4x + 5y = 48
Y=3x + 2

Answers

Answer 1
4x + 5(3x+2) = 48
4x + 15x + 10 = 48
19x + 10 = 48
19x = 38
x = 2

y = 3x + 2
y = 3(2) + 2
y = 6 + 2
y = 8
Answer 2

The solution of the given equation is x = 2 and y = 8.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The value of x and y will be calculated as,

4x + 5(3x+2) = 48

4x + 15x + 10 = 48

19x + 10 = 48

19x = 38

x = 2

Calculate the value of y,

y = 3x + 2

y = 3(2) + 2

y = 6 + 2

y = 8

Therefore, the solution of the given equation is x = 2 and y = 8.

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Related Questions

Consider the function f denoted by:
[tex]f(x) = ln(x) [/tex]
Find the nth derivative of f(x) denoted by:
[tex]f {}^{(n)} (x ) [/tex]
Irrelevant answers will be reported immediately.

Answers

Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

The temperature was 56 degrees this morning, but dropped one degree per hour through the rest of the day. The equation is y=-x+56. You may usey=56-x . They are the same equation. Use x-values: 0, 5, and 10.

Answers

At x=0

y=56-0y=56°C

At x=5

y=56-5y=51°C

At x=10

y=56-10y=46°C

9 cos(sin¯¹(x)) = √81 – 81x²

Answers

The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

What is an equation?

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}]   (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

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Which of the following inequalities has no solutions?
Ox>3 and x < 2
Ox>3 and x < -2
Ox>3 and x < 2
Ox>3 and x > - 2

Answers

Answer:

A) x > 3 and x < 2 has no solutions

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

It has no solutions since the two inequalities have no common interval.

B) x > - 3 and x < - 2,

Its solution is -3 < x < - 2, the interval between two given endpoints.

C) x > - 3 and x < 2,

Similar to option B, the interval is between two endpoints:- 3 < x < 2

D) x > - 3 and x > - 2,

Its solution is x > - 2, the two inequalities cover almost same interval.

find x and y

can someone pls solve

Answers

First, we need to understand that these two triangles are

similar.

we know this because their lines (the arrows) prove they are the same direction. A similar triangle does

NOT mean they are proportional,

they are just similar by ratio.

Lets call the triangle on the left ABC and the triangle on the right A'B'C'.

I will attach an image of the labels.

Because they are similar triangles, angle A is the same as angle A'. Angle B is the same as angle B', angle C is the same as angle C'.

Based on that information, we know xº is = 65º. We know that the interior angles add up to 180º. So for triangle A'B'C', we can do 180º-40º-65º which is 70º. This means angle C' is 70º.

Now the important part is getting yº. A line is 180º. That means that 180º-70º=yº which is 110º.

If you do not understand anything, please let me know and I will try to teach you.

The arrival times of geese to a gaggle were recorded (in seconds) and given in the stemplot below.

Stem&Leaf

What is the 12th fastest time a goose took to join the gaggle? Make sure to use labels and avoid the use of abbreviations.

Answers

The 12th fastest time a goose took to join the gaggle is 49 seconds.

What is the 12th fastest time a goose took to join the gaggle?

A Stem and Leaf Plot is a type of graph where the data is divided into a stem (the first digit or digits) and a leaf (usually the last digit).

The data in the stem plot arranged from the first fastest time it takes a goose to join the gaggle is: 13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62.

The 12th fastest time is 49

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A recipe for a cake instructs you to bake it at 220° C for 45 minutes. How many degrees Fahrenheit is this?

Answers

This is an exercise on Thermometric scales.

We have as data:

T = 220 °CT =  °F ??

We apply the following formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]

We substitute data in the formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]

First multiply 9 x 220, then the result of this division is divided by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]

Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.

What is 13 2/3 subtracted from 49 1/3

Answers

Answer:

35 2/3

Step-by-step explanation:

49 1/3 - 13 2/3

First convert both into improper fractions, which is

148/3 - 41/3

Then subtract!

107/3

Next simplify the fraction.

35 2/3

Find the missing coordinate.
x=t+2
y = 1 + 3/t

(-1,[?])

Answers

Answer:

0

Step-by-step explanation:

Since the x coordinate is -1, 2+t = -1, and thus t = -3.

So, y = 1+(3/(-3)) = 0.


Pakistan scored 270 runs and fell short of India's score by 10%. How much did
India score?

Answers

Answer:

India score 290 more than pakistan

Step-by-step explanation:

India score 20 more

India score is
= 270/90 x 100
= 300 runs

Q.3 Write the factors of 28 in circle A and the factors of 32 in circle B. Write
heir common factors in the common part of both. Which is the biggest
common factor of 28 &32?

