What is the price called at which the quantity demanded is equal to the
quantity supplied?
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Answer: U = 600 m/s

Step-by-step explanation:

Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.

After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.

From the first statement

Speed = distance/ time

Distance = speed × time

1500 = Ut

Make t the subject of the formula

t = 1500/U ..... (1)

From the second statement

Distance = speed × time

1500 = (U + 100) × ( t - 0.5 )

Open the bracket

1500 = Ut - 0.5U + 100t - 50

Collect the like terms

1550 = Ut - 0.5U + 100t .... (2)

Substitutes equation 1 into 2

1550 = 1500U/U - 0.5U + 100(1500/U)

1550 = 1500 - 0.5U + 150000/U

1550 - 1500 = (150000 - 0.5U^2)/U

Cross multiply

50U = 150000 - 0.5U^2

0.5U^2 + 50U - 150000 = 0

Divide all by 0.5

U^2 + 100U - 300000 = 0

Using completing the square method

U^2 + 100U = 300000

U^2 + 100U + 50^2 = 300000 + 50^2

(U + 50)^2 = 302500

U + 50 = sqrt(302500)

U + 50 = +/-(550)

U = 50 + 550 or 50 - 550

U = 600 or - 500

Since U is of the same direction, it is

positive. Therefore, the previous speed of the aeroplane is 600 m/s

Answer:

500km/hr

Step-by-step explanation:

The formula for Speed (km/hr) = Distance / Time

Where S = Speed

D = Distance

T = Time

S = D/T

From the question, the aeroplane covered a distance of 1500 km

S = 1500/ T

ST = 1500

Time taken( T ) = 1500/S ......... Equation 1

We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time

This is expressed mathematically as:

The new speed =S + 100km/hr

The new Time taken = 1500/ S - 1/2....... Equation 2

Also since Time = Distance / Speed

The new Time taken also = 1500/ S + 100 ......... Equation 3

Step 1

We would simplify Equation 2:

Time = 1500/S - 1/2

Find the Lowest common multiple = 2

Time = (2 × 1500 - S )/ 2S

Time = 3000 - S / 2S ......... Equation 4

Step 2

Equate Equation 4 and 3 together since they are both equal to time taken

1500/ S + 100 = 3000 - S / 2S

We cross multiply

2S × 1500 = (S + 100) ( 3000 - S)

3000S = 3000S - S² + 300000 - 100S

3000S - 3000S + S² - 300000 + 100S = 0

S² + 100S - 300000 = 0

Step 3

We solve for S = Speed by using factorisation method.

S² + 100x - 300000 = 0

S² - 500S + 600S - 300000 = 0

(S² - 500S) + (600S - 300000) = 0

S(S - 500) + 600(S - 500) = 0

(S - 500) (S + 600) = 0

S - 500 = 0, S = 500

S + 600 = 0 , S = -600

Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr

Answer:

Step-by-step explanation:

Adult's ticket price= $2.50

Children's ticket price= $1.25

One performance sells 12 more tickets to  adult than children.

In total they make $183.75.

Therefore, we have that:

1.25x+2.50(x+12)=$183.75

We solve the resulting equation for x.

Open the brackets

1.25x+2.5x+30=183.75

Collect like terms

3.75x=183.75-30

3.75x=153.75

Divide both sides by 3.75

x=41

Therefore:

Answer:

see below

Step-by-step explanation:

From the graph the slope is -1 and the y-intercept is 9. Therefore we can use slope-intercept form (y = mx + b) which will be y = -x + 9.

