1. Find the equation of each of the straight line graphs that passes through the given
points.
(i) (1, 7) (2, 10)
(ii) (3, -1) (-2, 9)
(iii) (4, 3) (8,4)
(iv) (2, -5) (-2, 7
(v) (-1, -8) (3, 12)
(vi) (-5, 1) (10, –5)

(viii) (2, 2) (0, -4)

The horizontal distance from the base of the skyscraper out to the ship is 349.8feet

The angle situated above the hill is known as  the angle of depression

Given the following parameters

Height of the harbor = 824 feet

Angle of depression = 67degrees

According to SOH CAH TOA identity:

tan 67 = opp/adj
tan 67 = 824/d

d = 824/tan67
d = 349.8 feet

Hence the horizontal distance from the base of the skyscraper out to the ship is 349.8feet

Learn more on angle of depression here: https://brainly.com/question/12483071

4/(√x - √(x - 2)) × (√x + √(x - 2))/(√x + √(x - 2))

= 4 (√x + √(x - 2)) / ((√x)² - (√(x - 2))²)

= 4 (√x + √(x - 2)) / (x - (x - 2))

= 4 (√x + √(x - 2)) / (x - x + 2)

= 4 (√x + √(x - 2)) / 2

= 2 (√x + √(x - 2))

Answer:

2110

Step-by-step explanation:

4100-1990=2110

⇛6(2 - 6x) = -24

⇛12 - 36x = -24

⇛-36x = -24 - 12

⇛-36x = -36

⇛x = -36/-36

⇛x = 1

Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

Answer:

25827165

Step-by-step explanation:

from the question that we have here

the total population = 54 students

the sample size = 6 students

So given this information carol has to pick the total samples from the 54 students that we have here

the total ways that she has to do this

= 54 combination 6

= 54C6

= [tex]\frac{54!}{(54-6)!6!}[/tex]

= 25827165

this is the total number of possible samples that could occur given the total population of 54 students.

Answer:

c

Step-by-step explanation:

took the test so i assume its this question

Answer:

11

Step-by-step explanation:

8 + 9 + -6

8 + 9 = 17

17 + (-6) = 11

Answered by Gauthmath

Answer:

$15798.4

Step-by-step explanation:

We will have to use this formula A = Peᵃᵇ

A = Final amount

P = Initial amount (12,000)

e = Mathematical constant: 2.7183

a = Interest rate (5.5% or 0.055)

b = Years

So our equation will look like this

A = 12,000e⁵ ⁰·⁵⁵

A = 12,000(2.7183)·²⁷⁵

A = 12,000(1.316533)

A = 15798.396

Answer:

1^1 + 0^1 =1

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

sin^2 (pi/2)   + cos^2  (pi/2)  =1

1^1 + 0^1 =1

Answer:

1/3

Step-by-step explanation:

common ratio is

9÷27=1/3

3÷9=1/3

1÷3=1/3

therefore common ratio is 1/3

Answer: 1/3

Step-by-step explanation:

Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.

Answer: y = -3/2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

y = -3/2x + 5

Answer:

y = -3/2x + 5 totally

Step-by-step explanation:

The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the

tunnel with a cross section that is the shape of half of a sine curve and the

height of the tunnel at the edge of the road, (approximately 7.07 ft.) are

found by applying the following steps

(a) The equation for the sine curve is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is approximately 7.07 feet

The reason for the above answers are presented as follows;

(a) From a similar question posted online, the missing part of the question

is, what is the height of the tunnel at the edge of the road

The known parameters;

The shape of the tunnel = One-half sine curve cycle

The height of the road at its highest point = 10 ft.

The opening of the tunnel at road level = 24 ft.

The unknown parameter;

The equation of the sine curve that fits the opening

Method;

Model the sine curve equation of the tunnel using the general equation of a sine curve;

The general equation of a sine curve is y = A·sin(B·(x - C) + D

Where;

y = The height at point x

A = The amplitude = The distance from the centerline of the sine wave to the top of a crest

Therefore;

The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.

D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)

The period is the distance between successive points where the curve passes through the center line while rising to a crest

Therefore

The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.

T = 48 ft.

We get;

48 = 2·π/B

B = 2·π/48 = π/24

By plugging in the values for A, B, C, and D, we get;

y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)

The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is given by substituting

the value of x at the edge of the road into the equation for the sine curve

as  follows;

The width of the shoulders = 6 feet

∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.

Therefore, we get;

y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2

y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2

The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.

Learn more about the sine curve here;

https://brainly.com/question/3827606

Answer:

-6/5

Step-by-step explanation:

- 2/3 (2 - 1/5)

Distribute

-2/3 *2 -2/3 *(-1/5)

-4/3 + 2/15

Get a common denominator

-4/3 *5/5 +2/15

-20/15 +2/15

-18/15

Simplify

-6/5

Answer:

the answer to this equation is c (10)

Answer:

40

Step-by-step explanation:

Let x represent the mystery number.

