Solve the system of equations algebraically.
5x - 3y = 6
6x - 4y = 2
a. many solutions
C.
no solution
b. (8, 14
d. (9. 13)
Please select the best answer from the choices provided
Ο Α
ОВ
О С

Answers

Answer 1

Answer:

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=9,\:y=13[/tex]

the option 'd' is correct.

Step-by-step explanation:

Given the system of the equations

[tex]\begin{bmatrix}5x-3y=6\\ 6x-4y=2\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}5x-3y=6\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:30x-18y=36[/tex]

[tex]\mathrm{Multiply\:}6x-4y=2\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:30x-20y=10[/tex]

[tex]\begin{bmatrix}30x-18y=36\\ 30x-20y=10\end{bmatrix}[/tex]

[tex]30x-20y=10[/tex]

[tex]-[/tex]

[tex]\underline{30x-18y=36}[/tex]

[tex]-2y=-26[/tex]

[tex]\begin{bmatrix}30x-18y=36\\ -2y=-26\end{bmatrix}[/tex]

solve for y

[tex]-2y=-26[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex]

[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]

[tex]y=13[/tex]

[tex]\mathrm{For\:}30x-18y=36\mathrm{\:plug\:in\:}y=13[/tex]

[tex]30x-18\cdot \:13=36[/tex]

[tex]30x-234=36[/tex]

[tex]30x=270[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}30[/tex]

[tex]\frac{30x}{30}=\frac{270}{30}[/tex]

[tex]x=9[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=9,\:y=13[/tex]

Therefore, the option 'd' is correct.


Related Questions

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of

Answers

Answer:

Answer and Explanation:

We have:

Population mean,

μ

=

3

,

000

hours

Population standard deviation,

σ

=

696

hours

Sample size,

n

=

36

1) The standard deviation of the sampling distribution:

σ

¯

x

=

σ

n

=

696

36

=

116

2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.

Therefore:

The expected value of the sampling distribution is equal to the population mean,

μ

¯

x

=

μ

=

3

,

000

The standard deviation of the sampling distribution,

σ

¯

x

=

116

The shape of the sampling distribution of

¯

x

is approximately normal. As the sample size is more than

30

.

3) The probability that the average life in the sample will be between

2670.56

and

2809.76

hours:

P

(

2670.56

<

x

<

2809.76

)

=

P

(

2670.56

3000

116

<

z

<

2809.76

3000

116

)

=

P

(

2.84

<

z

<

1.64

)

=

P

(

z

<

1.64

)

P

(

z

<

2.84

)

=

0.0482

Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)

4) The probability that the average life in the sample will be greater than

3219.24

hours:

P

(

x

>

3219.24

)

=

P

(

z

>

3219.24

3000

116

)

=

P

(

z

>

1.89

)

=

0.0294

Using Excel: =NORMSDIST(-1.89)

5) The probability that the average life in the sample will be less than

3180.96

hours:

P

(

x

<

3180.96

)

=

P

(

z

<

3180.96

3000

116

)

=

P

(

z

<

1.56

)

=

0.9406

The expected value, standard deviation, and shape of the sampling distribution of will be 116.

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.

And, A simple random sample of 36 bulbs is taken.

Now,

Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.

And, A simple random sample of 36 bulbs is taken.

Hence, The expected value, standard deviation, and shape of the sampling distribution of is,

⇒ Standard error = 696 / √ 36

                            = 696 / 6

                            = 116

Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.

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giving brainliest !!!

Answers

It is given that AB is parellel to CD. These two lines are cut by a transversal, creating angles BAC and DCA. Thus, angle BAC is congruent to angle DCA because alternate interior angles are congruent. It is also given that angle ACB is congruent to angle CAD. Therefore, triangle ABC is congruent to triangle CDA because of the ASA theorem.

I NEED HELP WITH THIS PICTURE IS PROVIDED

Answers

Is this an exam? Nehshdgdsusu

A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places

Answers

Answer:

0.0475 or 4% professional language translators get paid less than $250 per hour

Step-by-step explanation:

Mean = 320

Standard Deviation = 41.75

We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)

First we will find value of z

Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]

We have x=250, finding z

[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]

Now we will find P(z<-1.67) by looking into the normal distribution table

[tex]P(z<-1.67)=0.0475\\[/tex]

So,0.0475 or 4% professional language translators get paid less than $250 per hour

The sum of three consecutive odd integers is 153. Find the three odd integers.

First integer =


Second integer =


Third integer =

PLEASE HELPPPP!!

Answers

Answer:

49, 51, 53

Step-by-step explanation:

Let the first odd integer be n.

