Solve the equation showing ALL steps, and check for extraneous solutions.

2|2 - 4x| = 2x + 6

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer: The total distance covered by the car is 331 9/16 km.

Step-by-step explanation:

We know that, speed= distance/time taken

Therefore, distance = speed x time taken

= 132 5/8 x 2 1/2

= 5/2 x 1061/8

= 5305/16

= 331 9/16 km

Therefore, total distance is 331 9/16 km.

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Answer:

The line of symmetry is -2

Step-by-step explanation:

I like to plug in equations and coordinates into a graphing calculator in order to get my answers. If you don't own a graphing calculator there is a site called desmos that is free.

The answer is f(x−3)=x2

Answer:

C

Step-by-step explanation:

x²-9x<-8

x²-9x+(-9/2)²<-8+(-9/2)²

(x-9/2)²<-8+81/4

(x-9/2)²<(-32+81)/4

(x-9/2)²<49/4

|x-9/2|<7/2

-7/2<x-9/2<7/2

add 9/2

9/2-7/2<x-9/2+9/2<7/2+9/2

2/2<x<16/2

1<x<8

At first Sound level increases then for an instant it becomes constant then in decreases for a while then again becomes constant for an instant then again starts to increase .

What is sound level of a conversation?

A decibel (dB) is a unit used to measure sound. A motorbike engine operating is around 95 dB louder than a whisper (30 dB louder than typical conversation).

                          Your hearing may begin to deteriorate if exposed to noise levels exceeding 70 dB for an extended length of time. Your ears might suffer instant damage from loud noises exceeding 120 dB.

The relationship of sound level w.r.t time can be described as ,

a) At first Sound level increases then for an instant it becomes constant then in decreases for a while then again becomes constant for an instant then again starts to increase .

b) At both the instances the sound level is increasing as the slope of the tangent drawn to the curve at those points is positive but absolute value of sound level at instance (1) is clearly lower than the value of sound level at instance (3).

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Answer:

51

Step-by-step explanation:

67 minus 16 equals 51

Answer:

The missing number is 51.

Answer:

1. Not possible

2. Possible

3. Possible

4. Possible

Step-by-step explanation:

Answer:

  14

Step-by-step explanation:

You want the greatest common factor of the terms {98ab^3, 84a, 140b, 112ab​}.

There are no variables that are common to all terms. 'a' and 'b' are each common to 3 of the 4 terms, but not all.

The greatest common factor of the constants cannot be larger than the smallest difference of the constants. That difference is ...

  98 -84 = 112 -98 = 14

Since 14 is a divisor of all of the constants, 14 is the greatest common factor.

__

Additional comment

Factoring out the greatest common factor, we have ...

  = 14{7ab³, 6a, 10b, 8ab}

The two options that represent the equation of the circle are:

x² + (y – 3)² = 36

x² + (y + 8)² = 36

Options A and E are the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle is (x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius.

Now,

Diameter of the circle = 12 units

This means,

Radius = 12/2 units = 6 units

Now,

Center of the circle = y-axis.

This means,

x = 0,

y = a

Center = (0, a)

Now,

The equation of the circle.

(x - 0)² + (y - a) = 6²

x² + (y - a)² = 36

Where a can be any number.

Thus,

The equation of the circle can be:

x² + (y – 3)² = 36

x² + (y + 8)² = 36

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Answer:

angle KNM = 131 degree

Step-by-step explanation:

angle MNJ = angle KNL ( vertically opposite angles)

angle KNM + angle KNL = 180 degree ( linear pair)

8x-5 + 4x-19 = 180 degree

8x + 4x -5 -19 = 180

12x - 24 = 180

12x = 180+24

12x= 204

x= 204/12

x= 17

angle KNM = 8x-5

                  = 8(17) -5

                  = 136 -5

                  = 131

Angle KNM = 131 degree

Hope this helps.

Answer:

Step-by-step explanation:

Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y

If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.

