Answer:
5 unitsStep-by-step explanation:
A right angled triangle is a triangle that has one of this angles to be 90°. According to the ΔABC, the angle at B is 90°.
Area of a triangle = 1/2 * base * height
According to the diagram shown, the base is BC and the height is AB which is the required side.
Area of the triangle = 1/2 * BC * AB
Given area of the triangle = 10 square units
BC = 4 units
AB is the required length.
Substituting this values into the formula above;
10 = 1/2 * 4 * AB
10 = 2AB
Dividing both sides by 2
2AB/2 = 10/2
AB = 5 units
Hence the length of AB is 5 units.
In high school, a teacher gave two sections of a class the same arithmetic test. The results were as follows:
Section I: Mean 45, Standard
Deviation 6.5
Section II: Mean 45,
Standard deviation 3.1
What conclusions is correct?
Answer:
Section I test scores are more dispersed that that of section II.
Step-by-step explanation:
Consider the data collected from the arithmetic test given to two sections of a school.
Section I: Mean = 45, Standard Deviation = 6.5
Section II: Mean = 45, Standard deviation = 3.1
The mean of both the sections are same, i.e. 45.
So there is no comparison that can be made from the center of the distribution.
The standard deviation for section I is 6.5 and the standard deviation for section II is 3.1.
The standard deviation is a measure of dispersion, i.e. it tells us how dispersed the data is from the mean or how much variability is present in the data.
The standard deviation for section I is higher than that of section II.
So, this implies that section I test scores are more dispersed that that of section II.
It takes a graphic designer 1.5h to make one page of a website. Using a new software, the designer could complete each page in 1.25h, but it takes 8h to learn the software. How many web pages would the designer have to make in order to save time using the new software?
Answer:
33 web pages (at least)
Step-by-step explanation:
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
1.5x represents the number of hours it will take normally, and 1.25x + 8 represents the time with the new software. 1.5x (amount of hours using old software) needs to be larger than the time it takes with the new software.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
So, the designer would have to make at least 33 pages.
The number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
The time with the new software is represented by 1.25x + 8 and the normal time is represented by 1.5x. The number of hours spent using the old software must be 1.5 times greater than the time spent using the new product.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
Therefore, the number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
To know more about inequality follow
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Please help me I will mark brainliest! The ratio of the number of boys to the number of girls in a school is 3:4. One-third of the boys and three-eighths of the girls wear spectacles, If there are 612 pupils who do not wear spectacles, a)find the total number of the pupils in the school, and b) how many more girls than boys are there in the school
Answer:
a) 952
b) 136
Step-by-step explanation:
Ratio of b:g = 3:4, based on this we have:
Number of boys = 3xNumber of girls = 4xTotal number of pupils = 3x+4x = 7xNumber of spectacle wearers:
1/3*3x + 3/8*4x = x + 3/2x = 2.5xNumber of those not wearing spectacles:
7x - 2.5x= 4.5xAnd this number equals to 612, then we can find the value of x:
4.5 x = 612x= 612/4.5x= 136a) Total number of pupils:
7x = 7*136 = 952b) The difference in the number of boys and girls:
4x-3x= x = 136Answer:
total number of students: 952
number of girls more than boys :136 more girls
Step-by-step explanation:
1/3 of boys +3/8 girls= spectacles
612 people do not wear spectacles
3:4= boys: girls
total number of students
3+4=7
boys + girls = total ratio
7= total ratio
1/3×3=1 3/8×4=3/2
1+3/2=5/2
7-5/2=9/2 9/2=612 students
If 9/2=612 Then 7=?
7= 7÷ 9/2×612
=952 people
Girls more than boys
if 7= 952
3= 3/7 × 952=408 boys
if 7 = 952
4= 4/7 ×952=544girls
Girls - boys
544- 408 = 136 girls
Assume a significance level of alpha = 0.05 and use the given information to complete parts (a) and (b) below. Original claim: The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm. The hypothesis test results in aP-value of 0.2761.a. State a conclusion about the null hypothesis.(Reject H0 or fail to reject H0.) Choose the correct answer below.A. Fail to reject H0 because the P-value is less than or equal to alphaα.B. Reject H0 because the P-value is less than or equal to alphaα.C.Fail to reject H0 because the P-value is greater than alphaα.D. Reject H0 because the P-value is greater than alphaα.b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?A. The standard deviation of pulse rates of the group of adult males is more than 11 bpm.B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.C. The standard deviation of pulse rates of the group of adult males is less than or equal to 11 bpm.D. There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.
