Answer:
2nd option,
The function is negative for all read values of x where -6<x<-2
The function f(x) = (x + 2)(x + 6) is a quadratic function, and the function is negative for all real values of x where –6 < x < –2.
What are quadratic functions?Quadratic functions are functions that have an exponent or degree of 2
The function is given as:
f(x) = (x + 2)(x + 6)
From the graph of the function, the vertex is at (-4,-4) and the x-intercepts are at x = -6 and x = -2
Since the vertex is minimum, then the function is negative for all real values of x where –6 < x < –2.
Read more about x-intercepts at:
https://brainly.com/question/3951754
6. Solve for x: 3|x - 7| = 15
Please give steps! ❤️
3 | x - 7 | = 15
Divide both sides by 3
3 | x - 7 | ÷ 3 = 15 ÷ 3
| x - 7 | = 5
_________________________
" Reminder "
| a | = t ===》 a = + t OR a = - t
__________________________
| x - 7 | = 5
x - 7 = 5 ====》 x = 12
OR
x - 7 = - 5 ===》 x = 2
Given the following constraints, find the maximum and minimum values for z. Constraints: 2x−y≤124x+2y≥0x+2y≤6 Optimization Equation: z=2x+5y
Answer:
Minimum = 0
Maximum = 15
Step-by-step explanation:
Given
Optimization Equation: [tex]z = 2x + 5y[/tex]
Constraints:
[tex]2x- y \le 12[/tex]
[tex]4x + 2y \ge 0[/tex]
[tex]x + 2y \le 6[/tex]
[tex]x,y\ge 0[/tex]
Required
The maximum and the minimum values of z
To do this, we make use of graphical method.
Plot the constraints on a graph (see attachment)
Get the corner points from the points.
These are the points where [tex]x,y\ge 0[/tex]
So, we have:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
Substitute these points in the optimization equation:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]z = 2x + 5y[/tex]
[tex]z = 2 * 0 + 5 * 0 = 0[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex]z = 2 * 0 + 5 * 3 = 15[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
[tex]z = 2 * 6 + 5 * 0 = 12[/tex]
So, the values are:
Minimum = 0
Maximum = 15
Answer:
max= 16 min= -24
Step-by-step explanation:
The function f(x)=log4x is dilated to become g(x)=f(13x).
What is the effect on f(x)?
Answer:
f(x) is compressed horizontally
Step-by-step explanation:
Given
[tex]f(x) = \log(4x)[/tex]
[tex]g(x) = f(13x)[/tex]
Required
The effect on f(x)
[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.
So, we have:
[tex]f(13) = \log(4 * 13x)[/tex]
[tex]f(13) = \log(52x)[/tex]
So:
[tex]g(13) = \log(52x)[/tex]
HELP PLEASE I DONT KNOW THIS ONE
Answer:
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
Step-by-step explanation:
2 3x
-------- - ----------
X^2-9 x^2 -5x+6
Factor
2 3x
-------- - ----------
(x-3)(x+3) (x-3)(x-2)
Get a common denominator
2 (x-2) 3x(x+3)
-------- - ----------
(x-3)(x+3)(x-2) (x-3)(x-2)(x+3)
2x-4 - (3x^2 -9x)
-------------------------------
(x-3)(x-2)(x+3)
Distribute
2x-4 - 3x^2 +9x
-------------------------------
(x-3)(x-2)(x+3)
Combine like terms
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]
[tex]\sf{\dfrac{2}{ x^2-9}-\dfrac{3x}{x^2-5x+6}}[/tex] [tex]\sf{\dfrac{2}{ (x)^2-(3)^2}-\dfrac{3x}{x^2-2x-3x+6} }[/tex] [tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{x(x+2)-3(x+2)} }[/tex][tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{(x+2)(x-3)}}[/tex][tex]\sf{\dfrac{2(x-2)-3x(x+3)}{(x+3)(x-2)(x-3)} }[/tex] [tex]\sf{\dfrac{2x-4-(3x^2-9x)}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{2x-4-3x^2+9x}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{-3x^2+7x-4}{(x+3)(x-2)(x-3) }}[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
Which of the following is the solution set of 6x + 5 = -29? {-4}
Answer:
[tex]{ \tt{6x + 5 = - 29}} \\ { \tt{6x = - 36}} \\ { \tt{x = - 6}}[/tex]
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
If you vertically stretch the absolute value parent function, f(x) = [xl, by a
factor of 5, which of these is the equation of the new function?
Answer:
[tex]g(x) = 5|x|[/tex]
Step-by-step explanation:
Given
[tex]f(x) = |x|[/tex]
[tex]b =5[/tex] --- vertically stretch
Required
The new function
The rule for vertical stretch is:
[tex]g(x) = bf(x)[/tex]
So, we have:
[tex]g(x) = 5 * |x|[/tex]
[tex]g(x) = 5|x|[/tex]
A bag contains 9 red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 6 white balls numbered 10, 11, 12, 13, 14, 15. One ball is drawn from the bag. What is the probability that the ball is white, given that the ball is even-numbered
Answer:
3/ 7
Step-by-step explanation:
We know that it is an even ball
2,4,6,8,10,12,14 are even balls
2,4,6,8 are red and 10,12,14 are white
P ( white) = white even / total even
= 3/ 7
Write 4 with denominator 5
Answer:
4/5
Step-by-step explanation:
I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
Two sides of a triangle have the same length. The third side measures 5 m less than twice the common length. The perimeter of the triangle is 23 m. What are the lengths of the three sides?
What is the length of the two sides that have the same length?
Answer:
Length of all 3 sides: 7, 7, and 9
Length of the two sides that have the same length: 7
Step-by-step explanation:
Let the two sides with equal lengths have a length of [tex]x[/tex]. We can write the third side as [tex]2x-5[/tex].
The perimeter of a polygon is equal to the sum of all its sides. Since the perimeter of the triangle is 23 meters, we have the following equation:
[tex]x+x+2x-5=23[/tex]
Combine like terms:
[tex]4x-5=23[/tex]
Add 5 to both sides:
[tex]4x=28[/tex]
Divide both sides by 4:
[tex]x=\frac{28}{4}=\boxed{7}[/tex]
Therefore, the three sides of the triangle are 7, 7, and 9 and the length of the two sides that have the same length is 7.
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
How many counting numbers have three distinct nonzero digits such that the sum of the three digits is 7?
Answer:
6
Step-by-step explanation:
You have 2 conditions.
1. The digits must be different.
2. The digits must add to 7.
There aren't very many
124
142
214
241
412
421
That's it. That's your answer. There are 6 of them
As part of a statistics project, a teacher brings a bag of marbles containing 500 white marbles and 400 red marbles. She tells the students the bag contains 900 total marbles, and asks her students to determine how many red marbles are in the bag without counting them. A student randomly draws 100 marbles from the bag. Of the 100 marbles, 45 are red. The data collection method can best be described as
Answer:
Survey
Step-by-step explanation:
During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.
Find the sample correlation coefficient for the following data.
X Y
3 8
7 12
5 13
9 10
11 17
13 23
19 39
21 38
a. .8911.
b. .9132.
c. .9822.
d. .9556.
Answer:
quneotentendeiporoqenouteetendxdin
Step-by-step explanation:
9 3/5 % as a decimal, rounded to 3 decimal places, is:
Answer:
0.054
Step-by-step explanation:
9 3/5% as a decimal is 0.054 (already to 3 decimal places)
Answer from Gauthmath
9 are just, well..., 9
3/5 are 0.6
because 1/5 is 0.2
so it's 9.6%, not so complicated I guess
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
someone please help
Answer:
28
Step-by-step explanation:
78
Identify the possible rational roots for the equation x^4-3x^2+6=0
Answer:
[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]
Step-by-step explanation:
One is given the following equation, and the problem asks one to identify the rational roots of the equation:
[tex]x^4-3x^2+6=0[/tex]
The rational root theorem states that the list of positive and negative factors of the constant term over the factors of the coefficients of the term to the highest degree will yield a list of the rational roots of the equation. Use this theorem to generate a list of all possible ration roots of the equation.
[tex](+-)\frac{6,3,2,1}{1}[/tex]
Now rewrite this list in a numerical format:
[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]
This is the list of the possible rational roots. One has to synthetically divide each of these numbers by the given polynomial equation to find the actual rational roots. However, the problem only asks for the possible rational roots, not the actual rational roots, thus, this is not included.
What is the true solution to the equation below? 2 lne^ln2x-lne^ln10x=ln30
It looks like the equation is
[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]
Right away, we notice that any solution to this equation must be positive, so x > 0.
For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to
[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that
[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]
[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that
[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]
For x ≠ 0, we have [tex]\frac xx=1[/tex], so that
[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]
Take the antilogarithm of both sides:
[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]
[tex]\dfrac{2x}5 = 30[/tex]
Solve for x :
[tex]2x = 150[/tex]
[tex]\boxed{x=75}[/tex]
Simplify
x * x^5 / x^2 * x
HELPP!!!! Which answer includes the intervals that contain the solution to the inequality?
x^2-1/3x+9 <_0
Answer:
It is the last one.
Step-by-step explanation:
You must factor out the top expression, and then factor the bottom expression. Then, cancel out all of the terms that are equivalent to get one expression on the left side of the inequality sign. Then, subtract the answers to the "0" side and divide to find the coordinates.
Answer:
Last option
Step-by-step explanation:
I have attached the explanation above. hopefully this will help
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help.
Answer:
mean=256229+253657+218747+246163+235626+288694+316265+196721+285077+215152+253291+315011+199901+265443+291806+303556+215359+258554+293658+289935÷21
=5198845÷21
=247564.0
=247564 to the next whole number
B.6 times
fastest answer gets brainiest !
Which data value has the highest frequency?
116
316
38
58
Answer:
A. 1/16Step-by-step explanation:
The most repeated value is:
(1/4)/4 = 1/16There are 4 of them.
Correct choice is A
125. Albert surveyed a class of 25 students on sports. 5 kids love baseball. 7 kids love basketball. 10 kids
love football. How many students did not like baseball, basketball, or football?
25 students
12 students
22 students
3 students
Answer:
3 students
Step-by-step explanation:
since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.
7+5+10+x=25
x=25-22
=3
I hope this helps
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (-1, -6)
B. (-1, 0)
C. (20, -6)
D. (20, 0)
Answer: A. (-1, -6)
Step-by-step explanation:
Use the midpoint formula:
Endpoint #1 = (x₁, y₁) = (13, -2)Endpoint #2 = (x₂, y₂)[tex]midpoint = (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}) \\\\(6, -4) = (\frac{13+x_{2}}{2}, \frac{-2+y_{2}}{2})\\\\\frac{13+x_{2}}{2} =6\\\\13+x_{2}=6*2\\\\x_{2}=12-13=-1\\\\ \\ \frac{-2+y_{2}}{2}=-4\\\\-2+y_{2}=(-4)*2\\\\y_{2}=-8+2=-6\\\\\\\left \{ {{x_{2}=-1} \atop {y_{2}=-6}} \right.[/tex]
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=12
Step-by-step explanation:
each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle
ex: 8*4=32 and 17*4=68
so we can assume that 15*4= 4x+12
60=4x+12
48=4x
x=12
Answer:
x = 12
Step-by-step explanation:
The triangles are similar so we can use ratios
4x+12 32
------- = ------------
15 8
Using cross products
(4x+12) *8 = 15 * 32
(4x+12) *8 = 480
Divide each side by 8
(4x+12) *8/8 = 480/8
4x+12 = 60
Subtract 12 from each side
4x+12 -12 = 60-12
4x = 48
Divide by 4
4x/4 = 48/4
x = 12
