Answer:
the answer is 60
Step-by-step explanation:
Solve the equation (linear equation)
[tex](\frac{16}{9}) ^{2x +5} =(\frac{3}{4})^{x-7}[/tex]
Answer: [tex]x=-\frac{3}{5}[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
You can rewrite 16 and 9 as following:
16=4²
9=3²
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}[/tex]
As the base are equal, then:
[tex]-2(2x+5)=x-7[/tex]
Solve for x:
[tex]-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}[/tex]
12 points! Pls help.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the circle equations in general form with their corresponding equations in standard form.
Answer:
1) x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
2) x² + y² + 6x - 8y - 10 = 0 ⇒ No choice
3) 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
4) 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ No choice
5) 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
6) x² + y² + 2x - 6y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
Step-by-step explanation:
- The general form of the equation of the circle is:
* x² + y² + Dx + Ey + F = 0
where D , E and F are constant
- The standard form of the equation of the circle is:
* (x - h)² + (y - k)² = r²
where (h , k) is the center of the circle, r is the radius of it
- To chose the circle equations in general form with their
corresponding equations in standard form lets do that
1) x² + y² - 4x + 12y - 20 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-4)/2(1) = 2
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(12)/2(1) = -6
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (2)² + (-6)² - (-20) = 4 + 36 + 20 = 60
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 2)² + (y + 6)² = 60 ⇒ x² + y² - 4x + 12y - 20 = 0
2) x² + y² + 6x - 8y - 10 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(6)/2(1) = -3
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-8)/2(1) = 4
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-3)² + (4)² - (-10) = 9 + 16 + 10 = 35
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 3)² + (y - 4)² = 35 ⇒ there is no choice
3) 3x² + 3y² + 12x + 18y - 15 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(12)/2(3) = -2
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(18)/2(3) = -3
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-2)² + (-3)² - (-15/3) = 4 + 9 + 5 = 18
- We divide F by 3 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 2)² + (y + 3)² = 18 ⇒ 3x² + 3y² + 12x + 18y - 15 = 0
4) 5x² + 5y² - 10x + 20y - 30 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-10)/2(5) = 1
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(20)/2(5) = -2
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (1)² + (-2)² - (-30/5) = 1 + 4 + 6 = 11
- We divide F by 5 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 1)² + (y + 2)² = 11 ⇒ there is no choice
5) 2x² + 2y² - 24x - 16y - 8 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-24)/2(2) = 6
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-16)/2(2) = 4
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (6)² + (4)² - (-8/2) = 36 + 16 + 4 = 56
- We divide F by 2 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 6)² + (y - 4)² = 56 ⇒ 2x² + 2y² - 24x - 16y - 8 = 0
6) x² + y² + 2x - 12y - 9 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(2)/2(1) = -1
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-12)/2(1) = 6
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-1)² + (6)² - (-9) = 1 + 36 + 9 = 46
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 1)² + (y - 6)² = 46 ⇒ x² + y² + 2x - 6y - 9 = 0
Answer and Step-by-step explanation:
Answer:
# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
Step-by-step explanation:
* Lets study the problem to solve it
- Use the terms of x and y in the general form to find the standard form
∵ x² + y² - 4x + 12y - 20 = 0
- Use the term x term
∵ -4x ÷ 2 = -2x ⇒ x × -2
∴ (x - 2)²
- Use the term y term
∵ 12y ÷ 2 = 6y ⇒ y × 6
∴ (y + 6)²
∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60
∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
∵ x² + y² + 6x - 8y + 10 = 0
- Use the term x term
∵ 6x ÷ 2 = 3x ⇒ x × 3
∴ (x + 3)²
- Use the term y term
∵ -8y ÷ 2 = -4y ⇒ y × -4
∴ (y - 4)²
∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5
∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer
∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3
∴ x² + y² + 4x + 6y - 5 = 0
- Use the term x term
∵ 4x ÷ 2 = 2x ⇒ x × 2
∴ (x + 2)²
- Use the term y term
∵ 6y ÷ 2 = 3y ⇒ y × 3
∴ (y + 3)²
∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18
∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5
∴ x² + y² - 2x + 4y - 6 = 0
- Use the term x term
∵ -2x ÷ 2 = -x ⇒ x × -1
∴ (x - 1)²
- Use the term y term
∵ 4y ÷ 2 = 2y ⇒ y × 2
∴ (y + 2)²
∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11
∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer
∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2
∴ x² + y² - 12x - 8y - 4 = 0
- Use the term x term
∵ -12x ÷ 2 = -6x ⇒ x × -6
∴ (x - 6)²
- Use the term y term
∵ -8y ÷ 2 = -4y ⇒ y × -4
∴ (y - 4)²
∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56
∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
∵ x² + y² + 2x - 12y - 9 = 0
- Use the term x term
∵ 2x ÷ 2 = x ⇒ x × 1
∴ (x + 1)²
- Use the term y term
∵ -12y ÷ 2 = -6y ⇒ y × -6
∴ (y - 6)²
∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46
∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
Evaluate the expression
Answer:
The answer is
D.16
Step-by-step explanation:
Santos walks 2 kilometers south and then a certain number of kilometers east. He ends 5 kilometers away from his starting position.How many kilometers east did Santos walk?
