WILL GIVE 100 POINTS



1. In a music stadium, there are 18 seats in the first row and 21 seats in the second row. The number of seats in a row continues to increase by 3 with each additional row.

(a) Write an explicit rule to model the sequence formed by the number of seats in each row. Show your work.

(b) Use the rule to determine which row has 120 seats. Show your work.

Answer:

7-c < 30

Step-by-step explanation:

its in your question.

Answer:

Step-by-step explanation:

Let's angle be x and y

Then......

⅓x+12=y......eqn(I)

Since are linear

x+y=180

y=180-x.....eqn(ii)

Substitute the eqns

You get x=126°

From eqn (iii)

You get y=54°

Those are angles

The measures of both angles are 126° and 54°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given that,

Two angles are a linear pair.

Let x and y be the measures of two angles.

We have,

y = 1/3 x + 12

Sum of the angles is supplementary.

x + y = 180

x + 1/3 x + 12 = 180

4/3 x = 168

x = 126°

y = 180 - 126 = 54°

Hence the angles are 126° and 54°.

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Answer:

The top cable is 115.52 feet long

The bottom cable is 110.86 feet long

Step-by-step explanation:

The ground anchor #2, the tower, ground level, and both cables form a figure made of two right triangles as shown in the figure below

We are required to compute L1 and L2 which are the hypotenuses of both triangles from which we have both legs

We'll apply the Pythagoras's theorem. If a and b are the legs of a right triangle and c its hypotenuse, then

[tex]c^2=a^2+b^2[/tex]

For the bottom ground support cable, a=41, b=103

[tex]L2^2=41^2+103^2[/tex]=110.86\ feet

For the top ground support cable, a=41, b=108

[tex]L1^2=41^2+108^2[/tex]=115.52\ feet

The top cable is 115.52 feet long

The bottom cable is 110.86 feet long

Answer:

The length of the diagonal measures 54.2 meters

Step-by-step explanation:

Pythagorean theorem,

a² + b² = c²

a = 21

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

√2941 = c

54.23098... = c

54.2 = c

The length of the diagonal measures 54.2 meters.

We have given that,

A rectangular swimming pool is 21 meters

wide and 50 meters long.

We have to determine the length of the diagonal.

a² + b² = c²

a and b are sides of the triangle and c is the hypotenuse

a = 21,

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

Taking square root on both side

√2941 = c

54.23098 = c

54.2 = c

Therefore the length of the diagonal measures 54.2 meters.

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Answer:

The order pair is (2,0)

Step-by-step explanation:

On the picture

Answer:

(2,6)

Step-by-step explanation:

The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:

[tex]y+5 = \frac{5}{3}(x-10)[/tex]

Step-by-step explanation:

Given

Slope = m = 5/3

Point = (x1,y1) = (10, -5)

Point-slope form is:

[tex]y-y_1 = m(x-x_1)[/tex]

As the slope and point is already given, we only have to put the values in the equation to get the equation of required line:

[tex]y-(-5) = \frac{5}{3}(x-10)\\y+5 = \frac{5}{3}(x-10)[/tex]

Hence,

The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:

[tex]y+5 = \frac{5}{3}(x-10)[/tex]

Keywords: equation of line, point-slope form

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Answer:

14,747.20

There are 52 weeks in a year being paid bi-weekly means being paid every other week or 26 times a year. So 567.20 * 26 is 14747.20.

Answer:

The rate of interest applied fro compound interest is 24.5 %  

The rate of interest applied simple interest is 37.5 %

Step-by-step explanation:

Given as :

The Principal amount that is deposited = $ 800

The Time period = 24 months = 2 years

The Interest earn = $ 200

Let the rate of interest = R %

So, The Amount = Principal deposited - interest earn

Or, A = $ 800 - $ 200

∴ Amount = $ 600

From compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]

Or, $ 600 = $ 200 × [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, [tex]\frac{600}{200}[/tex] = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, 3 = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, [tex]3^{\frac{1}{2}}[/tex] = (1 +[tex]\frac{R}{100}[/tex])

