The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which of the following describes the domain of (g o f) (x)?
all real values except x not-equals negative 3 and the x for which f (x) not-equals 7
all real values except x not-equals negative 3 and the x for which f (x) not-equals negative 3
all real values except x not-equals 7 and the x for which f (x) not-equals 7
all real values except x not-equals 7 and the x for which f (x) not-equals negative 3

Answer:

The zeros are:

[tex]x=-1,\:x=\frac{3}{2}[/tex]

Step-by-step explanation:

As the function is given by

[tex]F(x)=4x^4-4x^3-11x^2+6x+9[/tex]

We have to find the zeros of [tex]4x^4-4x^3-11x^2+6x+9[/tex].

So,

[tex]4x^4-4x^3-11x^2+6x+9=0[/tex]

Factor left side of equation.

[tex]\left(x+1\right)^2\left(2x-3\right)^2=0[/tex]

[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]Solving\:x+1=0[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]

[tex]x+1-1=0-1[/tex]

[tex]x=-1[/tex]

[tex]Solving\:2x-3=0[/tex]

[tex]x=\frac{3}{2}[/tex]

So, the zeros are:

[tex]x=-1,\:x=\frac{3}{2}[/tex]

Keywords: zeros, equation

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Answer:

2.58

Step-by-step explanation:

47 1/2=95/2

122.55/(95/2)=(122.55/1)(2/95)=245.1/95=2.58

Answer:

606 and 612

Step-by-step explanation:

A number is a multiple of 6 if:

1. the sum of its integers can be divided by 3

2. The number is even (ending in 0, 2, 4, 6, 8

With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.

606:

6 is even

6 + 6 = 12

12 divided by 4 is 3

612:

2 is even

6 + 1 +  2=  9

9 divided by 3 is 3

Step-by-step explanation:Given that Carter lives on a street where all the house numbers are multiples of 6. We are given to name any two possible house numbers between 601 and 650.The numbers lying between 601 and 650 are602, 603, 604, 605, . . . ,648, 649.And the numbers among these which are multiples of 6 are606, 612, 618, 624, 630, 636, 642, 648.So, any two of these eight numbers can be possible.Thus, the numbers are 606 and 650.

Answer:

5

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Given function.

[tex]f(x)=6x-4[/tex]

To find the inverse function [tex]f^{-1}(x)[/tex]

Step 1:

Replace [tex]f(x)[/tex] with[tex]y[/tex] in the function.

[tex]y=6x-4[/tex]

Step 2:

Interchange [tex]y[/tex] with [tex]x[/tex] in the equation.

[tex]x=6y-4[/tex]

Step 3:

Solve for [tex]y[/tex].

We have [tex]x=6y-4[/tex]

Adding 4 to both sides,

[tex]x+4=6y-4+4[/tex]

[tex]x+4=6y[/tex]

Dividing each term by 6 to isolate [tex]y[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=y[/tex]

Simplifying fractions by dividing the numerator and denominator by  their GCF.

[tex]\frac{x}{6}+\frac{4\div 2}{6\div 2}=y[/tex]

[tex]\frac{x}{6}+\frac{2}{3}=y[/tex]

Thus the equation of [tex]y[/tex] is:

[tex]y=\frac{x}{6}+\frac{2}{3}[/tex]

Step 4:

Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex] (Answer)

Thus, we have the inverse function

Answer:

Step-by-step explanation:

the easiest way is to convert these fraction to decimals because as you can see on the number line the numbers are whole and decimals on the small tik mark

-3 3/4 would convert to as -3.75

1/2 would convert into 0.5

now plot those on a number line

*remember the small tiks are worth .25*

Answer:

x = -4 , y = 3

Step-by-step explanation:

5x - 7y = -41 ... (i)

-3x - 5y = -3 ... (ii)

Multiplying (i) by -3 and (ii) by 5 ;

-15x + 21y = 123 ... (i)

-15x - 25y = -15 ... (ii)

Subtracting (i) by (ii) ;

0 + 46y = 138

46y = 138

y = 138 ÷ 46 = 3

Returning to equation (ii) ;

-3x - 5(3) = -3

-3x = -3 + 15

-3x = 12

x = -4

Answer: The values of x and y in the given equations are [tex]x=-4[/tex] and [tex]y=3[/tex]

