2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?

sinE is 0.5

What are similar triangles?

Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

Clearly, given triangle AFB and triangle DFE are similar.

We know that Similar Triangles have the same corresponding angle

We can find sinE as show below:

From diagram clearly

∠A=∠E

and ∠B=∠D

Since, ∠A=∠E

Taking sin on both sides

sinA=sinE

Give, sinA=0.5

sinA=sinE=0.5

⇒ sinE=0.5

Hence, sinE is 0.5

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Answer:

[1 , +∞)

Step-by-step explanation:

Solving the inequality 6x ≥ 6

6x ≥ 6

⇔ x ≥ 1   (Divide both sides by 6)

⇔ x ∈ [1 , +∞)

Answer:

84

Step-by-step explanation:

Since we are given line OP perpendicular to line DR, then angles PDR and ODR are right angles.

Angles PDA and ADR are complementary.

Angles ODU and UDR are complementary.

Angles ADR and UDR are given as congruent.

We can conclude that angles PDA and ODU are congruent.

By AA Similarity, triangles APD and UMD are similar.

DP/DM = PA/MU

3.75/10 = 4.5/MU

3.75MU = 10 × 4.5

MU = 12 (altitude of triangle DUO)

OD = OM + MD =  4 + 10 = 14 (base of triangle DUO)

area = base × height / 2

area = 14 × 12 / 2

area = 84

Answer:

84

Step-by-step explanation:

correct me if im wrong

The limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]

since the degree of the numerator exceeds the degree of the denominator.

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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Answer:

34.51ft³

Step-by-step explanation:

The formula to find the volume of a cylinder is :

V = π r² h

Here,

r ⇒ radius ⇒ 1.3ft

h ⇒ height ⇒ 6.5ft

Let us find now.

V = π r² h

V = π × ( 1.3 )² × 6.5

V = π × 1.69 × 6.5

V = 34.51ft³

The system of inequalities has Infeasible solutions option (B) Infeasible is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The inequality:

2x + y ≤ 5

3x + y ≤ 12

First plot the above two inequality on a coordinate plane.

As we can see the intersection region on a coordinate plane for both the inequality:

f(x, y) = 2x + 2y

As we can see there is so many points in the intersection region for the above function so there will no single solution.

Thus, the system of inequalities has Infeasible solutions option (B) Infeasible is correct.

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Answer:

51,840

Step-by-step explanation:

The format of P(n, r) is used for permutations,

where      [tex]P(n, r) = \frac{n!}{(n - r)!}[/tex]

To evaluate this expression, P(9,2), we use the formula of permutation,

We have the value of n = 9 and r = 2, thus,

[tex]P(n, r) = P(9, 2) = \frac{9!}{(9 - 2)!} =\frac{9!}{7!} =\frac{9*8*7!}{7!} = 9 *8 =72\\[/tex]

To evaluate this expression, P(6, 5), we use the formula of permutation,

We have the value of n = 6 and r = 5, thus,

[tex]P(n, r) = P(6, 5) = \frac{6!}{(6 - 5)!} =\frac{6!}{1!} =\frac{6*5*4*3*2*1!}{1!} = 6*5*4*3*2 = 720[/tex]

Therefore the product of P(9, 2) · P(6, 5) is

72 · 720 = 51,840

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Answer: 5/11

Solution: x = 5/11

Step-by-step explanation:

Question: -(x+3)=-8+10x

Result -x-3=10x-8

Hope this help :)

Please give brainless

-(×+3)=-8+10× is a math equation with the solution of 5/11

The behavior of the graph of I and what it means in context can be explained below:

Sound intensity, serves as the  power that is been carried by sound waves per unit area and this is usually in the direction perpendicular to that area.

we were given the  function [tex]I = \frac{P}{4pir^2}[/tex]

r  represent the Distance from the source of sound

P represent the Power of the sound

when there is increase in the  distance from the source the intensity moves to zero.

we can see that there is is an inverse proportion between the Intensity and the distance r  which implies that The intensity decreases  when the distance increases.

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Answer:

(6 / 4) * (7 + 9)

Step-by-step explanation:

sry that took me so long lol

Angles 2 and 4 are corresponding angles. They are congruent, not supplementary because they have the same measure and do not add up to 180 degrees. Therefore, the answer is the third option. Corresponding angles are congruent.

it is that wich is klweijxmpx

The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.

