[tex]3y - 5x = 10[/tex]
Find the gradient of the linear relation

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

Learn more about midpoint here:

https://brainly.com/question/5127660

#SPJ1

Answer:$6

Step-by-step explanation:

If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44

62-44=18

18/3=6

$6 per child ticket

The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

To learn more on inequalities: https://brainly.com/question/20383699

#SPJ1

The distance between the ships changing at 92.29 Knots

                              [tex]d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\[/tex]

The rate of change of distance is -

                              [tex]\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }[/tex]

after putting t = 5 into this rate of change ,

we get, answer = 92.29

To learn more about differentiation from the given link

https://brainly.com/question/25081524

#SPJ4

Answer:

p - 4

Step-by-step explanation:

Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.

Let p = 7.

2p = 2*7 = 14                  14 = 1*2*7*14

7p = 7*7 = 49                 49 = 1*7*49

p - 4 = 7 - 4 = 3              3 = 1*3

p^2 = 7^2 = 49               49 = 1*7*49

The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Learn more about exponential at https://brainly.com/question/2456547

#SPJ1

Answer:

x=10.5

Step-by-step explanation:

if the two triangles were ratios it would be like

19.3:7.2 to x:3.9

so 75.27 = 7.2x

whcih is 10.45 which is approximately 10.5

The height of the cone in terms of y is h = 12x⁴y

The cylinder and the cone have the same volume.

Volume of a cylinder = πr²h

where

Therefore,

Volume of a cylinder = πx²y

volume of a cone = 1 / 3 πr²h

where

Therefore,

πx²y = 1 / 3 × π × (1 / 2x)² × h

πx²y = πh / 12x²

πx²y × 12x² / π = h

h = 12x⁴y

Therefore, the height of the cone in terms of y is h = 12x⁴y

learn more on volume here: https://brainly.com/question/1984638

#SPJ1

Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:

n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.

Thus the number of ways is:

N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.

The inequality can be solved as the same way as we solve an algebraic equation.

Here in the question the inequality to be solved is given:

- 3x + 7 < 4

By subtracting 7 from both sides of the inequality we get,

⇒ - 3x + 7 - 7 < 4 - 7

⇒ - 3x < - 3

To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,

we get,

⇒ 3 x > 3

Now finally by dividing the whole inequality by 3 we get,

⇒ x > 1

The number line representation can be done by marking values from 1 to numbers greater than 1.

Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.

Learn more about inequality here:

brainly.com/question/20383699

#SPJ1

Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,

[tex]a_2 = a_1 + 2[/tex]

[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]

[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]

[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]

and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,

[tex]b_2 = 2b_1[/tex]

[tex]b_3=2b_2 = 2^2 b_1[/tex]

[tex]b_4=2b_3=2^3b_1[/tex]

[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

It follows that

[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)[/tex]

so the left side is

[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]

Also recall that

[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]

so that the right side is

[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]

Solve for [tex]c[/tex].

[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]

Now, the numerator increases more slowly than the denominator, since

[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]

[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]

and for [tex]n\ge5[/tex],

[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]

This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].

[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].

If [tex]n=2[/tex], then

[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]

If [tex]n=3[/tex], then

[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]

If [tex]n=4[/tex], then

[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]

There is only one value for which the claim is true, [tex]c=12[/tex].

The distance from the center to where the foci is located is 8 units

The formula associated with the focus of an ellipse is given as;

c² = a² − b²

where;

Let's use the Pythagorean theorem

Hypotenuse square = opposite square + adjacent square

Substitute the values into the formula

c² = 10² - 6²

Find the square

c² = 100 - 36

c² = 64

Find the square root

c = √64

c = 8

Thus, the distance from the center to where the foci is located is 8 units

Learn more about Pythagorean theorem here:

https://brainly.com/question/654982

#SPJ1

The probability of getting a reading between 1.50 and 2.25 is; 0.00546

We are given the following information in the question:

Mean; μ = 0 °C

Standard Deviation; σ = 1 °C

We are given that the distribution of thermometer readings is a bell shaped distribution that is a normal distribution.

Formula for z-score is;

z = (x' - μ)/σ

P(Between 1.50 degrees and 2.25 degrees) is expressed as;

P(1.5 ≤ x ≤ 2.25)

= P((1.5 - 0)/1 ≤ z ≤ (2.25 - 0)/1))

= P(z ≤ 2.25) -  P(z < 1.5)

= 0.0546 = 5.46%

The graph that correctly describes this is the first graph

Read more about Z-score Probability at; https://brainly.com/question/25638875

#SPJ1

Answer:

49,2

Step-by-step explanation:

i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length

The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.

The area of a rectangle is the product of the length and width of the same rectangle.

Given that:

The area of the painting, A = 4081 cm².

The width of the painting, b = 53 cm.

To find the length of the painting, use the following formula to obtain the area of the rectangle:

Area = length × breadth

Let the length of the painting is l, then

A = l × b

4081 = l × 53

l = [tex]\frac{4081}{53}[/tex]

l = 77

Thus, the length of the painting is 77 cm.

