Find the distance-
Which shows the values inputted into the distance formula?
*See photo*

Adam can see the horizon at a distance of [tex]\sqrt{6}mi.[/tex]

Given that the height of Pam's eye level above sea level is [tex]324ft[/tex] and the height of adam's eye level above sea level is [tex]400ft[/tex].

The formula used to find the distance they see in miles is [tex]d=\sqrt{\frac{3h}{2}}[/tex].

Let the height of Pam's is [tex]h[/tex] and the height of adam's is [tex]h'[/tex].

The distance of Pam from the horizon can be given as [tex]d=\sqrt{\frac{3h}{2}}[/tex].

Substitute these values,

[tex]\begin{aligned}d&=\sqrt{3\times \frac{324}{2}}\\ d&=\sqrt{486}\\ d&=\sqrt{81\times 6}\\ d&=9\sqrt{6}\end[/tex]

And the distance of adam from the horizon can be given as [tex]d=\sqrt{\frac{3h'}{2}}[/tex].

Substitute these values,

[tex]d'=\sqrt{3\times \frac{400}{2}}\\ d'=\sqrt{600}\\ d'=\sqrt{100\times 6}\\ d'&=10\sqrt{6}[/tex]

The net distance of adam from the horizon is

[tex]\begin{aligned}d_{\text{net distance}}&=d'-d\\ &=10\sqrt{6}-9\sqrt{6}\\&=\sqrt{6}\end[/tex]

Hence, the adam can see the horizon at a distance of [tex]\sqrt{6}mi[/tex].

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Answer:

B

Step-by-step explanation:

it said sooo

From the given mappings, we have

[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]

and

[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]

Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is

[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]

since

[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]

[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]

[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]

Answer:

C

Step-by-step explanation:

Answer C is correct.  The absolute value of 10 is 10 and that of -10 is 10.  Same result.

Answer:

T=5

Step-by-step explanation:

Step-by-step explanation:

get the lcm of the numerals and the denominators then simplify

hope it is correct

Answer:

The point-slope form is y - 8 = 4(x - 2)

Step-by-step explanation:

Given:

the point-slope form is y - y1 = m(x - x1)

Hence the point-slope form is y - 8 = 4(x - 2)

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The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have given a three-dimensional figure.

As we can see the arrow is pointing at the plane.

A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.

A plane is a plane of symmetry.

Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.

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The solution to the quadratic equation 3x² + 8x - 10 by using the quadratic formula is x = 0.927 or -3.594

Quadratic equations are algebraic expressions that are represented in the power of the second degree. They usually take the form ax² + bx + c

From the given information, we are to solve the quadratic equation:

Using the quadratic formula:

[tex]\mathbf{=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

where:

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{(8)^2 - 4(3 \times (-10))}}{2(3)}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64 -4 (-30)}}{6}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64+120}}{6}}[/tex]

x = 0.927 or -3.594

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[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81

hope it helps!

60 forks 60÷3=$20

60 spoons 60÷4=$15

$20+$15=$35 total spent for forks and spoons

Answer: same slope, y int are different

Step-by-step explanation:

Both these lines never intersect because they have the same slope.

they both go down 1 over 1, and also their y interecepts are different

Answer:

0.5 hours

Explanation:

Given:

Formula:

Solve:

Answer:

I will assume that the term "x+2/2" is meant to be "(x + 2)/2)."  Otherwise the equation would read (x/3) = x + 1

Step-by-step explanation:

(x/3) = (x + 2)/2

x = 3*(x+2)/2   [Multiply both sides by 3]

x = (3x + 6)/2

x = (3/2)x + 6/2

x - (3/2)x = 3

-0.5x = 3

x = -6

====================

Check:

Does (x/3) = (x + 2)/2 for x = -6?

(-6/3) = (-6 + 2)/2

-2 = -4/2

-2 = -2  YES

Answer:

5700000

Step-by-step explanation:

Answer:

-104

Step-by-step explanation:

1) Substitute 50 into n.

