Dylan buys 5 teas and 5 coffees for £3.75. Raphi buys 2 teas and 3 coffees for £1.75. Work out the cost of one tea and one coffee.​

Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Answer:

42.5 cm²

Step-by-step explanation:

1/2x17x5 = 42.5

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

yes there is room for Mr. Kastelan

Step-by-step explanation:

60-17=43 which leaves enough room for the teacher

Answer:

yes

Step-by-step explanation:

there are only 17 cars in the lot so there are still 43 more spots for him to park in.

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

Check the picture below, so the circle looks more or less like so, with a radius of 9.

\(\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57\)

Answer:

5945

Step-by-step explanation:

The sum for an arithmetic series is given by the formula:

\(S=(x_1+x_k)\cdot\frac{k}{2}\)

Where x₁ is the initial term, x_k is the last term, and k is the number of elements in the series.

From the sequence, we can see that the first term is 32. The last term is 113.

To determine how many elements we have, subtract 113 and 32:

\(113-32=81\)

However, we must add 1 to this number since this doesn't include the first term. Thus:

\(81+1=82\)

So, there are 82 terms in total.

Therefore, our sum is:

\(S=(32+113)\cdot\frac{82}{2}\)

\(S=(145)\cdot 41=5945\)

Answer:

5945

Step-by-step explanation:

an = a1 + ( n - 1) 1

a1 = first term

n = number of terms

an = last term

113 = 32 + ( n - 1 ) 1

113 = 32 + n -1

113 = 31 + n

n = 113 - 31

n = 82.

Sn = n/2(a1 + an)

S82 = 82/2 (32 + 113)

S82 = 41 (145)

S82 = 5945.

The sample space for the event of rolling an even number on a number cube with faces labeled from 1 to 6 is {2, 4, 6}.

To determine the sample space for the event of rolling an even number on a number cube with faces labeled from 1 to 6, we need to list all the possible outcomes that satisfy the given condition.

The numbers that can be rolled and their corresponding labels are as follows:

1 → Odd

2 → Even

3 → Odd

4 → Even

5 → Odd

6 → Even

From this, we can see that the possible outcomes for rolling an even number are 2, 4, and 6.

Therefore, the sample space for the event of rolling an even number is {2, 4, 6}.

This set represents all the possible outcomes when rolling the number cube where the outcome is an even number. The elements of the set, 2, 4, and 6, represent the three possible even numbers that can be obtained from the roll.

the sample space includes only the outcomes that satisfy the condition of rolling an even number. The sample space does not include the odd numbers 1, 3, and 5, as these outcomes do not meet the specified event criterion.

To summarize, the sample space for the event of rolling an even number on a number cube with faces labeled from 1 to 6 is {2, 4, 6}.

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Step-by-step explanation:

y=kx

where k is a constant

-5=k25

k=-5÷25

k=-1/5

The relationship between x an y is y=-1/5x

when x is -10

y= -1/5×-10

y=2

Pls follow

The value of y is equal to 2 when x is equal to - 10.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Assuming x = ky.

When y = - 5, x = 25.

25 = - 5k.

k = - 5.

Now, x = - 10 and k = - 5.

∴ - 10 = - 5y.

y = 2.

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Answer:

4\(\frac{5}{12}\) or \(\frac{53}{12}\)

Step-by-step explanation:

I hope this helps!

9514 1404 393

Answer:

  -1/2

Step-by-step explanation:

The constant in the equation is the value that y has when x=0, because the x-term evaluates to zero when x=0. The constant term in this equation is -1/2, so that is the y-value when x=0.

  (x, y) = (0, -1/2) . . . . where the graph crosses the y-axis

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The answer will be $68 and Here's Why:

Samantha received $59 for her birthday. That will be the base of the equation. She spent $25 on a charm bracelet so that will be the number being subtracted.

$59 - $25 = $34

We also know that he brother has twice as much money as she does. So that means he has 2x more money than her.

So: $34 x 2 = $68.

So here brother has $68 more than her.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

B 4x^2-16

Step-by-step explanation:

The answer is 4x^2-16

Answer:

4x^2-16

hope it's helpful ❤❤❤❤

THANK YOU.

\(\\ \sf\longmapsto \dfrac{4}{m+m}\times \dfrac{4}{m-m}\)

\(\\ \sf\longmapsto \dfrac{4\times 4}{(m+m)(m-m)}\)

\(\boxed{\sf (a-b)(a+b)=a^2-b^2}\)

\(\\ \sf\longmapsto \dfrac{16}{m^2-m^2}\)

\(\\ \sf\longmapsto \dfrac{16}{0}\)

\(\\ \sf\longmapsto \infty\)

Answer:

(16-m^4)/m^2

Step-by-step explanation:

=(\(\frac{4}{m}\)+m)(\(\frac{4}{m}\)-m)

=\(\frac{4+m^2}{m}\)*\(\frac{4-m^2}{m}\)  (LCM)

\(\frac{16-m^4}{m^2}\) (a-b)(a+b)

Answer:

-4x+4y+3=0

Step-by-step explanation:

(4x-2y+9=0)+(-8x+6y-6=0)

Add like terms:

-4x+4y+3=0

Answer:

the answer is 4200

Step-by-step explanation:

? = 4200

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)

Answer:

11

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

Currently, there is 1 red circle and 3 blue circles, making the ratio 1: 3.

The ratio 12:3 can be simplified to get 4:1.

Therefore, you will need to add 11 red circles to get the ratio 4: 1.

Answer:

The number is not written in scientific notation.

Step-by-step explanation:

Scientific notation is normally represented by \($x\times10^d\), 'd' being the number of digits.

Answer:

for example you are given a percentage and numbers you cross multiply

Step-by-step explanation:

hope it helps cause I don't know how to explain the answer

Answer:

28 5 dollar bills

12 10 dollar bills

Step-by-step explanation:

You can write two equations to model this situation'

x will be the number of 5 dollar bills

y will be the number of 10 dollar bills

x+y=40

5x+10y=260

There are a couple of ways you can solve this but but I will be doing it through substitution because that looks easier (I can explain other methods if you're interested)

So we have x+y=40

If I subtract y from both sides and divide by -1 we get

-x+40=y

We can then plug this value in for y in the second equation

5x+10(-x+40)=260

Distribute the 10 and combine like terms to get

-5x+400=260

subtract 400 from both sides and divide by -5 to get

x=28

This means that there are 28 5 dollar bills. We can plug this value back in for x into our first equation to solve for y

28+y=40

Subtract 28 from both sides

y=12

This means that there were a total of 28 5 dollar bills and 12 10s

I doubled checked this in desmos and it checks out

The only equation from the options given which shows exactly one solution is x = 2

Evaluating the options given :

Therefore, only the equation x =2 gives exactly one solution for the value of x

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Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Step 1:

Write the function.

Step 2:

Rearrange the function in the form of y = mx + c

Step 3:

You can plot the graph using the coordinates (0, 3) and (6, 0)

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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