The solution to an absolute value inequality is shown on the graph below.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to show the solution?
x> -3 or x < 2
{x|x <-3 orx <2}
[-3, 2]
O (-3, 2).

The domain of the function f(x)= [tex]\sqrt{x-2}[/tex]is all numbers greater than or up to 2.

Given Function f(x)=[tex]\sqrt{x-2}[/tex]

We have to search out the domain of the function f(x)=[tex]\sqrt{x-2}[/tex]

Domain is that the value of x which we put within the function to induce the various values and range is that the value which we get after putting the worth.

f(x)=[tex]\sqrt{x-2}[/tex]

put the function =0

squaring either side we get

x-2=0

x=2

So the domain of the function f(x)=[tex]\sqrt{x-2}[/tex] is [2,∞) because we are able to put all values greater than 2 within the function.

Hence the domain of the function is [2,∞).

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The expression that is equivalent to the given complex fraction is; (-2y+5x) / (3x - 2y)

The given algebraic sentence can be rewritten as;

((-2/x) + (5/y))/((3/y) - (2/x))

The LCM is xy and as such when we put it in the denominators of each fraction, we have:

((-2y + 5x)/xy)/((3x - 2y)/xy)

Putting 'xy' in the numerator and denominator of the whole fraction:

(-2y + 5x)/(3x - 2y)

The final expression we have is (-2y + 5x)/(3x - 2y)

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Answer:

its A -2y+5x ÷ 3x-2y

Step-by-step explanation:

Edge 2022

By the quotient and product rules,

[tex]\left(\dfrac fg\right)'(0) = \dfrac{g(0) f'(0) - f(0) g'(0)}{g(0)^2} = 1[/tex]

[tex](f\times g)'(0) = f(0) g'(0) + f'(0) g(0) = 21[/tex]

Given that [tex]f'(0)=5[/tex] and [tex]g'(0)=3[/tex], we have the system of equations

[tex]\dfrac{5g(0) - 3f(0)}{g(0)^2} = 1 \implies 5g(0) - 3f(0) = g(0)^2[/tex]

[tex]3f(0) + 5g(0) = 21[/tex]

Eliminating [tex]f(0)[/tex] gives

[tex]\bigg(5g(0) - 3f(0)\bigg) + \bigg(3f(0) + 5g(0)\bigg) = g(0)^2 + 21[/tex]

[tex]10g(0) = g(0)^2 + 21[/tex]

[tex]g(0)^2 - 10g(0) + 21 = 0[/tex]

[tex]\bigg(g(0) - 7\bigg) \bigg(g(0) - 3\bigg) = 0[/tex]

[tex]\implies \boxed{g(0) = 7 \text{ or } g(0) = 3}[/tex]

Solve for [tex]f(0)[/tex].

[tex]3f(0) + 5g(0) = 21[/tex]

[tex]3f(0) + 35 = 21 \text{ or } 3f(0) + 15 = 21[/tex]

[tex]3f(0) = -14 \text{ or } 3f(0) = 6[/tex]

[tex]\implies \boxed{f(0) = -\dfrac{14}3 \text{ or } 3f(0) = 2}[/tex]

Answer:

[tex](x+1)(x-3)[/tex]

Step-by-step explanation:

A quadratic in factored form is usually expressed as: [tex]a(x\pm a)(x \pm b)[/tex] where the sign of a and b depends on the sign of the zero. And I said "usually" since sometimes the x will have a coefficient. Anyways in the quadratic there are two zeroes at x=-1 and x=3. This can be written as: [tex]a(x+1)(x-3)[/tex]. Notice how the signs are different? This is because when you plug in -1 as x you get a factor of (-1+1) which becomes 0 and it makes the entire thing zero since when you multiply by 0, you get 0. Same thing for the x-3 if you plug in x=3. Now a is in front and it can influence the stretch/compression. To find the value of a, you can take any point (except for the zeroes, because it will make the entire thing zero, and you can technically input anything in as a)

I'll use the point (1, -4) the vertex

-4 = a(1+1)(1-3)

-4 = a(2)(-2)

-4 = -4a

1 = a. So yeah the value of a is 1

So the equation is just: [tex](x+1)(x-3)[/tex]

Answer:

2x^2+56x

Step-by-step explanation:

For the given linear equation:

We know that Sarah buys one pair of sneakers and several pairs of laces.

We know that the amount that she spends is:

$35 + $3*l

The first term, the constant one, represents the cost of the pair of sneakers.

