Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.


f(x)
f(x) = −4(x − 8)2 + 3
h(x)
graph of negative 1 times the quantity of x minus 3 squared, plus 2

Answer:

10812

Step-by-step explanation:

books sold=106

number of pages=102

106 × 102=10812

Answer:

106^102

Step-by-step explanation:

Because there are 106 copies of the book and each book has 102 pages

After solving the given inequality the answer is x = 0.7/5log.

So,

Then,

Therefore, after solving the given inequality the answer is x = 0.7/5log.

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The probability that a boy selected at random is a Junior is 0.23 and the probability of randomly choosing a student who is a Junior and a boy is 0.14

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The table that completes the question is added as an attachment

From the table, we have the following values

n(Boys and Junior) = 65

n(Boys) = 285

So, the probability that a boy selected at random is a Junior is

P = n(Boys and Junior)/n(Boys)

This gives

P = 65/285

Evaluate

P = 0.23

From the table, we have the following values

n(Boys and Junior) = 65

Total = 465

So, the probability of randomly choosing a student who is a Junior and a boy is

P = n(Boys and Junior)/Total

This gives

P = 65/465

Evaluate

P = 0.14

Hence, the probability of randomly choosing a student who is a Junior and a boy is 0.14

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Explanation:

CCW = counter-clockwise

The rule for a 90 degree CCW rotation is this

[tex](\text{x}, \text{y})\to(-\text{y}, \text{x})[/tex]

it only works if the center of rotation is the origin.

The x and y coordinates swap places. Then you change the sign of the first coordinate after the swap occurred.

Applying that rotation rule to point C(5, 6) gets us to C ' (-6, 5).

Then to reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. The notation would be [tex](\text{x}, \text{y})\to(\text{x}, -\text{y})[/tex]

So we go from C ' (-6, 5) to C '' (-6, -5)

The sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

The continuous compounding formula is as follows:

So,

According to the first point, we know that atr = 0.02,  and t = 1.

Thus for advantage > 1$ we need is as follows:

According to the second point, we got that:

Then,

Now we hold that r > 0.04439:

According to the third point, we got to know that:

Now 2nd equation holds t > 4.621.

Therefore, the sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

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The expression given as -15 + 0 is a representation of the identity property of integer

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

-15 + 0

The identity property of integer states that

x + 0 = x

This means that

-15 + 0 is a representation of the identity property of integer

Hence,  the expression given as -15 + 0 is a representation of the identity property of integer

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The result of simplifying each number (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃  using the exponent rules is -3

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(-3)¹/₃⁺ ¹/₃ ⁺ ¹/₃

(-3)³/₃

(-3)¹

-3

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

now we also know that

the height in that triangle is twice its baseline.

so,

height = 2×baseline

so, for the given area we have

49 = baseline × 2 × baseline / 2 = baseline²

baseline = 7 ft.

therefore,

height = 2×baseline = 2×7 = 14 ft.

and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.

the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.

the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.

so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.

then I can calculate :

leg² = (baseline/2)² + height² = 3.5² + 14² =

= 12.25 + 196 = 208.25

(each) leg = 14.43086969... ft

if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.

and the height is one leg and the other leg is again via Pythagoras

leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245

leg = 15.65247584... ft

all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.

The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

time is calculated using the formula

[tex]Time=\frac{Distance}{Speed}[/tex]

In the given question

driver drove 50 miles at slower speed.

Let the slower speed be x miles per hour.

So the time taken to cover 50 miles at slower speed = [tex]\frac{50}{x}[/tex]    ...(i)

driver drove 300 miles at faster speed.

given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = [tex]\frac{300}{(x+20)}[/tex]....(ii)

According to the question

the time spent driving at the faster speed was thrice that spent driving at the slower​ speed.

From equation (i) and (ii) we get

[tex]3*(\frac{50}{x} )=\frac{300}{x+20}[/tex]

[tex]\frac{150}{x} =\frac{300}{x+20}[/tex]

Cross Multiplying we get

[tex]150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20[/tex]

Slower speed = x = 20mph.

Faster speed = (x+20) = 20+20 = 40mph.

Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

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Answer:

2.97%

Step-by-step explanation:

Answer:

2.72807     (aprox)

Step-by-step explanation:

14% = 14/100 = 0.14

100% = 100/100 = 1

It was a increase

then 14% = 100% + 14% = 1 + 0.14 = 1.14

3.11 / 1.14 = 2.72807    (aprox)

Check:

2,72807 + (2.72807*0.14) = 2.72807 + 0.38193 = 3.11

Answer:

AB has the slope of 4/3

CD has the slope of 3/2

Step-by-step explanation:

CD I chose the points (0,2) and (3,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 2}{3 - 0} \\ m = \frac{ - 2}{3} [/tex]

AB I chose the points (0,6) and (8,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 6}{8 - 0} \\ m = \frac{ - 3}{4} [/tex]

The correct answer of the question is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

The given quadratic equation is 3 x²+ 9 x=27

To begin, we must transform the equation in the form

ax² + bx + c = 0, then apply the quadratic formula i.e.

x = {-b±√(b²- 4ac)}/ 2a .