Answers

Answer: The largest common factor of 28 and 32 is 4.

Step-by-step explanation:

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 32 are 1, 2, 4, 8, 16, 32

The x-intercept of a line is 2 and the y-intercept is 4. Explain how to use this information to write the equation of the line.

Answers

Answer:

y = -2x + 4

Step-by-step explanation:

The x-intercept would be the point (2,0) and the y intercept would have the point (0,4).  Once we know two points we can write the equation in the line intercept for of y = mx + b.  

We need to find the slope and the y intercept.  The slope is the steepness of the line and it is the change in y over the change in x.

The ordered pairs are written in  the form of (x, y).  From our two points, we will subtract the y's to find the top number of our fraction.

0 - 4 = -4 that is the numerator (top number) of our slope.  We do the same with the two x numbers that we have been given.

2 - 0 = 2  This is our numerator (or bottom number of our slope)

Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2

Now that we have the slope we need to find the y-intercept.  We can use either of our original two points and our slope to determine the y-intercept.  It does not matter if you use the point (2,0) or (0,4).  I will use (2,0) and the slope of -2

y = mx + b

0 = -2(2) + b  

0 = -4 + b   add 4 to both sides of the equation

4 = b

Now that we have the slope and the y-intercept, we can write the equation

y = mx + b

y = -2x + 4

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

Answers

hi

f(x) = x² -2x

g(x) = 6x+4

(f+g) (x) = x²-2x +6x+4 =  x²+4x +4 =  (x+2)² =  (x+2) (x+2)

(f+g) (x) = 0  means  =  (x+2) (x+2) = 0  

so x+2 = 0

   x = -2

(f+g) (x) = 0  for x = -2

Which of the following inequalities matches the graph?
Ox=-7
Oxs-7
Oys-7
Oyz-7

Answers

Answer:

Second option

Step-by-step explanation:

As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7

PLEASE HELP!
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.

What is the theoretical probability of landing on a question mark space on your first roll.
A 1/6
B 1/4
C 1/3
D 1/2

Answers

Answer:

C 1/3

Step-by-step explanation:

out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3

If f(x) = 3x + 10x and g(x) = 2x - 4, find (f+ g)(x).

Answers

Answer:

25x-4

Step-by-step explanation:

3x+10x

+ 2x. -4

=5x+10x-4

=15x-4

Find the arc length of the partial circle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answers

The arc length of the partial circle is 7.5π

Calculating arc length

From the question, we are to determine the arc length of the partial circle

The length of an arc can be calculated by using the formula

[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]

Where [tex]l[/tex] is the length of the arc

[tex]\theta[/tex] is the angle subtended

and r is the radius

From the diagram,

θ = 270°

r = 5

Putting the values into the equation, we get

[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]

[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]

[tex]l = \frac{30\pi}{4}[/tex]

[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π

Hence, the arc length of the partial circle is 7.5π

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Evaluate 8xy+16y/5x

if x = 4 and y=-5.
A-42
B-7
C-23
D-12

Answers

Answer:

D

Step-by-step explanation:

substitute x = 4 , y = - 5 into the expression

[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]

= [tex]\frac{-160-80}{20}[/tex]

= [tex]\frac{-240}{20}[/tex]

= - 12


Determine the interval(s) on which the given function is decreasing?

Answers

Answer:

[tex](-\infty, -1) \cup (0, \infty)[/tex]

Step-by-step explanation:

The function is decreasing if, as x increases, the value of the function (y) gets smaller.  This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.

From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.

Nan is 20 year old. In 8 years,she will be twice as old as Clarisse.how old is clarisse now?

Answers

Answer:

6

Step-by-step explanation:

The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.

Simplify the trigonometric expression (sin^2(x/2)) (1 + cos(x)) using Half-Angle Identities.

Answers

Answer:

B

Step-by-step explanation:

1-cos2x=2sin²(x/2)

[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]

select all the statements that are true

Answers

Answer:

C & D

Step-by-step explanation:

A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.


B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.

C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.

D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.

i need the answer to this.

Answers

The simplifications of all the given ratios are as detailed below.

How to simplify ratios?