The linear term:

$3*l

Represents the cost of buying l pairs of laces, assuming that each pair costs $3.

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The balanced equation for the given reaction [tex]\mathbf{AgNO_3+NaCl \to AgCl_{(s)} + NaNO_3}[/tex]

A double replacement is a chemical reaction that takes place in which two reactants swap cations or anions to produce two distinct products.

Whenever the cations representing one of the reactants interact with the anions from another reactant to produce an insoluble ionic compound, a precipitate occurs.

The balanced equation for the given reaction:

[tex]\mathbf{AgNO_3+NaCl \to AgCl_{(s)} + NaNO_3}[/tex]

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Answer:

y + 2 = 5/3(x - 4)

Step-by-step explanation:

Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)

It looks like this:

y - Y = m(x - X)

The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.

y - -2 = m(x - 4)

Fill in the slope for the m.

y - -2 = 5/3(x - 4)

Simplify if possible.

y + 2 = 5/3 (x - 4)

Answer:

This could be described by the stock market. Suppose you had stock of tesla that went up then flat then down

Step-by-step explanation:

you went for a walk : you started at home, walked away, first slower, then a little bit faster, stayed a little bit first at one place, then started walking back home, stayed a really short time at a second place and finally walked back home.

Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is  [tex]\frac{8,586}{1}[/tex] meters.

1. The number 8,848 is an integer and the number 8,586 is also an integer.

2. Therefore, to solve this problem you must convert the integers shown above to fractions (Because a rational number is that one that can be written as a fraction), as you can see below:

Write each integer as the numerator of the fraction a write 1 as the denominator. This will not change the value.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Then you obtain the following fractions:

[tex]\frac{ 8,848}{1}[/tex]

[tex]\frac{8,586}{1}[/tex]

3. Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is  [tex]\frac{8,586}{1}[/tex] meters.

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we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

We know that at 8:00 a.m. there were t inches of snow in the ground.

At 5:00 p.m. there were 3t inches of snow in the ground.

Then the difference between the heights of the snow is:

3t- t = 2t

And we know that at 5:00 p.m. there were 12 inches of snow then we can solve the linear equation for t:

3t = 12in

t = (12in)/3 = 4 in

Replacing that in the difference of heights:

2t = 2*4in = 8in

From this, we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

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The quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x+6[/tex] is (x-2_.

Given the polynomial [tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x+6[/tex] and the first expression or polynomial is divided by second.

Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.

To find the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by  , we have to divide the expression first.

We know that ,

Divident=Divisor*Quotient+remainder

[tex]x^{3}+3x^{2} -4x-12[/tex]=[tex]x^{2} +5x-6[/tex]*(x-2)-12

If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).

Hence the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x-6[/tex] is (x-2).

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Question is incomplete as the given expressions are incomplete as they should be like this:

[tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x-6[/tex].

Answer: Option (4)

Step-by-step explanation:

We need factors of [tex](x+2), (x+1), (x-4)[/tex]

Assuming you drove the car 78 miles than driving it 77 miles, the total rental cost would be equal to $0.40.

Assuming you drove the car 78 miles than driving it 77 miles, the total rental cost would be calculated by determining the slope of the line for Quick Car Rental (Q) and for Speedy Car Rental.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope = \frac{55\;-\;15}{100\;-\;0}\\\\Slope = \frac{40}{100}[/tex]

Slope = 0.40.

Therefore, the total rental cost would be equal to $0.40.

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Complete Question:

At both Quick Car Rental and Speedy Car Rental, the cost, in dollars, of renting a full - size car depends on a fixed daily rental fee and a fixed charge per mile that the car is driven. However, the daily rental fee and the charge per mile are not the same for the 2 companies. In the graph below, line Q represents the total cost for Quick Car Rental and line S represents the total cost for Speedy Car Rental. If you rent a full-size car from Quick Car Rental for 1 day how much would the total rental cost be if you drove the car 78 miles than if you drove it 77?

Step-by-step explanation:

first we need to find the length of CD, so that we can use Pythagoras to find AC.

to get CD we use again Pythagoras. there is a smaller right-angled triangle on top of the BCD rectangle.

so, AD = 11 = 4 + 7

7 = the vertical leg of the upper right-angled triangle.

the horizontal leg is congruent to CD and is

sqrt(16² - 7²) = sqrt(256 - 49) = sqrt(207).