Answer:
a
The correct option is B
b
The correct option is D
Step-by-step explanation:
From the question we are told that
The level of significance is [tex]\alpha = 0.05[/tex]
The p-value is [tex]p = 0.2761[/tex]
Considering question b
Given that the [tex]p< \alpha[/tex] then the null hypothesis is rejected
Considering question b
Given that the original claim is The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm
Then the null hypothesis is [tex]H_o : \sigma = 11[/tex]
The reason why the null hypothesis is write like this above is because a null hypothesis expression can not contain only a > or a < but only allows = [tex]\le , \ and \ \ge[/tex]
and the alternative hypothesis is [tex]H_a : \sigma > 11[/tex]
Now given that the null hypothesis is rejected, it mean that there is sufficient evidence to support original claim
Help me please please please please
Answer:
1.
d. (-14) + (-8)
2.
a. (-14) + 8
Step-by-step explanation:
(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.
(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.
Answer:
1. D
2. A
Step-by-step explanation:
1. It asks you what expression has the same value as (-14)-8. All you need to do is find other equations that have the same value as that. So the equation is -14-8. IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5. If it's both negative: -(-5), it will be +5. If it is both positive: +(+5), it is going to be +5.
IMPORTANT!
- and + = -
- and - = +
+ and + = +
What we are looking for: -14-8
So choice A is (-14)+8 which is simplified to -14+8. So, this one isn't right.
Choice B: 14-(-8)= 14+8. So, it's incorrect.
Choice C: 14+(-8)= 14-8. Again, it's not -14-8 so it's not right.
Choice D: (-14)+(-8)= -14-8. This equation matches the one we are looking for! So it's correct!
2. Same thing as number 1. Let's simplify the equation it wants us to find first.
(-14)-(-8)= -14+8
So -14+8 is what we are looking for.
Choice A: (-14)+8= -14+8. It matches! So it is correct. Let's look at the other options anyway.
Choice B: 14-(-8)= 14+8. Nope. Not right.
Choice C: 14+(-8)= 14-8 because - always beats +. So, this one is also incorrect.
Choice D: (-14)+(-8)= -14-8. Oops, this is also wrong. So choice A is the right answer.
Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:
(When there is a number outside and inside a parentheses, multiply them.)
2(5)=10, CORRECT! 2+(5) is not 2 times 5. It's whatever is closest to the parentheses, in this case being the positive sign. So + and 5 is just 5!
IMPORTANT!
-2(-5)= - and - is positive, so positive (2 times 5). Positive 10.
-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.
+2(+5)= + and + is positive, so positive (2 times 5). Positive 10.
In the figure below.. Please help!!!
====================================================
Explanation:
Both AB and XY are the first two letters of ABC and XYZ respectively. So we have one fraction of AB/XY = 2/7.
AC and XZ are the first and last letters of ABC and XYZ respectively. We can form another fraction AC/XZ. I'm dividing in the same order of small over large to keep things consistent. As you can probably guess, the order of the letters ABC and XYZ are important so we see how the angles match up and how the proportional sides match up.
Because the triangles are similar, the two fractions formed earlier are equal to one another.
The equation we need to solve is AB/XY = AC/XZ
-----
AB/XY = AC/XZ
2/7 = 3/N ... plug in given values
2N = 7*3 .... cross multiply
2N = 21
N = 21/2 .... divide both sides by 2
N = 10.5
ZX is 10.5 units long.
what percent of sales were shoes or socks? A.9% B. 39% C.52% D. 61%
Answer:
it is 9%
Step-by-step explanation: the socks persent is the correct answer
Answer: D. 61%
Step-by-step explanation:
In a random sample of people, the mean driving distance to work was miles and the standard deviation was miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a % confidence interval for the population mean . Interpret the results. Identify the margin of error.
Complete Question
In a random sample of ten people, the mean driving distance to work was 23.1 miles and the standard deviation was 6.6 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 99% confidence interval for the population mean Interpret the results. Identify the margin of error.
