Solve 4x + 2 = 12 for x using the change of base formula log base b of y equals log y over log b.a. −1.442114 b. −0.207519 c. 2.55789 d. 3.79248

The shortest distance between planet Q and planet R is 1.64 * 10⁷ km

An equation is an expression that shows the relationship between variables and numbers.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:

hypotenuse² = adjacent² + opposite²

From the diagram, QR is the shortest distance between planet Q and planet R. Hence using Pythagoras:

QR² = QP² + PR²

QR² = (3.6 * 10⁶)² + (1.6 * 10⁷)²

QR = 1.64 * 10⁷ km

The shortest distance is 1.64 * 10⁷ km

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Answer:

Step-by-step explanation:

-2x-3=-7

+3 +3
-2x=-4

/-2 /-2

x=2

Y=5(2)-9

Y=10-9

Y=1

Answer:

Step-by-step explanation:

y = 5x - 9 (eq'n 1)

-2x - 3 = -7 (eq'n 2)

Solve for x in (eq'n 2)

-2x -3 = -7 (add 3 to both side of the eq'n)

(-2x - 3) + 3 = -7 + 3

-2x = -4 (divide both side by -2)

x = 2

Therefore the value of y is:

From  (eq'n 1), Substitute the value of x

y = 5x - 9

y = 5(2) - 9

y = 1

Answer: The expression (st)(6) means to substitute the value of 6 into the function (st) which is the composition of two functions s and t. The order of applying the functions is crucial, so the first function s will be applied to the result of the second function t after being applied to the 6. So the correct equivalent of (st)(6) is s(t(6))

Step-by-step explanation:

The answer choices which represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.

As evident in the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.

It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).

On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.

Consequently, the required equations which model the total yards of of fabric Sophie will buy are; x + y = 28, 28 - x = y and 28 - y = x.

Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.

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Answer:

x+y=28
28-x=y
28-y=x

[tex]3 (2x - 4) = 3 (2x + 4)[/tex]

Distribute:

[tex](3)(2x)+(3)(-4)=(3)(2x)+(3)(4)[/tex]

[tex]6x-12=6x+12[/tex]

Subtract 6x from both sides:

[tex]6x-12-6x=6x+12-6x[/tex]

[tex]-12=12[/tex]

Add 12 to both sides:

[tex]-12+12=12+12[/tex]

[tex]0=24[/tex] (false)

[tex]\fbox{No solution}[/tex]

Answer:

False Expresion, Wrong , Error

Step-by-step explanation:

if solving for x

3 (2x - 4) = 3 (2x + 4) insert the 3 into the parenthesis [remember to imput for each element])

6x - 12 = 6x +12 False expression

if we decide to go further we would get

0x = 24

Answer:

A

Step-by-step explanation:

Your answer was correct.

Answer:

A, B, C, and G

Step-by-step explanation:

f(0)=75 is true because that's the y-intercept

f(30)=100 is true

f(20)=175 is true

f(0)=0 is not true because we already identified f(0) as 75

f(x)=100 when x=20 is not true because we already identified f(20) as 175

f(10)<f(5) is not true because looking at the graph, f(10)>f(5)

f(10)=f(15) is true because the graph is constant between the two points

Because it has a variable and that variable is raised to a certain power, the expression 3x2+2x is a polynomial.

A polynomial is a mathematical formula that involves only the operations addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

A polynomial term, a series term, or an expression's multiplicative factor is known as a coefficient in mathematics. In addition to being any statement, it is frequently a number. If the coefficients are variables in and of themselves, they may also be known as parameters.

The fact that the above phrase 3x2+2x contains a variable makes it a polynomial. The power of that variable is likewise increased. The mathematical expression that results becomes a polynomial.

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Answer:

D

Step-by-step explanation:

to find the 10th term substitute n = 10 into the rule, that is

2(10)² + 3

= 2(100) + 3

= 200 + 3

= 203

the 10th term is 203

The derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).

The given equation is x/y + y/x = 3y.

To find the derivative of y with respect to x (Dy/Dx), we will use implicit differentiation.