AC² = sqrt(207)² + 11² = 207 + 121 = 328

AC = sqrt(328) = 18.11077028... cm ≈ 18.1 cm

The answer to the Diophantine equation (x³+y³+z³=k) is given below. First lets us see the definition of the same.

A Diophantine equation in mathematics is a polynomial equation with two or more unknowns, where the only solutions of interest are integer ones.

A linear Diophantine equation is equal to the sum of two or more monomials of degree one.

Unknowns can emerge in exponents in an exponential Diophantine equation.

Recall that this problem is called the "summing of three cubes." Thus, from the values given, the minimum value of K can be 1.

To arrive at that, we can do

x = 0, y = 0, z = 1

so  0³+0³+1³; hence

k = 1

and maximum value  of k can be 99

with that we work with x=2,y=3, z=4

2³+3³+4³=99

Hence, so x can be 0, or 2

y can be 0 or 3; and

z can be 1 or 4.

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The turning point of the parabola is (64, -43)

Turning point is that point on a parabolic curve in which the gradient of the curve changes value.

It is also the point on the curve in which the curve starts rising or falling.

Analysis:

[tex]27(x-64)^{2}[/tex] + 43

27(x-64)(x-64) + 43

27([tex]x^{2}[/tex] -64x -64x +4096) + 43

27[tex]x^{2}[/tex] -3456x +110592 +43

27[tex]x^{2}[/tex] -3456x +110635

at turning point dy/dx = 0

dy/dx = 54x - 3456

54x - 3456 = 0

54x = 3456

x = 3456/54 = 64

To find the value of y at x = 64

27[tex](64)^{2}[/tex] -3456(64) +110635

110592 - 221184 +110635 = -43

Therefore the turning point of the parabola is (64, -43)

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The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.

It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.

It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.

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Answer:

2(-5 - 7j) = -10 - 14j

Step-by-step explanation:

Using the distributive property means that we have to multiply both -5 and -7j by 2:

2(-5 - 7j)

⇒ 2 × -5  +  2 × -7j

⇒ -10 - 14j

The value of b is [tex]1 \cdot02[/tex].

What is compound interest?

Compound interest is when you earn interest on both the money you have saved and the interest you earn.

Formula for compound interest is

[tex]A= P(1+\frac{r}{100})^n[/tex] ...................(1)

where, A = total amount( principal + interest )

r = rate of interest in compound interest

n = number of years

Given,

For [tex]n=1[/tex]

Principal amount [tex]p=\$ 1000[/tex]

Total amount [tex]A=\$ 1020[/tex]

For [tex]n=2[/tex]

Principal amount [tex]p=\$ 1000[/tex]

Total amount [tex]A=\$ 1040[/tex]

This scenario can be represented by an exponential function of the form of [tex]f(x)=1000(b)^x[/tex]

Comparing the above function with equation (1), we get

[tex]A=f(x)\\P=1000\\b=(1+\frac{r}{100})[/tex]

For 1st year

[tex]f(x)=1000(b)^1\\\Rightarrow 1020=1000(b)\\\Rightarrow b=\frac{1020}{1000}\\\Rightarrow b= \frac{102}{100}\\\Rightarrow b= 1\cdot02[/tex]

now, check the amount for 2nd year

[tex]f(x)=1000 \times (1 \cdot01}^2\\\Rightarrow f(x)=1000 \times \frac{102}{100}\times \frac{102}{100}\\\Rightarrow f(x)=1040[/tex]

Hence, the value of b is [tex]1 \cdot02[/tex] .

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Answer:

[tex]39 yd^2[/tex]

Step-by-step explanation:

So, let's start by calculating the surface area of the base, which in this case is a square. The area of a square can be calculating by taking any of the lengths and squaring it, since all the sides should be equal if it's a square. Since one of the sides of the square is 3 yd, you have the equation: [tex](3 yd)^2 = 9yd^2[/tex]. Now to calculate the area of the four triangles. The area of a triangle can be calculating by using the formula: [tex]\frac{1}{2}bh[/tex], and in this case the base is 3 yd, and the height is 5 yd (lengths can be determined by looking at the given values in the diagram). But there's 4 of the triangles so we multiply it all by 4, and this gives you the equation: [tex]4(\frac{1}{2}(5 yd)(3 yd)) = 4(\frac{15 yd^2}{2}) = 4(7.5 yd^2)=30yd^2[/tex]. So now all that's left is to add this to the area of the square which gives you the equation: [tex]30yd^2+9yd^2=39yd^2[/tex] which is the surface area

Answer:

A is x - 4n / 3, B is 6k + 9n, C is 11k + 16n

Step-by-step explanation:

Pretty simple, you are adding the algebra grids, or substituting variables and making out an equation.

