Pat and Alex have a combined total of £63.

The ratio of Pat’s money to Alex’s money is 5 : 2

They each spend an equal amount on sweets.

The ratio of Pat’s money to Alex’s money is now 3 : 1
How much did Pat spend on sweets?

Answer: y = x^2 - 2x - 8

Step-by-step explanation:

Answer:

-7/4 seeing how the line touches -3,4 and 1, -3 only it goes down 7 and 3 to the right

Step-by-step explanation:

sub to imagine fn

Answer:

w = 5

Step-by-step explanation:

2w - 15w - 18 = -83

combine w on left side:

-13w - 18 = -83

add 18 to both sides:

-13w - 18 + 18 = -83 + 18

-13w = -65

divide both sides by -13:

-13w/-13 = -65/-13

w = 5

Answer:

the answer is 3/1

Step-by-step explanation:

u do 8-5/4-3 which is 3/1

Answer:

Step-by-step explanation:

Triangles ADC and BDC are right triangles, since CD⊥AB.

Use Pythagorean to find the length of CD:

Use trigonometry to find the angle ABC:

This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t2 + 45.

How can one determine a function's maximum height?

The vertex, which is a maximum (or minimum) in a parabola, can be located by solving the square (yuck!) or by using the formula x = -b/2a. By re-entering the original equation with this x value as the vertex's x, we can determine the appropriate maximum height.

By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can get the height of the item of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 meters if theta is 50 degrees and D is 40 meters.

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The square root of 10 will be greater than 3.

The square root of a number is the value which when multiplied by itself results into the number. Mathematically -

n = x²

then -

x = [tex]\sqrt{n}[/tex]

Given are two numbers as -

[tex]\sqrt{10}[/tex] and 3.

Now, the square root of 10 will be 3.16 (approx.)

On comparing the square root of 10 with 3, we can clearly see that the square root of 10 will be greater than 3. Mathematically -

[tex]\sqrt{10}[/tex] > 3.

Therefore, we can conclude that the square root of 10 will be greater than 3.

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An estimate of the real height of the lamp post is 9m.

The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm

Scale = length of the lamp post / height of the car

10.8 / 1.8 = 6

Now, multiply the scale by the width of the car.

The real height of the lamp post = 6 x 1.5 = 9m

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The coordinates of the image of any point P(x, y), from any geometric locus, after being reflected over the x-axis.

Geometric loci are geometrical constructions formed by one or more points, these may represent a point or a figure formed by finite or infinite set of points.

Let P(x, y) = (x, y) a point of the geometric locus, which has to be modified by using reflection over the x-axis. This can done by adding the vector (- 2 · x, 0) to the vector P(x, y):

P'(x, y) = P(x, y) + (- 2 · x, 0)

P'(x, y) = (x, y) + (- 2 · x, 0)

P'(x, y) = (- x, y)

Where P'(x, y) is the image of point P, from any geometric locus, after making the reflection over the x-axis.

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The value of y in the equation is 12.

What are internal angles of a triangle?
According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent.

BD falls on CE, thus angles dividing BD on CE will sum up to 180°.
Given ∠BDC = 4x - 5 and ∠BDE = 10y - 3
Thus, ∠BDC + ∠BDE = 180° ⇒ (4x - 5) + (10y - 3) = 180° - (i)
Therefore, rearranging (i), we get 4x + 10y = 188° -- (A)
Again, since alternate angles are equal, thus ∠BDC = ∠AEC
Thus, 4x - 5 = 97 - 2x ⇒ 6x = 102 ⇒ x = 102/6 = 17 --(ii)
From (A) and (ii), we get, 4(17) + 10y = 188 ⇒ 10y = 120 ⇒ y = 12
Therefore the value of y is 12.

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Answer: 58

Step-by-step explanation: you divide 290 into 5

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =135 \end{cases}\implies A=\cfrac{(135)\pi (8)^2}{360}\implies A=24\pi \implies A\approx 75.4[/tex]

Considering the definition of an inequality, an inequality that represent the possible values for the number of hotdogs purchased and the number of drinks purchased is 5h + 1.50d≤ 50.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

In this case, you know that:

Being:

the inequality that expresses the previous relationship is

5h + 1.50d≤ 50

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If  Tia rounds a number, x, to 3 sf and the result is 7.68. the error interval for x in the form a ≤ x < b is 7.685  ≤ x ≤ 7.684

The accuracy thresholds that apply when a number has been rounded or truncated are known as error intervals. In other words, they represent the range of values that a number might have taken had it not been rounded off or truncated.

To do this, we consider the smallest and largest numbers that could be rounded or truncated to a value while maintaining a certain level of accuracy.

We know that if this digit is smaller than 5, then we round down.

