x-5=√x + 1
solve and check for extraneous solutions

0.528176817681768176 is a rational number as it is non terminating but repeating decimal number.

A rational number is a number that can be expressed in the form of p / q where q is not equal to 0.

It can be terminating or non terminating but repeating number.

We are given a decimal number:

0.528176817681768176

We can see that, after .52, the digits 8176 keeps on repeating itself.

So, the number can also be written as:

0.528176 ( bar on 8176)

This means that the decimal number that is given is a non terminating but repeating rational number.

Therefore, 0.528176817681768176 is a rational number as it is non terminating but repeating decimal number.

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Answer:

27 units

Step-by-step explanation:

First lets add the 2 segments on the top.

8x-11 + 14x-15

Then we can add the like terms together to get

22x-26

The equation above is equal to the equation below the number line, since we added the two on top together, so:

22x-26=19x-17

Now we can start solving

Add 26 to both sides and subtract 19 from both sides

3x=9

Now we can divide by 3

x=3

TU is 14x-15, so we can substitute in 3 for x

14*3-15

42-15

27

Answer:

27 units

Step-by-step explanation:

Set up an equation:

8x -11 + 14x -15 = 19x - 17

Combine like terms:

22x - 26 = 19x -17

Subtract 19x on both sides:

(22x - 26) - 19x = (19x - 17) - 19x

3x - 26 = -17

Add 26 on both sides to isolate the x term:

(3x - 26) + 26 = (-17) + 26

3x = 9

Then, divide by 3 on both sides to fully isolate x:

3x / 3 = 9 / 3

x = 3

Plug 3 for x into the formula for TU:

14(3) - 15 = x

42 - 15 = x

x = 27

TU = 27 units

Hope this helps!

Answer:

Julia is 15

Step-by-step explanation:

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers

therefore Julia is 15

Julia's age out of the three is equal to 15 years.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42.

Julia's age will be calculated as,

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers.

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The quadratic equation, x(2) + 2 =420 can be used to find x.

you can use trial and error

x(2) + 2 =420

210(2)=420 but we need to add the two so lower the [tex]120[/tex]

209(2)=418+2 = 420

so, the x value must less than 21.

A quadratic equation with variable x is written in standard form as [tex]ax2 + bx + c = 0[/tex], where a, b, and c are constants such that the value of an is non-zero but the values of b and c can both be zeros.

Let's change [tex]ax2 + bx + c = 0[/tex] from its standard form to its vertex form, which is [tex]a (x - h)2 + k = 0[/tex], where (h, k) is the vertex of the quadratic function [tex]f(x) = a (x - h)2 + k[/tex]. Keep in mind that 'a' has the same value in both equations. Just set them equal so we can determine how the variables relate to one another.

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Moo berry can make 8 milkshakes with 1 gallon of ice cream.

Moo uses 2 cups of ice cream in each milkshake

He is using 1 gallon of ice cream

Therefore the number of milk shakes he can produce can be calculated as follows

16  cups makes 1 gallon

= 16/2

= 8

Hence 8 milkshakes can be made with one gallon of ice cream

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Answer: 1024 inches

Step-by-step explanation:

New Murals,

Length= 245+33 =278 inches

Width = 234 inches

Perimeter= 2*(278+234) = 1024 inches

The option a. 13,000,090,416 is correct standard form.

Firstly, separating the numbers and finding the number of zeroes each unit will have. As per the known fact, the number in billion contains nine zeroes. The number ninety thousand will contain four zeroes. The number four hundred will contain two zeroes.

In the given options, every 13 is succeed by nine zeroes. So, checking the number of values after digit nine. Option a has four digits, option b has seven digits, option c has 5 digits and option d has three digits. So, option a will be correct. The number 416 will be at end, and it correct in each option.

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Answer:

A

Step-by-step explanation:

x + 4(x + 5) = 40 ← distribute parenthesis and simplify left side

x + 4x + 20 = 40

5x + 20 = 40 ( subtract 20 from both sides )

5x = 20 ( divide both sides by 5 )

x = 4

The required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

Given that,
f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2
(f / g)(x) =  To be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here.
f(x) = 2x² - 5x - 3
f(x) = (2x + 1) (x - 3 )
g(x) = 2x² + 5x + 2
g(x) = (2x + 1)(x + 2)

(f / g)(x) = (2x + 1) (x - 3 ) /  (2x + 1)(x + 2)
(f/g)(x) = (x - 3) / (x + 2)

Thus, the required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

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The Segment Addition Postulate states if three points J, K, and L are collinear and J is between K and L, then KJ + JL = KL.