96 = 4x+y

y = 96-4x

Substituting the value of x into the formula for calculating the volume, we will have;

V(x) = x²(96-4x)

V(x) = 96x²-4x³

To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.

V'(x) = 192x-12x²

192x-12x² = 0

Factoring out x;

x(192-12x) = 0

x = 0 and  192-12x = 0

12x = 192

x = 192/12

x = 16

This shows that we have a maximum value at x = 16 and minimum at x = 0

To get y, we will substitute x = 16 into the expression y = 96-4x

y = 96-4(16)

y = 96-64

y = 32

- The dimensions of the largest package is therefore 16in by 16in by 32in

- Volume of largest package = x²y = 16²*18 = 8,192in³

Answer:

Tuba, French Horn, Trombone, Trumpet, Cornet.

The solutions to the quadratic equation are [−5/2,1/3]. Option A

Given the inequality;

6x^2≥5−13x

First, convert to quadratic equation

\(6 {x}^{2} - 5 + 13x \geqslant 0 \)

No, let's solve the quadratic equation using the factorization method

\(6 {x}^{2} + 13x - 5 \geqslant 0\)

Multiply 6 by -5 and find two factor that their product equals the number and their sum equal 13. Those two number are + 15 and -2

Substitute as 15x and 5

-2x in the inequality, we have;

\(6 {x}^{2} +15x - 2x - 5 \geqslant 0\)

Factor the common multipliers

\(3x(2x + 5) - 1(2x + 5) \geqslant 0\)

We have two expressions, written as;

\((3x - 1) (2x + 5)\geqslant 0\)

Let's solve to get the roots of x

\(3x+ 1 \geqslant 0 \)

\(x \geqslant 1/3\)

\(2x + 5 \geqslant 0\)

\(x \geqslant \frac{ - 5}{2} \)

Thus, the solutions to the quadratic equation are [−5/2,1/3]. Option A

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Answer:

y = -x + 5

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is -1. Substituting into point-slope form, we get the equation to be

\(y+2=-(x-7)\)

which rearranges into slope-intercept form as follows:

\(y+2=-x+7 \\ \\ y=-x+5\)

Answer:

y=-x+5

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

5:4 = 60:48

Answer: YES

Step-by-step explanation: both equal 5 when divided.

 V kubus = s³

= (36 cm)³

= 46.656 cm³

Kubus adalah sebuah bangun ruang tiga dimensi yang panjang semua rusuknya sama. Dan semua sisinya berbentuk persegi.

SEMOGA MEMBANTU

The price of each of these be

A. Price  \(}=\left(\frac{100 \%-20 \%}{100 \%}\right) * 120=\frac{80}{100} * 120=96 \\\)

B. Price =\(\left(\frac{100 \%-20 \%}{100 \%}\right) * 750=\frac{80}{100} * 750=600 \\\)

C. Price \(=\left(\frac{100 \%-20 \%}{100 \%}\right) * 250=\frac{80}{100} * 250=200\)

The complete question is.

A shop gives 20% discount. What would the price of each of these be?

A dress market at Rs.120

A pair of shoes market at Rs.750

A bag market at Rs.250

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Step-by-step explanation:

LxB

8x7

equals :56

Area equals to 56cm

The relationship between pendulum length and period is nonlinear. As the period is dependent on the square root of the length.

To  anatomize this relationship, the scholars would need to gather data on pendulum length and period, also fit a regression model.However, the residuals from the model would be  erratically distributed around zero, If the relationship is direct.

If the relationship is nonlinear, the residuals would parade a pattern, indicating that a direct model is not the  swish fit. In this case, a nonlinear model  analogous as the square root of pendulum length would give a better fit for the data. The scholars  probably set up that the residuals from the direct model were not  erratically distributed, hence they didn't favor the direct model.

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W

L=2w-3

Area=(L×w)

65=[(2w-3)×w]

65 =(2w²-3w)

65=2w²-3w

2w²-3w-65=0

by using the quadratic equation

you'll get 2 values in which one will be negative

Obviously a length can't be negative so you take the positive.

w=6.5m

L=2(6.5)-3

=10m

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

The given function is Ƒ(t) = –1/(2t²) + 2t + 6.

This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.

Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.

So, the function Ƒ(t) can be written as:

Ƒ(t) = (-1/2)t² + 2t + 6

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

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Answer:

c. there is a positive correlation in-between x and y

Step-by-step explanation:

A regression line is a line that suggests that all the points in a scatter diagram lie on or near one particular line. In a simple regression analysis in which y is the dependent variable and x is the independent variable. If the slope is positive, the bivariate data is also said to have a positive correlation. The positive correlation in-between two variables x and y implies that in general, an increase in x goes hand in hand with an increase in y.

Regression Analysis is defined as the set of statistical and reliable processes for establishing the relationship between the independent and dependent variables.

The correct statement can be given as:

In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that there is a positive correlation between x and y.

The regression line suggests that all the points lie near a particular line. It can be explained as:

1. In a simple regression analysis, the dependent variable is y.

2. Similarly, the independent variable is x.

3. Given, if the slope is positive, then the correlation will be positive.

4. The positive relation implies that if x increases then they will also increase in simple regression analysis.

Thus, in the simple regression analysis there exists a positive correlation between x and y.

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The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.

Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.

The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).

Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.

However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.

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Answer:

141

Step-by-step explanation:

First, we choose two variables to represent the two unknown numbers, the number of hamburgers and the number of cheeseburgers.

Let x = number of hamburgers.

Let y = number of cheeseburgers.

Now we use the given information to write two equations using the variables we defined above.

"If a hamburger shop sold a combined total of 423 hamburgers and cheeseburgers"

x + y = 423

"the number of cheeseburgers sold was two

times the number of hamburgers sold"

y = 2x

We have a system of two equations.

x + y = 423

y = 2x

Since the second equation is already solved for y, we can easily use the substitution method. We substitute what y equals to (2x) for y in the first equation.

x + y = 423

x + 2x = 423

3x = 423

x = 141

Since we let x = number of hamburgers, we have the answer.

Answer: 141

Answer:

E

Step-by-step explanation:

So we already know that:

\(\lim_{x \to 5} f(x)=2 \text{ and } \lim_{x \to 5} g(x)=-6\)

So, go through each of the choices and see which ones are correct.

I)

We have:

\(\lim_{x \to 5} (f(x)+g(x))\)

This is the same as saying:

\(\lim_{x \to 5} f(x)+ \lim_{x \to 5} g(x)\)

And since we already know the values:

\(=(2)+(-6)\\=-4\)

So, the limit does indeed exist.

II)

We have:

\(\lim_{x \to 5} \frac{f(x)}{g(x)+6}\)

This is the same as:

\(\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+ \lim_{x \to 5} 6 }\)

The bottom right one is just 6. Simplify:

\(\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+6}\)

Substitute the values we know:

\(=\frac{(2)}{(-6)+6} \\=2/0\)

This is a value over zero. Unlike the indeterminate form 0/0, this limit does not exist.

III)

We have:

\(\lim_{x \to 5} \frac{f(x)-2}{g(x)}\)

Again, this is the same as:

\(\frac{ (\lim_{x \to 5} f(x))-2}{ \lim_{x \to 5} g(x)}\)

Substitute in the values we know:

\(=\frac{(2)-2}{(-6)}\\ =0/-6=0\)

The limit does exist and it is 0.

So, the limits of only I and III exist.

The correct answer is E.

Answer:

14

Step-by-step explanation:

the angle of 20° and the angle where it says (2x-8)° are the same.

Then find the number that substituted for x, multiplied by 2 and subtracted 8, gives 20°.

And it's 14.

Indeed:

([2×14]-8)° = 20°