folue the √(x-3) ³ - 64 equation √(ac-3)solve the equation​

The linear equations of the lines are y = 1/3x and y = 4x + 17, respectively

The parallel line

The equation is given a

x - 3y = 9

So, we have

3y = x - 9

y = x/3 - 3

Slope = 1/3

The slopes of parallel lines are equal

So, the slope of the required line is 1/3

The equation is then calculated as

y = mx + c

So, we have

y = 1/3x + c

Using the points, we have

2 = 1/3 * 6 + c

c = 0

So, we have

y = 1/3x

The perpendicular line

The equation is given a

y + 1/4x - 5 = 0

So, we have

y = -1/4x + 5

Slope = -1/4

The slopes of parallel lines are opposite reciprocals

So, the slope of the required line is 4

The equation is then calculated as

y = mx + c

So, we have

y = 4x + c

Using the points, we have

5 = 4(-3) + c

c = 17

So, we have

y = 4x + 17

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The fish population in Lake Collins is estimated to be about 938 fish in 2009.

Given that:

Rate, r = 4%

Let P(x) be the population of fish in Lake Collins after x years, where x is measured from 2004. Since the fish population is decreasing at a rate of 4% per year, we can write:

P(x) = 1,150 (0.96)ˣ

To find the population in 2009 (which is 5 years after 2004), we substitute x = 5 into the equation:

P(5) = 1,150 * (0.96)⁵

P(5) = 1,150 * 0.8154

P(5) = 937.8 or 938

Therefore, the fish population in Lake Collins is estimated to be about 938 fish in 2009.

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Garnier's Opera House is a revival of the Gothic style.

The Palais Garnier usually referred to as the Garnier Opera House is a renowned opera house in Paris, France. Charles Garnier, a French architect, created the design which was finished in 1875.

The opera house is well-known for its spectacular Beaux-Arts and Gothic-inspired architecture as well as for its extensive history and connections to some of the most well-known composers and performers of the 19th and 20th centuries.

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4.5 radians when rounded off to the nearest tenth approximates a degree angle of 257.83.

To turn an angle from radians into degrees, is achieved relying on the following established formula:

Angle in Degrees = Angle in Radians * (180 / π)

where

π (pi) is approximately equal to 3.14159.

For conversion of 4.5 radians we have  

Angle in Degrees = Angle in Radians * (180 / π)

substituting to the above formula

Angle in Degrees = 4.5 * (180 / π)

use a calculator to get the value of pi:

Angle in Degrees = 4.5 * (180 / π)

Angle in Degrees ≈ 257.821 (rounded two decimal places)

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The measures of the three angles are 30°, 86° and 64°.

Given that, in a triangle the sum of the measures of the second and third angles is five times the measure of the first angle.

The third angle is 22 more than the second.

If x, y, and z represent the measures of the first, second, and third angles, respectively, we need to find the measure of the angles.

So,

y + z = 5x...........(i)

z - y = 22...........(ii)

x + y + z = 180...........(iii)

Use eq(i) in eq(ii)

x + 5x = 180

6x = 180

x = 30°

Put x = 30 in eq(iii)

z + y = 150.......(iv)

add eq(ii) and eq(iv)

2z = 172

z = 86°

Put the values of z and x in eq(iii)

30° + 86° + y = 180°

y = 64°

Hence, the measures of the three angles are 30°, 86° and 64°.

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The approximate population after 3 years is 1526.

Given that, principal=820, rate of interest=23% and time period=3 years.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Here, population after 3 years is 820(1+23/100)³

= 820×1.23³

= 820×1.860867

= 1525.91094

≈ 1526

Therefore, the approximate population after 3 years is 1526.

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The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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The calculated measure of m∠DEF is 45 degrees

From the question, we have the following parameters that can be used in our computation:

The image of the protractor

The reading from the protactor is

Angle = 0 degrees + 45 degrees

Evaluate the sum

So, we have

Angle = 45 degrees

This reading represents the angle DEF

Hence, the measure of m∠DEF is 45 degrees

The required difference cannot be calculaed from the given parameter

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The domain of the function in the graph can be written as: -4 ≤ x < 4

or [-4, 4)

To identify the domain look at the horizontal axis. Remember that the domain is the set of the inputs, and the inputs go in the horizontal axis (or the x-axis)

You can see that there is a closed dot (which means that the value belongs to the domain) at x = -4, and there is a open dot (which means that the value does not belong to the domain) at x = 4.

Then the domain of the graph is:

-4 ≤ x < 4

Or, written in interval form, it is [-4, 4)

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Answer:

To determine whose mix will be more watery, we need to calculate the percent of water in each mix.

For Cameron's mix, the total amount of liquid (water + lemon mix) is 3 cups + 2 cups = 5 cups. The percent of water in the mix is (3/5) x 100% = 60%.

For Sophie's mix, the total amount of liquid is 9 cups + 4 cups = 13 cups. The percent of water in the mix is (9/13) x 100% ≈ 69%.

Therefore, Sophie's lemonade will be more watery.

Answer:Sophie mix is more watery

Step-by-step explanation:Cameron—->3 cups water and 2 cups lemon

Sophie——>9 cups water and 4 cups lemon

Cameron = 3/(3+2)*100=60%

Sophie=9/9+4*100=9.*7.5=69.2%

Hence Sophie uses more water

Answer:

its d

Step-by-step explanation:

The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

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The equivalent value of the expression are A = -8x + 19 , B = -6x - 2x + 19

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 14 - 8x + 5

On simplifying , we get

A = -8x + 19

And , the equivalent values of the expression are

B = -6x - 2x + 19 = A

C = -8 ( x - 2 ) + 3

Hence , the expression is A = -8x + 19

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The solution to the given inequality expression is: x ≤ -2

The inequality expression is given as:

5(0.5)ˣ + 1 ≤ 21

Subtract 1 from both sides to get;

5(0.5)ˣ ≤ 20

Divide both sides by 5 to get:

(0.5)ˣ ≤ 4

Using logarithm we have:

x In 0.5 ≤ In 4

x ≤ In 4/In 0.5

x ≤ -2

Thus, that is the solution of the inequality expression

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Answer:

31x3

Step-by-step explanation:

there was 93 people who attended the second meeting

The probability that a randomly selected bag contains fewer than 1050 chocolate​ chips is 0.84.

(a) The probability of a randomly selected bag containing between 1000 and 1400 chips is 0.75.

This is calculated using the standard normal distribution formula:

P(1000 < X < 1400)

= P(z < (1400-1252)/129) - P(z < (1000-1252)/129)

= 0.75

(b) The probability of a randomly selected bag containing fewer than 1050 chips is 0.26.

This is calculated using the standard normal distribution formula:

P(X < 1050) = P(z < (1050-1252)/129)

= 0.26

(c) The proportion of bags containing more than 1175 chips is 0.84.

This is calculated using the standard normal distribution formula:

P(X > 1175) = P(z > (1175-1252)/129)

= 0.84

(d) The percentile rank of a bag containing 1050 chips is 26%.

This is calculated using the standard normal distribution formula:

P(X < 1050) = P(z < (1050-1252)/129)

= 0.26

Therefore, the probability that a randomly selected bag contains fewer than 1050 chocolate​ chips is 0.84.

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The temperature at the end of 5 minutes is given as 87.09 F

71 = 60 + (135 - 60) * e^(-2k)

11 = 75 * e^(-2k)

e^(-2k) = 11/75

-2k = ln(11/75)

k = -0.5 * ln(11/75) ≈ 0.2036

Now we have the value of k, we can find the temperature of the object at the end of 5 minutes, T(5):

T(5) = 60 + (135 - 60) * e^(-0.2036 * 5)

T(5) = 60 + 75 * e^(-1.018)

T(5) ≈ 60 + 75 * 0.3612

T(5) ≈ 60 + 27.09

T(5) ≈ 87.09

The temperature at the end of 5 minutes is given as 87.09 F

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The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The coordinate of B'  after the sequence of transformations is B' = (-6, 2)

From the question, we have the following parameters that can be used in our computation:

B = (-1, 1)

The sequence of transformations is given as

When applied, we have

Translate (‒5, ‒3)

B = (-1 - 5, 1 - 3)

B = (-6, -2)

Reflect over the x-axis

B' = (-6, 2)

Hence, the image is B' = (-6, 2)

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Answer:

$1.16

Step-by-step explanation:

Area of the circle

a = [tex]\pi r^{2}[/tex]

a = (3.14)[tex]1.5^{2}[/tex]

a = 3.14(2.25)

a = 7.065

Area of the triangle

a = 1/2bh

a = 1/2(1.5)(1)

a = .75

There are two triangle so the blue area is 1.5 [tex]ft^{2}[/tex]

.33 x 1.5 = .495  This is the cost of the blue paint

The circle minus the triangle is the area of the whit part

7.065 - 1.5 = 5.565

5.565 x .12 = .6678

The total cost of paint will be .495 + .6678 = 1.1628 Rounded to the nearest cent is $1.16

Helping in the name of Jesus.

