Call these numbers [tex]x,y[/tex]. Then [tex]x+y=7[/tex] or [tex]y=7-x[/tex].
We want to maximize their product,
[tex]f(x,y)=xy\implies f(x,7-x)=F(x)=7x-x^2[/tex]
We could consider the derivative, but I think that's overkill. Instead, let's complete the square:
[tex]7x-x^2=-\left(x^2-7x+\dfrac{49}4\right)+\dfrac{49}4=\dfrac{49}4-\left(x-\dfrac72\right)^2[/tex]
whose graph is a parabola opening downward with vertex at [tex]\left(\dfrac72,\dfrac{49}4\right)[/tex], so that the maximum product is [tex]\dfrac{49}4[/tex].
Now if [tex]x=\dfrac72[/tex], it follows that [tex]y=7-\dfrac72=\dfrac72[/tex].
The two numbers that have the maximum possible product and a sum of 7are 3.5 and 3.5
System of equationsLet the two number be x and y
If the sum of the numbers is 7, then;
x + y = 7 ........................ 1
If their product is at maximum, then;
xy = P ............................. 2
From equation 1, y = 7 - x
Substitute into equation 2 to have:
x(7-x) = P
P = 7x - x²
If the function is at maximum, then;
dP/dx = 7 - 2x
0 = 7 - 2x
x = 7/2
x = 3.5
Recall that x + y = 7
x = 7 - y
x = 3.5
Hence the two numbers are 3.5 and 3.5
learn more on system of equation here: https://brainly.com/question/14323743
Rectangle moat has vertices m(1,2), p(1,3), a(3,3) and t(3,2). Rectangle moat was translated 1 unit right and 2 units up to produce rectangle m’p’a’t’. Which coordinates describes the vertices of the image?
Answer:
M'(2,4), P'(2,5), A'(4,5), T'(4,4)
Step-by-step explanation:
The translation 1 unit to the right and 2 units up has the rule
(x,y)→(x+1,y+2)
Rectangle MPAT has vertices at points M(1,2), P(1,3), A(3,3) and T(3,2). The image rectangle is rectangle M'P'A'T'. According to translation rule:
M(1,2)→M'(2,4);P(1,3)→P'(2,5);A(3,3)→A'(4,5);T(3,2)→T'(4,4).The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is
g(x)?
ANSWER
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 6x + 9[/tex]
This can be rewritten as:
[tex]f(x) = {(x - 3)}^{2} [/tex]
If this function is shifted 5 units to the left to create g(x), the
[tex]g(x) = f(x + 5)[/tex]
We substitute x+5 into f(x) to get:
[tex]g(x) = {(x + 5 - 3)}^{2} [/tex]
[tex]g(x) = {(x + 2)}^{2} [/tex]
We expand to get:
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
A roulette wheel has 38 spaces: 18 red, 18 black, and 2 green. Suppose that in each spin of the wheel, the ball is equally likely to land on any of the 38 spaces, and that spins are independent. The wheel will be spun five times.
The chance that the ball lands on black in all five spins is closest to
a) 0.688%
b) 6.366%
c) 12.044%
d) 17.722%
e) 23.401%
Answer:
2.29%
Step-by-step explanation:
1. Chance of landing on black for one spin:
There are 38 spaces, and 18 lead to the wanted result. That means the chance is ¹⁸/₃₈, or about 0.47.
2. Chance for 5 spins.
We need to find (0.47)⁵, which is about 0.0229, which is 2.29%
That is none of the choices, but from every way I did this problem, that is the only solution I got.
Type the correct answer in the box. If you cut a 12-inch loaf of bread into 1/2-inch slices, you would have slices of bread.
Answer:
you would have 24 slices of bread
Step-by-step explanation:
(12 in)/(1/2 in/slice) = 12·2/1 slices = 24 slices
which of the following sets is closed under subtraction?
A. Integers
B. Whole Numbers
C. natural numbers
D. irrational numbers
Answer:
A. Integers
Step-by-step explanation:
Subtraction of whole or natural numbers can result in a negative number that is not in the set. Subtraction of irrational numbers can result in a rational number (√2 -√2 = 0, for example).
