Tommy went to the shop where there was a 20% off sale taking place
The shirt he wanted to buy was originally £20
How much money does he save in the sale?

Answer:

x = 24

Step-by-step explanation:

mathematically, in a cyclic quadrilateral, two opposite angles are supplementary

what this mean is that they add up to be 180

From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees

thus, we have it that;

(4x + 9) + (3x + 3) = 180

4x + 3x + 9 + 3 = 180

7x + 12 = 180

7x = 180-12

7x = 168

x = 168/7

x = 24

Answer:

2 sheep

Step-by-step explanation:

If you have 36 sheep  and you sell:

first day    1/2 of them  you sold               18

second day  1/3  them you sold                12

On thhe third day  1/9  them you sold       4

Therefore you sold 18 + 12  + 4  = 34

And you still have  2 sheep

Answer:

t ≈ 3.65 s

Step-by-step explanation:

Let the distance the object travels after leaving the balloon be x.

Using Newton's equation of motion, we have;

s = ut + ½gt²

We are given;

s = 30 m

u = -10 m/s (negative because it is an upward motion)

Thus;

30 = -10t + ½(10)t²

30 = -10t + 5t²

5t² - 10t - 30 = 0

Using quadratic formula, we have;

t ≈ 3.65 s

Answer:

67°

Step-by-step explanation:

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

The one in the middle 100% correct

Answer:

second option

Step-by-step explanation:

Ratio of square to circle = 1 : 3

In the second option:

Square = 2  & circles = 6

Ratio = 2 : 6  and after simplifying, Ratio = 1 : 3

Answer:

-1

Step-by-step explanation:

1. Sets the exponents equal

3b-1 = b-3

2. collect like terms and calculate it

3b-b=1-3

2b= -2

(divide both side by 2)

b=-1

Answer:

156

Step-by-step explanation:

area = 4*4 + 14 * 10

        = 16 + 140

        =156 cm²

Answer:

A.

Step-by-step explanation:

4y = 12x + 16

3x = y - 4

=>

y = 3x + 4

using that in the first equation

4(3x+4) = 12x + 16

12x + 16 = 12x + 16

=> both lines/equations are identical, so they have infinitely many solutions.

Answer:

The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.

The equation will be:

25 + d = t

where t is total money

Answer:

Step-by-step explanation:

The easiest way to solve this is with calculus, believe it or not. The position function is

[tex]s(t)=-16t^2+64t[/tex]. The first derivative of this is the velocity function:

v(t) = -32t + 64. From physics, we know that at the max height of an object's path, the velocity is equal to 0, so setting this velocity equation equal to 0 and solving for time, will tell us the time it took to get to the max height (which we don't know yet, but we will in a bit):

0 = -32t + 64 and

-64 = -32t so

t = 2 seconds. It takes 2 seconds to reach a max height. Plugging that 2 in for t in the position function will tell you the max height that corresponds to this time:

[tex]s(2)=-16(2)^2+64(2)[/tex] and

s(2) = 64 feet.

So the max height is 64 feet and it is reached at 2 seconds after launching.

Also from physics we know that at halfway through a parabolic path, which is also the max height, we are halfway through time-wise as well. That means that if it takes 2 seconds to reach the max height from the ground, it will take another 2 seconds to fall to the ground.

So the total time the rocket is in the air is 4 seconds: 2 seconds to reach the max height and another 2 to fall back down.

Answer:

Step-by-step explanation:

Answer:

18 pencils in 3 packs.

Step-by-step explanation:

Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:

36/6 = 6

There are 6 pencils in each pack.

Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:

Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)

                                       = 3 x 6

                                       = 18

There are 18 pencils in 3 packs.

~

Answer:

1.25% and 16 times

Step-by-step explanation:

Since the interest is compounded quarterly it will be compounded 4 times a year. So 4 x 4 is 16, so it will be compounded 16 times.

Then you have to divide the 5% by four to get how much will be compounded each quarter. So, (0.05 / 4) = 0.0125, which is 1.25%.

Answer:

1.25% and 16 times

Step-by-step explanation:

Answer:

For two vectors to be orthogonal it means that their dot product must be equal to zero.

Usually dot product of perpendicular vectors is zero and thus all perpendicular vectors are orthogonal.

Answer:

D

Step-by-step explanation:

Answer:

Only 10 base units to learn

Step-by-step explanation:

The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units

During conversion in the metric system, which is decimal based, it is only required to move the decimal point

The prefixes which are used to specify multiples and submultiples are the same through out

The decimal system is based on the powers of ten

The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)

Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn

Answer:

The slope is -2/3 and the y-intercept is -1.

Step-by-step explanation:

In a linear equation like this, the slope is the coefficient in front of the x after the expression has been completely simplified. In this case, the slope is -2/3.

For the y-intercept, that is simple too; since it is simplified, it is just the number that comes after the x package. So, for this, the y-intercept is -1.