Answer:
The 99% confidence interval is [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
The margin of error is [tex]E = 6.783[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 23.1[/tex]
The standard deviation is [tex]\sigma = 6.6 \ miles[/tex]
The sample size is n = 10
Generally the degree of freedom is mathematically represented as
[tex]df = n-1[/tex]
=> [tex]df = 10-1[/tex]
=> [tex]df =9[/tex]
Given that the confidence level is 99% , the n the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha =1\%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] with a df of 9 from from the student t-distribution table the value is
[tex]t _{\frac{\alpha }{2} , df } = 3.250[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , df } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 3.250 * \frac{6.6 }{\sqrt{10} }[/tex]
[tex]E = 6.783[/tex]
The 99% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]23.1 - 6.78 < \mu <23.1 + 6.78[/tex]
=> [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
If 5x + 2 =12x- 5, then x = ?
Answer:
x = 1
Step-by-step explanation:
First, move all the variables to one side by subtracting 5x on both sides:
5x + 2 = 12x - 5
2 = 7x - 5
Add 5 to both sides:
7 = 7x
1 = x
Answer:
x=1
Step-by-step explanation:
5x + 2 =12x- 5
Subtract 5x from each side
5x-5x + 2 =12x-5x- 5
2 = 7x-5
Add 5 to each side
2+5 = 7x-5+5
7 = 7x
Divide each side by 7
7/7 = 7x/7
1 =x
A recent national survey found that high school students watched an average (mean) of 7.1 movies per month with a population standard deviation of 1.0. The distribution of number of movies watched per month follows the normal distribution. A random sample of 33 college students revealed that the mean number of movies watched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students? State the null hypothesis and the alternate hypothesis.
Answer:
H0: μc ≤ μs Ha :μc > μs
Step-by-step explanation:
The null and alternate hypotheses can be stated as
H0: μc ≤ μs Ha :μc > μs one tailed test
Where
μc = Mean of college students watching movies in a month
μs = Mean of school students watching movies in a month
For one tailed test of α =0.05 the value of Z= ± 1.645
The critical region will be Z > ± 1.645
It is of importance to note that by rejecting the null hypothesis and accepting the alternate hypothesis we are automatically rejecting all values of mean that are greater than 7.1
6th grade math. :) help me please
Answer:
8 3/4
Step-by-step explanation:
The decimal 3.5 as an improper fraction is 35/10.
Answer:
[tex]8\frac{3}{4}[/tex]
Step-by-step explanation:
To write as a mixed number means that you will have a whole number and a fraction together. To find the mixed fraction version, see how many times the denominator (bottom) fits into the numerator (top) evenly.
4, 8, 12, 16, 20, 24, 28, 32, 36
1 2 3 4 5 6 7 8 9
4 can go into 35 '8' times without being greater than the numerator. 8 is the whole number. Now subtract the original numerator by the product of 4 and 8, which is 32:
[tex]35-32=3[/tex]
3 is the new numerator. Keep the same denominator. Insert all values:
[tex]\frac{35}{4}=8\frac{3}{4}[/tex]
:Done
Which table represents the same linear relationship as the equation y=2x•6? (answers are in the image) Please include ALL work!
Answer:
Table in option C represents the linear relationship as the equation, [tex] y = 2x + 6 [/tex]
Step-by-step explanation:
The equation given seems to be wrong. The equation should be [tex] y = 2x + 6 [/tex], because, taking a look at the tables given, the table in option C is the only table that has values that conforms to the equation, [tex] y = 2x + 6 [/tex].
In table C, when x = 2 using the equation, [tex] y = 2x + 6 [/tex], thus,
[tex] y = 2(2) + 6 = 4 + 6 = 10 [/tex].