Or, 1.245 = (1 +[tex]\frac{R}{100}[/tex])

or, 1.245 - 1 = [tex]\dfrac{R}{100}[/tex]

or, 0.245 × 100 = R

So, the rate is = 24.5 %

Hence The rate of interest applied fro compound interest is 24.5 %  Answer

From Simple Interest method

Simple Interest = [tex]\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}[/tex]

Or, $ 600 = [tex]\dfrac{\textrm 800\times \textrm R\times \textrm 2}{100}[/tex]

Or,  $ 600 × 100 = $ 800 × R × 2

Or, R = [tex]\frac{60000}{1600}[/tex]

∴ R = 37.5 %

So, The rate is 37.5 %

Hence The rate of interest applied simple interest is 37.5 %Answer

Answer:

31 is a positive number, while -169, -369, and -569 is negative.

Step-by-step explanation:

Negative numbers, are numbers less then 0 and include a negative sign that looks like this "-".

Positive numbers are numbers above 0 and don't include a negative sign.

-169, -369, and -569 is negative because they have a negative symbol and the number is below 0, while 31 is positive because it's above 0 and doesn't include a negative sign.

Answer: 12

Step-by-step explanation: To solve this equation, since x is being divided by 2, in order to get x by itself, we need to multiply by 2 on both sides of the equation.

On the left side of the equation, the 2's cancel and we have x and on the right side of the equation, 6 × 2 gives us 12 so we have x = 12 which is the solution for our equation.

To check our solution, we plug 12 in for x in the original equation.

Image provided.

Answer:

C = 13%

Step-by-step explanation:

Answer:

a. yes

b. no

c. yes

d. yes

Step-by-step explanation:

For a, 27 + 38 can be broken apart. 27 is broken up by adding smaller numbers (20 + 7 = 27) and the same is done with 38 (30 + 8 = 38), so A and C shows a way to add 27 and 38. In C, the numbers are just put into a different order. B is not a way to add 27 and 38, because the sum is different.

27 + 38 = 65, however 20 + 70 + 38 = 128. The addition problem for D is a way to solve for 27 + 38, because it is broken up differently than A and C. They instead added the 20 and 30 together first, then split up 15 (from 8+7) into 10 and 5. So D is a way to solve, because it gets the same answer as 27 and 38 :D

Slope formula: y2-y1/x2-x1

Line AB:

= 7-4/7-3

= 3/4

Line CD:

= 8-0/-6-0

= 8/-6

= -4\3

______

Best Regards,

Wolfyy :)

Answer:

The result is 10.42 kilometers, or 10,420 meters or 1'042,000 centimeters.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

8 kilometers plus 2,300 meters plus 12,000 centimeters

2. Let's do the conversions to find the result either in kilometers, meters or even centimeters.

A. In kilometers:

8 kilometers

2,300 meters = 2.3 kilometers

12,000 centimeters = 120 meters = 0.12 kilometers

10.42 kilometers

B. In meters

8 kilometers = 8,000 meters

2,300 meters

12,000 centimeters = 120 meters

10,420 meters

C. In centimeters

8 kilometers = 8,000 meters = 800,000 centimeters

2,300 meters = 230,000 centimeters

12,000 centimeters

1'042,000 centimeters

The final sum is 10,420 meters.

To solve the mathematical problem of adding different units of measurement, we first need to convert everything to the same unit. In this case, let's convert all measurements to meters (m).

Now, add these values together:

8000 m + 2300 m + 120 m = 10,420 meters

After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

To find the height of the image after it has been scaled by 80% multiple times, we can use the formula for scaling:

[tex]\[ \text{New height} = \text{Original height} \times (\text{Scale factor})^{\text{Number of times scaled}} \][/tex]

Given that the original height is 150 mm and the scale factor is 80% (or 0.8), we can calculate:

a. After being scaled 3 times:

[tex]\[ \text{New height} = 150 \times (0.8)^3 = 150 \times 0.512 = 76.8 \, \text{mm} \][/tex]

b. After being scaled 6 times:

[tex]\[ \text{New height} = 150 \times (0.8)^6 = 150 \times 0.262 \approx 39.3 \, \text{mm} \][/tex]

As the image is scaled down by 80% each time, its height decreases significantly with each iteration.

