Answer:
x(x + 1) ≤ 0
-1 ≤ x ≤ 0
{x | x ≥ -1 and x ≤ 0}
Follow steps:
Solving the Inequality x(x+1)≤0
To solve x(x+1)≤0, we need to find values of x where the product is negative or zero. X can be split into the regions x < 0 and x > 0. As x approaches zero from either direction, x(x+1) approaches zero as well. The function is zero at the roots of the equation x(x+1) = 0, which are x = 0 and x = -1. These two roots divide the real line into three intervals: (-∞, -1), (-1, 0), and (0, ∞). Analyzing each interval:
For x in (-∞, -1), x < -1 and x+1 < 0, so the product x(x+1) is positive.
For x in (-1, 0), x is negative and x+1 is positive, so the product x(x+1) is negative.
For x in (0, ∞), both x and x+1 are positive, and thus, the product x(x+1) is positive.
The inequality is only satisfied in the interval where the product is negative or zero. Therefore, the solution is [{-1}, 0], which can be written in interval notation as (-1, 0]. This is a single continuous interval that includes the root x = 0 and excludes the root x = -1.
Finally, using interval notation, we express the solution to the inequality x(x+1)≤0 as (-1, 0].
Find the greatest common factor of the
following monomials:
2n 36n
Answer:
2n
Step-by-step explanation:
2n = 2*n
36n = 2*3*2*3 n
They both have 2*n in common, so the greatest common factor is 2n
The triangles below are similar.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Answer:
B,C,D,E
Step-by-step explanation:
The similarity statement that describe the relationship is similarities by (AAA)
What are similar triangles?Similar triangles have corresponding angles equal and proportional sides. Their shapes are identical, but sizes may differ.
For two triangles to be similar, the corresponding angles must be equal, and the ratio of the corresponding sides must be equal.
From the diagram, The similarity statement that describe the relationship is similarities by (AAA)
angle R =angle Z
angle S = angle X
angle P = angle Y.
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Complete the proportion you can use to convert 110 inches to centimeters. Enter your answer with one decimal place. 1 inch = 2.54 centimeters
Answer: 279.4 centimeters hope this helped
Step-by-step explanation: 110 x 2.54 = 279.4
For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
Answer:
The the vertex is: (2, 4)
Domain: all real numbers
Range: [tex][4 \infty)[/tex]
Step-by-step explanation:
Quadratic functions can be written vertically as follows
[tex]f(x) = a(x-h)^2 +k[/tex]
Quadratic functions can be written vertically as follows
Where the point (h, k) represents the vertex of the quadratic function.
For this type of functions the domain is always all real numbers and the range is [tex][k, \infty)[/tex] or if [tex]a <0[/tex] then the range is [tex](-\infty, k][/tex]
In this case the function is:
[tex]f(x) = (x - 2)^2 + 4[/tex]
So
[tex]h = 2\\k=4[/tex]
The the vertex is: (2, 4)
Domain: all real numbers
Range: [tex][4, \infty)[/tex]
Two friends shared 3/4 gallon of ice cream equally. What fraction of a gallon did each friend get ?
Answer:
I've done this question before and the answer is really weird. its 3/8
A salesperson has January sales of $20,000(1,$20,000) and April sales of $80,000 (4,$80,000). What is the rate of change?
Answer:
60000/4 pr 15000
Step-by-step explanation:
Rate of change = change in population / change in time
80000 - 20000 = 60000
January to April is 4 months
so the rate of change will be 60000/4 or 15000
Calculate each probability, given that P(A) = 0.3, P(B) = 0.7, and A and B are independent.
P(A and B)
Answer:
0.21
Step-by-step explanation:
If A and B are independent, then:
P(A and B) = P(A) × P(B)
Given P(A) = 0.3 and P(B) = 0.7:
P(A and B) = 0.3 × 0.7
P(A and B) = 0.21
Answer:
P(A and B) = 0.21
Step-by-step explanation:
Two events are said to be independent when the occurrence of event 1 does not affect the occurrence of event 2
Given two probabilities A and B whose probabilities are given as follows
P(A) = 0.3, P(B) = 0.7
P(A and B) is calculated as follows;
P(A and B) is calculated by multiplying both probabilities together
P(A and B) = P(A) * P(B)
P(A and B) = 0.3 * 0.7
P(A and B) = 0.21
Hence, P(A and B) = 0.21
Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?