-2(50) - 4

-100 - 4

-104

Answer:

D.) A and D

Step-by-step explanation:

To find which set of equations has the solution (3,1), you need to identify where on the graph this point lies. Remember, in a point, the first number listed (3) is the "x" value and the second number (1) is the "y" value.

First, look for x = 3. This is the number located on the x-axis (horizontal line).

From this spot, since y = 1, move up 1 unit.

At this point, two lines intersect. These lines are lines A and D.

[tex]9-10x=2x+1-8x\\\\9-10x=-6x+1\\\\9=4x+1\\\\8=4x\\ \\ x=\boxed{2}[/tex]

The value of the x in the equation 9 - 10x = 2x + 1 - 8x is 2. The correct answer is A) x = 2.

An equation is a combination of numbers, variables, functions, and often symbols arranged in a peculiar order. The equation comprises two or more expressions distinguished by the equality sign(=). The equations are solved to estimate the values of variables.

The given equation is

9 - 10x = 2x + 1 - 8x

-10x - 2x + 8x = 1 - 9

-4x = -8

4x = 8

x = [tex]\frac{8}{4}[/tex]

x = 2.

Thus, the correct option is A) x = 2.

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Answer:

f(x) = 7.5x

Step-by-step explanation:

you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).

(30-15)/(4-2) = 15/2 = 7.5.

now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.

for this example I'll be using (2, 15) but you could use any of the values you gave.

15 = 7.5(2) + b

15 = 15 + b

0 = b

so now we have the function rule

f(x) = 7.5x + 0 or just f(x) = 7.5x

Answer:

An algebraic expression containing two or more terms is called a polynomial

Answer:

Its C

Step-by-step explanation:

it worked finally

Considering the direction of the wind, it is found that the plane's speed needs to be of 520 knots.

The ground speed, considering that the wind is flowing from Kansas City to Washington, and the trip is Washington to Kansas City, is given by:

G = Plane speed - Wind speed.

Hence:

450 knows = Plane speed - 70 knots.

Plane speed = 520 knots.

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Answer:

66560 pairs

Step-by-step explanation:

let the number of pairs of boots the company makes in 260 days = X

1day -----------------256pairs

260days-------------X

cross multiplying

1×X = 260×256

X= 66560

therefore, in 260days, he makes 66560 pairs

Answer:D

Step-by-step explanation:

this expression gives the original price reduce by 15%. The second term adds the tax to the price after the sale has been applied

The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression  [tex](\sqrt[4]{16})^{3x[/tex].

The rules of the exponent are

(a) [tex]a^m*a^n=a^{m+n[/tex]

(b)[tex]a^m/a^n=a^{m-n[/tex]

(c)[tex](a^b)^c=a^{bc}[/tex]

(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]

here the given expression is [tex]16^{3x/4}[/tex]

we can rewrite the expression as

[tex]16^{3x/4}[/tex]

as we know by the rule of the exponent that    [tex](a^b)^c=a^{bc}[/tex]

=[tex](16^{1/4})^{3x[/tex]

as we know by the rule of the exponent  [tex]\sqrt[n]{a}=a^{1/n[/tex]

=[tex](\sqrt[4]{16})^{3x[/tex]

Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]

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As IJK is isosceles

Hypotenuse must not counted counted among equal sides so

Apply roots

Option C

Answer:

-12

Step-by-step explanation:

Answer:

[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]

Step-by-step explanation:

Calculate the value of m

Given:

[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]

Therefore:

[tex]\implies 3=\dfrac{2}{3}m[/tex]

[tex]\implies m=3 \times \dfrac{3}{2}[/tex]

[tex]\implies m=\dfrac{9}{2}[/tex]

Calculate the value of H

Given:

[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]

Therefore:

[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

Calculating m × H

[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]