Then the consecutive odd integer will be (n+2).

This will be followed by (n+4).

We know that the sum of these three is 153. In other words:

[tex]n+(n+2)+(n+4)=153[/tex]

Solve for n. Combine like terms:

[tex]3n+6=153[/tex]

Subtract 6 from both sides:

[tex]3n=147[/tex]

Divide both sides by 3:

[tex]n=49[/tex]

Therefore, our first odd number is 49.

So, our consecutive numbers must be 51 and 53.

Hence, our sequence is:

49, 51, 53

Notes:

If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.

Answer:

49, 51, 53

Step-by-step explanation:

All odd numbers:

49 + 51 = 100

100 + 53 = 153

By visual inspection, determine the best-fitting regression model for the data plot below.

Answers

Answer:

Quadratic

Step-by-step explanation:

It looks like it’s forming a very wide arch so quadratic formulas are arches

The equation of the regression line model for the data plot determines a quadratic equation

What is linear regression line?

The connection between the independent (x) and dependent (y) variables in the graph can be graphically represented using regression lines.

In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. Analysis of experimental, monetary, and biological data as well as complex system prediction are both possible using linear modelling.

A statistical technique used to build a linear model is called linear regression. The model explains how one or more independent variables Xi relate to a dependent variable y (also known as the response) (called the predictors). The distance between each data point and the regression line is called a residual.

Given data ,

Let the linear regression line be represented as A

Now , the value of A is

Let the first coordinate on the graph be P ( 1 , 5.5 )

Let the second coordinate on the graph be Q ( 2 , 6 )

And , the data plots on the graph represents a curve or parabolic equation

So , it is a quadratic equation

Hence , the data plot of the regression line is quadratic

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EAST MATH PLS HELP ASAP PLEASE PLEASE
If one side of a square is represented by x + 7, and the perimeter of the square is
represented by 8x - 20, what is the value of X?

Answers

4(x+7)=8x-20

4x+28=8x-20

28=4x-20

48=4x

x=12

what is the answer for 6.8×10² ​

Answers

Answer:

680

Step-by-step explanation:

Answer:

680

Step-by-step explanation:

10 to the  2nd power is 10 times 10 which is 100.

Now, 6.8 times 100 is 680.

Hope this helps you!!

a bus is full of passengers. if you count them by either twos, threes, or fives, there is one left. if you count them by seven there will be none left. find the least number of passengers in the bus?​

Answers

the number of passengers is not a multiple of 2, 3 or 5 but it is a multiple of 7

The lowest multiple of 7 that is not a multiple of 2, 3 or 5 is 7

The next multiple after 7 that is not a multiple of 2, 3 or 5 is 49

7 x 1 = 7
7 x 2 = 14 ( can be divided by 2 )
7 x 3 = 21 ( can be divided by 3 )
7 x 4 = 28 ( can be divided by 2 )
7 x 5 = 35 ( can be divided by 5 )
7 x 6 = 42 ( can be divided by 2 )
7 x 7 = 49

Please help with this as soon as you can. Really need help and no idea how to do it.

Answers

Answer:

DE, BC, BA, CA

Step-by-step explanation:

basically just find the ones that do not cross and those are parellel.

Solve plz, this is due Tomorrow!!

Answers

.

Step-by-step explanation:

25) h=11

26). two sides are same = 12cm

27). time = 15 hours

28). veronica travelled = 6+1 = 7 days

29). number of tickets buyed by people each showing : 231

30) ©

A box of 11 transistors has 4 defective ones.
A) If 2 transistors are drawn from the box together, what is the probability that both transistors are defective?
B) If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective?
C) If 2 transistors are drawn from the box together, what is the probability that one transistor is defective?

Answers

Answer:

(a) 0.1325

(b) 0.4045

(c) 0.463

Step-by-step explanation:

Let X denote the number of defective transistors.

The proportion of defective transistors is, p = 4/11 = 0.364.

All the transistors are independent of the others.

The random variable X follows a binomial distribution.

(a)

Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]

(b)

Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]

(c)

Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]

Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it
cost her to fill the gas tank from empty?
Submit
O
Lenovo

Answers

Answer:

$40.23

Step-by-step explanation:

Answer:

40.23

Step-by-step explanation:

easy just do 13.5*2.98

What is 56/15 as a decimal rounded to the nearest tenth

Answers

Answer:

3.73

Step-by-step explanation:

56/15

3 11/15

3.73

56/15 = 3.7333333...

