What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) -4 = 0 as a quadratic equation?
Ou= (x + 5)
Ou= (x-5)
u = (x + 5)²
O u =(x-5)²

The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

Transformation is the technique used to change the position of a figure on an xy-plane.

Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

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Answer: 1 bottle, 6 bottle, 8 bottle

Answer: 1 bottle for $1.07, 8 bottles for $8.56 and 6 bottles for $6.42

The statement of expressions is two terms and three factors.

According to the question, the statement that teaches us about expression is made up of two terms, each of which has three factors.

The ABC and DEF expressions define the expression of two terms, each of which comprises two elements.

As a result, the answer is two terms and three factors.

Therefore, the answer is two terms and three factors.

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Using translation concepts, a stretch of a decay exponential function is given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

An exponential decay function is given by:

[tex]y = ab^x[/tex]

In which |b| < 1.

A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

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Answer:

x=1

Step-by-step explanation:

Answer:

Step-by-step explanation:

A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?

32 : 2 + 14 = 30

Answer:

Step-by-step explanation:

Since there are 32 passenger cabins, each half of the wheel has:

It means the opposite cabins on the Ferris wheel have number difference of 16.

If one of the cabins has a number 14, the opposite cabin has number of:

20 gallons is consumed from the first car and 25 gallons is consumed from the second car.

A mathematical statement that relates two algebraic expression using an equal sign is called an equation.

It is given that

Fuel Efficiency of the first car is 20 miles per gallon of gas

Fuel Efficiency of the second car is 40 miles per gallon of gas

Total miles travelled = 1400 miles

Total gas consumption = 45 gallons

Let the gallons consumed from the first car is x

then the gallons consumed by the second car is (45 - x)

The equation formed will be

20* x + 40 * (45 -x) = 1400

20x +1800 - 40x = 1400

-20x = -400

x = 20

Therefore 20 gallons is consumed from the first car and

45-20 = 25 gallons is consumed from the second car.

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Answer:

x = 8

Step-by-step explanation:

Every angle in an EQUILATERAL triangle = 60°

so   9x -12 = 60

       9x = 72

         x = 8  

Step-by-step explanation:

[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]

[tex]9x = 60 + 12[/tex]

[tex]9x = 72[/tex]

[tex]x = \frac{72}{9} \\ [/tex]

[tex]x = 8[/tex]

hence the value of x is 8...

A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.

Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

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1. y= 2x

2.  (0, 5)

3. y  = 3x + 12

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. let us take (0,0) and (1, 2)

m= 2-0/1-0

m= 2

So equation of line

y- 0 = 2(x-0)

b

2. y= 3x+5

passes through (0, 5)

3. y= 3x+5

  m = 3

We need the equation of a line with slope 3 that passes through point (0, 12).

y - y1 = m(x - x1)

y - 12 = 3(x - 0)

y - 12 = 3x

y  = 3x + 12

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Using the combination formula, it is found that there are 16,800 ways for them to do it.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

Hence the number of ways is:

[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]

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Hello,

Answer:

C. (b - c)(a + b)

Step-by-step explanation:

A = (b - c)(a - c)

A = ba - bc - ac - c² ≠ ab + b² - ac - bc

B = (b + a)(b + c)

B = b² + bc + ab + ac ≠ ab + b² - ac - bc

C = (b - c)(a + b)

C = ba + b² - ca - cb

= ab + b² - ac - bc

→ That is answer C

Answer:

337.5Ft

Step-by-step explanation:

Answer:

33:21

Step-by-step explanation:

The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.

The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.

The utilization of two or more additional numbers that compares is known as the ratio.

The expression is given below.

⇒ 12 x 2 / 7

⇒ 24 / 7

Divide 54 into the ratio 11:7.

⇒ 54 x 11 / (11 + 7)

⇒ 594 / 18

⇒ 33

⇒ 54 x 7 / (11 + 7)

⇒ 378 / 18

⇒ 21

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The equation [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex] has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Given function,
= [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex]
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).