What is increasing function?

⇒ The function is said to be increasing if the y value increases as the x value increase over a given range

What is average rate of change?

⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another

As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)

And it is true for the interval [0,2]

The faster the growth rate higher the average rate of change

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Answer:

C.

Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.

Answer:

[tex]\bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]

Step-by-step explanation:

There was no figure but the question is clear

Volume of a cylinder is given by the formula [tex]\bold{\pi r^2h}\\[/tex]

where r is radius of base of cylinder, h is the height

Volume of a cone is given by [tex]\bold{\frac{1}{3} \pi r^2 h}[/tex]

where r is the radius of base of cone, h is the height

The radius of the cylinder = [tex]\frac{1}{2}[/tex](diameter) = [tex]\frac{1}{2}[/tex](12) = 6cm

Height of cylinder = 15cm

Volume of cylinder [tex]V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}[/tex]

Radius of cone = [tex]\frac{1}{2}[/tex] (radius of cylinder) = [tex]\frac{1}{2}[/tex](6) = 3 cm

Height of cone same as height of cylinder = 15cm

Volume of cone, [tex]V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\[/tex]

Difference is the volume of the remaining solid

[tex]V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]

For this, let's go through each problem carefully and step-by-step.

According to the question, the rate of change of the temperature of any object that is defined by T, is directly proportional to the difference of T and the temperature of the environment around it, which we'll denote as X.

[tex]\frac{dT}{dt}[/tex][tex]= k (T-X)[/tex]

K is a constant of proportionality here. And the temperature of the surrounding environment is said to be (-18°C). Thus,

[tex]\frac{dT}{dt} = k(T+18)[/tex].

For part A, in order to find the differential equation for T, we need to solve for k. So we separate the variables and then integrate to solve the equation.

[tex]\int\limits{\frac{dT}{T+18} } = \int\limits {k} \, dt[/tex]

[tex]ln(T+18) = kt+c[/tex]

Now thw inital temperature of a pot of chili is 23°C, so at [tex]t = 0, T_0 = 23*C[/tex].

Substituting 23 for T and 0 for t, we have the following:

[tex]ln(23+18) = k(0)+c[/tex]

[tex]ln(41) = c[/tex]

We know the temperature of chili after 2 hours is 7°C, so we know that when [tex]t = 2, T_1 = 7[/tex]

Substituting t for 2, and T for 7, we get:

[tex]ln(7+18) = 2k+ln(41)[/tex]

[tex]ln(25) = 2k + ln(41)[/tex]

Solving for 2k

[tex]2k = ln(25) -ln(41)[/tex]

[tex]2k = ln(\frac{25}{41})[/tex]

[tex]k = \frac{1}{2}ln(\frac{25}{41})[/tex].

Substituting the value of [tex]\frac{dT}{dt} = k (T+18)[/tex], the differential equation obtained is [tex]\frac{dT}{dt} = \frac{1}{2}ln(\frac{25}{41})(T+18)[/tex].

For part B, to find the temperature of the chili after four hours, we first need to solve the above differential equation.

The solution of the differential equation is given by the equation [tex]ln(T+18) = kt+c[/tex]. Substituting the values of k and c, we have:

[tex]ln(T+18) = \frac{1}{2}ln(\frac{25}{41})t+ln(41)[/tex].

Using the above relation, at any time (t), the temperature (T) can be found out in the following.

At [tex]t = 4, T_2 = \phi[/tex]

[tex]ln(T_2+18)=\frac{1}{2}ln(\frac{25}{41})*4+ln(41)[/tex]

[tex]ln(T_2+18)=2ln(\frac{25}{41})+ln(41)[/tex]

[tex]ln(T_2+18)=-0.989 + 3.714[/tex]

[tex]ln(T_2+18)[/tex] ≅ [tex]2.725[/tex]

Solving the natural logarithm,

[tex]T_2+18 = e^{2.725} = 15.256[/tex]

[tex]T_2 =15.256 - 18[/tex]

[tex]T_2 = -2.744[/tex].

So the temperature of the chili after four hours would be -2.744°C approximately.

To find part C in what time the chili would be 10°C, we need to substitute again.

