Answer:
2x - 3 2x +3
Step-by-step explanation:
so its 2,3,2,3
The function 4x^2 - 9 is a quadratic function, and the factorized expression of 4x^2 - 9 is (2x - 3)(2x+ 3)
What is factorization?Factorization involves splitting a function into several factors
The expression is given as:
[tex]4x^2 - 9[/tex]
Express 4 as the square of 2
(2x)^2 - 9
Express 9 as the square of 3
(2x)^2 - 3^2
Apply the difference of two squares
(2x - 3)(2x+ 3)
Hence, the factorized expression is (2x - 3)(2x+ 3)
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The difference of two numbers is 13. The sum of two numbers is 75
Answer:
The numbers are 31 and 44.
Step-by-step explanation:
Given that the difference of two numbers is 13, and the sum of two numbers is 75, to determine what these numbers are, the following calculations must be performed:
(75 - 13) / 2 = X
62/2 = X
31 = X
31 + (31 + 13) = X
31 + 44 = X
75 = X
Therefore, the numbers are 31 and 44.
Which statement is true about the function shown in the graph?
Answer:
A
Step-by-step explanation:
The function that is shown in the graph is strictly decreasing
What is a function?"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."
The given function has a value of (- 5) at a certain point.
After that the function is decreased to a value of (- 10).
Therefore, we can conclude that the function is strictly decreasing.
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write a quadratic function f whose zeros are 2 and -6
Answer:
hope this will help u
Step-by-step explanation:
⇒ Given zeros are α=2 and β=−6.
⇒ Sum of zeros =α+β=2+(−6)=−4
⇒ Product of zeros =α×β=2×(−6)=−12
⇒ Quadratic polynomial =x
2
−(α+β)x+(α×β)
⇒ Quadratic polynomial =x
2
−(−4)x+(−12)
∴ Quadratic polynomial =x
2
+4x−12
The quadratic function having 2 and -6 as zeros is f(x) = x² + 4x - 12.
What is the quadratic function with roots 2 and -6?Given the parameters:
Zeros of the function: 2 and -6.
To find the quadratic function f(x) with zeros at 2 and -6, first set up the equation:
x = 2 and x = -6
These are the real solutions to the quadratic equation:
This means that; ( x - 2 ) and ( x + 6 ) are the factors of the quadratic equation:
Hence:
( x - 2 )( x + 6 ) = 0
Expand using distributive property:
x( x + 6 ) - 2(x + 6 ) = 0
x² + 6x - 2x - 12 = 0
Collect and add like terms:
x² + 4x - 12 = 0
Therefore, the function will be:
f(x) = x² + 4x - 12.
The quadratic function is f(x) = x² + 4x - 12.
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Please help with this!! Urgent
9514 1404 393
Answer:
see attached
Step-by-step explanation:
When p and q are roots, (x -p) and (x -q) are factors. The quadratic equation is then ...
0 = (x -p)(x -q) = x^2 -(p+q)x +pq
That is, the constant term is the product of the roots and the linear term coefficient is the opposite of the sum of the roots.
Using the given sum and product, the equation can be written ...
0 = x^2 -(-5/4)x +3/4
Multiplying by -8 gives ...
0 = -8x^2 -10x -6 . . . . . matches lower right choice
_____
Check
The product of roots is positive, so both roots have the same sign. The sum of roots is negative, so both roots are negative. That means there are no positive real roots to the equation. Descartes' Rule of Signs tells you this means the sequence of coefficients has no sign changes. Only the choice shown below has no sign changes. All of the others have at least 1 sign change.
Suppose X is a random variable with a mean of 10 and a variance of 100. Suppose Y is a random variable with a mean of 2 and a standard deviation of 16. Also, suppose X and Y are independent. What is the mean of 10 X + 3 Y?
