Two APs have the same first and last terms. Tye first AP has 21 terms with a common difference of 9. How many terms has the other AP if it's common difference is 4

Answer:

480 cm³

Step-by-step explanation:

volume = width × heigh × length

volume = 10 cm × 8 cm × 6 cm

volume = 480 cm³

Hope it Help~

Let

y ----> total charge in a month

x ----> number of minutes

so

Plan A

y=0.21x+11

Plan B

y=0.10x+20

Equate both equations

0.21x+11=0.10x+20

solve for x

0.21x-0.10x=20-11

0.11x=9

x=9/0.11

x=81.82 minutes

Convert to hours and minutes

81.82 minutes=60+21.82=1 hour 22 min

therefore

The following are the properties of the given logarithmic function f(x) = -log3x+6:

The function's domain is (0, ∞).

The function's range is  (-∞, ∞) i.e. the set of all real numbers.

At x = 0, the component shows the presence of a vertical asymptote.

The constant reflects the x-axis logarithm.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the function f(x) = -log3x+6

As per the above function,

The function's domain is (0, ∞).

The function's range is  (-∞, ∞) i.e. the set of all real numbers.

At x = 0, the component shows the presence of a vertical asymptote.

The constant reflects the x-axis logarithm.

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Answer:

85x10.5%=8.925

Step-by-step explanation:

Using the numeric value of functions, it is found that the pole vaulter will run 50 feet farther in 2 seconds.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

The formula for the velocity is given as;

v=8√h

where h is the height.

we have the height is of h = 9.8,

hence:

v = 8√(9.8) = 25 feet per second.

The holder was running at the rate of 25 feet per second.

Then, within two seconds, the distance is given as;

d = 25 x 2 = 50 feet.

Hence, The pole vaulter will run 50 feet farther in 2 seconds.

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Answer:

-11, -3

Step-by-step explanation:

[tex]n^2 + 14n+33=0 \\ \\ (n+11)(n+3)=0 \\ \\ n=-11, -3[/tex]

y = (x - 1)² - 10 is the vertex form of the equation y = x² - 2x - 9.

Given, y = x² - 2x - 9

The equation is already in standard form : y = ax² + bx + c

where a=1, b=-2 and c=-9 according to the equation y = x² - 2x - 9.

The vertex form of parabola is: y = a (x - h)² + k

The "a" in y = ax² + bx + c equation  and the "a" in equation y = a (x - h)² + k are the same attributes of a parabola, therefore, substitute 1 for "a" in equation y = a (x - h)² + k: y = (x - h)² + k.

"h" is the x coordinate of the axis of the vertex: h = [tex]\frac{-b}{2a}[/tex]

Substitute in the values: h = - ( -2 ) ÷ 2(1)

∴ h = 1

Then, Substitute the value of h into the y = (x - h)² + k.

y = (x - 1)² + k.

Using the coordinates x and y from the above equations,

k = 1² - 2(1) - 9

k = 10

Now, Substitute the value of k into the equation y = (x - 1)² + k.

y = (x - 1)² - 10.

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The most appropriate choice for trigonometric function will be given by

Greatest value = 2, least value = -3

What are trigonometric functions?

Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.

There are six trigonometric functions-

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta=\frac{perpendicular}{hypoteunse}\\ \\cos\theta=\frac{base}{hypoteunse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]

Here,

5 ii)

[tex]2 sin^{2} x - 3cos^{2}x \\2(1-cos^2x)-3cos^2x\\2 - 2cos^2x -3cos^2x\\2 - 5cos^2x\\[/tex]

Now,

[tex]0\leq cos^{2}x \leq 1\\ -1 \leq -cos^2x\leq 0\\-5\leq -5cos^2x\leq 0\\-5+2\leq 2-5cos^2x\leq 0+2\\-3\leq 2-5cos^2x\leq 2[/tex]

Greatest value = 2, least value = -3

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When written as a biconditional statement, the definition becomes D. A state is Alaska if and only if it is the biggest state in the United States of America.

When writing a biconditional statement, you are to combine the statement in question, with the converse of the same equation and then join them by using the words, "if and only if."

This kind of statement lets it be known that if the first statement is correct, then the second definition or statement is correct as well. The biconditional definition here is that a state can only be Alaska if and only if that state is the largest in the country.

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A graph of the linear equation (3x + 2y = 6) in standard form is shown in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship such as a linear equation is characterized by a straight line as shown in the image attached below.

Next, we would rewrite the linear equation in standard form as follows:

3x + 2y = 6

2y = 3x + 6

Dividing all through by 2, we have:

2y/2 = 3x/2 + 6/2

y = 3x/2 + 3

In conclusion, a graph which represents the linear equation (y = 3x/2 + 3) shows a proportional relationship between the value of x and y.

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Answer:

x = 2, 4

Step-by-step explanation:

[tex](2x-4)^2=2x(x-2)+48 \\ \\ 4x^2 - 16x+16=2x^2-4x+48 \\ \\ 2x^2-12x-32=0 \\ \\ x^2-6x-8=0 \\ \\ (x-2)(x-4)=0 \\ \\ x=2, 4[/tex]

Answer:

Step-by-step explanation:

5 1/4 feet above sea level minus 15 1/2 will equal the distance the diver is below sea level.

