sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read

Given:

A length of a side of an equilateral triangle = 32 cm

Formula Used:

If in an equilateral triangle with side length 'a' then,

Area of an equilateral triangle = [(√3)/4] × a2 

Calculations:

Area of an equilateral triangle = [(√3)/4] × 322

⇒ (1024 × √3)/4

⇒ 256√3 cm2

Answer:

y = x - 2

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

Choose any two points on the line.            

 (2,0)  ; (0,-2)

Now, find the slope.

        [tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                   [tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]

m = 1.

Now, y = 1x +  b

The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.

       0 = 1*2 + b

       0 =  2 + b

        -2 = b

Equation of line:

              y = x - 2

Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

Answer:

5 kg.

Step-by-step explanation:

2 kg for $0.96 is more expensive than 5 kg for $1.95

The inverse of ∼P→∼Q is P->Q.

Given ∼P→∼Q

Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.

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Answer:

85+7.5v=160

7.5v=160-85

7.5v=75

V=75/7.5

V=10

Ryan would need to take 10 visits to get a free ticket.

Answer:

one solution

Step-by-step explanation:

The two lines cross at exactly one point.  That means there is one solution.

Answer:  -100

Step-by-step explanation:   -7(15)+5

It said x=15 so put 15 in and solve from there and that would be -100

HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN

The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.

An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.

Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:

Total amount to be paid for the mortgage: $315,000

Rate of interest: 5.85% (Depreciating rate)

Time = 2 years:

a. Remaining amount to be paid after 2 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)²

= $315,000 × (1 - 0.0585)²

= $279,223.01

Time = 3 years:

a. Remaining amount to be paid after 3 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)³

= $315,000 × (1 - 0.0585)³

= $262,888.46

Difference in payments from year 2 to year 3:

= Remaining amount after 2 years - Remaining amount after 3 years

= $279,223.01 - $262,888.46

= $16,334.55

The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:

$16334.546/12 = $1361.21

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Answer: J' (8, -9); K' (8, -2); L' (3, -2); M' (3, -9)

Step-by-step explanation:

A rotation of 90 degrees counterclockwise is (x, y) -> (-y, x), so

J (-9, -8) -> J' (8, -9)

First, you take negative 8 (y) of J and make it positive 8 for the x of J'. Then, take -9 (y) of J and switch it to x of J'.

You repeat this process for the rest of the points. X switches to Y with the opposite sign and Y switches to X but stays the same.

K (-2, -8) -> K' (8, -2)

L (-2, -3) -> (3, -2)

M (-9, -3) -> (3, -9)

The value of x in this problem is 2.

Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.

Use the transposing method to isolate the variable x and then solve for it.

distribute brackets on both sides of the equation.

= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x

= 15x - 10 = 10 + 6 + 2x

collect terms in x to the left side and numeric values to the right side.

= 15x - 2x = 10 + 6 + 10

= 13x = 26

= x = 26/13 = 2

Therefore the final value of x in this equation will be 2.

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Answer:

Step-by-step explanation:

8x+18=2x+x+4x-3

8x+18=7x-3

perimeter = x+21

The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.

A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.

Let us set up the following variables:

R, Radius of conical cup (cm) = 30 cm

H, Height of the conical cup (cm) = 10 cm

Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2

By similar triangles we have

r : h = R : H

r/h = 30/10

⇒ r = 3h

The volume of a cone is 1/3π r²h, So:

V = 1/3π r²h

simplifying the equation, we get

= 1/3π (3h²)h

= 1/3π 9h²h

= 3π h³

Differentiating wrt h we get:

dV/dh = 9π h²

Applying the chain rule we have:

dV/dt = (dV/dh)(dh/dt)

= 9π h² × 2

= 18π h²

If h = 9 then

[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

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The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar

In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.

The amount of sugar in 200 ml of juice is :

= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice

= ( 16. 5 x 200 ) / 250

= 3, 300 / 250

= 13. 2 grams of sugar

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Answer:

60 degrees

Step-by-step explanation:

The total measure of a circle is 360 degrees.

360-140-100 = 120

Angles MON and NOP are equivalent which makes MN and NP equivalent.

120/2 = 60 degrees = MN

P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.

Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.

The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.

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According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.

What is Triangle Inequality Theorem?

According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The two sides of a triangle are -

a=7, b=x and c=17, where a, b and c are the sides of the triangle.

As, 17 is a bigger number so let it be the biggest side.

Now, according to triangle inequality theorem -

a + b = c

7 + x = 17

x = 17 -7

x = 10

Therefore, the third side of the triangle measures 10 units.

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The equation for new function is,

⇒ f (x) = ∛( 1/4x - 6) - 5

A relation between a set of inputs having one output each is called a function.

Given that;

The parent function is,

⇒ g (x) = ∛x

Now, After  reflected and stretched by 4, we get;

⇒ g (x) = f (1/4x) = ∛ 1/4x

And, After translated 6 units to the right, we get;

⇒ g (x) = f (x - 6) = ∛ 1/4x - 6

And, After 5 unit down, we get;

⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5

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The length of other base  is 15 cm.

The area of a trapezoid can be found by using the formula:

Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.

Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.

Area = (b1+b2) * h / 2 = 135cm^2

We can solve for the other base length by isolating b1

b1 = 2*Area/h - b2

b1 = 2*135/10 - 12 = 27 - 12 = 15

So, the other base length is 15 cm.

Therefore, The length of other base  is 15 cm.

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The Earth orbits the Sun and rotates around its own axis. The Moon orbits the Earth and is held in place by the Earth’s gravity. This is why the length of a day is gradually increasing over time.

The Moon’s gravitational pull causes the tides, which is why the ocean’s water level rises and falls. The gravitational pull of the Moon also affects the Earth’s rotation by slowing it down slightly. This is why the length of a day is gradually increasing over time.

The Earth orbits the Sun and rotates around its own axis, while the Moon orbits the Earth and is held in place by the Earth’s gravity. The Moon’s gravitational pull causes the tides and affects the Earth’s rotation by slowing it down slightly, resulting in a gradual increase in the length of a day.

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4.68

find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36

Answer:

16 inches of ribbon cost- $2.08

36 inches of ribbon cost- ?

36*$2.08/ 16

$74.88/16

= $4.68

Thus, 36 inches of ribbon would cost $4.68

The value of x from the given triangle is 7√2 units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, one of the angle in right angle triangle is 45°, opposite side is 7 units and hypotenuse is x units.

We know that, sinθ =Opposite/Hypotenuse

sin45°=7/x

1/√2=7/x

x=7√2 units

Therefore, the value of x is 7√2 units.

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Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.

Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for  creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

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We can solve the inequality to get:

h ≤ -3

And its graph can be seen below.

Here we have the following inequality:

-(1/3)*h ≥ 8

To solve the inequality, we need to isolate h.

So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)

So we will get:

-3*(-1/3)*h ≤ -3*h

h ≤ -3

Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.

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An investor writes a s&p 100 Jan. 185 put at $6 on May 4. In this situation, his function maximum potential benefit is $600.

We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.

A benefit is a positive outcome or advantage that results from something. It can refer to the positive aspects or advantages of a product, service, or action, and can be tangible or intangible. Benefits can include increased efficiency, cost savings, improved safety, increased customer satisfaction, and many other positive outcomes.

Here,

As a put buyer, the most you may lose is the premium you previously paid to purchase the put option.

The option price must be reduced to equal the strike price less any already-paid premium in order to break even.

The strike price less the premium is your maximum gain as a put buyer. The most bullish option strategy is thought to be purchasing call options.

This tactic allows the buyer of the call option the choice, but not the responsibility, to purchase the stock at a certain price at a precise moment.

Whenever the price of the security increases using this approach, the buyer benefits. A long position is one in which a call or put option is purchased or held.

Investors have the option of purchasing from or selling to the other investor at a predetermined price.

On the other hand, a short position is when you sell a call or put option. Writers must purchase from people holding long positions or buying options.

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On May 4th an investor writes on s&p 100 Jan 185 put at $6. his function maximum potential gain in this position is $600.

We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.

Your maximum loss as a put buyer is the premium already paid to buy the put option. To break even the option price must be lowered to cover the strike price minus the premium already paid. Your maximum profit as a put buyer is the strike price minus the premium. Buying call options are considered the most bullish options strategy.

This strategy gives the call option buyer the right but no obligation to buy the security at a specific price at a specific time. With this strategy, the buyer benefits when the price of the security rises. Buying or holding a call or put option is a long position. Investors have the right to buy or sell to the writing investor at a specified price. Conversely selling or selling a call or put option is a short position. Writers must buy or sell from long position holders or option buyers.

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The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)

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

Perimeter = 4x - 8

Factor out 2 from the expression

So, we have the following representation

Perimeter = 2 * 2x - 2 * 4

So, we have

Perimeter = 2(2x - 4)

Hence, the perimeter is 2(2x - 4)

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The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.

Explanation:

8x + 6+5 - x - 6x - 2

= x + 9.

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We can check if a function has an inverse function using horizontal  Line Test.

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect

horizontal  Line Test

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.

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