Answer:
[tex]E(10x + 3y) =106[/tex]
Step-by-step explanation:
Given
[tex]E(x) =10[/tex]
[tex]Var(x) = 100[/tex]
[tex]E(y) =2[/tex]
[tex]Var(y) = 16[/tex]
Required
[tex]E(10x + 3y)[/tex]
To do this, we make use of the following equation
[tex]E(ax + by) =aE(x) + bE(y)[/tex]
So, we have:
[tex]E(10x + 3y) =10 * E(x) + 3 *E(y)[/tex]
[tex]E(10x + 3y) =10 * 10 + 3 *2[/tex]
[tex]E(10x + 3y) =100 + 6[/tex]
[tex]E(10x + 3y) =106[/tex]
Here is the question
Answer:
X = 4
UV = 24
Step-by-step explanation:
Opposite sides are equal
5x+4=6x
subtract 5x from both sides
4 = x
then substitute the 4 into 5x+4
5(4) + 4 = 24
Help please i need it
Answer:
0.51
Step-by-step explanation:
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 29 cups of coffee, using 444 ounces of coffee, while collecting a total of $35.90. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answer:
10 oz: 7
14 oz: 8
20 oz: 6
Answer:
Kyle filled 4 servings of 10oz 16 servings of 14 oz 9 servings of 20 oz
Step-by-step explanation:
10oz 95c = x
14oz 1.15c = y
20oz 1.50c = z
444 given divided by 29 cups
= 444/29 = 15.3103448 average cup weight so the higher size were used more.
9 servings of 20 oz cups = 180 = cost check at 1.50 x 9 = $13.50
16 servings of 14 oz cups = 224 = cost check at 16 x 1.15 = $18.40
4 servings of 10 oz cups = 40 = cost check at 4 x 0.95 = $3.80
Where given collection total said to be $35.90 we total 13.5+18.4+3.8 = 35.7 so we are 0.20 out and can try again.
OR just submit this. 4 servings of 10oz 16 servings of 14 oz 9 servings of 20 oz
i need to find the area. please help
Answer:
A = 190 inches^2
Step-by-step explanation:
The total area would be area for a rectangle + half the area of a circle:
Area for a rectangle:
A = l x w
A = 12 x 15
A = 180 [tex]inches^{2}[/tex]
Area for half of the circle:
A = [tex]\frac{\pi r^{2} }{2}[/tex]
[tex]A = \frac{\pi 2.5^{2} }{2} \\\\= \frac{19.63}{2} \\\\= 9.8 inches^{2}[/tex]
Total area: Rectangle area + half of the circle area
= 180 + 9.8 = 189.8 = 190 inches^2
Step-by-step explanation:
Find the rectangle area first by using the formula A=length * width then find the semicircle area by using the formula A=pi*r²/2
Whats the nth term in this sequence
1 , 7, 13, 19
Step-by-step explanation:
the answer is in the above image
Answer to the question
Answer:
7
Step-by-step explanation:
Step-by-step explanation:
AB//CD (Opposite sides of parallelogram are parallel)
Angle A + Angle B = 180 (Sum of interior angles=180)
179 + 3x - 20 = 180
3x - 20 = 180 - 179
3x - 20 = 1
3x = 1 + 20
3x = 21
x = 21/3
x = 7
Thirty less than four times a number is fifty
4x-30= 50
mark me brainliestttt :))
Answer:
The number is 20
Step-by-step explanation:
Let the number be x
Four times the number means = 4x
30 less than the number is 50 means = 4x - 30 = 50
Solve for x :
4x - 30 = 50
4x - 30 + 30 = 50 + 30 [ adding 30 on both sides ]
4x = 80 [ - 30 + 30 = 0 ]
x = 20 [ dividing by 4 on both sides ]
In Oregon, the mean annual rainfall in Rockaway Beach is 118.88 inches and the mean annual rainfall in Falls City is 122.28 inches. Which conclusion can you make using this information?
