/4 is,

⇒ n

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The expression is,

⇒ n/4 + n/4 + n/4 + n/4

Now, We can simplify the expression as;

⇒ n/4 + n/4 + n/4 + n/4

⇒ (n + n + n + n) / 4

⇒ 4n/4

⇒ n

Thus, The expression is equivalent to n.

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Answer:

Est: 517

Answer: 517.499999974

Step-by-step explanation:

Answer:

function-function relation

Step-by-step explanation:

To determine if the inverse of a function is a function, we can use the horizontal line test.

A function is a set of ordered pairs (x, y) where each x value corresponds to one and only one y value. The inverse of a function is a set of ordered pairs (y, x) where each y value corresponds to one and only one x value.

To use the horizontal line test, we draw a horizontal line on a graph of the original function. If the line intersects the graph in more than one point in any vertical section, the inverse is not a function. But if the horizontal line intersects the graph in at most one point in any vertical section, the inverse is a function.

Another way to check if the inverse of a function is a function is to check that the original function is a one-to-one function, meaning that each x value corresponds to one and only one y value. If the original function is not one-to-one, then the inverse is not a function.

It's also possible to check if the inverse of a function is a function by analyzing the equation of the function. If the original function is a one-to-one function, its inverse is also a function

The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is also called Avogadro's number.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.

To find out how much of the 6.45-ounce bottle is not juice, we need to subtract the amount of juice in the bottle, which is 1.751 ounces, from the total volume of the bottle, which is 6.45 ounces.

6.45 ounces - 1.751 ounces = 4.699 ounces

So, 4.699 ounces of the 6.45-ounce bottle is not juice.

Alternatively, we can express the answer as a percentage of the total volume of the bottle:

(4.699 / 6.45) x 100 = 73.14 %

So, 73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.

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The true statement is that blood pressure increases by 1 mm HG per year.

In geometry, we have seen the lines drawn on the coordinate plane. To predict whether the lines are parallel or perpendicular or at any angle without using any geometrical tool, the best way to find this is by measuring the slope. In this article, we are going to discuss what a slope is, slope formula for parallel lines, perpendicular lines, slope for collinearity with many solved examples in detail.

What is a Slope?

The equation that represents the linear model is:

y =x+95

Linear regression is represented as:

y=mx+b

Where:

m represents the slope

b represents the y-intercept

By comparison, we have: m=1

This means that:

The blood pressure increases by 1 mm HG per year.

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Jazz Band Makes $785 in Profit.

31 huge boxes and 74 little boxes of fruit are sold by the jazz band.

The cost is $x and the price is $20 for each huge fruit box.

Price minus Cost is referred to as profit.

Profit therefore equals 20 - x for one large fruit box.

31 huge fruit boxes at a profit (20 - x)

Each little fruit box costs $10 and costs $10 per small fruit box.

Each tiny fruit box has a profit of 10–y.

74 little fruit boxes worth of profit (10 - y)

For 74 small boxes and 31 large boxes, the overall profit will be:

Profit overall equals 31 (20-x) + 74. (10 - y)

We can reduce the problem above by using the distributive property as follows:

Total profit is equal to 31(20)-31x + 74(10)-74y.

Profit total = 1360 - 31 x - 74 y

Part B)

Each large package is estimated to cost $9.

Accordingly, x = 9.

Each tiny box is stated to cost $4.

Therefore, y = 4.

We can determine the Jazz Band's profit by using the x and y numbers from the profit equation.

Profit of Jazz Band = 1360 - 31(9) - 74. (4)

Jazz Band Makes $785 in Profit

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1500 Lower Level seats and 600 Upper Level seats were sold.

Linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x is a variable. In this equation, a is referred to as the coefficient of x and b is referred to as the constant. Linear equations are used to represent relationships between two variables and can be used to solve for either variable. Linear equations are used in many different fields of mathematics, including algebra, calculus, and geometry.

System of linear equations:
50x + 20y = 66000
x + y = 2100

Solving the system of equations gives:
x = 1500
y = 600

Therefore, 1500 Lower Level seats and 600 Upper Level seats were sold.

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If a 2×2 matrix A is reverse and is multiplied by its inverse (indicate by the symbol A−1), the develop product is the Identity matrix which is indicate by I.

In fact, I can control the order or direction of multiplication between matrices A and A−1, and I would still get the Identity matrix I. That means reverse matrices are commutative.

A×A^-1= I.

In normal, the inverse of a matrix A is found using the formula (adj A)/ (det A), where "adj A" is the "adjoint of A" and "det A" is the "determinant of A".

the inverse of a 2x2 matrix, say A, is a matrix of the similar order known by A^-1 such that AA^-1 = A^-1A = I, where I is the identity matrix of order 2x2.