Given function has x intercept at (14, 0) and y intercept at (0, 6).

Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).

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500 people

200 people wearing red shirts

200x15%= 30 people

30 =6% of 500

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.

Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:

10 - 8 < s > 8 + 10

2 < s > 18

The range of values for the third side is: A. 2 < s < 18.

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Answer: A. 2 < s < 18.

Step-by-step explanation:

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

The correct answer is option D which is the side length will be (64n)¹⁸.

The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.

Given that:-

The sides of the square will be calculated as follows:-

A = (64n)³⁶

a² = (64n)³⁶    Here a = Side of the square.

a = √ (64n)³⁶

a = 64n¹⁸

Therefore the correct answer is option D which is the side length will be (64n)¹⁸.

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Step-by-step explanation:

So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]

Distribute the multiplication on the left side:

[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]

Distribute the multiplication on the right side:

[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]

Add like terms on the left side:

[tex]100a+10b+c+111=130a+13b+1.3c[/tex]

Subtract 100a, 10b, and c from both sides

[tex]111=30a+3b+0.3c[/tex]

So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.

So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value

111 = 30(3) + 3b + 0.3c

111 = 90 + 3b + 0.3c

Now subtract the 90 from both sides

21=3b+0.3c

Well 3 can fit into 21, 7 times!

21 = 3(7) + 0.3c

21 = 21 + 0.3c

subtract 21 from both sides

0 = 0.3c

and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant

c = 0

This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!

part b:

So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.

So let's start with the same equation except this time instead of 1.3 it's 1.4

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]

Distribute on the left side;

[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]

Distribute on the right side:

[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]

Add like terms on left side:

[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]

Subtract 100a, 10b, and c from both sides:

[tex]111 = 40a + 4b + 0.4c[/tex]

Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.

So only 2 40's can fit in 111 without going over the value

111 = 40(2) + 4b + 0.4c

Subtract 80 from both sides

[tex]31=4b+0.4c[/tex]

4 can fit into 31, 7 times

31 = 4(7) + 0.4c

31 = 28 + 0.4c

subtract 28 from both sides

3 = 0.4c

divide both sides by 0.4

7.5 = c.

Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The mean is the average of the numbers.

if you rearrange the data, you will get the order, 3,3,4,5,5.

you add all of them together to get the number twenty, then you divide 20 by the total number of data plots which is five. Then you get the number 4 which is your answer

3+3+4+5+5 = 20

20/5 = 4

The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).

Given sample size=1002 and confidence level of 99%.

In a sample with a number n of people surveyed with a probability of a success of π and a confidence level of 1-α, we have the following confidence interval of proportions.

π±z[tex]\sqrt{}[/tex]π(1-π)/n

in which z is the z score that has a p value of 1-α/2

n=1002,π=701/1002

So α=0.01, z is the value of Z that has a p value of 1-0.01/2=0.995, so Z=2.575.

Lower limit=π-[tex]z\sqrt{}[/tex]π(1-π)/n

=0.6996-2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]

=0.6623

Upper limit=π+[tex]z\sqrt{}[/tex]π(1-π)/n

= 0.6996+2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]

=0.7369

Hence the 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).

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Lets simplify the given problem,

The speed with which the plane flies = 350 mph

The direction of flight of the plane = N 40° E

The speed with which the wind blows = 40 mph

The direction in which the wind blows = S 40° E

Therefore, we have;

The resolution of the components of the motion of the plane, given as follows;

= 350 × sin(40°)·i + 350 × cos(40°)·j

The resolution of the components of the motion of the wind, given as follows;

= 40 × sin(40°)·i - 40 × cos(40°)·j

The resultant motion of the plane is given as follows;

= 262.563·i + 254.435·j

The direction of motion of the plane = tan⁻¹(262.563/254.435) ≈ N 45.9° E

Therefore, the plane's drift = Plane's Track - Plane's Heading  = N 45.9° E - N 40° E ≈ 5.9° ≈ 5.89°

Drift Angle of the plane is 5.89 degree.