First, we will take the derivative of both sides of the equation with respect to x:

(1/y) * (Dy/Dx) + (1/x) * (Dy/Dx) + (y/x^2) * (Dx/Dx) = (3)(Dy/Dx)

We can simplify this expression by combining the terms with Dy/Dx and Dx/Dx:

(Dy/Dx)(1/y + 1/x + 3) = (y/x^2)(Dx/Dx)

Now we can solve for Dy/Dx by rearranging the equation:

Dy/Dx = (y/x^2)(Dx/Dx) / (1/y + 1/x + 3)

Finally, we can plug in our known values and solve for Dy/Dx:

Dy/Dx = (x/y)(Dx/Dx) / (3y - x - y)

Therefore, the derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).

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Answer:

X = 10

Step-by-step explanation:

In an ordered pair (x,y), the x-coordinate comes first, followed by the y-coordinate. The x-coordinate represents the horizontal position of the point on a coordinate plane and the y-coordinate represents the vertical position of the point on a coordinate plane.

For example, in the ordered pair (4,3), 4 is the x-coordinate, and it represents the horizontal position, and 3 is the y-coordinate, and it represents the vertical position of the point (4,3) on a coordinate plane.

Answer:

-4 and -4

Step-by-step explanation:

The account balance after 9 years is $528.28. The result is obtained by adding the interest to the initial deposit.

The simple interest of an amount of money can be counted by the following formula.

I = P₁ - P

I = P × r × t

Where

We have

Find the final account balance!

After 9 years, the simple interest of the savings is

I = P × r × t

I = $425.00 × 2.7% × 9 years

I = $3,825.00 × 0.027

I = $103.28

The final account balance would be

I = P₁ - P

$103.28 = P₁ - $425.00

P₁ = $425.00 + $103.28

P₁ = $528.28

Hence, after 9 years, the account balance would be $528.28.

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The percentage and the z-scores for specific heights of the given normal distributions are as detailed below.

The first step is to draw the Normal curve with 8 regions, and then we now label the 7 vertical dividing lines with the mean plus/minus one/two/three standard deviations:

By adding the percentage values in the areas indicated in the question, we will arrive at;

The percentage of Ixxians that are;

i) Over 30 inches tall = 100% - (2.35% + 0.15%) = 97.5%

ii) Over 45 inches tall =  13.5% + 2.35% + 0.15% = 16%

iii) Under 50 inches tall = 100% - (2.35% + 0.15%) = 97.5%

iv) under 40 inches tall = 34% + 13.5% + 2.35% + 0.15% =  50%

v) between 35 and 55 inches tall = 34% + 34% +  13.5% + 2.35% = 83.85%

vi) between 25 and 35 inches tall = 13.5% + 2.35% 15.85%

The z-score is defined as the number of standard deviations above the mean corresponding to the given value. Thus;

i. For a height of 32 inches, the z-score is;

z = [32-40]/5

z = -1.6

ii. For a height of 47 inches, the z-score is;

z = [47 - 40]/5

z = 1.4

iii. For a height of 51 inches, the z-score is;

z = [51 - 40]/5

z = 2.2

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Complete question is;

The hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]

a) What percentage of Ixxians are

i over 30 inches tall?

ii over 45 inches tall?

iii under 50 inches tall?

iv under 40 inches tall?

v between 35 and 55 inches tall?

vi between 25 and 35 inches tall?

b) What is the z-score for an Ixxian of height?

i. 32 inches?

ii. 47 inches

iii. 51 inches

According to the mathematical notations, we can say that in this case, Antonhy's reasoning is incorrect, because the expression abc is only one term and not three as he stated.

It corresponds to a term that has letters and numbers, which are separated only if there is a mathematical sign between them, such as the plus or multiplication sign, for example, to be an expression of three terms, the expression should be like this:

Therefore, we can consider that the term abc corresponds to a monomial, as it is only one term in an expression, and not three as supposed by Anthony.

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The rule for the linear function in the table include the following: y = 2x.

In order to write a rule for the linear function, we would have to use the point-slope form formula. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear function representing the relationship between the x-value and y-value in the given table as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (4 - (-4))/(2 - (-2))(x - (-2))

y + 4 = 8/4(x + 2)

y + 4 = 2(x + 2)

y = 2x + 4 - 4

y = 2x

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The expression (x+9) (x+3) ​in the simplified expanded form will be x² + 12x + 27.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (x+9) (x+3) ​

Simplify the expression, then we have

⇒ (x+9) (x+3) ​

⇒ x (x+3) ​+ 9(x+3) ​

⇒ x² + 3x + 9x + 27

⇒ x² + 12x + 27

The expression (x+9) (x+3) ​in the simplified expanded form will be x² + 12x + 27.

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The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r

This is defined as the ratio of distance to time taken usually in kilometers per hour, miles per hour.

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

How to write equation

Distance Saul biked = 300 kilometers

Number of hours it takes train travel = t

Speed of train travel (kilometers per hour) = r

Speed = Total distance travelled / Time taken

r = 300 / t

Equation that represents how many hours

Make t the subject of formula

r = 300 / t

cross product

r × t = 300

t = 300/r

Therefore,

The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r

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When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

The mass of an object determines the acceleration it experiences.

The force is 6 N if the object's acceleration increases to 3 m/s2.

Reason:

The parameters listed are;

The occupying force the object's acceleration.

The acceleration produced by a force, F, of 18 N is equal to 6 m/s2.

Newton's Second Law of Motion states that;

F = M × A

Where;

m = The object's mass

In light of the parameters, F = 18 N and a = 6 m/s2, we may determine the mass of the

the following is the provided object;

Weight = F/A

Therefore, the force acting when the acceleration is an is;

20 = 3 kg, where a = a = 6.67 m/s2.

When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

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The end behavior of the graphs of polynomial functions is determined by the highest degree of the polynomial.

For example, a polynomial with degree n will eventually approach infinity as x increases or decreases without bound. This can be expressed mathematically as:

f(x) = axn -> lim x->∞ f(x) = ∞

and

f(x) = axn -> lim x->-∞ f(x) = ∞

where a is a constant.

For a polynomial of degree n, the graph will have n-1 turning points. As the degree increases, the graph approaches a smooth curve. Additionally, the graph will have either one up-turn or one down-turn depending on the sign of the leading coefficient. If the leading coefficient is positive, the graph will have an up-turn; if the leading coefficient is negative, the graph will have a down-turn.

For example, the end behavior of the graphs of the polynomial f(x) = 2x3 + 2x2 - 2x - 1 has degree 3, so it will have 2 turning points and will have an up-turn as the leading coefficient is positive.

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A table of values basically lists the values of y for the given line given the values of x.

A table of values is a graphic organizer or chart that enables you to choose two or more points from which to make your graph.

Here is an illustration of a table of values for the equation y = 2x + 1.

Put x = 0, y = 1

Put x = 1, y = 3

The method to solve table of values are-

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Answer:

Table of Values of a Function displays the table of values for the given function.

Step-by-step explanation:

The procedure to use the table of values of a function calculator is as follows:

Step 1: Making a table of values allows you to graph a line using a slope-intercept form equation.

Step 2: To determine the coordinate point's corresponding y-values.

Step 3: Choose a few x values and enter those values into the equation.

Step 4: Create a graph and plot the points.

To draw the line, join the points together.

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Answer:

A

Step-by-step explanation:

using BODMAS

3×7=21+2=23

Answer:

134 + 48 = 182

182 + x = 335

x = 153

Answer:

153

Step-by-step explanation:

335-134=201

201-48=153

Step-by-step explanation:

f(x) = 2x² - 7x - 7

f(6) = 2(6)² - 7(6) - 7

f(6) = 72 - 42 - 7

f(6) = 23

The exponent 3 is called the power or index. It is the number that indicates how many times the base number (in this case 3) is multiplied by itself.

To determine this

For example, 3³ means 3 multiplied by itself 3 times, or 3 x 3 x 3 = 27. So 3 is the base number and 3 is the exponent or power.

In mathematical notation, the exponent is written as a small number or variable above and to the right of the base number, with a caret symbol (^) separating them. For example, 3³ is written as 3³, and x² is written as x².

Additionally, in mathematics, exponents are also used to represent the number of times a number is multiplied by itself, the exponent number represents how many times the number is being multiplied.

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On solving the provided question, we can say that volume of cylinder  =  [tex]\pi r^2h[/tex] = 13564.8

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

volume of cylinder  =  [tex]\pi r^2h[/tex]

[tex]\pi[/tex] = 3.14

r = 15 cm\

h = 18 cm

V = [tex]3.14*15*16*18[/tex] = 13564.8

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