Section 5.2-9. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).2x+y = 2-3x-2y = -8

The expression equivalent to [tex]2 log_4 x + 3 log_4 y - 5 log_4 z[/tex] is the first option that is [tex]log_4(\frac{x^2y^3}{z^5} )[/tex].

Logarithms

A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation.

For example, if  [tex]10^2 = 100[/tex] then [tex]log_{10} 100 = 2[/tex].

In a log function of the form [tex]log_ab=x[/tex] ,

a is the base of the log

b is the argument of the log and,

x is the real number

It is the most convenient way to express large numbers.

The properties of logarithms are,

1) [tex]xlog_ab =log_ab^x[/tex]

2) [tex]log_ab-log_ac=log_a(\frac{b}{c} )[/tex]

Hence,

According to 1) , we can write,

[tex]2 log_4 x =log_4x^2\\3 log_4 y = log_4y^3\\ 5 log_4 z = log_4z^5[/tex]

According to 1) and 2), we can write,

[tex]2 log_4 x + 3 log_4 y - 5 log_4 z= log_4(\frac{x^2y^3}{z^5} )[/tex]

Hence, the answer is the first option.

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Answer:

alphabet

Step-by-step explanation:

By algebra properties, the standard form with rational coefficients is the polynomial x³ - 11 · x² + 7 · x + 51, whose lead coefficient is 1 and comprise the roots 3 and 4 + i.

A polynomials of least degrees includes all the roots and the given lead coefficient, which can used in the following formula:

p = a · Π (x - rₐ)

Where:

If we know polynomial has rational coefficients, then the complex root 4 + i has a "twin" equal to 4 - i in accordance with the quadratic formula, otherwise the polynomial will have at least an irrational coefficient. Then, the least degree polynomial is introduced below:

p = 1 · (x - 3) · (x - 4 - i) · (x - 4 + i)

Then, we expand the expression by algebra properties:

p = (x - 3) · [x² - 8 · x - (16 - i²)]

p = (x - 3) · (x² - 8 · x - 17)

p = x³ - 8 · x² - 17 · x - 3 · x² + 24 · x + 51

p = x³ - 11 · x² + 7 · x + 51

The standard form is the polynomial p = x³ - 11 · x² + 7 · x + 51.

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Answer:

b

Step-by-step explanation:

because it is tht simpl

For the given figure, all the intersecting sides meet at right angles

The lengths of the vertical sides are 14, 8, and ?

Let the missing side = x

So,

so,

so, the answer will be the length of the missing side = 6 yd

The amount that Sidney will have in her account in 1 year is $ 95,704.

Given that:-

Principal amount = $85,450

Interest Rate = 12 % per annum

i = prt

Where,

i represents interest,

p represents the principal,

r represents the interest rate, and

t represents the time (in years)

Hence, putting the values in the formula of simple interest, we get,

i = 85450*(12/100)*1 = $ 10,254

Hence, the amount that Sidney will have in her account in 1 year is

85450 + 10254 = $ 95,704

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Given function:

Finding x when f(x) = -4

Thus, the value of x is 3 and 5.

The number of non-members is 12 and the number of members is 24.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of members, and the number of non-members.

3x + 5y = 132

x = 2y

After solving the above two linear equations:

6y + 5y  = 132

11y = 132

y = 132/11

y = 12 non-members

x = 24 members

Thus, the number of non-members is 12 and the number of members is 24.

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Answer: -12 and -9

Step-by-step explanation:

4p + 6 <3p

4p - 3p < -6

p < -6

So, -12 < -6 is CORRECT

     -9 < -6 is CORRECT

     -6 is not less than -6 SO THIS IS INCORRECT

     6 is not less than -6 so this is INCORRECT

olution

2a.

The graph of as described is given below (showing at least five points)

The (clear) graph that has the dashed line of asymptotes

The table will be

Bb.

o write the equation

We start from

Translate the graph up by 3 units

Translate the graph 4 units to the left

2c.

o get the equation of asymptotes

The statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.

Let us check it with the help of an example.

Let A = {1,2,3,4,5,6} ,

B = {5,6,7,8,9,10} and ,

A universal set S = {1,2,3,4,....,15}

Now, we can write,

A ∪ B = {1,2,3,4,5,6,7,8,9,10}

LHS = (A ∪ B)' = {11,12,13,14,15}

A' = {7,8,9,10,11,12,13,14,15}

B' = {1,2,3,4,5,11,12,13,14,15}

RHS = A' ∩ B' = {7,8,9,10,11,12,13,14,15} ∩  {1,2,3,4,5,11,12,13,14,15} = {11,12,13,14,15}

As we can observe from above,

LHS = RHS

Hence, the statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.

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The perimeter of a rectangle can be calculated using the following formula:

Where

"w" represents the width of the rectangle

"l" represents the length of the rectangle

If you know the perimeter and length of a rectangle, you can use the formula to determine the width. The first step is to write the formula for the width:

-Pass 2l to the left side of the expression by applying the opposite operation to both sides of it:

-Divide both sides by 2

Now that we have determined a formula for w, replace the value of the length and perimeter and calculate the width:

P=84in

l=28in

The width of the rectangular frame is 14 inches long

Answer:

Step-by-step explanation:

Multiply like this

2 x 2

How to do this

Just double 2

Answer:

multiplication is like doing repeated addition so let’s try doing 5x5

In repeated addition form it would be 5+5+5+5+5 which equals 25

I don’t know how to really explain it but I hope this helps!

Step-by-step explanation:

Here are some tips that may help you feel better:

1. Rest: Get plenty of sleep and rest as much as possible to allow your body to recover.

2. Hydration: Drink lots of fluids to stay hydrated and help flush out any toxins in your body.

3. Nutrition: Eat healthy foods that are easy to digest, such as soups, broths, and fruits.

4. Medication: Take any prescribed medication as directed and follow the instructions on the label.

5. Warmth: Use warm blankets and a hot water bottle to soothe aches and pains.

6. Avoiding stress: Stay away from stress as much as possible since it can interfere with your immune system's functioning.

7. Humidifier: Use a humidifier to help ease congestion and dryness in the air.It's also essential to see a doctor if your symptoms persist or worsen. Don't hesitate to seek medical attention if necessary.

Furthermore, the information given in the question, "x does not equal 12 and D isn't 95," seems unrelated to the context of the problem. It's unclear what information the question is asking for, so please provide more details if you have any.

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A) There are two parallel lines and a line that goes through them in this diagram. The line that goes through them causes perpendicular lines to form.

What are perpendicular lines?

Perpendicular lines are lines that intersect and create 90° angles. The two angles in this diagram are 90° due to this intersection.

B) There are two types of angles: supplementary and complementary: complementary angles are angles whose measurements add up to 90°. Supplementary angles are angles whose measurements add up to 180°. As you can see in this problem, the two angles (7x+11 and -1+8x) are 90°. When added they would equal 180°. These angles are supplementary.

C) Now that you know what supplementary angles are, you can use its characteristics to solve for x:

D) Now, solve for the two equations by plugging in x [you final answers should be 90]:

The amount that will be made by the local festival given the expression m=2p - 0.75p - 50 is 225.

From the information, at the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each.

The expression given was illustrated as:

m=2p - 0.75p - 50

Therefore since we are given the value of p as 220. This will be:

m=2p - 0.75p - 50

m = 2(220) - 0.75(220) - 50

m = 440 - 165 - 50

m = 440 - 215

m = 225

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At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.

Find the profit when the number of the ice cream pops represented by p is 220.

Given:

The equations are given as,

Required:

Direct and inverse variation verification.

Explanation:

(a) The equations are given as follows:

On simplifying further,

The given equation is not a direct variation.

(b) The equation is given as,

The given equation represents inverse variation.

Answer:

Thus the required result is,

a) Not a direct variation

b) A direct variation( k = -2)

Hence the equation of the parabola is y = -x² + 4

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

The general equation of a parabola is given by y = ax² + bx+ c

The parabola passes through (-3,-5) , (-1,3) , and (0,4).

Now substituting the values in the parabola we get :

-5 =  a(-3)² + b(-3)+ c

or , -5 = 9a -3b + c

again:

3 = a(-1)² + b(-1)+ c

or, 3 = a -b + c

again

4 = a(0)² + b(0)+ c

or, c =4

Solving the equation we get :

9a - 3b = -9 and a-b = -1

a= -1 and b = 0

Hence the equation of the parabola is

y = -x² + 4

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The option that is unique to only skeletal muscle is Option(B.) They can fatigue with too much movement or exercise.

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Using combinations, we concluded that  the probability that fewer than 2 of the next 5 vehicles are from out of state is 0.907.

A checkpoint sees 75% of its traffic coming from within the state.

Therefore, there is a 0.75 percent chance that the car comes from the state.

1-0.75=0.25 represents the likelihood that the car is from outside the state.

Let x now act as the random variable. Consequently, n=9 and X=4

It is necessary to determine the likelihood that less than 2 of the following 5 automobiles are from another state.

We are to calculate the probability of x<2

p=0.25

q=0.75.

Using the formula,

P(x≤2) = ∑ ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

P(x≤2) = ∑ ⁵C₂ p² q³ + ⁵C₁ p¹ q⁴ +  ⁵C₀ p⁰ q⁵

P(x≤2) = ∑ [tex]\frac{5!}{2! 3!}[/tex] (0.25)² (0.75)³ + [tex]\frac{5!}{1! 4!}[/tex] (0.25)¹ (0.75)⁴ + [tex]\frac{5!}{0! 5!}[/tex] (0.75)⁵

P(x≤2) = 10 × 0.065 × 0.421875 + 5 × 0.25 × 0.3164 + 0.2373

P(x≤2) = 0.2742 + 0.3955 + 0.2373

P(x≤2) = 0.907

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Answer:

the answer is 93

Step-by-step explanation:

I'm very sure....

Answer: I really wish I could help you but I don't know the answer either

Step-by-step explanation:

JK

Answer:

B) [tex](2,\infty)[/tex]

Step-by-step explanation:

Since we are given the graph of [tex]f'(x)[/tex], this gives us the value of the derivative, or the rate of change, of [tex]f(x)[/tex] given an x-value. For [tex]f(x)[/tex] to be increasing, then [tex]f'(x) > 0[/tex], which is a positive rate of change. As you may have noticed, when [tex]x > 2[/tex], the value of [tex]f'(x)[/tex] is positive. This means that f increases on the interval [tex](2,\infty)[/tex], or answer B.

The numbers that represent the first 5 members selected is A. 24, 07, 59, 62, 20.

From the information, the members of a running club would like to survey the rest of the members to determine which 5K races the club should enter.

In this case, they decide to use a random number table to sample 10 of the 78 members. The numbers illustrated are 24000 75983 62200 91518 11198 88936.

Therefore, the appropriate numbers chosen will be (24) 000 (7) (59) 83 (62)(20)0.

The correct option is A.

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Answer:

[tex]x = 3 - {e}^{12} [/tex]

Step-by-step explanation:

first let's isolate the logarythm:

[tex]ln(3 - x) = 12[/tex]

at this point we can apply the definition of logarythm to obtain

[tex]3 - x = {e}^{12} [/tex]

which, with some simple algebra returns

[tex]x = 3 - {e}^{12} [/tex]

Applying the definition of the midpoint of a line and other properties, the proof that shows that AC ≅ CD is shown in the image attached below.

A line is divided into two equal parts by its midpoint. Thus, the midpoint of that line is that point where the line segment is bisected into two parts that are equal.

Given the image showing two lines that intersect each other at point C, the proof below shows that AC is congruent to CD:

1. C is the midpoint of line AE

C is the midpoint of line BD

AE is congruent to BD

(Reason: Given)

2. AC = CE; BC = CD

(Reason: Definition of midpoints)

3. AE = BD

(Reason: Definition of congruent segments)

4. AE = AC + CE;

BD = BC + CD

(Reason: Segment addition property)

5. AC + CE = BC + CD

(Reason: substitution property)

6. AC + AC = BC + BC

(Reason: substitution property)

7. 2AC = 2BC

(Reason: Simplify)

8. AC = CD

(Reason: division property)

9. AC ≅ CD

(Reason: definition of congruent segments).

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Answer:

209 out of 230 completed   that is   209/230 x 100% = 90.869 %     the rest did NOT complete   100% - 90.8% = 9.13 %

The four winning numbers are 24, 32, 27 and 37 respectively

It is important to note the following;

From the information given;

a. First number =  square root of 576

This is represented as

First number = √576

First number = 24

b. Second number =  multiple of 8 between 30 and 39

Second number = 32

c. Third number =  cube of 3

This is represented as;

Third number =  3³

Third number =  37

d. largest prime number less than 40

Fourth number = 37

Hence, the numbers are 24, 32, 27 and 37

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The smaller the sample size the greater the variability and higher the chance of getting an overestimate

From the given data

Median = $200,000

IQR = $100,000

The sample size for the median above to $250,000 is n =10

Because n=10 shows a sample with the fewest values, it is most likely that the sample median will be farther from the true median.

Answer : A) n = 10

Given data,

Use the law of cosines.

Thus, the value of b is

The cosines formula for angle A isThus, angle A will be

Therefore, angle A is 52.67 degrees.