What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)

Answer:

The correct answer is option a.

a. 5( √3+ 1 )

Step-by-step explanation:

Given that the angle changes from 45° to 60° in 10 minutes.

This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).

AB is the tower (A be its top and B be its base).

Now, we need to find the time to be taken to cover the distance D to B.

First of all, let us consider [tex]\triangle[/tex]ABC.

Using tangent property:

[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]

Using tangent property in [tex]\triangle[/tex]ABD:

[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]

Now distance traveled in 10 minutes, CD  = BC - BD

[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]

[tex]Speed =\dfrac{Distance }{Time}[/tex]

[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]

Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'

So, more time required = Distance left divided by Speed

[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]

So, The correct answer is option a.

a. 5( √3+ 1 )

Answer:

52

Step-by-step explanation:

a(n)=-5+(n-1)3

a(20)=-5+(20-1)3

a(20)=52

The 20th term of the arithmetic sequence is 52.

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

For example,

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.

The nth term of an arithmetic sequence is given by an = a + (n – 1)d.

Given:

a(n)=-5+(n-1)3

First term,

a(1)= -5 + 0

a(1)= -5

second, a(2)= -5 + 1*3

a(2)= -2

Third, a(3)= -5+6

a(3)= 1

d= 3

So, the 20th term

a(20)= -5+ (20-1)3

a(20)= -5 + 57

a(20)= 52

Hence, the 20th term is 52.

Learn more about Arithmetic Sequence here:

https://brainly.com/question/10396151

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Answer:

[tex]d \approx 5.8[/tex]

Step-by-step explanation:

Just use the distance formula.

[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]

[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]

[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]

[tex]d=\sqrt{9+25}[/tex]

[tex]d=\sqrt{34[/tex]

[tex]d \approx 5.8[/tex]

Answer:

Correct option: D

Step-by-step explanation:

In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:

[tex]a^2 = b^2 + c^2[/tex]

Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).

So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:

[tex]x^2 = 40^2 + 42^2[/tex]

[tex]x^2 = 1600 + 1764[/tex]

[tex]x^2 = 3364[/tex]

[tex]x = 58[/tex]

So the correct option is D.

Answer:

b, c, e

Step-by-step explanation:

the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right

Answer:

B. a=d

C. c=d

E. b + d=180°

Step-by-step explanation:

Got Correct On MyPath.

Answer:

1112

Step-by-step explanation:

6458 + 2994  = 9452

7013  - 6945  = 68

9452/68 = 139

139 * 8 = 1112

​

Answer:

quadratic

Step-by-step explanation:

This graph has a parabola form wich is a propertie for qaudratic functions

Answer:

A

Step-by-step explanation:

Answer:

answer D

Step-by-step explanation:

Lets have a look to the graph and to the  each of given functions.

As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6

Function A  has the roots x1=+3 and x2=+6 => doesn' t fit

Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit

Function C has 2 roots  x1=4  and x2=-5 => doesn' t fit

Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!

We can also notice that the coefficient near x²  is equal to 1  and is positive.

That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.

Answer:

Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

Step-by-step explanation:

Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:

[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]

Let integrate both sides in terms of x:

[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]

[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.

Answer:

Step-by-step explanation:

Given the system of equation  x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.

x−3y=−3_____________ 1

x+y=5 ______________2

From equation 2; x = 5- y ________ 3

Substitute equation 3 into equation 1

Since x - 3y = -3

(5-y)-3y = -3

5-y-3y = -3

5-4y = -3

Subtract 5 from both sides of the equation

5-4y-5 = -3-5

-4y = -8

Divide both sides by -4

-4y/-4 = -8/-4

y = 2

Substitute y = 2 into equation 2 to get the value of y;

From equation 2, x+y = 5

x+2 = 5

Subtract 2 from both sides of the equation

x+2-2 = 5-2

x = 3

Hence the value of x and y from the graph will be 3 and 2 respectively.

Answer:

Step-by-step explanation:

The statement

3x less than two times the sum of 2X and one is written as

2( 2x + 1) - 3x

the sum of 2 and 5 is written as

2 + 5

Equate the two statements

We have

2( 2x + 1) - 3x = 2+5

Expand

4x + 2 - 3x = 7

Simplify

4x - 3x = 7 - 2

We have the final answer as

Hope this helps you

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System          System B

n1=120             n2=100

x1=4.1 min       x2=3.4 min

σ1=2.2 min     σ2= 1.5 min

Let [tex]\mu_1[/tex] = population mean checkout time of the first new system

[tex]\mu_2[/tex] = population mean checkout time of the second new system

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

                          T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex]  ~ N(0,1)

where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min

[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min

[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min

[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min

[tex]n_1[/tex] = sample of the first new systems = 120

[tex]n_2[/tex] = sample of the second new systems = 100

So, the test statistics =  [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]  

                                    =  2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Answer:

14.05

Step-by-step explanation:

We have the following:

Current Dividend = D0 = $ 1.40

g = growth rate = 2%

r = discount rate = 13%

Dividend in Year 5

= D5 = D0 * (1 + g) ^ 5

= $ 1.40 * (1 + 2%) ^ 5

= $ 1.40 * (1.02) ^ 5

Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)

= $ 1.40 * (1.02) ^ 5 / (13% -2%)

= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)

Therefore, firm stock at the end of year 4 is

P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05

Answer:

Discount : $34.25 off. Percent of the discount : 25%

Step-by-step explanation:

137 - 102.75 = 34.25.

34.25/137 x 100 = 25%

Answer:

The  probability is   [tex]P(A') = 0.485[/tex]

Step-by-step explanation:

Let assume that the number of computer produced by factory C is  k = 1  

 So  From the  question we are told that

       The number produced by  factory A is  4k =  4

        The  number produced by factory B is  7k  = 7

        The  probability of defective computers from A is  [tex]P(A) = 0.04[/tex]

        The  probability of defective computers from B is  [tex]P(B) = 0.02[/tex]

        The  probability of defective computers from C is [tex]P(C) = 0.03[/tex]

Now the probability of factory A producing a defective computer out of the 4 computers produced is  

       [tex]P(a) = 4 * P(A)[/tex]

substituting values

        [tex]P(a) = 4 * 0.04[/tex]

        [tex]P(a) = 0.16[/tex]

The probability of factory B producing a defective computer out of the 7 computers produced is  

       [tex]P(b) = 7 * P(B)[/tex]

substituting values

        [tex]P(b) = 7 * 0.02[/tex]

        [tex]P(b) = 0.14[/tex]

The probability of factory C producing a defective computer out of the 1 computer produced is  

       [tex]P(c) = 1 * P(C)[/tex]

substituting values

        [tex]P(c) = 1 * 0.03[/tex]

        [tex]P(b) = 0.03[/tex]

So the probability that the a computer produced from the three factory will be defective is  

     [tex]P(t) = P(a) + P(b) + P(c)[/tex]

substituting values

     [tex]P(t) = 0.16 + 0.14 + 0.03[/tex]

     [tex]P(t) = 0.33[/tex]

Now the probability that the defective computer is produced from factory A is

      [tex]P(A') = \frac{P(a)}{P(t)}[/tex]

       [tex]P(A') = \frac{ 0.16}{0.33}[/tex]

        [tex]P(A') = 0.485[/tex]

Answer:

3.27 hours

Step-by-step explanation:

Calculate the difference in speed and distance between the trains.

The relative speed:

101 - 90 = 11 mph

Difference in distance:

42 - 6 = 36 miles

[tex]time=\frac{distance}{speed}[/tex]

[tex]t=\frac{36}{11}[/tex]

[tex]t = 3.27[/tex]

Answer:

yeah she is correct

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

Follow the PEDMAS order (from top to bottom):

Parentheses

Exponents

Division and Multiplication

Addition and Subtraction

(-5 × 9 - 1) ÷ 2 + (5)2 - 7

(-45 - 1) ÷ 2 + 10 - 7

-46 ÷ 2 + 10 - 7

-23 + 10 - 7

-13 - 7

-20

Answer:

-20

Step-by-step explanation:

