9514 1404 393
Answer:
{-2, 9}{-7, -1.5}Step-by-step explanation:
Finding the x-intercepts means finding the solutions to ...
equation = 0
There are a number of ways you can do this, including ...
the quadratic formularewriting to vertex form and solvingfactoringgraphingasking on BrainlyOften, these can be solved fairly easily by factoring. The methods used for a leading coefficient of 1 and for leading coefficients other than 1 are not so different. In general, you are looking for factors of a number that have some particular sum. Familiarity with multiplication tables is helpful for this.
__
1. x^2 -7x -18 = 0
You want factors of -18 that have a sum of -7.
-18 = -18(1) = -9(2) = -6(3) . . . . . sums are -17, -7, -3
The factors -9 and 2 are the ones of interest here. These make up the constants in the binomial factors of the expression:
x^2 -7x -18 = (x -9)(x +2)
The x-intercepts are the values of x that make these factors zero. Basically, they are the opposites of the factor constants:
x -9 = 0 ⇒ x = 9
x +2 = 0 ⇒ x = -2
The x-intercepts are -2 and 9.
__
2. 2b^2 +17b +21 = 0
You work this almost the same way, but you're looking for factors of (2)(21) = 42 that have a sum of 17. That is, the leading coefficient multiplies the constant to give the number being factored.
42 = 1(42) = 2(21) = 3(14) = 6(7) . . . . sums are 43, 23, 17, 13
The factors 3 and 14 have a sum of 17.
When the leading coefficient is not 1, several methods are taught for finding the binomial factors. One that works is to rewrite the middle (linear) term using the factors found, then factor by grouping pairs of terms:
(2b^2 +3b) +(14b +21) = 0
b(2b +3) +7(2b +3) = 0
(b +7)(2b +3) = 0
The same deal applies for finding the x-intercepts. They are the values of x that make these factors zero:
b +7 = 0 ⇒ b = -7
2b +3 = 0 ⇒ b = -3/2
The x-intercepts are -1.5 and -7.
_____
I attached the graph of these expressions to show the correctness of the above, and to illustrate my favorite way to answer these questions: let a graphing calculator show the answer.
Someone help my cousin has been stuck on this question and please explain how you got the answer thank you!!!
Answer:
the first one is 6 and the second one is -2
Step-by-step explanation:
bc/2 ---> (3)(4)/2 = 12/2 = 6
4a + 6 = 4(-2) + 6 = -8 + 6 = -2
Why did the troll give us the clues
We had no money in our pockets
He was nice
So we can get confused
Answer:
lol
Step-by-step explanation:
im laughing in class
Use the following data from two independent samples, one group of students who received six months of standard treatment for their adjustment disorder, and a separate group of students who received six months of multicultural orientation treatment for their adjustment disorder. You will do the calculations below that will lead to conducting a t-Test for Two Independent Samples. Based on your results, you will then determine if the post-treatment adjustment scores are significantly different for the two independent samples. Your lab instructors will inform you how to submit this Lab Individual Assignment for grading.
Multicultural Framework (Sample A) Standard Treatment (Sample B)
9 7
11 8
13 10
10 6
11 8
9 5
15 7
14 12
10 5
Required:
a. n1= _________ and n2=________
b. df1= _________ and df2=_______
c. Total df=______
Answer:
[tex]n1 = 9[/tex] and [tex]n2 = 9[/tex]
[tex]df1 = 8[/tex] and [tex]df2 = 8[/tex]
[tex]df = 16[/tex]
Step-by-step explanation:
Given
The above data
Solving (a): n1 and n2
This is the number of rows in each category
For sample A
[tex]n1 = 9[/tex]
For sample B
[tex]n2 = 9[/tex]
Solving (b): df1 and df2
This is calculated as:
[tex]df = n - 1[/tex]
For n1:
[tex]df1 = n1 - 1[/tex]
[tex]df1 = 9 - 1[/tex]
[tex]df1 = 8[/tex]
For n2:
[tex]df2 = n2- 1[/tex]
[tex]df2 = 9- 1[/tex]
[tex]df2 = 8[/tex]
Solving (c): Total df
Since there 2 categories of data, the total degrees of freedom is:
[tex]df = n1 + n2 - 2[/tex]
[tex]df = 9 + 9 - 2[/tex]
[tex]df = 16[/tex]
An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answer:
The value of the test statistic is -2.64.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected(claimed) mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating.
This means that [tex]\mu = 40.3[/tex]
After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4.
This means, respectively, that:
[tex]n = 250, X = 39.9, \sigma = 2.4[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{39.9 - 40.3}{\frac{2.4}{\sqrt{250}}}[/tex]
[tex]t = -2.64[/tex]
The value of the test statistic is -2.64.
