At first it decreased by 60 percent and it increased by 80 percent

The expression for the total area of the wall is 10x.

What is area of rectangle?

Let l be length and b be breadth of the rectangle.

Then the area is the product of length and breadth of the rectangle.

That is area = l* b

We can find the expression for the total area of the wall as shown below:

Let the total length of the wall be x.

Height=10 ft

Total area = Height*Length

Putting the value of length and breadth in the above formula.

Total area = 10*x

Total area = 10x

Hence, the expression for the total area of the wall is 10x.

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The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B  + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA

BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

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Answer:

There is only 1 solution, and it is ½

Step-by-step explanation:

-46x - 23 = 46x + 23

46x + 46x = 23 + 23

92x = 46

x = 46 / 92

x = ½

SOLUTION :

YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,

& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).

________________________________

MARK BRAINLIEST!

Answer:

Step-by-step explanation:

∫(cos(1/x)/x² dx

[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]

The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor

it is also called the logarithmic return, compounded return, or the force of interest.

Note that the general formula for growth rate is given as;

[tex]P(t) = P0 e^k^t[/tex]

Where,

Po =  Initial value = 400 squirrels

r = Rate of growth

k = constant of proportionality = 0. 5 per year

t = time = 1 year

The function P(t) is given as;

P(t) = 400 e^0.5t

Note that the formula for doubling time is given as;

[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]

r = 4

t = 1

substitute into the formula

[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]

Doubling time  = 1 × 17. 68

Doubling time = 17. 68 years

Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

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Answer:

angles of the triangle are equal 180

so 42+82=124

180-124=56

so the answer is 56

Step-by-step explanation:

Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

[tex]x + y = 2.7[/tex]

DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of

[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]

[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]

[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]

For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.

Then the dwarves need

• total gold: [tex]0.21x = 0.189[/tex]

• total silver: [tex]0.09x = 0.081[/tex]

• total steel: [tex]0.70x + y = 2.43[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.

The surface area of the triangular prism is 93 squared feet.

The surface area of triangular prism is expressed as;

S.A = bh + ( s₁ + s₂ + s₃ )H

From the diagram;

We substitute our given values into the equation above.

S.A = bh + ( s₁ + s₂ + s₃ )H

S.A = (3ft × 2ft) + ( 3ft + 3ft + 3ft )10ft

S.A = 3ft² + ( 9ft )10ft

S.A = 3ft² + 90ft²

S.A = 93ft²

The surface area of the triangular prism is 93 squared feet.

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Answer:

A. 8/7

Step-by-step explanation:

4/7 - (-4/7) --> 4/7 + 4/7

The two minutes turn into a plus, removing the bracket.

4/7 + 4/7 = 8/7

Add the two fractions together.

Answer:

A. 8/7

Step-by-step explanation:

Considering that the graphs have two intersection points, the two lines are equal.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In a graph, the solution of two linear equations is the intersection of the two lines. Hence, if there are two solutions, as is the case in this problem, the two lines are equal.

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The length of the line segment SR is 15 units.

In Δ SRQ as seen in the attached image, we see that;

∠SRQ is a right angle

SQ is the hypotenuse

RT ⊥ SQ

Thus, by triangular rules, we know that;

(RQ)² = TQ × SQ

RQ = 20 units and TQ = 16 units

Thus;

(20)² = 16 × SQ

400 = 16 × SQ

SQ = 400/16

SQ = 25 units

By using Pythagoras theorem in Δ SRQ, we have;

(SR)² + (RQ)² = (SQ)²

RQ = 20 units and SQ = 25 units

Thus;

(SR)² + (20)² = (25)²

(SR)² + 400 = 625

(SR)² = 225

SR = √225

SR = 15 units

The length of the line segment SR is 15 units.

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The resale value of the car after four years is $4820

The given parameters are:

initial value, a = $27,000

Rate, r = 35%

The value of the car each year is represented as:

Value = a *(1 - r)^t

So, we have:

Value = 27000 *(1 - 35%)^t

After four years, we have:

Value = 27000 *(1 - 35%)^4

Evaluate

Value = 4820

Hence, the resale value of the car after four years is $4820

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Answer:

2

Step-by-step explanation:

8/3 = 2 with a Remainder of 2

The average cost per issue of magazine is $3

The given parameters are:

Cost = $36

Issue = 12

The cost per issue is calculated as:

Average = Cost/issue

This gives

Average = 36/12

Evaluate

Average = 3

Hence, the average cost per issue of magazine is $3

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Answer:

hexagon and pentagon structure. also known as a truncated icosahedron

Step-by-step explanation:

hope that gives you a good enough description.

Percent of the total was spent on veterinary​ care is 31.3186% .

Applying simple percentage formula,

let x be the percentage

x=[tex]\frac{17.1}{54.6} \ 100[/tex]

x=31.3186 %

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Answer:

16 chairs

Step-by-step explanation:

800 - 300 = 500

500/30 = 16.6 since it's money you can only afford 16

Answer: 19

Step-by-step explanation:

Using the sum of an arithmetic series formula,

[tex]\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211[/tex]

Multiplying the second equation by 2 gives us [tex]32a+2b=166[/tex].

Subtracting this from the second equation, we get that [tex]9a=45 \implies a=5[/tex].

Substituting this back into the first equation, we get that [tex]b=3[/tex].

Therefore, [tex]2a+3b=2(5)+3(3)=19[/tex]

This graph has its maximum at 4. There is no minimum while the inflection is at 2, 10/3.

We have ( x-2²) (x-4)

x-2²) = 0, or x - 4

x - 2 = 0, x = 2

Hence we can see that the graph has its minimum at x = 4

b. The graph here does not have a local maximum

To do this you have to differentiate the equation

Use the product rule of differentiation in order to solve for the solution.

(x-2)²[ (x-4) 2 (x-2)]

This would then give us

x -2, 3x -10

In both equations we have to make x the subject of the equation

X = 2, x = 10/3

Hence the point of inflection is 2 and 10/3

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The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1

Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.

So, the general form of a sine function y(t) is

y(t) = Asin(2πt/T) + K where

Now since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.

Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.

Also, it rotates once every 16 seconds, so its period T = 16 s.

So, y(t) = Asin(2πt/T) + K

y(t) = Asin(2πt/16) + K

y(t) = Asin(πt/8) + K

At maximum value

15 = Asin(πt/8) + K

15 = A + K  (1)

At minimum value

1 = Asin(πt/8) + K

1 = A(0) + K  

1 = 0 + K

K = 1

Substituting K into (1), we have

15 = A + 1

15 - 1 = A

14 = A

A = 14

So, y(t) = Asin(πt/8) + K

y(t) = 14sin(πt/8) + 1

So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1

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The conversion is given as 1, 760 feet per second

We need to convert 20miles per hour to feet per second

First, we should convert miles to feet

1 mile = 5280 feet

Then,

20 miles = x

Cross multiply

20 × 5280 = x

x = 105, 600

Per hour = I hour = 60 seconds

To find the conversion, we divided the conversion to feet by that of the time

= 105, 600/60

= 1, 760 feet per second

Thus, the conversion is given as 1, 760 feet per second

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Answer:

[tex]\frac{16}{32}[/tex]

Step-by-step explanation:

given

[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )

= [tex]\frac{16}{32}[/tex]

The angle which is coterminal with -60 between 0 and 360 is; 300°.

Since, it follows that the representation of the angle -60 corresponds to 60° span in the clockwise direction.

Therefore, by going the conventional anticlockwise direction, the angle which is coterminal with -60 is; 300°.

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To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups

In the Kingdom of Gallons (Write a big G on your paper)

Inside the G write 4 Qs

There were four Queens

Inside the Qs write 2 ps

Each Queen had to princess

In each princess write 2 Cs

And each princess has two Cats

Now we know that there is 2 Cups in each Pints so

since she sold 34 cups of juice in cups then we divide 34 by 2 to get

17 PINTS

Answer:

150 pints

Step-by-step explanation:

I believe you meant "By the end of the day, 3/4th of the quantity was sold."

Recall that 2 cups = 1 pint, so 400 cups = 200 pints, and

3/4 th of that would be 150 pints.

Using it's concept, a radical equation is given as follows:

[tex]\sqrt{x} + 3 = 13[/tex].

A radical equation is an equation in which the variable is inside the radical.

Hence, among the equations given, the radical equation is:

[tex]\sqrt{x} + 3 = 13[/tex].

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Answer:

C

Step-by-step explanation:

took edge test and got 100

The sample size required is mathematically given as

n=1454

Generally, the equation for Margin of error is  mathematically given as

[tex]M=Z_{\alpha/2} > \frac{\sigma}{\sqrt{n}}[/tex]

Therefore

[tex]M= 0.11 \leq \frac{ 2.33*1.8}{\sqrt{n}}\\\\\sqrt{n} \leq 38.127[/tex]

n=1453.69.

In conclusion, The sample size required is mathematically given as

n=1454

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Using the inverse functions property:

Two functions f(x) and f⁻¹(x) are inverses if:

f( f⁻¹(x) ) = x

f⁻¹(f(x)) = x

We want to get:

f⁻¹(f(93)) = m

By using the above definition we get:

f⁻¹(f(93)) = m = 93

Now for the second one we want:

f(7) = n

If you look at the table, you can see that f(x) contains the point (7, -6), then:

f(7) = n = -6

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