What is the axis of symmetry for f(x) = x2 + 4x + 6

Answer:

- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Earth and the Sun.

Step-by-step explanation:

Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.

Then:

The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

The scientist can substitute these measurements into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], and solve for the distance "d".

Knowing that:

[tex]\alpha=x\°\\adjacent=d\\hypotenuse=y[/tex]

Then:

[tex]cos(x\°)=\frac{d}{y}[/tex]

And solving for "d":

[tex]ycos(x\°)=d[/tex]

The scientist can use the tangent function in trigonometry with the measured angle x and distance y to calculate the distance between the Earth and the Sun by rearranging the formula to solve for the opposite side of the right triangle formed.

The scientist can calculate the distance between the Earth and the Sun using the measurements of angle x and distance y through a process known as triangulation or the parallax method. The right triangle formed with vertices at the Earth, Sun, and Shooting Star allows for the application of trigonometric functions. Specifically, the scientist can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side.

To find the distance between the Earth and the Sun, the scientist applies the formula:

tan(x) = opposite/adjacent

Where opposite is the distance between the Earth and the Shooting Star, and adjacent is the distance between the Sun and the Shooting Star (y). By rearranging the formula to solve for the opposite side, we get:

Distance between Earth and Sun = y * tan(x)

This calculation allows the scientist to determine the distance from the Earth to the Sun, given that they have the measurements of angle x and distance y.

Answer:

15%

Step-by-step explanation:

To calculate the percent of the bill that was left as a tip, you would divide the amount of the tip ($4.80) by the cost of the meal ($32) to get 0.15. This is then multiplied by 100 to give a tip percentage of 15%.

To determine the percentage of the bill that was left as a tip, you would divide the amount of the tip by the cost of the meal and then multiply by 100 to convert the decimal to a percentage. This would calculate as follows:

So, Michael and his friends left a 15% tip on the bill.

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Answer:

(10,6) is a positive and (-2, -3) are negative

Step-by-step explanation:

Answer:

[tex]\frac{1}{4096}[/tex]

Step-by-step explanation:

To solve this we are using the formula for the nth term of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

where

[tex]a_1[/tex] is the first term

[tex]r[/tex] is the common ratio

[tex]n[/tex] is the position of the term in the sequence

The common ratio is just the current term divided by the previous term in the sequence, so [tex]r=\frac{16}{64} =\frac{4}{16} =\frac{1}{4}[/tex]. We can infer from our sequence that its first term is 64, so [tex]a_1=64[/tex].

Replacing values

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

We want to find the 10th term, so the position of the term in the sequence is [tex]n=10[/tex].

Replacing values

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{10-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{9}[/tex]

[tex]a_{10}=\frac{1}{4096}[/tex]

We can conclude that the 10th term of the sequence is [tex]\frac{1}{4096}[/tex]

Answer:

10th term of the sequence 64,16,4... = 1/4096

Step-by-step explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here  

T₁₀ = ar⁽ⁿ⁻¹⁾

 = 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

 = 4³/4⁹ = 1/4⁶ = 1/4096

Answer:

lower section

Step-by-step explanation:

Given:

Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.

Pyramid B: Base is square with 10 meter sides.

Heights are the same.

Volume of rectangular pyramid = (L * W * H) / 3

Volume of square pyramid = a² * h/3

Let us assume that the height is 10 meters.

V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³

V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

The volume of pyramid A is TWICE the volume of pyramid B.

If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),  

V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³

The new volume of pyramid B is EQUAL to the volume of pyramid A.

The volume of the pyramid A is twice the volume of pyramid B. If the height of B is increased to twice, the volumes of A and B are equal.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters.

The base of pyramid B is a square with 10-meter sides.

The heights of the pyramids are the same.

Volume of a rectangular pyramid = lwh / 3, where l, w and h are length, width and height respectively.

Volume of pyramid A = 10 × 20 × h /3 = 200/3 h

Volume of a square pyramid = a²h/3, where a is the side length of the base and h is the height.

