A quadratic function
y
=
f
(
x
)
y=f(x) is plotted on a graph and the vertex of the resulting parabola is
(
−
5
,
6
)
(−5,6). What is the vertex of the function defined as
g
(
x
)
=
f
(
x
−
2
)
g(x)=f(x−2)?

Answer:

(x,y)=(0,4)

Step-by-step explanation:

write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)

The cost of covering the felt with glitter is $3,317.60.

The cost of the outdoor carpeting to cover the patio is $240.

The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

52 x 58 = 3,016 in²

Cost of covering the felt = cost of the glitter per feet  are of the felt

$1.10 x 3,016 = $3,317.60

A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

Area of a trapezoid =   1/2 x (19 + 13) x 10

Area of a trapezoid =  1/2 x 32 x 10 = 160 ft²

Cost of the outdoor carpeting =cost per square feet x area of the patio

$1.50 x 160 = $240

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Answer:

Step-by-step explanation:

Hi,  Danna,  these are tough to figure out...

so,  first check to see if the 3 known angles add up to 180°,  they don't I checked, so, it tells us that the one angle 96° up at the top,  does not include ∠2 , which is good, b/c we now know 2 of the angles in that inner triangle.. and we know that a triangle adds up to 180° , so just find that last angle... the one opposite to ∠1 .... nice, if we get the ∠1' angle we can then also figure out ∠1

180-96-30=54

∠1' =54°

so ∠1= 180-54 =126°

we now know ∠1

use that , and that the next smaller triangle also adds up to 180

to find ∠2

∠2= 180-28-126=26°

∠1=126°

∠2 = 26°

:)  it's tough to think all of that through.  don't worry.  just keep working these , they will get easier.

Answer:

t = 1/9

Step-by-step explanation:

Combine multiplied terms into a single fraction

-3/2 (t) + 1/3 = 2/4

3t/2+ 1/3 = 2/4

Find common denominator

3 x 3t/6 + 2/6 = 2/4

Combine fractions with common denominator

3 x 3t/6 + 2/6 = 2/4

3x3t + 2

/ 6= 2/4

Multiply the numbers

9t+2

/6 = 2/4

Divide the numbers

9t+2 divided by 6 is 1/2

Multiply all terms by the same value to eliminate fraction denominators

6 x 9t+2 divided by 6 = 6 x 1/2

Cancel multiplied terms that are in the denominator

9t+2=3

Subtract 2 from both sides

9t+2-2=3-2

Simplify

9t=1

Divide both sides by the same factor

9t/9+=1/9

Simplify

t= 1/9

The required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

The outside-inside rule, the composite function rule, and the function of a function rule are all synonyms for this chain rule in differentiation. It is exclusively used to calculate the derivatives of composite functions.

The chain rule formula as shown below

d/dx ( f(g(x) ) = f' (g(x)) · g' (x)

The function is given in the question

g(z) = ln√(16- z² / 16+z²)

We have to differentiate g(z) = ln√(16- z² / 16+z²)

Differentiation with respect to z in the given function,

[tex]\frac{d}{dz}\left(\ln \left(\sqrt{\left(\left(\frac{16-z^2}{16+z^2}\right)\right)}\right)\right)[/tex]

We have to apply the chain rule of differentiation for finding derivatives,

[tex]\dfrac{1}{\sqrt{\dfrac{16-z^2}{16+z^2}}}\dfrac{d}{dz}\left(\sqrt{\dfrac{16-z^2}{16+z^2}}\right)[/tex]

[tex]-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

Therefore, the required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

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Answer:

  y = -3x +7

Step-by-step explanation:

You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).

The median will go through the midpoint of the segment opposite vertex A. That midpoint is ...

  D = (B +C)/2

  D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)

The slope of the line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

Then the slope of AD is ...

  m = (4 -1)/(1 -2) = 3/-1 = -3

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

The equation of the line with slope -3 through point A(2, 1) is ...

  y -1 = -3(x -2) . . . . . equation of the median line

This can be simplified to slope-intercept form:

  y = -3x +6 +1 . . . . . eliminate parentheses, add 1

  y = -3x +7 . . . . . slope-intercept equation of the median line

Answer:

25.12

Step-by-step explanation:

C = [tex]\pi[/tex]d  The d is the diameter.  This is the distance across the ha that goes through  the middle of the circle.