Step by step explanation:

Given system of equations are

[tex]5x-7y=-41\hfill (1)[/tex]

[tex]-3x-5y=-3\hfill (2)[/tex]

To find the values of x and y :

by using Elimination method

Now multiplying the equation (1) into 3 we get

[tex]15x-21y=-123[/tex]

Now multiplying the equation (2) into 5 we get

[tex]-15x-25y=-15[/tex]

Adding the above two equations

[tex]15x-21y=-123[/tex]

[tex]-15x-25y=-15[/tex]

_________________

[tex]-46y=-138[/tex]

_________________

[tex]46y=138[/tex]

[tex]y=\frac{138}{46}[/tex]

[tex]y=3[/tex]

Therefore [tex]y=3[/tex]

Substitute y value in equation (1)

[tex]5x-7y=-41[/tex]

[tex]5x-(7\times 3)=-41[/tex]

[tex]5x-21=-41[/tex]

[tex]5x=21-41[/tex]

[tex]5x=-20[/tex]

[tex]x=-\frac{20}{5}[/tex]

[tex]x=-4[/tex]

Therefore [tex]x=-4[/tex]

The values of x and y are [tex]x=-4[/tex] and [tex]y=3[/tex]

Answer:

x = - 0.25, x = 1.25

Step-by-step explanation:

The solutions to the equation are the values of x where the graph crosses the x- axis, that is as an estimate

x ≈ - 0.25 and x ≈ 1.25

Answer:

[tex]x=-0.4[/tex]

[tex]x=1.7[/tex]

Hopefully the answers are accepted to the nearest tenths.

Step-by-step explanation:

Since the left hand side was already graphed, we just need to graph the right hand side which is [tex]x+1[/tex].

We are going to still let [tex]y[/tex] represent the outputs of [tex]x+1[/tex].

So we want to graph the equation [tex]y=x+1[/tex] on the same graph as the parabola, the almost U shaped graph.

You could make a table to plot the equation.

[tex]y=x+1[/tex]

[tex]x[/tex]     |      [tex]y[/tex]         |     ordered pair to graph [tex](x,y)[/tex]

-------------------------------------------------------------------------------------------------------

     -2                     -2+1=-1                          (-2,-1)

     -1                       -1+1=0                           (-1,0)

      0                       0+1=1                            (0,1)

      1                         1+1=2                           (1,2)

      2                        2+1=3                          (2,3)

The purple line I made is the line formed from these points which was generated from the equation [tex]y=x+1[/tex].

Now where the blue curve touches the purple line is our solutions. I put those in orange.

The solutions are approximately, [tex]x=-0.4[/tex] or [tex]x=1.7[/tex].

Hopefully, it accepts solutions to the nearest tenths.

We are trying to approximate where those orange dots are on the number line. Please see attachment 2.      

Answer:

-17/10

Step-by-step explanation:

-4(1/8)-3(2/5)=-4/8-6/5=-20/40-48/40=-68/40=-17/10

Answer:

y=9

Step-by-step explanation:

2+y=-7+2y

2=-7+2y-y

2=-7+y

y=2-(-7)

y=2+7

y=9

Answer:

2 + y = -7 + 2y

collect like terms

y-2y=-7-2

-y=-9

y=9

Step-by-step explanation:

Asa has 15 dimes and 32 quarters.

Step-by-step explanation:

Given,

Total coins = 47

Worth of coins = $9.50 = 9.50*100 = 950 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of dimes = x

Number of quarters = y

According to given statement;

x+y=47      Eqn 1

10x+25y=950   Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{480}{15}\\y=32[/tex]

Putting y=32 in Eqn 1

[tex]x+32=47\\x=47-32\\x=15[/tex]

Asa has 15 dimes and 32 quarters.

Keywords: linear equation, elimination method

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The question involves setting up and solving a system of linear equations based on the total number and value of the coins. It's a high school level mathematics question about algebra.

The subject of this question falls into the field of Mathematics, specifically algebra. We need to find the number of dimes (let's denote it as D) and quarters (Q) Asa has saved, knowing their total amount and value. We can set up a system of equations based on the information provided:

Solving this system of equations will give us the precise numbers of each coin that Asa has saved.

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Answer:

0.6

Step-by-step explanation:

The the exponent is positive , move it 3 times to the right.

If it was a negative exponent , you would move it to the left.

Answer:

Step-by-step explanation:

the only way I knew this was division was because of the word quotient. Before u post, please check ur question to see if it is worded correctly....equals does not mean division.

197.6 / 5.48.....estimate

197.6 rounds to 200

5.48 rounds to 5

so the best way would be : C. 200 / 5 = 40 <===

the real answer is : 197.6 / 5.48 = 36.058.......so an estimate is not exact...but it can be close

The best way for Elena to estimate the quotient of 197.6 divided by 5.48 is to round 197.6 to 200 and 5.48 to 5, and then calculate 200 divided by 5, which gives 40 as the estimated result. This corresponds to Option C: 200 ÷ 5 = 40.

Elena wants to estimate the quotient of 197.6 divided by 5.48. Estimation involves rounding numbers to make calculations easier while still getting a number that is close enough to the actual answer for practical purposes. The ideal way to estimate is to round each number to a convenient figure that is easy to divide mentally.

In our case, 197.6 can be rounded to 200 since it is very close to it, and 5.48 can be rounded to 5 or 10. The options provided suggest rounding to the nearest whole number or to the nearest ten. Thus:

Option C (200 ÷ 5 = 40) uses rounding to the nearest fifth, which provides an estimate that is most accurate.

Option D (200 ÷ 10 = 20) also provides a reasonable estimate, but it rounds the divisor to the nearest ten, which might lead to a less accurate estimate.

Therefore, the number sentence that shows the best way to estimate this quotient is Option C: 200 ÷ 5 = 40.

Answer:

Step-by-step explanation:

reduced amount  = 70 - 40 = $30

Percent of reduction =  [tex]\frac{30}{70}*100\\=\frac{300}{7} \\=42\frac{6}{7}[/tex]%

0r 42.86%

Answer:

Step-by-step explanation:

percent decrease = (original number - new number) / (original number) * 100

                              = (70 - 40) / 70 * 100

                             = 30/70 * 100

                             = 0.42857 * 100

                             = 42.857 % decrease....if u need it rounded, 42.86%....or if u

                               need it rounded to the nearest whole percent, its 43%

Answer:

Step-by-step explanation:

When you add the numbers of students with A's in history and math, you get  8+15 = 23. However, this counts the 3 kids who got A's in both subject two times! So, there are 23-3=20 (20 students) different students who got an A in at least one of the courses. That gives us 35-20=15 who didn't get an A in either.

So, the answer is 15!!

Hope this helped, have a great day! :D

Answer:

8x^2y= 8x^3 - 4x^2

y = x - 1/2

y = (2x - 1)/2

the answer is c

Answer:

6 minutes.

Step-by-step explanation:

She ascends at a rate of 5 feet per minute from the reef.

Once she reaches  a height of -30 feet, she must rest for 15 minutes and she then continues to the surface at the same rate.

So, she dives from - 30 feet height to water surface i.e. 0 feet height with a rate of 5 feet per minute.

Therefore, she will take [tex]\frac{30}{5} = 6[/tex] minutes to reach the surface.  

(Answer)

Answer:

6 min

Step-by-step explanation:

Answer:

x ≤ 11

Step-by-step explanation:

Simplify the equation, then isolate "x" by using reverse operations in reverse BEDMAS order.

3x + 2 ≤ 5(x-4)     Distribute over the bracket by multiplying.

= 3x + 2 ≤ 5x - 20     Start isolating "x" on the left side.

= 3x + 2 - 2 ≤ 5x - 20 - 2     Subtract 2 from both sides.

= 3x ≤ 5x - 22    

= 3x - 5x ≤ 5x - 22 - 5x     Subtract 5x from both sides to move x to left side

= -2x ≤ -22

= -2x/-2 ≤ -22/-2     Divide both sides by -2 to isolate x

= x ≤ 11     Final answer

Janice earns $12.50 per hour. If her tours last 1 hour each, that's also her rate per tour. She needs to give 40 tours to reach her goal of $500.

First, we need to find out how much Janice earns per hour. She earns $62.50 for 5 hours of work, so we divide $62.50 by 5 to find her hourly rate. This gives us $12.50 per hour. If Janice's goal is to earn $500 by the end of the summer, we divide $500 by her hourly rate of $12.50 to find out how many hours she needs to work. This equals 40 hours total.

