Pocket money is split between Paula, Alan and Henry in the ratio 7:3:2. Alan gets £3.75.
How much do the others get?
How much altogether?

Answer:

6 ft

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2

216 = 6s^2

Divide each side by 6

216/6 = 6s^2/6

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 =s

Each side is 6ft

Answer:

The answer would be 60cm.

Step-by-step explanation:

If triangle ABC has a side length of 4 cm and the area is equal to 40, the triangle PQR with a side length of 6 cm would have an area of 60.

Answer:

[tex]x=5+\frac{29}{z}-\frac{y}{z}[/tex]

[tex]y=5z+29-xz[/tex]

Step-by-step explanation:

Given: [tex](4z^2+7z-8)(-z+3)=-4z^3+xz^2+yz-24[/tex]; find x and y.

Let's start with finding x first. Let's distribute the left side of the equation.

[tex]-4z^3+5z^2+29z-24=-4z^3+xz^2+yz-24[/tex]

Let's move everything we can to the left side of the equation. Some things will cancel out.

[tex]5z^2+29z=xz^2+yz[/tex]

Now, let's move the term that includes [tex]x[/tex] to the left side of the equation. Everything else should be moved to the right.

[tex]-xz^2=-5z^2-29z+yz[/tex]

Let's get rid of the negative sign in front of [tex]x[/tex] by dividing both sides by -1.

[tex]xz^2=5z^2+29z-yz[/tex]

To get [tex]x[/tex] completely isolated, divide both sides by [tex]z^2[/tex].

[tex]\frac{xz^2}{z^2}=\frac{5z^2}{z^2}+\frac{29z}{z^2}-\frac{yz}{z^2}[/tex]

Simplify.

[tex]x=5+\frac{29}{z}-\frac{y}{z}[/tex]

Let's solve for y. We will start with the distributed and simplified equation to make it easier.

[tex]5z^2+29z=xz^2+yz[/tex]

Now, let's move the term that includes [tex]y[/tex] to the left side of the equation. Everything else should be moved to the right.

[tex]-yz=-5z^2-29z+xz^2[/tex]

Again, let's get rid of the negative sign in front of the [tex]y[/tex] by dividing both sides by -1.

[tex]yz=5z^2+29z-xz^2[/tex]

To isolate y, divide both sides by z.

[tex]\frac{yz}{z}=\frac{5z^2}{z}+\frac{29z}{z}-\frac{xz^2}{z}[/tex]

Simplify.

[tex]y=5z+29-xz[/tex]

Answer:

x = 5

y = 29

Step-by-step explanation:

Edge Answer

The approximate percentage increase of the number of seats in the movie theater after the renovation is 34.8% when rounded to the nearest tenth of a percent.

To calculate the approximate percentage increase of the number of seats in the movie theater, we start by finding the difference in the number of seats before and after the renovation. We then divide this difference by the original number of seats and multiply by 100 to get the percentage increase.

Original number of seats = 138
New number of seats = 186
Increase in seats = New number of seats - Original number of seats
Increase in seats = 186 - 138 = 48

Next, we calculate the percentage increase:

Percentage increase = (Increase in seats \/ Original numbe of seats) x 100
Percentage increase = (48 \/ 138) x 100
Percentage increase \/= 34.7826...

When rounded to the nearest tenth of a percent, the percentage increase is approximately 34.8%.

Answer:

By using math skills, lol.

Step-by-step explanation:

Thats easily how you solve the problem..

Answer:20.5

Step-by-step explanation:

1.5+1.45+1.40+1.35+1.30+1.25+1.20+1.15+1.10+1.05+1.00+0.95+0.90+0.85+0.80+0.75+0.70+0.65+0.60+0.55=20.5

Answer:

The volume of the cone is 128π mm³ ⇒ answer (C)

Step-by-step explanation:

* Lets study the cone

- Its base is a circle

- Its height the perpendicular distance from its vertex to

 the center of the base

- The length of its slant height = √(h² + r²)

- The volume of the con is 1/3 the volume of the cylinder

∵ The volume of the cylinder = πr²h

∴ The volume of the cone = (1/3) πr²h

* In our problem:

- r = 4 mm

- h = 24 mm

∴ Its volume = (1/3) × π × (4)² × 24 = 128π mm³

* The volume of the cone is 128π mm³

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ To find the median of the numbers, you have to order them:

14, 16, 18, 20, 20, 24

Then, you find the average of the middle two numbers if the amount of numbers is even.

18+20/2

18+20=38

38/2=19

Final answer:

The median of those numbers is 19

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ To find the median, you need to order your numbers first.

14, 16, 18, 20, 20, 24

There is an even amount of numbers, so you find the mean of the middle two numbers.

18+20=38/2=19

Median=19

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

Answer:

8

Step-by-step explanation:

Evaluate 3x^2+x-2 when x=-2

Just plug in x = - 2 into the expression

= 3(-2)^2 + (-2) -2

= 3(4) -2 - 2

= 12 - 4

= 8

The value of the expression [tex]3x^2+x^{-2}[/tex] at x=2 will be equal to 8.