Then the largest number that can be rounded down to 7.68 is:

7.684

Now we want to find the smallest number that can be rounded up to 7.68

We know that if the next digit is 5 or bigger, then we round up.

Then the number 7.685 is rounded up to 7.68

Then the error interval is:

7.685  ≤ x ≤ 7.684

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In order to depict alchemy and the philosopher's stone, which is the ultimate goal of alchemy, a sign of a circle within a square within a triangle within a larger circle started to be used in the 17th century.

What do the symbols for a circle, triangle, and square mean?

It has deep philosophy where a circle symbolizes heaven and represents number one, a square represents earth and represents number two, and a triangle represents people and represents number three.

An enduring representation of good fortune, the triangle enclosed within a circle was thought to stave off evil spirits. It was accepted by Alcoholics Anonymous as a symbol of a person's transition from an alcohol preoccupation to a life saturated with the triangle of Recovery, Unity, and Service.

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The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.

The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.

It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.

On this note, the correct representation of the situation above involves an absolute value equation such that;

| x- 3.5 | = 0.8

Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.

x = 0.8 + 3.5. OR. x = -0.8 + 3.5

x = 4.3 OR x = 2.7.

Ultimately, the required values are; 4.3 and 2.7.

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The required probability is 0.132 .

What is normal approximation?

The sampling distribution of averages or proportions from a large number of independent trials approximately and the expectation of a sample proportion or average is the corresponding population value.

On solving using mean sampling method, we get

P(E) = 0.132

Hence, the required probability is 0.132 .

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Answer:

I believe that it should be less than 2,000.

Step-by-step explanation:

11038 < 11405 = 9405 + 2000

11038 - 9405 < 2000

D(ex) = ex = 1.ex + 0.xex + 0.x2ex

D(xex) = ex + x.ex = 1.ex + 1.xex + 0.x2ex

D(x2ex) = x2ex + 2x.ex = 0.ex + 2.xex + 1.x2ex

So the matrix is:

          1    0    0

A =     1     1    0

          0    2    1

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Answer:

48 push-ups

Step-by-step explanation:

40 to 5 = 48 to 6

John has $595 in his possession.

An expression that has been created utilizing integers, constants, variables, and algebraic operations is known as an algebraic expression.

For instance, [tex]x^{2} + 2x + 2[/tex]

2x + 3

etc

The answer to the query is

John has the same amount of more money over Torrie as he has under Sonia.

Let's suppose it is $x since John has the same amount of money more than Torrie as he has less than Sonia.

Case 1

Actual amount that John has is $430 plus $x.

Case 2

Actual amount that John has is $760 less $x.

⇒ $430 + $x = $760 - $x

⇒ $2x = $330

⇒ $x = $165

John currently possesses $595 ($760 - $x) or ($430 + $x) in his possession.

John therefore has $595 in his bank account.

The amount of money that john has is $595

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Answer:

| 56x² + 14xy

Step-by-step explanation:

14x(4x + y)

Apply the Distributive Property

14x x 4x + 14xy

Multiply the monomials

56x² + 14xy

Apply the distributive property on 4x + y, distributing 14x.

14x(4x + y)
(14x x 4x) + (14x x y)
56x + 14xy

Answer:

the answer is 0

Step-by-step explanation:

a negative plus a positive is a positive

Answer:

I'm pretty sure the answer is 191/30 when simplified

Step-by-step explanation:

Yup

The government levies a consumption tax known as a sales tax on the purchase of goods and services.At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.

Calculate sales tax ?

   equation sales tax = purchase price x sales tax rate.

   Sales tax = $800*7.5%

         = $60

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Answer:

24°

Step-by-step explanation:

the interior angle of a triangle is 180°

therefore Let <ACB =x

128°+28°+x=180°

156°+x=180°

make x the subject

x=180°-156°

x=24°

Answer:

y =-0.25x + (-6)

Step-by-step explanation:

crosses y axis at -6 so that's your y-intercept

to find gradient use change in y / change in x

so make a triangle -1 / 4 = -0.25

Using given area and base length of a rectangle we got that the height of the given rectangle is 6.5 inches.

Rectangle is closed geometric figure that has four perpendicular sides with opposite sides equal.

The formula for the area of the rectangle :

Area of the rectangle = Length × Breadth

Given that the area of a rectangle is 45.5 square inches.

The base of the rectangle is given 7 inches

To find : Height of the rectangle

Let the base length is the length of the rectangle and height is the Breadth of the rectangle.

Then, Area of the rectangle = Length × Breadth

⇒ 45.5 = 7 × Height

⇒ 45.5 /7 = Height

⇒ 6.5 = Height  of the rectangle

Therefore, the height of the rectangle is 6.5 inches.

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