Answer:

y=1x

Step-by-step explanation:

theirs no b because it goes through (0,0)

to find slope you do 2-4 over 2-4 and it equals 1

hope this helps:)

[tex]\\ 1. (3x ^{2} + 2xy + 7) - (6x ^{2} - 4xy + 3) \\ = 3x ^{2} + 2xy + 7 - 6x ^{2} + 4xy - 3 \\ = 3x ^{2} - {6x}^{2} + 2xy + 4xy + 7 - 3 \\ = { - 3x}^{2} + 6xy + 4 \\ 2. \: {9x}^{2} - 2x + 3 - ( {4x}^{2} + 7x - 5) \\ = 9x ^{2} - 2x + 3 - 4x ^{2} - 7x + 5 \\ = {9x}^{2} - {4x}^{2} - 2x - 7x + 3 + 5 \\ = {5x}^{2} - 9x + 8 \\ 3. \: {x}^{2} - 5x + 6 \\ = {x}^{2} - (3 + 2)x + 6 \\ = {x}^{2} - 3x - 2x + 6 \\ = x(x - 3) - 2(x - 3) \\ = (x - 3)(x - 2) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer with step by step explanation

[tex](1)(3 {x}^{2} + 2xy + 7) - (6 {x}^{2} - 4xy + 3) \\ 3 {x}^{2} + 2xy + 7 - 6 {x}^{2} + 4xy - 3 \\ = - 3 {x}^{2} + 6xy + 4[/tex]

[tex](2)9 {x}^{2} - 2x + 3 - (4 {x}^{2} + 7x - 5) \\ 9 {x}^{2} - 2x + 3 - 4 {x}^{2} - 7x + 5 \\ = 5 {x}^{2} - 9x + 8[/tex]

[tex](3) {x}^{2} - 5x + 6 \\ {x}^{2} - 3x - 2x + 6 \\ x(x - 3) - 2(x - 3) \\ (x - 2)(x - 3)[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Large box = 31/2 = 15.5 kgs

Small box = 27/2 = 13.5 kgs.

Step-by-step explanation:

Let x be large box

Let y be small box

5x + 3y = 118

5x = 118 - 3y

x = 118/5 - 3/5y

2x + 12y = 193

2(118/5 - 3/5y) +12y = 193

y = 27/2 = small box

Large box

5x + 3(27/2)=118

x = 31/2 = large box

Answer:

the average number of 2 and 3 is 2.5 and 10 is an integer

Step-by-step explanation:

Answer:

The circumference of circle is 101 units.

Step-by-step explanation:

Given that the diameter of circle is 32 units so you have to find radius by dividing it by 2 :

[tex]radius = diameter \div 2[/tex]

[tex]radius = 32 \div 2[/tex]

[tex]radius = 16 \: units[/tex]

Next, we have to apply circumference formula, C = 2×π×r where r represents radius which is 16 units :

[tex]c = 2 \times \pi \times r[/tex]

Let π = 22/7,

Let r = 16,

[tex]c = 2 \times \frac{22}{7} \times 16[/tex]

[tex]c = 32 \times \frac{22}{7} [/tex]

[tex]c = \frac{704}{7} [/tex]

[tex]c = 101 \: units \: (3s.f)[/tex]

__________________________________

Hey!!

Solution,

Diameter=32

Radius=32/2=16

Circumference of circle=?

Now,

Circumference of circle=2 pi r

=2*22/7*16

=100.57

hope it helps...

Good luck on your assignment

_________________________________

Answer:

Area =28.27

Step-by-step explanation:

Answer:

The area of circle:

[tex]A \approx 28.27[/tex] [tex]m^2[/tex]

Step-by-step explanation:

To find the area of circle, you need this formula:

[tex]A = \pi r^2[/tex]

-After have the formula set up, use the given radius for the formula:

[tex]A = \pi 3^2[/tex]

-Then, you solve:

[tex]A = \pi \times 3^2[/tex]

[tex]A = \pi \times 9[/tex]

[tex]A = 9\pi \approx 28.27[/tex] [tex]m^2[/tex]

-So, the area of a circle is [tex]28.27[/tex] [tex]m^2[/tex] .

When dividing indices with the same base, the rule is to subtract the index of the denominator from the index of the numerator, and to keep the base the same.

In this case, the index of our denominator is 6, and the index of the numerator is 2.

2-6 = -4

The answer is [tex]4^{-4}[/tex].