Final answer:
The Integers are closed under subtraction because the difference of any two integers is always an integer, while Whole Numbers, Natural Numbers, and Irrational Numbers are not, as their differences can result in numbers outside of their respective sets. Therefore, the correct answer is A.
Explanation:
When considering which of the following sets is closed under subtraction, we must understand what it means for a set to be 'closed' under an operation. A set is closed under subtraction if, when you subtract any two elements in the set, the result is also an element of the set.
Integers include whole numbers as well as their negative counterparts, such as -1, 0, and 1. When you subtract any two integers, the result is always another integer. Therefore, the set of integers is closed under subtraction.
Whole numbers, on the other hand, include 0 and all the positive integers. Subtracting a larger whole number from a smaller one would result in a negative integer, which is not included in the set of whole numbers. Thus, this set is not closed under subtraction.
Natural numbers are like whole numbers but don't include 0. Just like whole numbers, subtracting a larger natural number from a smaller one would result in a negative integer, which is not a natural number. Hence, natural numbers are not closed under subtraction.
Irrational numbers include quantities like π and √2. Subtracting two irrational numbers might result in a rational number, which is not an irrational number. Therefore, the set of irrational numbers is not closed under subtraction.
Therefore, the correct answer is A. Integers.
Let f(x)=x^2−9 and g(x)=x^2−7x+12 . What is (f/g)(x) ?
The answer is:
[tex]\frac{f(x)}{g(x)}=\frac{x+3}{x+4}[/tex]
Why?To solve the problem, we need to factorize the quadratic functions in order to be able to simplify the expression.
We can factorize quadratic functions in the following way:
[tex]a^{2}-b^{2} =(a-b)(a+b)[/tex]
Also, we can factorize/simplify quadratic expressions in the following way, if we have the following quadratic expression:
[tex]ax^{2}+bx+c[/tex]
We can factorize it by finding two numbers which its products give as result "c" (j) and its algebraic sum gives as result "b" (k), and then, rewrite the expression in the following way:
[tex](x+j)(x+k)[/tex]
Where,
x, is the variable.
j, is the first obtained value.
k, is the second obtained value.
We are given the functions:
[tex]f(x)=x^{2} -9\\g(x)=x^{2} -7x+12[/tex]
Then, factoring we have:
First expression,
[tex]f(x)=x^{2} -9=(x+3)(x-3)[/tex]
Second expression,
[tex]\g(x)=x^{2} -7x+12[/tex]
We need to find two number which product gives as result 12 and their algebraic sum gives as result -7. Those numbers are -4 and -3.
[tex]-4*-3=12\\-4-3=-7[/tex]
Now, rewriting the expression we have:
[tex]\g(x)=x^{2} -7x+12=(x-4)(x-3)[/tex]
So, solving we have:
[tex](f/g)(x)=\frac{f(x)}{g(x)}=\frac{(x+3)(x-3)}{(x+4)(x-3)}=\frac{x+3}{x+4}[/tex]
Have a nice day!
find the width of the rectangular prism if the volume is 165,000 the length is 100 mm and the height is 55
Answer:
30 mm
Step-by-step explanation:
The volume of a rectangular prism is the product of its three dimensions. To find the missing dimension, divide the volume by the product of the two that are given:
(165000 mm^3)/((100 mm)(55 mm)) = 165000/5500 mm^3/mm^2 = 30 mm
Answer:
30mm
Step-by-step explanation:
30mm
Solve the problem of exponential growth. In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
Answer:
[tex]127,000\ members[/tex]
Step-by-step explanation:
In this problem we have an exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
The base is equal to
b=1+r
r is the average rate
In this problem we have
a=23,000 members
r=5%=5/100=0.05
b=1+0.05=1.05
substitute
[tex]f(x)=23,000(1.05)^{x}[/tex]
x ----> is the number of years since 1985
How many members will there be in 2020?
x=2020-1985=35 years
substitute in the function
[tex]f(x)=23,000(1.05)^{35}=126,868\ members[/tex]
Round to the nearest thousand
[tex]126,868=127,000\ members[/tex]
Find the volume of the composite solid. Round your answer to the nearest tenth
Answer:
1131.0 m^3
Step-by-step explanation:
Let h1 represent the height of the top cone, and h2 the height of the bottom cone. The volume of a cone is given by the formula ...
V = (1/3)πr^2·h
so the volumes of both cones together will be ...
V = (1/3)πr^2·h1 + (1/3)πr^2·h2 = (1/3)πr^2·(h1 +h2)
= (1/3)π(6 m)^2(12 m + 18 m) = 360π m^3
≈ 1131.0 m^3
NEED HELP ASAP!
Find the area of the shaded region. All angles are right angles.
Answer:
166 m^2
Step-by-step explanation:
The enclosing rectangle is 9m by 29m, so is 261 m^2. From that, the white space of 5m by 19m = 95 m^2 must be subtracted. The result is that the shaded area is ...
261 m^2 -95 m^2 = 166 m^2
745 mmHg into psi
727 mmHg into kPa
55.5kPa into atm
Answer:
14.4059 psi96.9254 kPa0.5181347 atmStep-by-step explanation:
Google is your friend for such conversions. It will generally give answers correct to 6 significant figures.
___
Normal atmospheric pressure is defined as 1 atmosphere.
1 atm = 101,325 Pa = 760 torr (mmHg) ≈ 14.695 948 775 514 2 psi
To convert 745 mmHg into psi, divide the value by 51.71. 745 mmHg is approximately equal to 14.41 psi. To convert 727 mmHg into kPa, divide the value by 7.5. 727 mmHg is approximately equal to 96.93 kPa. To convert 55.5 kPa into atm, divide the value by 101.325. 55.5 kPa is approximately equal to 0.55 atm.
Explanation:To convert 745 mmHg into psi, divide the value by 51.71. Therefore, 745 mmHg is approximately equal to 14.41 psi.
To convert 727 mmHg into kPa, divide the value by 7.5. Therefore, 727 mmHg is approximately equal to 96.93 kPa.
To convert 55.5 kPa into atm, divide the value by 101.325. Therefore, 55.5 kPa is approximately equal to 0.55 atm.
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).
Answer:
secant slopes: -213.5, -187, -145, -113, -85tangent slope: -166Step-by-step explanation:
A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...
(change in gallons)/(change in time)
where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...
(3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute
__
B) The average of the secant slopes for points Q adjacent to P is ...
(-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute
The tangent slope at point P is estimated at -166 gpm.
The secant line joins two points on the curve of a graph.
The slopes of secant lines PQ are: -213.5, -187, -145, -113.5, -85The average slope of the tangent line is -166Point P is given as:
[tex]P = (15,1275)[/tex]
(a) The slopes of the secant lines PQ
The points are given as:
[tex]Q = \{(5,3410),(10, 2210),(20, 550) ,(25, 145),(30, 0) \}[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
For Q = (5,3410), the slope of the secant line is:
[tex]m_1 = \frac{1275 - 3410}{15 - 5}[/tex]
[tex]m_1 = \frac{-2135}{10}[/tex]
[tex]m_1 = -213.5[/tex]
For Q = (10, 2210), the slope of the secant line is:
[tex]m_2 = \frac{1275 - 2210}{15 - 10}[/tex]
[tex]m_2 = \frac{-935}{5}[/tex]
[tex]m_2 = -187[/tex]
For Q = (20, 550), the slope of the secant line is:
[tex]m_3 = \frac{1275 - 550}{15 - 20}[/tex]
[tex]m_3 = \frac{725}{-5}[/tex]
[tex]m_3 = -145[/tex]
For Q = (25, 145), the slope of the secant line is:
[tex]m_4 = \frac{1275 - 140}{15 - 25}[/tex]
[tex]m_4 = \frac{1135}{-10}[/tex]
[tex]m_4 = -113.5[/tex]
For Q = (30, 0), the slope of the secant line is:
[tex]m_5 = \frac{1275 - 0}{15 - 30}[/tex]
[tex]m_5 = \frac{1275}{-15}[/tex]
[tex]m_5 = -85[/tex]
(b) The slope of the tangent by average
The closest secant lines to tangent P are
[tex]Q = \{(10, 2210),(20, 550)\}[/tex]
This is so, because point P (15, 1275) is between the above points.
The slopes of secant lines at [tex]Q = \{(10, 2210),(20, 550)\}[/tex] are:
[tex]m_2 = -187[/tex]
[tex]m_3 = -145[/tex]
The average slope (m) is:
[tex]m = \frac{m_2 + m_3}{2}[/tex]
[tex]m = \frac{-187 - 145}{2}[/tex]
[tex]m = \frac{-332}{2}[/tex]
[tex]m = -166[/tex]
Hence, the average slope is -166
Read more about slopes of secant and tangent lines at:
https://brainly.com/question/20356370
twin bothers, collin and cameron get jobs immediately after graduating from college at the age of 22. collin opts for the higher starting salary, $55,000 and stays with the same company until he retires at age 65. his salary doubles every 15 years. cameron opts for the lower starting salary, $35,000 but moves to a new job every few years so that he doubles his salary every 10 years until he retires at age 65. what is the annual salary of each brother upon retirement?
Collin
22 years = 55,000 USD
+15 years
37 years = 2 x 55,000 = 110,000 USD
+15 years
52 years = 2 x 110,000 = 220,000 USD
Cameron
22 years = 35,000 USD
+10 years
32 years = 2 x 35,000 = 70,000 USD
+10 years
42 years = 2 x 70,000 = 140,000 USD
+10 years
52 years = 2 x 140,000 = 280,000 USD
+10 years
62 years = 2 x 280,000 = 560,000 USD
Retirement Salaries
Collin = 220,000 USD
Cameron = 560,000 USD
The graph given above shows the following function.
Period of a function is [tex]2\pi[/tex]. You can see on graph, the distance between two points lying on intersection with x axis and function is [tex]2\pi[/tex] so A would be an answer.
Jared bought one share of stock for $225.
A. He sold the stock for a profit of $55. what was the selling price of the stock?
B. The price of the stock dropped $40 the day after Jared sold it. At what price would Jared had sold it if he had waited until then?
Write equate and solve! Please Help!
Answer:
A. 280
B. 185
Step-by-step explanation:
A. Buying price of share stock= $ 225
Profit = $55
Selling price= Buying price + profit
[tex]= 225+ 55= 280[/tex]
Selling price= $280
B.
Decrease in price was by $40
Buying price= $225
New selling price if he had waited till then will be=
[tex]= 225-40 = 185[/tex]
=$185
What is Fermat’s Last Theorem?
Answer:
That is a VERY famous math problem first published in 1637 by Pierre Fermat. He said that in an equation of the type
x^n + y^n = z^n
you will ONLY find solutions when "n" is no greater than 2. He said he had a proof but the margin in his note book was too small to fit it in.
(It is now believed he never had any such proof.)
Anyway, we can find an infinite number of solutions when n = 2
3^2 + 4^2 = 5^5
5^5 + 12^2 = 13^2
but you cannot find any solutions when n = 3 or higher.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem
Finally in 1995, (358 YEARS after Fermat first published this theorem), the British mathematician Andrew Wiles published his own proof of this theorem.
https://en.wikipedia.org/wiki/Andrew_Wiles
Step-by-step explanation:
Final answer:
Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century, stating that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. The theorem remained unproven for over 350 years until Andrew Wiles presented a proof in 1994.
Explanation:
Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century. The theorem states that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. In other words, there are no whole number solutions to this equation when n is greater than 2.
This conjecture remained unproven for over 350 years and became one of the most elusive problems in mathematics. However, in 1994, the British mathematician Andrew Wiles presented a proof of Fermat's Last Theorem, which is considered one of the most significant achievements in the history of mathematics.
