The vertex form of the given equation is (x - 9/2)² - 1/4
Vertex form
The general vertex form is written as
y = a (x - h)² + k
Where, a, h, and k are real numbers, where a ≠ 0.
And x and y are variables where (x, y) represents a points.
Given,
Here we have the equation x² = 9x - 20
Now, we have to convert this equation into vertex form.
In order to convert this into vertex form, first we have to rewrite the given equation as follows:
=> x² - 9x + 20 = 0
Here the coefficient of the x is 9, so now we divide this by 2 :
=> 9 ÷ 2 = 9/2
And then we have to square it (9/2) ² then we get the value 81/4.
So we add and subtract 81/4, then we get,
=> x² - 9x + 81/4 - 81/4 + 20 = 0
Now, we have to rewrite it as,
=> [x² - 9x + 81/4] + [-81/4 - 20]
When we simplify it then we get,
=> (x - 9/2)² - 1/4
Therefore, the vertex form of the equation is (x - 9/2)² - 1/4.
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Find the sum of the first n terms of the geometric sequence. n=5, a₁ =4, r = 3
The sum of n terms of geometric sequence with n=5, a₁ =4, r=3 is given by = 484.
Given that the sequence is geometric.
First term is = a₁ = 4
Common ratio is = r = 3
The number of terms for which the sum to be determined = n = 5
So the required sum of n terms of given geometric sequence is given by,
S [tex]=a_1\times\frac{r^n-1}{r-1}[/tex]
S [tex]=4\times\frac{3^5-1}{3-1}[/tex]
S = 4*((243-1)/2)
S = (4*242)/2
S = 484
Hence the sum of the given geometric sequence is 484.
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The function f(x) is graphed below. What is true about the graph on the interval from x = -∞ to x = a?
Tickets for movie admission for adults are
$4.00 each, but half-price is charged for
children. If 265 adult tickets were sold and
he box office collected $1,200, how many
children's tickets were sold?
A) 70
B) 35
C) 280
[D) 140
Answer:
[ D ] 140
Step-by-step explanation
4 x 265 = 1060
1060 - 1200 = -140
the answer is 140 i hope this helped <3
NO CALCULATOR PORTION
Let a polynomial be defined by:
f(x) = x(x + 6)(x - 2) and
f(x) = x³ + 4x² - 12x
a. Name all zeros of the function.
Step-by-step explanation:
a polynomial of degree n (that means the highest exponent of x is n) must have n zeroes.
in our case that means 3 zeroes.
the best way to find them is to have the factorial form of the polynomial : to see how several terms are multiplied to give us the polynomial.
the first f(x) gives us exactly that (the second f(x) is just the form with all the multiplications done) :
f(x) = x(x + 6)(x - 2)
when is the product of factors 0 ?
only when at least one factor is 0.
so, let's see,
when is x 0 ? well, x = 0.
when is (x + 6) = 0 ? x = -6.
when is (x - 2) = 0 ? x = 2.
so, the 3 zeroes are
x = -6
x = 0
x = 2
Help pls pls shsjsjsjsjs
Answer:
The answer would be the first one because when you factor -3 out, inside of the parentheses should be all positive because negative times negative is positive.
A small startup skateboard coMpany projects that the cost per month of manufacturing x skateboards will be C(x)= 10x +500 and the revenue per month from selling x skateboards will be r(x)= -x2+70x. Given that the profit is revenue minus cost for what values of x will the company break even or make a profit
The startup company needs to sell 68 skateboards in order to break even
Profit FunctionTo solve this problem, we have to find the profit of the company and what is required to break-even from total sales.
C(x) = 10x + 500
r(x) = -x² + 70x
Profit = revenue - cost
profit = (-x² + 70x) - 10x + 500
profit = -x² + 70x - 10x + 500
profit = -x² + 60x + 500
Solving the quadratic equation
x = 67.4 ≅68
For the startup to break even, they need to sell at least 68 skateboard.
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If 10 pants cost 240u.m, how much will 8 pants cost?
8 pants wil cost 192 u.m.
Step-by-step explanation:1. Establish a rule of 3.10 pants ----> 240u.m
8 pants ----> x
2. Solve for x.In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:
x= (8 x 240) / 10
x= 192
Check the attached image to get a better understanding of this process.
3. Conclude.
8 pants wil cost 192 u.m.
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Proportional quantities are divided into directly and inversely proportional.
Two magnitudes are said to be directly proportional
when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.
Problem :
If 10 pants cost 240u.m, how much will 8 pants cost?
We have:
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.
Therefore we will have:
[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]
So the 8 pants cost 192.
A quadratic function
y
=
f
(
x
)
y=f(x) is plotted on a graph and the vertex of the resulting parabola is
(
−
4
,
6
)
(−4,6). What is the vertex of the function defined as
g
(
x
)
=
f
(
x
)
−
4
g(x)=f(x)−4?
g(x) is a vertical dilation of f(x), then the x-value of the vertex does not change, using that we will see that the vertex of g(x) is (-4, 24)
What is the vertex of g(x)?
We know that there is a parabola graphed called f(x), such that the vertex of f(x) is at (-4, 6).
We also have a vertical dilation of this function defined as:
g(x) = 4*f(x)
Notice that because this is a vertical dilation, the x-value of the vertex does not change, then the vertex is at x = -4, like on f(x).
Evaluating there we get:
g(-4) = 4*f(-4)
And because the vertex of f(x) is (-4, 6), then we know that:
f(-4) =6
Replacing that we get:
g(-4) = 4*f(-4) = 4*6 = 24
Then the vertex of g(x) is at (-4, 24)
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Ms. McCool asked Zina to write 5 numbers whose average is 85. Zina immediately wrote
83, 84, 85, 86, and 87. How did she know what to write?
To find the set of numbers with a given mean we can assume them as consecutive terms, Zina did the same thing.
Mean of data:Mean or Arithmetic mean is the average of the given set of numbers. It is also denoted as the equal distribution of values for a given data. To calculate the mean of data, we can use the following formula
Mean/Average = Sum of observations ÷ Number of observations
Here we have
The average of 5 numbers is 85
Let's assume that the 5 numbers are 5 consecutive numbers and the five numbers are x, x+1, x+2, x+3, x+4, and x+5 [ for simple calculations ]
Average of 5 numbers = Sum of numbers / 5
⇒ 85 = (x+ x+ 1 + x+2 + x+3 + x+4 ) /5
⇒ 425 = 5x + 10
⇒ 5x = 415
⇒ x = 83
Then the 5 numbers are 83, 84, 85, 86, and 87
Therefore,
To find the set of numbers with a given mean we can assume them as consecutive terms and we can calculate the mean, Zina did the same thing.
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pediatricians work an average of 40 h per week. The standard deviation is 15 hours. What percentage of pediatricians work more than 70 h per week?
The percentage of pediatricians that work more than 70 h per week is; 2.275%
How to find the percentage from z-score?The formula for z-score of a normal distribution is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
sample mean; x' = 70 hours
population mean; μ = 40 hours
standard deviation; σ = 15 hours
Thus;
z = (70 - 40)/15
z = 2
From online p-value from z-score calculator, we have;
p-value = 0.02275 = 2.275%
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True or False
1 The total number of outcomes in tossing 3 fair coins is 6.
2 The totality of all outcomes is called an event.
3 Empty set of events is considered an event.
4 Sample Space is considered an event.
5 Empirical probability uses frequency to determine the probability.
6 The total number of outcomes in tossing a fair coin and rolling a die at the same time is 12
7 Weather forecasting is considered a subjective probability.
8 The probability of getting odd numbers in rolling a fair die is ⅓
9 If there are 18 students in a room. Where 5 of them are male then the probability of selecting male in a class is 5/18.
10 The probability of the sample space is always 1.
Answer:false
Step-by-step explanation:
iply Mixed Numbers What is the product of 1 and 12
Answer: 12
Step-by-step explanation: When multiplying (in this case finding a product,) by one, the number you are multiplying will always be the answer.
ron picked 7/10 bushels of apples ben picked 9/10 bushels of apples how many apples did they pick all together give your answer in lowest terms
1 3/5
1 1/2
1 6/10
1 3/10
Answer: 1 3\5
explanation : since the denominator of both fractions are same we can go ahead and the numerators which will make the fraction 16\10 or 8/5 (simplified) and to make this a mixed numeral 5 fits into 8 once with 3 leftover thus making 1 3/5.
hope this helps .
25 x 10 to the power of 6 in a standard form
Isosceles triangle JKL has a perimeter of 36 units and the given vertices.
J (-3, -9)
K (-3, 7)
L (X, -1)
What is the possible x-coordinate for point L?
Based on the perimeter of this isosceles triangle, the possible x-coordinate for point L is either -16.85 or 10.85.
How to determine the possible x-coordinate for point L?In Mathematics, the perimeter of an isosceles triangle can be determined by summing up all of its side lengths that encloses. Mathematically, the perimeter of isosceles triangle JKL is given by this mathematical expression:
Perimeter, P = JK + JL+ KL
36 = JK + JL+ KL
Next, we would determine the distance between each vertices by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance JK = √[(-3 - (-3))² + (-9 - 7)²]
Distance JK = √0 + 256
Distance JK = √256
Distance JK = 16
Distance JL = √[(-9 - (-1))² + (-3 - x)²]
Distance JL = √8² + (-3 - x)²
Distance JL = √64 + (-3 - x)²
Distance KL = √[(7 - (-1))² + (-3 - x)²]
Distance KL = √8² + (-3 - x)²
Distance KL = √64 + (-3 - x)²
Note: Side JK is equal to side KL as an isosceles triangle.