Learn more about Area here:

https://brainly.com/question/1631786

SPJ3

Answer:

C

Step-by-step explanation:

4 is a perfect square.  2 x 2.  You can pull the 2 out and everything else would be left under the square root symbol.

The domain is the water balloon's height increasing will be (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

Part A:

As seen from the graphic, increase from 0 to 2 sec.

The domain is (0, 2), where the height of the water balloon increases.

Part B:

The water balloon stays the same from 2 to 4 sec.

The field means that the height of the water balloon remains the same (2, 4).

Part C:

Height decreasing fasted at 4 to 6 sec.

Because the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.

The domain is where the height of the water balloon decreases rapidly (6, 10).

Part D:

The balloon's height will be almost near the ground as resistance will play its role.

But it will almost touch the ground.

The height of the water balloon will be 0 in 16 seconds.

To learn more about Slope, refer to:

https://brainly.com/question/3493733

#SPJ9

The simplified form of the expression is given as 83x/56 -(97/105)

Alphabets are usually represented as unknown variables in a equation or expression.

Given the following expression shown below

6/7 x -2/3 + 3/5 + 5/8 x -6/7

Collect the like terms to have;

6/7 x+ 5/8 x  -2/3 + 3/5 -6/7

Simplify

48x+35x/56 - (70-63 + 90)/105

The final expression will be given as;

83x/56 -(97/105)

Hence the simplified form of the expression is given as 83x/56 -(97/105)

Learn more on expression simplification here: https://brainly.com/question/723406

#SPJ1

Answer:

[tex]X1 = 6-\sqrt{2} , X2 = 6+\sqrt{2}[/tex]

Step-by-step explanation:

Answer: x= √2 + 6, - √2 + 6

Step-by-step explanation:

The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 4.47.

Given data set: 13 17  9 21

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]

Mean [tex]$=\frac{60}{4} \\[/tex]

Mean = 15

To find the difference of each data point from the mean as:

Deviation:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

Now we have to square the above deviations we obtain:

4, 4, 36, 36

To estimate the variance of the above sets:

variance [tex]$=\frac{4+4+36+36}{4}$[/tex]

Variance [tex]$=\frac{80}{4}$[/tex]

Variance = 20

The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].

To learn more about standard deviation refer to:

https://brainly.com/question/475676

#SPJ4

Answer:

4.4

Step-by-step explanation:

The answer above is correct.

volume of pyramid = 1/3(5.2)h cm3

Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.

we know that,

The volume of the pyramid is equal to

volume = (1/3) × base area × height

we have height = h cm

area of base = 5.2 cm^2

substitute in the formula

                       v = 1/3 × 5.2 × h

                        volume = 1.73h cm^3

To lean more about volume from the given link

https://brainly.com/question/11779865

#SPJ4  

Answer:

9

Step-by-step explanation:

listing the factors

27 : 1, 3, 9, 27

36 : 1, 2, 3, 4, 9, 12, 18, 36

the common factors are 1, 3, 9

the highest common factor is 9

Hi :)

The highest common factor is also known as the HCF

Let's find the HCF of [tex]\boldsymbol{27}[/tex] and [tex]\boldsymbol{36}[/tex].

[tex]\boldsymbol{Factors\:of\:27: 1, 3, 9, 27}[/tex]

[tex]\boldsymbol{Factors\:of\:36:1,2,3,4,6,9,12,18,36}[/tex]

HCF : [tex]\boldsymbol{9}[/tex]

[tex]\tt{Learn\:More;Work\;Harder}[/tex]

:)

Answer:

$4.58

Step-by-step explanation:

Lets convert 10 feet to meters.

1 ft = 0.305m

10ft = 0.305 * 10

10ft = 3.05m

Now we will work out the cost of the fabric.

Given 1m = $1.50

3.05m = 3.05 * $1.50 = $4.58 (nearest cent)

Answer:

D. Midpoint...

Step-by-step explanation:

I hope it helps You:)

The power output is  = 5W

Correct option is B.

Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power

Power is characterized as the rate at which a thing performs labor.

P = W/T ..... (1)

Work is calculated as the product of force applied to an item and the distance that object has traveled.

W = F.s

When we plug this value into the equation above, we get:

P = (F. s)/t

where,

power = P =?W

F = 10N Force Exercised

s = Displacement = 400cm = 4m  (1 meter = 100 centimeters).

t = Time required = 8s

Using the values in the equation above, we obtain

P = (10 x 4)/8

P = 5W

Hence, the correct option is Option b.

To know more about Power visit :

https://brainly.com/question/2289248

#SPJ4

I understand that the question you are looking for is :

Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.

What is his power output? (Power: P = W/t)

a. 1.25 W

b. 5 W

c. 40 W

d.500 W

The given set of functions are not linearly independent.

Given,

[tex]f_{1} (x) = x\\f_{2} (x) = x^{2} \\f_{3} (x) = 6x-2x^{2}[/tex]

We need,

[tex]c_{1} f_{1} (x)+c_{2} f_{2} (x)+c_{3} f_{3}(x)=0[/tex]

Substituting the values in equation we get,

[tex]c_{1} x+c_{2} x^{2} +c_{3} (6x-2x^{2} )=0\\[/tex]

Computing the equation we get,

[tex]c_{1} x+c_{2} x^{2} +c_{3} 6x-c_{3} 2x^{2}=0[/tex]

[tex](c_{1} +6c_{3} )x+(c_{2} -2c_{3} x^{2} =0[/tex]

This resolves to two equations

[tex](c_{1} +6c_{3})x =0\\(c_{2} -2c_{3} )x^{2} =0[/tex]

These will have an infinite set of solutions:

[tex]c_{1} =-6c_{3} \\c_{2} =2c_{3}[/tex]

Two functions are said to be linearly independent if neither function is a constant multiple of the other.

Here, it is clear that the given functions are not linearly independent.

Learn more about linearly dependent or independent functions here:https://brainly.com/question/18331568

#SPJ4

1885.5 m^3 of water will fill the container.

To find how many cubic feet of water will it contain:

Given -

The pool comprises a 12-foot-radius cylinder with a height of 4.5 feet.

The volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed.

Therefore, 1885.5 m^3 of water will fill the container.

Know more about volumes here:

https://brainly.com/question/1972490

#SPJ4

The complete question is given below:

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14

A cylinder with a radius of 12 feet and a height of 4.5 feet.

Answer: 797.4 m²

Step-by-step explanation:

The surface area is just the total of the areas of each face of of a solid. In this solid, we have 2 triangles and 3 rectangles.

We know that the two triangles of this solid are congruent, so they will have the same area. Since the area of a triangle is [tex]\frac{1}{2}bh[/tex], two triangles would have an area of [tex]bh[/tex]. Hence, the total area is

[tex]A=9 * 15\\A=135[/tex]

The area of a rectangle is lw, where l is the length and w is the width. Let's find the total area of all of them.

[tex]A=9*16+15*16+17.4*16[/tex]

All of the areas are a product of some number and 16. This makes sense as the length of this prism is 16. We can un-distribute this 16 to make the calculation easier.

[tex]A=16(9+15+17.4)\\A=16(41.4)\\A=662.4[/tex]

We can add both totals to get the total surface area of the solid.

[tex]135+662.4\\=797.4[/tex]

The surface area of this right triangular prism is 797.4 m².

The area of the region is: 63.585 square inches.

If we have a circle of radius R, the area of said circle is:

A = pi*R^2

Particularly, if we have a section of the circle defined by an angle θ, the area of that region is:

A = (θ/2pi)*pi*R^2 = (θ/2)*R^2

In this case we have:

θ = 90° = pi/2

R = 9in

Replacing that we get:

A = (pi/4)*(9in)^2 = (3.14/4)*(9in)^2 = 63.585 in^2

If you want to learn more about circles:

https://brainly.com/question/1559324

#SPJ1

[tex]d = \sqrt{ \frac{4h}{5} } \\ square \: both \: sides \\ d {}^{2} = \frac{4h}{5} \\ multiply \: both \: sides \: by \: 5 \\ 5d {}^{2} = 4h \\ divide \: both \: sides \: by \: 4[/tex]

[tex]h = \frac{5d {}^{2} }{4} [/tex]

Add 8 to both sides.

Add 7 and 8 to get 15.

Divide both sides by 3.

Divide 15 by 3 to get 5.

Subtract 9 from both sides.

Subtract 9 from −15 to get −24.

Divide both sides by 8.

Divide −24 entre 8 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Add 13 to both sides.

Add 8 and 13 to get 21.

Divide both sides by 3.

Divide 21 by 3 to get 7.

Subtract 22 from both sides.

Subtract 22 from 4 to get −18.

Divide both sides by 6.

Divide −18 entre 6 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Subtract 51 from both sides.

Subtract 51 from 84 to get 33.

Divide both sides by 11.

Divide 33 by 11 to get 3.

Solution 1 :-

>> 3k - 8 = 7

>> 3k = 7 + 8

>> 3k = 15

>> k = 15 / 3

>> k = 5

Solution 2 :-

>> 8b + 9 = -15

>> 8b = -15 - 9

>> 8b = -24

>> b = -24 / 8

>> b = -3

Solution 3 :-

>> 8 = 3x - 13

>> 3x = 13 + 8

>> 3x = 21

>> x = 21 / 3

>> x = 7

Solution 4 :-

>> 6p + 22 = 4

>> 6p = 4 - 22

>> 6p = -18

>> p = -18 / 6

>> p = -3

Solution 5 :-

>> 84 = 51 + 11c

>> 11c = 84 - 51

>> 11c = 33

>> c = 33 / 11

>> c = 3