The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.
Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
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find the other end point of the line segment with the given endpoint and midpoint endpoint: (6.9), midpoint (,-6)
The other endpoint of the line segment is (13.8, 6).
The midpoint of a line segment is the point that lies exactly halfway between the two endpoints.
In this case, we have one endpoint, (6.9), and the midpoint (0,-6). Here is how we find the other endpoint:
To find the other endpoint, we need to subtract the midpoint from the given endpoint and then multiply by 2. The midpoint formula is given by:
M = (x1 + x2) / 2 and (y1 + y2) / 2
Where M is the midpoint, (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
So, in our case, the other endpoint will be given by:
(x2, y2) = 2 * (6.9, 0) - (0, -6)
Expanding the expression, we get:
x2 = 2 * 6.9 - 0 = 13.8
y2 = 2 * 0 - (-6) = 6
Therefore, the other endpoint of the line segment is (13.8, 6).
Complete question:
Find the other end point of the line segment with the given endpoint and midpoint endpoint: (6.9), midpoint (0,-6)
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The US National Science Foundation collects data on the dollar amount for a grant given to a scientist in the Engineering field. A sample of this year’s grants is: (given in thousands of dollars)
22 5 26 23 27 50 100 70 90 25
Calculate and interpret the following statistics (show work to receive credit).
a. Median b. Q1 c. Q3 d. IQR e. Range
The statistics interpreted from the given data is:
a. Median = 26.5
b. Q1 = 22.5
c. Q3 = 60
d. IQR = 37.5
e. Range = 95
The given data sample of this year’s grants(given in thousands of dollars) in ascending order is :
5 22 23 25 26 27 50 70 90 100
The median of a data set is the middle value when the data is arranged in ascending or descending order. When number of values is even, there are two values in the middle, so we take the average of the two. So the median is
= (26 + 27)/ 2
= 26.5
The first quarter or the lower quartile (Q1), is the value under which 25%, that is first quarter of the data points are found when they are arranged in increasing order. Here Q1 is 0.25*10, that is 2.5th value, but its not possible. So we should interpolate
Q1 = 22.5
Similarly third quartile, Q3 is the value under which 75% of the data points are found when they are arranged in increasing order. So
Q3 = (70 + 50)/2
= 60
And inter quartile range (IQR)
= Q3 - Q1
= 60 - 22.5
= 37.5
Range is
= 100 - 5
= 95
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Suraj took a slice of pizza from the freezer and put it in the oven. The pizza was heated at a constant rate.
The table compares the pizza's temperature (in degrees Celsius) and the time since Suraj started heating it (in minutes).
Time (minutes) Temperature (degrees Celsius)
4
44
25
2525
6
66
40
4040
8
88
55
5555
How long did it take the pizza to reach
100
100100 degrees Celsius?
To reach a temperature of 100 degrees the pizza would take 750 minutes.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated.
The slope is given as:
m = (y2 - y1)/(x2 - x1)
Let
(x1,y1) = (6, 40)
(x2,y2) = (8, 55)
m = (55 - 40) / ( 8 - 6 )
m = 7.5 degrees per minute.
The pizza heats up an average of 7.50 degrees per minute
To reach a temperature of 100 degrees the pizza would take:
(100)(7.50) = 750 minutes.
Hence, to reach a temperature of 100 degrees the pizza would take:
(100)(7.50) = 750 minutes.
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Complete the steps for factoring 2x3 - 36x2 + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x =
(x²-18x+81)
=________ [x²-2(___)x+ ( )²]
(x-
_)(x-.
= 2 x (x-_9_²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.
What is expression ?There is a need for mathematical variable operations such addition, multiplication, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
Given :
=> 2x³ - 36x² + 162x
=> 2x(x²-18x+81)
=> 2x[ x² - 2 (9)x + (9)²]
=> 2x[(x-9)²]
Thus ,
factor comes out to be 2x[(x-9)²].
Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.
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If f ( x ) = x 2 + 2 x − 3 and g ( x ) = x 2 − 9 , find ( f g ) ( 4 ) and ( f + g ) ( 4 ) . ( f g ) ( 4 ) is , and ( f + g ) ( 4 ) is .
(Photo)
Pls help…
Answer:
3
28
Step-by-step explanation:
The expression (f/g) (4) is equal to f(4) / g(4).
f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21
g(4) = 4^2 - 9 = 16 - 9 = 7
So, (f/g) (4) = 21 / 7 = 3.
The expression (f + g) (4) is equal to f(4) + g(4).
f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21
g(4) = 4^2 - 9 = 16 - 9 = 7
So, (f + g) (4) = 21 + 7 = 28.
show that the additive inverse, or negative, of an even number is an even number using a direct proof.
Let x be an even number. Then, x = 2k for some integer k. The negative of x, -x, is equal to -2k, which is also an even number. Thus, the additive inverse of an even number is an even number.
An even number is any number that can be divided by 2 without any remainder, meaning that it can be written in the form x = 2k for some integer k. The additive inverse, or negative, of an even number, x, is -x. By definition, this is equal to -2k. As -2k can still be divided by 2 without any remainder, it is also an even number.
This can also be understood by looking at the positive and negative sides of the number line. If x is an even number, then it is two units away from 0. Therefore, -x is also two units away from 0, which means it is an even number. This shows that the additive inverse of an even number is an even number.
To prove this, we can look at a specific example. Let x = 8. Then, 8 = 2x4. The negative of 8, -8, is equal to -2x4, which is still an even number. Thus, this proves that the additive inverse of an even number is an even number.
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El largo de un terreno rectangular es 10 cm más que cuatro veces su
ancho. El perímetro es 70 cm. Halla las dimensiones.
multiplicativa, x=5 is Halla las dimensiones.
Describe the dimension formula with an example.The physical quantity is correctly described in terms of its fundamental unit according to the formulation of the dimensional formula. For instance, the formula for dimensional force is F=[MLT2]. It's because the unit of force is the Newton, or kg/s2.
Finding the required dimensiones:De acuerdo con las condiciones dadamultiplicativa s, plantear: 2x(10+x+4x) = 70 Aplicar la ley multiplicativa de distribución: 20+2+8x= 70
Reordenar los términos desconocidos al lado izquierdo de la ecuación: 2x+8x= 70-20
Combinar como términos: 10x = 70-20
Calcular la suma o diferencia: 10x = 50
Dividir ambos lados de la ecuación por el coeficiente de la variable: = 50 10
Calcular los dos primeros términos: a = 5
Therefore, Halla las dimensiones is x=5.
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Consider the function below. x= -1, 0,1,2 and f(x)= -2,3,8,13 Which of the following functions could be the inverse of function f?
Answer:
Step-by-step explanation:
A function is the inverse of another function if it "undoes" the original function. In other words, if you apply the original function to an input and then apply the inverse function to the result, you get the original input.
To find the inverse of a function, you can swap the input and output values of the original function, and then solve for the new input variable. For example, if the original function is f(x) = y, the inverse function would be f^-1(y) = x.
Given the function f(x) = -2, 3, 8, 13, it is not possible to find a simple algebraic inverse function for the given values of x = -1, 0, 1, 2. The inverse of a function is only well-defined if the function is one-to-one, meaning that for every output value, there is only one input value that maps to it. In this case, the function does not appear to be one-to-one, so it does not have an inverse function.
Although there are many treatments for bulimia nervosa, some subjects fail to benefit from treatment. In a study to determine which factors predict who will benefit from treatment, Wendy Baell and E.H. Wertheim found that self-esteem was one of the important predictors. The mean and standard deviation of posttreatment self-esteem scores for n = 21 subjects were
= 26.6 and s = 7.4, respectively. Find a 95% confidence interval for the true posttreatment self-esteem scores.
95% CI for the true posttreatment self-esteem score is:
(24.47, 28.73)
The formula for calculating a 95% confidence interval for the mean self-esteem score is as follows:
(standard deviation/square root of sample size) * (mean (critical value)
The standard deviation of a set of data is a measure of its spread or dispersion. It denotes the average deviation of individual values in a data set from the data set's mean.
A low standard deviation indicates that the data points are close to the mean, whereas a high standard deviation indicates that the data points are scattered across a wide range.
