The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.
How to find the number of terms ?In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:
62 x- 4 y 5 zEach term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.
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The full question is:
How many terms are in the following expression 6 + 2 x - 4 y + 5 z
what is sum of a geometric series?
A geometric progression is the sum of the terms of a geometric progression. The nth partial sum of a geometric sequence can be calculated from the first term a1 and the common quotient r as: Sn=a1(1−rn)1−r.
A geometric progression is a sequence of numbers formed by multiplying the common quotient 'r' by each of the preceding numbers. The first term in this series is a1. And the nth partial sum of the series, Sn is calculated by multiplying the first term a1 by the magnitude (1-rn) divided by (1-r).
This equation gives us the sum of the first n terms of a geometric progression. For example, if a1 = 2 and r = 2, then partial sum S3 of the first three terms in the series is 2*(1-2^3)/(1-2)= 2/1 = 2. In other words is the sum of the first three terms of series '2.' The subsumed equation is very useful tool for computing sum of any number of terms in a geometric series.
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how many billion in a trillion
Answer:
1,000,000,000,000 = 1,000,000,000 × 1,000
Step-by-step explanation:
1,000,000,000,000 = 1,000,000,000 × 1,000One trillion equals a thousand billions, or a million millions.
Which of the following equations represents a linear function?
A. y = x/12
B. y = 1/2x^2
C. y= 3x
D. y = 2 (2 + 3)
Answer: Option A,C and D represents a linear equation
Step-by-step explanation:
In linear function the variable has the power raised to one.
In equation ,y=x/12 ,y=3x and y=2(2+3) all the variables has the power of 1
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we say a definite integral is improper if one is infinite, or if the is infinite.
One _____is infinite, or if
The_______is infinite
From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.
One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.
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what is the perimeter of a square whose diagonal is 3√2?
The perimeter of the square is 12 units.
Let's call the side length of the square "s". We can use the Pythagorean theorem to relate the side length of the square to its diagonal:
s² + s² = (3√2)²
2s² = 18
s² = 9
s = √9 = 3
So the side length of the square is 3. Since all sides of a square are equal, the perimeter of the square is 4 times the side length:
Perimeter = 4s = 4(3) = 12
Therefore, the perimeter of the square is 12 units.
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Explain :Multiply: 23.2 x 0.14 ___________________
As a result, 23.2 x 0.14 equals 3.248.
What does math's multiple mean?One of the four fundamental math processes, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual adding of sets of identical size.
To multiply 23.2 and 0.14,
23.2
x 0.14
---------
32.48 (0.2 x 0.14 = 0.028, write down 8 and carry over 2)
+ 232.0 (3 x 0.14 = 0.42, add carried over 2 to get 4, write down 0 and carry over 4)
--------
3.248 (the final answer)
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The correlation coefficient ranges from which two values? a. 0 and 1 b. −1 and +1 c. minus infinity and plus infinity d. 1 and 100
The correlation coefficient ranges from -1 to +1. (option b)
What is correlation?Correlation is a measure that is used in statistics to measure the relationship that exists between two variables. Correlation can either be positive, negative or zero.
Positive correlation exists when two variables move in the same direction. The correlation coefficient usually ranges from 0 to 1. Negative correlation exists when the two variables move in different direction. The correlation coefficient usually ranges from -1 to 0. Zero correlation is when there is no relationship between the variables.
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what is kilograms to pounds conversion?
Kilograms and pounds are two commonly used units of weight or mass.
The kilogram is the base unit of mass in the International System of Units (SI), while the pound is commonly used in the United States and other countries that use the imperial system. To convert from kilograms to pounds, you can multiply the weight in kilograms by 2.20462, since one kilogram is equivalent to 2.20462 pounds.
This conversion factor is useful in a variety of situations, such as when weighing people, animals, or objects in different parts of the world, or when calculating dosages of medications based on body weight.
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If CE=8 and ED=4, what are the possible lengths for AE and EB in the figure below?