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1: Convert the mixed number into an improper fraction.

2: Multiply the numerators and denominators of the two fractions separately.

3: Simplify by eliminating the common factors to get the lowest form of the result.

Now, According to the question:

A mixed number is a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers.

For Example:

[tex]4\frac{1}{2}[/tex] and [tex]3\frac{1}{3}[/tex]

[tex]4\frac{1}{2}[/tex] = (4 × 2 +1)/2 = 9/2

[tex]3\frac{1}{3}[/tex] = (3 × 3 + 1)/3 = 10/3

[tex]4\frac{1}{2}[/tex]  × [tex]3\frac{1}{3}[/tex] = 9/2 × 10/3 = 90/6 = 15

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a) X'(-6, -4), Y'(0, -6), Z'(-4, -2)

b) X'(-9, -6), Y'(0, -9), Z'(-6, -3)

Rotation and dilation in geometry

For the rotation of 180° counterclockwise about the origin, we will use the rotation formula:

(x, y) → (xcosθ - ysinθ, xsinθ + ycosθ)

Where θ is the angle of rotation.

For our 180° rotation, θ = 180°.

We calculate the new coordinates for each vertex:

X(-6, 4) → X'(-6, -4):

(-6cos180° - 4sin180°, -6sin180° + 4cos180°)

Y(0, 6) → Y'(0, -6):

(0cos180° - 6sin180°, 0sin180° + 6cos180°)

Z(-4, 2) → Z'(-4, -2):

(-4cos180° - 2sin180°, -4sin180° + 2cos180°)

For the dilation of the triangle with a scale factor of 3/2 centered at the origin, we will use the dilation formula:

(x, y) → (kx, ky)

Where k is the scale factor.

For our dilation, k = 3/2.

We calculate the new coordinates for each vertex:

X(-6, 4) → X'(-9, -6):

(-6*3/2, 4*3/2)

Y(0, 6) → Y'(0, -9):

(0*3/2, 6*3/2)

Z(-4, 2) → Z'(-6, -3):

(-4*3/2, 2*3/2)

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The probability that Louis takes two green counters is 1/9, since there is only one green counter in the box.

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Answer:

6/x = 3/28

Step-by-step explanation:

Answer:

[tex]\sf{Choice \;B.\;\; (x-9)^2 + (y-2)^2 = 25[/tex]

Step-by-step explanation:

The standard form equation of a circle with center (a, b) and radius r is

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

where (a, b) is the center of the circle.

Here we are given that the circle has center (9, 2)

So the equation becomes

[tex](x-9)^2 + (y-2)^2 = r^2\cdots(1)[/tex]

All we have to do is find the radius and we are done

Circumference of a circle with radius r
[tex]= 2 \pi r\\[/tex]

Given circumference [tex]= 10\pi[/tex]

[tex]10\pi = 2\pi r\\\implies r = 10/2 = 5[/tex]

Substitute this into equation (1):
[tex](x-9)^2 + (y-2)^2 = 5^2\\\\(x-9)^2 + (y-2)^2 = 25\\[/tex]

This corresponds to option B.

The equation of a circle is (x - 9) + (y - 2) = 25.

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

The equation of a circle is (x - h) + (y - k) = r² _____(A)

Where (h, k) is the center and r is the radius.

Now,

Centre = (9, 2)

This means,

(h, k) = (9, 2) _____(1)

Circumference = 10π

This means,

2πr = 10π

2r = 10

r = 5 in ____(2)

Now,

Substituting (1) and (2) in (A).

(x - h) + (y - k) = r²

(x - 9) + (y - 2) = 5²

(x - 9) + (y - 2) = 25

Thus,

The equation of a circle is (x - 9) + (y - 2) = 25.

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The bearing of D from A is given as follows:

24º.

The bearing of D from A is obtained using the angle addition postulate, which states that  if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.

The angle measures for this problem are given as follows:

x, 166, 15 and 155.

The total of these measures is of 360º, hence the value of x, representing the bearing of D from A, is given as follows:

x + 166 + 15 + 155 = 360

x + 336 = 360

x = 24º.

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Poll only students in 9th and 11th grades would be the best way to get an accurate response. Thus, option A is correct.

In electoral campaigns, math is frequently used. The goal of polling is to predict how the electorate will vote overall by taking a small sample of voters and extrapolating their results to the entire population. Pollsters must ensure that their sample of respondents is representative of the entire electorate, or if it is not, they must use a variety of statistical techniques to increase the representativeness of their findings.

In essence, this means that a survey is conducted, and not only are respondents' voting intentions recorded, but also their age, gender, race, and other demographics. As a result, it is possible to make predictions about the voting intentions of various social groups.

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