However, to fully answer this question, we also need to know the duration of a single tour. Without knowing how long each tour lasts, it's impossible to calculate how many tours Janice needs to give. Let's imagine each tour lasts 1 hour for simplicity. In that case, Janice would need to give 40 tours to reach her goal of $500.

So, Janice's unit rate per tour (assuming each tour is 1 hour long) is $12.50, and she needs to give 40 tours to reach her summer earnings goal of $500.

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Answer:

B. [tex]y=8x[/tex]

Step-by-step explanation:

A proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Where, 'k' is called as the constant of proportionality.

So, the graph of a proportional relationship always crosses the origin.

This means that the 'x' and 'y' intercepts of a proportional relationship is always at the origin (0, 0).

From among all the options, the option that matches the definition of a proportional relationship is option B. [tex]y=8x[/tex]

Here, [tex]k=8[/tex].

Therefore, the correct option is option B.

Answer:

[tex]x^2-4x+4[/tex]

Step-by-step explanation:

In order to complete the square, we need to half b and then square it. This allows us to find c.

In this case, the coefficient of x is b and the unknown term is c

From this, we can see that b = -4

First, we need to half it

[tex]-\frac{4}{2} \\\\-2[/tex]

Next we need to square it

[tex](-2)^2\\\\4[/tex]

This gives us our answer of 4.

To complete the square, we want to form a perfect square trinomial from the given quadratic expression, x^2 - 4x + _____.
A perfect square trinomial is an expression that can be factored into (x - p)^2, which when expanded, is x^2 - 2px + p^2.
This means we're looking for a value that will allow us to write our given expression in the form of (x - p)^2 where -2p will be the coefficient of x, which in our case is -4.
Now, go through the steps to find the value needed to complete the square:
1. We start with the coefficient of x, which is -4.
2. To find p, we divide this coefficient by 2: -4 / 2 = -2.
3. Finally, we square this result to find the number that completes the square: (-2)^2 = 4.
Therefore, the number needed to complete the square in the expression x^2 - 4x + _____ is 4.
When you add 4, the expression becomes x^2 - 4x + 4, which is equivalent to (x - 2)^2, thus completing the square.

Answer:

-$4

Step-by-step explanation:

The expected payback formula is the sum of probability multiply the value

E(x) = p(x1)*x1 + p(x2)*x2 + .....

In this case, we have two possibility of payback

1) winning

The payback is $400 -$8 = $392

x1 = 392

The probability of winning is one out of 100 (since the choices are 0 to 99)

p(x1) = 1/100

2. Losing

The payback is -$8 since the person didn't win anything is loose

x2 = -8

Since there is only one winning number, the other 99 numbers are loosing numbers

p(x2) = 99/100

Therefore expected payback is

E(x) = p(x1)*x1 + p(x2)*x2

= (1/100)*392 + (99/100)*(-8)

= -400/100

= -$4

The expected payback for a game in which you bet $8 on any number from 0 to 99, and win $400 if your number comes up, is -$4.00, indicating an average loss of $4.00 per game.

In this probability problem, you are betting $8 on a number from 0 to 99. This means there are 100 possible outcomes, each equally likely if the game is fair. Your profit if you win is $400. Since there's a 1 in 100 chance of winning, we can calculate the expected return as follows:

Expected Return = Probability of winning * Payoff when winning = (1/100) * $400 = $4.00

However, since you are always paying $8 to play the game, in expectation you are losing money in every game. The expected payback from this game is hence $4-$8=-$4.00 and not $48.00. In other words, we can anticipate losing $4.00 on average every time we play this game.