Answer:

1) 4^-4

2) 1/256

Step-by-step explanation:

did on edge

Answer:

Question (8). m∠1 = 142°

                     m∠2 = 300°

Question (9). m∠1 = 73°

                     m∠2 = 82°

Step-by-step explanation:

Question (8). m∠1 + 38° = 180° [Supplementary angles]

                              m∠1 = 180 - 38

                              m∠1 = 142°

                              m∠x = 38° [Alternate interior angles]

                               m∠y = 22° [Alternate interior angles]

                Now, m∠2 = 360° - (m∠x + m∠y)

                                   = 360° - (38 + 22)°

                          m∠2 = 300°

Question (9). m∠RMN + 98° = 180°

                       m∠RMN = 180 -98

                                      = 82°

                       m∠RMN = m∠ARM = 82°

                             m∠2 = 82°

                        m∠SNM = 73° [Vertical angles]

                        m∠SNM = m∠OSR = 73°[Corresponding angles]

                               m∠1 = 73°

Answer:

(A)[tex]56.5^\circ[/tex]

Step-by-step explanation:

From the diagram attached:

Angle 1 and Angle 6 are Co-Interior Angles.

The sum of co-interior angle is 180 degrees.

Therefore:

[tex]m\angle 1+ m\angle 6=180^\circ\\\\m\angle 6=123.5^\circ,$ therefore:\\m\angle 1+ 123.5^\circ=180^\circ\\m\angle 1=180^\circ-123.5^\circ\\m\angle 1=56.5^\circ[/tex]

The measure of angle 1 is therefore 56.5 degrees.

The correct option is A.

∠6 and ∠1 are same-side interior angles, m∠6 = 123.5°, therefore m∠1 will be: A. 56.5°

Recall:

The image showing the two parallel lines that is cut by a transversal creating angles is shown in the diagram attached below.

Given:

m∠6 = 123.5°

∠6 and ∠1 are same-side interior angles.

m∠6 + m∠1 = 180°

123.5° + m∠1 = 180°

m∠1 = 180° - 123.5°

m∠1 = 56.5° (Option A)

Learn more about same-side interior angles on:

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Answer:

1 in^2

Step-by-step explanation:

area of a rectangle=l*w

l=7/6

w=6/7

7/6 * 6/7 = 1

Answer:

B

Step-by-step explanation:

The slope is negative since the line decreases from left to right. This means  that the slope is -1/3.

Answer:

(4,8)

Step-by-step explanation:

The solution is where the two lines intersect.

The graphs intersect at x=4 and y = 8

(4,8)

Answer:    B: (4,8)

Step-by-step explanation:

y = 3x +2           you will go to positive to on the graph and go up 3 and to the right two because it is positive until you can't no more.

y = -6x + 32

you will go to +32 on the graph and then go down six and since there is no number under -6 you will replace it with one so it will look like this -6x/1

[tex]\text{Simplify:}\\\\(3x^2-4x+2)-(2x^2-4x-5)\\\\3x^2-4x+2-2x^2+4x+5\\\\x^2-4x+2+4x+5\\\\x^2+2+5\\\\x^2+7\\\\\boxed{\text{Two terms}}[/tex]

Answer:

12 miles

Step-by-step explanation:

monday=4 miles

tuesday=4 miles

wednesday= 4 miles

4+4+4=12

Answer:

x=1 y=-4

Step-by-step explanation:

Answer:

(1, - 4 )

Step-by-step explanation:

Given the 2 equations

y = - 5x + 1 → (1)

y = - x - 3 → (2)

Since both are expressed in terms of y, equate the right sides, that is

- x - 3 = - 5x + 1 ( add 5x to both sides )

4x - 3 = 1 ( add 3 to both sides )

4x = 4 ( divide both sides by 4 )

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (2)

y = - 1 - 3 = - 4

Solution is (1, - 4 )

Answer: 40

ADE = 70 por suma de angulos interiores en triangulo ADE

En triangulos BDE y AED

AE=BE por dato

DE lado comun

AED= BED= 90

por tanto los triangulos son iguales por tener dos lados y el angulo comprendido respectivamente iguales