C 3.14(8)  The c stands for the circumference or the distance around the circle.  We generally use 3.14 for [tex]\pi[/tex]

C= 25.12

Answer:

1 intersection point at (11,96)

Step-by-step explanation:

Comment

The best way to solve this is to start with a graph. Then you can work out the actual intersection points.

The graph shows that there is only 1 intersect point. Let's try and find it.

Givens

y = (x - 5)(x + 5) = x^2 - 25

y = (x +1)(x - 3) = x^2 -2x - 3

If the intersect points are what you want, then the y value for both equations must be equal.

Solution

x^2 - 25 = x^2 - 2x - 3                     Subtract x^2 from both sides

x^2 - x^2 - 25 = x^2 - 2x - 3            Combine

- 25 = - 2x - 3                                   Add 3 to both sides

-25+3 = -2x - 3 + 3                           Combine

-22 = - 2x                                         Divide by - 2

 -22/-2 = x

x = 11

y = x^2 - 25

y = 11^2 - 25

y = 121 - 25

y  = 96

Answer:

Estimation and Confidence Intervals

Step-by-step explanation:

Just found it on a math website basically.

Answer:

Step-by-step explanation:

Solving word problems is always hard.  even w/o any learning challenges.  I'm kind of good at word problems but what I notice is that people have ways to ask word problem questions that can be very much about their own thought process, not really about the math.  Often it matters who is asking the word problem more than what the question is about for understanding the problem.   I don't think Josie will stand a chance with some peoples questions, like she'll solve it .01% of the time.  Not 85% of the time.  Just my perspective. :)

The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.

According to the question,

We have the following information:

The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line.

We know that the distance can not be negative in any case even when the points given are negative.

So, when we find the distance from -8 to 0, then we have the distance as 8 units.

Now, when we find the distance from 8 to 0, then we have the distance as 8 units.

Hence, the distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.

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The probability of either A or B is 0.48 and the probability neither A nor B would be 0.52

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event

probability A will occur pr(A) = 0.39, probability A will not occur pr(A') = 1 - 0.39 = 0.61,

Probability B will occur pr(B) = 0.42, probability B will not occur, pr(B') = 1 - 0.42 = 0.58

For mutually exclusive events if A will occur it means that B will not occur

So, probability either A or B is

= pr(A) x pr(B') + pr(B) x Pr(A')

= 0.39 x 0.58 + 0.42 x 0.61

= 0.4824 and to 2 decimal places the answer becomes 0.48

The probability neither A nor B is equal to 1 - 0.48 = 0.52

In conclusion the probability Either A or B will occur is 0.48 and the probability neither A nor B is 0.52

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A function that is negative over its entire domain can be having its values of x and y negative i.e. it can be (-3,-4). Yes, the graph has an X-intercept.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

X-intercept illustration:

Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

Calculate the x-intercept:

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

An illustration of y-intercept:

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

If we can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.

The x-intercept can be positive or negative.

Summary:

The location on the graph where our line crosses the x-axis is known as the x-intercept.

Positive numbers are to the right of the origin and negative numbers are to the left of the origin on the x-axis.

The location on the graph where our line crosses the y-axis is known as the y-intercept.

The side of a graph is negative:

Consider the numbers as being on the x-axis to help us remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.

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The smallest number of roses the customer will have to buy from each vendor is 24.

It should be noted that the multiple simply means the product of a number.

In this case, Kristen's Blossoms sells roses in groups of 8 and across town, Hector's Blooms sells roses in groups of 12.

The multiples of 8 = 8, 16, 24, 32 ....

The multiples of 12 = 12, 24, 36...

Therefore, the least number of roses is 24.

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Answer:

you multiply the numbers to find the area so W*H with times hight so the answer would be 6,250

Step-by-step explanation:

[tex] \sf - 18p = p^2+81 [/tex]

Moving all the expression to the Left side of the equation,

[tex] \sf -18p + p^2 - 81 = 0 [/tex]

To find the discriminant of the above equation we can simply use the Quadratic formula.