Now,

3 x²+ 9 x=27

⇒ 3 x²+ 9 x - 27 = 0

⇒  3(x²+ 3 x - 9 )= 0

⇒  x²+ 3 x - 9 = 0

Here, a = 1, b = 3 and c = --9

Now, applying quadratic formula

{-b±√(b²- 4ac)}/ 2a

= {-3±√(3²- 4 × 1 × -9)}/ (2 × 1)

= {-3±√(9 + 36)}/ 2

= {-3±√45}/ 2

= {-3±3√5}/ 2

= 3{-1 ±√5}/ 2

= 3{-1+√5}/ 2 or 3{-1-√5}/ 2

Therefore, the ultimate answer to the given equation is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

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Answer:

1.87

Step-by-step explanation:

The first step in this problem is to get rid of the percent by making it a number. The way you do this is divide by 100.

11%/100=0.11

The "of" after 11% means multiply, so you multiply 0.11 and 17

0.11*17=1.87

The answer to the following listed algebra questions are below:

6 = a/4 + 2

substract 2 from both sides

6 - 2 = a/4

4 = a/4

cross product

4 × 4 = a

a = 16

-6 + x/4 = -5

x/4 = -5 + 6

x/4 = 1

x = 4 × 1

x = 4

9x - 7 = -7

Add 7 to both sides

9x = -7 + 7

9x = 0

x = 0/9

0 = 4 + n/5

0 - 4 = n/5

-4 = n/5

-4 × 5 = n

-20 = n

-4 = r/20 - 5

-4 + 5 = r/20

1 = r/20

1 × 20 = r

r = 20

-1 = (5+x) / 6

-1 × 6 = (5 + x)

-6 = 5 + x

-6 - 5 = x

x = -11

(v+9)/3 = 8

v + 9 = 8 × 3

v +9 = 24

v = 24 - 9

v = 15

2(n + 5) = -2

2n + 10 = -2

2n = -2 - 10

2n = -12

n = -12/2

n = -6

-9x + 1 = -80

-9x = -80 - 1

-9x = -81

x = -81/-9

x = 9

-6 = n/2 - 10

-6 + 10 = n/2

4 = n/2

4 × 2 = n

n = 8

-2 = 2 + v/4

-2 - 2 = v/4

-4 = v/4

-4 × 4 = v

-16 = v

144 = -12(x + 5)

144 = -12x - 60

144 + 60 = -12x

204 = -12x

x = 204 / -12

x = 17

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Answer:

[tex]\frac{1}{8b^6 a^12}[/tex]

Step-by-step explanation:

Hope this helps you :))

From the given table, the equations that represent the relationship between the amount of money, A, and the number of months, m are:

First, find the slope of the line:
= (1,300 - 1,200) / (6 - 5)

= 100 / 1

= 100

The slope is 100. We can use this to find the y-intercept:

y = mx + b

1,400 = 100(7) + b

b = 1,400 - 700

b = 700

The form of the relationship between the amount of money and the number of months is:

y = mx + b

y = 100x + 700

The variants of this equation are:

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Answer:

It looks like the chart says time and hours.

Step-by-step explanation:

Using the axis title we found that the time is the measurement represented on the x- axis  and and time is measured in hours

The axis title is a title in the form of words or numbers that describes the  entire axis . The title that describes that what quantity varies along x-axis is called x-axis title and the title which describes what quantity varies along y- axis is called y- axis title.

Some times units of the quantities measured along the respective axis  is also mentioned in the title of the axis in a bracket.

From the Given graph in the question we can see that a Distance vs Time graph is given

And the title of the x- axis is Time (hours )

Therefore , the measurement along the x- axis is of time and unit of time is hours.

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The value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

2x^2 - 10x + 13

When the value of x is 2, the quadratic equation becomes

2x^2 - 10x + 13 = 2 x 2^2 - 10 x 2 + 13

Evaluate the exponent

So, we have

2x^2 - 10x + 13 = 2 x 4 - 10 x 2 + 13

Evaluate the product

So, we have

2x^2 - 10x + 13 = 8 - 20 + 13

Evaluate the difference

So, we have

2x^2 - 10x + 13 = -12 + 13

Evaluate the sum

So, we have

2x^2 - 10x + 13 = 1

Hence, the value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1

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Complete question

What is the value of 2x^2-10x+13 when x = 2

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y = -3/4x - 5}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{Slope = -3/4 and passes through (4, -8)}[/tex]

Find:  [tex]\textsf{Determine the equation of the line that fits the criteria}[/tex]

Solution:  The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.