Answer:
4.6 Or 4.60
Step-by-step explanation:
Like the other person said, 4.56. The question says "round to the nearest tenth" so 4.56 rounds to 4.60
Hope it helps~
To determine how many kilometers east Santos walked, we can use the Pythagorean theorem to find the distance traveled for each leg of the journey.
Explanation:To determine how many kilometers east Santos walked, we need to use the Pythagorean theorem to find the distance traveled for each leg of the journey. Since he ends up 5 kilometers away from his starting position, we can form a right triangle with the hypotenuse representing the total distance walked.
Let's assume Santos walked x kilometers east. The other leg of the triangle represents the 2 kilometers south he walked. Using the Pythagorean theorem, we have x2 + 22 = 52.
This simplifies to x2 + 4 = 25. Subtracting 4 from both sides gives us x2 = 21. Taking the square root of both sides, we find that x ≈ 4.58. Therefore, Santos walked approximately 4.58 kilometers east.
If -7(y – 3) = – 14, what is the value of y?If -7(y – 3) = – 14, what is the value of y?
Answer:
y = 5
Step-by-step explanation:
-7 (5 - 3) = -14
y = 5
I took the test.
Uncle Percy and the ratiolas are donating 75% of $84 where does the $84 fit in to proportion
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x-----> amount corresponding to 75%
we know that
using proportion
[tex]\frac{100}{84}\frac{\%}{\$} =\frac{75}{x} \frac{\%}{\$}\\ \\ x=84*75/100\\ \\ x=\$63[/tex]
A sandwich shop offers 4 different meats and 2 different cheeses. Suppose the sandwich shop offers 24 different meat-cheese sandwiches. How many different breads does the sandwich shop use?
Answer:
Step-by-step explanation:
You would do this question like this.
4 meats * 2 cheeses * x breads = 24 different kinds of sandwiches.
8x = 24
8x/8 = 24/8
x = 3
There are 3 different kinds of breads.
What is m∠A ? Can someone help me
Answer:
38°
Step-by-step explanation:
The triangle solver app on your calculator, phone, or tablet can solve this for you readily. There are on-line triangle solvers, too.
___
For solution "by hand", the Law of Cosines is useful. It tells you ...
a^2 = b^2 + c^2 -2ab·cos(A)
Then the angle A can be found as ...
cos(A) = (b^2 +c^2 -a^2)/(2ab) = (3^2 +7^2 -5^2)/(2·3·7) = 33/42 = 11/14
A = arccos(11/14) ≈ 38°
_____
In formulas like the Law of Cosines or the Law of Sines, the uppercase letters stand for the measures of angles, and the lowercase letters stand for their opposite side lengths.
A stack of playing cards contains 4 jacks, 5 queens, 3 kings, and 3 aces. two cards will be randomly selected from the stack. what is the probability that a queen is chosen and replaced, and then a queen is chosen again?
Answer:
1/9.
Step-by-step explanation:
There is a total of 15 cards in the stack.
Prob( Queen is chosen) = 5/15 = 1/3.
The probability of a second queen being chosen is also 1/3
Required probability = 1/3 * 1/3 = 1/9.
Choose the best definitions of parameter and statistic. A statistic is a variable that describes a sample and a parameter is a variable that describes a population. A parameter is an unknown characteristic of a group and a statistic is a known characteristic of a group. A statistic is a number that describes a population and a parameter is a number that describes a sample. A statistic is a number that describes a sample and a parameter is a number that describes a population. A parameter is a number that describes a population. A statistic is a number that is used to estimate a parameter.
Answer:
A statistic is a number that describes a sample and a parameter is a number that describes a population.
Step-by-step explanation:
The definition of "statistic" is:
A piece of data from a portion of a population.
The definition of "parameter" is:
A value that tells you something about a population.
Using these definitions, the correct answer to the question is that a statistic is a number that describes a sample and a parameter is a number that describes a population.
The correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.
What are parameters and statistics?A parameter is a number that describes the entire population (for example, the population mean).
What is a statistic?A statistic is a number that describes a sample (e.g., sample mean).
A few examples of statistics are:
The percentage of 2000 people who support the death penalty, as determined by a random sample.The median salary of 850 Boston and Wellesley college students.Weights of avocados from a single farm's standard deviation.Average screen time of 3000 Indian high school pupils.Hence, the correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.
Learn more about Parameter and statistics:
https://brainly.com/question/15077367
ow Important Is Regular Exercise? In a recent poll1 of 1000 American adults, the number saying that exercise is an important part of daily life was 753. Use StatKey or other technology to find a 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life. Click here to access StatKey. Round your answer to three decimal places. The 90% confidence interval is Enter your answer; the 90% confidence interval, value 1 to Enter your answer; the 90% confidence interval, value 2 . 1Rasmussen Reports, "75% Say Exercise is Important in Daily Life," March 26, 2011. eTextbook and Media
Answer:
0.731 < p < 0.775
Step-by-step explanation:
We have a sample proportion of 753/1000 = 0.753
We need to construct a 90% confidence interval for the population proportion. Since n > 30, we use the corresponding z-value of 1.645.
See attached photo for the formulas and construction of the confidence interval.
The 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life is 0.749 to 0.757.
Explanation:To find the 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life, we can use the formula for the confidence interval of a proportion. The formula is: CI = p ± Z * sqrt((p * (1-p))/n), where p is the sample proportion, Z is the z-score corresponding to the desired confidence level, and n is the sample size.
First, we need to calculate the sample proportion: p = 753/1000 = 0.753.
Next, we need to find the z-score for a 90% confidence level. Looking up the z-score in the standard normal distribution table, we find that the z-score for a 90% confidence level is approximately 1.645.
Now we can plug in the values into the formula: CI = 0.753 ± 1.645 * sqrt((0.753 * (1-0.753))/1000).
Calculating the expression inside the square root gives us approximately 0.0027. Plugging this value into the formula gives us the 90% confidence interval for the proportion: CI = 0.753 ± 1.645 * 0.0027.
Calculating this expression gives us the lower and upper bounds of the confidence interval: CI = 0.753 ± 0.0044.
Learn more about Confidence interval here:https://brainly.com/question/34700241
#SPJ3
Condense the following log into a single log:
[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]
Answer:
[tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]
Step-by-step explanation:
Given in the question an expression
[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]
To Condense this log into a single log we will use logarithm rules
1)Power rulelogb(x^y) = y ∙ logb(x)
[tex]\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}[/tex]
[tex]5log_{3} z = log_{3} z^5[/tex]
2)Product rulelogb(x ∙ y) = logb(x) + logb(y)
[tex]log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )[/tex]
3)qoutient rule[tex]logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5[/tex]
= [tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]
In quadrilateral ABCD the measures of, A , B , C, and D are the ratio of 1 :2:3:4, respectively. Find the measures of the four angles
So the ratio are 1:2:3:4 and all these add up to 10
Now we divide 360 by 10 resulting to 36
A=(36)
B=(72)
C=(108)
D=(144)
All these add up to 360 and has been divided equally according to the ration provided
Final answer:
To find the measures of the angles in quadrilateral ABCD with ratios 1:2:3:4, we set the angles as x, 2x, 3x, and 4x, and use the fact that their sum equals 360 degrees. Solving for x, we find x to be 36 degrees, which gives us the individual angles as 36 degrees, 72 degrees, 108 degrees, and 144 degrees respectively.
Explanation:
Calculating the Measures of the Angles in a Quadrilateral
Given that the measures of the angles A, B, C, and D in quadrilateral ABCD are in the ratio of 1:2:3:4 respectively, we first need to understand that the sum of the interior angles in a quadrilateral is always 360 degrees. To find the measure of each angle, we should express the ratio in terms of x, which would give us the angles as x, 2x, 3x, and 4x. Summing these and setting them equal to 360 degrees, we get the equation x + 2x + 3x + 4x = 360. Simplifying, we have 10x = 360, which when solved for x yields x = 36 degrees. Therefore, the measures of the angles are:
Angle A = 1x = 36 degrees
Angle B = 2x = 72 degrees
Angle C = 3x = 108 degrees
Angle D = 4x = 144 degrees
Hence, each angle's measure has been found using the given ratio and the property of the sum of interior angles in a quadrilateral.
evaluate tangent ^-1 1
Answer:
45° or π/4 radians
Step-by-step explanation:
You want the angle whose tangent is 1.
ArctangentYour calculator can evaluate the inverse tangent function for you.
arctan(1) = 45° = π/4 radians
Use the x-intercept method to find all real solutions of the equation.
x^2-9x^2+23x+15=0
Answer:
b.[tex]x=1,3,\:or\:5[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-9x^2+23x-15=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing tool.
The corresponding function is
[tex]f(x)=x^3-9x^2+23x-15[/tex]
The solution to [tex]f(x)=x^3-9x^2+23x-15=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(1,0),(3,0) and (5,0).
Therefore the real solutions are:
[tex]x=1,3,\:or\:5[/tex]
Find the value of the lesser root of x2 - 8x + 7 = 0.
A) -1
B) 1
C) 3
D) 5
Answer:
B) 1.
Step-by-step explanation:
x^2 - 8x + 7 = 0
(x - 1)(x - 7) = 0
x= 1, 7.
Answer:
x = 1
Step-by-step explanation:
Please express exponentiation using the symbol " ^ " : x^2 - 8x + 7 = 0
Let's solve this equations using "completing the square:"
x^2 - 8x + 7 = 0
1) Identify the coefficient of the x term. Here it's -8.
2) take half of that and square it: we get (-4)² = 16
3) insert " +16 - 16 " between the 8x and the 7:
x^2 - 8x + 16 - 16 +7 = 0
4) Rewrite this perfect square:
(x - 4)² - 16 + 7 = 0 -> (x - 4)^2 = 9
5) Solve for (x -4) by taking the square root of both sides:
x - 4 ± sqrt(9) -> x - 4 ± 3
6) Solve for x: x = 4 ± 3, or x = 7 and x = 1.
7) Take the lesser root of 7 and 1. That would be x = 1. Answer B is correct.
Subtract. Write your answer as a mixed number in simplest form. 5 5 over 11 - 1 3 over11
[tex] \frac{55}{11} - \frac{13}{11} = \frac{42}{11} \: or \:3 \frac{9}{11} [/tex]
A norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. what is the area of the largest possible norman window with a perimeter of 25 feet
Answer:
43.75 ft²
Step-by-step explanation:
Let r = the radius of the semicircle
and h = the height of the rectangle
Then 2r = the width of the window
The formula for the perimeter of a circle is C = 2πr,
so, πr = the perimeter of the semicircle
The perimeter of the window is
P = πr + 2h + 2r = 25
2h + (π +2)r = 25
h = ½[25 - (π + 2)r]
(1) h = 12.5 - (π/2 +1)r
The formula for the area of a circle is A= πr², so
½πr² = the perimeter of the semicircle
The area of the window is
(2) A = ½πr² + 2rh
Substitute (1) into (2).
A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²
A = 25r - (π + 2 - π/2)r²
(3) A = -(π/2 + 2)r² + 25r
This is the equation for a downward opening parabola.
One way to find the vertex is to set the first derivative equal to zero.
dA/dr = -2(π/2 + 2)r + 25 = 0
-(π + 4)r + 25 = 0
-(π + 4)r = -25
r = 25/(π + 4)
(4) r ≈ 3.50 ft
The maximum area occurs when r = 3.50 ft.
Substitute (4) into (1).
h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50) = 12.5 - 9.00 = 3.50
(4) h = 3.50 ft
Substitute (4) into (2)
A = 1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50
A = 43.75 ft²
The area of the largest possible Norman window with a perimeter of 25 ft is 43.75 ft².
The maximum area of a Norman window with a given perimeter of 25 feet can be found by creating an equation for the area, taking its derivative, setting it equal to zero and solving for the window's dimensions. This involves calculus, namely the method for optimization problems.
Explanation:The problem involves maximizing the area of a Norman window given a certain perimeter. The Norman window is composed of a rectangle and a semicircle, where the diameter of the semicircle equals the width of the rectangle. First, let's denote the width of the rectangle or the diameter of the semicircle as x. The radius of the semicircle will then be x/2. The height of the rectangle can be represented as 25 - x (since the perimeter of the window should equal 25 feet).
The area of a rectangle is height multiplied by width. The area of a semicircle is (1/2)πr2. So to find the area A of the Norman window, we add the area of the rectangle and the semicircle: A = x(25-x) + (1/2)π*(x/2)2.
