find the least common denominator of 8/x^2-3x-40 and -2/x^2-8x​

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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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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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 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

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 approximate population 3 years after the population started being recorded is 2584.

What is an exponential function:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given that,

The population of a community is modeled by this exponential function, where x represents the number of years since the population started being recorded:

p(x) = 2,400(1.025)×

Plug x = 3 years in the above function.

P(3) = 2400(1.025)³

P(3) = 2400x1.0768

P(3) = 2584.53 ≈ 2584 people

Therefore,

The approximate population 3 years after the population started being recorded is 2584 people.

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The answer of -1/5 - (1/2 + -1/4) divided by 1/3 is [tex]-\frac{27}{20}[/tex]

We have given an expression [tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))[/tex] .

On simplifying , we get

  [tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=-\frac{1}{5}-(\frac{1}{2} -\frac{1}{4} )\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-(\frac{2-1}{4} )\\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-\frac{1}{4} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-4-5}{20} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-9}{20}[/tex]

Now , we are asked to divide -9 /20 by 1 /3 .

On dividing, we get

           [tex]\frac{\frac{-9}{20} }{\frac{1}{3} } =\frac{-9}{20} \times\frac{3}{1} \\\\=\frac{-27}{20}[/tex]

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Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.

Option b)25.12 in³ is the correct answer.

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The volume of a cone is expressed as;

V = (1/3)πr²h

Given the data in the question;

Plug the given values into the volume formula above and simplify.

V = (1/3)πr²h

V = (1/3) × 3.14 × (2in)² × 6in

V = (1/3) × 3.14 × 2in² × 6in

V = (1/3) × 3.14 × 4in² × 6in

V = 25.12 in³

Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.

Option b)25.12 in³ is the correct answer.

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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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[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 diagonal of the given brick using the Pythagorean Theorem is 5√2.

So, let the diagonal be 'x'.

Pythagorean formula: x² = b² + h²

Now,

Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.

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The x coordinate of the solution to the system is 4

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

x + 2y = 6

5x - 4y = 16

Next, we plot the graph of x + 2y = 6  and 5x - 4y = 16 (see attachment)

From the attached graph, the point of intersection is

(x, y) = (4, 1)

Remove the y coordinate

x = 4

Hence. the x coordinate of the solution to the system is 4

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Answer:

7

Step-by-step explanation:

-4d+3

-4(-1) + 3   Insert -1 for d

4+3=7

Answer:

7.25, 0​, -9.8

Step-by-step explanation:

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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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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For each annual rate of change , the corresponding growth or decay factor is - 0.75 .

Given : annual rate of change = - 75 % .

To find : corresponding growth or decay factor .

For an exponential growth function ,

y = a ( [tex]1 + r^{t}[/tex] ) ,

( 1 + r ) is the growth factor and

for an exponential decay function y = a ( [tex]1 - r ^{t}[/tex] ) ,

( 1 - r ) is the decay factor .

According to question ,

( - 75 ) / 100 = - 0 .75

Hence , for each annual rate of change , the corresponding growth or decay factor is - 0.75 .

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Answer:

4

Step-by-step explanation:

9 - 5 = 4

The year in which we predict the population to reach 1,000,000 based on annual growth rate of 5% is 2009

How many years would population will be 1,000,000?

The year that the population of the city would reach 1,000,000 can be determined by first of all computing the number of years beginning from 1990 that it would take the population size of 400,000 to reach 1,000,000

FV=PV*(1+G)^n

FV=future population size=1,000,000

PV=present population size=400,000

g=population growth rate per year=5%

N=number of years it takes population to become 1,000,000=unknown

1,000,000=400,000*(1+5%)^N

1,000,000/400,000=(1+5%)^N

2.50=(1.05)^N

take log of both sides

ln(2.50)=N*ln(1.05)

N=ln(2.50)/ln(1.05)

N=19(rounded to the nearest whole number)

number of years before population reach 1m=1990+19

number of years before population reach 1m=2009

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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 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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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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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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By solving the improper fractions, there are 18 water stations in all.

This problem can be solved by two methods:

Method 1 :

First of all, calculate 13²/₃ miles in fraction. The value is 13.5 miles. Then calculate 3/4 mile in fraction. The value is .75 miles.

Now divide 13.5 miles by 0.75 miles.

13.5 ÷ 0.75 = 18

So, 18 water stations are there in all.

Method 2 :

Convert 13 ¹/₂ miles into an improper fraction from 27/2 miles.

Now, again divide 27/2 miles by 3/4.

27/2 ÷ 3/4 = ²⁷/₂ ₓ ⁴/₃ = 18

So, 18 water stations are there in all.

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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 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