The segment addition postulate states that if a line segment has two endpoints, say, A and C, then a third point B will lie somewhere on the line segment AC if and only if the following equation is satisfied-

AB + BC = AC

The segment addition postulate is applicable only to a line segment, and does not apply to a ray or a line. A line segment differs from a ray or a line as it is bounded by two defined endpoints.

Here, if three points J, K, and L are collinear and J is between K and L, then as per Segment Addition Postulate-

KJ + JL = KL

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Answer:

3300cm² is the answer of this question i guess so

The dimensions of the container is r = 6.828 cm and h = 13.656 cm.

Volume of the Cone:

Volume of the cone is define the space or the capacity of the cone.

The formula for the volume of the cone is,

V = πr²h

Where

r represents the radius of the cone

h represents the height of the cone

Given,

Cylindrical container must hold 2l or 2,000 cm³ of liquid.

Here we need to find the dimensions of the container which will minimize the amount of material needed.

Let height = h and radius of the base = r.

We know that the volume of the container,

V = 2000

We know the formula of volume of the cone is,

V = πr²h

2000 = πr²h

Here we need the value of h,

So,

h = 2000/πr²

and surface area of the can

S = 2πr² + 2πrh

Apply the value of h,

S = 2πr² + 2πr (2000/πr²)

S = 2πr²+ (4000/r)

S = 2πr²+ 4000 x r⁻¹

S′=(−1)(4000r⁻²)+4πr

S′=4πr−(4000/r²)

Consider,

4πr−(4000/r²) = 0

4πr³−4000 = 0

πr³−1000 = 0

πr³ = 1000

r³ = 1000 / π

r = √1000 / π

r =  6.828 cm

Apply the value of r on the equation to find the value of h,

h = 2000/(π∗(6.828)²)

h = 2000/146.46

h = 13.656

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The average speed was 60[tex]\frac{k+300}{96+t}[/tex]

We are given that a plane travelled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 =8/5 hours

We are also given that the Plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average Speed = total distance/ total time

Average Speed = (k +300)/(8/5 + t/60)

Average speed = (k + 300) / ((96 + t)/60)

Hence, Average Speed = 60(k + 300)/ (96 + t)

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Answer:

0.894 is your correct answer.

Answer:

0.894 because the 0.01 will affect the hundredths so the 0 will be affected in 0.904 and the 9 will change to an 8 because there's nothing left in 0 so you have to substitute.

Using relations in a right triangle, we have that:

1 - a) x = 54.28º.

1 - b) y = 57.794º.

1 - c) z = 31.056º.

2) The angle is of 62.8º.

3) The angle is of x = 53.017º.

4) The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

5) The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

The relations in a right triangle are given as follows:

For item 1a, we have that the sides, hence:

tan x = 8.9/6.4

x = arctan(8.9/6.4)

x = 54.28º.

For item 1b, we have the adjacent side and the hypotenuse, hence:

cos y = 9.7/18.2

y = cos^-1 (9.7/18.2)

y = 57.794º.

For item 1c, we have the opposite side and the hypotenuse, hence:

sin z = 6.5/12.6

z = sin^-1(6.5/12.6)

z = 31.056º.

For item 2, we have the sides, given at the graph at the end of the answer, hence:

tan x = 7.2/3.7

x = tan^-1(7.2/3.7)

x = 62.8º.

The angle is of 62.8º.

For item 3, first we find the hypotenuse of the bottom triangle, by the Pythagorean Theorem, as follows:

h² = 7.9² + 18.6²

h = sqrt(7.9² + 18.6²)

h = 20.21.

Then:

sin x = 20.21/25.3

x = sin^-1(20.21/25.3)

x = 53.017º.

For item 4, we have the adjacent side and the hypotenuse, hence:

cos(x) = 3/3.2

x = cos^-1 (3/3.2)

x = 20.364º.

The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

For item 5, we have the opposite side and the hypotenuse, hence:

sin y = 1.8/2.9

y = sin^-1 (1.8/2.9)

y = 38.37º.

The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

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Answer:

= 65

Step-by-step explanation:

= 2×(-5)² - 5×(-5) - 10

= 2×25 + 25 - 10

= 50 + 15

= 65

Answer:

65

Step-by-step explanation:

Step-by-step explanation:

+25y + 35x = -1. × 5

+35x - 14y = -161. × 7

-. +. +

39y = 156

y=4

putting value of y in 5y + 7x =-1

5×4+7x =-1

7x = -21

x= -3

The transformation that will move vertex B (-2,3) to (-2,5) is transforming the point B up 2 units into y axis.