The discriminant formula of a quadratic equation[tex] \sf ax^2 + bx + c = 0 \: is \: (d = b^2 - 4ac )[/tex]

Where d represents the discriminant

a, b and c are the coefficient of the above equation,

p^2, here coefficient of p² is a = 1

-18p, here coefficient of p is b = -18

81, here the number is constant so coefficient is c = 81.

So simply by substituting the value of a, b and c in the above discriminant formula we get,

[tex] \sf d = b^2 - 4ac [/tex]

[tex] \sf d = (-18)^2 - (4 \times 1 \times 81) [/tex]

[tex] \sf d = 324 - 324[/tex]

[tex] \sf d = 0 [/tex]

Therefore, The discriminant of 18p = p² + 81 is 0.

Answer:

0 (zero)

Step-by-step explanation:

To find the discriminant of the quadratic equation -18p = p² + 81, we first need to rewrite the equation in standard form, which is of the form ax² + bx + c = 0.

[tex]\begin{aligned}-18p&=p^2+81\\p^2+81&=-18p\\p^2+81+18p&=-18p+18p\\p^2 + 18p + 81 &= 0\end{aligned}[/tex]

Compare the coefficients of the rewritten quadratic equation with the standard form:

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is given by the formula:

[tex]\boxed{\textsf{Discriminant} = b^2 - 4ac}[/tex]

Substitute the values of a, b, and c into the formula:

[tex]\begin{aligned}\textsf{Discriminant} &= (18)^2 - 4(1)(81)\\&=324-4(81)\\&=324-324\\&=0\end{aligned}[/tex]

Therefore, the discriminant of the given quadratic equation is zero.

The mean is  47.73.

The median is 46.

The dataset has no mode.

The midrange is 44.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Mean = (70 + 54 + 46 + 85 + 61 + 81 + 45 +  6 + 35+  39 + 3) / 11

= 525 /11 = 47.73

Median is a measure of central tendency that is used to determine the number that is at the center of a set of values when the numbers are arranged in either ascending or descending order.

3, 6, 35, 39, 45, 46, 54, 61, 70, 81, 85

The median is 46.

Mode is the most frequent number in a dataset. The jersey numbers only occur once. Thus, there is no mode.

Midrange is the average of the maximum and minimum values of the dataset.

Midrange = (maximum value + minimum value) / 2

Midrange = (3 + 85) / 2

Midrange = 88 / 2

Midrange = 44

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The distance between the top and the bottom of the iceberg is 417 feet.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The top of an Iceberg is 67 ft above sea level, while the bottom is 283 ft below sea level.

We can draw as,

Top of an iceberg

|

|

|   (67 feet)

|

Sea level

|

|  (283 feet)

|

|

Bottom of the iceberg

The distance above the sea level = 67 feet

The distance below the sea level = -283 feet

( negative sign due to below-sea level

Now,

The distance between the top and the bottom of the iceberg.

= 67 - (-283)

= 67 + 283

= 417 feet

Thus,

The distance between the top and the bottom of the iceberg is 417 feet.

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Answer: The required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).

Step-by-step explanation:  Given that the figure ABCD is reflected across the X-axis.

We are to find the co-ordinates of A, B, C and D after reflection.

From the figure, we note that the co-ordinates of the vertices of ABCD are

A(2, 3), B(5, 5), C(7, 3) and D(5, 2).

After reflection from X-axis, the y co-ordinate of each vertex will change its sign (y → -y).

Therefore,  the vertices of ABCD after reflection are

A(2, 3)  ⇒ A'(2, -3),

B(5, 5)  ⇒  B'(5, -5),

C(7, 3)  ⇒  C'(7, -3),

D(5, 2)  ⇒ D'(5, -2).

Thus, the required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).

Kaitlin will have $4657 as the total amount in her account after 3 years which was found using the compound interest formula.

What exactly is Compound Interest?

Given: Kaitlin put $4000 into an account earning 5.2% annual compound interest.

We need to find how much will she have in the account after 3 years.

