(r+2)(r-7)+2r+64 Solve by factoring.

Answer: The answer is C

Step-by-step explanation:

We are given to find the true solution of the following equation involving logarithms:

We will be using the following properties of logarithms in the solution.

The solution is as follows:

Since we can find the logarithm of a positive integer only, and both the solutions x = 1 and 4 satisfy this condition after substituting in the given equation, so both the solutions are TRUE.

Thus, the correct option is (C).

The true solution to the given equation is x = 1 and x = 4. The correct answer would be an option (C).

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

The given equation is as follows:

2log₃(6x) - log₃(4x) = 2log₃(x+2)

Using the property that logₐ(xⁿ) = n logₐx,

log₃((6x)² - log₃(4x) = log₃(x+2)²

Using the property that logₐ(x/y) = logₐx - logₐy,

log₃((6x)²/4x) = log₃(x+2)²

log₃((36x²)/4x) = log₃(x+2)²

log₃(9x) = log₃(x+2)²

Now we can solve for x by setting the expression inside the logarithm equal to 1, which gives:

9x = (x+2)²

9x = x² + 4x +4

x² - 5x + 4 = 0

Solving for x, and we get

x = 1 and x = 4

Thus, the true solution to the equation is x = 1 and x = 4.

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We need to know about z-score to solve the problem. The z-score of the soda is 0.6

A z-score tells you how many standard deviations away an individual data falls from the mean. We can calculate z-score from the standard deviation and mean of the data. In this question we know that the cost of a soda is $1.15 and the mean is $1.00 and the standard deviation is $0.25.We need to calculate the z-score of the soda with the given information.

z-score=x-μ/σ=1.15-1.00/0.25=0.15/0.25=0.6

Therefore the z-score of the soda is 0.6

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Answer:

When you divide the amount you have by the total amount and then multiply the quotient by 100, you are calculating the percentage of the total amount that the amount you have represents.

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

A percentage is a fraction expressed as a part per hundred.

It is calculated by dividing the number you want to express as a percentage by the total number and then multiplying by 100%.

This can be expressed using the formula:

Answer:

x<9

Step-by-step explanation:

Answer:

the first step is to change the mixed fraction into an improper fraction so 4 and 1/5 will be 21/5 so then you question will be three times 21/5 and the answer is 12 and 3/5

Answer:

Step-by-step explanation:

Since the lines are parallels and should equal 180 degrees, with the other being 140 degrees, I would think it's 40 degrees to make the 180. I hope  this is right. It's been a while for geometry.

The response will be A. 34 based on the details provided.

Multiplication is the reverse of division. If the three sets of 4 add up to 12, then 12 split into 3 groups of identical size results in 4 in each group. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a reasonable distribution.

We can divide the overall number of attendees by the number seated in each section to determine the number of sections in the auditorium:

Number of sections = Total number of attendees / Number of people in each section

Number of sections = 5,406 / 159

Number of sections ≈ 34.04

We are able to round up to the closest whole number because we are unable to have a fractional portion of a section, which results in:

Number of sections ≈ 34

Therefore, the answer is A. 34

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The scope of a variable specifies where a variable can be referenced within a program. Scope determines the visibility and accessibility of a variable in different parts of the program.

The scope of a variable is the area within a program where the variable can be accessed and manipulated. This area is typically defined by the location of the variable's declaration statement. Variables that are declared within a specific function or block of code have a limited scope and can only be accessed within that function or block. On the other hand, global variables have a wider scope and can be accessed from any part of the program. Understanding variable scope is essential for writing effective programs that are both efficient and easy to maintain. By properly managing variable scope, developers can avoid errors and ensure that their code is reliable and easy to understand. There are typically two types of scope: local scope and global scope. Local scope variables can only be accessed within the function or block where they are declared, while global scope variables can be accessed throughout the entire program. Understanding the scope of variables is important for managing data and avoiding conflicts or errors in your code.

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Answer:

$216

Step by step

Explanation:

First we subtract  $ 20 from  $ 84  giving us a total of  $ 64 and when we add that to  $ 152  we get  $ 216

.

Answer:

-60

Step-by-step explanation:

Answer:

14/3

Step-by-step explanation:

The quotient of triple a number less four and five equals two. What is the number?

"triple a number" means 3x, if we say x is the "number"

"triple a number less four" means (3x-4)

"quotient of [triple a number less four] and five equals two." means

(3x-4)/5 = 2

3x-4 = 10

3x = 14

x = 14/3

===

Does ((14/3)3 - 4)/5 = 2 ???

(14 - 4)/5

10/5 = 2                         YES

What is the number?

Answer:

\(\huge\boxed{\sf h = 24}\)

Step-by-step explanation:

So,

2h + 8 + 3h - 3 + 31 + h = 180

Combine like terms

2h + 3h + h + 8 - 3 + 31 = 180

6h + 36 = 180

Subtract 36 to both sides

6h = 180 - 36

6h = 144

Divide 6 to both sides

h = 144/6

\(\rule[225]{225}{2}\)

Answer:

The discriminant of a quadratic equation determines the nature of its roots. If the discriminant is negative, the quadratic equation has no real roots.

Therefore, the correct answers are:

2x^2 + x – 4 = 0

2 x^2 – 5 x – 3 = 0

3x^2 – 2 x + 4 = 0

–x^2 + x – 3 = 0

The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.

A square is a four sided polygon with 4 equal angles and length.

The fourth corner = 90° - 36°

= 54°

Recall,

Alternate angles are equal

So,

(4x + 4)° = 36°

substract 4 from both sides

4x = 36 - 4

4x = 32

divide both sides by 4

x = 32/4

x = 8

(4y + 10)° = 54°

substract 10 from both sides

4y = 54 - 10

4y = 44

divide both sides by 4

y = 44/4

y = 11

In conclusion, the value of the following given equations are:

(4x + 4)° = 36°

4(8) + 4 = 36

32 + 4 = 36

36° = 36°

(4y + 10)° = 54°

4(11) + 10 = 54

44 + 10 = 54

54 ^= 54°

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Line AB intersects line CD at point F. If m∠AFC = (9x − 3)° and m∠BFD = (6x + 9)°, then m∠AFC is 33 degrees.

What are the intersections of lines?

Two or more lines that share exactly one common point are called intersecting lines. This common point exists on all these lines and is called the point of intersection.

We can start by using the fact that the sum of the angles on one side of a transversal is 180 degrees. Since point F is the point where lines AB and CD intersect, we can write:

m∠AFC + m∠CFD = 180° (angles on one side of the transversal)

Similarly, for the other side of the transversal, we have:

m∠BFD + m∠CFD = 180° (angles on one side of the transversal)

We are given that m∠AFC = (9x - 3)° and m∠BFD = (6x + 9)°, so we can substitute these values into the equations above:

(9x - 3) + m∠CFD = 180°

(6x + 9) + m∠CFD = 180°

Simplifying these equations, we get:

m∠CFD = 183 - 9x

m∠CFD = 171 - 6x

Since both of these expressions are equal to m∠CFD, we can set them equal to each other and solve for x:

183 - 9x = 171 - 6x

3x = 12

x = 4

Now that we have found x, we can substitute it back into the expression for m∠AFC to find its value:

m∠AFC = 9x - 3

m∠AFC = 9(4) - 3

m∠AFC = 33

Therefore, Line AB intersects line CD at point F. If m∠AFC = (9x − 3)° and m∠BFD = (6x + 9)°, then m∠AFC is 33 degrees.

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Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Total number of baseball cards will be given by expression 129 + c.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that represents a value or a quantity. Expressions can be written using various mathematical symbols such as addition, subtraction, multiplication, division, exponents, and parentheses.

Now,

If Raina had 129 baseball cards yesterday and got c more today, then the expression for the total number of baseball cards will be calculated after adding

So,

she has now can be written as:

Total number of baseball cards = 129 + c

Here, c represents the number of additional baseball cards that Raina got today, and the expression 129 + c gives us the total number of baseball cards she has now, including the cards she had yesterday and the new ones she got today.

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The number that is less than a whole, in 3 decimal places and when rounded to the nearest tenth is 0.78 will be 0.775.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position. The word decimus, which means tenth in Latin, is derived from the base word decem, or 10.

It should be noted that 0.775 is in 3 decimal places. In this case, the last 5 will be converted and this will become 0.78.

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The arrow's motion can be described by parametric equations: x = V₀cosθt and y = -4.9t² + V₀sinθt + h, where V₀ is the initial velocity, θ is the launch angle, t is the time, and h is the initial height. To determine the time the arrow is in the air before touching the ground and the maximum height reached, we need to solve for the corresponding values in the equations.

(a) To find the time the arrow is in the air before touching the ground for the final time, we need to determine the value of t when y equals zero (the ground level). We can set the equation -4.9t² + V₀sinθt + h = 0 and solve for t. This equation represents the vertical motion of the arrow. Once we find the value of t, we can round it to the nearest tenth.

(b) To determine the maximum height reached by the arrow, we need to find the vertex of the parabolic equation -4.9t² + V₀sinθt + h. The maximum height occurs at the vertex of the parabola, which corresponds to the highest point of the arrow's trajectory. We can use the formula t = -b/2a, where a = -4.9 and b = V₀sinθ, to find the time at which the maximum height is reached. Once we find the value of t, we can substitute it into the equation y = -4.9t² + V₀sinθt + h to calculate the maximum height, rounding it to the nearest whole number.

By solving for the time when the arrow touches the ground and finding the maximum height, we can better understand the arrow's motion and trajectory.

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Answer:

14.2 cm

Step-by-step explanation:

The hypotenuse of a triangle is measured using the pythagorean theorem. This formula sums up the squares of both legs of the triangle which would give the squared value of the hypotenuse. Therefore, we can then square root that value to find the hypotenuse. This would be the following...

\(9^{2} + 11^{2} = x^{2}\)

81 + 121 = \(x^{2}\)

202 = \(x^{2}\)

14.21 = \(x^{2}\)

Finally, we can see that the value of the hypotenuse is 14.2 cm

Answer:

Step-by-step explanation:

The dashed lines are included in the figure to help you see how it can be decomposed into shapes you know the area formulas for.

The relevant area formulas are ...

  rectangle: A = LW . . . . . product of length and width

  triangle: A = 1/2bh . . . . . half the product of base and height

__

There are three rectangles here:

  left: A = (8 cm)(9 cm) = 72 cm²

  top: A = (12 cm)(9 cm) = 108 cm²

  lower right: A = (12 cm)(9 cm) = 108 cm²

The total area of these three rectangles is ...

  (72 +108 +108) cm² = 288 cm²

The area of Figure 1 is 288 cm².

__

There is a rectangle here, along with a triangle.

  rectangle: A = (10 ft)(4 ft) = 40 ft²

  triangle: A = 1/2(6 ft)(3+4 ft) = 21 ft²

The total area of the parts of the figure is ...

  (40 +21) ft² = 61 ft²

The area of Figure 2 is 61 ft².

_____

Additional comment

Figure 1 can be decomposed other ways:

Another way to decompose Figure 2 is as a trapezoid with a rectangle removed from the lower left. The trapezoid would have bases 10 and 10+6=16, and a height of 4+3=7. The removed rectangle is 10×3. (The computation we did is probably simpler.)

Answer:2,100

Step-by-step explanation:

The distribution of X₁ - 3X₂ is a normal distribution with mean μ₁ - 3μ₂ and variance s₁² + 9s²₂ - 6rhos₁s₂.

To find the distribution of X₁ - 3X₂, we need to find the mean and variance of this new variable.

The mean of X₁ - 3X₂ is:

E(X₁- 3X₂) = E(X₁) - 3E(X₂) = μ₁ - 3μ₂

The variance of X₁ - 3X₂ is:

Var(X₁ - 3X₂) = Var(X₁) + 9Var(X₂) - 6Cov(X₁,X₂)

Since X₁ and X₂ have a bivariate normal distribution with means μ₁ and μ₂, variances s₁ and s₂ and correlation rho, we know that:

Var(X₁) = s²₁

Var(X₂) = s²₂

Cov(X₁,X₂) = rhos₁ s₂

Substituting these values into the variance equation, we get:

Var(X₁ - 3X₂) = s₁² + 9s²₂ - 6rhos₁s₂.

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Answer:

Congruent segments added to congruent segments forms congruent segment .

Answer:

y = 4x

Step-by-step explanation:

formula is y=kx, where k is factor of proportionality

Looking at the graph where y and x meet...

2/0.5 = 4 so 2 = 4(0.5)

Therefore, 4 is k (constant)

4=4(1)

6=4(1.5)

10=4(2.5)

and so on...

We have proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷  .

In the given question

we have to prove that

(2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷

For proving we will solve the LHS and RHS separately and then equate them .

First Solving LHS

we have

=(2*10²)*(3*10⁵)

=(2*3)*(10²*10⁵)

=6*10²⁺⁵       ...( because aⁿ.aˣ = aⁿ⁺ˣ )

=6*10⁷    ...(i)

Now solving RHS

we have

=3.5*10⁷+2.5*10⁷

taking 10⁷ common , we get

=(3.5+2.5)*10⁷

Adding the terms in the bracket we get

=6*10⁷     ...(ii)

As we can see that from equation (i) and (ii) we have LHS=RHS

Hence proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷

Therefore , Proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷  .

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The simplification of the expression given above would be =-8/171.

To simplify that expression given, the mixed fractions should first be converted to a single fraction.

That is

4¾ = 19/4

Then convert the division to multiplication sign;

That is ;

= -2/9 ÷ 19/4

= -2/9 × 4/19

= -8/171

Therefore, after the simplification of the given expression, the fraction determined would be = -8/171

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