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Answer:

Step-by-step explanation:

a₂ = 14

a₃ = 18

d = a₃ -a₂ = 18 - 14 = 4

a₁ = 14 - 4 = 10

nth term = a + (n-1)d

a₅₁ = 10 +  50 * 4

  = 10 + 200

 = 210

Answer:

the first one is "perpendicular"

the second one is also  "perpendicular"

Step-by-step explanation:

Answer:

1. Perpendicular; 2, perpendicular  

Step-by-step explanation:

1. Segments JK and LM

(a) Calculate the slopes of the segments

(i) Segment JK

[tex]m_{1} = \dfrac{4 - 9 }{7 - 1} = -\dfrac{5}{6}[/tex]

(ii) Segment LM

[tex]m_{2} = \dfrac{13 - 1 }{8 - (-2)} = \dfrac{12}{8 + 2} = \dfrac{12}{10 } = \dfrac{6}{5}[/tex]

(b) Compare their slopes

[tex]m_{2} =\dfrac{6}{5} = -\dfrac{1}{m_{1}}[/tex]

The two segments are perpendicular.

Their graphs are shown in Figure 1.

2. Equations

(a) Calculate the slopes of the segments

(i) First equation

4x + 5y = 10

5y = 10 - 4x

y = 2 - ⅘x

m₁ = -⅘

(ii) Second equation

5x - 4y = -28

-4y = -28 - 5x

y = 7 + ⁵/₄x

m₂ = ⁵/₄

(b) Compare the slopes

m₂ = ⁵/₄ = -1/m₁

[tex]m_{2} =\dfrac{5}{4} = -\dfrac{1}{m_{1}}[/tex]

The two lines are perpendicular.

The graphs are shown in Figure 2.

Answer:

6 pounds.

Step-by-step explanation:

70-25.36= 44.64 (the amount of money she spent)

44.64/7.44 (per pound cost)= 6

Answer:

Rachel bought 6 pounds of coffee.

Step-by-step explanation:

First, do $70-$25.36, because that will give you the total amount of money she spent on coffee.

$70-$25.36= $44.64.

Rachel spent $44.64 on coffee.

Next, you know that every pound of coffee costs $7.44.

So, $7.44x = $44.64

x= the number of pounds of coffee Rachel purchased.

So, we have to now isolate x.

$7.44x / $7.44 = $44.64 / $7.44

x= 6

Therefore, Rachel purchased 6 pounds of coffee.

If you need anymore help on any math problems, email me at: icecreamforest7@aol.com

I also tutor.

Hope this helps:)

Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.

Step-by-step explanation :

Step 1:

Consider the system of equations:

5x + y =13  

3x=15 - 3y

Step 2 :  

y is the easiest variable to isolate in the first equation, because it has no coefficient:

y = 13 - 5x

Step 3 :

In the second equation, substituting for y :

3x = 15 - 3(13 - 5x)

Step 4 :

Solve the equation:

3x = 15 - 39 + 15x

3x = 15x - 24

-12x = - 24

x = 2

substituting this x-value into the "isolated equation" to find y:

y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3

The solution to the system is (2, 3).  This point is used to check for solutions in both equations.

Interpreting the solution of a system of equations involves determining the type of solution (unique, infinitely many, or no solution) and understanding how it relates to the problem being solved. It allows us to find the specific values for the variables that satisfy all the equations and provides insights into the relationships between the variables.

Interpreting the solution of a system of equations is a crucial step in solving a problem. It allows us to understand the relationship between the variables and determine the values that satisfy all the equations in the system. Here's how you can interpret the solution:

1. Determine the type of solution: A system of equations can have three types of solutions: a unique solution, infinitely many solutions, or no solution. To determine the type of solution, solve the system of equations using methods such as substitution, elimination, or matrices.

2. Unique solution: If the system of equations has a unique solution, it means that there is only one set of values for the variables that satisfies all the equations. This solution represents the point where all the equations intersect. In practical terms, this means that there is a specific answer to the problem being solved.

3. Infinitely many solutions: If the system of equations has infinitely many solutions, it means that there are multiple sets of values for the variables that satisfy all the equations. This usually occurs when the equations represent the same line or planes that overlap. In practical terms, this may indicate that there are multiple valid solutions to the problem.

4. No solution: If the system of equations has no solution, it means that there are no values for the variables that satisfy all the equations simultaneously. This usually occurs when the equations represent parallel lines or planes that do not intersect. In practical terms, this may indicate that the problem being solved is not feasible or does not have a valid solution.

