We need to examine each expression at a time.
(A) x^2 + x - 6
notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:
x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)
(B) In this cubic expression we cannot use the reverse FOIL to extract factors.
(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.
(D) x^2 + 8 x + 12
We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:
x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)
Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).
Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
12
x
−
9
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two
x
intercepts of the parabola and write them as a list of points of form (x, y) separated by commas:
It is OK to round your value(s) to to two decimal places.
The features of the given parabola are as follows:
a) Vertex: (3,9).
b) Vertical intercept: y = -9.
c) x-intercepts: (-5.12, 0) and (-0.88, 0).
Features of the quadratic functionThe equation of the parabola is given by:
f(x) = -2x² - 12x - 9.
Hence the coefficients are:
a = -2, b = -12, c = -9.
The formula for the coordinates of the vertex, considering the coefficients of a quadratic equation, is given as follows:
x = -b/2a.y = -(b² - 4ac)/(4a).The coordinates of the vertex are given as follows:
[tex]x_v = -\frac{-12}{2(-4)} = -3[/tex]
[tex]y_v = -\frac{(-12)^2 - 4(-2)(-9)}{4(-2)} = 9[/tex]
Hence (3,9).
The vertical intercept is given as follows:
f(0) = -2(0)² - 12(0) - 9 = -9.
The roots are given as follows:
[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{12 + \sqrt{(-12)^2 - 4(-2)(-9)}}{2(-2)} = -5.12[/tex][tex]x_{2} = \frac{-b - \sqrt{b^2 - 4ac}}{2a} = \frac{12 - \sqrt{(-12)^2 - 4(-2)(-9)}}{2(-2)} = -0.88[/tex]Hence the points are:
(-5.12, 0) and (-0.88, 0).
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Which term describes the slope of the line below?
•
A. Undefined
B. Zero
• C. Positive
D. Negative
Answer:
D. Negative
Step-by-step explanation:
The slope is negative because the line goes down from left to right. In other words, as x increases, y decreases.
A slope would be positive when the line goes up from left to right. In other words, as x increases, y increases.
A slope would be zero if the line is horizontal, so as x increases, y remains constant.
A slope would be undefined if the line is vertical. It is undefined because x remains constant while y changes. Lines are functions, which mean for every input there is exactly 1 output. If there are multiple y values for 1 x value, then this is not a function and therefore has an undefined slope.
A manufacturing machine has a 4% defect rate.
If 9 items are chosen at random, what is the probability that at least one will have a defect?
The probability that at least one will have a defect is 19%.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
p = 4% = 0.04
q = Prob of a defective product is 0.03; hence, Prob(non-defective) = 1 - 0.04 = 0.96.
Prob(at least one flaw) is now equal to 1 - Prob (0 defects)
= 1 - 9C0 x 0.04^0 x 0.96^9
= 1 - 1 x 1 x 0.815
= 0.19 or 19%
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Helppppp please !!!
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
i only need help with 12 & 13 only and show work please. note the picture is sideways
Answer:
12. 65:6 = 65/6 = 65 to 6
13: 21:4 = 21/4 = 21 to 4
Step-by-step explanation:
You want the numerical values of the given ratios of blood donors written three ways.
In each case, replace the blood type with the corresponding number of donors. Ratios can be written using a colon, a division bar, or the word "to".
12. A+ and B+ to AB+Using the numbers, this is ...
(45 +20) : 6 = 65 : 6 = 65/6 = 65 to 6
13. A- and B- to AB-Using the numbers, this is ...
(21 +0) : 4 = 21 : 4 = 21/4 = 21 to 4
HELP ASAP 100 POINTS!!!!!!!!!
The points (6,2) and (10,4) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-2=\dfrac{1}{2}(x-6)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define the points:
(x₁, y₁) = (6, 2)(x₂, y₂) = (10, 4)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{4-2}{10-6}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Therefore, the slope of the line is ¹/₂.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-2=\dfrac{1}{2}(x-6)[/tex]
Write in terms of the cofunction of a complementary angle.
given the expression
[tex]sin(\frac{\pi}{15})[/tex]since
[tex]sin(\theta)=\frac{1}{csc(\theta)}=cos(\frac{\pi}{2}-\theta)[/tex]then
[tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{\pi}{2}-\frac{\pi}{15})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{(15-2\pi)}{30})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=cos(\frac{13\pi}{30})[/tex]ten the correct answer is
Option C
Find the intercepts (if an answer does not exist enter DNE) be sure to graph the line as well
Question:
Solution:
x-intercept:
the x-intercept is when y= 0. Thus replacing this value into the given equation we get:
[tex]15x+10(0)\text{ = 30}[/tex]this is equivalent to:
[tex]15x+0\text{= 30}[/tex]this is equivalent to:
[tex]15x\text{ = 30}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{30}{15}\text{ = 2}[/tex]so the point of x-interception is :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept:
the y-intercept is when x= 0. Thus replacing this value into the given equation we get:
[tex]15(0)+10y=30[/tex]this is equivalent to:
[tex]0\text{ + 10y = 30}[/tex]this is equivalent to:
[tex]10y\text{ = 30}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{30}{10}=\text{ 3}[/tex]so the point of y-interception is :
[tex](x,y)\text{ = (0,3)}[/tex]We can conclude that the correct answer is:
x-intercept :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept is :
[tex](x,y)\text{ = (0,3)}[/tex]Which situation yields data with variability?The distance covered by different vehicles traveling at a constant rate of 60 mph for 45 minutes The length of different professional American football fieldsThe weight of 6th grade studentsThe moon cycle duration in a year
Answer:
The weight of 6th-grade students
Explanation:
We have variability if each value in the data is different.
When a vehicle travels at a constant rate for the same amount of time, the distance covered will be always the same. So, this situation doesn't yield data with variability.
In the same way, the length of a professional American football field and the moon cycle duration in a year are standard, they always have the same value so these situations don't yield data with variability.
Finally, each student of 6th grade has a different weight, so this is the situation that yields data with variability.
Therefore, the answer is:
The weight of 6th-grade students
Your grandmother was in the hospital and was put on a liquid diet. After examining her chart, a mistake was found stating that her weight was 500 kg. The dietician decided my grandma weighed too much and put her on a liquid diet. How much did they believe that she weighed in pounds? (Show all work using dimension analysis, round to nearest whole pound)
Your grandmother was in the hospital and was put on a liquid diet. The approximate weight of grama in pounds is 1100 pounds
This is further explained below.
What is the conversion?Generally, Simply rephrasing the query as "what is the equivalent of 500 kg in Pounds" will accomplish the same thing.
In order to do this, we need to know how many kilograms are in one pound: It weighs something about 2.2 pounds.
Therefore, one hundred and ten kilograms is equal to five hundred and two point two pounds (and a little more since one kg is a little more than 2.2 pounds).
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1) Movie Checkout for the week Days 2 3 4 A. 10 How many movies were checked out on Day 1? Number of Movies 30 45 60 C. 20 B. 15 D. 25
Please Answer the following 2 questions asked in the image provided, Asap.
1 Fristly you do M1=M2 as it is parallel
You get M2 then use it to find equation
note that y= -1.5
2 for second question you find coefficient of X and y you get M1 then find equation of given line easily.
#note equaction of straight line passing through two points is y-y1=m(x-x1)
Express 55 miles per hour in kilometers per hour.km/hr(Round to the nearest whole number as needed.)
Okay, here we have this:
Considering the provided amount in miles per hour, we are going to convert it to kilometers per hour, so we obtain the following:
[tex]\begin{gathered} \frac{55mi}{h}\cdot\frac{1.6km}{1mi} \\ =\frac{55\cdot1.6km}{h} \\ =88\frac{\text{ mi}}{h} \end{gathered}[/tex]Finally we obtain that 55 miles per hour are equivalent to 88 kilometers per hour.
The variable cost for a product is $1.00 and the total fixed costs are $88,000. The company sells the products for $3.00 each. How many products will the company have to sell to break even?
The breakevenpoint is the point at which costs and sales are equal to each other and therefore, the profit is zero.
The breakeven point in terms of number of units sold can be determined as follows;
[tex]\begin{gathered} Breakeven\text{ units=}\frac{Fixed\text{ costs}}{\text{ Selling price per unit-}Variable\text{ cost per unit}} \\ \text{Breakeven units=}\frac{88000}{3-1} \\ \text{Breakeven units=}\frac{88000}{2} \\ \text{Breakeven units=44000} \end{gathered}[/tex]In order to breakeven, the company will have to sell 44,000 units
What is a rule for the nth term of Geometric sequence -3,-6,-12,-24,-48
The sequence is given as,
[tex]-3,\text{ -6, -12, -24, -48.......}[/tex]For the given sequence,
[tex]\begin{gathered} First\text{ term\lparen a\rparen = -3} \\ Common\text{ ratio\lparen r\rparen = }\frac{-6}{-3}=\text{ 2} \end{gathered}[/tex]nth term of a geometric progression is given as,
[tex]a_n\text{ = ar}^{n-1}[/tex]Where,
a = First term
r = common ratio
Therefore the nth term is calculated as,
[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex]Thus the required answer is,
[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex](a) Give a secant line.(b) Give a chord.(c) Give a tangent line.
Solution
Secant is a line that touches a circle at two distinct points
See figure below
Chord is a straight line that touches two points on the the circumference of the circle
A
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
Since the number of years must be non-negative, we can eliminate all the options except for d.
In the figure above, if k II I, what is the value of y?
B. 45
C. 50
A. 40
D. 60
The values of measure of angle y is found as 65 degrees.
What is defined as the linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair has always been 180°. These angles are also referred to as supplementary angles. A adjacent angles are those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
Line k || Line l
(x + 5) + (3x + 15) = 180 (linear pair)
Solving;
4x + 20 = 180
4x = 160
x = 40
Put the value of x in angles (2x + 30)
2x + 30 = 2×40 + 30 = 110
Now,
2x + 30 = y + (x + 5) (alternate interior angles)
Solving;
110 = y + 40 + 5
y = 110 - 45
y = 65 degrees.
Thus, the values of measure of angle y is found as 65 degrees.
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I have a question for quantitative reasoning. Alcohol use by high school seniors in a certain state decreased from 50.3% in 2000 to 32.7% in 2015. Describe this change as an absolute change in terms of percentage points and as a relative change in terms of a percentage.
The of senior high school students who reported consuming alcohol is mathematically given as
33.99% of
This is further explained below.
What percentage of senior high school students report consuming?Absolute change is the straightforward difference between the indicator's two time periods.
Absolute change = final value - initial value
Absolute change =(33 *1-50.3)% points
=-17.2% points
Decrease absolute change $=17.2% point
- ve hours decreased
+ve shows increased
The percentage of high school seniors using alcohol decreased by 17.2%. point
Relative change expresses absolute change as the ax of the value in the initial period
[tex]$=\frac{\text { absolute change }}{\text { intial value }} \times 100$$=\frac{33.1-50.3}{50.3} \times 100$[/tex]
=-33.99 %
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3. How many tens are there between 9,312 and 9,522? Explain your thinking
The number of tens between the given numbers are 1883.
The number of tens between two numbers can be calculated by the concept of proportions. A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem. Now, to find the number of tens we divide the number by 10. So, the number of tens in the given numbers are
9312/10 = 931 (approximately)
9522/10 = 952 (approximately).
Now, the numbers of tens between the two given numbers can be calculated by adding the number of tens in them that is,
952 + 931 = 1883 tens between the two numbers.
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what number is not part of the solution set for the inequality below?3x-18> 1210, 11, 15,8 _
First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:
1. 3x-18> 12 , add 18 on both sides:
3x - 18 + 18 > 12 + 18
3x > 30
2. Divide both sides by 3:
3x/3 > 30/3
x > 10
So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then the answer is 8.
For each relation, decide whether or not it is a function.
Relation 1: No, the inputs of desk and leaf each correspond to two different outputs.
Relation 2: No, the input of 7 corresponds to three different outputs.
Relation 3: Yes, each input corresponds to only one output.
Relation 4: No, the input of -7 corresponds to two different outputs: a and h.
Find the average rate of change of f(x)=x²-4x+1 from x=3 to x=7.
Simplify your answer as much as possible.
( explain pls )
At x=3 to x=7, the average rate of change of the given function
f(x) = x2- 4x + 1 is 6.
Solution:Given function,
f(x) = x² - 4x + 1
given x=3 and x=7
To find the average rate of change of a function, find its slope(m),
To find m ,
m= (y2 - y1) / (x2 - x1)
here y1 and y2 not given.
then substitute the given values of x into f. (x)
when x=3 ,
y1 = (3² - 4×3 +1)
= (9 - 12 +1)
= -2
so (x1,y1) = (3,-2)
similarly to find y2,
substitute x = 7 to f(x)
y2 = (7² - 4×7 + 1)
= (49 - 28 +1)
= 22
so (x2,y2) = (7,22)
To find m, substitute the values.
m= (y2 - y1) / (x2 - x1)
= (22 -( - 2)) / (7 - 3)
= 24/4
= 6
As a result, the average rate of change of the function x2-4x + 1 is 6.
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Are the following ratios equivalent?5cookies:9 glasses of milk and 3 cookies :12 glasses of milk
Answer:
No
Step-by-step explanation:
5:9 and 3:12 do not divide with the same number
For example:
3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6
A pole that is 3.1 m tall casts a shadow that is 1.46 m long. At the same time, a nearby tower casts a shadow that is 38.5your answer to the nearest meter.long. How tall is the tower RoundIM
82 meters
Explanation
Step 1
Draw:
as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion
[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so
[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is
82 meters
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
Step-by-step explanation:
h = number of hours
s = number of shirts made
28h+2s=144
4h=s
h=4, s=16
(Didn't I already answer this? i think i might have.. lol)
Write the exponential function y - 45(1.085)^t in the form y = ae^kt(a) Once you have rewritten the tormula, give & accurate to at least four decimal places.K=If T is measured in years, indicate whether the exponential function is growing or decaying and find he annual and continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing decay the negative rate is implied).(b) The annual (growth/decay) rate is ___ % per yearC) The continuous (growth/decay) rate is ___ % per year
EXPLANATION
Given the exponential function:
45(1.085)^t
We have that 45=a is the initial value and 1.085 is the growth rate,
1.085 - 1 = 0.085* 100 = 8.5 % (This is the growth rate)
Let's compute the function with two values of t, as for instance, t=0 and t=1:
[tex]f(0)=45(1.085)^0=45\cdot1=45\longrightarrow\text{ (0,45)}[/tex][tex]f(1)=45\cdot(1.085)^1=48.825\text{ }\longrightarrow\text{(1,48.825)}[/tex]Now, the function in the form y = ae^kt will be as follows:
[tex]y=45\cdot e^{kt}[/tex]Substituting t by 1:
[tex]y(1)=45\cdot e^k=48.825[/tex]Dividing both sides by 45:
[tex]e^k=\frac{48.825}{45}=1.085[/tex]Applying ln to both sides:
[tex]k=\ln 1.085[/tex]Computing the argument:
[tex]k=0.0816[/tex]The expression will be as follows:
[tex](a)---\longrightarrow y=45e^{0.0816t}[/tex]As this is a growing function, the rates are positive.
The annual growth rate is 8.5% and It's was calculated above.
Now, we need to compute the continuous rate because It's given by the value of k:
k = 0.0816 --> Multiplying by 100 --> 0.0816 * 100 = 8.16%
The continuous growth rate is 8.16%
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
1 5/6+1 3/6 pls help
Answer:
10/3
Step-by-step explanation:
[tex]1\frac{5}{6} = \frac{11}{6}\\ \\\ 1\frac{3}{6} = \frac{9}{6}[/tex]
11/6 + 9/6 = 10/3 =3.333333333