[tex]t = \phi[/tex][tex], T = -10[/tex]

[tex]ln(-10 + 18) = \frac{1}{2}ln(\frac{25}{41})t + ln(41)[/tex]

[tex]ln(8) = \frac{1}{2}ln(\frac{25}{41})t + ln(41)[/tex]

Solving for [tex]\frac{1}{2}ln(\frac{25}{41})t[/tex],

[tex]\frac{1}{2}ln(\frac{25}{41})t = ln(8) - ln(41)[/tex]

[tex]\frac{1}{2}ln(\frac{25}{41})t = ln(\frac{8}{41})[/tex]

[tex]\frac{1}{2}ln(\frac{25}{41})t = -1.634[/tex]

[tex]ln(\frac{25}{41})t[/tex][tex]= -1.634 * 2[/tex]

[tex](-0.494)t=-3.268[/tex]

[tex]t = \frac{-3.268}{-0.494}[/tex]

[tex]t=6.615[/tex] hours, approximately.

Thus, the chili would reach -10°C at around 6.615 hours.

Hope this helped. This took me a long time.

a. The value of v is 9.2

b. The value of u is 9.9

Vectors are physical quantities that have both magnitude and direction

Since we have vectors

We resolve them into component form

So, u = -(ucos70°)i - (usin70°)j

u = -(0.3420u)i - (0.9397u)j

v = -(vcos47°)i + (vsin47°)j

v = -(0.6820v)i - (0.7314v)j

w = (wcos15°)i + (wsin15°)j

w = (0.9659w)i + (0.2588w)j

w = (9.659)i + (2.588)j

Since the sum of the three vectors is zero, we have that

u + v + w = 0

u + v = -w

So,

-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]

-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]

-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]

-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j

Equating i components, we have

-[0.3420u + 0.6820v]i = -9.659i

0.3420u + 0.6820v = 9.659

Dividing through by 0.3420. we have

u + 1.994v = 28.242 (1) and

Also, equating j components, we have

- [0.9397u + 0.7314v]j = -2.588j

0.9397u + 0.7314v = 2.588  

Dividing through by 0.9397 we have

u + 0.778v = 2.754 (2)

Subracring equation (2) from(1),we have

u + 1.994v = 28.242 (1)

-

u + 0.778v = 2.754 (2)

2.772v = 25.488

v = 25.488/2.772

v = 9.19

v ≅ 9.2

The value of v is 9.2

Substituting v into (1), we have

u + 1.994v = 28.242 (1)

u + 1.994(9.19) = 28.242

u + 18.325 = 28.242

u = 28.242 - 18.325

u = 9.917

u ≅ 9.9

The value of u is 9.2

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Step-by-step explanation:

chicken nuggets are so bussing that the answer is c

Answer: -221

Step-by-step explanation:

31 is smaller than 252. Therefore, since 31 MINUS x equals 252, x needs to be a negative number in order to complete the equation (recall that a negative number times a negative number equals a positive number).

Therefore, if we subtract 31 on both sides, in other words transpose, we get,

-x = 221

The coefficient of -x is -1, however it is not written as it's implied that if there is not written coefficient in from of a variable then the coefficient of the variable is 1 or -1, depending on its sign.

Therefore, dividing -1 on both sides, we get,

x = -221

Hence, the desired answer is -221.

A circle is a shape formed by a curved side. Therefore, the required answers are:

1. An example of an inscribed angle is: <SQT or <QST or <QTS

2. An example of a minor arc is: arc QT or RS or QR

3. An example of a semicircle is: QRS or QTS

4. <QPR =  [tex]\frac{264600}{44r}[/tex] degrees

An angle is said to be formed whenever two or more straight lines intersect or meet. But an inscribed angle is an angle formed within a given circle.

A circle is a shape formed by a curved side. Some of its parts are semicircle, radius, diameter, chord, sector, segment, etc.

Thus the following can be deduced from the given question:

1. An example of an inscribed angle is: <SQT or <QST or <QTS

2. An example of a minor arc is: arc QT or RS or QR

3. An example of a semicircle is: QRS or QTS

4. <QPR.

length of an arc = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r

where r is the radius of the circle

105 =   [tex]\frac{x}{360}[/tex] x 2 x [tex]\frac{22}{7}[/tex] x r

      = [tex]\frac{44xr}{2520}[/tex]

44 xr = 105 x 2520

44xr = 264600

x = [tex]\frac{264600}{44r}[/tex]

Therefore the measure of angle QPR in terms of r is  [tex]\frac{264600}{44r}[/tex] degrees.

5. The length of arc QTR can be determined by;

Arc QTR =  [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r

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a. The velocity t = [tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]

b. v60 = 7164

mdv/dt = ck - mg

dv/dt = ck/m - mg/m

= ck/m - g

dv = [tex](\frac{ck}{Mo-Kt} -g)dv[/tex]

Integrate the two sides of the equation to get

v [tex]-\frac{ck}{k} e_{n} (Mo- kt)-gt+c[/tex]

[tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]

b. fuel accounts for 55% of the mass

So final mass after fuel is burned out is = 0.45

c=2500

g=9.8

t=60

v = -2500ln0.45 - 9.8 x 60

= 7752 - 588

= 7164

A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation where g is the acceleration due to gravity.

dv dt m =ck - mg

(a) Find v(t) keeping in mind that the mass m is a function of t.

v(t) =

m/sec

(b) Suppose that the fuel accounts for 55% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]

v(60) =

m/sec [Round to nearest whole number]

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If the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.

Given the distance between trains be 664 miles and the speed of one train is 16 miles more than the other train.

We are required to find the speed of both the trains.

Speed is basically the distance that a thing covers in a particular time period.

Speed=Distance/Time

let the speed of first train be x miles per hour.

According to question the speed of the second train be (x+16) miles per hour.

Taking first train:

Speed =Distance/Time

x=664/4

=166

Taking second train:

Speed=Distance/Time

x+16=664/4

x+16=166

x=150

Hence if the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.

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The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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The company sells all that it produces, the profit function is:-0.5x2+60x-250.

P(x)= R(x)-C(x)      

=-0.5(x-110)2 +6050-(50x+250)

Let Distribute Negative Sign      

P(x)= -0.5(x-110)2 + 6050 +-1(50x+250)

P(x)= -0.5(x-110)2 + 6050 +-1(50x) + (-1) (250)

P(x)= -0.5(X-110)2 +6050 +-50x + -250

Distribute P(x)= -0.5x2+110x+-6050+6050+-50x+-250

Combine Like Terms

P(x)= -0.5x2 +110x+-6050+6050+-50x+-250

P(x)=(-0.5x2) + (110x+-50x) + (-6050+6050+-250)  

P(x)= -0.5x2+60x-250

Therefore the company sells all that it produces, the profit function is:-0.5x2+60x-250.

The missing requirement is:

Assuming that the company sells all that it produces, what is the profit function?

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Answer:

Step-by-step explanation:

A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.

The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.

1/3π2.5²×10 =

1/3π6.25×10 =

1/3π62.5 =

1/3×196.25 =

196.25:3 =

65.41 u³

Answer:

f(4)=14

Step-by-step explanation:

a) u do it by substituting 4 in places where there r 'x'

since this one say f(4) it only can go to the function which says f(x)
f(x)=4x-2
f(4)=4(4)-2, so according to BODMAS rule multiplication comes first rather than subtraction

so, f(4)=16-2=14
f(4)=14
do the others based on this, hope i explained well, if i did, please gimme brainliest :)

Answer:

  f(x) = x³ -12x² +46x +148

Step-by-step explanation:

When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.

Given the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...

  f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))

Rearranging a bit, this is ...

  f(x) = (x +2)((x -7) -5i)((x -7) +5i)

The latter two factors are recognizable as the factors of the difference of squares, so this is ...

  f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)

Multiplying the factors, we have ...

  f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)

  f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property

  f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms

The slopes of OA, OB and OC are integer values.

According to the statement

we have given that the some points on the graph and we have to find that the slopes of these points have integer value or not.

So, For this we know that the

If a line passing through two points then the slope of the line is

So, [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Then

The slope of line OA is 4 because 8/2 = 4.

And

The slope of line OB is 3 because 9/3 = 3.

And

The slope of line OC is 2 because 8/4 is 2.

And

The slope of line OD is 8/5 because it is 8/5.

And

The slope of line OE is 7/6 because it is 7/6.

And

The slope of line OE is 6/7 because it is 6/7.

From all this it is clear that

So,The slopes of OA, OB and OC are integer values.

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