When x = 3,
[tex] y = 2(3) + 6 = 6 + 6 = 12. [/tex]
Theredore, the equation, [tex] y = 2x + 6 [/tex], represents the relationship between the X and y variables in the table in option C.
i need help really bad
Answer:
see explanation
Step-by-step explanation:
If f(x) and [tex]f^{-1}[/tex] are inverse functions, then
f([tex]f^{-1}[/tex])(x) = x
Thus substitute x = [tex]f^{-1}[/tex] (x) into f(x)
f([tex]\frac{x+6}{5}[/tex] )
= 5 ([tex]\frac{x+6}{5}[/tex] ) - 6
= x + 6 - 6
= x
Thus f(x) and [tex]f^{-1}[/tex] (x) are inverse functions
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Is the following relation a function? (1 point) x y −1 −2 2 3 3 1 6 −2 No Yes
Answer:
Yes because no same x-value resulted in different y-values.
Answer:
Yes
Step-by-step explanation:
If you have $100 in a savings account earning 3% interest per year, how much will you have in
two years?
Answer:
$106
Step-by-step explanation:
You have 100$ in savings account
Interest rate =3%
Time = 2 years
Total in 2 years:
100 + 2*3% = 100 *1.06= $106The interest formula is as follows:
Amount Invested · Rate = Interest Earned
If we invest $100 at 3% interest per year,
how much do we earn that year?
Well based on our formula, we can simply multiply 100 · 3%.
Think of the 3% as 3/100.
So we have 100 · 3/100 and the 100's cancel and we're left with 3.
So $3 is earned in 1 year.
So after two years, you will have double that or $6.
Open the graphing tool. Move the slider for the equation y = kx3 to a position of your choice, where k ≠ 1. Next, move the slider of y = (kx)3 so the two graphs lie on top of one another. How do the values of k compare with one another in this situation? Why do you think that is?
Answer:
For the functions to coincide, the value of k in y = (kx)3 must be smaller than in y = kx3. This is because the value of y changes more rapidly when k is cubed inside the parentheses. The behavior of the functions is similar since a vertical stretch is similar to a horizontal compression.
Step-by-step explanation:
PLATO
Solve for y:1(y+3)=2(y+−4)+−7
Answer:
[tex]\large \boxed{{y=18}}[/tex]
Step-by-step explanation:
[tex]1(y+3)=2(y+-4)+- 7[/tex]
Expand brackets.
[tex]y+3=2y-8+- 7[/tex]
Simplify.
[tex]y+3=2y-15[/tex]
Add -y and 15 on both sides.
[tex]y+3-y+15=2y-15-y+15[/tex]
Simplify.
[tex]3+15=2y-y[/tex]
[tex]18=y[/tex]
Answer:
18
Step-by-step explanation:
● 1 (y+3) = 2 (y+(-4) )+ (-7)
When you multiply by 1 you get the same result.
● y+3 = 2 (y+(-4))+(-7)
When you have a + sign with a - sign write -.
● y+3 = 2(y-4)-7
Multiply 2 by (y-4) and simplify
● y+3 = (2y-8)-7
● y+3 = 2y -8-7
● y+3 = 2y -15
Add 15 to both sides
● y +3+15 = 2y-15 +15
● y + 18 = 2y
Sibstract y from both sides
● y +18 - y = 2y -y
● 18 = y
PLZZZZ helpppp will give good rating say thanks and say thank you on your account
Yak Travel Agency arranges trips for climbing Mount Everest. For each trip, they charge an initial fee in addition to $0.15 for each vertical meter climbed. For instance, the price for climbing all the way to the summit, which is 3500 meters above the base of the mountain, is $645. Let F represent the fee (in dollars) of a trip where they climbed ddd vertical meters. Complete the equation for the relationship between the fee and vertical distance.
Factor.
x2 – 5x - 36
(x - 9)(x + 4)
(x - 12)(x + 3)
(x + 9)(x - 4)
(x + 12)(x - 3)
Answer:
The answer is option AStep-by-step explanation:
x² - 5x - 36
To factor the expression rewrite -5x as a difference
That's
x² + 4x - 9x - 36
Factor out x from the expression
x( x + 4) - 9x - 36
Factor out -9 from the expression
x( x + 4) - 9( x+ 4)
Factor out x + 4 from the expression
The final answer is
( x - 9)( x + 4)Hope this helps you
Answer:
[tex] \boxed{(x - 9) \: (x + 4) }[/tex]
Option A is the correct option.-
Step-by-step explanation:
( See the attached picture )
Hope I helped!
Best regards!
An oblique cone has a radius of 5 units and a height of 9 units. What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth. 117.8 cubic units 141.3 cubic units 235.5 cubic units 282.6 cubic units
Answer:
235.6 units^3
Step-by-step explanation:
The formula for the volume of the oblique cone is the same as for the volume of a right circular cone: V = (1/3)(base area)(height).
Here that comes to V = (1/3)(π)(5 units)^2*(9 units), or
V = 75π units^3, or approximately 235.6 units^3
Answer:
235.5 cubic units
Step-by-step explanation:
Order the following from least to greatest.
1/16
.0173
1/7
2.2
-0.25
Answer:
1.-0.25 2..0173 3. .1/16 4. 1/7 5.2.2
Step-by-step explanation:
You want to put all numbers in fractions to see which numbers are smallest
Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
The sequence below represents Marisa’s fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa’s library fine as a function of a book that is n days overdue? f(n) = 0.15n f(n) = 0.50n f(n) = 0.15n + 0.35 f(n) = 0.50n + 0.15
Answer:
f(n) = 0.15n + 0.35Step-by-step explanation:
The sequence of the problem above is an arithmetic sequence
For an nth term in an arithmetic sequence
F(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
To find the equation first find the common difference
0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15
The first term is 0.5
Substitute the values into the above formula
That's
f(n) = 0.5 + (n - 1)0.15
f(n) = 0.5 + 0.15n - 0.15
The final answer is
f(n) = 0.15n + 0.35Hope this helps you
Answer:
The correct option is: f(n) = 0.15n + 0.35Step-by-step explanation:
Took the math test on edge
simplify each expression 17x + 4 - 3x
Answer:
14x+4
Step-by-step explanation:
17x-3x=14x
A set of 9 numbers {3, 3, 4, 5, 5, 5, 6, 7, 7} has a mean of 5. Another number is added to the set, and the mean becomes 6. What number is added to the set?
Answer:
15
Step-by-step explanation:
3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7=45
You would then divide that my 9(the amount of numbers) to get three
(3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7)/9
=3
If you are adding a number the numbers would be
3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7+?/10
Its ten because now you would have 10 numbers.
You know it equals 6, so you ask yourself: What divided by 10 would give you 6 or this equation:
( 3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7+?)/10=6
(45+?)/10=6
multiply both sides of the equal sign by 10
10(45+?)/10=6*10
The 10 on the bottom of the left side cancels out.
(45+?)=60
Subtract 15 from both sides of the equal sign
45+?-45=60-45
?=15
In the number 5,794,032,861, which digit is in the ten millions place?
09
0 5
o 7
0 4
A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively In order to test the equal variance assumption for two populations, Can we assume population variances are equal at the 10% significance level? (sigma subscript 1 superscript 2 space equals space sigma subscript 2 superscript 2 )
Answer:
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
Step-by-step explanation:
The null and alternative hypothesis are given by
H0: σ₁²= σ₂² against Ha: σ₁² ≠ σ₂²
Confidence interval for the population mean difference is given by
(x`1- x`2) ± t √S²(1/n1 + 1/n2)
Where S ²= (n1-1)S₁² + S²₂(n2-1)/n1+n2-2
Critical value of t with n1+n2-2= 50+ 35-2= 83 will be -1.633
Now calculating
S ²=34* (12.8)²+ (14.6)²*49/83= 192.96
Now putting the values in the t- test
(75.1 -72.1) ± 1.633 √ 192.96(1/35 +1/50)
=3 ± 5.09
=-2.09, 8.09 is the 90 % confidence interval for the difference
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
what is the equation for a parabola with a focus at (2,2) and a directix of x=8
Answer:
( y-5) ^2 =-12(x-2)
Step-by-step explanation:
focus at (2,2) and a directrix of x=8
Using the equation
( y-k) ^2 = 4p(x-k)
where ( h,k) is the vertex
The vertex is 1/2 way between the focus and the directrix
( 2+8)/2 , 2
5,2 is the vertex
( y-5) ^2 = 4p(x-2)
distance from the focus to the vertex and from the vertex to the directrix is
| p|
2-5 = p
-3 = p
( y-5) ^2 = 4*-3(x-2)
( y-5) ^2 =-12(x-2)
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