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Density of wooden block is 850 kilogram per cubic meter

Solution:

Given that wooden block immersed partially into water

There were 15% of the total volume of the block  exposed and 85% of the total volume immersed in water

To find: density of the wooden block

The upward force exerted by any fluid upon a body placed in it is called buoyant force

Buoyant force is balanced by weight force of block

Buoyant force is weight of water displaced by block

Buoyant force = [tex]\rho_{w} V_{2} g[/tex]

Density of water = [tex]\rho_w[/tex] = 1000 kg/m3

[tex]V_2[/tex] = volume of block in water = 0.85 V

[tex]V_1[/tex] = Volume of block in air = 0.15 V

Weight of block = [tex]\rho V g[/tex]

Therefore,

[tex]\rho V g = \rho_{w} V_{2} g\\\\\rho V = \rho_{w} V_{2}\\\\ \rho V = 1000 \times 0.85V\\\\\rho = 1000 \times 0.85\\\\\rho = 850[/tex]

Thus density of wooden block is 850 kilogram per cubic meter

Answer:

A = (90°, 1)

B = (270°,-1)

Step-by-step explanation:

if we don't use a calculator, we can explain by reasoning.

Observation 1:

recall y=sin x and y=cos x take values between -1 ≤ y ≤ 1, hence we know that the largest possible value for both functions is 1 and the smallest possible value is -1.

Observation 2:

we also know that both sin and cos functions are cyclic, which means that at some point, the function repeats itself every 360 degrees.

in question 1, we see that point A is located at the top most part of the curve, by observation 1, we can conclude that the y-value must be the maximum value of 1.

We also see that point A is 1/4 of the distance between the starting point of the curve at x=0 and to the end of the curve at x=360 before the curve begins to repeat itself,

hence the x - value is 1/4 of 360 = 90 degrees

Similarly, for point B, we see that B is at the lowest point of the curve, hence by observation 1, we can say that at B, y = -1.

B is also 3/4 of the distance between the start point and the end of the curve before it repeats itself,

hence the x-value of B is 3/4 x 360 = 270 degrees

The greater number is 121

Step-by-step explanation:

The given is:

We need to find the greater number

Assume that the smaller number x and the greater number is y

∵ The smaller number is x and the greater number is y

∵ Their sum is 151

∴ x + y = 151 ⇒ (1)

∵ The lesser number is 19 more than the square root of the greater

   number

∴ x = 19 + √y ⇒ (2)

- Substitute x in equation (1) by equation (2)

∵ (19 + √y) + y = 151

- Subtract 151 from both sides and re-arrange the terms from

  the greatest power y

∴ y + √y - 132 = 0

Chang [tex]\sqrt{y}[/tex] to [tex]y^{\frac{1}{2}}[/tex] and substitute  [tex]y^{\frac{1}{2}}[/tex] by h

∵ [tex]y^{\frac{1}{2}}[/tex] = h

∴ y = h²

- Substitute each y by h

∴ h² + h - 132 = 0

- Factorize it into two factors

∴ (h - 11) (h + 12) = 0

- Equate each factor by 0 to find h

∵ h - 11 = 0

- Add 11 to both sides

∴ h = 11

∵ h + 12 = 0

- subtract 12 from both sides

∴ h = -12

∵ h = [tex]y^{\frac{1}{2}}[/tex]

∴ [tex]y^{\frac{1}{2}}[/tex] = 11 and -12

∵ [tex]y^{\frac{1}{2}}[/tex] = √y

∴ √y = 11

∴ √y = -12 ⇒ rejected square root can't give -ve number

∴ √y = 11 only

- To find y square the both sides

∴ y = 121

The greater number is 121

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You can learn more about the word problem in brainly.com/question/4034547

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The solution involves setting up two equations from the given information and then substituting one into the other to create a quadratic equation in terms of the greater number, x, and solving for x.

The question involves finding two positive numbers given that their sum is 151 and that the lesser number is 19 more than the square root of the greater number. To find the greater number, let's denote the greater number as x and the lesser number as y. The two conditions given are:

We can substitute the second condition into the first:

After simplifying the quadratic equation and solving for x, we will find the value for the greater number.

Answer:

Step-by-step explanation:

f: y=x^2

g: y= -x^2

h: y= -x^2-5

first we transform the graph of f to the graph of g using the reflexion across y-axis .

then we transform of g to the graph of h using the translation -5( vector j )

look at the photo below for the graphics.

:)

Answer: a translation 5 units to the left