Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.
f(x)=-3(x+2)²+1
Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.

The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°

A secant line is a straight-line which has two points of intersection with a circle.

From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°

The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.

Mathematically;

[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]

Where;

The outside angle formed by the secant ZW and ZV, m∠z = 41°

[tex]\widehat{VW}[/tex] = 112°

Which gives;

[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]

2 × 41° = 112° - [tex]\widehat{XY}[/tex]

82° = 112° - [tex]\widehat{XY}[/tex]

[tex]\widehat{XY}[/tex] = 112° - 82° = 30°

[tex]\widehat{XY}[/tex] = 30°

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The equation used to find the length of each afternoon practice is given as follows:

4(h + 3) = 20.

The variables in this problem are defined as follows:

During the summer, the team practices 4 days per week, for a total of 20 hours each week, hence the equation is of:

4(x + h) = 20.

The number of hours practiced during the morning is of:

x = 3.

Hence the equation to solve for h is given as follows:

4(3 + h) = 20

Applying the commutative property:

4(h + 3) = 20.

Hence the second option is correct.

The problem is given by the image shown at the end of the answer.

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Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.

Which equation can you use to find h, the length of each afternoon practice in hours?

Summer swim practice is 4 days per week. Each day has 3 hours of morning practice and h hours of afternoon practice. So, the number of hours of practice each day is h+3. Weekly practice is a total of 20 hours. This equation represents the situation.

4 (h+3)

=

20

days of practice per week

hours of practice each day

total hours of practice each week

The equation 4(h+3)=20 can be used to find the length of each afternoon practice in hours. Solve the equation for h.

4(h+3)

= 20

h+3

= 5 Divide both sides by 4

h

= 2 Subtract 3 from both sides

Each afternoon practice is 2 hours.

The point estimate of the population mean  is 22 and margin of error for the confidence interval is 3.

1. Point estimate

Point estimate = Upper bound+ Lower bound/2

Point estimate = (25+19) /2

Point estimate = 44/2

Point estimate = 22

2. Margin error

Margin error = Upper bound  - Lower bound/2

Margin error = ( 25-19) /2

Margin error = 6 /2

Margin error = 3

Therefore the point estimate is 22.

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The total distance of the triathlon is 12000 m.

Two or more expressions with an equal sign are defined as an equation.

Let the total distance of the triathlon be x.

Tasneem swims 1/4of the total route, therefore, she swims for a distance of S = (1/4)x.

Now the remaining route is,

x - (1/4)x

=3/4x

After swimming, she cycles 3/5 of the remaining route, therefore, she cycles for a distance of C = (3/5)×(3/4)x,

C = (9/20)x

Now, she runs for the rest of the route, therefore, she runs for a distance of R = x - (1/4)x-(9/20)x

Or, R = (20x - 5x - 9x)/20

R = (6x)/20

Given that Tasneem runs 3600 m, therefore, substitute R = 3600 into the above equation,

3600 = (6x)/20

(3600×20)/6 = x

12000 = x

Therefore, the total distance of the triathlon is 12000 m.

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If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of  different random samples of four accounts that are possible is 230,300.

Given data:

Number of population of bank account = 50

Random sample = 4 accounts

Now let find the different random samples of four account that are possible

Different random sample = 50! / (50 -4)! × 4!

Different random sample = 50! / 46! × 4!

Different random sample = 230,300

Therefore the different random samples is 230,300.

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Answer:

x= 68  z= 180  y=38

Step-by-step explanation:

The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.

We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.

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As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .

As given in the question,

Time period to calculate the compound interest  = 3years

Interest rate compounded monthly = 5.50%

Each month interest output is 5.64079

Rate of interest compounded semi- annually = 5.70%

Each month interest output is 5.78123

Compounded monthly gives interest every month and semi-annually gives twice a year.

Monthly is more frequent  compare to semi-annually.

Investor should choose monthly.

Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .

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The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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The time required for for the balance to reach $4635 is 5 years.

The formula for simple interest can be expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

First convert the interest rate from percent to decimal

Interest rate = 0.6%

Interest rate = 0.6/100

Interest rate = 0.006

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

t = ( 4635/4500 - 1) / 0.006

t = ( 1.03 - 1) / 0.006

t = ( 0.03) / 0.006

t = 5 years.

Therefore, the required time is 5 years.

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If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.

Given data;

Sharing ratio 8:5

Amount Elliot got = 21

In order to determine  the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.

Equation

21 × 8 ÷ (8-5)

Hence,

£21 × 8 ÷ (8-5)

£168 ÷ 3

=  £56

Therefore Elliot received £56.

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The highlighted point is (9, -7) . A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.

A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.

If the picture is the point (-7, -9)

Detailed explanation:

When the point (x, y) rotates 90 degrees counterclockwise with respect to the origin, its image is (-y, x)

When the point (x, y) rotates 180 degrees counterclockwise around the origin, its image is (-x, -y)

The picture of the point (x, y) if it were rotated 270 degrees counterclockwise with respect to the origin is (y, -x)

The highlighted point is (9, -7)

∴ x = 9 and y = -7

The provided point is turned 270 degrees counterclockwise with respect to the origin.

Utilizing the third rule listed above

The illustration of the point is (y, -x)

That is to say, alter the x-sign coordinate's before switching them.

∵ x = 9 and y = -7

The illustration if the point is (-7,-9).

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The product of linear factors for f(x) is given as (x + 1)(x² + 4x + 2) for -1 as a zero of the polynomial x³ + 5x² + 6x + 2.

The factor theorem states that;

f(x) is divisible by x - a if and only if f(a) = 0

f(x) is divisible by x + a if and only if f(-a) = 0

in both cases, a and -a are the zeros of the polynomials.

From the question, given that -1 is a zero of

f(x) = x³ + 5x² + 6x + 2, then it is divisible by x + 1 and f(-1) = 0.

Dividing x³ + 5x² + 6x + 2 by x + 1 using the long division will result to another factor x² + 4x + 2 with a remainder of zero. (complete long division is attached as a photo!)

Therefore we can then conclude that (x + 1)(x² + 4x - 2) is the product of linear factors for f(x) = x³ + 5x² + 6x + 2 and -1 as a zero.

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Answer:

x = - 10

Step-by-step explanation:

2(x + 3) = x - 4

==> distribute the 2

2x + 6 = x - 4

==> subtract 6 from both sides

2x = x - 10

==> subtract x from both sides

x = - 10

Answer:

$93.75

Step-by-step explanation:

$125 × 0.75 = $93.75

Answer:

$93.75

Step-by-step explanation:

125x0.25

31.25

125-31.25

$93.75

Hopes this helps

The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.

Let

x + y = 48

29x + 51y = 50*48

x + y = 48

29x + 51y = 2400

Solve simultaneously

From (1)

x = 48 - y

Substitute into (2)

29x + 51y = 2400

29(48 - y) + 51y = 2400

1392 - 29y + 51y = 2400

- 29y + 51y = 2400 - 1392

22y = 1008

y = 1008/22

y = 45.82 pounds

Substitute y = 45.82 pounds into (1)

x + y = 48

x + 45.82 = 48

x = 48 - 45.82

x = 2.18 pounds

So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.

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Answer: AB

Step-by-step explanation:

Radius of a circle is defined as the distance from the center of a circle to its perimeter (the edge).  Line AB is the only choice that meets this definition. CE is the diameter of the circle.

Answer:

AB

Step-by-step explanation:

radius goes in half the circle

The required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.

Given that,
A rectangular floor is long and wide. Pablo wants to carpet the floor with carpet titles sold by the square yard.

Surface area is defined as the area of the surface that is uncovered.

here,
Let for a tile the length be L and the width be W,
Assume that the number of tiles required is N,
The area of the N tiles is equal to the area of the rectangular floor,
Area of the floor = N [area of the tile]
Area of the floor (A = N [L× W]

Thus, the required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.

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The number of Hamilton Circuits with 8 vertices are 5040.

Given that, a complete, weighted graph with 8 vertices.

A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.

For N vertices in a complete graph, there will be (n−1)!=(n−1)(n−2)(n−3)…3⋅2⋅1 routes. Half of these are duplicates in reverse order, so there are (n−1)!/2 unique circuits.

A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes.

Therefore, the number of Hamilton Circuits with 8 vertices are 5040.

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The penguin's depth after 4 minutes is d = 10.7 + 146m

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

if the penguin moves with a speed of 146 meters per minute, then its distance after m minutes is  = 146 x m

Since it moved from an elevation 10.7 below the sea surface, its total distance(d) would be = 10.7 + 146m

substitute m = 4 minutes,

we have

d  = 10.7 + 146(4)

d = 594.7metres

In conclusion, the function rule is 10.7 + 146m and the distance d covered after 4 minutes is 594.7 meters

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Answer:

  x = 5

Step-by-step explanation:

You want to know what number must be excluded from the domain of f(x) = 15/(x -5).

The domain of a function is the set of numbers for which it is defined. The function f(x) = 15/(x-5) will be undefined when the denominator is zero:

  x -5 = 0

That will be the case when x = 5.

The domain of f must exclude x=5.

The statement that is true about the quadratic function is (b) the graph of the function is a parabola.

The quadratic function is given as

f(x) = x2 – 5x + 12

Rewrite as

f(x) = x² – 5x + 12

All quadratic functions are parabola

This means that option (b) is true

Set x = -10 to calculate f(-10)

So, we have

f(-10) = (-10)² – 5(-10) + 12

Evaluate

f(-10) = 162

This means that option (a) is false

Set x = 20 to calculate f(20)

So, we have

f(20) = (20)² – 5(20) + 12

Evaluate

f(20) = 312

This means that option (d) is false

Set x = 0 to calculate f(0)

So, we have

f(0) = (0)² – 5(2) + 12

Evaluate

f(0) = 12

This means that option (e) is false

The leading coefficient in f(x) = x² – 5x + 12 is positive

Graphs with positive leading coefficient opens up

This means that option (c) is false

Hence, the true statement about the quadratic function is (b)

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Solving for X the value is = 45, 6

acc to our question-

90/x=90/x+15+1/2

(15-x)90 - 90x/15x-x^2 = 5

x= 45 or 6

hence, for X the value is = 45, 6

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(7,0); (7,−5) ;(7,3); (7,10);. (7,y)

Step-by-step explanation:

Answer:

The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.

Step-by-step explanation:

For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.

A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.

Points that are on the line x = 7 include:

(7, 0)

(7, 1)

(7, 2)

(7, 4)

(7, 5)

(7, 6)

Answer:

so the answer would be a protozoa

Step-by-step explanation:

.

Answer:

a = 7

Step-by-step explanation:

Substitute x for 2 and f(x) for 14

14 = -2(2³) + a(2²) + 2

14 = -16 + 4a + 2

14 = -14 + 4a

14 + 14 = 4a

28 = 4a

4a = 28

Divide both sides by 4

4a/4 = 28/4

a = 7

Alternative:

Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.

Angle x= 45

acc to the question-

Hence, Angle x= 45

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Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:

[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]