After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

These heights fall within the acceptable range for a U.S. passport photo (25-35 mm).

The probable question may be:

The distance from Elena's chin to the top of her head is 150 mm in an image. For a U.S. passport photo, this measurement needs to be between 25 mm and 35 mm. PASSPORT PHOTO 1. Find the height of the image after it has been scaled by 80% the following number of times. Explain or show your reasoning. a. 3 times b. 6 times

Step-by-step explanation:

When a factor appears in both the numerator and denominator, that is a hole in the function.

Therefore, the domain of h(x) is (-∞, 4) (4, ∞).

Which means the range of h(x) is (-∞, 5) (5, ∞).

Graph: desmos.com/calculator/j58gdgugxy

Each team will paint 238 ft of the fence.

Step-by-step explanation:

Length of fence = 1666 ft

Number of students teams = 7

Let x be the length covered by each team, therefore,

7x=1666

Dividing both sides by 7;

[tex]\frac{7x}{7}=\frac{1666}{7}\\x=238\ ft[/tex]

Each team will paint 238 ft of the fence.

Keywords: length, division

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Answer:

[tex]\large\boxed{5\dfrac{1}{5}\ decimeters=52\ centimeters}[/tex]

Step-by-step explanation:

[tex]1\ dm=10\ cm\qquad\text{(1 decimeters = 10 centimeters)}\\\\\text{Therefore}\\\\5\dfrac{1}{5}\ dm=\dfrac{5\cdot5+1}{5}\ dm=\dfrac{26}{5}\ dm=\dfrac{26}{5}\cdot10\ cm=\dfrac{260}{5}\ cm=52\ cm[/tex]

To convert 5 1/5 decimeters to centimeters, you can multiply 5 by 10 and add the result to the centimeters part (1/5).

To convert decimeters to centimeters, we need to know that there are 10 centimeters in 1 decimeter. So, to convert 5 1/5 decimeters to centimeters, we can multiply 5 by 10 and add the result to the centimeters part (1/5). Converting 1/5 to centimeters gives us 2 centimeters. Therefore, 5 1/5 decimeters is equal to 51 centimeters.

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Answer:

D) 0.0004

Step-by-step explanation:

(0.02)^2=0.02*0.02=0.0004

Answer:

38 Weeks

Step-by-step explanation:

1999$ x .05% = 99.95 Down Payment

Remaining Balance = 1899.05

1899.05$ / 50$ = 37.98100

It would approximately take a total of 38 weeks to pay it off!

Answer: 38 weeks

Step-by-step explanation:

$1999 * 0.05 = $99.95

1999 - 99.95 = 1899.05

1899.05/50 = 37.981

38 weeks

√5 • √80

Combine the two using the product rule for radicals:

√(5 • 80)

Multiply:

√400

Rewrite 400 as 20^2

√20^2

= 20

The answer is 20

Answer: No, he burns 480

Step-by-step explanation: you multiply 8 by 60, the amount of minutes in an hour

Answer:

The approximate perimeter of the trapezoid is 31 units

Step-by-step explanation:

step 1

Plot the trapezoid

Let

A(-5, -3), B(-2, 5), C(2, 5), and D(5, -3)

see the attached figure

step 2

Find the perimeter of trapezoid

we know that

The perimeter of trapezoid is equal to

[tex]P=AB+BC+CD+AD[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

we have

[tex]A(-5, -3),B(-2, 5)[/tex]

substitute in the formula

[tex]d=\sqrt{(5+3)^{2}+(-2+5)^{2}}[/tex]

[tex]d=\sqrt{(8)^{2}+(3)^{2}}[/tex]

[tex]d_A_B=\sqrt{73}\ units[/tex]