Plug in the values

Distribute and simplify

Solve for y

Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is [tex]\textsf{y = -3/4x - 5}[/tex]

Answer:

the length is 19

the width is 13

Step-by-step explanation:

well since a rectangle has two even sides the width have to be the same and the lengths have to be the same

perimeter is all the sides added together

since the length is the bigger size choose a sensible number (for example 15) and add another 15 to get the length and since it's 6cm smaller take 6 away from 15 which is 9 and add the two 9s together but 15+15+9+9 isn't 64 so you try again with a higher number until you each a total of 64

[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{Answer:-}}}[/tex]

To solve this problem, let's denote the width of the rectangle as $w$ (in cm).

According to the given information, the length of the rectangle is 6 cm more than the width, so the length can be represented as $w + 6$ (in cm).

The perimeter of a rectangle is given by the formula:

$$\text{{Perimeter}} = 2(\text{{length}} + \text{{width}})$$

Substituting the values, we have:

$64 = 2((w + 6) + w)$

Now, let's solve for $(w)$:

$64 = 2(2w + 6)$

$64 = 4w + 12$

$4w = 64 - 12$

$4w = 52$

Dividing both sides of the equation by 4, we get:

$w = \frac{{52}}{{4}}$

$w = 13$

So, the width of the rectangle is 13 cm.

Substituting the value of $w$ back into the expression for the length:

$$\text{{Length}} = w + 6 = 13 + 6 = 19$$

Therefore, the dimensions of the rectangle are 13 cm (width) and 19 cm (length).

If you earn a manager point every 30 minutes, then the number of minutes you would need to work for 50 manager points is equal to 1500.

The number of minutes needed to work for 50 manager points can be calculated using multiplication. Multiplication is one of the arithmetic parts and is thought to be the opposite of division. It represents the basic idea of the repeated addition of groups of equal sizes.

As,

one manager point = 30 minutes

50 manager points = x

Here x represents the number of minutes required to earn 50 manager points

Cross multiplying,

30 × 50 = x

x = 1500

Hence the number of minutes required to earn 50 manager points if a manager point is earned every 30 minutes is calculated to be 1500 minutes.

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Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

|-5|+|7|

|-5|=5

|7|=7

=5+7

=12

hope this helps u ; )

Answer: 53412

Step-by-step explanation:

17

6.5−1−21

−(−5)2−

Answer:

[tex]x=\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{30x^1}{3}=1[/tex]

Multiply both sides by 3

[tex]\frac{3\cdot \:30x^1}{3}=1\cdot \:3[/tex]

Simplify

[tex]30x=3[/tex]

divide both sides by 30

[tex]\frac{30x}{30}=\frac{3}{30}[/tex]

Simplify

[tex]x=\frac{1}{10}[/tex]

Statement 2 is true. The contrapositive of a biconditional statement is always true.

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

A biconditional statement can be defined as a statement which combines a conditional statement with its converse. This ultimately implies that, a biconditional statement is generally created when a conditional statement is combined with its converse.

In Mathematics, a biconditional statement typically has the form "P if and only if Q." Therefore, the biconditional statement, "p if q," is true whenever the two statements have the same truth value. Otherwise, the biconditional statement is false.

In this context, we can reasonably infer and logically deduce that since statement 2 is true because the contrapositive of a biconditional statement is always true.

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The statements are true regarding the area of circles and sectors are:

1). The area of a sector depends on the ratio of the central angle to the entire circle.

2) The area of the entire circle can be used to find the area of a sector.

3)The area of a sector can be used to find the area of a circle.

Option (B) ,(D) and (E) is correct.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

Given:

The statements are true regarding the area of circles and sectors.

According to given question we have

WE know that

Area of a circle= π[tex]r^{2}[/tex]

So, area is dependent only on the radius.

The area of a sector depends on the ratio of the central angle to the entire circle is   1: 5.

The area of the sector of a circle is /360° *([tex]r^{2}[/tex]) where r is the radius of the circle and is the angle of the sector,.

Therefore, statements are true regarding the area of circles and sectors are:

1). The area of a sector depends on the ratio of the central angle to the entire circle.

2) The area of the entire circle can be used to find the area of a sector.

3)The area of a sector can be used to find the area of a circle.

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