Translation in geometry means moving a figure on x-y coordinate without changing it's size and shape.We can translate a triangle with given vertices by adding or subtracting values for points(x,y)

The triangle ABC has vertices  A(-1,1), B(-2,3) and C(-1,-4).

Now to transform vertex B to(-2,5) from (-2,3) we have to make a transformation of 0 units on x axis and 2 units up on y axis which is translation.

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The correct question is Triangle ABC has vertices A(-1,1), B(-2,3) and

C(-1,-4). Which composition of transformations will move vertex B to the Point(-2,5)?

Answer:

Hi the proof steps shown in the picture are correct.

Table: x and y increments must be the same. X and y increments need not be the same.

The x and y exponents should be 1. Linear equation.

Graphs should be straight.

This is further explained below.

Generally, Based on the table, you need to ensure that the increments for the x values and the y values are the same.

It is not necessary for the increment to be the same for both the x and y values.

The following conclusion may be drawn from an equation: both the x and y exponents should be set to 1.

It seems like we need a line equation for this problem.

In conclusion, Inferred from a graph: the shape of the graph ought to be that of an unbroken line.

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Answer:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

Explanation:

Equation:

[tex]V = \dfrac{4}{3} \pi r^3[/tex]

Task: make pie the subject.

cross multiply

[tex]\sf \dfrac{3V}{4} = \pi r^3[/tex]

divide both sides by r³

[tex]\sf \dfrac{3V}{4} \div r^3= \pi r^3 \div r^3[/tex]

simplify following

[tex]\sf \dfrac{3V}{4r^3} = \pi[/tex]

Hence:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

Answer:

[tex]\sf 2^{8}[/tex]

Step-by-step explanation:

             [tex]\sf \boxed{(a^m)^n=a^{m*n}}[/tex]

To convert to single power, multiply the powers.

[tex]\sf (2^2)^4= 2^{2*4}[/tex]

        [tex]\sf =2^8[/tex]

[tex] \bf\implies \: {2}^{8} [/tex]

The exponent (^) rule to solve this problem that is :

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \bf \longrightarrow \: {(a^{m})}^{n} = {(a)}^{m \times n} [/tex]

According to the question :-

[tex] \bf \longrightarrow \: {(2^{2}) }^{4} [/tex]

[tex] \bf \longrightarrow \: (2)^{2 \times 4} [/tex]

[tex] \bf\longrightarrow \: {2}^{8} \: \boxed { \bf \: \red{ ans.}}[/tex]

Answer:

Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.

Step-by-step explanation:

Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.

Hope this helps!

Answer:

or, 147-4x=180

or, 4x=180-147

or, 4x=33

or, x=33÷4

×=8.25

The pedestrian route that runs diagonally across the​ park will be [tex]6\sqrt{10}[/tex] miles long.

Here, we are given that a rectangular park is 18 miles long and 6 miles wide.

As we know that the angles formed by any two adjacent sides of a rectangle are all 90°, the diagonal divides the rectangle into 2 right angled triangles.

One side of the right angled triangle will be 18 miles and another side will be 6 miles.

According to the Pythagoras theorem,

[tex]hypotenuse^{2} = base^{2} + height^{2}[/tex]

Here, the diagonal will be the hypotenuse as it is the side opposite the right angle.

Hence we get the following equation-

[tex]hypotenuse^{2} = 18^{2} + 6^{2}[/tex]

[tex]hypotenuse^{2}[/tex] = 324 + 36

[tex]hypotenuse^{2}[/tex] = 360

Hypotenuse = [tex]\sqrt{360}[/tex]

Hypotenuse = [tex]6\sqrt{10}[/tex]

Thus, the pedestrian route that runs diagonally across the​ park will be [tex]6\sqrt{10}[/tex] miles long.

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From the graph, the average rate of change of the function is negative, which means that the number of farmland is decaying.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

This problem is incomplete, and the options were not found on a search engine, but from the graph, what we can see is that the graph is decaying, that is, for any interval [a,b], f(a) > f(b), hence the average rate of change of the function is negative.

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Answer:

Yes, the cube root of a negative number can be calculated.

Step-by-step explanation:

Answer:

The formula for scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape

To simplify the ratio just reduce it to the simplist form.

Divide each number in the ratio by the same amount to get the answer.

Step-by-step explanation:

hope this helps :)