Answer:
[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]
Find the slope between the two points given. Then, use the slope and one of the points to write the
equation of the line in Slope-Intercept form. State the slope and y-intercept.
Answer:
The slope is -2
y =-2x - 1
Step-by-step explanation:
The slope is -2 or -2/1.
The slope is the change in y over the change in x. The ordered pair is written in the form (x,y) The first number is the x coordinate and the second number is the y coordinate.
(1, -3) (0, -1) The -1 and the -3 are the y coordinates. We subtract these.
-1 -(-3) is the same as
- 1 + 3 which is 2.
(1, -3) (0, 1,) the 1 and the 0 are the x coordinates. We subtract these
0 - 1 is -1
The change in y is 2 and the change in x is -1, so our slope is -2/1 which is the same as -2.
To write the equation we need the slope and the y intercept. We have the slope now. We need to find the y-intercept. We will use the slope and one of the points to find the y-intercept. It does not matter which of the two points (1,-3) or (0,-1). I will use (0,-1)
y = mx + b The b is the y-intercept which is what we are looking for
-1 = -2(0) + b
-1 = 0 + b
-1 = b
y = -2x -1
1. Solve x² +5x+3=0
Give your solutions correct to 2 decimal places.
Answer:
Step-by-step explanation:
hello :
x² +5x+3=0
delta = b²-4ac when : a =1 and b=5 c=3
delta =5²-4(1)(3) =13
X1 =(-b-sqrt(delta))/2a
X2 =(-b+sqrt(delta))/2a
continu.....
Difference of Squares gives which complex factors for the expression x² +11?
A. (x+√11)2(x-i√11)²
B. (x+√11)(x+√11)
C. (x-i√11)(x-√11)
D. (x+√11)(x - √11)
Answer:
Step-by-step explanation:
Discussion
i has to appear somewhere. That lets D and B out. They are both wrong.
C has only one i. It can't be right either. You need 2 i-s which will multiply to +1 when squared. That leaves you with a.
The way a is written, it can't be the answer either. For one thing, that 2 makes the answer question at best.
I would say there is no correct answer. Could you check the question? Also it would be a good idea to ask your instructor how this works, in case I'm wrong.
Find QR.
A).12
B).-8
C).9
D).6
Answer:
D. 6
Step-by-step explanation:
Let's first find x :-
[tex]\sf 3 + 2x + 22 = x + 17[/tex]
[tex]\sf 2x + 25 = x + 17[/tex][tex]\sf 2x - x = 17 - 25[/tex][tex]\sf x = - 8[/tex]Now that we found x, let's find QR :-
QR = 2x + 22
[tex]\sf QR = 2( - 8) + 22[/tex][tex] \sf - 16 + 22[/tex][tex]\sf 6[/tex]Therefore, QR = 6 !!!
Triangle abc has vertices at A(-6, 3) , B(3, 5) and C(1, -4). Show that triangle abc is isosceles and find the area of this triangle.
Using the formula for the distance between two points, it is found that:
Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.The area is of 38.63 units squared.What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we use the formula to find the lengths for each side of the triangle.
For example, side AB has length given by the distance between (-6,3) and (3,5), hence:
[tex]AB = \sqrt{(-6 - 3)^2 + (3 - 5)^2} = 9.22[/tex]
Side AC has length given by:
[tex]AC = \sqrt{(-6 - 1)^2 + (3 - (-4))^2} = 9.9[/tex]
Side BC has length given by:
[tex]BC = \sqrt{(3 - 1)^2 + (5 - (-4))^2} = 9.22[/tex]
Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.
What is the area of a triangle?The area of a triangle is given by half the length of the base multiplied by the height.
The midpoint of side BC, of length of 9.22 units, is of (2,0.5). The height is the distance of this point from point A, hence:
[tex]d = \sqrt{(-6 - 2)^2 + (3 - 0.5)^2} = 8.38[/tex]
Hence the area is:
A = 0.5 x 9.22 x 8.38 = 38.63 units squared.
More can be learned about the distance between two points at https://brainly.com/question/18345417
#SPJ1
Find the Simple Intrest on
#60,000.00 for 3 years at
5% per annum
Answer:
the ans is 9000
Step-by-step explanation:
simple interest= 60000*3*5/100
Round to 4 significant figures 2.3581x10^3
Answer:
2358.1
Step-by-step explanation:
2.3581 x 10^3
= 2.3581 x 10000
=2358.1
3 p2 9 p = 6 Add 6 to both sides to set the right side to o 3 p2 9 p 6=04 Divide everything by 3 p2 3 p 2 =0 ( P 1)(p 2) = 0 P 1 = 0 OR P 2 = 0 P=-1 P= -2
The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
Finding the solution of a quadratic equation
The given equation is:
[tex]3p^2-9p=6[/tex]
This can be re-written as:
[tex]3p^2-9p-6=0[/tex]
Solve for p by factorization
[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]
Equate each of the factors to zero
3p - 6 = 0
3p = 6
p = 6/3
p = 2
p - 1 = 0
p = 1
Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
Learn more on quadratic equation here: https://brainly.com/question/1214333
#SPJ1
Molly wants to buy a dress that costs $20. She has a coupon for 40% off, and there is a 10% sales tax. how much will she pay all together
1. after using the coupon what is the sale price of the dress Show Your Work
2.how much is th 10% tax on the sale price Explain how you found your answer
Answer:
$13.50
Step-by-step explanation:
If I am taking off 40%, that means that the dress now cost 60% of the original cost. .6 x 20 is 12.
You could also calculate the 20% off and subtract that from the original cost. .4 x 20 =8. Now 20 - 8 is also 12.
Now, we have to calculate the tax. 10% of 12 is .1 x 12 or $1.20. We add the tax to the 12 to get 13.50.
I need the answer to this
Answer:
63.2
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
ST/16 = 31.6/8ST = 63.2Which equation is an integer?
5-3 =
6-10 =
11.6 - 3 =
63 - 4 x 5 =
[tex]5-3=2\\\\6-10=-4\\\\11.6-3=8.6\\\\63-4\times 5=63-20=43[/tex]
So, the first, second, and fourth equations are integers.
The first and last are positive integer and second is negative integer.
What are integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
a) 5-3 =2
b) 6-10 = -4
c) 11.6 - 3 =8.6
d) 63 - 4 x 5 =63- 20 = 43
So, among the above first and last are positive integer and second is negative integer.
Learn more about integers here:
https://brainly.com/question/15276410
#SPJ2
Question for 60 Points
Using the Factor Theorem to find the equation of the parabola, we have that:
[tex]a + b + c = -\frac{48}{7}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, we have a horizontal parabola, defined as follows:
[tex]f(y) = a(y - y_1)(y - y_2)[/tex].
The roots are [tex]y_1 = -1, y_2 = -7[/tex], hence:
f(y) = a(y + 1)(y + 7)
f(y) = a(y² + 8y + 7).
The x-intercept is of x = -3, hence f(0) = -3, so:
[tex]-3 = 7a[/tex]
[tex]a = -\frac{3}{7}[/tex]
Then the equation is:
[tex]x = -\frac{3}{7}y^2 - \frac{24}{7}x - 3[/tex]
Then the sum of the coefficients is:
[tex]a + b + c = -\frac{3}{7} - \frac{24}{7} - \frac{21}{7} = -\frac{48}{7}[/tex]
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
#SPJ1
Answer:
Hello!
Step-by-step explanation:
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 11 ounces.
Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.
a) 68% of the widget weights lie between________and_______
b) What percentage of the widget weights lie between 24 and 57 ounces?
c) What percentage of the widget weights lie below 79
Using the Empirical Rule, it is found that:
a) 68% of the widget weights lie between 35 and 57.
b) The percentage is 81.5%.
c) The percentage is 99.85%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For this problem, we have that:
In item a, 68% of the widgets are within 1 standard deviation of the mean, hence between 35 and 57.In item b, between 2 standard deviations below the mean(95% of 50% due to the symmetry of the normal distribution) and 1 above(68% of 50%), hence the percentage is: P 34% + 47.5% = 81.5%.For item 3, below 3 standard deviations above the mean, hence removes only the top 0.15%, hence 99.85%.More can be learned about the Empirical Rule at https://brainly.com/question/4079902
#SPJ1
Determine the function f(x)= kx+m if f(x-1)-f(x)=2 and f(-2)=1-m
[tex]f(x) = kx + m \\ f(x - 1) = k(x - 1) + m[/tex]
[tex]f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2[/tex]
[tex]f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2} [/tex]
[tex]f(x) = - 2x - \frac{3}{2} [/tex]
In science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. If x represents a student's score, write an equation that represents the
minimum and maximum scores.
The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.
Which equations represents the minimum and maximum possible scores of each student?According to the task content, the
Average score of the students in the science class is; 87 points
All students are within 1.8 points of the average,
it therefore follows from the task content that the
minimum score is;
= 87 -1.8
= 85.2
maximum score is;
= 87+1.8
= 88.8 points.
Read more on average and deviation;
https://brainly.com/question/285157
#SPJ1
Answer:
Step-by-step explanation:
A. |x − 87| = 1.8
-hope this helps.
p(m) = 2m² − 4m + 3, find p(1/3)
Answer:
17/9
Step-by-step explanation:
Plug in 1/3 as m.
2*(1/3)^2 - 4(1/3) + 3 = 17/9
You are offered two different sales jobs. The first company offers a straight commission of 5% of the sales.
The second company offers a salary of $ 210 per week plus 2% of the sales. How much would you have to
sell in a week in order for the straight commission offer to be at least as good?
Answer:
The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.
Step-by-step explanation:
.05x = .02x + 210 Subtract .02x from both sides.
.03x = 210 Divide both sides by .03
x = $7,000.
The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. Which statements are true about g(x)? Select three options. The axis of symmetry is the line x = –5. The vertex of the graph is (5, –37). The parabola has a minimum. The parabola opens up. The value of a, when the equation is written in vertex form, is negative.
Answer:
The vertex of the graph is (5, -37) [see attached image]The parabola has a minimum [the coefficient of x² is positive]The parabola opens up [the coefficient of x² is positive]All the correct statements are,
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function g(x) = 10x² - 100x + 213 written in vertex form is,
⇒ g(x) = 10(x – 5)² – 37.
Since, General equation is,
y = a (x - h)² + k
Where, (h, k) is vertex of parabola.
Hence, We get;
The vertex of the graph is (5, -37)
Since, the coefficient of x² is positive
Hence, The parabola has a minimum
And, The parabola opens up.
Thus, All the correct statements are,
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ5
Which of the following is true about horizontal asymptotes?
a.) A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ .
b.) All horizontal asymptotes describe what happens when x gets close to 0 .
c.) All rational functions have at least one horizontal asymptote.
d.) All horizontal asymptotes describe what happens when the denominator's value gets close to 0.
A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
What are horizontal asymptotes?A horizontal asymptote of a graph can be defined as a horizontal line at y = b where the graph tend to approach the line as an inputs approach to infinity ( ∞ or –∞).
A slant asymptote of a graph is known as a slanted line y = mx + b where the graph approaches the line as the inputs approach the positive infinity ∞ or to the infinity –∞.
Thus, a function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
Learn more about horizontal asymptotes here:
https://brainly.com/question/1851758
#SPJ1
In 2012, the population of a city was 6.38million. The exponential growth rate was 2.38% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9million?
d) Find the doubling time.
Question content area bottom
Part 1
a) The exponential growth function is P(t)
enter your response here, where t is in terms of the number of years since 2012 and P(t) is the population in millions.
The exponential growth function is P(t) = 6.38 million x (1.0238^t).
The population of the city in 2018 is 7.35 million.
The year the population would be 9 million is 14.46 years.
The doubling time is 29.12 years.
What is the exponential growth function?FV = P (1 + r)^n
FV = Future populationP = Present populationR = rate of growthN = number of years6.38 million x (1.0238^t)
Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million
Number of years when population would be 9 million : (In FV / PV) / r
(In 9 / 6.38) / 0.0238 = 14.46 years
Doubling time = In 2 / 0.0238 = 29.12 years
To learn more about exponential functions, please check: https://brainly.com/question/18760477
#SPJ1
please no scam please answer ASAP 30 points need steps
QUE :
75 - [5 + 3 of (25 - 2 × 10)]
= 75 - [5 + 3 of ( 25 - 20)]
= 75 - [5 + 3 of 5]
= 75 - [5 + 15]
= 75 - 20
= 55
________________________________
HOPE IT HELPS
MARK BRAINLIEST!
FOLLOW ME!
A tree is 14 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet
Please Help! Brainliest Avaliable! Literally Multiple Choice!
It's very simple. Subract 554.26 from 866.32
then, we got the difference is
312.06
thank you
Brainlist please.
I need help with this geometry problem see the image
The coordinate of each point is just the number it corresponds to.
a) 6
b) -5
c) 9
d) 0
inverse function of f(x)=x-7/x+4
Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7
A rectangular waterbed is 8 ft long, 7 ft wide, and 1.5 ft tall. How many gallons of water are needed to fill the waterbed? Assume 1 gallon is 0.13 cu ft. Round to the nearest whole gallon.
646 gallons of water are needed to fill the waterbed
How to determine the gallons of water?The dimensions are given as:
8 ft long, 7 ft wide, and 1.5 ft tall
The volume is calculated as:
Volume = Length * Width * Height
So, we have
V = 8 * 7 * 1.5 cubic feet
Evaluate
V = 84 cubic feet
1 gallon = 0.13 cubic feet
So, we have:
V = 84/0.13 gallon
Evaluate
V = 646 gallons
Hence, 646 gallons of water are needed to fill the waterbed
Read more about volume at:
https://brainly.com/question/1972490
#SPJ1
3
If a product costs $15,000 for the first unit and there is
a 15% discount starting on the second unit, a 30%
discount (from the original price) starting on the 4th
unit, what would be the cost for 7 units?
It would cost $72,000 for 7 units of that product.
The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price. It is simply to say, 'discount' is a percentage of the listed price. A discount is a kind of price deduction in products that is noticed in consumer transactions, where the buyers have proposed a percentage of rebates on various products in order to boost sales. This rebate offered by the seller to buyer is known as a discount.
Original cost of product = $15,000.
For the second product there is a discount of 15%, thus selling price for the second product = $15,000 x 0.85 = $12750
For the fourth product and on there is a discount of 30%, thus selling price for the fourth product and on = $15,000 x 0.70 = $10500.
Thus total price of 7 units = $15,000 + $12750x2 + $10500x3
= $15,000 + $25,500 + $31500
= $72,000
Thus it would cost $72,000 for 7 units of that product.
Learn more about Discount here :
https://brainly.com/question/13501493
#SPJ1
Which graph represents the function f(x) =3(2)*?
I assume you meant [tex]f(x)=3(2)^x[/tex].
a company has six employees.The salary of five of the employees are P2200,P1300,P800,P940 and P560.When the sixth employee is included,the total monthly salaries of the employees becomes P7000.
Calculate the salary of the sixth employees
The company is joined by two more employees whose salaries are of equal amounts.The mean salary of all 8 employees is P1100
Calculate the monthly salary of each of the new employees
Answer:
First answer is 1200
Second answer is 900 for each new employee
Step-by-step explanation:
First answer:
2200+1300+800+940+560+x = 7000
5800+x = 7000 subtract 5800 from both sides and you get your answer
x = 1200
Second answer:
x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.
To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.
(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/
7000 +2x = 8800 Subtract both sides by 7000
2x = 1800 Divide both sides by 2
x = 900
Calculate the t-score for a sampling distribution mean of 10.5, a standard deviation of 1.5, and a size of 36 drawn from a population that has a mean of 10.
The t- score for a sampling distribution is 2
The t-score is the number of standard deviations from the mean in the t-distribution.
The upper and lower bounds of a confidence interval when the data are approximately normally distributed.
T-scores and confidence intervals
Confidence intervals use t-scores to calculate the upper and lower bounds of the prediction interval. The t-score used to generate the upper and lower bounds is also known as the critical t or t* value.
The t- distribution is given by
t=(x – μ) / (S / √n)
t = T – Distribution
x = sample mean
μ = population mean
S = standard deviation
n = Sample size
It is given that sampling distribution mean of 10.5, a standard deviation of 1.5, and a size of 36 drawn from a population that has a mean of 10.
We need to find the t-score for sampling distribution
t=(x – μ) / (S / √n)
Here, x= 10.5 , μ= 10, S=1.5, n=36
t = (10.5 - 10)/ (1.5 /√36)
t= 2
Hence the value of t-score is 2
Learn more about t-score here
https://brainly.com/question/13667727
#SPJ1