a. Solve 3-√(x-3)=x algebraically.

The solution is 10

Firstly rewriting the equation to frame the steps of solution -

√(5x-1) + 3 = x

Shifting 3 to the Right Hand Side of the equation -

√(5x-1) = x - 3

Now taking square of both sides of the equation

(√(5x-1))² = (x - 3)²

On solving the square we get the equation -

(5x - 1) = x² + 9 - 6x

Further solving the equation -

5x - 1 - 9 = x² - 6x

5x - 10 + 6x = x²

x² - 11x + 10 = 0

Solving the equation by factorizing -

x² - 1x - 10x + 10 = 0

x (x - 1) - 10(x - 1) = 0

(x - 1)  (x - 10) = 0

x = 1, 10

Keeping the value of x in equation to find the solution and check the results-

x = 1

√(5×1-1) +3 = 1

√(5 - 1) + 3 = 1

√4 + 3 = 1

2 + 3 = 1

5 = 1

x = 10

√(5×10-1) +3 = 10

√(50 - 1) + 3 = 10

√49 + 3 = 10

7 + 3 = 10

10 = 10

Since, 10 = 10, the result is correct.

Hence, the solution is 10

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Answer:

7.25, 0​, -9.8

Step-by-step explanation:

The number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35  = 154.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jackson has a points card for a movie theater. He receives 35 reward points just for signing up. He earns 8.5 points for each visit to the movie theater.

Let x be the number of visits Jackson must make to earn a free movie ticket.​

8.5x + 35  = 154

8.5x = 154 - 35

8.5x = 119

x = 119/8.5

x = 14

Thus, the number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35  = 154.

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Answer:

12,000

Step-by-step explanation:

Since we're just estimating, we can just round the two numbers.

180 rounded to the nearest hundred is 200.

586 rounded to the nearest hundred is 600.

200 * 600 = 12,000

Therefore, 180 * 586 is roughly 12,000.

The rate of increase in the water pressure will be

0.000993 atmosphere per kilometers.

From the information given,it should be noted that the water pressure on Mustafa was illustrated by 0.993 atmosphere per meter.

Therefore, it should be noted that the rate of increase per kilometers will be illustrated as:

1000 meters = 1 kilometer

This will be

= 0.993 / 1000

= 0.000993

This will be illustrated as 0.000993 atmosphere per kilometers.

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The extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.

We are given an equation:

5(3 x + 1)^ ( 1 / 4) = 10

Divide each side by 5, we get that:

⁴√3 x + 1 = 2

Raise both sides to the power 4, we get that:

3 x + 1 = 2⁴

3 x + 1 = 16

3 x = 16 - 1

3 x = 15

x = 15 / 3

x = 5

Therefore, we get that, the extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.

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The number 8 is a natural number, whole number, integer, rational number, real number.

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well. In this post, let's study all there is to know about whole numbers.

The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.

Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers.

Real number is a value of a continuous quantity that can represent a distance along a line. Real numbers can be defined as the union of both rational and irrational numbers.

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Answer:

14x+18

Step-by-step explanation:

2(5x+7) + 2(2x+2)

10x+14+4x+4

14x+18

Answer:

hope it helped!

Step-by-step explanation:

With the SmartScore, the learning process is rewarded and your students are constantly reassessed. When a student starts practicing a skill, the SmartScore ...

Missing: s ‎h, ‎r, ‎p. ‎Quest ‎12th ‎Leap: ‎MI

A = $ 1100.76 the amount in a continuously compounded account for the given conditions.

What does compound interest entail?

principal: $ 1000 annual

interest rate: 4.8%

time: 2 years

We know that continuously compound interest

A = [tex]P_{0} e^{rt}[/tex]

   = [tex]1000 e_{(0.048)(2)}[/tex]

   = [tex]1000 (e)^{0.096}[/tex]

   = [tex]1000 ( 1.10075906 )[/tex]

  = 1100 . 75906

A = $ 1100.76

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Step-by-step explanation:

the total charge is £195.

we have 36 students. each paying £4.25.

we have 3 parents. each paying 2×£4.25 = £8.50

we have 3 teachers. each paying £0.

a.

the payments are

36×4.25 + 3×8.50 = 153 + 25.5 = £178.50

that is clearly below the total charge of £195.

there is a deficit of 195 - 178.5 = £16.50

b.

3 teachers.

so, each should pay

16.5 / 3 = £5.50

c.

8 students drop out.

that means

8× 4.25 = £34.00 are not paid.

we have now

28 students

3 parents

3 teachers

on the bus.

these are 34 persons.

34 / 34 = £1.00

they each would have to pay £1.00 as extra payment.

The angle number that represents the linear pair of angle FHC is: angle 5.

The linear pair consists of two adjacent angles that are on a straight line, whose sum will be equal to 180 degrees when added together.

Thus, the two adjacent angles share a common side and a common vertex, and they are supplements of each other. That is, they have a sum of 180 degrees.

Angle 4 represents angle FHC. Angle 5 is adjacent to angle 4, and both lie on a straight line.

Therefore, angle FHC + angle 5 = 180 degrees.

In conclusion, we can state that, the angle number that represents the linear pair of angle FHC is: angle 5.

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Reflexive Property of congruence justifies the statement

∠K ≅ ∠K

The Reflexive Property of congruence states that any geometric figure is congruent to itself. The figures are being the reflection of itself. They have the line segments of same length, an angle has the same angle measure and the figure has same shape and size as itself.

If two triangles have a common side or a common angle, then Reflexive Property of congruence is used to prove that the two triangles are congruent.

Since the given angle is K, therefore by the Reflexive Property of congruence  we could say that the angle K is congruence to angle K.

⇒ ∠K ≅ ∠K

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The relationship must hold for the point to be equidistant from the origin and the x z-plane is a^2+b^2+c^2 > b^2.

What is equidistant point:

A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.

Now,

distance from P(a, b, c) and the Origin (0,0,0)

[tex]\sqrt{(a-0)^2+(b-0)^2+(c-0)^2} =\sqrt{a^2+b^2+c^2}[/tex]

distance from p(a ,b, c) and the x-z plane

[tex]\sqrt{(0-0)^2+(b-0)^2+(0-0)^2} = |b|[/tex]

Here,

P is equidistant from the Origin and the x - z plane

[tex]\sqrt{a^2+b^2+c^2} = |b|[/tex]

[tex]a^{2} +b^2+c^3 = b^2[/tex]

[tex]a^{2} +c^2 = 0[/tex]

Hence a=c=0 ,thus the point P must be of the form (0,b,0) for any b ∈R

Again,

point P far the from the origin than from the x z plane

[tex]\sqrt{a^2+b^2+c^2} > |b|[/tex]

[tex]a^{2} +b^2+c^2 > b^2[/tex]

[tex]a^{2} +c^2 > 0[/tex]

Hence a, c ∈R such that atleast one of the a ,b ,c is non-zero.

Therefore,

(a ,b ,c) for any b∈ R and for a, c ∈ R with atleast one of the a and c is non-zero.

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The values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2

[tex] {(x + 1) }^{3/2} [/tex] - 2 = 25

Adding 2 on both the sides of the equation we get

[tex] {(x + 1) }^{3/2} [/tex] - 2 + 2 = 25 + 2

[tex] {(x + 1) }^{3/2} [/tex] = 27

On squaring both the sides of the equation we get

[tex] {x + 1}^{3/2 \times 2} [/tex] = 27²

(x + 1)³ = 729

Now, using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we get

x³ + 1 + 3x² + 3x = 729

x³ + 3x² + 3x - 728 = 0 : Equation 1

By hit and trial method x = 8 is the solution of the equation 1.

Now, by remainder theorem we can write the equation 1 as

x³ + 3x² + 3x - 728 = (x - 8)(x² + 11x + 91) + 0

On solving quadratic equation x² + 11x + 91, we get

x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a

x = -11+✓(11² - 4×1×91)/2×1 and -11-✓(11² - 4×1×91)/2×1

x = -11+✓(121 - 364)/2 and -11-✓(121 - 364)/2

x = -11+✓(-243)/2 and -11-✓(-243)/2

x = -11/2 + ✓243i/2, -11/2 - ✓243i/2

Thus, the values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2

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[tex]\bf \implies{The \: correct \: option \: is \: (c) \: 240}[/tex]

[tex] \large \frac{40}{5} . \: 6 \: . \: \frac{10}{2} [/tex]

Step 1) : Cross out the common factor

[tex] \bf \longrightarrow\frac{ \cancel{40}}{ \cancel{5}} . \: 6 \: . \: \frac{ \cancel{10}}{ \cancel{2} } \\ \\ \bf \longrightarrow8 \times 6 \times 5[/tex]

Step 2 : Multiply it

[tex] \bf \longrightarrow8 \times 6 \times 5 \\ \bf \longrightarrow8 \times 5 \times 6 \\\bf \longrightarrow 40 \times 6 \\ \bf \longrightarrow240[/tex]

The range of the quadratic function is {y |0 ≤ y < 9}

The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.