For a normal distribution and a 95% confidence level, the critical value is 1.96.
As a result, the 95% confidence interval for the mean posttreatment self-esteem score is as follows:
26.6 ± 1.96 * (7.4/sqrt(21)) = 26.6 ± 2.13
As a result, the 95% CI for the true posttreatment self-esteem score is:
(24.47, 28.73)
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The cost of direct materials transferred into the Bottling Department of Mountain Springs Water Company is $27,225. The conversion cost for the period in the Bottling Department is $7,596. The total equivalent units for direct materials and conversion are 60,500 liters and 63,300 liters, respectively. Determine the direct materials and conversion cost per equivalent unit. Round your answers to the nearest cent.
Cost of direct materials per equivalent unit = $0.45.
Conversion cost per equivalent unit = $0.12.
What is FIFO method?The FIFO method is the First In First Out method. It is an accounting method used for cost flow assumption purposes in the cost of goods sold calculation.
In the Bottling Department,
The cost of direct materials transferred = $27,225.
The conversion cost = $7,596.
The total equivalent units for,
Direct materials = 60,500 liters.
conversion = 63,300 liters.
By using FIFO method,
The cost of Direct materials per equivalent unit = [tex]\frac{27,225}{60,500}[/tex]
=$0.45
Conversion cost per equivalent unit = [tex]\frac{7596}{63,300}[/tex]
= $0.12
Hence, the cost of direct materials and conversion cost per equivalent unit is $0.45 and $0.12 respectively.
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If you want to solve the equation by completing the square, then rearrange the equation as x2−6x=11
and add 9 to each side.
If you want to solve the equation by using the quadratic formula, rearrange the equation as x2−6x−11=0
and substitute the values of 1, −6
, and −11
into the formula
Round to the nearest hundredth.
3±2√5 is the solution of the equation x²−6x=11
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation is s x²−6x=11
By completing the square, then rearrange the equation as x²−6x=11
add 9 to each side.
To find the solution of equation by quadratic formula, substitute 11 on both sides
x²−6x-11=0
a=1, b=-6 and c=-11
x=-b±√b²-4ac/2a
=6±√36+44/2
=6±√80/2
=3±2√5
Hence, 3±2√5 is the solution of the solution of the equation x²−6x=11
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Solve the inequality. Express your solution using interval notation. graph the solution set. -5(x-3) ≥ 3[4-(x+4)]
On solving the provided question we can say that The inequality we have here is -5(x-3) ≥ 3[4-(x+4)] => 15/17 ≥ x
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
The inequality we have here is
-5(x-3) ≥ 3[4-(x+4)]
-5x + 15 ≥ 12x
15 ≥ 17x
15/17 ≥ x
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How would the break-even period in this scenario change if you lived in another state? Research another state’s minimum coverage requirement and calculate the break-even period you calculated above for that state’s minimum coverage requirements. Assume that all other variables (premium, deductible, etc.) are the same. Specify the state you researched and its minimum coverage requirements in your answer.
The break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.
What is meant by break-even period?In business accounting, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company within a specified time period.
To calculate the break-even point in units use the formula:
Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or in sales dollars using the formula: Break-Even point (sales dollars) = Fixed Costs ÷ Contribution Margin.
Insurance Requirements the part of a commercial contract in which the types and minimum amounts of insurance the parties agree to provide in connection with their performance of the contract are specified.
A break even point is used in multiple areas of business and finance. In accounting terms, it refers to the production level at which total production revenue equals total production costs. In investing, the break even point is the point at which the original cost equals the market price.
Therefore, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.
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Use Figure 1 to evaluate the trigonometric function.
The values of the trigonometric functions for the angle theta in Figure 1 are:
sin (theta) = 0.6 ,cos (theta) = 0.8, tan (theta) = 0.75.
A right triangle with sides of 3, 4, and 5 units is shown in Figure 1. The definitions of sine, cosine, and tangent allow us to evaluate the trigonometric properties of the triangle's angles as follows:
Theta = opposite / adjacent = 3 / 4 = 0.75 Tan = opposite / adjacent = 3 / 5 = 0.6 Cos = adjacent / hypotenuse = 4 / 5 = 0.8
As a result, the trigonometric functions' values for the angle theta in Figure 1 are as follows:
Tan(theta) = 0.75, sin(theta) = 0.6, cos(theta), and 0.8.
