2 cups and 3 plates costs £18. 5 cups and 1 plate costs £19. Find the cost of a cup. Find the cost of a plate

Answer: \((\frac{\sqrt{3} }{2} ,-\frac{1}{2} )\)

Step-by-step explanation:

this forms a 30 degree reference angle

and this is in the 4th quadrant

When the angle is 30 degrees, the coordinates are:

\((\frac{\sqrt{3} }{2} ,-\frac{1}{2} )\)

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

The polar coordinate system in geometry is a two-dimensional latitude and longitude that uses the distance from a reference point and the angle from an optical axis are used to identify each point's location on a plane. This polar axis is the ray emanating from the pole in the direction of the point of comparison, which is referred to as the pole.

The cartesian coordinate is (x, y) and polar coordinate is (r, θ). Then the relation is given as,

x = r cos θ

y = r sin θ

The angle is 330° and the radius is one. Then we have

x = 1 x cos 330°

x = (√3) / 2

y = 1 x sin 330°

y = - 1/2

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

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Answer:

Step-by-step explanation:

12 ≤ t ≤ 25

t ≤ 13 miles

Answer:

Step-by-step explanation:

Area of the shape of the table = Length * Breadth (Rectangular in nature)

Area of the study table = 2m * 1.25m

Converting the units to cm

Since 100cm is equivalent to 1m, hence;

Area of the study table = 200cm * 125cm

Area of the study table = 25000cm²

If the study table is decorated with square design of size 10cm x 10cm, then the area of one square of such design will be 100 cm².

The number of square designs = Area of the study table/area of one square design

= 25000/100

= 250

Hence the number of such design on the study table is 250

Answer:

B

Step-by-step explanation:

3(2x-50)=2(8x-7)+4x

6x-150=16x-14+4x

6x-150=20x-14

150-14=20x-6x

136=14x

x=136/14

x=9.7=10

X = 4×3 X + 7

Resultado

X = 12 X + 7

Forma alternativa

-11 X - 7 = 0

X = -7/11

Answer:

lol

Step-by-step explanation:

that sucks

The total change in the water level over the two years is \(- 1\frac{1}{2}\) inches.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, In two years the water level in a lake has changed \(- 1\frac{1}{5}\) by inches and  \(- 1\frac{3}{10}\) inches respectively.

∴ The total change is the sum of these two fractions ( -6/5) + ( -3/10) inches.

= (- 12 - 3)/10 inches.

= - 15/10 inches.

= - 3/2 Or \(- 1\frac{1}{2}\) inches.

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Using a proportional relationship, it is found that:

a. The function is d = 21g.

b. Values less than 0 and greater than 20 are excluded from the domain.

c. The greatest distance that Armando can travel on the highway after the low fuel light comes on is of 52.5 miles.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Armando’s vehicle averages 21 miles per gallon on the highway, hence the distance that he can travel on g gallons is given by:

d = 21g.

The domain is the set that contains all possible input values, hence:

Hence:

Values less than 0 and greater than 20 are excluded from the domain.

The low fuel light comes in when the number of gallons remaining is:

g = 1/8 x 20 = 20/8 = 2.5 gallons.

The distance that he can travel is:

d = 21g = 21 x 2.5 = 52.5 miles.

The greatest distance that Armando can travel on the highway after the low fuel light comes on is of 52.5 miles.

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Answer:

C. (0,-1)

Step-by-step explanation:

the line passes through the y-axis at the point (0,-1) which makes it the y- intercept.

Answer:

x=(t+a)/4

Step-by-step explanation:

To make a variable the subject of an equation, you have to isolate it on one side of the equation.

Start with 4x-t=a

Add T to both sides to get:

4x=t+a

Divide both sides by four to get:

x=(t+a)/4

Answer:

The answer is C. -3/4x+4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y=(-3/4)x + 4

take any point on the line and go up 3 than left 4 and you will end up on the line again because slope is rise/run

the slope is negative because from left to right the line is downhill

Answer:

counting numbers is another name

\(\huge\blue{ANSWER}:—\)

Plz mark me as brainliest as I have solve all the questions for you

Answer:1 : x is 95/3

4 x is -32/10

7 b is 6

10 x is 20/7

13 x is 9/2

Step-by-step explanation:

Answer:

3.9

Step-by-step explanation:

Add all the numbers up then divide by how many there are.

Adding All the Numbers Up = 39

Then Divide By 10

so, 39/10= 3.9

Option C is the real-world situation that can be represented by 2m + 3. The equation 2m + 3 represents the number 3 more than twice a certain number (m).

In option A, the equation that represents the situation would be 3d + 2, where d is the number of downloads. In option B, the equation that represents the situation would be 2i + 3, where i is the number of items purchased.

In option D, the equation that represents the situation would be 2l - 3, where l is the number of laps Dan swims.

Therefore, option C is the correct answer as it is the only option that represents the situation where one person bikes 2 more than 3 times the miles another person bikes.

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9514 1404 393

Answer:

  x = 25; ∠3 = ∠6 = 60°

Step-by-step explanation:

Angles 3 and 6 are alternate interior angles, so are congruent.

  2x +10 = 3x -15

  25 = x . . . . . . . . . . . add 15-2x

  2x +10 = 2(25) +10 = 60

The measures of angles 3 and 6 are 60°.

The correct answer to inequality is option A .

What is inequality equation?

The mathematical expressions with inequalities area unit those with unequal sides on each side.

Main body:

For this case we have the following inequality:

-4(x+3)≤ -2 -2x

Applying distributive property on the left side we have:

-4x - 12≤ -2 -2x

Adding 2x to both sides of the inequality we have:

-4x +2x -12 ≤-2

-2x-12≤-2

Adding 12 to both sides of the inequality we have:

-2x-12 +12≤ -2 +12

Dividing by 2 to both sides of the inequality:

-2x ≤ 10

Multiplying by -1 on both sides, taking into account that the sense of inequality changes:

x≥ -10/2

x ≥ -5

hence, the solutions are given by all values ​​greater than or equal to -5.

so , option A is correct.

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Answer:

B. Yes, because it passes the vertical line test.

Step-by-step explanation:

Vertical line test - if a vertical line passes through more than one pone, the relation is not a function

Any vertical line will only pass through one point, so this relation is a function

The relation is a function because it passes the vertical line test

Answer:

24

Step-by-step explanation:

The order of operations is:

Parentheses, Exponents, Multiplication, Division (left to right), Addition, Subtraction (left to right)

Left to right means whichever comes first.

Now let's solve

3*4=12

12/2=6

24-6+6=18+6=24

Answer:

24

Step-by-step explanation:

PEMDAS

first you multiply -3×4=-12

24-12÷2+6

then divide -12/2=-6

24-6+6

add -6+6=0

24+0

subtract 24+0=24

Answer: 15

Step-by-step explanation:

This is a right angle and right angles always add up to 90 degrees.

You would take away 30 from 90 which equals 60.

Then because it is 4x you would do the inverse and divide 60 by 4 to get x on its own.

60/4=15

Answer:

P = 3/11

Step-by-step explanation:

There are:

6 red marbles

4 blue marbles

2 yellow marbles.

So there are a total of 12 marbles in the bag, such that each one has the same probability of being randomly picked.

We want to find the probability that the first pick is not yellow (so it can be either blue or red), and the second pick is a blue marble.

Now there are two cases.

The first marble is red and the second blue

the first marble is blue and the second blue

We need to find the probability in each case.

The probability that the first marble is red is equal to the quotient between the number of red marbles (6) and the total number of marbles (12)

p = 6/12

Now, for the second draw, we need a blue marble, the probability in this case is the quotient between the number of blue marbles (4) and the total number of marbles in the bag (now there are 11, because one is already taken)

q = 4/11

The joint probability is equal to the product of the individual probabilities, then:

P₁ = p*q = (6/12)*(4/11) = 2/11

And for the other case, we draw two blue marbles:

For the first draw, the probability is:

p = 4/12

And for the second draw, now there are 3 blue marbles and 11 total marbles, then the probability is:

q = 3/11

The joint probability is:

P₂ = (4/12)*(3/11) = 1/11

The total probability is then:

P = P₁ + P₂ = 2/11 + 1/11 = 3/11

Area of ∆ABC = 36,

Area of ∆ABC = 36,Area of ∆PQR = 64

Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12

Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.

Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.To find: PQ = ?

Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.To find: PQ = ?For this,

Recall the property,

Ratio of areas of two similar triangles = Ratio of squares of the corresponding sides

Area of ∆PQR / Area of ∆ABC =(PQ/AB)²

64 /36 = (PQ/AB)²

(PQ/AB) = √64 /36

(PQ/AB)= 8/6

PQ=AB ×8/6

PQ = 12×8/6

⇒ PQ = 2 × 8

⇒ PQ = 2 × 8⇒ PQ = 16

⇒ PQ = 2 × 8⇒ PQ = 16Thus, answer is 16.

i hope it's helpful for u ☺️

Answer:

16(2z -3)

Step-by-step explanation:

There are two ways of solving this problem.

List out the factors of the numbers:

32z - 48

= 32 * z - 48

32= 1, 2, 4, 8, 16, 32

48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

the largest common factor that both numbers have in common is 16,

So factoring the equations means the one has to divide the equation by 16 and write it outside of the parenthesis.

16 * ( 2 * z - 3)

16(2z -3)

Another way of solving the problem:

prime factorize the number:

32 = 2^5

48 = 2^4 * 3

Both numbers have 2^4 as their largest factor in common meaning that that is their GCF. 2^4 is 16.

Now factor out 16 and write it on the outside of the parenthesis.

16 * ( 2 * z - 3)

16(2z -3)

Answer:

8(x+6)

Step-by-step explanation:

hope this helps

Answer:

13x+5

Step-by-step explanation:

(2x+9)+(11x-4)

2x+9+11x-4

2x+11x+9-4

13x+5

Step-by-step explanation:

2x+9+11x-4

2x+11x+9-4

13x+5

Answer:

Check your question well

Step-by-step explanation:

U didn't ask to draw angle p so how can we get the angle r

Answer:

Step-by-step explanation:

12 frdb

Answer:

15°

Step-by-step explanation:

45 + 15 = 60° (which is 4x since they're vertically opposite angles)

4x = 60°

x = 60 ÷ 4 = 15

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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The length of the wire is approximately 7.8 meters (m) to 1 decimal place.

Pythagoras' theorem is a fundamental concept in mathematics that relates to the sides of a right-angled triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

In the given question,

We can use Pythagoras' theorem to find the length of the wire, k.

According to the theorem, the square of the hypotenuse (the wire) is equal to the sum of the squares of the other two sides (the height of the pole and the distance from the base to the wire).

So, we have:

k^2 = 6^2 + 5^2

k^2 = 36 + 25

k^2 = 61

Taking the square root of both sides, we get: k = √61 ≈ 7.8

Therefore, the length of the wire is approximately 7.8 meters (m) to 1 decimal place.

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