Approximate value of √17

So the point is (8,4)

As we can see in graph the point is contained by the circle

Hence the distance

Approximately 9 units

Option D

Answer:

Yes, the distance from the origin to the point (8, √17) is 9 units

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given:

Substitute the given values into the formula to create the equation of the circle:

[tex]\implies (x-0)^2+(y-0)^2=9^2[/tex]

[tex]\implies x^2+y^2=81[/tex]

To find if point [tex]\sf (8, \sqrt{17})[/tex] lies on the circle, substitute x = 8 into the found equation and solve for y:

[tex]\implies 8^2+y^2=81[/tex]

[tex]\implies 64+y^2=81[/tex]

[tex]\implies y^2=81-64[/tex]

[tex]\implies y^2=17[/tex]

[tex]\implies y=\sqrt{17}[/tex]

As y = √17  when x = 8, this proves that point (8, √17) lies on the circle.

The distance from the origin to any point on the circle is the radius.

Therefore, as the radius is 9 units, the distance from the origin to the point (8, √17) is 9 units.

The dot plot of the data recorded by Tricia about number of pets owned by each of her classmates looks like scattered and some points are in one line.

Given number of pets owned by each of her classmates are: 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3.

We have to create dot plot of the data given in the question.

Firstly we have to give a code to each value which represents friend of Tricia.

A dot plot is a statistical chart which have points but they are presented in dot form. Each dot shows a value .There are two common, yet different versions of the dot chart.

After giving codes the table will look like:

Friend                       Number of pets

1                                      0

2                                      3

3                                      2

4                                      4

5                                      1

6                                      0

7                                      0

8                                      3

9                                      2

10                                    1

11                                    2

12                                    1

13                                    1

14                                    3

15                                    4

16                                    2

17                                    0

18                                    0

19                                    1

20                                    1

21                                    1

22                                    0

23                                    3

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132/3 = 44

5/8 / 3 = 5/8 x 1/3 =5/24

answer: 4. 44 5/24 watts

Answer:

[tex]\sf 4. \quad 44\frac{5}{24}\:\:watts[/tex]

Step-by-step explanation:

Given information:

To find the number of watts used per hard drive, divide the total amount of watts by 3.

Convert the mixed number into an improper fraction:

[tex]=\sf 132 \frac{5}{8}[/tex]

[tex]\sf =\dfrac{132 \times 8+5}{8}[/tex]

[tex]\sf =\dfrac{1061}{8}[/tex]

Divide by 3:

[tex]=\sf \dfrac{1061}{8} \div 3[/tex]

[tex]\sf =\dfrac{1061}{8} \times \dfrac{1}{3}[/tex]

[tex]\sf =\dfrac{1061 \times 1}{8 \times 3}[/tex]

[tex]\sf =\dfrac{1061}{24}[/tex]

Convert back into a mixed number:

[tex]\sf =\dfrac{1061}{24}[/tex]

[tex]\sf =\dfrac{1056+5}{24}[/tex]

[tex]\sf =\dfrac{1056}{24}+\dfrac{5}{24}[/tex]

[tex]= \sf 44\frac{5}{24}[/tex]

Therefore, the number of watts used per hard drive is [tex]\sf 44\frac{5}{24}[/tex] watts.

Answer:

? = 26

Step-by-step explanation:

Challenge accepted!

For the bottom left corner:

[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]

Now, 10 - 6 = 4

136 / 4 = 34

For the top left corner:

[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]

Now, 7 - 5 = 2

74 / 2 = 37

For the top right corner:

[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]

Now, 8 - 4 = 4

80 / 4 = 20

For the bottom right corner:

[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]

Now, 6 - 4 = 2

52 / 2 = 26

Another method:

5×6+7=37

7×6-5=37

6×4+10=34

10×4-6=34

4×3+8=20

8×3-4=20

So, 4×5+6=26

6×5-4=26

Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question