Answer:
The translation is left 4 units
Step-by-step explanation:
we know that
[tex]y=2(x-15)^{2}+3[/tex]
Is a vertical parabola open upward with vertex at (15,3)
[tex]y=2(x-11)^{2}+3[/tex]
Is a vertical parabola open upward with vertex at (11,3)
so
The rule of the translation of (15,3) ----> (11,3) is equal to
(x,y) ----> (x-4,y)
That means ----> The translation is left 4 units
Look at the sample below 2x-8=12
Answer:
x = 10
Step-by-step explanation:
Make x the subject
2x - 8 = 12
2x = 12 + 8
2x = 20
x = 20/2
x = 10
!!
What is the product in simplest form? 3/5 x 2/3 = ?
1) 6/15
2) 9/10
3)5/8
4)2/5
Answer:
option 4
Step-by-step explanation:
Given
[tex]\frac{3}{5}[/tex] × [tex]\frac{2}{3}[/tex]
Cancel the 3's on the numerator/denominator of the fractions, leaving
= [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form
The product of 3/5 x 2/3, in simplest form, is 2/5 after multiplication and reduction.
Explanation:In order to answer your question about the product of 3/5 x 2/3, you need to multiply the two fractions. To do this, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So, for this problem, you would multiply 3 by 2 to get 6, and 5 by 3 to get 15. Therefore, 3/5 x 2/3 = 6/15. However, to put it in simplest form, you should always reduce the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor, which in this case is 3. Therefore, 6/15 reduces to 2/5.
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For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx+b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We need two points through which the line passes to find the slope:
[tex](0,1)\\(1, -2)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {-2-1} {1-0} = \frac {-3} {1} = - 3[/tex]
So, the equation is of the form:
[tex]y = -3x + b[/tex]
We substitute a point to find "b":
[tex]1 = -3 (0) + b\\1 = b[/tex]
Finally, the equation is:
[tex]y = -3x+1[/tex]
Answer:
Option C
Use the properties of exponents to rewrite the expression
(-4qr)(-4qr)(-4qr)(-4qr)
[tex](-4qr)(-4qr)(-4qr)(-4qr)=(-4qr)^4=256q^4r^4[/tex]
To rewrite the expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we can rewrite it as (-4qr)^4 = 256q^4r^4.
Explanation:To rewrite the given expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we need to understand that multiplying the same base with different exponents is equivalent to adding the exponents. In this case, the base is (-4qr) and the exponents are 1 for each occurrence. So, we can rewrite the expression as:
(-4qr)4 = -44q4r4 = 256q4r4
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the length of a rectangle is 9 cm more than the width the perimeter is 270 cm find the length and the width
Answer:
length=72
width=63
Step-by-step explanation:
Let us start by supposing the following:
w=w
l=9+w
2l+2w=p(perimeter)
2(9+w)+2*w=270
2w+2w+18=270
4w+18=270
4w=252
w=63
l=72
We used the perimeter formula, 2l+2w=P(perimeter)
Final answer:
To calculate the dimensions of the rectangle, we use the perimeter formula P=2l+2w. After setting up an equation with the given perimeter and relationship between length and width, we find the width to be 63 cm and the length to be 72 cm.
Explanation:
The problem states that the length of a rectangle is 9 cm more than its width and that the perimeter is 270 cm. To find the dimensions of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let's denote the width of the rectangle as w cm. Then the length would be w + 9 cm. We can substitute these expressions into the perimeter formula to obtain:
270 = 2(w + 9) + 2w
Simplify and solve for w:
270 = 2w + 18 + 2w
270 = 4w + 18
252 = 4w
w = 63 cm
Now that we have the width, we can find the length:
l = w + 9 = 63 + 9 = 72 cm
Therefore, the width is 63 cm, and the length is 72 cm.
