Maths assignment
y^2-36

Answer:

2√10 km

Step-by-step explanation:

By Pythagoras theorem,

x^2 + 9^2 = 11^2

x^2 + 81 = 121

x^2 = 121 - 81

x^2 = 40

= 4 x 10

x^2 = 2^2 x 10

x = 2√10 km

Step-by-step explanation:

Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)

= 200+625-1156 ÷ (2000)

= 1069 ÷2000

Cos A = 0.5345

A= cos inverse 0.5345

A = 57.7

Answer:

57.7

Step-by-step explanation:

took the test

Answer:

3

Step-by-step explanation:

We are going to be using cofunction identity cos(90-x)=sin(x).

Apply to either side but not both.

cos(22f − 1) = sin(7f + 4)

sin(90-[22f-1])=sin(7f+4)

90-[22f-1]=7f+4

Distribute

90-22f+1=7f+4

Combine like terms

91-22f=7f+4

Add 22f on both sides

91=29f+4

Subtract 4 on both sides

87=29f

Divide 29 on both sides

3=f

f=3 is between 0 and 90

Answer:

The answer is "3."

Step-by-step explanation:

Just submitted the test and got the answer correct!

Answer:

x =  20

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, sum to 180°

5x + 4x = 180

9x = 180 ( divide both sides by 9 )

x = 20

Answer:

The value of x is 40⁰.

Step-by-step explanation:

5x + 4x = 360⁰

DUE TO THE SUM OF QUADRATIC ANGLE.

Answer:

B.

Step-by-step explanation:

Since the numbers in the root is all the same, lets say [tex]\sqrt{2}[/tex] is a variable.

7x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex]

Group with like terms:

7x[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

Combine like terms:

8x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

There you have it! Since all the square roots are the same thing, we can treat them like variables.

the answer is B..................

Answer:

8/15

Step-by-step explanation:

The ratio of perpendicular to base is tan B .

Here ,

=> tan B = 8 ft/ 15ft

=> tan B = 8/15

Answer:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

Answer:

the angle <ABC is equal to 65°

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

Answer:

2.5 years

Step-by-step explanation:

The given amount invested, which is the principal, P = $16,800

The simple interest rate, R = 5% per annum

The intended total value of the investment, A = $18,900

The simple interest on the principal, I = A - P

∴ I = $18,900 - $16,800 = $2,100

The formula for the simple interest, I, is given as follows;

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Therefore, we have;

[tex]T = \dfrac{I \times 100}{P \times R}[/tex]

Plugging in the values, gives;

[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]

The time it will take the investment to grow to $18,900 is T = 2.5 years

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

Answer:

x = 27.5.

Step-by-step explanation:

There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.

So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.

With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.

Therefore, x = 27.5.

Answer:

20

Step-by-step explanation:

3 (b + a) = c

3 (4 + 5) = 7

12 + 15 = 7

27 = 7

27 - 7

20

[tex]\huge\boxed{ \sf{Answer}} [/tex]

Given,

[tex]a = 5 \\ b = 4 \\ c = 7[/tex]

And the equation we need to solve is,

[tex]3(b + a) = c[/tex]

To find the answer, you need to substitute the values of a, b & c in the equation.

[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]

↦ The answer is 20.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

answer:

to test whether agraph is linear

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

Answer:

2/60 = 1/30 = 3.3%

Step-by-step explanation:

Answer:

the answer is -3

Step-by-step explanation:

0.7x - 1.4 = -3.5

add 1.4 to both sides of the equation

you're left with 0.7x = -2.1

then divide both sides by 0.7

you're left with your answer of -3

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]

[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]

[tex]y+2=\dfrac{12}{8}(x-1)[/tex]

[tex]y+2=\dfrac{3}{2}(x-1)[/tex]

Multiply both sides by 2.

[tex]2(y+2)=3(x-1)[/tex]

[tex]2y+4=3x-3[/tex]

[tex]2y-3x=-3-4[/tex]

[tex]-3x+2y=-7[/tex]

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

[tex]-3x+2y>-7[/tex]

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

[tex](-3x+2y)(-1)<-7(-1)[/tex]

[tex]3x-2y<7[/tex]

Therefore, the correct option is D.

Answer:

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

Step-by-step explanation:

Given

[tex]\{(5, -9), (6, -6), (-3, 8), (9, -6)\}[/tex]

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

[tex]\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}[/tex]

[tex]\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}[/tex]

Required

Which is not a function

An ordered pair is represented as:

[tex]\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}[/tex]

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

l

Step-by-step explanation:

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Answer:

160=130+x

x=160-130

x=30

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.