From the question, we have the following parameters:

Write out the vertex

So, we have

Vertex = (0, 0)

Remove the x value

y = 0

From the question, we have

The parabola opens upward

This means that the vertex is a minimum

So, the range is

y ≥ 0

Rewrite as

0 ≤ y

Recall that:

Closed circle point = (-2, 4)

Open circle point = (3, 9)

Remove the x values

Closed circle point = 4

Open circle point = 9

Remove the smaller y value

Open circle point = 9

This means that the highest value of y is at open circle point = 9

This is represented as

y < 9

So, we have

0 ≤ y and y < 9

Combine both

0 ≤ y < 9

Rewrite properly as

{y |0 ≤ y < 9}

Hence, the range of the quadratic function is {y |0 ≤ y < 9}

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{y |0 ≤ y < 9}

The person above need the shine, im just making it simple

Answer:

184

Step-by-step explanation:

92 x 4.6 is 423.2 then you divide it by 2.3 which gets you 184.

Answer:

184

92 times 4.6 = 423.2

423.2 divided by 2.3 = 184

Step-by-step explanation:

Hope it helps! =D

Answer: 36 degrees

Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees

Answer:

A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45

We need to know about logarithm to solve this problem. The logarithm expanded is [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]

Logarithm is the power to which a base should be raised to get a given number. Expanding logarithm is writing logarithms usisng addition, subtraction, simplifying the logarithm. In logarithm, log ab can be written as log a+ log b and log a/b can be written as log a -log b, [tex]log_{a} b[/tex] can be written as log b/log a. We will be using these rules to expand the given logarithm. In the given logarithm we have the base of the log as 3 and we have logarithm of fraction, which we can expand.

[tex]log_{3} \frac{250}{37} =log_{3} 250 - log_{3} 37=\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]

So we found the expansion of the given algorithm using the rules for expansion of algorithm to be [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex].

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Based on the data points given, the type of function shown is a Quadratic function.

A quadratic function is one where the values of x and y form data points that lead to a parabola being formed.

This parabola forms when the values of the data points start away from 0 and then reach zero and rise again. This is what happens with these points so the function must be a quadratic function.

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Answer:

Measures of each angle are as follows:

4.     ∠BXC = 20°

5.     ∠FXE = 85°

6.     ∠GXD = 75°

7.     ∠BXF = 75°

Step-by-step explanation:

#4
 ∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°

#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°

#6
Angles  ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°

Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°

#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°

The values for

[tex]f(g(x)) = 6x^3 +2 \\g(f(x)) = 6x^2 + 4[/tex]

[tex]Given : f(x)=3 x²+2, g(x)=2 x[/tex]

1.

[tex](f.g)(x) = f(g(x)) \\g(x) = 2x \\f(x) = 3 x^2+2 \\f(2x) = 6x^3 +2[/tex]

2.

[tex](g.f)x = g(f(x)) \\fx = 3x^2 + 2 \\g(3x^2 + 2) = 2 (3x^2 + 2) = 6x^2 + 4[/tex]

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Raj is incorrect as the negative signs are put in different place.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

given:

-(5^4) = (-5^4).

Raj is incorrect because the in LHS part the negative sign is out of the exponent term and in RHS part the negative sign is within exponent.

-(5^4) gives - 625

and,  (-5^4) gives 625

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The intersection point of two lines are (-4 , -19)

The intersection point are those point where two line met of cut each other are called intersection point.

the given line of equation are

y = 5x + 1

y = 2x - 11

On solving these two equation we get the values as follow,

value of x = -4

value of y = -19

hence by this we can say the the intersection point of the above lines are

( -4 , -19 )

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When the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2 ,the value of HJ is 27.

Fronxrye information, the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2.

Therefore, the value of HJ will be:

= (1 + 2)/(1 + 2 + 3) × 45

= 3/5 × 45

= 27

Therefore, the value of HJ is 27.

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The length of the golden gate bridge is -163.250975.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

What is length?

Length is a measure of distance. According to the International System of Quantities, length has the dimension of distance. Most measurement systems select a length base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.

Given that,

The height of the bridge is 300m,

The angle of depression in the middle of the river are 25⁰ and 32⁰ respectively.

[tex]\frac{300}{tan(32)}[/tex] -[tex]\frac{300}{tan(25)}[/tex],

[tex]\frac{300}{0.624869}[/tex]-[tex]\frac{300}{0.466308}[/tex],

= -163.250975.

The length of the golden gate bridge is -163.250975.

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Answer:

7

Step-by-step explanation:

-4d+3

-4(-1) + 3   Insert -1 for d

4+3=7