Answer:
Step-by-step explanation:
Based on this information, you could conclude that the annual rainfall in Falls City is generally more than that of the annual rainfall in Rockaway Beach. This is based on the information provided since the numbers given are the mean annual rainfall. Meaning that this is the average amount of rain that falls in any given year in that specific location. Since the amount provided for Falls City is a larger number then it means it gets more rainfall than Rockaway Beach on average and would therefore be the safest conclusion that can be made.
Answer:
I hope this helps
Step-by-step explanation:
Can Someone help me please?
Answer:
the last option is coorect
R(-9, 4) and S(2, -1); Find T.
Answer:
AYYYYYYYYYYYYYYYYYYYYY
Step-by-step explanation:
simplify the following expression <3
Answer:
4x^12y^6/z^5
Step-by-step explanation:
See image below:)
FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
Choose the equation that represents the line that passes through the point (6, -3) and has a slope of
1/2
y=-x+6
y=2x-6
y=2x+3
Answer:
y=1/2x-6
Step-by-step explanation:
slope=1/2, (6,-3)
plug in the x and y coordinates into the equation
-3= 1/2 (6) +b
-3=3+b
subtract 3 from both sides
b=-6
y=1/2x-6
A file that is 226 megabytes is being downloaded if the download is 12.&% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth
Answer:
28.7
Step-by-step explanation:
12.7% = 0.127
226 * 0.127 = 28.702
Rounded
28.7
which expression is equivalent to 6 + 3 * 4 - 1 / 3
Answer:
12 2/3
Step-by-step explanation:
add the integers to get 6+3 + 4 = 13
Now subtract 1/3
13 = 12 + 1 - 1/3
but one is equal to 3/3
12 + 3/3 - 1/3
12 2/3
Suppose that attendance at the concerts by the band "Keane" is a normally distributed random variable X with a mean of 18,500. You are told that P(X ≥ 15,000) = 0.6981. What are the two values of X that delineate the "82% middle pack" of this random variable?
A random variable has a population mean equal to 1,973 and population variance equal to 892,021. Your interest lies in estimating the population mean of this random variable. With that in mind, you take a representative sample of size 79 from the population of the random variable. You then use this sample data to calculate the sample average as an estimate for the population mean.
Required:
Using your knowledge about the central limit theorem (CLT), and assuming that the CLT has already "established itself" / "kicked in" when the sample size is 79, what is the probability that the sample average that you calculated will lie between 1,702 and 1,948?
Answer:
The two values of X that delineate the "82% middle pack" of this random variable are 9480 and 27520.
0.4017 = 40.17% probability that the sample average that you calculated will lie between 1,702 and 1,948.
Step-by-step explanation:
To solve the first question, we use the normal distribution, while for the second quetion, it is used with the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
First question:
Mean of 18,500:
This means that [tex]\mu = 18500[/tex]
You are told that P(X ≥ 15,000) = 0.6981.
This means that when [tex]X = 15000[/tex], Z has a o-value of 1 - 0.6981 = 0.3019, which means that when [tex]X = 15000, Z = -0.52[/tex]. We use this to find [tex]\sigma[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.52 = \frac{15000 - 18500}{\sigma}[/tex]
[tex]0.52\sigma = 3500[/tex]
[tex]\sigma = \frac{3500}{0.52}[/tex]
[tex]\sigma = 6731[/tex]
What are the two values of X that delineate the "82% middle pack" of this random variable?
Between the 50 - (82/2) = 9th percentile and the 50 + (82/2) = 91st percentile.
9th percentile:
X when Z has a p-value of 0.09, so X when Z = -1.34.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.34 = \frac{X - 18500}{6731}[/tex]
[tex]X - 18500 = -1.34*6731[/tex]
[tex]X = 9480[/tex]
91st percentile:
X when Z has a p-value of 0.91, so X when Z = 1.34.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.34 = \frac{X - 18500}{6731}[/tex]
[tex]X - 18500 = 1.34*6731[/tex]
[tex]X = 27520[/tex]
The two values of X that delineate the "82% middle pack" of this random variable are 9480 and 27520.
Question 2:
A random variable has a population mean equal to 1,973 and population variance equal to 892,021.