Solve. x 5 + 3 = 2
a) -5
b) 25
c) 5
d) - 1/5
The answer is D. Have a nice day.
Your answer should be d!
Help with IXL please
Answer:
$77.18
Step-by-step explanation:
Fill in your equation like this:
[tex]B=70(1+.05)^2[/tex] and
[tex]B=70(1.05)^2[/tex] and
[tex]B=70(1.1025)[/tex] so
B = $77.18
You invested $4,200 into an account that pays an interest rate of 3.5% compounded continuously. What is the balance of your account in 5 years?. Use formula
A=Pert
Answer:
[tex]A=\$5003.2[/tex]
Step-by-step explanation:
Use the exponential growth formula
[tex]A = Pe ^ {rt}[/tex]
Where A is the final amount in the account, P is the initial amount, r is the growth rate and t is the time in years
In this problem
We know that
[tex]P=4,200\\\\r=\frac{3.5\%}{100\%}= 0.035\\\\ t=5\ years[/tex]
So
[tex]A = 4,200e^{0.035t}[/tex]
Finally after 5 years the balance of the account is:
[tex]A=\$5003.2[/tex]
Salska and colleagues (2008) studied height preferences among dating partners. In their first study, they reviewed Yahoo personals for heterosexual individuals living within 250 miles of Los Angeles, California, and recorded the acceptable range of heights for their dating partners. The following table lists some of the results. Overall, did men or women show greater variability in their responses? Explain.Women MenPreferences M SD M SDShortestacceptableheight, inches 68.9 2.6 60.6 3.7Tallestacceptableheight, inches 75.3 2.2 69.8 2.7a) Women showed greater variability overall because the standard deviations for women were smaller than for men. b) Women showed greater variability overall because the means for women were larger than for men. c) Men showed greater variability overall because the means for men were smaller than for women.d) Men showed greater variability overall because the standard deviations for men were larger than for women
Answer:
D
Step-by-step explanation:
The larger standard deviation, the greater the variability. So even before looking at the data, we can eliminate a) and c).
The standard deviations of men's preference of shortest and tallest acceptable height (3.7 and 2.7, respectively) were more than the standard deviations of women's preference of shortest and tallest acceptable height (2.6 and 2.2, respectively).
So men showed greater variability overall because the standard deviations for men were larger than for women. Answer D.
Final answer:
Men showed greater variability in their height preferences for dating partners than women, as indicated by the larger standard deviations in men's responses.
Explanation:
The question asks whether men or women showed greater variability in their height preferences among dating partners based on a study by Salska and colleagues (2008). In the given study, variability is indicated by the standard deviation (SD) values. A larger standard deviation signifies greater variability in the responses. For the shortest acceptable height, men had an SD of 3.7 inches, while women had an SD of 2.6 inches. Likewise, for the tallest acceptable height, men had an SD of 2.7 inches versus women's 2.2 inches. These SD values clearly show that men displayed greater variability in their height preferences compared to women.
Will give brainliest if answered please answer quick
Given: circle k(O)
m∠OFQ = 52°
measure of arc FQ = (5x+1°)
Find: x
Answer:
x = 15°
Step-by-step explanation:
m∠DFQ = m∠OFQ = 52° (given), so arc DQ = 2·52° = 104°. Then arc FQ is the supplement of that, 180° -104° = 76°. The given relation to x is then ...
76° = 5x +1°
75° = 5x . . . . . . . subtract 1°
15° = x . . . . . . . . .divide by 5
A kite has a height of 36 inches and a width of 30 inches. Explain how to use the area formula for a triangle to find the area of the kite. 34
Answer:
You can view a kite as 4 triangles
Step-by-step explanation:
A geometric kite can easily be viewed as 4 triangles. The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.
According to the formula to calculate the area of a kite, we would get:
(36 x 30)/2 = 540.
If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.
The area of each triangle would then be: (18 x 15)/2 = 135
If we multiply this 135 by 4... we get 540.
Answer:
Draw a vertical line to break the kite into two equal triangles with a base of 36 and a height of 15. Use the formula A = 1/2bh to find the area of each. The sum of the areas is the area of the kite.
Step-by-step explanation:
What is (f−g)(x)? f(x)=5x^4+4x^3+3x^2+2x+1 g(x)=x^4+2x^3+3x^2+4x+5. Enter your answer, in standard form, in the box.
Answer:
[tex](f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]
Step-by-step explanation:
Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:
[tex](f-g)(x)=f(x)-g(x)[/tex]
Let's solve (f-g)(x) with [tex]f(x)=5x^{4}+4x^3}+3x^{2}+2x+1[/tex] and [tex]g(x)=x^{4}+2x^{3}+3x^{2}+4x+5[/tex]
[tex](f-g)(x)=(5x^{4}+4x^3}+3x^{2}+2x+1)-(x^{4}+2x^{3}+3x^{2}+4x+5)\\(f-g)(x)=5x^{4}+4x^3}+3x^{2}+2x+1-x^{4}-2x^{3}-3x^{2}-4x-5\\(f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]
.
Factor the expression. 6x^2 + 31x + 28
A.) (x + 4)(6x + 7)
B.) (x + 2)(6x + 14)
C.) (3x + 7)(3x + 4)
D.) (x + 14)(6x + 2)
Answer:
(6 x + 7) (x + 4) thus A:
Step-by-step explanation:
Factor the following:
6 x^2 + 31 x + 28
Factor the quadratic 6 x^2 + 31 x + 28. The coefficient of x^2 is 6 and the constant term is 28. The product of 6 and 28 is 168. The factors of 168 which sum to 31 are 7 and 24. So 6 x^2 + 31 x + 28 = 6 x^2 + 24 x + 7 x + 28 = 4 (6 x + 7) + x (6 x + 7):
4 (6 x + 7) + x (6 x + 7)
Factor 6 x + 7 from 4 (6 x + 7) + x (6 x + 7):
Answer: (6 x + 7) (x + 4)
The factored form of the expression '6x^2 + 31x + 28' is '(x + 4) (6x + 7)', which corresponds to option A.
Explanation:In factoring the expression '6x^2 + 31x + 28', we need to find two numbers whose product equals '6x2 * 28' (the product of the first and the last term), and sum equals '31x' (the middle term). The numbers that fit these conditions are '4' and '7'.
So, this means you can factor out 'x' from the terms '6x^2' and '31x' to get '6x*(x + 4)'. Then, you will be left with '+ 28'. The number '7' fits perfectly here, because '4 * 7 = 28'. Hence, the factored form of the expression is '(x + 4) (6x + 7)'.
This corresponds to the answer choice A.) (x + 4) (6x + 7).
Learn more about Factoring expressions here:https://brainly.com/question/34538246
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Select the correct answer from each drop-down menu.
The table shows the heights of the 10 tallest buildings in San Francisco and Los Angeles.
The average height of the 10 tallest buildings in Los Angeles is than the average height of the tallest buildings in San Francisco. The mean absolute deviation for the 10 tallest buildings in San Francisco is
The answer:
Answer with explanation:
[tex]\text{Average}=\frac{\text{Sum of all the observation}}{\text{Total number of Observation}}[/tex]
Average Height of tallest Building in San Francisco
[tex]=\frac{260+237+212+197+184+183+183+175+174+173}{10}\\\\=\frac{1978}{10}\\\\=197.8[/tex]
Average Height of tallest Building in Los Angeles
[tex]=\frac{310+262+229+228+224+221+220+219+213+213}{10}\\\\=\frac{2339}{10}\\\\=233.9[/tex]
→→Difference between Height of tallest Building in Los Angeles and Height of tallest Building in San Francisco
=233.9-197.8
=36.1
⇒The average height of the 10 tallest buildings in Los Angeles is 36.1 more than the average height of the tallest buildings in San Francisco.