Luego ADE = BDE = 70 y AD=BD=BC por ser triangulos BDE y AED iguales

Luego triangulo BDC isosceles de base DC

ADE + BDE + BDC = 180 por suma de angulos consecutivos

BDC = 180 - 70 -70 = 40

Ф = BDC =BCD = 40 por ser angulos bases de un triangulo isosceles

Answer:

200 kg

Step-by-step explanation:

To satisfy the ratio 1:2:3, Mark must use 100 kg cement, 200 kg sand, and 300 kg gravel

Answer:

6 kg

Step-by-step explanation:

Answer:

He needs approximately 46 feet of fencing.

Step-by-step explanation:

John's garden has a shape of a composite figure as shown in the annexed drawing. To find the length of the fencing he needs we need to find the perimeter of the rectangle and subtract it with the width and find the length of the circle and divide it by two. This is done below:

[tex]\text{fence} = (\text{rectangle perimeter} - \text{width}) + (\frac{\text{circle perimeter}}{2})\\\text{fence} = (2*14 + 2*7 - 7) + (\frac{2*\pi*3.5}{2})\\\text{fence} = 35 + 11 = 46 \text{ feet}[/tex]

He needs approximately 46 feet of fencing.

Answer:

46

Step-by-step explanation:

Answer:

6²

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] , thus

[tex]\frac{6^{7} }{6^{5} }[/tex] = [tex]6^{(7-5)}[/tex] = 6²

The answer is 6^2.

Division is the process of splitting a number or an amount into equal parts.

here, we have,

6^7/6^5

we know,

a^m/a^n

=a^(m-n)

so, we get,

6^7/6^5

=6^2

hence, The answer is 6^2.

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Answer:

-1/19 = x

Step-by-step explanation:

(x - 1)/x = 20

Multiply each side by x

(x - 1)/x *x = 20*x

x-1 = 20x

Subtract x from each side

x-1-x = 20x-x

-1 = 19x

Divide each side by 19

-1/19 = x

Answer:

X1,Y1

Step-by-step explanation:

If the Quadrilateral was rotated 90 degrees clockwise around point C, C would still be on the same X line that it is currently on but, point B would also rotate down to that same horizontal line. Between point C and point B there is a space of 3 units, so if that rotated 90 degrees clockwise it would be 3 units to the right of the current position of point C.  

Hope this helps!

Answer:

28 numbers

Step-by-step explanation:

There is a distance of 81 between -0.5 and 80.5. Divide this number by 3, since you are only counting every third number and you will get 27, but you need to count the first number, which has been excluded. Add one more to get the answer, 28.

Answer:

6 seconds

Step-by-step explanation:

h(x) = 0 m , when the ball is on the ground.

h(x) = - (x-2)² + 16

0 = - (x-2)² + 16

(x-2)² = 16

√(x-2)² = +/- √16

(x-2) = 4  ,        (x-2) = - 4

x - 2 = 4  ,         x = -2

x = 6

We can use only positive solution.

Answer:

XZ

Step-by-step explanation:

The intersection of the 2 planes is along the line XZ

The intersection of the two planes in the image below is along the line XZ.

The intersection of the x-axis, the horizontal line, and the y-axis, the vertical line, creates a coordinate plane, which is a two-dimensional plane. The origin is the point at which these parallel lines cross one another.

A coordinate plane is a framework for graphing and describing lines and points. The coordinate plane is made up of a vertical (y) axis and a horizontal (x) axis.

In the given image there are two planes one is horizontal and the second is vertical they are intersecting at line XZ.  The intersection of the 2 planes is along the line XZ.

Therefore, the intersection of the two planes in the image below is along the line XZ.

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A U B={ 1,2,3,4,5,6,7,8}

Solution,

A={2,4,6,8}

B={1,3,5,7}

A U B={ 2,4,6,8} U{1,3,5,7}

={1,2,3,4,5,6,7,8}

Hope it helps

Good luck on your assignment