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Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube as shown in the table below. Which sample will result in the greatest mean?
The sample that have the greatest mean is sample {4, 5, 2, 4, 3, 6}
The correct option is D.
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given:
Peter wants to estimate the mean value rolled on a fair number cube.
He has generated four samples containing five rolls of the number cube, as shown in the table below.
The mean of the data sample 1:
(1 + 4 + 5 + 2 + 4 + 3)/6 = 3.167
The mean of the data sample 2 = 3.83
The mean of the data sample 3 = 3.67
The mean of the data sample 4 = 24/6 = 4
Therefore, the mean of the data sample 4 has greatest mean.
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The complete question:
Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube, as shown in the table below. Which sample will result in the greatest mean? Sample Data Sample 1 4 5 2 4 3 Sample 2 2 2 6 5 6 Sample 3 4 6 3 4 2 Sample 4 5 2 4 3 6
need help
please help me
The shaded region in the graph represents the possible solution sets to the inequality.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the inequality -
x² + 15 ≥ 23
The given inequality is -
x² + 15 ≥ 23
Refer to the graph attached.
The shaded region represents the possible solution sets to the inequality above.
Therefore, the shaded region in the graph represents the possible solution sets to the inequality.
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Please help I will give brainleist
What is the balance after 3
years on a CD with an initial
investment of $2,200.00 and a
2.95% interest rate?
A. $2,205.90
C. $6,490.00
B. $2,329.80
D. $2,400.50
Answer:
Step-by-step explanation:
The balance after 3 years can be calculated as follows:
I = P * r * t
Where:
I = interest
P = principal amount (2200)
r = interest rate (0.0295)
t = time in years (3)
So,
I = 2200 * 0.0295 * 3
I = 153.1
The final balance would be:
P + I = 2200 + 153.1
P + I = 2353.1
The final balance after 3 years is $2353.1, which is closest to option B ($2,329.80).
Ariana Garnde is coming to north gulfport middle school for fundraising concer! nevaeh is selling this week, she sold 3 kids and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 6 adult tickets for $67. how much was each adult ticket, and how much was each kids tickets, i need graph solution, subtituion and elimination.
There are seven kids tickets and 4 adult tickets.
What is simultaneous equation?
We know that we have to solve the simultaneous equation here;
Let cost of one kids ticket be x and the cost of one adult ticket be y
3x + 9y = 75 ---- (1)
8x + 6y = 67 ----- (2)
We then have that multiplying (1) by 8 and (2) by 3
24x + 72 y = 600 ---- (3)
24x + 18 y = 201 --- (4)
Subtract (4) from (3)
54 y = 399
y = 7
Then;
3x + 9(7) = 75
x = 4
We are going to end up having that there are seven kids tickets and 4 adult tickets.
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Solve the triangle:
Answer: 101.6
Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:
[tex]Sin (Angle) = \frac{Opposite}{Hypotenuse} \\Cos (Angle) = \frac{Adjacent}{Hypotenuse} \\Tan (Angle) = \frac{Opposite}{Adjacent}[/tex]
For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:
[tex]Tan(Angle) = \frac{Opposite}{Adjacent}[/tex]
Since [tex]x[/tex] is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us [tex]x\\[/tex].
We can input our values to solve each triangle's side lengths.
(You have to use the calculator for these)
Small one:
[tex]Tan(60) = \frac{88}{Adjacent}\\Adjacent = \frac{88}{Tan(60)}\\Adjacent = \frac{88\sqrt{3} }{3} = 50.807 (3 d.p)[/tex]
Big one:
[tex]Tan(30) = \frac{88}{Adjacent} \\Adjacent = \frac{88}{Tan(30)} \\Adjacent = 88\sqrt{3} = 152.420 (3d.p)[/tex]
Now, to calculate [tex]x[/tex] , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)
[tex]88\sqrt{3} - \frac{88\sqrt{3} }{3} = 101.6 (1 d.p)[/tex]
That is the answer. If you did not understand it completely, please reach me back and I will help you :)
Write a paragraph summarizing how Chandragupta Maurya built and ruled the Mauryan Empire. Use these words or phrases in your summary: kingdoms, conquer, unite, force, central government.
The Maurya Empire was founded in 322 B.C. by Chandragupta Maurya, after overthrowing Dhana, the king of the Nanda dynasty. Chandragupta initiated battles to defeat and conquer the kingdoms left by Alexander the Great and gained additional lands west of the Indus River by force. He enlarged his power westward across central and western India, and by 320 B.C., the empire had fully occupied Northwestern India. Chandragupta Maurya became the first emperor to unite India into one state, under a central government.
Who is Chandragupta Maurya?Chandragupta Maurya was the creator of the Maurya Empire in ancient India. He established one of the largest empires on the Indian subcontinent.
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Express the statement as an equation. (Use k as the constant of proportionality.). A varies inversely as r. Use the given information to find the constant of proportionality. If r = 3, then A = 7. k=
The equation expressing the statement is A = k/r, where k is the constant of proportionality. Given that r = 3 and A = 7, the constant of proportionality can be found by rearranging the equation to k = A × r and substituting the given values to calculate: k = 7 × 3 = 21.
The statement "A varies inversely as r" can be expressed mathematically as an equation: A = k/r, where k is the constant of proportionality. This equation states that A is proportional to 1/r, meaning that as r increases, A decreases, and as r decreases, A increases. To find k, we can rearrange the equation to k = A × r and substitute the given values. In this case, if r = 3 and A = 7, then k = 7 × 3 = 21. Therefore, the constant of proportionality is 21. This equation can be used to determine the values of A, given a value of r, or the values of r, given a value of A. For example, if r = 4, then A = k/4 = 21/4 = 5.25. Conversely, if A = 10, then r = k/A = 21/10 = 2.1. This equation can be used to determine the values of A and r for any given situation.
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Let $\triangle ABC$ be a right triangle, and let $H$ be the point on side $\overline{AB}$ so that $\overline{CH} \perp \overline{AB}.$
[asy]
// Coordinates for 3-4-5 triangle
pair A = (5, 0);
pair B = (0, 0);
pair C = (1.8, 2.4);
pair H = foot(C, A, B);
draw(A--B--C--cycle);
draw(rightanglemark(B, C, A));
draw(C--H);
draw(rightanglemark(C,H,A));
label("$A$", A, E);
label("$B$", B, W);
label("$C$", C, N);
label("$H$", H, S);
label("$x$", midpoint(B--H), S);
label("$y$", midpoint(A--H), S);
label("$h$", midpoint(C--H), E);
label("$a$", midpoint(B--C), NW);
label("$b$", midpoint(A--C), NE);
[/asy]
Prove that
\[(x + h)^2 + (y + h)^2 = (a + b)^2.\]
The Proof of ( x + h)² +( y + h)² = (a + b)² is shown below.
What is Similarity?In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.
Given:
BHC and BCA are similar
HC / BC = CA / BA
so, h / a = b / ( x + y) ........... (1)
Working with your expansion
x² + h² = a² and
y² + h² = b²
So, subtracting out the equal parts we are left with
2xh + 2yh = 2ab ..........(3) divide through by 2
xh + yh = ab
h( x + y) = ab which we can rearrange as
h / a = b / ( x+ y)..............(2)
Since this is equal to (1) and it's just a rearrangement of (3) adding all the other equal parts of the expansion shows that
(x² + h²) + (y² + h²) + ( 2xh + 2yh) = a²+ b²+ 2ab
( x² + 2xh + h²) + ( y² + 2yh + h²) = ( a + b)²
( x + h)² + ( y + h)² = (a + b)²
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if the positive numbers from 1 to 116, inclusive, are written on a piece of paper, then the sum of all of the numbers that are written on the paper is
The sum of all the positive numbers from 1 to 116, inclusive, is 6350.
The sum of the first n positive integers can be found using the formula n(n+1)/2. In this case, n=116, so the sum of all the positive numbers from 1 to 116, inclusive, is 116 * 117 / 2 = 6350. This formula can be useful in a variety of mathematical and real-world applications, such as finding the total number of objects in a sequence or the total distance traveled by an object moving at a constant speed.
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Consider the basis B
of R2
consisting of vectors [5−1]
and [−7−4]
. Find x
in R2
whose coordinate vector relative to the basis B
is [x]B=[25]
x=?
The value for x vector is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].
What is a vector?
A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
Given a vector v ∈ R² let (x, y) be its standard coordinates, i.e., coordinates with respect to the standard basis [tex]e_1=\left[\begin{array}{ccc}5\\-1\end{array}\right][/tex] and [tex]e_1=\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex].
The desired coordinates x, y satisfy -
v = xe1 + ye1
So, the vector v is -
[tex]v=2\left[\begin{array}{ccc}5\\-1\end{array}\right] +5\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}10\\-2\end{array}\right] +\left[\begin{array}{ccc}-35\\-20\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex]
Therefore, the matrix is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].
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An inch is exactly 2.54
centimeters.
Write an equation to convert the number of inches x
to the corresponding length in centimeters.
Enter the equation in the box.
Answer:
x * 2.54 = centimeters
Step-by-step explanation:
The equation to convert inches to centimeters is as follows:
x inches * 2.54 cm/inch = y centimeters
Where x is the number of inches and y is the equivalent length in centimeters.
To elaborate, the conversion factor between inches and centimeters is 2.54 cm/inch, meaning that for every inch there are 2.54 centimeters. To convert from inches to centimeters, we simply multiply the number of inches by the conversion factor. This gives us the equivalent length in centimeters.
What is the sum of the first 45 terms of an arithmetic sequence if the sum of its 18 th and 28 th term is 36?
The sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.
Let the first term of the arithmetic progression be A and the common difference for the same be D.
So 18th term of the progression is = A + (18 - 1) D = A + 17D
28th term of the progression is = A + (28 - 1) D = A + 27D
Given that the sum of the 18th and 18th terms of the progression is 36.
So, A + 17D + A + 27D = 36
2A + 44D = 26
So now the sum of 45 terms of the arithmetic progression is given by,
= 45/2 [2A + (45 - 1)D]
= 45/2 [2A + 44D]
= (45/2) * 36
= 45 * 18
= 810
Hence the sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.
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the heights of a group of students, in centimeters, are 158, 162, 172,.157, 161.com. A) caculate the mean heaight . B) another student joins the group. his height is 169cm. calculate the new mean height?
Step-by-step explanation:
So basically To find the mean you have to add all the numbers and divide by how many numbers you have, but to do that you have to make sure the numbers are lined up correctly so
157,158,161,162,172 ( Correct Order ) Smallest to biggest now add these up
157 + 158 + 161 + 162 + 172 = 810 / 5 = 162
The mean height is 162 cm
The new mean height
Again we're going to do the same thing
157 + 158 + 161 + 162 + 169 + 172 = 979/6 = 163.16666 = 163 cm
Hence the first mean height is 162 cm and the new mean height is 162 cm
Which of the following are quadratic functions ? Check all that apply . A y = 3x - 4; y = (5x - 3x ^ 2)/4 + 1 B . . y = 2x ^ 2 - 3x + 7 D. y = x - x ^ 3
The answer options that are quadratic functions include the following:
B. y = (5x - 3x^2)/4 + 1.
C. y = 2x^2 - 3x + 7.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
Generally speaking, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function. c represents the constant.In this context, we can reasonably infer and logically deduce that the expressions that are quadratic functions include both y = (5x - 3x²)/4 + 1 and y = 2x² - 3x + 7 because they have a maximum exponent of two.
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Choose the lotion brand with lowest price per ounce. (2 points)
Brand A: 24 ounces for $2.25
Brand B: 40 ounces for $3.75
Both brands have the same price per ounce.
Not enough information is given.
Brand B
Brand A
Answer: Brand A: 24 ounces for $2.25
Brand B: 40 ounces for $3.75
Price per ounce for Brand A = $2.25 / 24 ounces = $0.09375
Price per ounce for Brand B = $3.75 / 40 ounces = $0.09375
Both brands have the same price per ounce.
Step-by-step explanation: