Use the locus definition of a circle and dilations to prove that all circles are similar.

Answer:

2(3-8y)=

6-16y

Step-by-step explanation:

FA recursive formula allows us to find each term in the geometric sequence using the previous term. Each new term is the product of the common ratio for that sequence and the previous term of that unknown or to-be-found term. If the common ratio is 9, each term is nine times the previous term.

The general term for the geometric sequence is

an= a1 * r ^ (n-1)

Where "an" refers to the nth term of the sequence, a1 is the first term known as the sequence, and r is the common ratio, n is its position or the number.

Now the term is,

where a₁ = 1 and r = 2

Sequence: 1, 2, 4, 8, 16, ....

3rd value: 4

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The function that models the horizontal shink of f(x) by a scale factor k = 3 is:

g(x) = |3*x| + 5

Here we want to apply a transformation to a given function where the transformation is a shrink.

For a function f(x), a horizontal shrink (or compression) of scale factor K is written as:

g(x) = f(k*x)

In this case we have the absolute value function:

f(x)= |x| + 5

And we want to apply an horizontal shrink of scale factor k = 3, so we will have a new function defined as:

g(x) = f(3*x)

If we replace f(x) by the function above we will get:

g(x) = f(3*x) = |3*x| + 5

So we conclude that the transformed function is just:

g(x) = |3*x| + 5

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Answer:

[tex] - 1 \geqslant x \geqslant 2[/tex]

The equation of the line 4x = 2 + y expressed in slope-intercept form is y = 4x - 2 with a slope equal to 4.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 4x = 2 + y, express it in slope-intercept form by isolating the variable y in one side.

4x = 2 + y

y = 4x - 2

Hence, the equation of the line in slope-intercept form is y = 4x - 2 where the slope, m, is equal to 4.

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The term "total moles of a solute contained in a kilogram of a solvent" exists utilized to define molality. The amount of water required exists 252ml.

Given: Mass of urea = 25 g

Required Molality = 1.65m

Density of water = 1000 kg/m³

Formula for urea = CH₄N₂O

Mass of Carbon atom = 12 u

Mass of Oxygen atom = 16 u

Mass of Nitrogen atom = 14 u

Mass of Hydrogen atom = 1 u

Molecular Mass of Urea

= (1)12 + (4)1 + (2)14 + 16

= 12 + 4 + 28 + 16

= 60 u

Molar mass = 60 g

No of moles = Given mass/Molar mass

No of moles = 25/60 = 5/12

Molality = Mass of solute / Mass of solvent(g)

Let the weight of water be x kg

1.65 = (5/12)/x

simplifying the above equation, we get

1.65 x = (5/12)

x = (5/12) / 1.65

x = 5 / 1.98

x = 0.2525

Mass of water = 0.252 kg.

Volume of water = 0.252 ÷ 1000 kg/m³

= 0.000252 m³

= 0.252 liters

= 252 ml

Therefore, the require amount of water is 252 ml.

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It should be noted that the place the square root of 75 minus 13 would be plotted on a number line is C. Between −4 and −5, but closer to −4.

It should be noted that a square root simply means the numbers that can be multiplied by itself that will give the original number.

It should be noted that the square root of 75 is 8.66. Therefore, square root of 75 minus 13 would be:

= ✓75 - 13

= 8.66 - 13

= -4.3397

Therefore, it should be noted that the place the square root of 75 minus 13 would be plotted on a number line is vetween −4 and −5, but closer to −4

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Answer:

inequality form would be x<-6 or x>-6

Answer:

v= cube root of 12 or 2. 2894 or 2.3

Step-by-step explanation:

cube root of v³ = v

cube root of 12 = ³√12

Answer:

Step-by-step explanation:

Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.

For any two given perpendicular lines, they must have slope (m) values that are negative reciprocals of each other. The equation of any line can be written in slope-intercept form as, y = mx + b, where m is the slope of the line.

Given the equation, 4x - 3y = -8, rewrite in slope-intercept form:

-3y = -4x - 8

-3y/-3 = -4x/-3 - 8/-3

y = 4/3x + 8/3

This means that the line has a slope of 4/3. Thus, the slope of the line that is perpendicular to the given line would be the negative reciprocal of 4/3, which is: -3/4.

Thus, we can see that Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.

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The geometric mean of two positive numbers can be determined by multiplying the numbers and taking their square root.

Geometric mean is the mean or average value which expresses the central tendency of the set of numbers by taking root of the product of their values. In other words, we multiply the n values and take the nth root of the numbers. Geometric mean can also be expressed as the nth root of the product of n numbers.

The formula for finding geometric mean is:

GM = n√ x1*x2*x3…xn

Let the two terms be 2 and 8. Hence, x1=2, x2=8 and n=2.

GM = √2*8=√16=4

Hence, the geometric mean of the two chosen positive number 2 and 8 is 4.

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The equation of the circle that passes through the point (-5 , 0) and has a center located at the origin is x^2 + y^2 = 25

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-5 , 0).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-5 - 0)^2 + (0 - 0)^2

radius= √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 5

(x - 0)^2 + (y - 0)^2 = 5^2

x^2 + y^2 = 25

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The given statement exists true that "The orthocenter of a right triangle is always found at the right angle's vertex".

The orthocenter is the point at which the triangle's three altitudes cut or intersect. The altitude is the line drawn from the triangle's vertex that is perpendicular to the opposite side. There are three altitudes because the triangle has three vertices and three sides.

The given statement exists true that "The orthocenter of a right triangle is always located at the vertex of the right angle".

The altitudes from the two non-right vertices (A and B) will always be the legs of the triangle, which intersect at the vertex containing the right angle, as shown in the right triangle below (C). Because the altitude to the triangle's hypotenuse originates at the vertex, the three altitudes (the red rays) intersect there. As a result, the vertex of a right triangle is always the orthocenter.

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Einstein's mass energy relation, and the formula for finding the percentage error gives;

7) a) 9.0 × 10¹⁶ Joules

b) The bulb could be powered for approximately 47533146.96 years

8) 16.46%

9) The possible values are;

61.093 Joules and 96.77 Joules

Percentage error is the ratio of the difference between estimated value and the actual value to the actual value expressed as a percentage.

7) a) The Einstein mass energy relation is presented as follows;

E = m•c²

The speed of light, c = 3×10⁸ m/s

The mass, m = 1 kg, gives;

E = 1 kg × (3×10⁸ m/s)² = 9.0 × 10¹⁶ Joules

b) Energy consumption of the light bulb = 60 J/sec

The duration, t, the light bulb will remain lit is therefore;

8) Percentage error, %error, is found as follows;

%error = ((Approximate value - Actual value)/(Actual value)) × 100

Appreciate value = 46,620 km

Actual value = 40,030.2 km

Which gives;

%error = ((46,620 - 40,030.2)/(40,030.2))×100 ≈ 16.46%

9) The calculated value of the kinetic energy = 74.9 J

The observed error in the calculation = 22.6%

Required; The two possibilities for the correct kinetic energy

Solution;

E% = ((Approximate value - Actual value)/(Actual value)) × 100

Taking the calculated value as the approximate value, and the correct value as the actual value, we have;

22.6% = ((74.9 - Actual value)/(Actual value)) × 100

(22.6/100)×Actual value = 74.9 - Actual value

Actual value + 0.226×Actual value = 74.9

1.226 × Actual value = 74.9

Which gives;

The actual value can also be given as follows;

22.6% = ((Actual value - 74.9)/(Actual value)) × 100

Actual value - 0.226×Actual value = ,74.9

Actual value = 74.9 J/(1-0.226) ≈ 96.77 J

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A four seat Cessna airplane does an average of 5.84 miles per gallon of fuel traveling from Olympia to Hoquiam

Given that a four seat Cessna airplane uses an average of 11 gallons of avgas per hour, and it traveled from Olympia to Hoquiam for 28minutes, then we can solve for the amount of fuel it consumed for that flight.

amount of fuel = average consumption x time

amount of fuel = 11 gallons of avgas per hour x 28 minutes

amount of fuel = 11 gallons of avgas per hour x (28/60)h

amount of fuel = 77/15 gallons

If the flight from Olympia to Hoquiam is 30 miles and the amount of fuel used by the Cessna airplane is 77/15 gallons, then

average number of miles per gallon of fuel = distance traveled / amount of fuel consumed

average number of miles per gallon of fuel = 30 miles / (77/15 gallons)

average number of miles per gallon of fuel = 450/77

average number of miles per gallon of fuel = 5.84 miles / gallon of fuel

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21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2) so option (D) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear b. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given the equation,

17x⁵+3x²+2-(-4x⁵+3x³-2)

⇒ 17x⁵+3x²+2 + 4x⁵- 3x³+ 2

⇒ 17x⁵ + 4x⁵ - 3x³ + 3x² + 4

Hence "21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2)".

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The equation best represents the population, y, of Midtown .x years after 1990 is x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)    

Based on the given conditions, stated: x *(1+2%) (199-1990) = 2050

Calculate the sum or difference: x*1.02-1791 = 2050

Divide both sides of the equation by the coefficient of variable: Inferentially, when you divide, you assume that the number you are dividing by is not equal to zero. By dividing, you rule out the chance that the given number is zero, which may result in the elimination of the right answers. x = 2050 / 1.02-1791    

Simplify using negative exponent rule: For every number “a” with negative exponents “-n”, take the reciprocal of the base number and multiply the value according to the value of the exponent number.  For every number “a” in the denominator with negative exponent “-n” (i.e.,) 1/a-n, the result can be written in the form of a × a ×.. n times.

a-n = 1/an : x= 2050*1.021791

Convert decimal to fraction: x = 2050* (102/100)1791

Cross out the common factor: x = 2050 * (51/50)1791

Simplify using exponent rule with same exponent: (ab) n = an. bn  

x= 2050 * 511791 / 501791

Write a single fraction: x= 2050 * 511791 /501791

Hence, the equation represents the population is,  x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)  

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Answer:

10

Step-by-step explanation:

5 outside the star 5 inside the star

Answer:

This is a survey

Step-by-step explanation:

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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The expression that is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 is D. 9^8

It should be noted that this is a question relating to indices.

It should be noted that we have to count the number of 9s that we gave in this case.

Therefore, 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 will be equivalent to 9^8.

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Which expression is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9? A. 9 B. 9 C. 99,999,999 D. 9^8

Answer:

C

Step-by-step explanation:

there are 8 of 9s so it is 99,999,999 tricky question!

Augusto has 24 ways to put one coin in each pocket.

Permutation:

Permutation is the way arranging the objects or numbers in order.

It can be calculated using the formula,

ₙPₓ = n!/(n - x)!

where,

ₙPₓ   = number of combinations

n = total number of objects in the set

x = number of choosing objects from the set

Given,

Augusto has 3 pockets and 4 different coins.

Here we need to find how many ways can he put one coin in each pocket.

We know that,

Augusto has 4 different coins that he is choosing 3 at a time.

So, it can be written as,

The number of ways to put one coin in each pocket is the permutation of 4 coins taken 3 at a time.

Therefore, the number of permutations is calculated as,

=> ₄P₃ = 4! / (4 - 3)!

=> ₄P₃ = 4! / 1!

=> ₄P₃ = 4 x 3 x 2 x 1

=> ₄P₃ = 24

Therefore, there are 24 ways to put one coin in each pocket.

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The simplification of the given expression 5(a -2b) -3(a -2b) is

2(a - 2b).

According to the given question.

We have an expression 5(a -2b) -3(a -2b).

As we know that, the simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplificantion of the expression  5(a -2b) -3(a -2b) is given by

5(a -2b) -3(a -2b)

= 5a - 10b - 3a + 6b         (by distributive rule)

= 5a -3a -10b + 6b

= 2a -4b                              (adding and subtracting the like terms)

= 2(a - 2b)

Hence, the simplification of the given expression 5(a -2b) -3(a -2b) is

2(a - 2b).

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Answer:-1.5

Step-by-step explanation:

Answer:  The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Step-by-step explanation:  Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.

We are to find the price per pound of apples and bananas.

The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.

Then, according to the given information, the system of equations describing the situation is as follows:

Multiplying equation (i) by 2, we have

and multiplying equation (ii) by 3, we have

To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at

From equation (i), we get

Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Answer:Bro the answer is price per pound of apples is $1.25

and the price per pound of bannanas is $0.75

The polynomial function f(x) = (x - a)(x - b) is a quadratic function and values of a and b are 1 and - 1 respectively.

A polynomial is an algebraic expression that consists of variables and constants connected by arithmetic operations.

Given the polynomial function f(x) = (x - a)(x - b) and if we observe the graph we can see that the polynomial has two roots,

one at x = 1 and another at x = -1.

If x = 1 is a root of this polynomial we can write this in factor form as.

x = 1.

x - 1 = 0

And

x = -1.

x + 1 = 0.

∴ f(x) = (x - 1)(x + 1).

f(x) = x² - 1², So it is a quadratic function.

∴ Values of a and b are 1 and - 1.

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Answer:

Slope is -2/5

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

I used points (5,-3) (-10,3)

Taking into account the definition of a system of linear equations, she sold 102 student tickets.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

Knowing that:

the system of equations to be solved is

[tex]\left \{ {{A+S=145} \atop {5A+3S=521}} \right.[/tex]

Of the multiple methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable A from the first equation:

A= 145 - S

Replacing this expression in the second equation:

5(145 - S) + 3S= 521

5×145 - 5S + 3S= 521

725 - 5S + 3S= 521

-5S + 3S= 521 - 725

-2S= -204

S= (-204)÷(-2)

S= 102

Finally, she sold 102 student tickets.

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The number of bandages made from the fabric is 35 and the number of hours traveled is 14 hours

The given parameters are

Area of a bandage = 2 4/5 square inches

Area of fabric = 98 square inches

The number of bandages made from the fabric is calculated as

n = Area of fabric/Area of a bandage

This gives

n = 98/(2 4/5)

Evaluate

n = 35

Hence, the number of bandages made from the fabric is 35

Here, we have

Speed = 3 1/3 miles per hour

Distance = 46 2/3 miles

The number of hours traveled is calculated as

Time = Distance/Speed

So, we have

Time = (46 2/3)/(3 1/3)

Evaluate

Time = 14

Hence, the number of hours traveled is 14 hours

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