Volume of pyramid B = 10²h/3 = 100/3 h

So volume of pyramid A = 2 × volume of B.

If height of B increased to twice that of pyramid A,

Volume of B = 100/3 (2h) = 200/3 h

So both are equal in this case.

Hence the volume of pyramid A is twice that of B in the first case and the volumes are equal in the second case.

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Negative one is a natural number.

Answer:

303.6ft²  or 347.88 ft²

Step-by-step explanation:

The question is on area

The dimensions of the living room are given as;

Length= L = 22'-0"

Width= W= 12' -0" or 13'- 9"

Area= L× W

22'×12'=264ft²

Allow 15% waste

264× 115/100 =303.6ft²

or

Length= 22' and width = 13' 9"

change 9" to ft ⇒1'=12"...........................divide by 12"

9/12=0.75'................add to 13'

13'+0.75'=13.75'

Area=L×W

22'×13.75'=302.5ft²

Add 15% allowed waste

302.5 × 115/100 =347.88 ft²

Answer:

. from line l. In a coordinate plane, the locus of points 5 units ... 30. * .. ... The distance between parallel lines 6 and m is 12 units. Point A is on ...

Step-by-step explanation:

Answer:

from sloping up to sloping down ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Now lets solve the problem

∵ The equation of the line is y = 2x - 6

∵ The equation is changed to y = -2x - 6

- If the both signs of x and the number are changed means the

 equation is multiplied by -1

∴ The line is reflected across the x-axis

- If the sign of x only is changed

∴ The line is reflected across the y-axis

- From the equation 2x changed to -2x, but -6 not changed

∴ The sign of x only changed

∴ The line is reflected across the y-axis

* The graph is reflected across the y-axis

∴ from sloping up to sloping down

The line is reflected over the x axis

Answer:

B.  50 km/hr

Step-by-step explanation:

speed of train relative to man = [tex]\frac{125}{10}[/tex] m/sec

= [tex]\frac{25}{2}[/tex] m/sec

= ([tex]\frac{25}{2}[/tex] x [tex]\frac{18}{5}[/tex] ) km/hr

= 45 km/hr

let the speed of the train be x km/hr (x=-5)

x -5 = 45

x -5 + 5 = 45 + 5

x = 50 km/hr

Answer:

50 km/hr.

B

Step-by-step explanation:

I get the same answer (50 km/hour) but I did it slightly differently and both solutions are worth seeing.

First of all you have to figure out how far the man runs. Assume he starts right at the tip of the cow catcher (the furthest point out on one of those old fashioned engines.

He runs at 5km / hour for 10 seconds.

5 km = 5000 meters.

5000 meters / hour * [1 hour / 3600 seconds ] = 1.38889 m/sec.

He does this for 10 seconds

d = r * t

d = 1.38889 * 10

d = 13.8889

Now look at what the train has to do. It passes him in 10 seconds. (The train has gone from the tip of the cow catcher to the end of the caboose in 10 seconds.)

d = 125 + 13.8889 meters

d = 138.8889 meters.

Now we have to convert this to km / hour

138.8889 m / 10 seconds [ 1 km/ 1000 m] *  [ 3600 sec / 1 hr.]

(138.8889 * 1 * 3600 ) / (10 * 1000 * 1 )

50.000004

So the answer is 50 km/hr.

Answer:

( ( 3(8) ) /2 ) - 7 = 5

Step-by-step explanation:

Eliminate the denominator by reducing the fraction by 2

3(4) - 7

Solve:

12 - 7

= 5

Answer:

5

Step-by-step explanation:

Given

[tex]\frac{3x}{2}[/tex] - 7

To evaluate substitute x = 8 into the expression

[tex]\frac{3(8)}{2}[/tex] - 7 = [tex]\frac{24}{2}[/tex] - 7 = 12 - 7 = 5

Answer:

c

Step-by-step explanation:

ANSWER

A. 12

EXPLANATION

From the stem-and-leaf plot, the trees that are between 610 inches tall and 640 inches tall are:

613,616,622,622,624,625,631,631,633,637,637,and 638.

Counting the number of trees gives 12 of them.

Therefore, the number of trees that are between 610 inches tall and 640 inches tall is 12.

The correct answer is A.

Range: [0, ∞), {y|0 ≤ y}

Answer:

Part 1) The surface area is [tex]SA=35.1\ cm^{2}[/tex]

Part 2) The volume is equal to [tex]V=12.15\ cm^{3}[/tex]

Step-by-step explanation:

The question in English is

The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume

Part 1) Find the surface area

The surface area is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the area of the base B

[tex]B=(1.5)(1.8)=2.7\ cm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2*(1.5+1.8)=6.6\ cm[/tex]

we have

[tex]h=4.5\ cm[/tex]

substitute the values

[tex]SA=2(2.7)+(6.6)(4.5)=35.1\ cm^{2}[/tex]

Part 2) Find the volume

The volume is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

we have

[tex]B=2.7\ cm^{2}\\ h=4.5\ cm[/tex]

substitute

[tex]V=(2.7)(4.5)=12.15\ cm^{3}[/tex]

Answer:

Step-by-step explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex]              cross multiply

[tex]14(x+8)=10(2x-5)[/tex]             use the distributive property

[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]

[tex]14x+112=20x-50[/tex]           subtract 112 from both sides

[tex]14x=20x-162[/tex]           subtract 20x from both sides

[tex]-6x=-162[/tex]         divide both sides by (-6)

[tex]x=27[/tex]

Answer:

27.

Step-by-step explanation:

I just did this question and I got it incorrect by answering 12. It's 27!

Answer:

2. Given

3. Definition of supplementary angles

4. Substitution Property

5 Subtraction Property

Step-by-step explanation:

2. Given

We are given in the statement that m<1 = 112°

3. Definition of supplementary angles

Supplementary angles definition: Two angles are supplementary if there sum is equal to 180°. That statement states:

m<1 + m<2 = 180°

4. Substitution Property

We put the value of m<1 = 112° in the equation. This is substitution property.

5. Subtraction Property

To find the value of m<2 we subtract 112 from both sides of the equation.

This is subtraction property.

Answer:

$9.75

Step-by-step explanation:

Answer:

Step-by-step explanation: $9.75 per hour

243.75/25= 9.75

Answer:

(-3,4)

Step-by-step explanation:

The axis of symmetry, or X coordinate for a parabolic function is [tex]\frac{-b}{2a}[/tex]

By plugging in 6 for b, and 1 for a, you have -3.

By then plugging back into the function you can get the Y coordinate of the vertex.

[tex]f(x)=(-3)^{2}+6(-3)+13[/tex]

Or 4.

The answer is (-3,4)

ANSWER

(-3, 4)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 6x + 13[/tex]

We complete the square to obtain the vertex form:

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 6x + {3}^{2} + 13 - {3}^{2} [/tex]

The first three terms form a perfect square trinomial.

[tex]f(x) = {(x + 3)}^{2} + 13 - 9[/tex]

[tex]f(x) = {(x + 3)}^{2} + 4[/tex]

Comparing this to the vertex form;

[tex]f(x) = {(x - h)}^{2} + k[/tex]

h=-3 and k=4

Answer:

(3z - 1)(z + 9)

Step-by-step explanation:

Answer:

(z + 9)(3z - 1)

Step-by-step explanation:

Given

3z² + 26z - 9

To factor the quadratic

Consider the factors of the product of the z² term and the constant term which sum to give the coefficient of the z- term

product = 3 × - 9 = - 27 and sum = + 26

The factors are + 27 and - 1

Use these factors to split the z- term

3z² + 27z - z - 9 ( factor the first/second and third/fourth terms )

3z(z + 9) - 1(z + 9) ← factor out (z + 9) from each term

(z + 9)(3z - 1) ← in factored form

Answer:

15/36 = 5/12 = 41.66%

Step-by-step explanation:

If a die is rolled twice in a row, and the up face value of both throws are added, that's basically like if you had thrown 2 dice at the same time.

If you throw 2 dice at the same time, there are 36 possible outcomes, from (1,1), (1,2)... to (6,5), (6,6).

You just then have to calculate how many combinations are greater than 7.  We have (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5) and (6,6)... a total of 15 values above 7.

So, the probability is 15 totals  >7  out of 36 possible outcomes:

15/36 = 5/12 = 41.66%

Answer:

(6,000 + 800 +20) /10

(60,000 + 8,000 + 200) / 100

682,000 / 1,000

Step-by-step explanation:

Use a calculator

Do the parenthesis first and divide

The division problems that result in a quotient of 682 are 682,000 ÷ 1,000 and 6,820,000 ÷ 10,000. This is because when we divide these large sums by their respective divisors, we get 682 as the quotient.

To figure out which division problems result in a quotient of 682, we need to remember how division works. Division is basically the opposite of multiplication - if you multiply the quotient by the divisor, you should get the dividend. Essentially, we're looking for problems where we divide a total (dividend) by a number (divisor) and get 682 (quotient).

For instance, if we were to have a division problem like 682,000 ÷ 1,000, we would get 682 as our quotient. The same would be true for 6,820,000 ÷ 10,000, where the quotient would also be 682.

However, the problems such as (600 + 80 + 2) ÷ 10, and (60,000 + 8,000 + 200) ÷ 100 do not result in a quotient of 682 and therefore don't apply. So only the two problems with the larger sums (682,000 ÷ 1,000 and 6,820,000 ÷ 10,000) are valid solutions.

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Answer:

[tex]36.5\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x----> the perimeter of the larger figure

y ----> the perimeter of the smaller figure

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=28\ cm[/tex]

[tex]y=20\ cm[/tex]

substitute

[tex]z=\frac{28}{20}=1.4[/tex]

step 2

Find the area of the larger figure

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x----> the area of the larger figure

y ----> the area of the smaller figure

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=1.4[/tex]

[tex]y=18.6\ cm^{2}[/tex]

substitute

[tex]1.4^{2} =\frac{x}{18.6}[/tex]

[tex]x=1.96*(18.6)=36.5\ cm^{2}[/tex]

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill \\\\ \cfrac{\textit{small polygon}}{\textit{large polygon}}\qquad \qquad \cfrac{3}{9}\implies \cfrac{1}{3}\implies \stackrel{ratio}{1:3}[/tex]

Answer:

-5x+2y+1>0

Step-by-step explanation:

Plug in -2 for x and -1 for y. This is the only answer that gives you a positive number that is greater than zero.

Answer: Second Option

Step-by-step explanation:

Substitute the point in each of the given inequalities and verify if the inequality is met.

If the inequality is fulfilled then the point belongs to the region

For

[tex]5x-2y +1>0[/tex]

[tex]5(-2)-2(-1) +1>0[/tex]

[tex]-10+2 +1>0[/tex]

[tex]-7>0[/tex]

-7 is not greater than zero. the inequality is not met

For

[tex]-5x+2y +1>0[/tex]

[tex]-5(-2)+2(-1) +1>0[/tex]

[tex]10-2 +1>0[/tex]

[tex]9>0[/tex]

9 is greater than zero. So the point belongs to inequality

For

[tex]-2x+5y -1>0[/tex]

[tex]-2(-2)+5(-1) -1>0[/tex]

[tex]4-5-1>0[/tex]

[tex]-2>0[/tex]

-2 is not greater than zero. the inequality is not met

For

[tex]2x+5y -1>0[/tex]

[tex]2(-2)+5(-1) -1>0[/tex]

[tex]-4-5 -1>0[/tex]

[tex]-10>0[/tex]

-10 is not greater than zero. the inequality is not met

Step-by-step explanation:

Of the 1000 people randomly selected, 638 wear glasses.