This means that [tex]\mu = 1973, \sigma = \sqrt{892021} = 944.5[/tex]
Sample of 79:
This means that [tex]n = 79, s = \frac{944.5}{\sqrt{79}}[/tex]
What is the probability that the sample average that you calculated will lie between 1,702 and 1,948?
This is the p-value of Z when X = 1948 subtracted by the p-value of Z when X = 1702. So
X = 1948
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1948 - 1973}{\frac{944.5}{\sqrt{79}}}[/tex]
[tex]Z = -0.235[/tex]
[tex]Z = -0.235[/tex] has a p-value of 0.4071
X = 1702
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1702 - 1973}{\frac{944.5}{\sqrt{79}}}[/tex]
[tex]Z = -2.55[/tex]
[tex]Z = -2.55[/tex] has a p-value of 0.0054
0.4071 - 0.0054 = 0.4017
0.4017 = 40.17% probability that the sample average that you calculated will lie between 1,702 and 1,948.
In the diagram of circle O shown to the right, PA and PB are tangent to circle O at points A and B, respectively. If mACB 266, then mAPB
Answer: 86 degrees
Step-by-step explanation:
please help me simplify the expression and please show work!!! <3
Step-by-step explanation:
[tex] \frac{x + 4}{3 {x}^{2} - 12x - 96} = \frac{x + 4}{3( {x}^{2} - 4x - 32) } = \frac{x + 4}{3(x - 8)(x + 4)} [/tex]
[tex] = \frac{1}{3(x - 8)} = \frac{1}{3x - 24} [/tex]
11. Choose the proportion that represents this problem:
If one meter is approximately 3.28 ft, how many meters are
in 20 ft?
a) 3.28
20
b) 3.28
20
1
1
m
O ) c) 3.28
20
1
d) 20
3.28
1
m
т
Answer:
D is the answer
Step-by-step explanation:
Item 23
What kind of angle is angle BCA ?
acute
obtuse
right
Answer:
BCA is obtuse
Step-by-step explanation:
BCA = 98 degrees
greater than 0 to less than 90 is acute angles
90 - right angle
greater than 90 to less than 180 is obtuse
98 is obtuse
Helpppppppppppppppp please y’all
[tex]\sf{3. \ \ Given : \dfrac{2}{3} - \dfrac{5}{4} + \dfrac{7}{2}}[/tex]
Let us solve the first two fractions : The LCM of 3 and 4 is 12
[tex]\sf{\implies \dfrac{4(2) - 5(3)}{12} + \dfrac{7}{2}}[/tex]
[tex]\sf{\implies \dfrac{8 - 15}{12} + \dfrac{7}{2}}[/tex]
[tex]\sf{\implies \dfrac{-7}{12} + \dfrac{7}{2}}[/tex]
LCM of 2 and 12 is 12
[tex]\sf{\implies \dfrac{-7 + 7(6) }{12}}[/tex]
[tex]\sf{\implies \dfrac{-7 + 42}{12}}[/tex]
[tex]\sf{\implies \dfrac{35}{12}}[/tex]
[tex]\sf{\implies 2 +\dfrac{11}{12}}[/tex]
[tex]\sf{\implies 2 \dfrac{11}{12}}[/tex]
---------------------------------------------------------------------------------------
[tex]\sf{4. \ \ Given : \dfrac{(2 - 7)^2 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{(-5)^2 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{25 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{30}{3}}[/tex]
[tex]\sf{\implies 10}[/tex]
Answer:
2/3-5/4+7/2
Step-by-step explanation:
collect like terms. that is the positive and negative terms2/3+7/2-5/4lcm of 3 and 2 is 6 hence 2/3+7/2= 25/625/6-5/4....lcm of 6 and 4 is 12 hence 25/6-5/4=35/12 the answer in its mixed fraction is 2 and 11/12Select all the pairs of expressions that are equivalent.