Expressions are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Evaluate [tex]3x^2+x^{-2 }[/tex]when x=-2

Just plug in x = - 2 into the expression

[tex]= 3(-2)^2 + (-2) -2[/tex]

[tex]= 3(4) -2 - 2[/tex]

[tex]= 12 - 4[/tex]

[tex]= 8[/tex]

Hence value of the expression [tex]3x^2+x^{-2}[/tex] at x=2 will be equal to 8.

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To find the circumference of a circle that lists only as a diameter, you would do pi*d so lets say the diameter is 6, you would do pi*6 which would end up giving you 18.84. I hope this helps a bit! (:

Answer:

pi * d

Step-by-step explanation:

Multiply 3.14 by the Diameter.

The value of graph of equation y =√(x+5) - 2​ is shown in figure.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

Equation is,

⇒ y = √(x + 5) - 2

Now, We can draw graph of equation y =√(x+5) - 2​ is shown in figure.

Hence, The figure is shown in image.

Learn more about the function visit:

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Answer: ABC = 32 degrees

Step-by-step explanation:

We are already given the measurement of angle ACB, which is 58. And given AC is tangent to circle B we also know that BAC is 90 degrees.

So,

ABC = 180 - (BAC + ACB)

ABC = 180 - (90 + 58)

ABC = 180 - (148)

ABC = 32 degrees

Hope I could help :)

Answer:

ABC is equal to 32 degrees

Answer:

See attached image.

Step-by-step explanation:

To easily solve this question, we use a graphing tool, or a calculator to plot the graph of the ellipse.

(1/16)*x^2  +  (1/4)*y^2  = 1

Please see image below

Answer:

Step-by-step explanation:

Answer:

132 miles

Step-by-step explanation:

miles ran + miles to run = total miles

28 + miles to run = 160

Subtract 28 from each side

28-28 + miles to run = 160-28

miles to run = 132

He still need to run 132 miles

Answer:

132 mi

Step-by-step explanation:

since he ran 28 miles but he has to run 160 miles, he still has to run some miles. if we make the amount he still has to run x, we can do 28+x=160. now we can solve this by subtracting 28 on both sides to getx=132

             28+x=160

             -28      -28

        -------------------------

            x=132

Answer:  $283.94

Step-by-step explanation:

[tex]A=P(1+r)^t\\\\\bullet P=100\\\bullet r=11\% \implies 0.11\\\bullet t=10\\\\\\A=100(1.11)^{10}\\.\ =283.94[/tex]

(8c+5)(-2c-3)

Multiply each term together, then combine like terms:

8c * -2c = -16c^2

8c *-3 = -24c

5 * -2c = -10c

5 *-3 = -15

Now combine:

-16c^2 - 24c -10c -15

Simplify:

-16c^2 -34c -15

Answer:

-16c^2 - 24c -10c -15

Step-by-step explanation:

The experimental probability of tossing tails in the given scenario is 0.4 or 40%, which is determined by dividing the number of tails (6) by the total number of tosses (15).

The student is asking to determine the experimental probability of tossing tails when a coin was tossed 15 times and resulted in 9 heads and 6 tails. Experimental probability is calculated by dividing the number of times an event occurs by the total number of trials. In this case, the coin landed as tails 6 times out of 15 tosses.

To find the experimental probability of tossing tails, use the formula:

Experimental Probability of Tails = Number of Tails / Total Number of Tosses

So, it would be:

Experimental Probability of Tails = 6 / 15

Experimental Probability of Tails = 0.4 or 40%

Answer:

1. is an acute angle

2. is an acute angle

Step-by-step explanation:

Both the angles are less than 90° so the angles are both acute.

Answer:

The value of y is -5

Step-by-step explanation:

we have

[tex]9x+2y=8[/tex] ------> equation A

[tex]7x+2y=4[/tex] ------> equation B

we know that

If x and y satisfy both equations, then (x,y) is the solution of the system of equations

Using a graphing tool

Remember that

The solution of the systems of equations is the intersection point both graphs

The intersection point is (2,-5)

therefore

The solution of the system of equations is the point (2,-5)

The value of y is -5

To find the value of y in the given system of equations, we can use the method of substitution.

To find the value of y in the system of equations 9x + 2y = 8 and 7x + 2y = 4, we can use the method of substitution. First, we solve one equation for one variable and substitute the expression into the other equation. In this case, we can solve the second equation for y: 7x + 2y = 4, y = (4 - 7x)/2. Now substitute this expression for y in the first equation: 9x + 2((4 - 7x)/2) = 8. Simplify and solve for x. Once we have the value of x, we can substitute it back into the second equation to find y.