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Answer: A 5.9

Step-by-step explanation:

cuz i said so

The radius or any additional information related to the circle to assist in calculating the length of the 40-degree arc.

To find the length of a 40-degree arc, to know the radius or diameter of the circle to which the arc belongs. Once you have that information, use the formula to find the arc length:

Arc Length = (θ / 360) × 2 ×π ×r

Where:

θ = Central angle in degrees (40 degrees in this case)

r = Radius of the circle

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Let's take an mathematical example

Let's find the ratio of volume of a cone and cylinder if radius and height are same for both .

See

The ratio is 1:3

#Example 1

Ratio of gems=3:4

#Example 2

Ratio of ocean to continents=5:7

Note:-

Two examples are already provided on your another question .You may refer there

Answer:

1960

Step-by-step explanation:

1960

times 56 times 7 time 5 = 1960

Answer:

[tex]y = 3x + 40[/tex]

Step-by-step explanation:

The slope-intercept equation takes the form

[tex]y = mx + c[/tex]

Where m is the gradient, and c is the y-intercept.

If we assume we are plotting a graph where the X axis is time, and the y axis is distance, and we know our time value starts at 40, then we can say that our y intercept value is 40.

Next, let's figure out how far she has travelled. 130-40 = 90, and she has travelled this distance in 30 seconds, so dividing 90 by 30, we know that she is travelling 3 feet a second. This leaves us with a gradient of 3.

Putting these two values together, we can find the final form of the equation to be:

[tex]y = 3x + 40[/tex]

Answer:

d = 3t + 40

Step-by-step explanation:

So, since you have a constant speed you're going to have a linear equation, which was also stated in the question. So it's asking for slope-intercept form which is expressed as: y=mx+b, where m=slope, and b=y-intercept. So it's important to know what these two things mean in certain contexts. In every single case, the slope is how much the y-value is changing as x increases by 1, and in this specific case, the distance is what is changing as time goes by. So this means that the distance would be the y-value, and x would be the t variable (time). And remember how it mentioned "constant speed", this means as one second passes, the distance increases by a constant distance. We can solve for this by using the given information.

She's already 40 feet from her starting position, and after 30 seconds she's 130 feet from her starting position. This means she traveled (130 - 40) feet, because she was already 40 feet away from her starting position. This means she traveled 90 feet. Now to find how much she travels in a second, divide it by the time which is 30 seconds, and you get: 90 feet / 30 seconds = 3 ft/s, this is her constant speed. This is the slope of the equation. So now we have the equation: d = 3t + b. Now all we need to find is the y-intercept

The y-intercept in this context, is how far away she is from her starting position initially. This is given in the problem, it's 40 feet. She's already 40 feet away when 0 seconds have passed. So this gives us the equation: d = 3t + 40

The number of pizza lunches sold more based on the survey is 5.

The information is incomplete and an overview will be given.

Let the number of pizza lunches sold be 24.

Let the number of hot dog lunches be 19.

Therefore, the number of pizza lunches sold more will be:

= 24 - 19

= 5

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Answer: C, 7

Step-by-step explanation:

Answer:

  1 ÷ 3

Step-by-step explanation:

You want 1/3 written as a quotient.

The quotient of A and B is "A divided by B." There are two ways to write this using math symbols:

  A/B

  A÷B

The fraction 1/3 is already written as a quotient. This set of symbols can be read as either of ...

The other way to write the quotient is ...

  1 ÷ 3

__

Additional comment

When you learn about exponents, you learn another way to write the quotient of A and B is ...

  A·B⁻¹

<95141404393>

Answer: 65

Step-by-step explanation:

By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]

So, by the Pythagorean theorem,

[tex]x=\sqrt{60^2 + 25^2}=65[/tex]