•14d + 21 and 7(2d + 3)
•9(5r - 2) and 14r - 7
•8(69 - 9) and 489 - 72
•16 + 4w and 2(2w + 8)
•32t + 16 and 16(2 – t)
Answer:
14d + 21 = 7(2d + 3)
16 + 4w = 2(2w + 8)
Step-by-step explanation:
14d + 21
7(2d + 3)
14d + 21
14d + 21 = 7(2d + 3)
9(5r - 2)
45r - 18
14r - 7
9(5r - 2) ≠ 14r - 7
8(69 - 9)
552 - 72
489 - 72
8(69 - 9) ≠ 489 - 72
16 + 4w
2(2w + 8)
4w + 16
16 + 4w = 2(2w + 8)
32t + 16
16(2 - t)
32 - 16t
32t + 16 ≠ 16(2 - t)
The pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)
How to determine the equivalent expressions?To do this, we test each pair of expression.
This is done as follows
14d + 21 = 7(2d + 3)
Expand
14d + 21 = 14d + 21 --- this is true
9(5r - 2) = 14r - 7
Expand
45r - 18 = 14r - 7 --- this is false
8(69 - 9) = 489 - 72
Expand
552 - 72 = 489 - 72 --- this is false
16 + 4w = 2(2w + 8)
Expand
16 + 4w = 4w + 16 ---- this is true
32t + 16 = 16(2 – t)
Expand
32t + 16 = 32 - 16t --- this is false
Hence, the pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)
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Select the correct answer from each drop-down menu.
What is the end behavior of function h?
h(x) = -4x2 + 11
As x approaches negative infinity, h(x) approaches
As x approaches positive infinity, h(x) approaches
Answer:
The first is negative and the second is also negative. Just took the test and passed.
Step-by-step explanation: Step by Step
Because the variable has an even power, we will see that:
As x approaches -∞, h(x) approaches -∞As x approaches ∞, h(x) approaches -∞.What is the end behavior of h(x)?Here we have h(x) = -4x^2 + 11
Notice that the variable is squared, this means that the sign does not matter, the outcome of:
-4x^2 will always be negative. So in both ends (when x tends to infinity and negative infinity), we will have the same end behavior.
When we take that limit, -4x^2 will just tend to negative infinity, then in both cases, the function tends to negative infinity.
So we have:
As x approaches negative infinity, h(x) approaches negative infinity.As x approaches positive infinity, h(x) approaches negative infinity.If you want to learn more about limits, you can read:
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out of 80,000 seats in a cricket stadium 12% seats were there occupied by vips and 39040 seats by general public what percentage of the stadium remained un occupied?
Answer:
% of unoccupied seats = 63.2 %
Step-by-step explanation:
Total seats = 80, 000
VIP seats = 12 % of 80, 000
[tex]= \frac{12}{100} \times 80000\\\\= 9600[/tex]
General Seats = 39040
Remaining seats = 80000 - 9600 - 39040 = 50, 560
Percentage of un-occupied seats,
[tex]= \frac{50560}{80000} \times 100 = 63.2 \%[/tex]
Answer:
THE NUMBER OF SEATS OCCUPIED BY VIPS=80000×12/100
=9600
occupied seats=9600+39040
=48640
number of unoccupied seats=80000-48640
=31360
percentage of unoccupied seats=31360/80000×100%
=39.2%
What is the value of n?
Answer:
A
Step-by-step explanation:
180-133= 47
180-142= 38
47+38= 85
180-85= 95
If the inside of n is 95, n has to be 85
find the product. write your answer in exponential form 9²•9-⁶
Answer:
9^8
Step-by-step explanation:
9²•9⁶ = 9^(2+6) = 9^8
Answer:
IF the 6 is negative : [tex]9^{2}[/tex] · [tex]9^{-6}[/tex] then the answer is 1/[tex]9^{4}[/tex]
If the 6 is positive then the answer is [tex]9^{8}[/tex]
Step-by-step explanation:
Exponents are add when their bases are similar.