Solving for B: 4k + 6n + 2k + 3n = 6k + 9n

Solving for A: (2k + 3n) + x = 5k + 7n = x - 4n / 3

Solving for C: 6k + 9n + 5k + 7n = 11k + 16n

Answer:

Function 1 has the larger maximum at (4, 1)

Explanation:

After observation, graph of function 1 has vertex at Maximum (4, 1)

In order to find vertex of function 2, complete square the equation.

f(x) = -x² + 2x - 3

f(x) = -(x² - 2x) - 3

f(x) = -(x - 1)² - 3 + (-1)²

f(x) = -(x - 1)² - 2

Vertex form: y = a(x - h)² + k where (h, k) is the vertex

So, here for function 2 vertex: Maximum (1, -2)

Function 1 = Maximum (4, 1), Function 2 = Maximum (1, -2)

Function 1 has greater maximum value of (4, 1) as "1 is greater than -2"

The expression is defined for all the real values except x = -y , y = -x.

An expression is a mathematical statement consisting of constants , variables and mathematical operators.

The expression given in the question is 1/(x +y)

An expression f(x) is undefined when the denominator = 0

f(x) = 1/(x +y)

For the denominator to be zero,

x = -y

or y = -x

So the expression is defined for all the real values except x = -y , y = -x

It can be written as

E = {x ∈ R ∧ x ≠ -y} or

E = {y ∈ R ∧ y ≠ -x}

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The solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.

In the question, we are given a system of equations,

y = 3 -2x ... (i), and

y = 8 - 7x ... (ii).

We have been asked to solve the given system of equations.

To solve the system of equations, we do as follows:

Substitute the value of y = 3 - 2x, from (i) in (ii), to get:

y = 8 - 7x,

or, 3 - 2x = 8 - 7x, which is a linear equation in one variable.

To solve this, we follow these steps:

3 - 2x = 8 - 7x,

or, 3 - 2x + 7x = 8 - 7x + 7x {Adding 7x to both side of the equation},

or, 3 + 5x = 8 {Simplifying},

or, 3 + 5x - 3 = 8 - 3 {Subtracting 3 from both sides of the equation},

or, 5x = 5 {Simplifying},

or, 5x/5 = 5/5 {Dividing both sides of the equation by 5},

or, x = 1.

Substituting x = 1, in (i), we get:

y = 3 - 2x,

or, y = 3 - 2(1),

or, y = 3 - 2 = 1.

Thus, the solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.

Note: The language seemed not gettable.

The question has been done assuming the question asking to solve the system of equations:

y = 3 - 2x, y = 8 - 7x.

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The value of x that will satisfy the equation is x=-1.

We have given that,

[tex]\left|x-1\right|=\left|x+3\right|[/tex]

We have to solve the above inequality

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

Find the positive and negative intervals

[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]

Solve the inequality for each interval

[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]

[tex]\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=-1[/tex]

Therefore we get,

[tex]x=-1[/tex]

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The solution which can be used to fill in both blanks in the table is; (6,7).

It follows from the task content that the system given has been simplified to the point that;

3x = 18

x = 18/3 = 6.

Hence, the value of y can be evaluated as follows;

2y - x = 8. where (x=6.

2y = 8+6

y = 14/2 = 7.

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Step-by-step explanation:

♦ Solution ♦ :-

Given Information :

The ratio of heights of the two girls = 5:7

Assumption

Consider their height be 5X cm and 7X cm

The height of the first girl = 5X cm

But According to the condition mentioned in given problem

The height of the first girl = 192 cm

=> 5X = 192

=> X = 192/5

=> X = 38.4

Therefore, X = 38.4 cm

Now the height of the second girl = 7X cm

=> 7 × 38.4 cm

=> 268.8 cm

♦ Alternative Method♦ :-

The ratio of the heights of the two girls = 5:7

The height of the first girl = 192 cm

Assume that the height of the second girl = X cm

Therefore, 5:7= 192:X

=> 5/7 = 192/X

=> 5X = 7×192

=> X = (7×192)/5

=> X = 7× 38.4

=> x = 268.8 cm

♦ Answer ♦ :-

The height of the second girl is 268.7 cm