decrease £16855.21 by 3.5% rounded to 2 dp

The triangles in the diagram indicates that ΔABD is an isosceles triangle, therefore;∠2 ≅ ∠1

The two-column method can be used to prove that the angle m∠BAC > m∠C as follows;

Statement       [tex]{}[/tex]                         Reasons

1. BC > BA       [tex]{}[/tex]                         1. Given

2. BA ≅ BD      [tex]{}[/tex]                        2. Given

3. ΔABD is an isosceles Δ[tex]{}[/tex]      3. Definition of isosceles triangle

4. ∠1 ≅ ∠2      [tex]{}[/tex]                         4. Base ∠s of isosceles triangle ΔABD

5. ∠1 = ∠2      [tex]{}[/tex]                          5. Definition of congruency

6. ∠1 = ∠3 + ∠C      [tex]{}[/tex]                 6. Exterior angle theorem

7. ∠2 = ∠3 + ∠C      [tex]{}[/tex]                7. Substitution property

8. ∠2 - ∠3 = ∠C [tex]{}[/tex]                     8. Subtraction property

9. ∠2 > ∠C [tex]{}[/tex]                             9. Definition

An isosceles triangle is a triangle that have a pair of congruent sides and one pair of congruent angles.

The reasons in the above two-columns used to prove m∠BAC > m∠C are as follows;

Isosceles triangle ΔABD

The triangle ΔABD that have side AB congruent to side BD is an isosceles triangle by definition of an isosceles triangle.

The base angles of an isosceles triangle that are angles opposite congruent sides in a triangle are also congruent.

Definition of congruency

A geometric figure is congruent to another figure if their measurements are the same.

Exterior angle theorem

The exterior angle of a triangle theorem states that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Substitution property

The substitution property of equality states that if a quantity a is equal to another quantity b then a can be substituted by b in expressions and equations without changing their value.

Subtraction property

The subtraction property of equality states that if the same quantity is subtracted from both sides of an equation, then the new amount obtained are also equal

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Answer:

XV = 16

Step-by-step explanation:

Triangle VWX is an isosceles triangle. Since the base angles are the same, the sides opposite the angle are also the same. See image. They gave VW so XV is the same as VW.

Answer:

whats the question

Answer:

What are you asking?

You need to find what x is equal to for each equation, so you can sub why x is equal to in the place I'd x to eliminate the variable

1. 6x-5y=-4

6x=5y-4

X=5/6y-2/3

2. 4x+2y=28

4x=-2y+28

X=-1/2y+7

Hope this helps!

He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.

We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.

1 Feet = 12 Inches

So, 6 Foot = 72 inches

The Length of sandwich- piece is 4 inch

So, when we convert 6 foot long sandwich into 4 inch,

Then we get number of piece is = 72/4 = 18

From 6 foot long sandwich we get 18 pieces of 4 inch long sub.

Now, Total people who will attend picnic is 40

and each people will eat 2 pieces.

It means total number of piece required = 2 (90) = 180

Mr. eaton required 180 pieces of sandwiches.

Number of sandwiches = 180 / 1.8 = 10

He should order 10 sandwiches of 6 foot long.

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Answer:

√12 = 3.46410161514

√50 = 7.07106781187

√84 = 9.16515138991

√200 = 14.1421356237

Step-by-step explanation:

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Answer:

1300=X

Step-by-step explanation:

Answer:

1,300

Step-by-step explanation:

You would first start off with adding 100 + 100= 200. Then you would add another 100 to 200 which is 300. Then comes the final step which is adding 1000 to 300 which = 1300

X= 1,300

Using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, we know that:

Lemons required to make 16 cups of lemonade: 4 lemons

Then, the rate of lemons being used in lemonade per cup:

4/16

1/4

Therefore, using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

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Answer:

35/9

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Every number you get is 4 higher than the previous number

20 minutes is [tex]1/3^{rd}[/tex] of an hour

The nth term of the pattern is (1+n)/(18+n)

What is a sequence?

succession is the act of doing something after another. successional order: a list of books organized by title. a running or interconnected sequence: a series of sonnets. something that happens after; a following event; a result; or a repercussion. In contrast to a set, the order of the components in a sequence does important, and the same elements may occur more than once at various positions. A series can officially be described as a function from natural numbers.