3.733333... —————> 3.7

This is soo hard can someone please help

Answers

Answer:

f(x)=1/4x+8

y=1/4x+8

x=1/4y+8

1/4y+8=x

y+32=4x

y=4x-32

f^-1(x)=4x-32

help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help

Answers

Answer:

41/200

This is solved and put in standard form

0.205
My explanation: 2*1/10=0.2
5*1/1000=0.005
0.2+0.005= 0.205, I think I’m right, hope this helps! :)

Find the value of θ from the following equation.(θ≤90°)​

Answers

Answer:   10°

__________________________________________________________

We are given:

Sin(6θ)  = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:  

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ)                             [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ                                            [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90                                                   [adding 3θ on both sides]

θ = 10°                                                     [dividing both sides by 9]

Clayton opens a savings account with 11 dollars he got from his grandmother

Answers

Answer:

The answer is "$3640.58"

Step-by-step explanation:

This question is incomplete, that's why we add another question in the attached file. Please find it.

P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2  

Total  [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:

[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]

[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]

[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]

The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]

Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5

Answers

Answer:

1.44

Step-by-step explanation:

Answer:

the answer is 1.44

Step-by-step explanation:

Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.

                      Your welcome

please answer as fast as possible see image

Answers

Answer:

388

Step-by-step explanation:

We need to find the area of the semicircle and parallelogram separately and then combine.

The formula for the area of a semicircle is 1/2(pi*r^2)

r = 12. 12^2 = 144

1/2(pi*144) = 226..1946711 which we can just round to 226

The formula for the area of a parallelogram is bh

b = 18, h = 9. 18*9 = 162.

226+162 = 388

Answer:

218.55

Step-by-step explanation:

total area = semi circle + parallelogram

                = (1/2 π 6²)  +  (9 x 18)

                = 56.55  + 162

                = 218.55 sq. units

After writing a check mike had -$34.50 in his account, he deposited $20.00 how much did he have now?

Answers

Answer:

-$14.50

Step-by-step explanation:

This is easily solved on a calculator.

-34.50 + 20.00 = -14.50

Mrs. Robert’s vegetable garden is 6 feet wide and 8 feet long. A drawing of the garden has a scale of 1 inch 2 feet. What is the area of the garden on the scale drawing? a. 192 in b. 12 in c. 7 in d. 28 in

Answers

Answer:

Step-by-step explanation:

It’s 24

Answer:

b.12 inch squared

Step-by-step explanation:

6 feet become 3 inches and 8 feet becomes 4 inches 3×4 = 12

At the start of the month, the value of an investment was $53.92. By the end of the month, the value of the investment changed by a loss of $17.40. What was the value, in dollars, of the investment at the end of the month​

Answers

Answer:

$36.52

you're welcome :)



A Fahrenheit thermometer shows that the temperature is 13 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit

Answers

Answer:

-13??? weird question... do you mean celcius themometer?

Step-by-step explanation:

Answer:

The integer that represents 13 degrees below 0 is -13°F.

Step-by-step explanation:

This is because the phrase "13 degrees below 0" is obviously not an integer meaning that the corresponding integer to this phrase would be -13.

P.S.

This question was asked by somebody else and I answered already so I am not copying the answer!

Hope this helps! :)

Use the distributive property to remove the parentheses (x+12)8

Answers

Answer:

Using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

Step-by-step explanation:

We need to used distributive property to solve (x+12)8

The distributive property of multiplication or addition states that: [tex]a(b+c)=ab+ac[/tex]

Using the property:

[tex](x+12)8\\=8x+8*12\\=8x+96[/tex]

So, using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

100.6 + 296.5 using
mental math

Answers

Answer:397.1....i think

Step-by-step explanation:

Answer:

397.1

Step-by-step explanation:

I used mental math

swear no calculator or work done

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

A rock is thrown upward with a velocity of 17 meters per second from the top of a 31 meter high cliff and it missies the cliff on the way back down when will the rock ve 8 meters from the ground level

Answers

Answer:

[tex]4.5\ \text{s}[/tex]

Step-by-step explanation:

t = Time taken

u = Initial velocity =17 m/s

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]

Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]

Time taken to reach the maximum height is 1.73 s.

[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]

Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.

So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].

what is the slope of the following line?

Answers

Answer:

-2

Hope this helps,

PumpkinSpice1

The slope of the line will be ( -1 / 2 ). The correct option is C.


What is the slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 0 - 3 ) / ( 6 - 0 )

Slope = -3 / 6 = -1 / 2

Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.

To know more about slopes follow

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Brainliest to RIGHT answer

Answers

Answer:

It's C

Step-by-step explanation:

please help can yall solve this

Answers

I understand this!! The answer is 15. Hope this helps!!
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