2 and 16
6 and 2
4 and 4
2 and 30
Answer:
Step-by-step explanation:
eay ma boi
What are the coordinates of the focus of the parabola?
y=−0.25x^2+6
Please answer asap
The set of equation that models the point of intersection of the arrow
and the target is the option; y = -0.004·x² + 0.25·x + 8 and y = 0.22·x
What is parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix. Parabola is an integral part of conic section topic and all its concepts parabola are covered here.
here, we have,
The given parameters are;
Point of intersection of the line and the parabola is the point (48.63, 10.7)
Therefore, the point (48.63, 10.7) satisfies both the equation of the
parabola and the equation of the line, which by plugging in the value x =
48.67 in the different parabolas, we have;
The first set;
y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7, which corresponds with the ordered pair.
The linear function in the first set should be excluded, given y ≠ x in the
ordered pair.
In third set,
y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7,
while, from the ordered pair, we have;
y = C·x
10.7 = 48.63·x
Therefore;
y ≈ 0.22·x
The set of equations that best models the point of intersection of the arrow and target are therefore;
y = -0.004·x² + 0.25·x + 8 and y = 0.22·x
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whats the common denominatior of 1/2 3/4 3/7
Answer:
28
Step-by-step explanation:
Smallest common multiple of 2, 4 and 7 -> 28
An angle in a circle with vertex on the circle itself___AngleCentral angleInscribed angleChord
Answer:
Inscribed angle
Step-by-step explanation:
Central angles have the vertex as the center of the circle, and chords are not angles
Kim donated half of her pants to charity, and kept her 7 favorite pants. When she was done, she was left with 35 pairs of pants. How many pairs of pants did she have in the beginning?
The answer is 84 pairs of pants.
Explanation:
According to the problem, she donated half of her pants to charity, which means she donated (1/2)x pairs of pants.
After donating half of her pants, she kept her 7 favorite pairs of pants. So, the number of pairs of pants she kept is 7.
The problem states that she was left with 35 pairs of pants after donating half of her pants and keeping her 7 favorite pairs. This means that the remaining number of pairs of pants is (x/2) - 7 = 35.
Solving for x, we get:
(x/2) - 7 = 35
x/2 = 42
x = 84
Therefore, Kim had 84 pairs of pants in the beginning.
Answer:
my guess is 17 .,.
Step-by-step explanation:
ANSWER QUICKLY PLEASE
If XY = 24. XZ = 22, JQ = 9, and the radius of the circumscribed circle of AXYZ is 15, find QK.
The required, measure of QK is approximately 10.82.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.
First, we can use the Pythagorean theorem to find the length of side XZ:
[tex]XZ^2 = XY^2 - YZ^2[/tex]
[tex]YZ = \sqrt{(XY^2 - XZ^2) }[/tex]
[tex]= \sqrt(24^2 - 22^2) = 10[/tex]
The length of the perpendicular bisector of XY is half the distance between points A and the midpoint of XY. The midpoint of XY can be found by dividing the length of XY by 2:
midpoint of XY = (X + Y)/2
Since we are given the length of XY, we can find the coordinates of its endpoints X and Y. Let X be the origin (0,0) and let Y have coordinates (24,0) (since XY = 24). Then the midpoint of XY is the midpoint of XY
= (X + Y)/2
= (0 + 24)/2
= (12,0)
Now we can use the distance formula to find the distance between A and the midpoint of XY distance between A and the midpoint of XY
= [tex]= \sqrt((12 - 0)^2 + (0 - 15)^2)[/tex]
= [tex]\sqrt(12^2 + 15^2)[/tex]
=[tex]3 \sqrt(29)[/tex]
This is the length of the perpendicular bisector of XY, which passes through the center of the circumscribed circle. So the distance from Q to the center of the circle is the distance from Q to center = 15 - 9 = 6
Finally, we can use the Pythagorean theorem to find QK:
[tex]QK^2 = QJ^2 + JK^2 = QJ^2 + (distance \ from \ Q \ to\ center)^2[/tex]
[tex]QK^2 = 9^2 + 6^2 = 81 + 36 = 117[/tex]
[tex]QK = \sqrt(117)\\ = 10.82[/tex]
Therefore, QK is approximately 10.82.