Answer:

0.037

Step-by-step explanation:

Given that,

Let a and b be the solutions to [tex]x^2 + x -3 = 0[/tex]

It can be solved using quadratic formula where a = 1, b = 1 and c = -3

So,

[tex]x=\dfrac{-1+\sqrt{1^2-4\times 1\times (-3)}}{2(1)},\dfrac{-1-\sqrt{1^2-4\times 1\times (-3)}}{2(1)}\\\\x=1.30,-2.3[/tex]

Let a = 1.3, b = -2.3

The value of [tex]a^3 -4b^2 + 19[/tex] can be given by :

[tex]a^3 -4b^2 + 19=(1.3)^3-4\times (-2.3)^2+19\\\\=0.037[/tex]

So, the value of the given expression is 0.037.

Given function:

Find

Substitute x with r = 5:

g(r + 5) = 5(r + 5) + 3 = 5r + 25 + 3 = 5r + 28

Answer:

G ( r + 5 ) = 5r + 28

Step-by-step explanation:

Given ;

G ( x ) = 5x + 3

To Find :-

G ( r + 5 )

Solution :-

plug r + 5 as x in the function.

distribute 5

combine like terms

Answer:

(-5,31/2)

Step-by-step explanation:

open bracket

y=1/2x^2+5x+28

compare with y=ax2+bx+c

use formula (-b/2a,4ac-b2/4a)

Answer: Commutative property of addition

Step-by-step explanation:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\text{1 + 3 + 4 = 4 + 3 + 1}[/tex]

[tex]\large\text{1 + 3 + 4}[/tex]

[tex]\large\text{4 + 4}[/tex]

[tex]\large\text{= \bf 8}[/tex]

[tex]\large\text{4 + 3 + 1}[/tex]

[tex]\large\text{7 + 1}[/tex]

[tex]\large\text{= \bf 8}[/tex]

[tex]\large\text{\bf 8 = 8}[/tex]

[tex]\large\textsf{We could remove Option C. because there’s no sign of multiplication.}[/tex]

[tex]\large\textsf{This leaves us to Option A and Option B because the equation(s) has}\\\large\textsf{sum/addition}[/tex]

[tex]\large\textsf{Associative Property of Addition formula is:}[/tex]

[tex]\bullet\large\text{ \bf (a + b) + c = a + (b + c)}[/tex]

[tex]\large\textsf{Commutative Property of Addition formula is:}[/tex]

[tex]\bullet\large\text{ \ \bf a + b = b + a}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf Commutative Property of Addition}}}\\\boxed{\huge\textsf{(Option B.)}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

Given

length of rectangular sheet of paper is 12 (1/2) i.e. (25/2)

Breadth of rectangular sheet of paper is 10 (2/3) i.e. (32/3)

But we know that perimeter of rectangle = 2 (length + breadth)

Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]

LCM of 2 and 3 is 6,

by taking this and simplifying we get

Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]

= 2[(75/6) + (64/6)]

= 2(139/6) = (139/3)

= 46 (1/3) cm

Answer:

Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]

LCM of 2 and 3 is 6,

by taking this and simplifying we get

Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]

= 2[(75/6) + (64/6)]

= 2(139/6) = (139/3)

= 46 (1/3) cm

Step-by-step explanation:

Answer:

(-7, -3)

Step-by-step explanation:

So the formula is (x, y) --> (-y, x) for a 90 degrees counterclockwise rotation.

To apply this formula to (-3,7), first identify which is the x-coordinate and which is the y-coordinate.

x-coordinate is -3 & y-coordinate is 7

Then you literally just substitute it into the formula like so:

(-y, x) -->(-(7), (-3)) --> (-7, -3)

Try to put parantheses around the coordinate when substituting to prevent confusion & incorrect negative signs.

Hope it helps and good luck (●'◡'●)

Answer:

(-7,-3)

Step-by-step explanation:

You could read (x,y)->(-y,x) as if I have the point (x,y), the image point is (opposite of y,x).

So shorthand the rule is just saying

(x,y)->(opposite of y, x)

(-3,7)->(-7,-3)

A few more examples:

(5,7)->(-7,5)

(-5,7)->(-7,-5)

(-5,-7)->(7-,5)

(5,-7)->(7,5)

This whole explanation comes down to reading-u as opposite of u.

Opposite just means to change the sign.

Another way to read -u is -1×u.

Example:

Q: evaluate -u if u=8

A: -8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×8=-8 or the opposite or 8 is -8.

Example:

Q: evaluate -u if u=-8

A: 8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×-8=8 or the opposite or -8 is 8.

Answer:

1/root(3)

Step-by-step explanation:

the steps are in the pic above.

The value of tan pi/6 is 0.5773502.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given that, what is the exact value of tan pi/6,

To find the value of tan π/6 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.

The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence, the value of tan pi/6 = y/x = 0.5774 (approx)

Learn more about trigonometric functions click;

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