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Answer:

Hundreds

Step-by-step explanation:

Answer:

An angle bisector intersects the middle of an angle and basically cuts it in half equally, leaving 2 parts. The relationship includes an angle having to exist in order to have a bisector. A ray starts at a one point, represented usually by a dot and goes off for ever in a direction whereas a line extends infinitely in both directions.

Step-by-step explanation:

Answer: [tex]120in^2[/tex]

Step-by-step explanation:

The formula that is used to calculate the area of a triangle is:

[tex]A_{(triangle)}=\frac{b*h}{2}[/tex]

Where the base of the triangle is b and the height of triangle  is h.

If the pennant has a base of 10 inches and a height of 24 inches, you know that:

[tex]b=10in\\h=24in[/tex]

As it is a triangular pennant, you can substitute the values of the base and the value of the height into the formula used to calculate the area of a triangle.

Then, total area of the pennant is:

[tex]A_{(pennant)}=\frac{(10in)(24in)}{2}\\\\A_{(pennant)}=120in^2[/tex]

Answer:

The solution set represented by the following graph is:

                {x | x∈ R, x < -2}

Step-by-step explanation:

Clearly from the figure we could see that the solution set is to the left of ' -2' and excluding the point '-2' since there is a open circle at -2.

This means that -2 is not included in the set.

Also in interval; form the set of points that belong to the solution set are:

                      (-∞,-2)

in set-builder form it is written as:

                      {x | x∈ R, x < -2}

Answer:

Option A.

Step-by-step explanation:

We need to find the solution set represented by the given graph.

From the given figure it is clear that there is an open circle around -2 and shaded region lie left side of -2.

Open circle around -2 represents that -2 is not included in the solution set.

Shaded area towards left of -2 represents that the solution must be less than -2. It means the sign of inequality is "<".

From the given graph it is clear that value of x lie in the interval (-∞,-2). So, the solution set is

[tex]\text{Solution set}=\{x|x\in R,x<2\}[/tex]

Therefore, the correct option is A.

Answer:

[tex]\large\boxed{(x+3)^2=x^2+6x+9}[/tex]

Step-by-step explanation:

Use the FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex](x+3)^2=(x+3)(x+3)\\\\=(x)(x)+(x)(3)+(3)(x)+(3)(3)\\\\=x^2+3x+3x+9\qquad\text{combine like terms}\\\\=x^2+(3x+3x)+9\\\\=x^2+6x+9[/tex]

You can use

[tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex](x+3)^2=x^2+2(x)(3)+3^2=x^2+6x+9[/tex]

Answer:

y = - 2 or y = 6

Step-by-step explanation:

Given the 2 equations

y = 2x → (1)

y = x² - 3 → (2)

Substitute y = x² - 3 into (1)

x² - 3 = 2x ( subtract 2x from both sides )

x² - 2x - 3 = 0 ← in standard form

(x - 3)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 1 = 0 ⇒ x = - 1

Substitute these values into (1) for corresponding values of y

x = 3 : y = 2 × 3 = 6

x = - 1 : y = 2 × - 1 = - 2

Answer:

0.07

.7 is 7 tenths or 70 hundredths

.07 is 7 hundredths

Answer:

A loan that you usually have to get from a bank to use specifically for paying for a car,which you later have to pay back

Step-by-step explanation:

A car loan is a type of secured loan, where we can say that the car we buy is collateral for the loan.

In case of failure of payment of loan, the lender can repossess the car and sell it to pay off the loan.

In other words, we can say the lender or banks purchase the car for us and gives us few years time to pay back that loan.

The loan is granted with interest rates, that one has to pay above the principle amount during the tenure of the loan.

Answer:

the other one is (2, 2)

the area is 24

Step-by-step explanation:

A = (2+2)(2+4) = 24

Answer:

Step-by-step explanation:

Your balance or -50$

Answer:

[tex]f^{-1}(x)=\dfrac{e^x}{3},\ x\in(-\infty,\infty),\ y>0[/tex]

Step-by-step explanation:

Consider the function [tex]f(x)=\ln 3x.[/tex] the domain of this function is x>0 and the range of this function is all real numbers. The inverse function has the domain all real numbers and the range y>0.

If

[tex]y=\ln 3x,[/tex]

then

[tex]3x=e^y,\\ \\x=\dfrac{e^{y}}{3}.[/tex]

Change x into y and y into x:

[tex]y=\dfrac{e^x}{3}.[/tex]

Thus, the inverse function is

[tex]f^{-1}(x)=\dfrac{e^x}{3}.[/tex]

ANSWER

[tex]{f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]

EXPLANATION

The given logarithmic function is

[tex]f(x) = ln(3x) [/tex]

Let

[tex]y = ln(3x) [/tex]

Interchange x and y.

[tex]x = ln(3y) [/tex]

Solve for y.

[tex] {e}^{x} = {e}^{ ln(3y) } [/tex]

[tex] {e}^{x} = 3y[/tex]

Divide both sides by 3.

[tex] \frac{ {e}^{x} }{3} = y[/tex]

Therefore

[tex] {f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]