The simplification of each of the given ratios are;

1) 56 : 49

The highest common multiple is 7 and so we divide by 7 to get;

56 : 49 = 8:7

2) 36:48

The highest common multiple is 12 and so we divide by 12 to get;

36 : 48 = 3:4

3) 48:42

The highest common multiple is 6 and so we divide by 6 to get;

48 : 42 = 8:7

4) 24:36

The highest common multiple is 12 and so we divide by 12 to get;

24 : 36 = 2:3

5) 20:30

The highest common multiple is 10 and so we divide by 12 to get;

20 : 30 = 2:3

6) 24:32

The highest common multiple is 8 and so we divide by 8 to get;

24 : 32 = 3:4

7) 18:27

The highest common multiple is 9 and so we divide by 9 to get;

18 : 27 = 2:3

8) 16:14

The highest common multiple is 2 and so we divide by 2 to get;

16 : 14 = 8:7

9) 9:12

The highest common multiple is 3 and so we divide by 3 to get;

9 : 12 = 3:4

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Compute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years

Answers

The monthly payments for each add-on interest loan is $29.7.

What is interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

According to the question,

Principal (P) = $1150

Rate of Interest(R) = 6%

Time (T) = 4 years

The interest is calculated as follows:

SI = (P × R × T)/100

SI = (1150 × 6 × 4)/100

SI=$ 276

Amount (A) = P + SI

A = $(1150 +276)

A = $1426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.7

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1. The mean urine sodium concentrationof18caseswas120mmol/L with standard deviation of 15 mmo/L. assume the urine sodium is normally distributed, what is the 95%confidence interval within which the mean of the total population of such cases is expected lie

Answers

Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:

(112.5, 127.5).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.

The parameters for this problem are:

[tex]\overline{x} = 120, s = 15, n = 18[/tex].

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]

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Compute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years.

Answers

The monthly payments for each add-on interest loan will be $29.71.

Given Information and Formula Used

Principal Amount, P = $1150

Rate of Interest, R = 6%

Duration of loan in years, T = 4

The formula for simple interest is given as,

I = (P × R × T)/100

Calculating the Add-On Interest For Each Month

Interest, I = (P × R × T)/100

Substituting the values of P, R, and T in the above formula, we get,

I = $ (1150 × 6 × 4)/100

I = $ 27600/100

I = $276

Calculating the Total Monthly Payment With Interest

Amount of add-on interest loan, A = P + I

A = $1150 + $276

A = $1,426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.71

Hence, the monthly payments for each add-on interest loan would be $29.71.

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what is f(x) in the expression?​

Answers

[tex]f(x) = 7x {}^{2} - 3x {}^{4} [/tex]

During a recent poll with a travel agency, 24 customers were surveyed to determine the most popular cities in the US to visit.

The Venn diagram shows this information for the three most popular cities: New York, Los Angeles, and Orlando.

a. Which customers chose Orlando but not New York or Los Angeles?

b. How many customers chose New York and Los Angeles, but not Orlando ?

c. Which customers liked Orlando and New York only?

Answers

Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:

5 people.1 person.2 people.

What cities were the most popular in the U.S.?

The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.

Only one customer in the person of Jordan preferred New York and Los Angeles.

2 people liked Orlando and New York only and they were Luke and Robert.

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a) Out of all items sent for refurbishing, %40 had mechanical defects, %50 had electrical
defects, and %25 had both. Denoting  defectmechanicalahasitemanA  and
 defectmechanicalahasitemanB  . Fill the probabilities into the Venn diagram and
determine the quantities listed below.
(i)  AP [2 Marks]
(ii)  BAP  [1 Mark]
(iii)  BAP c 

Answers

i. P(A) = 0. 4

ii. P(AB) = 0. 9

iii. P(A∩B) =0. 25

How to determine the probability

From the information given,

Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25

A = Mechanical defects = 40%

B = Electrical defects = 50%

A∩B =25%

i. Probability of A , P(A)

= [tex]\frac{40}{100}[/tex]

= [tex]0. 4[/tex]

ii. Probability of B, P(AB)

= [tex]\frac{40}{100} + \frac{50}{100}[/tex]

= [tex]0. 4 + 0. 5[/tex]

= [tex]0. 9[/tex]

iii. Probability of A∩B entails the common factor between A and B

P(A∩B)  = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]

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The table below shows some inputs and outputs of the invertible function f with domain all real numbers.

Answers

The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

How to evaluate the function?

As  a general rule;

f⁻¹(f(x)) = x

This means that:

f⁻¹(f(6.022)) = 6.022

Also, we have:

f⁻¹(10) + f(-6)


From the table of values, we have:

f⁻¹(10) = -6 and f(-6) =10

So, we have:

f⁻¹(10) + f(-6) = -6 + 10

Evaluate

f⁻¹(10) + f(-6) = 4

Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

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