638 / 1000 = 0.638

Since the sample is random, we can assume it is representative of the population.  So if there are 320 million people in the US, we would estimate the number that wears glasses is:

0.638 × 320 million ≈ 204 million

Answer:

204.16 million

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 638 of these people wear glasses.

The probability that a randomly selected person will wear glasses is:

[tex]P = \frac{638}{1000}\\\\P = 0.638[/tex]

Then, the expected number of people who wear glasses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.638[/tex]

[tex]N = 204.16\ million[/tex]

Answer:

one x-intercept.

Transformation: shift to the right 8 units.

Step-by-step explanation:

The parent function is [tex]f(t)=t^{2}[/tex]

To find the number of x-intercepts, we equate the function to zero.

[tex]\implies t^{2}=0[/tex]

[tex]\implies t=0[/tex]

There is only one x-intercept at t=0.

The transformed function is

[tex]g(t)=(t-8)^2[/tex]

This function is obtained shifting the parent function 8 units to the right.

The x-intercept will now be at t=8.

Hence the image function also has one x-intercept.

Answer:

any score that lies between 88.8 and 97.2 is within one std. dev. of the mean

Step-by-step explanation:

One std. dev. above the mean would be 93 + 4.2, or 97.2.  One std. dev. below the mean would be 93 - 4.2, or 88.8.

So:  any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.

The scores that fall within one standard deviation of the mean are between 88.8 and 97.2. This matches the last option provided.

The Empirical Rule helps us understand how data is distributed in a normal distribution. The rule states that approximately 68% of the data falls within one standard deviation of the mean.

Given a mean (μ) of 93 and a standard deviation (σ) of 4.2, we calculate the range within one standard deviation:

Therefore, the scores that fall within one standard deviation of the mean are between 88.8 and 97.2, which matches the last option.

Answer:

Interior

Step-by-step explanation:

The sum of the interior angles of a polygol with n sides is 180(n-2)

Answer:

Interior

Step-by-step explanation:

Answer:

-2（x+5）= -2（x-2）+5

-2x-10=-2x+4+5

-2x+2x=-4+5+10

0=19

No solution

Answer:

no solution

Step-by-step explanation:

They are no = in any way, shape, or form

Please mark me brainlyest my friend i really need it

Answer:

The length of a side of the base is 20 centimeters.

The area of a lateral side between the bases is about 126.5 square centimeters.

Step-by-step explanation:

It's a rectangular prism with a total volume of 800 cu cm, and a height of 20 cm.

So, the base has an area of...  800/20 = 40 sq cm.

The prism is a cube.   NO.  If it was a cube, the base would be 400 sq cm (20x20), since the height is 20.

The diagonal of the base is 4 centimeters. NO. with a base of 40 sq cm, it's impossible to have a diagonal of 4 cm.  A diagonal would form a hypotenuse... and an hypotenuse is longer than the two other sides... an hypotenuse of 4 would mean for example sides of about 2 and 3...  which gives 6 sq cm for the base, not 40.

The length of a side of the base is 20 centimeters.  COULD BE. The base is 40 sq cm, it could have a side of 20 and the other of 2.  Without knowing more about the prism than what's included in the question, we can't say YES and we can't say NO.

The area of a base is 40 square centimeters.  Yes

The area of a lateral side between the bases is about 126.5 square centimeters. YES, since the height is 20, that would mean one side of the base would be roughly 6.325 cm... for a base area of 6.325 x 6.325 = 40 sq cm.

1. The area of a base is 40 square centimeters.

2. The area of a lateral side between the bases is about 126.5 square centimeters.

The statements that describe the prism are:

1. The area of a base is 40 square centimeters.

To find the volume of any rectangular prism, we use the formula [tex]base \times height[/tex].

It is given that the volume of prism is 800 cubic centimeters and height is 20 centimeters.

Putting these values in the volume formula, to find base(B):

[tex]800=B(20)[/tex]

[tex]B=40[/tex]

Hence, area of base is 40 square centimeters.

2. The area of a lateral side between the bases is about 126.5 square centimeters.