From the perimeter of this isosceles triangle, we have:
36 = JK + JL+ KL
36 = 16 + JL+ JL
2JL = 20
JL = 10 units.
Now, we can determine the possible x-coordinate for point L:
256 = 64 + (-3 - x)²
256 - 64 = (-3 - x)²
192 = (-3 - x)²
13.85 = -3 - x
x = -3 ± 13.85
x = (-3 - 13.85) or (-3 + 13.85)
x = -16.85 or 10.85
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Solving an Equation Involving Inverse Trigonometric Functions
sec^-1 x = csc^-1 2
The solution of the trigonometry function is 2√3/3.
What is the trigonometric function?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given trigonometric function is
sec^(-1) x = csc^(-1) 2
Assume that,
csc^(-1) 2 = z
→ 2 = csc z
→ 1/2 =1/ (csc z)
→ 1/2 =sin z
The trigonometry identity is [tex]\cos x =\sqrt{1-\sin^2x}[/tex].
[tex]\sqrt{1-(\frac{1}{2})^2 } =\cos z[/tex]
→ cos z = √3/2
→ sec z = 2/√3
→ sec z = 2√3/(√3×√3)
→ sec z = 2√3/3
→ z =sec^(-1) ( 2√3/3) = csc^(-1) 2
Putting csc^(-1) 2 = sec^(-1) ( 2√3/3):
sec^(-1) x = sec^(-1) ( 2√3/3)
→ x = 2√3/3
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[10 POINTS] OMGGGGGGG!!!!!!!!!!!!! GUYS I NEED HELP ASAP!!!!!!!! I HAVE TO TURN THIS IN 5 MINUTES!!!!!!!! HELP ME PLEASE!!!!! I'LL GIVE 10 POINTS!!!
2+2= ?
please asap will give brainliest
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 400 feet of antique picket fencing are to be used to enclose the garden, find
the dimensions of the garden.
Answer:
[tex]10\sqrt{6}[/tex] feet by [tex]\frac{20}{3}\sqrt{6}[/tex] ft
Step-by-step explanation:
If the length is [tex]l[/tex], then the width is [tex]\frac{2}{3}l[/tex].
Using the formula for the area of a rectangle,
[tex]l \cdot \frac{2}{3}l=400 \\ \\ \frac{2}{3}l^2=400 \\ \\ l^2=600 \\ \\ l=10\sqrt{6}[ \\ \\ \implies w=\frac{20}{3}\sqrt{6}[/tex]
Consider the following scenario.
the three-number bet
(a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
dollars
(b) Interpret it. (Round your answer to one decimal place.)
Over time, you should expect to lose about
cents for every dollar you bet.
a) The expected value of each $1 bet in roulette is of: -$0.988.
b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is obtained as the sum of each outcome multiplied by it's respective probability.
The three-number bet is when one sequence of three numbers has to be correctly chosen, hence the probability of winning is of:
p = 1/(10³) = 1/1000.
(as there is only one correct sequence, and for each number, there are 10 outcomes).
The payout is given as follows:
11:1.
That is, if you win, you earn 11 times the amount you bet.
Considering a bet of $1, the distribution of earnings is given as follows:
P(X = 11) = 1/1000.P(X = -1) = 999/1000.Hence the expected value of the bet is:
E(X) = 11/1000 - 999/1000 = -$0.988.
Which is the amount you are expected to lose for every dollar you bet.
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Write the following polynomial function in standard form. f(x)=2x-x^5+2x³ - x²-1-3x¹
Answer:
-x^5+2x³-x²-1x-1
Step-by-step explanation:
First order the terms based on highest degree or exponent.
-x^5+2x³-x²-3x¹+2x-1
Next combine like terms.
-3x¹ is simply -3x so -3x+2x = -1x
-x^5+2x³-x²-1x-1
HELP, GIVING 20 POINTS FOR THIS!!!
The statement that are correct from the graph is:
Some input values are negative.
some output values are negative.
Some input values are integers.
Some output values are integers.
From the graph:
The x value is -2,-4 that is negative.
so the some inputs are negative.
Y has values -2 ,-4 which are negative.
So the some outputs are negative.
The point values from the graph is -4,-2,0,2,4 which belong to integers.
So some input values and output values are integers.
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see photo for question
1. The hypothesis are given as follows:
Null: [tex]H_0: \mu \leq 178258[/tex]Alternative: [tex]H_1: \mu > 178258[/tex]2. The critical value is of: t = 2.3974.
3. The test statistic is of: t = 2.35.
4. The decision is: Reject the null hypothesis.
5. The conclusion is: There is enough evidence to conclude that the mean is greater.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean in Los Angeles is greater, that is:
[tex]H_0: \mu \leq 178258[/tex]
At the alternative hypothesis, it is tested if there is enough evidence, hence:
[tex]H_1: \mu > 178258[/tex]
The t-distribution is used, as we have the standard deviation for the sample but not for the population. Using a t-distribution calculator, with 55 - 1 = 54 df, a right-tailed test, as we are testing if the mean is greater than a value and a significance level of 0.01, the critical value is:
t = 2.3974.
Hence the decision rule is defined as follows:
t < 2.3974: Do not reject the null hypothesis.t > 2.3974: Reject the null hypothesis.What is the test statistic and the conclusion?The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 191790, \mu = 178258, s = 42627, n = 55[/tex]
Hence the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{191790 - 178258}{\frac{42627}{\sqrt{55}}}[/tex]
t = 2.35.
The test statistic is greater than the critical value, hence:
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Convert each mixed number to a fraction greater than one, or each fraction greater than one to a mixed number 5 3/11
Use point-slope form to write the equation of a line that passes through the point (−7,−4) with slope 10/7
The equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6
The coordinates of the point = (-7, -4)
The slope of the line = 10/7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Where [tex](x_1,y_1)[/tex] is the coordinates of the point
Substitute the values in the equation
y -(-4) = 10/7(x - (-7))
y + 4 = (10/7)(x + 7)
Convert to slope intercept form
y +4 = (10/7)x + 10
y = (10/7)x + 10 - 4
y = (10/7)x + 6
Hence, the equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6
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40 pts GET MARKED BRAINLIEST
A committee consisting of faculty members and students is to be formed. Every committee position has the same duties and voting rights. There are faculty members and students eligible to serve on the committee. In how many ways can the committee be formed?
Answer: there are 4 ways the committee can be formed
Step-by-step explanation:
Please help me need help
The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
Given,
In the question:
The matrix is given as:
A = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] & B = [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex]
To find the AB :
Now, According to the question:
AB = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
The basic Addition and Multiplication:
= -4 x 3 + (-3)x (-5) + 5 x (-1) = -12 +15 -5 = -2
= (-4) x (-4) + (-3)x (-5) + 5x (-3) = 16 + 15 -15 = 16
=(-4)x (-1) + (-3) x 1 + 5x 2 = 4 - 3 +10 = 11
= (-5) x 3 +(-4) x(-5) + (-2) x (-1) = -15 + 20 +2 = 7
= (-5) x(-4) + (-4)x (-5) + (-2) x (-3) = 20 + 20 + 6 = 46
= (-5) x (-1) + (-4) x 1 + (-2) x 2 = 5 - 4 - 4 = -3
= (-1) x 3 + (-2) x (-5) + (-4) x(-1) = -3 + 10 +4 = 11
=(-1) x(-4)+ (-2)x (-5) + (-4) x (-3) = 4 + 10 + 12 = 26
= (-1) x(-1) + (-2) x 1 + (-4) x 2 = 1 - 2 +(-8) = -9
Hence, The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
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The large rectangle below represents one whole.
What percent is represented by the shaded area
The percent represented by the shaded area as in the task content is; 40%.
What percent of the whole is shaded?It follows from the task content that the percent of the whole that is shaded as in the task content be determined.
By observation, the whole is partitioned into 5 parts with 2 parts shaded.
Consequently, when expressed as a fraction; the shaded region is; 2 / 5 of the whole.
Ultimately, when expressed as a percentage, the shaded region is;
( 2 / 5 ) × 100% = 0.4 × 100%
= 40%.
Ultimately, the percent of the whole that is shaded is; 40%.
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For the figure shown find m 1
I need help with this please help me
Answer:
Step-by-step explanation:
they are expecting you to know a few things.
first, that ∠x is asking for the interior angle of the labeled angle, here they call it 1 , so find that angle and look at the inside of the triangle, it's also referred to as the minor angle.
second, they are expecting you to know how many degrees it is around the interior or a triangle... do you know?
then , just take that number and subtract the two given numbers to find the final number , or the ∠1
got it?
If tan(A + B) = −2 and tan B = 3, find tan A.
Answer:
Tan a =1
Step-by-step explanation:
TRIG identity:
Tan ( a+b) = (tan a + tan b )/ (1 - tan a tan b) Sub in the given values
-2 = ( tan a + 3) / ( 1 - 3 tan a)
-2 + 6 tan a = tan a + 3
5 tan a = 5
tan a = 1