Use properties to determine whether the expressions are equivalent. 8(9x − 2) and 72x − 2

The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).

The general equation of a quadratic equation is -

y = ax² + bx + c

It has two possible roots. It has a degree of 2.

Given is the graph of the function, f(x) = x² - 5x - 7.

We have the following -

f(x) = x² - 5x - 7.

We will draw the graph of this function.

Now, the graph cuts the [x] axis at (-1.14) and (6.14).

Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.

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The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.

The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function:

Parent function: f(x) = log(x)

Transformation function: g(x) = log(-3x + 9) + 4

Step 1 -  Shift 3 unit right, to achieve the function

y = log (x - 3) (x - 3)

Step 2 - Reduce the graph by thrice by multiplying x by three:

y = log 3(x - 3) (x - 3)

Step 3 -  The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)

Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach

Therefore, the function can be transformed by reflection and translation.

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Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

How to solve Algebra Word Problems?

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Step-by-step explanation:

The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.

It follows from the task content that the statement which represents the solution of the given equation be determined.

Since the given equation can be written algebraically as follows;

x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)

By observation; (x - 1) (x - 2) = x² - 3x + 2.

Therefore, by multiplying through the equation by; x² - 3x + 2; we have;

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

x² - 2x - x + 1 = 2x - 5

x² - 5x + 6 = 0.

Hence, the equation above can be solved quadratically so that we have;

(x - 3) (x - 2) = 0.

Therefore, the solution to the given equation is; x = -3 Or x = 2.

However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.

Therefore, the statement which reflects the solutions to the given equation is; x = 3.

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The line graphed with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m=(y₂-y₁) / (x₂-x₁)

It is given that,  the line is having the y-intercept 3 and slope -4/3.

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

The equation with the y-intercept 3 and slope -4/3 is,

y=mx+c

y= -4/3x+3

3y= -4x+9

Thus, the line graph with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.

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The real width of the building is given by 47 meters.

Given that the actual length of the building is 62 meters.

In a scale drawing, the length of the building is 12.4 cm.

So, 12.4 cm = 62 meters

1 cm = 62/12.4 = 620/124 = 5 meters.

Also given that the width of building on scale drawing = 9.4 cm

Hence the real width of the building = 9.4 * 5 = 47 meters.

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Answer: 125

Step-by-step explanation:

100% = 100

25% of 100 = 100/4 = 25

100 + 25% (25) = 125

Answer:

360

Step-by-step explanation:

it has four right angles 90×4 =360

The value of the fraction 2 2/3 + 2 1/4 is 4 11/12.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the addition of the fraction will be:

= 2 2/3 + 2 1/4

= 2 8/12 + 2 3/12

= 4 11/12

The value is 4 11/12.

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Answer:

  7.5 in²

Step-by-step explanation:

You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base length, and h is the height.

The figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...

  A = 1/2(6 in)(2.5 in) = 7.5 in²

__

Additional comment

The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.

The new function's equation is g(x) = (x - 2)² + 6

Given,

The parent function, f(x) = x²

We have to determine the equation for the new function g(x)

Vertical shift:

The parent function is clearly pushed 6 units upward from the graph.

The general formula to increase the c units on the graph is f(x) + c

As a result, by using the rule, the new function g(x)of vertical shift is provided by g(x) = x² + 6

Horizontal shift:

It is clear from the graph that the parent function has been moved 2 units to the right.

To move the graph's c units to the right, follow this basic formula: f(x - c)

Consequently, the new function g(xhorizontal )'s shift is given by g(x) = (x - 2)²

The new function g( x ) is as follows:

The equation results in the new function being shifted 2 units to the right and 6 units upward.

g(x) = (x - 2)² + 6

Therefore, the new function's equation is g(x) = (x - 2)² + 6

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The measure of the non-felex DOB in degrees is 140°.

It is important to note that the value of the angles at a point is 360°.

Therefore, it should be noted that also vertically opposite angles are equal.

Therefore, the angles will be:

3.5y + 3.5y + y + y = 360°

9y = 360°

Divide

y = 360° / 9

y = 40°

Therefore, DOB will be:

= 3.5y.

= 3.5 × 40

= 140°

DOB is 140°.

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The Correct option is D .

System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .

If a, b, and c are real numbers, the graph of the equation ax + by = c

is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.

given system of equations is

2x - y = 4 --(1)

and 5x + 4y = -10 ---(2)

comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2

we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,

c2= -10

Now, the ratio are

a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5

=> a1/a2 not equal to b1/ b2

therefore the given system of equations has unique solution.

Now , we find the soltion of given system using Elimination method,

multipling equation (1) by 4 to making same cofficient of y in both equations of system we get

8x - 4y = 16 --(3) and 5x +4y = -10

adding equation (2) from (3) we get,

8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13

putting this value of x in (1)

2×6/13 - y = 4 => y = 12/13-4 = -40/13

Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.

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Complete Question:

Alfred tried to solve the system of equations shown below..

2x - y = 4 and 5x + 4y = -10

He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?

He is correct. Both equations describe lines that have infinitely many solutions.

He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.

He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.

He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.

The total change in temperature is 58°F.

It should be noted that temperature simply means the degree of hotness and coldness in a body.

In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.

The change in temperature will be:

= Old temperature - New temperature

= 18°F - (-40°F)

= 18°F + 40°F

= 58°F

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The determinant of nxn matrix A  2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

From the given information, the matrix will appear as follows

[tex]A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right][/tex]

The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n

Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

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Answer:

There is no solution because after solving the absolute value, the number will be multiplied by -4 which would be getting positive 9 impossible.

The function h(x) is a translation of 4 units to the left, so the correct options is B.

h(x) = √(x + 4)

We know that h(x) is a transformation on the parent square root function:

f(x) = √x

If we look at the graphs, we can see h(x) is translated 4 units to the left.

Now, for a function f(x), we define a horizontal translation of N units as:

h(x) = f(x + N)

if  N < 0, the translation is to the right.

if N > 0, the translation is to the left.

In this case we have a translation of 4 units to the left, then N = 4, so we can write:

h(x)= f(x + 4)

Replacing the function f(x) we get:

h(x) = √(x + 4)

So the correct option is B.

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Answer:

THE ANSWER IS x= 33/20

hope it help

with the steps:

1) Multiply all terms by the same value to eliminate fraction denominators

2) Cancel multiplied terms that are in the denominator

3) Multiply the numbers

1) 4x//3==11/5 then 15 ✖️ 4x/3= 15 ✖️ 11/5

2) 5 ✖️ 4= 3 ✖️ 11

3) 5 ✖️ 4x=3 ✖️ 11

          20x=3 ✖️ 11

solution : x= 33/20

Answer:

x = [tex]\frac{33}{20}[/tex]

Step-by-step explanation:

[tex]\frac{4x}{3}[/tex] = [tex]\frac{11}{5}[/tex]  cross multiply and solve

20x = 33 divide both sides by 20

x = [tex]\frac{33}{20}[/tex]

If she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be 3.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given,

if she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be: 3.

$7.5= 1 hour various days

Sunday: $9.50 or ($7.50+$2.00) = 1 hour

Sunday = 4 + $9.50 = 38

Let Monday equal x $7.5 = 7.5x.

Let Wednesday equal x $7.5 equal x.

Let the total income be $83

Let x be the amount of hours.

Hence:

The first step is to create

Equation:

7.5x+7.5x+38=83

The next step is to determine the number of hours Laurie worked on Monday.

x =83-38÷ 7.5+7.5

x=83-38÷15

x=45÷15

3 hours =  x

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Answer: y = -4/5x - 5

Step-by-step explanation:

So you can view that fancy F with the parenthesis number inside of it as an input, just like X, and when -1 is the output, that means that y=-1, so your first set of numbers is (5,-1) now do the same with the second pair and you get (0,-5), we know that this is the Y intercept because X=0 in this pair.

-5 - (-1) = -4

0-5 = -5

slope = - 4/5

y intercept = -5

Really hope this helps you!

The number of time it take  Katherine to drive from home back to college is: 3 hrs 21 min.

Going home:

Rate =  65.1 mph , distance  = x miles ; time = distance /rate = x/ 65.1 hrs

Going to college:

Rate = 70.7 mph ; distance  = x miles ; time = x/70.7 hrs

Equation:

x/70.7+ x/ 65.1=  11

70.7x + 65.1x = 7 × 65.1 × 70.7

Combine like terms

135.8x = 32,217.99

Divide both side by 135.8x

x = 32,217.99/ 135.8

x = 237.25 miles

Home back to college

=  237.25 /70.7

=3.35 hrs

= 3 hrs 21 min

Therefore it take Katherine 3 hrs 21 min.

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The percentage of airline passengers covered by this fee is 85.99%.

If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is

less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.

This is the p-value of Z for X = 50 minus 1 as a

ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%

So, 85.99% of the airline passengers pay this fee.

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Answer:u dont

Step-by-step explanation:

Answer:

  7

Step-by-step explanation:

You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.

The triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...

  x +12 > 18

  x > 6 . . . . . . subtract 12

The smallest integer greater than 6 is 7.

The third side must be at least 7 units long.

__

Additional comment

Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.

Answer:

Question 1 is G.

Question 2 is B

Question 3 is D

Question 4 is A.

Step-by-step explanation:

Answer: 3.6

Step-by-step explanation: Annual means yearly, therefore 43.2 divided by 12 is 3.6. So 3.6 inches monthly.