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solve for this equation
8x+6=14-4(2-2x)
Answer: x should be equal to -2
Step-by-step explanation:
8x + 6 = 14 - 4(2 - 2x)
8x + 6 = 14 - 8 - 4x
8x + 6 = 6 - 4x
8x = - 4x
x = -2
What is the conversion of 60 pounds to dollars?
60 pounds when converted to dollars is 81.97 US dollars.
Countries like the United Kingdom, the South Sandwich Islands, the British Overseas Territories of South Georgia, and the British Antarctic Territory all use pounds as their official currency. Penny sterling, which is one-tenth of a pound, is the name for the lesser units that make up the pound.
The conversion rate of pounds to dollars can vary depending on the current exchange rate. However, as of February 20, 2023, the conversion of 60 pounds to dollars would be:
1 pound = 1.37 US dollars
Hence,
60 pounds = 60*1.37 dollars
= 81.97 dollars
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13. The temperature on a heated metal plate positioned in the first quadrant of the zy-plane is given by C(x, y) = 25e -(0–1)2-(3-1) a Assume that temperature is measured in degrees Celsius and that x and y are y each measured in inches. a. Determine Czz(x, y) and Cyy(x, y). Do not do any additional work to algebraically simplify your results. b. Calculate Cz(1.1, 1.2). Suppose that an ant is walking past the point (1.1, 1.2) along the line y=1.2. Write a sentence to explain the meaning of the value of C. (1.1, 1.2), including units. C. Calculate Cyy(1.1, 1.2). Suppose instead that an ant is walking past the point (1.1, 1.2) along the line z=1.1. Write a sentence to explain the meaning of the value of Cyy(1.1, 1.2), including units. d. Determine Czy(x,y) and hence compute Czy(1.1, 1.2). What is the meaning of this value? Explain, in terms of an ant walking on the heated metal plate. =
Answer: a)
C(x,y) = 25e^(-((x-1)^2 + (y-3)^2))
Czz(x,y) = ∂^2C/∂z^2 = 0 (since C does not depend on z)
Cyy(x,y) = ∂^2C/∂y^2 = 50e^(-((x-1)^2 + (y-3)^2))(2(y-3)^2 - 1)
b)
Cz(x,y) = ∂C/∂z = 0
Cz(1.1, 1.2) = 0
The value of Cz(1.1, 1.2) indicates the rate of change of temperature with respect to z at the point (1.1, 1.2), which is zero. In other words, the temperature does not change with respect to the height (z) at this point.
c)
Cyy(1.1, 1.2) = 50e^(-((1.1-1)^2 + (1.2-3)^2))(2(1.2-3)^2 - 1) ≈ -0.138
The value of Cyy(1.1, 1.2) indicates the rate of change of temperature with respect to y at the point (1.1, 1.2), which is approximately -0.138 °C per inch. In other words, as the ant moves along the line y=1.2, the temperature decreases by approximately 0.138 °C per inch.
d)
Czy(x,y) = ∂^2C/∂z∂y = 100e^(-((x-1)^2 + (y-3)^2))(y-3)
Czy(1.1, 1.2) = 100e^(-((1.1-1)^2 + (1.2-3)^2))(1.2-3) ≈ -43.44
The value of Czy(1.1, 1.2) indicates the rate of change of temperature with respect to both z and y at the point (1.1, 1.2), which is approximately -43.44 °C per inch per unit of height. In other words, as the ant moves along the line z=1.1 and simultaneously moves in the y-direction, the temperature decreases by approximately 43.44 °C per inch per unit of height.
Step-by-step explanation:
Anne and Beate together have $120, Beate and Cecilie together have $60, and Anne and Cecilie together have $70. How much money do they have in total?
Answer:
Step-by-step explanation:
$270 in total
Match each transformation of function fwith a feature of the transformed function.
domain of (0, ∞)
x-intercept of (-2, 0)
vertical asymptote of x =
j(x) = f(x+3)
g(x) = -f(x − 3)
h(x) = 3 f(x) - 3
range of (-3, ∞)
3
When we transform function f, the resulting transformed function may have certain features that are different from the original function.
⇒ g (x) = - f(x-3) is vertical asymptote of x=3
⇒ j (x) = f(x+3) is x-intercept of (-2,0)
⇒ h (x) = 3f(x) - 3 is domain of (0, ∞)
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given function is;
⇒ f(x) = log x
Hence, we get;
g(x) = -f(x+3)= - log(x+3)
g(x) =-f(x-3) is vertical asymptote of x = 3.
j (x) = f(x+3) = log (x+3)
Then, j(x) = f(x+3) is x-intercept of (-2,0)
Domain: As (0,∞),{x | x>0}
h(x) = 3f(x)-3 is domain of (0, ∞)
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The complete question is shown in figure.
Which digits are missing from this equation?
3. 58 × 100[(3 × 1) + (5 × 0. 1) + (8 × 0. 01)] × 100
= (3 × ) + (5 × ) + (8 × )
= 358
The digits missing from the equation are 100, 10 and 1 respectively. The solution has been obtained by using the concept of algebraic equation.
What is algebraic equation?
If a mathematical phrase has variables, constants, and algebraic operations, it is said to be "algebraic" (addition, subtraction, etc.). The expression must contain the equals sign and satisfy the algebraic equation.
We are given an expression as
3. 58 × 100[(3 × 1) + (5 × 0. 1) + (8 × 0. 01)] × 100
On multiplying, we get
= (3 × 100) + (5 × 10) + (8 × 1)
= 358
Hence, the digits missing from the equation are 100, 10 and 1 respectively.
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what is the answer to (7x + 2) (5x − 11)
Answer:
35xΔ2-67x-22
Step-by-step explanation:
Find an equivalent ratio in simplest terms: 56:88
Answer:
7:11
Step-by-step explanation:
The ratio is 56:88
We simplify by 8 and get the ratio
7:11
We can't simplify anymore, so the answer is 7:11
HURRY PLEASEEE
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 56.923 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 14 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
A) The hiker traveled 6.0 miles on the first day.
B) [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
C) The total number of miles the hiker will travel in 14 days≈168 miles.
Squence and Series:Series and sequence are the basic ideas in mathematics. A sequence is an ordered group of elements where repetitions of any kind are allowed, as opposed to a series, which is the sum of all components.
The distances are organized geometrically, with the first term being a1 and the common ratio being (1 + 10%) = 1.10.
The sum of the seven terms in the series is...
S7 = a1·(r^7 -1)/(r -1)
56.923 = a1·(1.1^7 -1)/(1.1 -1)
5.6923 = a1·0.9487171
Its value is obtained by dividing by the coefficient of a1:
5.6923/0.9487171 ≈ 5.999997 ≈ 6.000
The hiker traveled 6.0 miles on the first day.
Equation for Sn,
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
where ,
a= first term
r=common ratio
n=number of terms
[tex]S_{14} =\frac{6(1.1^{14}-1)}{1.1-1} \\\\S_{14}=167.84[/tex]
The total number of miles the hiker will travel in 14 days≈168 miles
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PLEASE !! HELP what is the slope of the line that contains the points ( -2, - 7/2) and (4,-4)
Work Shown:
-7/2 = -3.5
The two given points are (-2,-3.5) and (4,-4)
Let's use the slope formula.
[tex](x_1,y_1) = (-2,-3.5) \text{ and } (x_2,y_2) = (4,-4)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-4 - (-3.5)}{4 - (-2)}\\\\m = \frac{-4 + 3.5}{4 + 2}\\\\m = \frac{-0.5}{6}\\\\m = \frac{-1/2}{6}\\\\m = \frac{-1/2}{6/1}\\\\m = \frac{-1}{2}\div\frac{6}{1}\\\\m = \frac{-1}{2}*\frac{1}{6}\\\\m = -\frac{1}{12}[/tex]
The slope is -1/12
It means "go down 1 unit, then go to the right 12 units".
You can use a tool like GeoGebra to confirm the answer is correct.
how to convert 148 lbs to kg?
The value of the converting 148 pounds to kilograms is given by ( 67.1328 ) kilograms.
Units pounds and kilograms are required to measure the weight of a given object.One kilograms is equal to 2.20462 pounds.
⇒ 2.20462 pounds = One kilograms
⇒ One pounds = ( 1 / 2.20462 ) kilograms
⇒ One pounds = ( 0.4536 ) kilograms
Substitute the required value we have,
⇒ 148 pounds = ( 148 × 0.4536 ) kilograms
⇒ 148 pounds = ( 67.1328 ) kilograms
Therefore, the conversion of the 148 pounds to kilogram is equal to ( 67.1328 ) kilograms .
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The sum of a number times 9 and 30 is at most 15 what is the answer?
Answer:
x ≤ - 5/3
Step-by-step explanation:
Let the number be x
The sum of a number times 9 and 30 is at most 15 translates algebraically to
9x + 30 ≤ 15
Subtracting 30 both sides:
9x ≤ -15
Dividing by 9 both sides:
x ≤ - 15/9
or
x ≤ - 5/3
−f−5(2f−3)minus, f, minus, 5, left parenthesis, 2, f, minus, 3, right parenthesis ?
The expression f - 5(2f – 3) is equivalent to two other expressions, option (a) -11f-3 and option (b) -11f + 15.
In mathematics, an expression is a combination of symbols, operated on by certain mathematical operations to create a numerical value or a function.
To understand why this is the case, let's break down the expression.
The first part of the expression is just the variable f, so that is unchanged. The second part involves the multiplication of -5 and (2f – 3).
To evaluate this part, we need to use the order of operations. First, we multiply -5 and 2f and get -10f.
Then, we subtract 3 from this result and get -11f.
Therefore, the expression f - 5(2f – 3) is equivalent to -11f-3 and -11f + 15.
Therefore, the correct options are both (a) and (b).
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Complete Question:
Which expressions are equivalent to - f - 5(2f – 3)?
Choose all answers that apply:
a) -11f-3
b)-11f + 15
c) None of the above
How do you calculate Riemann sums?
Riemann sums are calculated by dividing the area under a curve into subintervals and approximating the area in each interval using a rectangle.
Riemann sums are a method of approximating the area under a curve by dividing the area into smaller subintervals and approximating the area in each interval using a rectangle. The width of each rectangle is determined by the size of the subinterval, and the height of the rectangle is determined by the value of the function at a specific point within the subinterval.
The sum of the areas of all the rectangles gives an approximation of the total area under the curve. The accuracy of the approximation increases as the width of the subintervals decreases, and as the number of subintervals increases, the approximation approaches the exact value of the area under the curve.
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2 dice are thrown simultaneously what is the probability that the sum of the faces that the
The probability of the sum of the faces that the 2 dice are thrown simultaneously can be found by using the formula for the probability of independent events, which is P(A) * P(B).
The probability of the sum of the faces when 2 dice are thrown simultaneously depends on the specific sum you are looking for. You can use the formula P(A) * P(B) and the number of possible outcomes for each sum to find the probability.
First, let's determine the probability of each event. The probability of rolling a specific number on a single die is 1/6, since there are 6 possible outcomes. Therefore, the probability of rolling a specific number on both dice is (1/6) * (1/6) = 1/36.
Next, we need to determine the number of possible outcomes for the sum of the faces. There are 11 possible sums (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), each with a different number of possible outcomes. For example, there is only one way to roll a 2 (1 + 1), but there are six ways to roll a 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1).
Finally, we can use the formula to find the probability of each sum. For example, the probability of rolling a 7 is (6/36) = 1/6. The probability of rolling a 2 is (1/36).
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Integral of the constant function f(x) = k is:
C
0
kx+C
k+C
Answer:
The integral of the constant function f(x) = k is: kx + C. This is because when you integrate a constant function, you are essentially finding the area under the graph. In this case, the area of the graph is equal to the value of k multiplied by the width of the graph (x) plus a constant.