Create an equation to represent the situation, then solve for x:

0.85x - 5 = 29

0.85x = 34

x = 40

So, the mystery number is 40.

9514 1404 393

Answer:

  50

Step-by-step explanation:

The number you choose depends on the location you consider to be zero height.

If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.

angle G

sin inverse (21/29) = 46.4

GH

c^2 - b^2 = a^2

29^2 - 21^2 = a^2

a = √(29^2 - 21^2)

GH = 20

therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20

Answer:

(a+b)(a-b)

Step-by-step explanation:

[tex]\\ \sf\longmapsto (a+b)(a-b)[/tex]

[tex]\\ \sf\longmapsto a(a-b)+b(a-b)[/tex]

[tex]\\ \sf\longmapsto a^2-ab+ba-b^2[/tex]

[tex]\\ \sf\longmapsto a^2-ab+ab-b^2[/tex]

[tex]\\ \sf\longmapsto a^2-b^2[/tex]

[tex]\large\bf{\orange{ \implies}} \: \tt \: {a}^{2} \: - \: {b}^{2} [/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: (a + b) \quad \: (a - b)[/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: a \: (a - b) \quad \: b \: (a - b)[/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: ab \: + \: ba \: - \: {b}^{2} [/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: ab \: + \: ab \: - \: {b}^{2} [/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: \cancel{ab} \: + \: \cancel{ab} \: - \: {b}^{2} [/tex]

[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: {b}^{2} [/tex]

The LEAST selling price of the laptop should be ;

$1024.1 in other to avoid loss.

Price of laptop = $770

Tax = 20%

VAT = 13%

TO avoid loss ;

both the VAT percentage and TAX must be added to the price of the laptop:

Total percentage = VAT + TAX = (20 + 13) = 33%

THEREFORE, Least selling price should be :

Price of laptop * (1 + 33%)

770 * 1.33

= $1024.1

Learn more about TAX :

https://brainly.in/question/31818297

Answer:

a=1, b=-2,c=-1

Step-by-step explanation:

1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1

The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The angle is given below.

⇒ 30.283°

Convert 30.283° into a degree-minute-second format. Then we have

⇒ 30° (0.83 x 60')

⇒ 30° 16.98'

⇒ 30° 16' (0.98 x 60'')

⇒ 30° 16' 58"

The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.

More about the conversion link is given below.

https://brainly.com/question/9414705

#SPJ2

Answer:

4

Step-by-step explanation:

if x+2 is a factor of the above expression then,

x=-2

so putting the value of x in above expression we get,

(-2)^3+2×(-2)^2+2×(-2)+k=0

or,-8+8-4+k=0

k=4

Answer:

Step-by-step explanation:

If (x + 2) is a factor of a polynomial then ( - 2 ) is the zero of that polynomial ⇒ ( - 2 )³ + 2( - 2 )² + 2( - 2 ) + k = 0 ⇒ k = - 4

Answer:

given

f(x).4x+5

fog(x).8x+13

now

fog(x):8x+13

4x+5(g(x)):: 8x+13

g(x):: 8x+13/4x+5

Answer:

g(x) = 2x + 2

Step-by-step explanation:

One is given the following information:

One is asked to find the following:

Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:

f(g(x)) = 8x + 13

Substitute the given infromation into the equation:

4(g(x)) + 5 = 8x + 13

Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:

4(g(x)) + 5 = 8x + 13

Inverse operations,

4(g(x)) + 5 = 8x + 13

4(g(x)) = 8x + 8

g(x) = (8x + 8) ÷ 4

g(x) = 2x + 2

Answer:

Step-by-step explanation:

Triangular cross-section.

Answer:

it is a triangle cross-section

hope this answer helps you

Plz make me a brainlist

Answer:

G(-1) = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

G(x) = 5x + 3

Step 2: Evaluate

Answer:

G = -2

Step-by-step explanation:

Plug in -1 for x.

5(-1) + 3

-5 + 3

-2

G = -2

Answer:

175731 is one of the answers of the 6 digit number

some others are:

275732

375733

475734

575735

675735

775734

875732

The 6-digit number is 175731.

The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.

Let the number would be ABCDEF

Given the condition that the value of its thousands of digits is 5,000.

So C = 5

Given the condition that the value of its hundreds of digits is 700.

So D = 7

Given the condition that Its tens digit is 2 less than the thousand digits.

So E = 5-2 = 3

Given the condition that Its hundred thousand digits is the same as the hundred digits.

So B = 7

Therefore, all possible answers:

275732

375733

475734

575735

675735

775734

875732

Hence, the 6-digit number is 175731

Learn more about the place value strategy here:

brainly.com/question/654419

#SPJ2

Answer:

(0, 3)

Step-by-step explanation:

y = 3 is the horizontal tangent to y = x^2+3, and passes the parobala at (0, 3)