Answer:
[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]
Step-by-step explanation:
One is given the following equation;
[tex]x^2-4x-9=29[/tex]
The problem asks one to find the roots of the equation. The roots of a quadratic equation are the (x-coordinate) of the points where the graph of the equation intersects the x-axis. In essence, the zeros of the equation, these values can be found using the quadratic formula. In order to do this, one has to ensure that one side of the equation is solved for (0) and in standard form. This can be done with inverse operations;
[tex]x^2-4x-9=29[/tex]
[tex]x^2-4x-38=0[/tex]
This equation is now in standard form. The standard form of a quadratic equation complies with the following format;
[tex]ax^2+bx+c[/tex]
The quadratic formula uses the coefficients of the quadratic equation to find the zeros this equation is as follows,
[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the coefficients of the given equation in and solve for the roots;
[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}[/tex]
Simplify,
[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}\\\\=\frac{4(+-)\sqrt{16+152}}{2}\\\\=\frac{4(+-)\sqrt{168}}{2}\\\\=\frac{4(+-)2\sqrt{21}}{2}\\\\=2(+-)\sqrt{21}[/tex]
Therefore, the following statement can be made;
[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]
(2x - y + 3) (2x - y - 3)using identities
Step-by-step explanation:
(2x-y+3)(2x-y-3)=
4x²-2xy-6x-2xy+y²+3y+6x-3y-9=
4x²-4xy+y²-9=
(2x-y)²-9
At Dubai English School, 549 students use buses to go to school. If this number is 75% of the total school enrollment, then how many students are enrolled in total?
Which relationship is always true for the angles x,y and z of triangle ABC
Answer:
B. y + z = x
Step-by-step explanation:
x is an exterior angle of the triangle.
y and z are the opposite angles opposite the exterior angle.
The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.
Thus:
y + z = x
Erin has 5 cans of juice and drinks 1/3 of a can daily. in how many days will she empty all the cans she has? I think it's 1/15 I'm not sure though.
Please I need help asap, I will mark the best answer as Brainliest and give 20 points. I really need this if Im going to be able to study
Answer: The new point might be is 47,8 by applying the rule to both x and y
Step-by-step explanation:
20 POINT MATH PROBLEM HELP PLEASE
Answer:
b. x=22
Step-by-step explanation:
3x-23=43
3x=43+23
3x=66
x=22
Complete the expressions.
Write each answer as a number, a variable, or the product of a number and a variable.
=7r6
=
7r
Commutative property of multiplication
=
Multiply
Complete question :
Complete the expressions Write each answer as a number, a variable, or the product of a number and a variable 7(9r + 2) = 7 . 9r + 7 . ___ = ___ +
Answer:
2 ; 63r ; 14
Step-by-step explanation:
Given :
7(9r + 2)
Opening the bracket :
7*9r + 7*2 - - - - (1)
Taking the product
63r + 14 - - - - (2)
Now filling the blanks :
First blank corresponds to 2 (from (1))
Second blank corresponds to 63r (from (2))
Third blank should be 14
Are these triangles congruent?
Answer:
yes...
Step-by-step explanation:
its a congrate triangle
Find Length of x line OR
Both figures r similar (given )
so :-[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]
Which statements are true of the given function?
Check all that apply.
9514 1404 393
Answer:
B, E
Step-by-step explanation:
The table tells you that f(0) = 3/2. (0 is found in the x-column; 3/2 is found in the f(x) column.)
__
You can find f(4) by evaluating the formula.
f(4) = 1/2·4 +3/2 = 4/2 +3/2
f(4) = 7/2 . . . . agrees with last answer choice
Answer:
A ,B and E ;)
Step-by-step explanation:
Find the measure of WX and show work
Ans : the measure of WX = 8
The average age of the 12 people in a classroom is 10. After Ms. Xu walks into the room,
the average age of everyone in the classroom increases to 12. How old is Ms. Xu?
Answer:
24
Step-by-step explanation:
First: 12*10=120
Then: 12*12=144
=> Ms. Xu's old: 144-120=24
Instructions: Find the value of x
I’ll mark brainliest please help
The little lines theu each section are telling you all those sections are identical, which mean they are the same length.
You are told one section is 10, which means x is also 10
X = 10
Graph the image of rectangle after a translation 6 units right and 1 unit down.
Answer:
see image
Step-by-step explanation:
one by one, move each point
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
Reason 5
Step-by-step explanation:
Reason 1 and 2 are Given
Reason 3 is Reflexive
Reason 4 is Side-Side-Side congruency
Answer:
Reason 5
Step-by-step explanation:
It helps to know what CPCTC means and how it's used.
CPCTC means "corresponding parts of congruent triangles are congruent."
To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.
Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.
In step 4, the triangles are proven congruent by SSS.
Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.
can anyone pls answer this! it's really urgent!
Answer:
The answer is C
Step-by-step explanation:
You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.
I am interested in determining how long students take on average, to finish the first exam in my class. I specifically am interested in looking at students who take the class during the summer semester. I randomly pick 50 students from previous summer semesters and note how long the took on the first exam (TIME), which class they took with me - Stator Stat (CLASS), and whether they took the class online or in person (FORMAT).
Identity the following viables as either quantitative or qualitative
Class
Time
Answer:
jwruaijoii9auhyahd9i3u
w daF
wf
w
a
s
w sfjweiaeadfawjasawwg
Step-by-step explanation:
Quantitative data is supported by the empirical value in the form of counts or numbers, where each data set is attached with a particular numerical value. Qualitative data describes and can be expressed as the number of the subject.
For the class:
It is qualitative because the qualitative data is used to describes the qualifies or characteristics.In the given scenario the variable class differentiates students based on the information when the book stat I or Stat II.For the Time:
It is quantitative because the quantitative data is used to includes measurable quantity numbers.These numbers are used for the time of the quantitative variable.Learn more:
brainly.com/question/555216
what is the highest common multiple of 120 and 150
Answer:
30 I suppose
Step-by-step explanation:
A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
answer only one question No 1 only
-10369
too lazy but that's the exact value
Answer:
Step-by-step explanation:
(-2)³ *(-4)² * 3⁴ = (-8) * 16 * 81
= -10368
TASKI
END OF THE YEAR - ESCAPE ROOM
Movie Theme
Fnd the area and circumference of each figure below. Use 31 for it. If needed,
round your answers to the nearest hundredths place
CODE Type the numeral answer. NO LABELS Part a crea, circumference, part b
area, circumference For example 765, 326, 2004, 3563
6
10 mm
MOVIE
TICKET
Your answer
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PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEE OUTTTTTTTTTTTTTTTTTTTT I DO ANYTHING
Emma and Zeke own an on-line business, EZ Coasters, that sells cork beverage coasters, which can be bought plain or with logos. The price for both types of coasters is $3.00 each. There is also a one-time set-up charge of $25 for coasters with a logo.
1) Write an equation describing the relationship between:
a) The number of plain coasters bought and the cost of the coasters.
b) The number of coasters with a logo bought and the price of the coasters.
c) Is either coaster relationship proportional? Explain in writing how you know.
d) Explain what the unit rate of the line described by each equation means in the context of the coasters.
2) EZ Sales also sells plain natural sandstone coasters for $4.00 each.
a) Write the equation describing this relationship.
b) Indicate whether or not it is a proportional relationship and explain why?
c) Will the graph of this equation ever intersect the graph of the equations for either of the other two EZ Coasters? Explain in typing how you made your decision.
Answer:
6
Step-by-step explanation:
Answer:
Q1.
a. y = 3x + 0
b. y = 3x + 25
c. Plain is proportional because the y-intercept is zero.
d. It shows the cost of each coaster.
Q2
a. y = 4x + 0
b. It is proportional since the y-intercept is zero.
c. No the graph will never intersect because the equations in combination will result in parallel lines since there is a slight variation in the cost of EZ Coaters
HELP MATH ANSWER QUESTION
Answer:
x = 84 , y = 168
Step-by-step explanation:
[tex]Sin 60 = \frac{opposite side}{hypotenuse}\\\\ \frac{\sqrt{3}}{2}= \frac{AB}{BC}\\\\ \frac{\sqrt{3}}{2} = \frac{84\sqrt{3}}{y}\\\\Cross\ multiply ,\\\\y*\sqrt{3} =2*84 \sqrt{3}\\\\y= \frac{2*84*\sqrt{3}}{\sqrt{3}}\\\\y=168[/tex]
[tex]Cos\60 = \frac{adjacent}{hypotenuse}\\\\ \frac{1}{2}= \frac{AC}{BC}\\\\ \frac{1}{2}= \frac{x}{168}\\\\ \frac{1}{2}*168=x\\\\x= 84[/tex]
Which expression are greater than 1/2? Choose all the apply
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%:
Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights of oranges are also normally distributed with a mean of 131 grams and a standard deviation of 20 grams. Amy has an apple that weighs 90 grams and an orange that weighs 155 grams.
Required:
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
Answer:
a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b) The weight that 80% of the apples exceed is of 78.28g.
Step-by-step explanation:
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.
Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.
This means that [tex]\mu = 85, \sigma = 8[/tex]
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
This is 1 subtracted by the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 85}{8}[/tex]
[tex]Z = 1.875[/tex]
[tex]Z = 1.875[/tex] has a p-value of 0.9697
1 - 0.9696 = 0.0304
0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X- 85}{8}[/tex]
[tex]X - 85 = -0.84*8[/tex]
[tex]X = 78.28[/tex]
The weight that 80% of the apples exceed is of 78.28g.
17.
What is the value of the expression
2a + 5b + 3c for a = 12, b = 6, and
C=3?
A 10
B 21
C49
D 63
D. 63
2a+5b+3c
2(12)+5(6)+3(3)
24+30+9=63
Hope this helps! :)
Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.MONTH DEMANDJanuary 59February 65March 65April 67May 71June 70July 77August 77September 77October 75November 83December 81Calculate the simple three-month moving average forecast for April through December. What is the forecast for December? (Round your answer to 2 decimal places)a) 78.33b) 74.67c) 76.33d) 77.00Calculate the weighted three-month moving average using weights of 0.50 (t-1), 0.30 (t-2), and 0.20 (t-3) for April through December. What is the forecast for December? (Round your answer to 2 decimal places)a) 79.40b) 77.00c) 76.00d) 73.70Calculate the single exponential smoothing forecast for February through December using an initial forecast (F1=F-January) of 63. (Use alpha of 0.2) What is the forecast for December? (Round your answer to 2 decimal places) a) 66.30b) 74.37c) 72.22d) 71.52Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in April through December. Which forecasting method do you prefer? (Round your answer to 2 decimal places)a) 3-month moving average (4.15)b) 3-month weighted moving average (3.99)c) Exponential smoothing method (alpha=0.30) (3.58)d) 3-month weighted moving average (3.58)
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the attached file.
For question 1:
Forecast for December:
[tex]\to \frac{(77+75+83)}{3} \\\\ \to 78.33[/tex]
For question 2:
Forecast for December:
[tex]\to (77 \times .5+75 \times 3+83 \times .2) \\\\\to 79.40[/tex]
For question 3:
Forecast for December:
[tex]\to 72.22+(83-72.22)\times 0.2 \\\\\to 74.37[/tex]
For question 4:
So, the 3-month weighted moving average (3.58)
In a regression analysis involving 30 observations, the following estimated regressionequation was obtained.y^ =17.6+3.8x 1 −2.3x 2 +7.6x 3 +2.7x 4For this estimated regression equation SST = 1805 and SSR = 1760. a. At \alpha =α= .05, test the significance of the relationship among the variables.Suppose variables x 1 and x 4 are dropped from the model and the following estimatedregression equation is obtained.y^ =11.1−3.6x 2 +8.1x 3For this model SST = 1805 and SSR = 1705.b. Compute SSE(x 1 ,x 2 ,x 3 ,x 4 )c. Compute SSE (x2 ,x3 ) d. Use an F test and a .05 level of significance to determine whether x1 and x4 contribute significantly to the model.
Answer:
(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]
(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant
Step-by-step explanation:
Given
[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation
[tex]n = 30[/tex]
[tex]p = 4[/tex] --- independent variables i.e. x1 to x4
[tex]SSR = 1760[/tex]
[tex]SST = 1805[/tex]
[tex]\alpha = 0.05[/tex]
Solving (a): Test of significance
We have:
[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
First, we calculate the t-score using:
[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]
[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]
[tex]t = 440 \div \frac{45}{25}[/tex]
[tex]t = 440 \div 1.8[/tex]
[tex]t = 244.44[/tex]
Next, we calculate the p value from the t score
Where:
[tex]df = n - p - 1[/tex]
[tex]df = 30 -4 - 1=25[/tex]
The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:
[tex]p =0[/tex]
So:
[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]
Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]
To calculate SSE, we use:
[tex]SSE = SST - SSR[/tex]
Given that:
[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]
[tex]SST = 1805[/tex]
So:
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
Solving (c): [tex]SSE(x_2 ,x_3)[/tex]
To calculate SSE, we use:
[tex]SSE = SST - SSR[/tex]
Given that:
[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]
[tex]SST = 1805[/tex]
So:
[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]
[tex]SSE_{(x_2,x_3)} = 100[/tex]
Solving (d): F test of significance
The null and alternate hypothesis are:
We have:
[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant
[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant
For this model:
[tex]y =11.1 -3.6x_2+8.1x_3[/tex]
[tex]SSE_{(x_2,x_3)} = 100[/tex]
[tex]SST = 1805[/tex]
[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
[tex]p_{(x_2,x_3)} = 2[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the t-score
[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]
[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]
[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]
[tex]t = 27.5 \div 1.8[/tex]
[tex]t = 15.28[/tex]
Next, we calculate the p value from the t score
Where:
[tex]df = n - p - 1[/tex]
[tex]df = 30 -4 - 1=25[/tex]
The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:
[tex]p =0[/tex]
So:
[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]
Hence, we reject the null hypothesis
If the first and last terms of a trinomial are perfect squares, the trinomial is a perfect square
trinomial.
True
O False
Answer:
A trinomial is a perfect trinomial if the first and last terms are positive, perfect squares and the middle term is twice the product of their square roots.
Therefore, if you mean perfect as in positive, the answer is True.