5 1/4 - 15 1/2 = 10 1/4 feet below sea level

0.5kg per foot

Answer:

Step-by-step explanation:

Answer: A straight line can be drawn through all the points, and the line passes through the origin.

Step-by-step explanation:

Answer:

t=n*c where t=total cost

Step-by-step explanation:

The new coordinates of the vertices a'b'c' are (-5, -2.5), (2.5, 5) and (5, -10) respectively of the triangle.

For the given question;

The vertices  of the triangle has the coordinates of a, b and c;

The dilation of the abc is factored with the scale factor of 2.5.

Thus, to find the new coordinates of a'b'c' multiply each value with 2.5.

Thus, the new coordinates of the vertices a'b'c' are (-5, -2.5), (2.5, 5) and (5, -10) respectively.

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The domain of the relation is 2, 5, 3, 6 and 7.

The domain of the relation can be found as follows;

The domain of a function is the set of all possible inputs for the function.

The domain are usually the independent variable of a function.

The domain are associated with the x values.

Hence, the domain of the relation is as follows:

domain = {2, 5, 3, 6 , 7}

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Answer:

0.0131086142

Step-by-step explanation:

I just put in the calculator.

Answer:

Step-by-step explanation:

The correct statement is all negative number are to the left of zero on a number line.

When you look at a number line you will see negative numbers, 0, then positive numbers ( -# ------- 0 -------- +#), you an see the negative numbers are on the left.

The polynomial function, x² + 7 is prime

What is a polynomial?

A polynomial is an expression in mathematics that consists of indeterminates (also known as variables) and coefficients and includes only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x² + 4x + 7 is an example of a polynomial with a single indeterminate x. In three variables, consider x³ + 2xyz² - yz + 1.

The polynomial function, x² + 7 is prime.

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At a speed of 10 mph below the freeway traffic one should enter the expressway.

The speed of an object, also known as v in kinematics, is a scalar quantity that depends on the magnitude of the change in that object's position over time or the magnitude of the change in that object's position per unit of time.

Now of the given options since the respective speeds on various expressways are different it is tangible than to enter an expressway one must use less speed than the speed of the traffic on the expressway.

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The value of the expression is 5x  + 3.14

The expression is given as

(3x + 2.05) + (-x + 1.09) + (2x) + (x)

Open the brackets

So, we have the following equation

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x + 2.05 - x + 1.09 + 2x + x

Collect the like terms

So, we have the following equation

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x - x + 2x + x  + 2.05 + 1.09

Evaluate the like terms

So, we have the following equation

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 5x  + 3.14

Hence, the value of the expression given as (3x + 2.05) + (-x + 1.09) + (2x) + (x) is 5x  + 3.14

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Possible question

What is (3x + 2.05) + (-x + 1.09) + (2x) + (x)

Answer:

64.9

Step-by-step explanation:

Since 7 is equal to or above 5 it will add +1 to the 8

Answer:

64.87 rounded to the nearest tenth is 64.9 since it is past 5 :)

Step-by-step explanation:

Answer: 4. 27x + 18            8. 4x - 5

Step-by-step explanation: should be right

The quadratic equation is [tex]9x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]

Quadratic Equation:

A quadratic function is a function of degree two.

The general form of the quadratic equation is as follows:

x² + (sum of roots)x + Product of roots.

Given,

Here we have the roots,

[tex]\frac{-1-\sqrt{2} }{3} ,\frac{-1+\sqrt{2} }{3}[/tex]

And the coefficient with x² is equal to 9.

Through the given details we have to find the quadratic equation.

To find the equation we have to identify the sum of roots and the product of roots.

So, the sum of roots is,

[tex]= > \frac{-1-\sqrt{2} }{3} +\frac{-1+\sqrt{2} }{3}[/tex]

[tex]= > \frac{-1 }{3} +\frac{-1 }{3}\\= > \frac{-2}{3}[/tex]

Now the product of roots is,

[tex]= > \frac{-1-\sqrt{2} }{3} \times\frac{-1+\sqrt{2} }{3}[/tex]

[tex]= > \frac{1-\sqrt{2}-\sqrt{2}-2 }{3}=\frac{-1-2\sqrt{2} }{3}[/tex]

So, the quadratic equation is,

[tex]= > 9x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]

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a) f is strictly increasing function then f is one to one

b) f: R-> R such that f(x) = x^n where n is even is not one to one

suppose that f is strictly increasing function

we have to prove that f is one to one

let us assume f(x1) = f(x2)

we have to prove x1=x2

since f is strictly increasing function

then x2>x1 and x1> x2

this implies that x1=x2

and Hence f is one to one function

b) f:R->R such that f(x) = x^ n where n is even is not one to one

because f(1)= f( -1)

but -1 is not equal to 1 therefore f is not one to one function

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Answer:

divide it in half it would be 339.878

Step-by-step explanation:

radius is half of a diameter

Hello

By definition:

 ⇒ the diameter of a circle is twice the length of the radius of the circle

Thus if the diameter is 679.756:

   [tex]\text{radius} = \dfrac{679.756}{2} = 339.878[/tex]

Hope that helps!