Identify the GCF and then factor out: 6x2y + 12xy2
Answer:
6xy(x+2y)
Step-by-step explanation:
6x²y+12xy²
The GCF between 6 and 12 is 6. Factor out 6.
= 6(x²y+2xy²)
The GCF between x² and x is x. Factor out x.
= 6x(xy+2y²)
The GCF between y and y² is y. Factor out y.
= 6xy(x+2y)
Therefore, the GCF of the expression is 6xy and the factored expression is 6xy(x+2y).
I hope this helps!
What is the value of x in the following figure?
A. 38°
B. 52°
C. 142°
D. 128°
Answer:
b
Step-by-step explanation:
What is the answer ??
Answer:
M=1
Step-by-step explanation:
2m = 7/2 - 3/2
2m= 4/2
2m=2
M=2/2
M=1
10) Julio rented a bike from Bill's Bikes. It
cost $20 plus $6 per hour. If Julio paid
$50, then he rented the bike for how many
hours?
......................
Answer:
[tex]-1/x^2[/tex]
Step-by-step explanation:
First, let's simplify the expression on the right:
[tex]1/\sqrt{x^2}=1/x[/tex]
Next, rewriting 1/x as x⁻¹, we can use the power rule to differentiate both sides with respect to x:
[tex]y=x^{-1}\\dy/dx=d/dx(x^{-1})\\dy/dx=-x^{-2}=-1/x^2[/tex]
so you have 5 feet into 13 rods what is the total length?
Answer:
15
Step-by-step explanation:
t¡yesç
Gabby is Mines >:) !
Answer:
b.nun1
Step-by-step explanation:
Lori has $450 in her bank account. She withdraws $20 a month for
her gym membership. Construct a linear equation to model Lori’s
bank balance for any given month.
Answer:
I cant give you a linear graph but i can give you the equation and you can graph it. y=20x+450
Step-by-step explanation:
Answer:
Y = -20x + 450.
Step-by-step explanation:
How many days are there in 6 weeks? Solve the related word problem to represent the inverse operation There are days in 6 weeks How many weeks are equal to 42 days? Since 42 =27= 42 days is equal to weeks 2
pls help me
Answer:
there a 42 days in 6 weeks
Step-by-step explanation:
multiply 6 x 7= 42
Please help me with this answer, thank you
Answer:
i think its A
Step-by-step explanation:
You are buying a coat that cost $150. You have a 10%
off coupon to use.
Answer: 135
Step-by-step explanation:
Answer:
$135
Step-by-step explanation:
the half-life of radium-224 is approximately 3.66 days. How much of a 5-gram sample of radium-224 would remain after 9 days? Round to three decimal places.
Answer:
Step-by-step explanation:
5×0.5^(9/3.66) = 0.9 gram
0.9 gm of radium-224 would remain after 9 days.
What is Half life?A radionuclide's half-life is the amount of time it takes for half of its radioactive atoms to decay. A good rule of thumb is that you will have less radiation than 1% of the original amount after seven half-lives.
We have,
The half-life of radium-224 is approximately 3.66 days.
Amount of radium- 224 to be decayed= 5 gm
So, the amount of radius-224 that remained after 9 days are
= 5 × [tex]0.5^{(9/3.66)[/tex]
= 5 x 0.1818
= 0.9 gram
Thus, the remaining amount is 0.9 gm.
Learn more about Half life here:
https://brainly.com/question/24710827
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What is 21+G as an algebraic expression?
Answer:
i dont know
Step-by-step explanation:
lol
Answer:
(20 + 1) + G
Step-by-step explanation:
PLEASE HELP!
find the missing value:
Answer:
um
Step-by-step explanation:
Which figure could be the result of dilating this triangle with a scale factor greater than 1? On a coordinate plane, a triangle has points (0, 0, (0, 3), (6, 0). On a coordinate plane, a triangle has points (0, 0), (0, 3), (9, 0). On a coordinate plane, a triangle has points (0, 0), (0, 1), (6, 0). On a coordinate plane, a triangle has points (0, 0), (0, 5), (10, 0). On a coordinate plane, a triangle has points (0, 0), (0, 2), (4, 0).
Answer:
C
Step-by-step explanation:
Edge
The required figure has been attached below could be the result of dilating a given triangle with a scale factor greater than 1. The correct answer would be an option (C).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle has points (0, 0), (0, 3), and (6, 0) which are given in the question.
As per option (C), we have
On a coordinate plane, a triangle has points (0, 0), (0, 5), and (10, 0).
This result of dilating a given triangle with a scale factor greater than 1.
The required figure has been attached below which represents the dilation.
The correct answer would be an option (C).
To learn more about the transformations click here :
https://brainly.com/question/28029674
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3. How far does the ant crawl to get from the base of the cone to the top of the hill?
Show your work
Write your answer in the space below.
Please helppp
Answer:
The ant has to crawl an approximate distance of 29mm
Step-by-step explanation:
Given
[tex]Volume = 8792mm^3[/tex]
[tex]r = 20mm[/tex] --- radius
See attachment
Required
Distance the ant has to crawl (i.e. the slant height)
First, we calculate the height of the hill
The volume of a cone is:
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
[tex]8792 = \frac{1}{3} * \frac{22}{7} * 20^2*h[/tex]
[tex]8792 = \frac{1}{3} * \frac{22}{7} * 400*h[/tex]
[tex]8792 = \frac{22* 400}{3*7} *h[/tex]
Make h the subject
[tex]h = \frac{8792 * 3 * 7}{22 * 400}[/tex]
[tex]h = \frac{184632}{8800}[/tex]
[tex]h = 20.98mm[/tex]
To calculate the slant height (s), we apply Pythagoras theorem
[tex]s^2=h^2 + r^2[/tex]
[tex]s^2=20.98^2 +20^2[/tex]
[tex]s^2=840.1604[/tex]
[tex]s=\sqrt{840.1604[/tex]
[tex]s=28.9855205232[/tex]
[tex]s= 29mm[/tex] --- approximated
Point A is translated 4 units left and 3 units up. What are the coordinates of point A in its new position ?
Answer:
A (-4,3)
Step-by-step explanation:
Answer:
(-4,3)
Step-by-step explanation:
know that left and right is the x axis we start from there. left is negative right is positive, so I know 4 unit left is -4.
knowing that up and down is the y axis and y axis always comes second. up is positive down is negative. so I know that 3 units up is positive.
thats how we got( -4,3)
Susan and Tom want to know the combined amount of money they earned last week. They both earned $9 per hour, but Susan also earned a $45 bonus. Susan added her earnings to Tom's earnings to write the expression (9S + 45) + 9T, where S is the number of hours she worked, and Tis the number of hours Tom worked. Tom added their combined hourly wages to Susan's bonus to write the expression 9(S + T) + 45. Which of the following statements is true?
Answer:
A - both correct
Step-by-ste
Question 1
1 pts
The area of triangle LMN is 36 square inches. Find the base.
8 in.
M
?
inches
Answer:
Step-by-step explanation:
Did you get the answer?
What is h?
Problem 23h=12
Answer:
h=[tex]\frac{12}{23}[/tex]
h=0.52173913043
Step-by-step explanation:
23h=12
divide 12 by 23
h=[tex]\frac{12}{23}[/tex]
h=0.52173913043
Hope this helps! :)
Answer:
it will be 1.91 or if want rounded to nearest tenth it will be 1.9
Step-by-step explanation:
dont have a explanation nut i hopes this help.
Please help me with this question:)!
Answer:
i think so option b is the correct option.
Step-by-step explanation:
because 3+7=10 not 11.
Find the surface area of the rectangular prism.
7 in
1 in
3 in
Answer:
[tex]62in^2[/tex]
Step-by-step explanation:
Formula of total surface area of a prism:
[tex]2(lb+bh+lh)[/tex]
= 2[(7x3)+(1x3)+(1x7)]
= 2[21+3+7]
= 2 x 31
= [tex]62in^2[/tex]
Alexa has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cups holds 8 ounces of lemonade and each large cup hold 16 ounces of lemonade. Alexa used 320 ounces of lemonade and sold twice as many small cups as large cups. Determine the number of small cups sold and the number of large cups sold. how do I set this equation up to get 10?
Answer:
l = large cups amount of large cups = 16 x ounces
small cups = 2x amount of small cups = 8 (2x) summed = 320 ounces
16x + 8 (2x) = 320 solve for 'x' the number of 16 ounce cups, the 8 ounce cups = 2x
Step-by-step explanation:
l = large cups amount of large cups = 16 x ounces
small cups = 2x amount of small cups = 8 (2x) summed = 320 ounces
16x + 8 (2x) = 320 solve for 'x' the number of 16 ounce cups, the 8 ounce cups = 2x
natural numbers start from 0 true or false
false it starts from 1 and continues
Answer:
False because natural numbers start from 1
Match the following key attributes for the graph
Answer:
Domain: [-4, ∞]
Range: [-6, ∞]
Step-by-step explanation:
The domain is the set of the possible x values
The range is the set of the possible y values.
In the graph, we can see that the function cuts in a given part. We can see that for the x-values, the smallest one is x = -4, and then the function extends to the right (we see no limit at the right, then there is none)
This means that the domain is:
D: [-4, ∞]
For the y-values, the smallest value is when x = -4, and the y-value is -6
Then we can see that, as x increases, the same happens for y.
Then the range is:
R: [-6, ∞]
0.0001859 in scientific notation
Answer:
1.859 x 10^-4
Step-by-step explanation:
To the -4 power means to move the decimal place to the right 4 spaces.