The first four terms of the sequence are -5, -3, 1 and 3

From the question, we have the following parameters that can be used in our computation:

Expression = n(n-1)-5

Set n = 1 to 4

So, we have

f(1) = 1(1 - 1) - 5 = -5

f(2) = 2(2 - 1) - 5 = -3

f(3) = 3(3 - 1) - 5 = 1

f(4) = 4(3 - 1) - 5 =3

Hence, the first four terms are -5, -3, 1 and 3

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The total number of people in attendance was 400 people in total.

Let:

x be the no of grandparents

y be the no of parents

z be the no of children

Since there are 400 people total, so we can write the equation:

x + y + z = 400

We also know that there were twice as many parents as grandparents, so we can write the equation:

y = 2x

We know that there were 50 more children than parents, so we can write the equation:

z = y + 50

Now we have a system of three equations with three variables:

x + y + z = 400

y = 2x

z = y + 50

We can solve this system using substitution method

First, we can use the second equation to express y in terms of x:

y = 2x

Next, we can use the third equation to express z in terms of x:

z = y + 50

z = 2x + 50

Now we can substitute these expressions for y and z into the first equation:

x + y + z = 400

x + (2x) + (2x + 50) = 400

5x + 50 = 400

5x = 350

x = 70

So there were 70 grandparents in attendance.

Using the second equation, we can find the number of parents:

y = 2x

y = 2(70)

y = 140

So there were 140 parents in attendance.

Using the third equation, we can find the number of children:

z = y + 50

z = 140 + 50

z = 190

So there were 190 children in attendance.

Therefore, the total number of people in attendance was:

70 grandparents + 140 parents + 190 children = 400 people in total.

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The ratio of Murkas age to Ivans age is M : I = 6 : 1

Given data ,

Let Murkas age be M and Ivans age be I

Given that 1/3 of Murka's age is twice as much as Ivan's age

So ,

1/3 ( M ) = 2 ( I )

On simplifying the proportion , we get

Multiply by 3 on both sides , we get

M = 6 ( I )

Divide by I on both sides , we get

M / I = 6

Hence , the proportion is 6 : 1

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Answer:

54 mm tall and 96 mm wide.

Step-by-step explanation:

Since our scale factor is 6, you simply multiply your given values by the scale factor.

9 × 6 = 54

16 × 6 = 96

The volume of the cylinder is approximately 1026 ft³. The Option B is correct.

To find the volume of a cylinder, we need to use the formula: V = πr² where V = volume, r radius and h = height.

Radius = diameter/2

Radius = 10ft/2

Radius = 5ft

Height of the cylinder, which is 13ft.

Now we can substitute these values into the formula to find the volume:

V = π(5ft)²(13ft)

V = π(25ft²)(13ft)

V = 25π(13ft³)

V ≈ 1025.92ft³

Full question "Find the volume of the cylinder. Diameter is 10ft, Height is 12ft. Answer choices O 1021 ft³ O 1026 ft³ O 4082 ft³ 4084 ft³"

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The surface area of the triangular prism is 191 cm².

The surface area (SA) of a triangular prism is given by the formula:

SA = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

First, we need to find the area of the triangular base.

Using the formula for the area of a triangle:

A = (1/2)bh = (1/2)(5 cm)(4 cm) = 10 square centimeter

Next, we need to find the perimeter of the base:

P = 5 cm + 6 cm + 8 cm = 19 cm

Now we can use the formula for the surface area of a triangular prism:

SA = 2A + Ph

= 2(10 cm²) + (19 cm)(9 cm)

= 20 cm²+ 171 cm²

= 191 cm²

Therefore, the surface area of the triangular prism is 191 cm².

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ans.= 10

we know that

formula for mean =  dividing the sum of all values in a data set by the number of values.

22 = 15+20+X+30+35/5

solving x

we x =10

hence the x = 10

A statement to describe the transformation include the following: B. to create the image, the preimage was reflected across the y-axis.

In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given triangle MTR, we have the following coordinates:

Coordinate T = (-4, 2)   →  Coordinate T' = (-(-4), 2) = (4, 2).

In this scenario and exercise, a line of reflection that would map triangle MTR onto itself is an equation of the line that passes through the origin i.e a reflection over or across the y-axis or line x = 0.

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Answer:

6.4

Step-by-step explanation:

First add 10 to 22 to get 32

Then divide 32 by 5 to get x