Let,

P = initial sum of money

r = interest rate, 

t = number of years in decimal form

A = total amount in her account

Using the compound interest formula we obtain,

A = P (1+r)^t

A = 4000(1 + 0.052)³

A = 4000(1.052)³

A = 4000(1.164)

A = $4657

Therefore, Kaitlin will have $4657 as the total amount in her account after 3 years.

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The equation to represent the total number of students taking the yoga classes is s = 13c.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of students = s

Let the number of classes = c

Therefore the total students will be:

s = 13 × c

s = 13c

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The five consecutive odd integers are 11, 13, 15, 17 and 19.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Odd numbers are whole numbers that cannot be divided exactly into pairs.

Therefore, odd integers are integers that cannot be divided exactly into pairs.

Hence, let's find five consecutive odd integers if the sum of the first three integer is 3 more than the sum of the last 2.

let

the first odd integer = x

x + x + 2 + x + 4 = x + 6 + x + 8 + 3

3x + 6 = 2x + 17

3x - 2x = 17 - 6

x = 11

Therefore, the consecutive odd integers are 11, 13, 15, 17 and 19.

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The following statements are marked true or false accordingly

A: n²+2 is odd         true    

B: n(n + 1) is odd     false

C: (n+1)² is odd        false

D: n² + 1 is odd       false

E: n(n + 2) is odd    true

F: (n + 2)² is odd     true

Examples are used to support or counter the statements

A: n²+2 is odd

3^2 + 2

= 9 + 2

= 11 (true)

B: n(n + 1) is odd

= 5(5+1)

= 5 * 6

= 30 (false)

C: (n+1)² is odd

= (7 + 1)^2

= 64 (false)

D: n² + 1 is odd

= 9^2 + 1

= 81 + 1

= 82 (false)

E: n(n + 2) is odd

= 3 ( 3 + 2)

= 3 (5)

= 15 (true)

F: (n + 2)² is odd

= (13 + 2)²

= 225 (true)

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Answer:

5.92

Step-by-step explanation:

Line in standard form

-6x + y - 7 = 0

distance = |-6 * 6 + 1 * 7 - 7|/([tex]\sqrt{(-6^2)+ 1^2)}[/tex]

|-36 +7 - 7| = √37

|-36|/√37

36/√37

5.918363 = 5.92

The strength of the solution is 2:5 g/ml expressed as a ratio and the strength expressed as percent is 20%

Total amount of drug = 20 gm

Total volume of solution = 50ml

Strength (as ratio)

= 20/50 g/mL

= 0.4 g /mL

Amount of drug = M = 20 g

Volume of solution = V = 50 mL

Concentration or strength (ratio) = M/V = 0.4 g/mL

Concentration or strength (percent)

= M/V × 100

=20/50 × 100%

= 40%

The concentration is 40% expressed as a percentage.

Solution concentration is the perfect measurement of how much of the  solute has been dissolved in a particular amount of solvent or solution.

A solution that contains a large amount of the dissolved solute is said to be highly concentrated. A solution that contains only a small quantity of dissolved solute is said to be diluted.

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Answer:75/5 = x/7

Step-by-step explanation:

Complete this equation and you will end up with the answer 105

The error that Bianka made in the algebraic expression is that; when 15 was distributed it should be '45 - 15y' rather than '45 + 15y'

An algebraic expression is defined as an expression that is made up of variables and constants, as well as algebraic operations such as multiplication, addition, division, subtraction, etc.

Now, the steps that Bianka took to solve the algebraic expression are;

12 + 15(3 - y) - 10y

12 + 45 + 15y - 10y

57 + 5y

Now, the first step according to the rule PEMDAS is to expand the bracket and when positive and negative are multiplied, the sign is negative and as such step 2 should have been 12 + 45 - 15y - 10y.

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The probability of getting a total that is a factor of 21 is 2/9

Tom rolls 2 fair dice and adds the results from each

Total number of outcomes = 6 × 6

= 36

The probability = Number  of favorable outcomes / Total number of outcomes

The factors of 21 = 1, 3, 7, 21

The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Number of possible outcomes = 8

The probability = Number  of favorable outcomes / Total number of outcomes

Substitute the values in the equation

= 8 / 36

= 2/9

Hence, the probability of getting a total that is a factor of 21 is 2/9

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