⇒Part B
Mean absolute deviation for the 10 tallest buildings in San Francisco
|260-197.8|=62.2
|237-197.8|=39.2
|212-197.8|=14.2
|197 -197.8|= 0.8
|184 -197.8|=13.8
|183-197.8|=14.8
|183-197.8|= 14.8
|175-197.8|=22.8
|174-197.8|=23.8
|173 -197.8|=24.8
Average of these numbers
[tex]=\frac{62.2+39.2+14.2+0.8+13.8+14.8+14.8+22.8+23.8+24.8}{10}\\\\=\frac{231.2}{10}\\\\=23.12[/tex]
Mean absolute deviation=23.12
Answer:
1st -36.1 meters or more
2nd -23.12
Step-by-step explanation:
An arithmetic series contains 20 numbers. The first number is 102. The last number is 159. Which expression represents the sum of the series?
A.(20 (159-102/2)
B.(20(102+159/2)
C.20(102+159)
D.20(159-102)
Answer:
Option B
Step-by-step explanation:
we know that
The sum of an arithmetic series is equal to
S=n(a1+an)/2
where
a1 is the first term
an is the last term
n is the number of terms
In this problem we have
n=20
a1=102
an=159
substitute the values in the formula
S=20(102+159)/2
Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale.
Base: 12 cm
Height: 11 cm
NEED HELP ASAP!!!!!!!!!!!!!!
Answer:
528 cm^3
Step-by-step explanation:
The volume of a pyramid is given by the formula ...
V = 1/3·Bh
where B is the area of the base and h is the height.
The area of a square of side length s is given by ...
A = s^2
Then the area of the base of the pyramid is ...
A = (12 cm)^2 = 144 cm^2
So, the volume of the pyramid is ...
V = 1/3·(144 cm^2)(11 cm) = 528 cm^3
consider the diagram below. which of the following statements are correct? select all that apply
Answer:
• ΔCFB ~ ΔEDB by the AA similarity
• mCE = 46°
Step-by-step explanation:
No lengths are marked equal on the diagram, so we cannot assume any of the chords is the same length as any other. Then there is no evidence that the conditions for SAS congruence are met for the given triangles. Likewise, there is no evidence that arcs DE and CF are the same length, which they would have to be to have measure 108°.
The angles with vertices C and E subtend the same arc, so have equal measures. Likewise for the angles with vertices D and F. The angles CBF and EBD are vertical angles, so also congruent. Hence the two triangles are AA similar.
The angle labeled 72° is half the sum of the measures of arcs CE and DF, so we have ...
(CE + 98°)/2 = 72°
CE = 144° -98° = 46° . . . . . multiply by 2 and subtract 98°
Answer:
Answer:
• ΔCFB ~ ΔEDB by the AA similarity
• mCE = 46°
Step-by-step explanation:
If r^8=5 and r^7= 3/t , what is the value of r in terms of t?
Answer:
5t/3
Step-by-step explanation:
r^8=5 and r^7=3/t
here r^8=5
r^7×r=5
3/t×r=5
r=5t/3
The value of r in terms of t is 5t/3.
What are exponents?A term written aˣ is an exponential term. Its value is obtained by multiplying a with itself x number of times. The term aˣ is read as
a raised to the power of x.
How do we solve the given question?Given r⁸ = 5, r⁷ = 3/t. We are asked to determine the value of r in terms of t.
We will apply the exponential rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex].
Let our equations be r⁸ = 5 ... (1), and r⁷ = 3/t ... (2).
Dividing (1) by (2), we get
r⁸/r⁷ = 5/(3/t)
or, r⁸-⁷ = 5t/3 (using the rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex] )
or, r = 5t/3.
∴ The value of r in terms of t is 5t/3.
Learn more about the exponential rules at
https://brainly.com/question/11761858
#SPJ2
What is the value of x? 24
What is the problem about? Does x equal 24 in the problem?
Normally, x is an unknown variable that needs to be evaluated, so I don’t really know what x is at the moment. Please show me the problem so that I can solve the equation.