We are given a sequence

1/18, 2/19, 3/20, 4/21

As we can see the second term is (1+1)/(18+1)

Third term is (1+2)/(18+2)

Hence the n th term of the sequence can be given as (1+n)/(18+n)

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∠mkj angle is an adjacent interior angle to ∠jkm

Adjacent interior angles are two angles that share a common vertex and a common side. In the given angle ∠jkm, the common vertex is at point "k" and the common side is the line segment joining points "j" and "m". Therefore, the adjacent interior angle to ∠jkm is ∠mkj.

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Using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.

A function of two or more variables can yield partial derivatives.

Writing the derivative with regard to x while treating all other variables as constants allows one to determine the partial derivative of a function with respect to one variable, let's say x.

The partial derivatives for each of the other

So, for a business making two different types of solar panels, the revenue and cost functions are provided by:

[tex]\begin{aligned}&R(x, y)=4 x+2 y \\&C(x, y)=x^2-4 x y+9 y^2+22 x-114 y-5\end{aligned}[/tex]

If revenue and cost are stated in millions of dollars annually, x represents the thousands of type A solar panels produced and sold annually, and y represents the thousands of type B solar panels produced and sold annually.

By deducting costs from revenues, the profit function is obtained as follows:

[tex]\begin{aligned}&P(x, y)=R(x, y)-C(x, y) \\&P(x, y)=4 x+2 y-\left(x^2-4 x y+9 y^2+22 x-114 y-5\right) \\&P(x, y)=-x^2-9 y^2-18 x+116 y+4 x y+5\end{aligned}[/tex]

The profit function's partial derivatives with regard to x and y are as follows:

[tex]\begin{aligned}&\frac{\partial P}{\partial x}=-2 x+4 y-18 \\&\frac{\partial P}{\partial y}=4 x-18 y+116\end{aligned}[/tex]

When both of these partial derivatives are equal to zero, the profit is maximized:

[tex]\begin{aligned}&0=-2 x+4 y-18 \\&0=4 x-18 y+116\end{aligned}[/tex]

The first equation above is multiplied by two, and the two equations are then added to yield:

[tex]\begin{aligned}&0=-10 y+80 \\&y=8\end{aligned}[/tex]

Inputting into the first equation results in:

[tex]\begin{aligned}&0=-2 x+4(8)-18 \\&2 x=14 \\&x=7\end{aligned}[/tex]

Therefore, using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.

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2 notebooks

Step-by-step explanation:

the variables I'm gonna use are t for textbooks and n for notebooks

t = (n•2)+3 (two times the notebooks then add 3)

now we'll plug in the amount of notebooks we have so t=7

7=(n•2)+3

we can subtract 3 from each side that leaves us with

4=n•2

then divide by 2

2=n

Guillermo bought 2 notebooks

AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240

Permutation:

In probability, permutation refers the arrangement of objects in a definite order.

Given,

Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.

Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.

While we looking into the given question, we know that,

Total number of games = 6

Possible values = 3 ( win, loss, or draw)

Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,

=> 6! / (6 - 3)!

=> 6! / 3!

=> 120

Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,

=> 6!/ (6 - 3)!

=> 120

So, the number of ways can Alice win or draw exactly three times is

=> 120 + 120 =  240

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Answer:

9 is 8 hours and 10 is 10 hours

Answer:

9.  8 Hours

10. 10 hours

Step-by-step explanation:

48 ÷ 4 = 12  The unit rate is 12 per hour

12x = 96  Divide both sides by 12

x = 8

54 ÷ 6 = 9  The unit rate is 9 per hour

9x = 90  Divide both sides by 9

x = 10

Answer:

CPCTC

Step-by-step explanation:

BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.

Using percentage formula, Malik can afford the board with the discount only if he has $120 with him

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

To know if Malik can afford the hoverboard, we have to calculate 20% of 150

20% of 150 = 20/100 = x /150

0.2 = x / 150

x = 150 * 0.2

x = 30

Subtracting the discount, the amount will be 150 - 30 = 120

Malik can afford the hoverboard if he has $120 with him.

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Answer:

  48 = 2⁴ · 3

Step-by-step explanation:

You want the prime factorization of 48.

You recognize that 48 is an even number, so you can divide by 2 and see what's left. You can keep doing that until you get a number divisible by another prime:

  48/2 = 24

  24/2 = 12

  12/2 = 6

  6/2 = 3

3 is prime.

The prime factorization of 48 is ...

  48 = 2⁴ · 3

Answer:

y = [tex]\frac{3}{4}[/tex]x + 2

Step-by-step explanation:

To find the slope we will use the slope formula of y2-y1/x2-x1.

Our two y values are 2 and -1.

Our two x values are 0 and 4.

2 - (-1) = 3

0 - 4 = -4

3/4 = [tex]\frac{3}{4}[/tex]

y = [tex]\frac{3}{4}[/tex]x + 2

Answer:

None of the Above?

Step-by-step explanation:

1.) If we put this into words, we would get -5y+7/3y=-5-8/3y-4

2.) By moving all y terms to one side, we get -5y + 7/3y + 8/3y = -5 - 4

3.) By simplifying, you would get -4 2/3y = -9.
4.) If you divide both sides by -4 2/3, you would get that y = -9 * - 3/14 = 27/14

Answer:

x = 31

Step-by-step explanation:

Distribute 2 to x which equals 2x, and 2 times 14 which equals 28, which gets you to 2x + 28 = 90, then subtract 28 from 90, which leads you to

2x =62, and the final step is to divide 2 from 62 which gets you 31.

The radius is increasing fastly at a rate of 2.75 feet per second when it is already 30 feet.

Here, it has been told that the rate of change of the area with respect to the time is = 520 ft²/sec - (i)

This can also be written as = dA/dt (ii)

We need to find the rate of change of radius with respect to the time at 30 feet. This can be written as = dr/dt (iii)

We already know that the area of a circle can be found out using the formula = πr² (iv)

Differentiating equation (ii) with respect to time, we get -

= d(πr² )/dt

= π*(dr²/dt)

= π*(dr²/dr)*(dr/dt)

= π*(2r)*(dr/dt)

= dr/dt = (dA/dt)*(1/ π*2r)

Using the given values, we get -

= (dr/dt) = 520 / π*2*30ft

= (dr/dt) = 2.75 ft/sec

Henceforth, we find that the rate of change of the radius with respect to time at 30 feet is going to be 2.75 ft/sec.

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Answer:

Using an Equation

Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.

Answer:

Step-by-step explanation:

To be linear it must have the form  y=mx+b.IN a linear equation the variables are shown in first degree and terms with products of variables are absent .

Answer:

$200

Step-by-step explanation:

so if peter has been depositing 50 each month for 8 months then you would just do 50x8 which equals 400 and 600-400=200

Jacob's smoking habit may shorten his life expectancy by an average of 10 years and 6 months.

Given,

The age of Jacob when he starts smoking  = 21 years

Jacob's present age = 48 years

In generally if 1 year of smoking reduces 6 months from the life.

Why does smoking cause life to be shorter?

Only a few of the illnesses that are directly linked to smoking and have a significant role in the increased mortality rate among smokers include cancer, lung disease, and cardiovascular disease. The link between smokeless tobacco and cancer is well known.

Here,

Jacob may live 10 years and 6 months less than normal due to his smoking habit.

I have answered the question in general as given question is incomplete.

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Answer: 40.24

Step-by-step explanation: Use the Pythagorean Theorem

a^2 + b^2 = [tex]\sqrt[2]{c}[/tex]

36^2 + 18^2 = [tex]\sqrt[2]{1620}[/tex]

1296 + 324 = 1620

[tex]\sqrt[2]{1620}[/tex] = 40.24

Answer:

Step-by-step explanation:

.36

Answer:

20-foot shadow

Step-by-step explanation: