a flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph, what is the speed of the flying carpet in the air?

Answer:

20 + 35x

Step-by-step explanation:

We have the expression 5(4 + 7x) and are asked to distrbute it.

When distributing, it's very simple, all you have to do is multiply the number outside the parenthesis with the numbers inside the parenthesis.

Therefore :

(5(4) + 5(7x))

20 + 35x

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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Answer:

Everything looks right except the first one which is Distributive Property.

Step-by-step explanation:

multiplying out - 3(x - 3) is considered distributive property as you are distributing the -3 to the x and the 3.

-3 * x = -3x and -3 * 3 = -9

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

A circle is defined as the set of equidistant points to a given point which is the center of the circle.

That distance to the center is called the radius.

Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.

From that, we conclude that the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

That is the only proof that we can (and should) use to prove that a point lies on a circle.

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Answer:

The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

Step-by-step explanation:

I did the test

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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The length and width of the rectangle is 15cm and 31cm respectively

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(L + W)

where

L is the length

W is the width

If its length is 1 cm more than twice its width, then;

L = 2W + 1

Substitute

92 = 2(2W + 1 + W)

46 = 3W + 1

3W = 45

W = 15cm

Determine the length

L = 2(15) + 1

L = 31cm

Hence the length and width of the rectangle is 15cm and 31cm respectively

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Answer:

\(7 < k < 13\)

\(-6>y>-12\)

\(m > 5\)

\(3 < p < \frac{15}{2}\)

Step-by-step explanation:

Given

\(5 < k -2 < 11\)

\(-4 > y + 2 > -10\)

\(5 -m < 4\ or\ 7m > 35\)

\(3 < 2p -3 < 12\)

Required

Solve

Solving (1):

\(5 < k -2 < 11\)

The above can be represented as:

\(5<k -2\) and \(k -2<11\)

Solving \(5<k -2\)

\(5 + 2 <k\)

\(7<k\)

Solving \(k -2<11\)

\(k < 2 + 11\)

\(k < 13\)

So, we have:

\(7<k\) and \(k < 13\)

This can be combined as:

\(7 < k < 13\)

Solving (2):

\(-4 > y + 2 > -10\)

Split as:

\(-4 > y + 2\) and \(y + 2 > -10\)

Solving \(-4 > y + 2\)

\(-4 - 2 > y\)

\(-6 > y\)

Solving \(y + 2 > -10\)

\(y > -10 - 2\)

\(y > -12\)

So, we have:

\(-6 > y\) and \(y > -12\)

This gives

\(-6>y>-12\)

Solving (3):

\(5 -m < 4\ or\ 7m > 35\)

Solve for m in both cases:

\(5 - m < 4\)

\(-m<4 - 5\)

\(-m<- 1\)

\(m > 1\)

\(7m > 35\)

Divide both sides by 5

\(m > 5\)

So, we have:

\(m > 1\) or \(m > 5\)

The solution is \(m > 5\) because \(5> 1\)

Solving (4):

\(3 < 2p -3 < 12\)

The above can be represented as:

\(3 < 2p - 3\) and \(2p - 3<12\)

Solving \(3 < 2p - 3\)

Add 3 to both sides

\(3 + 3 < 2p - 3 + 3\)

\(6 < 2p\)

Divide both sids by 2

\(3 < p\)

\(2p - 3<12\)

Add 3 to both sides

\(2p - 3 + 3 < 12 + 3\)

\(2p < 12 + 3\)

\(2p < 15\)

Solve for p

\(p < \frac{15}{2}\)

So, we have:

\(3 < p\) and \(p < \frac{15}{2}\)

Combined as:

\(3 < p < \frac{15}{2}\)

Answer:

B

it goes down by $16,000 in that time frame

Given the information about the triangle, we can use the cosine function on angle x to get the following:

solving for x, we get:

therefore, the value of x is 61.1

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Answer

what is 50 divided by 20 is 2.5

Step-by-step explanation:

Answer:

5/2 (in fraction) or 2.5 (in decimal)

Step-by-step explanation:

50 = 5*10

20 = 2*10

50 divided by 20,

50/20

= 5/2 (in fraction)

(or)

= 2.5 (in decimal)

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

1 Factor out the common term 22.

2(x+3y)=6

2(x+3y)=6

2 Divide both sides by 22.

x+3y=\frac{6}{2}

x+3y=

2

6

3 Simplify \frac{6}{2}

2

6

to 33.

x+3y=3

x+3y=3

4 Subtract 3y3y from both sides.

x=3-3y

x=3−3y

Answer:

x=3 and y=2

Step-by-step explanation:

I hope I"m right and if I am can I be marked brainliest.

(c) 15i + 4b ≥ 100 inequality represents this scenario.

To represent the scenario described in the problem, we need to use an inequality that relates the amount of money Emily spends on ink and brushes to the total amount of money she has available. Let's call the amount of ink Emily buys "x" and the number of brushes "y". Then the total amount of money she spends is:

Total cost = 8x + 18y

We want to know when this total cost is less than or equal to $100, so we can write:

8x + 18y ≤ 100

This inequality means that the total cost of ink and brushes must be less than or equal to the amount of money Emily has available. Therefore, the answer is (c) 15i + 4b ≥ 100.

Correct Question :

Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. Which inequality below represents this scenario?

a) 4i+100 ≤ 15b

b) 15i + 4b ≤ 100

c) 15i + 4b ≥ 100

d) 4i + 15b ≤ 100

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Answer:

\(\huge \boxed{2}\)

Step-by-step explanation:

\(8^\frac{1}{3}\)

Apply rule : \(a^\frac{1}{3}=\sqrt[3]{a}\)

\(8^\frac{1}{3}=\sqrt[3]{8}\)

8 is a perfect cube. Evaluate the cube root of 8.

\(\sqrt[3]{8}=2\)

Answer:

Radical expression

\( \sqrt[3]{2} \)

Evaluation

\( {8}^{ \frac{1}{3} } = 2\)

Step-by-step explanation:

8^(⅓) = ³√8

=³√(2×2×2)

=³√(2³)

= 2

BRAINLIEST PLEASE

Answer:

True

True

False

False

True

The graph describes Andres movement in the park relative to the position

of his bike with time.

The correct responses are;

Reasons:

An horizontal line of the graph represents a stationary point on the graph, the x-intercept represent the points when Andre is next to his bike, therefore;

The point with coordinates (17, 1) represent a local minimum of the graph, therefore;

The maximum points are points having higher vertical coordinate values compared to the surrounding points.

The point that gives the highest value of the maximum points, which is at (21, 8.3) is the point at which he was farthest away from the bike.

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The correct solution for the integral is \((ze - 1)^2 / e + (7/4) - C / e\), the correct option is B.

We are given that;

The integral \(z^2/e^z dz\)

Now,

To find the integral of \(2z e^z dz\), we can use integration by parts again. Let u = 2z and dv = \(e^z dz\). Then du = 2 dz and \(v = e^z\). Using the formula for integration by parts, we get:

integral of \(2z e^z dz = uv\)- integral of \(v du = 2z e^z\) - integral of \(2 e^z dz = 2z e^z - 2e^z + C\)

Substituting this result into the previous equation, we get:

integral of \(z2/ez dz = z^2 e^z - (2z e^z - 2e^z + C) = z^2 e^z - 2z e^z + 2e^z - C = e^z (z^2 - 2z + 2) - C\)

To simplify the expression in the parentheses, we can complete the square. We add and subtract (1/2)^2 to get:

\(e^z (z^2 - 2z + 1/4 - 1/4 + 2) - C = e^z ((z - 1)^2 + 7/4) - C\)

To write the answer in a standard form, we can multiply and divide by e inside the parentheses, and combine the constants outside the parentheses. We get:

\(e^z ((ze - 1)^2 + (7/4)e) / e - C = (ze - 1)^2 / e + (7/4) - C / e\)

Using these steps, I found that the correct solution for the integral is:

\((ze - 1)^2 / e + (7/4) - C / e\)

Therefore, by the integral answer will be\((ze - 1)^2 / e + (7/4) - C / e\).

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Answer:

12

Step-by-step explanation:

Here we use SOHCAHTOA

Seeing as we have the hypotenuse and we are working to find out the opposite, we use SOH

Sin(x)= Opposite/Hypotenuse

Sin(45) = x/\(12\sqrt{2} \\\)

×12 root 2

sin(45) times 12 root 2=  12

x=12

Answer:

40ft

Step-by-step explanation:

The volume of a square pyramid is given by:

\(V=\frac{l^2h}{3}\)

where V is the volume, l is the length of the square base, and h is the height.

Since we need to find the length, we solve for \(l\) in the last equation:

\(l^2h=3V\\\\l^2=\frac{3V}{h} \\\\l=\sqrt{\frac{3V}{h} }\)

and now, we substitute the known values:

\(V=19,200ft^3\\h=36ft\)

and we get the following:

\(l=\sqrt{\frac{3(19,200ft^3)}{36ft} }\\ \\l=40ft\)

the length of the square base is 40ft

The value of the expression on evaluation is 96π / 5.

Here we have to find the value of the expression.

∫∫∫x² dV

E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.

E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].

∫∫∫ x² dV = ∫\(\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0\) r² cos² Фrd dФ

             = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,\)r³ cos²Ф dz dr dФ

            = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,\) 3\(r^{4}\)cos²Ф dr dФ

           = 3 \(\int\limits^2\pi _0 {} \,\) 1/2 \(2^{5}\)/ 5 ( 1 + cos² Ф )dr dФ

           = 48 / 5 [( Ф + 1/2 sin 2Ф)\(]^{2\pi } _{0}\)

            = 96π / 5

Therefore the value of the expression is 96π/5.

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Answer:

32.2 units

Step-by-step explanation:

The perimeter of the figure = AB + BC + CD + DE + EF + FA

AB = |5 - 11| = 6 units

BC = |-8 - 0| = 8 units

\( CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( C(11, 0) = (x_1, y_1) \)

\( D(6, -3) = (x_2, y_2) \)

\( CD = \sqrt{(6 - 11)^2 + (-3 - 0)^2} \)

\( CD = \sqrt{(-5)^2 + (-3)^2} \)

\( CD = \sqrt{25 + 9} = \sqrt{34} \)

\( CD = 5.8 units \) (nearest tenth)

DE = |6 - 4| = 2 units

\( EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( E(4, -3) = (x_1, y_1) \)

\( F(0, -6) = (x_2, y_2) \)

\( EF = \sqrt{(0 - 4)^2 + (-6 -(-3))^2} \)

\( EF = \sqrt{(-4)^2 + (-3)^2} \)

\( EF = \sqrt{16 + 9} = \sqrt{25} \)

\( EF = 5 units \)

\( FA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( F(0, -6) = (x_1, y_1) \)

\( A(5, -8) = (x_2, y_2) \)

\( FA = \sqrt{(5 - 0)^2 + (-8 -(-6))^2} \)

\( FA = \sqrt{(5)^2 + (-2)^2} \)

\( FA = \sqrt{25 + 4} = \sqrt{29} \)

\( FA = 5.4 units \) (nearest tenth)

Perimeter = 6 + 8 + 5.8 + 2 + 5 + 5.4

= 32.2 units

Answer:

$ 1,057.22

Step-by-step explanation:

A = $ 1,057.22

A = P + I where

P (principal) = $ 800.00

I (interest) = $ 257.22

After 8 years, total amount will be $1057.

Given that,

According to the given data, calculation are as follows,

Compound interest formula,

A = \(P (1 + \frac{r}{n} )^{nt}\)

A = \(800 (1 + \frac{0.035}{4} )^{4\times 8}\)

A = \(800 (1 + 0.00875 )^{32}\)

A = $800 \(\times\) 1.3215

A = $1057.2 or $1057.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

Answer:

=====================================

We know that diagonals of rhombus are perpendicular to each other.

Hence its area is half the product of diagonals.

The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.

Let's find the length of diagonals, using the difference of coordinates:

Now find the area:

Answer:

A

Step-by-step explanation:

basta a hehehehhjshshshss