Is the inequality always, sometimes or never true?
9(x+2) > 9(x-3)
answer is 2>3 and i said it's never true, right?
2. 6x-13 < 6(x-2)
answer is 6x-13 < 6x-12 my answer is sometimes
3. -6(2x-10) + 12x less than or equal to 180. im stuck.,
Simplify the imaginary number square root of -12
The square root of -12, an imaginary number, can be simplified to 2i√3. This involves breaking -12 into -1 * 12 and taking the square root of both parts to get 'i' and 2i√3 respectively.
Explanation:The question asked is to simplify the imaginary number square root of -12. Imaginary numbers are those numbers whose square is less than or equal to zero. They are expressed in the form of 'i' where 'i' is the imaginary unit with the property i^2 = -1. When we take square root of a negative number, 'i' is involved in the solution.
To simplify the square root of -12, we can express -12 as -1 * 12. In this case, square root of -1 is 'i' and square root of 12 is 2 * square root of 3 (since 12= 4*3 and square root of 4 is 2).
Therefore, square root of -12 can be written as 'i' * 2 * square root of 3 or simply 2i√3.
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A regular n-gon has an interior angle and an exterior angle with equal measures. What is the value of n?
What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0
Answer:
The slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
Step-by-step explanation:
If a line is defined as
[tex]Ax+By+C=0[/tex] ... (1)
Then the slope of the line is
[tex]m=\frac{-A}{B}[/tex]
The given equation is
[tex]3x+2y-6=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=3, B=2, C=-6[/tex]
The slope of the line is
[tex]m=\frac{-3}{2}[/tex]
The slope of parallel line is same. So, the slope of required line is -3/2.
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of required line is -3/2 and y-intercept is at (0,0).
[tex]y=\frac{-3}{2}x+0[/tex]
[tex]y=\frac{-3}{2}x[/tex]
Therefore the slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
Solve 2x2 + 3x = −8.
Solving the quadratic equation 2x² + 3x = - 8 for x, x = - 3/4 ± i√55/4
To solve 2x² + 3x = - 8, we proceed as follows.
Since we have the quadratic equation 2x² + 3x = - 8, to solve by completing the square, we rewrite the equation as
2x²/2 + 3x/2 = - 8/2
x² + 3x/2 = - 4
Next, we add the square of half the coefficient of x to both sides. So, we have that
x² + 3x/2 + (3/2 ÷ 2)² = - 4 + (3/2 ÷ 2)²
x² + 3x/2 + (3/2 × 1/2)² = - 4 + (3/2 × 1/2)²
x² + 3x/2 + (3/4)² = - 4 + (3/4)²
(x + 3/4)² = - 4 + 9/16
(x + 3/4)² = (-64 + 9)/16
Now, taking the square root of both sides, we have that
(x + 3/4)² = -55/16
√(x + 3/4)² = ±√(-55/16)
x + 3/4 = ±√-55/4
x + 3/4 = ±i√55/4
x = - 3/4 ± i√55/4
So, the value of x = - 3/4 ± i√55/4
how do you solve "z+ma=ba" solve for a
Final answer:
To solve the equation for a, subtract z from both sides, factor out a, and then divide by (m - b), resulting in a = -z / (m - b), assuming m and b are not equal.
Explanation:
To solve the equation z + ma = ba for a, we need to isolate a on one side of the equation. We can rewrite the equation, moving all terms involving a to one side and all other terms to the opposite side. This process is called collecting like terms.
Here are the steps to isolate a:
Subtract z from both sides of the equation to get ma = ba - z.
Since both terms on the right hand side involve a, factor a out: a ( m - b ) = -z.
Finally, divide both sides of the equation by (m - b) to solve for a: a = -z / (m - b), assuming that m ≠ b.
This algebraic manipulation gives us the value of a in terms of z, m, and b.
If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
For a better understanding of the explanation provided here, please go through the graphs in the attached files. The first file contains the explanations to the first part of the question and the second file contains the three graphs required to explain the second part (the y intercept part) of the question.
It has been given to us that the pH concentration equation is:
[tex] p(t)=-log_{10}t [/tex]
where, The variable t represents the amount of hydronium ions and p(t) gives the resulting pH level.
As can be seen from the first graph, pH is 1 when the amount of hydronium ions, t is 0.1. This is as expected, because, from the concept of logarithms we know that:
[tex] log_{10}(0.1)=log_{10}(\frac{1}{10})=log_{10}(10^{-1})=-1\times log_{10}10=-1\times 1=-1 [/tex]
Thus, [tex] p(0.1)=-1\times-1=1 [/tex]
Again, the value of pH, p(t) is 0 when the concentration of the Hydronium ions, t is 1. This, again, is as expected, because, from the concept of logarithms we know that [tex] log(1)=0 [/tex].
If the pool maintenance man uses our graph and needs to find the the pH level if the amount of hydronium ions is raised to 0.50, then to do so, the pool maintenance man must draw a vertical line from t=0.5 and check the x coordinate of the point where this vertical line intersects the p(t) graph. As we can see from the graph this roughly comes out to be the horizontal line y=0.3.
Let us now move on to the second part of the question. For a better understanding of this part please go through the second graph which has been attached. This graph contains all translations on the original graph and the explanation to each one of them is provided below:
Let us start with the last one, -p(t). We know that, since, [tex] p(t)=-log_{10}(t) [/tex], therefore, [tex] -p(t)=log_{10}(t) [/tex], simply a vertical "flip" or reflection of the original graph. And because the original graph did not have a y intercept, this graph too will not have a y intercept.
Let us now move on to the first one. Here, [tex] p(t)+1=-log(t)+1 [/tex]. This graph will simply move the original graph vertically up by 1 unit and that will not have any bearing on the y intercept and thus, the graph of p(t)+1 will again, not have a y intercept.
Finally, let us move on to the graph of the equation p(t+1). As can be seen, this graph has a y intercept at the origin when t=0. This is because:
[tex] p(t+1)=log_{10}(t+1) [/tex]
and when t=0, [tex] p(t+1)=p(0+1)=log_{10}(0+1) [/tex]
[tex] p(1)=log_{10}(1)=0 [/tex]
Thus, when t=0, p(t+1)=0 too and thus we have a y intercept.
Therefore, out of the three transformations, only the middle transformation results in a y-intercept, the explanation for which has been provided.
calculate the length of the circumference of a circle with diameter of 9cm
Solve for x. x/2 = -5
How to tell whether a slope is positive negative zero or undefined?
What is the answer plz help
Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?
(from top to bottom, first pictures top option is A for example)
A.
B.
C.
D.
To prove similarity, the triangles must have three angles or any three components must be equal. According to the statement, option A seems to be proof the triangles are similar to each other.
There are two images given in the question.
Let us segregate the images into image 1 and image 2.
Take image 1.
In image 1, three different triangles are given,
One angle is equal in all the triangles, which is represented as a single arc.Another angle is represented as a double arc is equal.If two angles are equal in triangles then the third angle is automatic get equal.According to the above bullet points, image 1 qualifies all the requirements for the similarity of the triangles.
To know more about similarity, please refer to the link:
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if the xy-plane, the graph of y=x^2 and the circle with center (0,1) and radious 3 have how many points of intersection?
A. none
b. one
c, two
d. three
e. more than three
What is the value of this expression when z = 36?
10 - /z
4
6
-8
-26
The provided expression with 'z = 36' is incomplete and lacks an operation or additional numbers, making it impossible to calculate its value. The student is advised to provide the full expression for proper assistance.
Explanation:The student asked: What is the value of this expression when z = 36?
Unfortunately, there is a typographical error in the expression provided. It seems to be missing an operation or additional numbers. Given the format '/z', it seems like it should have been a mathematical operation involving the variable 'z'. However, without an operator such as '+' (plus), '-' (minus), '*' (multiply), or '/' (divide), we cannot determine what the expression is supposed to be or calculate its value given z = 36.
If this is an expression from a specific textbook or sheet, I recommend double-checking the source material for the correct expression. If it's a part of a larger problem or context, please provide the full details so that an accurate computation can be made.
Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer.
I understand the answer is x + y = 0
I want to understand how that is determined. Using point slope form and all that.,
Hey
Please someone help me!!!!!
Asap
The population density of ground crickets at oldmill farm is about 15 per square meter. assuming that the crickets are randomly distributed, about how many crickets would you expect to find in a rectangular section of land that is 6 meters × 2 meters?
In the diagram the figures are similar. What is x
A. 2.6ft
B. 3.4ft
C. 0.4ft
D. 2.3ft
The population of current statistics students has ages with mean mu and standard deviation sigma. samples of statistics students are randomly selected so that there are exactly 48 students in each sample. for each sample, the mean age is computed. what does the central limit theorem tell us about the distribution of those mean ages?
Leah has a piece of cloth that is 3 ft 8 in long. She decides to cut 2/11 of the cloth off. How long is the cloth now?
Please help me on that question for my Algebra. I don't understand it.
Also, how would you rate my pfp?
Simplify the expression below. (xy)^8
On Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. On Tuesday, apples were on sale for 20% off so she bought another 5 lbs. What was the price of apples on Tuesday? NEED ANSWER ASAP!
It is given that on Tuesday, apples were on sale for 20% off. Now, we know that on Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. This means that if we have a 20% off on Tuesday then this must be with respect to the price on Monday which is $4. Thus the price of Tuesday can be calculated as:
[tex] 4-\frac{20}{100}\times 4=4-0.8=3.2 [/tex]
Thus, the per pound price of apples on Tuesday was $3.2
Factor completely. a2+3a−28 Enter your answer in the box.
Solution :
To factor completely
[tex] a^{2} + 3a-28 [/tex]
To factor it completely , first take the product of first and third term, and then break the second term in two parts in such a way that its sum equals the second term and the product equals the product of first and third term.
Product of first and third term is [tex] (a^{2})(-28) = -28 a^{2} [/tex]
Second term is 3a, Re-write 3a as sum of 7a and -4a.
Lets check it Product of 7a and -4a is [tex] -28 a^{2} [/tex] wich is eaqual to product of first and third term and sum of 7a and -4a is 3a which is the second term.
Now factorise, we get
[tex] a^{2}+3a-28\\\\ = a^{2} +7a-4a-28\\\\=a(a+7)-4(a+7)\\\\=(a+7)(a-4) [/tex]
Hence, [tex] (a+7)(a-4) [/tex] is the factor of [tex] a^{2}+3a-28 [/tex].
Chris is building a large deck for the community center. The deck is shaped as a rectangle. The width of the deck is 29 ft. The perimeter of the deck is to be at least 134 ft. (please answer both questions)
1) Write an inequality that represents all possible values for the length of the deck.
2) Solve algebraically to find all possible values for the length of the deck.
16. For quadrilateral ABCD, determine the most precise name for it. A (-2, 3), B (9, 3), C (5, 6) and D (2, 6). Show your work and explain.
Answer:
Trapzoid
Step-by-step explanation:
Given: A (-2, 3), B (9, 3), C (5, 6) and D (2, 6)
We will find the slope of each line.
Formula:
[tex]\text{Slope, m}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Slope of AB, m}_1=\dfrac{3-3}{9+2}=0[/tex]
[tex]\text{Slope of BC, m}_2=\dfrac{6-3}{5-9}=-\dfrac{3}{4}[/tex]
[tex]\text{Slope of CD, m}_3=\dfrac{6-6}{2-5}=0[/tex]
[tex]\text{Slope of AD, m}_4=\dfrac{6-3}{2+2}=\dfrac{3}{4}[/tex]
Slope of AB = Slope of CD = 0
[tex]m_1=m_3=0[/tex]
Thus, AB is parallel to CD
Slope of BC ≠ Slope of AD
[tex]m_2\neq m_4[/tex]
Thus, BC is not parallel to AD
The quadrilateral ABCD has two sides are parallel and two are not parallel.
Hence, The quadrilateral is trapzoid
In a game played with a standard deck of cards, each face card has a value of 10 points, each ace has a value of 1 point, and each number card has a value equal to its number. two cards are drawn at random. it at least one card is an ace, what is the probability that the sum of the cards is 7 or less?
The sum of three consecutive odd integers is 327. find the integers
Final answer:
To find the three consecutive odd integers whose sum is 327, we set up an equation with n as the first odd integer, resulting in the integers being 107, 109, and 111.
Explanation:
The question asks for the three consecutive odd integers whose sum is equal to 327. To solve this, we can represent the first integer as n, the second as n+2, and the third as n+4 because odd numbers are two units apart. We can then set up the following equation to find the value of n:
n + (n + 2) + (n + 4) = 327
Simplifying this equation, we get:
3n + 6 = 327
Subtracting 6 from both sides gives us:
3n = 321
Dividing both sides by 3, we find that n = 107. Therefore, the three consecutive odd integers are 107, 109, and 111.
1.One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 describes the boundary within which motion can be sensed.
What is the greatest distance, in feet, a person could be from the lamp and be detected?
5 ft
10 ft
50 ft
125 ft
Answer:
5ft
Step-by-step explanation:
The required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Given equation
(x+15)²+(y−12)²=25
The above equation is the equation of the circle, so the longest distance that person could be from the lamp and be detected is the radius of the circle,
Which is given as,
r² = 25
r = √25
r = 5
Thus, the required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
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The answer could be A or c but idk which one is the right one please help