Find the distance BC

we have

[tex]B(-2, 5),C(2, 5)[/tex]

substitute in the formula

[tex]d=\sqrt{(5-5)^{2}+(2+2)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]

[tex]d_B_C=4\ units[/tex]

Find the distance CD

we have

[tex]C(2, 5),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-5)^{2}+(5-2)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(3)^{2}}[/tex]

[tex]d_C_D=\sqrt{73}\ units[/tex]

Find the distance AD

we have

[tex]A(-5, -3),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3+3)^{2}+(5+5)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(10)^{2}}[/tex]

[tex]d_A_D=10\ units[/tex]

step 3

Find the perimeter

[tex]P=AB+BC+CD+AD[/tex]

substitute the values

[tex]P=\sqrt{73}+4+\sqrt{73}+10[/tex]

[tex]P=31\ units[/tex]

Answer:

D) 28+32

Step-by-step explanation:

4(7+8)=4(15)=60

Answer:

45%

Step-by-step explanation:

27/60 = .45

First, divide.

27 / 60 = 0.45

Multiply by 100%.

0.45 * 100% = 45%

______

Jina spent 45% of her total on fruits.

______

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Wolfyy :)

Answer:

I think its 90°, since it l00ks like a right angle

Answer:

C. Rose oil

Step-by-step explanation:

Which medicinal product is made using animal products?

A. Flu vaccine

O

B. Aspirin

C. Rose oil

O

D. Morphine

SUBM

Answer:A. Flu vaccine

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

100 X 5 = 5 + 5 + 5 + 5...100 times = 100 + 100 + 100 + 100 + 100 = 500

Answer:

500

Step-by-step explanation:

yes

Distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.

Given that

Height of position of pilot from the ground = 30000 feet

Angle of depression when he looks down at runway = 6o

Need to measure along the ground, distance between runway and pilot that is horizontal distance between runway and pilot.

Consider the figure attached below

D represents position of runway.  

P represents position of pilot.

PG represents height of position of pilot from the ground that means PG = 30000 feet

PH is virtual horizontal line and HPD is angle of depression means ∠ HPD = 6 degree

AS DG and HP are horizontals, so DG is parallel to HP.

=>  ∠ HPD =∠ PDG =  6 degree  [ Alternate interior angle made by transversal PD of two parallel lines ]

We need to calculate DG

Consider right angles triangle PGD right angles at G

[tex]\text {As } \tan x=\frac{\text { Perpendicular }}{\text { Base }}[/tex]

[tex]\tan \angle \mathrm{PDG}=\frac{\mathrm{PG}}{\mathrm{GD}}[/tex]

[tex]\begin{array}{l}{=>\mathrm{GD}=\frac{\mathrm{PG}}{\tan \angle \mathrm{PDG}}} \\\\ {=>\mathrm{GD}=\frac{30000}{\tan 6^{\circ}}=285430.9336}\end{array}[/tex]

As one foot = 0.000189 miles

[tex]=>285430.9336 \text { feet }=285430.9336 \times 0.000189 \text { miles }=53.9464 \text { miles. }[/tex]

Hence distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.

Final answer:

To find the distance to the runway, we can use trigonometry and create a right triangle using the pilot's height and the angle of depression. Using the tangent function, we can solve for the distance. The pilot is approximately 58.47 miles away from the runway.

Explanation:

To find the distance to the runway, we can use trigonometry. The angle of depression of 6 degrees tells us that the runway is below the pilot's line of sight. We can create a right triangle with the pilot's height of 30,000 feet as the opposite side and the distance to the runway as the adjacent side. Using the tangent function, we can solve for the distance:

Tan(6) = Opposite/Adjacent

Tan(6) = 30,000/Adjacent

Adjacent = 30,000/Tan(6)

Using a calculator, we find that the pilot is approximately 308,517 feet away from the runway.

To convert this distance to miles, we divide by 5,280 (since there are 5,280 feet in a mile):

308,517/5,280 ≈ 58.47 miles

Therefore, the pilot is approximately 58.47 miles away from the runway.