The number of terms of the second arithmetic progression is 46.
How to find the number of terms of an arithmetic progression?The two arithmetic progression have the same first and last terms.
The first arithmetic progression has 21 terms with a common difference of 9.
The second arithmetic progression have common difference of 4.
Therefore,
using the first arithmetic progression,
a + (n - 1)d = nth term
a + 20(9) = last term
last term = a + 180
using the second arithmetic progression,
a + (n - 1)d = nth term
They have the same last and first term,
Hence,
a + 180 = a + (n - 1)4
a + 180 = a + 4n - 4
180 + 4 = 4n
184 = 4n
n = 184 / 4
n = 46
Therefore, the number of terms is 46
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Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to 9.
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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(2x-4)²=2x(x-2)+48 solve this ecuation
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]
Round 64.87 to the nearest tenth.
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:
what is the ratio for 1/3 kilograms to 2/3 foot
0.5kg per foot
Answer:
Step-by-step explanation:
At what speed should you enter an expressway? Question 1 options: 70mph 35mph the prevailing 10 miles below the freeway traffic
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.
The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The average speed of an object over a given period is calculated by dividing its total distance traveled over that time by its duration. Velocity and speed are not the same thing.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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Consider the relation
The domain of the relation is 2, 5, 3, 6 and 7.
How to find the domain of a relation?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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Which polynomial is prime?
x² + 7
x² - 25
3x²-27
2x²-8
answer is (a) just took the quiz
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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26. a)prove that a strictly increasing function from r to itself is one-to-one. b)give an example of an increasing function from r to itself that is not one-to-one.
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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After how much time to the nearest minute Will the cost of plan a be equal to the cost of plan b
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 answer is option AGiven y=x^2-2x-9 in standard form is y=(x+a)+b in vertexform, use completing the square to find a and b.
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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write an equation relating cost per student c to number of students n
Answer:
t=n*c where t=total cost
Step-by-step explanation:
Analyze the definition below and complete the instructions that follow.
Alaska is the biggest state in the United States of America.
Write the given definition as a biconditional.
A.
A state is Alaska if and only if it is the smallest state in the United States of America.
B.
A state is the biggest state in the United states of America if and only if it is not Alaska.
C.
If a state is Alaska, then it is the biggest state in the United States of America.
D.
A state is Alaska if and only if it is the biggest state in the United States of America.
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.
How to write a biconditional statement?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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You pay 10.5% sales tax on a $85 purchase. How much was the tax?
Answer:
85x10.5%=8.925
Step-by-step explanation:
Which statement best describes a graph of paired points that form a proportional relationship?
A straight line cannot be drawn through all of the the points, but the line passes through the origin.
A straight line can be drawn through all the points, but the line does not pass through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
A straight line cannot be drawn through all of the the points, and the line does not pass through the origin.
Answer: A straight line can be drawn through all the points, and the line passes through the origin.
Step-by-step explanation:
What is the volume of a cuboid with 10cm 8cm and 6cm
Answer:
480 cm³
Step-by-step explanation:
volume = width × heigh × length
volume = 10 cm × 8 cm × 6 cm
volume = 480 cm³
Hope it Help~
I NEED HELP RN WHAT IS (3x2.05+(_x1.09)+(2x_)+(_x_)
The value of the expression is 5x + 3.14
How to evaluate the expression?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)
The height h in feet that a pole vaulter can reach can be estimated using
the formula h = 20, where v is the velocity of the athlete in feet per second.
If the height for a women's pole vault is about 9.8 feet, about how fast was
the holder running? How far will the pole vaulter run in 2 seconds?
Using the numeric value of functions, it is found that the pole vaulter will run 50 feet farther in 2 seconds.
How to find the numeric value of a function/expression?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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I NEED HELP WITH THIS PLEASE
Answer: 4. 27x + 18 8. 4x - 5
Step-by-step explanation: should be right
A diver is standing on a diving board 5 1/4 feet above sea level.
He jumps off and dives into the water for a total of 15 1/2 feet.
How far below sea level is the diver?
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
Please help me do the Q1. 5 ii)
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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Line of Symmetry
Draw the line of Symmetry for each shape. Write how many
Which of the following is a true statement?
All negative numbers are above zero on the number line.
All positive numbers are to the left of zero on the number line.
All negative numbers are to the left of zero on the number line.
All statements are correct.
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.
Abc has vertices a(-2, "-1)" b(1,2 and c(2,-4) if a'b'c' is a dilation of abc with a scaled factor of 2.5 and center of dilation (0, 0), give the coordinates of the vertices of a'b'c
The new coordinates of the vertices a'b'c' are (-5, -2.5), (2.5, 5) and (5, -10) respectively of the triangle.
What is defined as the scale factor?Scaling (or dilation) is the process of making something bigger or smaller. As a result, if we scale this same coordinates points, we multiply the points by the scale factor to really get new coordinates points that are greater or less than the original points.For the given question;
The vertices of the triangle has the coordinates of a, b and c;
a = (-2, -1)b = (1, 2) c = (2, -4)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.
a' = 2.5×(-2, -1) = (-5, -2.5)b' = 2.5×(1, 2) = (2.5, 5)c' = 2.5× (2, -4) = (5, -10)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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There are 4 identical triangles, each with an area of 4 square units. When put together, they form a square. What is the side length of the square?
if you know this your smartest person in the world
SOMEONE please please pleaseee help me out...
Graph the lines in standard form.
A graph of the linear equation (3x + 2y = 6) in standard form is shown in the image attached below.
What is a graph?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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what is the fastest way to find the radius of a circle that's daimeter is 679.756
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!
75 [Chercher]
On considère l'expression suivante définie pour tout
ne Z par U(n)=n²+14n+33.
Résoudre U(n)=0.
Answer:
-11, -3
Step-by-step explanation:
[tex]n^2 + 14n+33=0 \\ \\ (n+11)(n+3)=0 \\ \\ n=-11, -3[/tex]
What is 7 divided by 534
Answer:
0.0131086142
Step-by-step explanation:
I just put in the calculator.
Features of the function f(x)=-log3x+6
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.
What are the properties of logarithms?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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