=> [tex](-5 * 9-1)/2+(5)2-7[/tex]

Expanding parenthesis

=> [tex](-45-1)/2+10-7[/tex]

=> [tex]-46/2 + 3[/tex]

=> -23 + 3

=> -20

Answer:

90/x=70/100 that's my answer

[tex]90 \x = 70 \100[/tex]

Answer:

90/x = 70/100

Step-by-step explanation:

Is means equals and of means multiply

90 = 70% *x

Changing to decimal form

90 = .70x

Changing to fraction form

90 = 70/100 *x

Divide each side by x

90/x = 70/100

Answer:

-3x^2 -5x +2

Step-by-step explanation:

-2x(x+3)-(x+1)(x-2)=

Distribute

-2x^2 -6x  -(x+1)(x-2)

Foil

-2x^2 -6x  -(x^2 -2x +x -2)

Combine like terms

-2x^2 -6x  -(x^2 -x  -2)

Distribute the minus sign

-2x^2 -6x  -x^2  +x +2

Combine like terms

-2x^2  -x^2  -6x +x +2

-3x^2 -5x +2

Answer:

[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]

Step-by-step explanation:

[tex]-2x(x+3)-(x+1)(x-2)[/tex]

Use the distributive property: a(b + c) = ab + ac

and FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]

Combine like terms:

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

Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Answer:

its 14/C

Step-by-step explanation:

i got i right on edg U^U

Answer:

16

Step-by-step explanation:

i did edge test yea dont  be imma fake :***    

Answer:

y = 1.8

Step-by-step explanation:

Question 39).

Let the operation which defines the relation between a and b is O.

Relation between a and b has been given as,

a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]

Following the same operation, relation between 3 and y will be,

3 O y = [tex]\frac{3+y}{3-y}[/tex]

Since 3 O y = 4,

[tex]\frac{3+y}{3-y}=4[/tex]

3 + y = 12 - 4y

3 + y + 4y = 12 - 4y + 4y

3 + 5y = 12

3 + 5y - 3 = 12 - 3

5y = 9

[tex]\frac{5y}{5}=\frac{9}{5}[/tex]

y = 1.8

Therefore, y = 1.8 will be the answer.

Answer:

-21/5 = -4.2

Step-by-step explanation:

-21.87 / 4.79 = -4.5657.....

So, the quotients is -4

Now, Let's see who's quotient is equal to think one:

-21/4 = -5.25

-21/5 = -4.2

-40/4 = -5

-20/5 = 4

Answer:

-21/5 = -4.2

Step-by-step explanation:

Answer:

pay the 11 AM ticket

Step-by-step explanation:

Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).

However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.

Therefore, the best choice is to pay the 11 AM ticket.

Answer:

Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19

Step-by-step explanation:

Given:

Number of balls = 1 to 19

Find:

Probability ball is an even numbered ball or a 4

Computation:

Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18

Probability to get even number P(A) = 9 / 19

Probability to get 4 number P(B) = 1 / 19

P(A and B) = 1 / 19 (4 common)

Probability ball is an even numbered ball or a 4 [P(A or B)]

P(A or B) = P(A) + P(B) -P(A and B)

P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]

Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19

Answer:

Step-by-step explanation:

f(x)=3x+15

let  f(x)=y

y=3x+15

flip x and y

x=3y+15

3y=x-15

y=1/3 x-5

or f^{-1}x=1/3 x-5

Answer:

d. 38

Step-by-step explanation:

AB = AD - BD = 54 - 36 = 18

AC = AB + BC = 18 + 20 = 38

Answer:

x = 4/3

Step-by-step explanation:

Direct variation:

y = kx

We use the given x-y point to find k.

6 = k * 2/3

k = 6 * 3/2

k = 9

The equation is

y = 9x

For y = 12,

12 = 9x

x = 12/9

x = 4/3

Answer:

4 : 5

Step-by-step explanation:

you can divide 120 and 150 by 30 and 8 and 10 by 2.

120/30 = 4

150/30 = 5

8/2 = 4

10/2=5

Answer: 4:5

Step-by-step explanation: