[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]
What are the measures of ∠1 and ∠2? Show your work or explain your answers.
Answer:
angle 1 is 105degrees and angle 2 is 75degrees
Step-by-step explanation:
The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.
Help me with this question please and thank you!! :)
[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].
We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).
This set is {3, 4, 11, 13, 14, 15, 17, 24}
f(x) = x² + (k-6) x +9, k * 0. The roots of the equation f(x) = 0 are a and B. (a) Find, in terms of k, the value of (i) a² + ß² (ii) a² ß² Given that 9(a²+ B²) = 2a²p². find the value of k. (b) (c) Using your value of k, and without solving the equation f(x) = 0. form a quadratic equation, with integer coefficients, which has roots and 33² f ( x ) = x² + ( k - 6 ) x +9 , k * 0 . The roots of the equation f ( x ) = 0 are a and B. ( a ) Find , in terms of k , the value of ( i ) a² + ß² ( ii ) a² ß² Given that 9 ( a² + B² ) = 2a²p² . find the value of k . ( b ) ( c ) Using your value of k , and without solving the equation f ( x ) = 0 . form a quadratic equation , with integer coefficients , which has roots and 33²
(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as
[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]
Expand the right side and match up coefficients:
[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]
Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that
[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]
and
[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]
(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then
[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]
Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].
(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is
[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]
which expands to
[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]
Reusing the identity from (a-i) and the result from part (b), we have
[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]
We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].
So, the simplest quadratic that fits the description is
[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]
To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].
Rick bought some tetra fish and goldfish for his fish tank. He bought twice as many goldfish as he did tetras. Each goldfish costs $1.50, and each tetra fish costs $2.00. He spent $20 on the fish. Which system can be used to represent x, the number of tetra fish, and y, the number of goldfish, he purchased?
x = 2 y. 2 x + 1.5 y = 20
2 x = y. 2 x + 1.5 y = 20
x = y. 2 x + 1.5 y = 20
x + y = 20. 2 x + 1.5 y
Answer:
B. 2x = y; 2x +1.5y = 20
Step-by-step explanation:
The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.
__
number of fishThe number of goldfish (y) is twice the number of tetras (x), so one equation can be ...
2x = y
cost of fishThe tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...
2x +1.5y = 20
Then the appropriate system of equations is ...
2x = y2x +1.5y = 20_____
Additional comment
The solution can be found by substituting for 2x to get ...
y +1.5y = 20 . . . . . . substitute for 2x
y = 20/2.5 = 8 . . . . divide by the coefficient of y
x = y/2 = 4 . . . . . . . find the number of tetras
Rick bought 4 tetras and 8 goldfish.
__
The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."
An object is dropped from 39 feet below the tip of the pinnacle atop a 715-ft tall building. The height of the object after seconds is given by the equation . h=16T^2+676.Find how many seconds pass before the object reaches the ground.
Answer:
6.5 seconds
Step-by-step explanation:
Ok so the equation you gave is -16T^2 + 676 in the comments which is what I'll be using for this problem. The problem is really just asking you to find the zeroes of the equation excluding any negative solutions since that doesn't really represent anything in this context since T is time.
So the first step is to set the equation equal to 0
[tex]0 = -16t^2 + 676[/tex].
Subtract 676 from both equations.
[tex]-676 = -16t^2[/tex]
Divide both sides by -16
[tex]42.25 = t^2[/tex]
Take the square root of both sides
[tex]\pm6.5 = t[/tex]
Ignore the negative and take only the positive solution, since in this context it doesn't make much sense. So after 6.5 seconds the height is 0, meaning it hits the ground after 6.5 seconds.
find the value of x
d:6
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: 5x = 3x + 12[/tex]
[ by vertical opposite angle pair ]
[tex]\qquad \sf \dashrightarrow \: 5x - 3x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 12 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6[/tex]
Therefore, the correct choice is D. 6
Find f(g(3)) and g(f(-2)).
f(x)=x²-1 and g(x)=2x-3
Answer:
1. 8
2. 3
Step-by-step explanation:
[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]
The sequence an = 1(3)n − 1 is graphed below: coordinate plane showing the points 1, 1; 2, 3; and 3, 9 Find the average rate of change between n = 1 and n = 3. (6 points)
Answer:
4
Step-by-step explanation:
[tex] \frac{9 - 1}{3 - 1} = 4[/tex]
The average rate of change on the interval [3, 9] will be 4.
How to find the average rate of change?The average rate of change between two points is given by the slope formula:
m = average rate of change = (y2 -y1)/(x2 -x1)
The sequence an = 1(3)n − 1 is graphed below:
m = (9 -1)/(3 -1) = 8/2
m = 4
The average rate of change on the interval [3, 9] will be 4.
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what is 2/3 x 6/7 answer
Answer:
4/7
Step-by-step explanation:
2/3 × 6
7
4/7
and bro that's really it
A cell phone towerbcast a shadow that is 40 feet long . An 10- foot- tall stop sign located near the tower casts a shadow that is 8 feet long. How tall is the cell phone tower?
Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:
8 feet - 10 feet
40 feet - h feet
Applying cross multiplication:
8h = 10 x 40
Simplifying by 8:
h = 10 x 5 = 50 feet.
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1 x 1 x 99 x 100 hat is the awnser
Which equation has x-intercepts located at (-1,0) and (-5,0)?
A. y=(x + 1)(x - 5)
B. y=(x + 1)(x + 5)
C. y=(x-1)(x - 5)
D. y=(x-1)(x + 5)
Answer:
B. y = (x+1)(x+5)
Step-by-step explanation:
If the x-intercepts are (-1,0) and (-5,0), then the solutions (also called zeros and x-intercepts) are
x = -1 and x = -5
This is a "working backwards" kind of problem. If you were solving the equation, right before the final step, x=-1 would have been:
x + 1 = 0
Right before x=-5
would have been,
x + 5 = 0.
These two: x+1 and x+5 are called the linear factors. You multiply them back together to find the equation.
y = (x+1)(x+5)
Q6. This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
The following is the actual question: Find the highest and lowest value of the equation in the given picture within the unshadowed region.
The graph of all the inequalities are given below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
y ≥ x, the region is left to the line.
y < -(3/7)x – 7, the region is left to the line.
y ≤ (5/3)x – 8, the region is right to the line.
y ≥ 14 – (11/12)x, the region is right to the line.
y = -(3/2)x + 5, this is the equation of line.
All the graphs are shown below.
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Item 6
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Juan buys one of the thickest books on the shelf. Min buys the third thinnest book on the shelf.
How much thicker is Juan’s book than Min’s book?
Answer:
There is no line plot
Step-by-step explanation:
If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]
[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]
Simple procedure :
[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]
[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]
[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³
Answer:
The volume of the pyramid with a base area of s² and the heights iss
The formula for calculating the volume of a square based pyramid is expressed as:
Volume = 1/3* Base area* Height
Since it is a square-based pyramid, the base area is calculated as:
Base Area = s ^ 2
If the height of the pyramid is equal to of the length of a side on the base, hence h = s
Substituting the base area and the height into the formula for the volume, this will give;
V = BH / 3
V = (s ^ 2 * s)/3
V = (s ^ 3)/3
V = 1/3 * s ^ 3
Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3
I’m going to need a serious answer through this one or I’m screwed.
Answer:
A = 60 ft²
Step-by-step explanation:
the area (A) of the shaded sector is calculated as
A = area of circle × fraction of circle
= 90 × [tex]\frac{240}{360}[/tex]
= 90 × [tex]\frac{2}{3}[/tex]
= 30 × 2
= 60 ft²
Answer:
58.83 ft^2
Step-by-step explanation:
Finding the radius:
A = πr^2
90 = πr^2
90/π = r^2
28.6 = r^2
5.3 = r
Using the area of a sector of a circle formula:
θ/360 x πr^2
240/360 x π(5.3)^2
= 58.83 ft^2
Can someone help me find AB and BC
3x + 2x + 5 + 5x + 15 = 180 [angles on a line add to 180 degrees]10x + 20 = 180 [combine like terms]10x = 160 [subtract 20 from both sides]x = 16 [divide both sides by 10]
Arc AB measures 3(16) = 48 degrees.
Arc BC measures 2(16) + 5 = 41 degrees.
Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (0,-3)
Using translation concepts, the equation for the transformed logarithm is given by:
[tex]f(x) = \log{(x + 3)} - 3.48[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The logarithm function is given by:
[tex]f(x) = \log{x}[/tex].
We have that:
It passes through (1,0), and in this problem it passes through (-2,0), that is, it was shifted left 3 units, hence x -> x + 3.Hence:
[tex]f(x) = \log{x + 3} + b[/tex]
To find the shift up/down, we consider that f(0) = -3, hence:
[tex]-3 = \log{0 + 3} + b[/tex]
[tex]b = -3 - \log{3}[/tex]
b = -3.48.
Hence the function is given by:
[tex]f(x) = \log{x + 3} - 3.48[/tex]
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What are the values for y when x is 2, 4, and 6?
y = 20x + 7
The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
If the function is reflected over the y-axis and then translated down 2 units. the resulting function will be -∛x - 2
Transformation of coordinatesTransformation is a technique used to change the position of an object on an xy-plane.
Given the function y = ∛x
If the function is reflected over the y-axis and then translated down 2 units to form f(x), the resulting function f(x) will be:
f(x) = -∛x - 2
The graph of the resulting function is attached
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Answer:
B
Edge 2023
The other answer is incorrect!!!
please help me :((((((
Answer:
Answer D
Step-by-step explanation:
It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4
Which of the following is a geometric sequence?
• A. 6, 18, 54, 162
O B. 1, 4, 5, 9, 14
O C. 3, 6, 9, 12, 15
O D. 3, 5, 8, 13, 21
Answer: A. 6, 18, 54, 162
Step-by-step explanation:
Each term is 3 times the last, meaning the common ratio is 3.
Use the In key on your calculator to estimate
the logarithm.
In 49
Round your answer to the nearest thousandth.
Answer:
3.8918
round the 1 from the 8 to get 2
3.892
What is the range of y=sin(x)?
The range of y = sin(x) is [-1,1]
How to determine the range?The function is given as:
y = sin(x)
The above function is the parent function of a sine function.
A sine function has a minimum of -1 and a maximum of 1.
This is represented by the interval [-1,1]
Hence, the range of y = sin(x) is [-1,1]
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find the missing number in ?/4 = 27/36
[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The missing number is 3}[/tex]
the height of a toy rocket
Please helpppp I really need please
Step-by-step explanation:
please mark me as brainlest
if n × 18 = ½ find n
Answer:
n = [tex]\frac{1}{36}[/tex]
Step-by-step explanation:
n × 18 = [tex]\frac{1}{2}[/tex]
To find the value of n we have to divide both sides by 18.
Let us solve it now.
18n = [tex]\frac{1}{2}[/tex]
[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]
n = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]
n = [tex]\frac{1}{36}[/tex]
What is the y-intercept of this quadratic function f(I)=-i2+10i-22
The y-intercept of the quadratic equation is -47.
What is Quadratic Equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given quadratic equation;
f(i) = i² + 10i - 22
or, y = i² + 10i - 22
y = i² + 2.5x - (47-25)
y = i² + 2.5x + 25 - 47
y = (i+5)² - 47
Thus, the y-intercept of the quadratic equation is -47.
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