To find the maximum area, we need to take the derivative of A with respect to x, set it equal to zero, and solve for x. We find x approximates to around 7.64 feet (after using calculus concepts). Then substitute x = 7.64 into the area function A and solve for A, which gives us the maximum area of the Norman window.
Learn more about Norman window here:https://brainly.com/question/33726043
#SPJ3
Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?
4, 12, 36, ...
4 + 12 + 36 + ...
4 + 12 + 20 + ...
4, 12, 20, ...
Answer:
4 + 12 + 36 + ...
Step-by-step explanation:
4, 12, 36, ... is a geometric sequence, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]
When we add the terms of a geometric sequence we get a geometric series.
4+12+36+ ... is a geometric series, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]
4 + 12 + 20 + ... is not a geometric series because it has no common ratio
[tex]\frac{20}{12}\ne \frac{12}{4}[/tex]
The second choice is correct
Select the correct answer from the drop-down menu.
Hector keep close tabs on his bank account. His account had a balance of -$22.80. The next day, he made a deposit of $56.60. His account balance changed to $.
Answer: $33.80
Step-by-step explanation: If Hector’s account was overdrawn by $22.80 and then he deposited $56.60 his balance would be $33.80
The formula to solve this is -22.80 + 56.60 = 33.80
Answer:
$33.80
Step-by-step explanation:
i did it on my test got it right
In a museum there is a sculpture in the shape of a cylinder the cylinder has a diameter of 12 feet and a height of h feet which equation can be used to find v the volume of the cylinder in cubic feet
Answer:
[tex]V=36 \pi h\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder (sculpture) is equal to
[tex]V=\pi r^{2}H[/tex]
In this problem we have
[tex]r=12/2=6\ ft[/tex] ----> the radius is half the diameter
[tex]H=h\ ft[/tex]
substitute the values
[tex]V=\pi (6^{2})(h)=36 \pi h\ ft^{3}[/tex]
Answer:
36πh cubic feet
Step-by-step explanation:
To find the volume of a cylinder with a diameter of 12 feet and a height of h feet, we must know the formula for finding the volume of a cylinder.
The volume V of a cylinder with a radius r and a height h is given as
V = πR^2h
where π = 22/7
Given that the radius of the given cylinder is 12 feet, the radius r
= 12/2 feet
= 6 feet
The volume v
= π * 6^2 * h
= 36πh cubic feet
Use substitution to write an equivalent quadratic equation. (3x + 2)2 + 7(3x + 2) – 8 = 0
Answer:
(u)^{2}+7(u)-8=0
Step-by-step explanation:
Answer:
The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0
Step-by-step explanation:
Here given (3x + 2)² + 7(3x + 2) – 8 = 0
Substitute 3x + 2 as y
Solving
y² + 7y – 8 = 0
The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0
help please 100 points
2 time legal assistant = 900,000 x 2 = 1,800,000
school teacher = 1,850,000
Difference = 1,850,000 - 1,800,000 = $50,000
Master degree for 26 weeks = 1326 x 26 = 34,476
Associates degree for 42 weeks: 792 x 42 = 33,264
Difference = 34,476 - 33,264 = $1,212
For 20 years she earned: $900,000
Twice that would be $1,800,000
So for 30 years the schoolteacher earns the same amount.
Answer:
The difference between the school teacher and the legal assistant is $50,000. The school teacher earns about twice as much in thirty years. The next answer is $1,212.
Step-by-step explanation:
The legal assistant makes $1,800,000 in 40 year. The school teacher in 30 years makes 1,850,000. 1,850,000 - 1,800,000= $50,000.
A person with the masters degree mages $34,476 in 26 weeks.The person with the Associates degree make $33,264 in 42 weeks.
For what value of x must ABCD be a parallelogram?
Justify your reasoning with theorems/postulates and show all work to receive credit.
Here is your answer
[tex]\bold{x= 6}[/tex]
REASON:
Theorem used: The diagonals of a parallelogram bisect each other.
Let diagonals AC and BD bisect each other at O
So, OA=OC
Now,
3x=4x-6 [OA=3x and OC=4x-6]
4x-3x= 6
x= 6
HOPE IT IS USEFUL
Answer:
Step-by-step explanation:
Parallelogram's diagonals theorem states that the diagonals in a parallelogram must bisect each other.
So for ABCD to be a parallelogram, the two diagonals must be divided in equal sections.
That is given for BD already.
For AC, 3x = 4x - 6
Rearranging, 4x - 3x = 6
x = 6
5 apples cost ?1.45. 3 apples and 2 bananas cost ?1.13. What is the cost of 1 banana
1.45÷5=0.29
0.29×3=0.87
1.13-0.87=0.26
0.26÷2=0.13
One banana costs 0.13
Final answer:
By setting up two equations based on the cost of apples and the combined cost of apples and bananas, we can calculate that the cost of one banana is \'0.13.
Explanation:
To solve the question about the cost of one banana, we need to set up two equations based on the given information. Let's denote the cost of one apple as 'A' and the cost of one banana as 'B'.
We are given that 5 apples cost \'1.45, which can be written as an equation: 5A = 1.45. We are also given that 3 apples and 2 bananas cost \'1.13, which can be expressed as the equation 3A + 2B = 1.13. By solving these two equations simultaneously, we can find the value of 'B', the cost of one banana.
First, we solve the first equation for A: A = 1.45/5. We get A = 0.29. Now, we substitute this value into the second equation: 3(0.29) + 2B = 1.13. This simplifies to: 0.87 + 2B = 1.13. Solving for B, we get: 2B = 1.13 - 0.87, hence B = (1.13 - 0.87)/2. After performing the subtraction and division, we find that B = 0.13.
Therefore, the cost of one banana is \'0.13.
A package shipment company recorded the number of packages received at each of two businesses, Aquarium World and Rare Vinyl. The line plots show the number of packages received at each business every day over 2 weeks.
What statement about the two plots’ distributions is true?
(A) The degree of overlap between the two distributions is moderate.
(B) There is no overlap between the two distributions.
(C) The degree of overlap between the two distributions is low.
(D) The degree of overlap between the two distributions is high.
Answer:B:There is no overlap between the two distributions hope this helps
Answer: There is no overlap between the two distributions
The base of a lampshade is in the shape of a circle and has a diameter of 13 inches. What is the circumference, to the nearest tenth of an inch, of the lampshade? (Use 3.14 for π.)
Question 3 options:
13.3 inches
20.4 inches
26.0 inches
40.8 inches
The circumference is found by multiplying the diameter by PI.
Circumference = 13 inches x 3.14 = 40.82
Rounded to the nearest tenth = 40.8 inches.
Answer:13.3
Step-by-step explanation:
plz help me
Charles and his friends started a community group in 2008 to address problems in their neighborhood and to host civic events. The group began with 40 members, and the number of members changed over time as shown in the graph, where the y-axis represents the number of members and the x-axis represents the number of years since 2008.
Which statement is true?
A.
The function indicates that the number of members is increasing at a rate that is constant.
B.
The function indicates that the number of members is increasing at a rate that is not constant.
C.
The function indicates that the number of members is decreasing at a rate that is constant.
D.
The function indicates that the number of members is decreasing at a rate that is not constant.
Answer:
B.
Step-by-step explanation:
Because the graph shown is not constant, if you look at when it hits a whole unit. It is increasing because it is moving right.
The true statement is:
B.
The function indicates that the number of members is increasing at a rate that is not constant.
Step-by-step explanation:We could write the data points as is given on the graph as follows:
x y
0 40
1 50
2 60
3 80
4 100
5 120
6 150
7 190
8 240
9 300
10 370
Hence, the rate of change from x=0 to x=1 is:
[tex]Rate=\dfrac{50-40}{1-0}\\\\\\Rate=\dfrac{10}{1}\\\\\\Rate=10[/tex]
Rate of change from x=3 to x=5 is:
[tex]Rate=\dfrac{120-80}{5-3}\\\\\\Rate=\dfrac{40}{2}\\\\\\Rate=20[/tex]
Hence, the rate is not constant.
Also we could see that with the increasing value of x the y-value also increases.
Hence, option: B is the correct answer.
Noah borrows $2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. The relationship between the amount of money, A, in dollars that Noah owes his father (including interest), and the elapsed time, t, in years, is modeled by the following equation. A=2000e^{0.1t}. How long did it take Noah to pay off his loan if the amount he paid to his father was equal to $2450? Give an exact answer expressed as a natural logarithm.
Answer:
ln(1.225)/0.1
Step-by-step explanation:
The credit all goes to @lucic , but the answer is expressed as a natural log
The difference of what number and 5 is 18?
Answer:
13
Step-by-step explanation:
18-5 = 13
X-5=18
Add 5 to both sides
X=23