The total cost to rent a row $18 times the number of hours the boat is used . Write an equation to model this situation if c = total cost and h = number of hours
Answer:
c=1`8h
Step-by-step explanation:
Based on the graph, which inequality is correct for a number that is to the right of -3?
A number line is shown from negative 8 to 8 at increments of 1. A circle is shown at negative 3. The entire portion of the number line to the right of negative 3 is shaded.
A 4 > −3
B −3 > 4
C −2 < −3
D−3 < −6
If f(x) = 2x2 + 2 and g(x) = x2 - 1, find (f - g)(x).
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x^2 - 1
(f - g)(x) = 2x^2 + 2 -( x^2 - 1)
Distribute the minus sign
2x^2 +2 -x^2 +1
x^2 +3
[tex](f-g)(x)=2x^2+2-(x^2-1)=2x^2+2-x^2+1=x^2+3[/tex]
Solve the compound inequality 6b < 42 or 4b + 12 > 8.
Step-by-step explanation:
6b < 42 or 4b + 12 > 8
6b < 42
= 6b/6 < 42/6
= b < 7
4b + 12 > 8
=4b - 12 + 12 < -12+8
= 4b > - 12 + 8
= 4b > -4
= 4b/4 = -4/4
b > -1
so
7 > b > -1
The solution of the compound inequality 6b < 42 or 4b + 12 > 8 is -1 < b < 42.
What is the inequality?The inequality represent the relationship between two expression, it can represent by < is less than > is greater than.
The inequality is;
[tex]\rm 6b < 42\\\\\dfrac{6b}{6} < \dfrac{42}{6}\\\\b < 7[/tex]
The solution of the inequality 6b < 42 is b < 7.
The inequality is;
[tex]\rm 4b + 12 > 8\\\\4b+12-12 > 8-12\\\\4b > -4\\\\\dfrac{4b}{b} > \dfrac{-4}{4}\\\\b > -1[/tex]
The solution of the inequality 4b + 12 > 8 is b > -1.
So combining both conditions, the compound equality will be:
-1 < b < 42
It depicts b is greater than -1 and smaller than 42.
Hence, the solution of the compound inequality 6b < 42 or 4b + 12 > 8 is -1 < b < 42.
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Ignore my writing
Solve the inequality
Answer:
x=1
Step-by-step explanation:
-5 - (15x-1) = 2(7x-16) -x
Distribute the negative sign
-5-15x+1 = 2(7x-16)-x
Distribute the 2
-5-15x+1 = 14x -32-x
Combine like terms
-4-15x = 13x-32
Add 15x to each side
-4-15x+15x = 13x+15x-32
-4 = 28x-32
Add 32 to each side
-4+32 = 28x-32+32
28 = 28x
Divide each side by 28
28/28 = 28x/28
1 =x
(4-2i).(6-3i) / (1-i).(1+i)
Answer:
2i + 6
Step-by-step explanation:
4-2 = 2
6-3 = 3
2 * 3 = 6
2i
Answer:
9 - 12i
Step-by-step explanation:
Noting that i² = - 1
Expand the factors on the numerator and denominator
(4 - 2i)(6 - 3i) = 24 - 12i - 12i + 6i² = 24 - 24i - 6 = 18 - 24i
(1 - i)(1 + i) = 1 + i - i - i² = 1 + 1 = 2
The division reduces to
[tex]\frac{18-24i}{2}[/tex]
= [tex]\frac{18}{2}[/tex] - [tex]\frac{24}{2}[/tex] i
= 9 - 121i
The following function describes the number of employees working at a company, in thousands, where t represents the number of years since the company revised the benefits package. f(t)=1.5(.90)^t Select the correct statement.
A. The number of employees is increasing by 50% every year.
B. The number of employees is decreasing by 10% every year.
C. The number of employees is decreasing by 90% every year.
D. The number of employees is increasing by 90% every year.
Answer:
The answer is (B)
Step-by-step explanation:
Try out each of the situations. It can't be A, since the 0.9 is less than 1, so it has to be decreasing. This leaves only B and C. Since decreasing by 90 percent is the same as multiplying by 10 percent, the only possible answer left is B.
Hope this helps!
Answer:
the number of employees is decreasing by 10% every year
Step-by-step explanation:
[tex]f(t)=1.5(.90)^t[/tex]
In the given function 1.5 represents the initial number of employees
Exponential function in the form of [tex]f(x) = a(b)^x[/tex]
When the value of b is less than 1 then it is exponential decay
When the value of b is greater than 1 then it is exponential growth
Exponential decay factor is 0.90
[tex]1-0.90= 0.10[/tex]
0.10 times 100 = 10%
So the number of employees is decreasing by 10% every year
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour. Which equation can be used to find t, the amount of time Amir spent hiking during the second, more difficult part of the hike? 3(2 – t) = 1.5t 3t = 1.5(2 – t) 3t + 1.5(2 – t) = 5 3(2 – t) + 1.5t = 5
The equation that will be used to find t is:
[tex]3(2-t)+1.5t=5[/tex]
Step-by-step explanation:Total distance that is traveled by Amir is: 5 miles.
and the total time taken by him is: 2 hours.
On the first part of the hike, Amir averaged 3 miles per hour.
Let t denote the time he spent hiking during the second i.e. difficult part of the hike.
Hence, the time he spent in first part of hike is: 2-t( Since, the total time was 2 hours)
Also, we know that:
[tex]Distance=Speed\times Time[/tex]
Hence, distance traveled in first part of hike is:
[tex]Distance=3\times (2-t)[/tex]
Now, the distance he will travel in second part of hike will be: 5-3(2-t)Since the total distance traveled by him is 5 miles.
It is given that his speed decreased to 1.5 miles per hour.
Now, we know that:
[tex]Time=\dfrac{Distance}{Speed}[/tex]
Hence, time spent by him in second part of hike is:
[tex]t=\dfrac{5-3(2-t)}{1.5}\\\\i.e.\\\\1.5t=5-3(2-t)\\\\i.e.\\\\3(2-t)+1.5t=5[/tex]
Which is a graph of a proportional relationship?
Answer:
bottom left graph
Step-by-step explanation:
A proportional relationship is linear, represented by a straight line graph passing through the origin.
The graph on the bottom left is straight line passing through the origin.
Which is true regarding the system of equations?
x-4y=1
5x-20y=4
The system results in a false statement.
The system results in an intersection at one point.
The system results in many solutions because they are the same line.
The system results in a true statement.
Answer:
NO SOLUTION
Step-by-step explanation:
Let's actually solve the system
x-4y=1
5x-20y=4
Let's eliminate y. To do this, multiply the first equation by -5, obtaining
-5x + 20y = -5
Now add this result to the second equation:
-5x + 20y = -5
5x - 20y = 4
--------------------
0 = -1
This result is never true. Thus, this system of linear equations has NO SOLUTION.
The system of equations results in a false statement.
How to estimate the value of the system of equations?Let's solve the system of equation
x - 4y = 1 ......(1)
5x - 20y = 4 ........(2)
By using the elimination method
Eliminate y by multiplying (1) by -5
We have,
-5x + 20y = -5 ...........(3)
Adding (3) and (2), then we get
(x - 4y = 1) + (-5x + 20y = -5)
-5x + 20y = -5
5x - 20y = 4
---------------------
0 = -1
Therefore, the correct answer is option (a). The system results in a false statement.
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Question 13 (1 point)
Jerome is starting a new job. His contract states he will earn $42,000 the first year, and will
get a 4% raise per year. Which function S(x) represents Jerome's salary after a certain number
of years, x?
Answer:
S(x)=42000 * 1.04^x
Step-by-step explanation:
now = 42000
in 1 year = 42000 *1,04, because 4% increase is to multiply 1,04
in 2 years = 42000 *1,04*1.04 = 42000*1.04^2
in x years = 42000 * 1.04^x
Answer:
[tex]S(x)=42,000*(1.04)^{x}[/tex]
Step-by-step explanation:
We have as data
a = $42,000 (salary during the first year)
x = number of years
i = 4% = 0.04 (annual increase interest)
S(x) = Salary based on the years elapsed
"a" and "i" are constant for each year, while "x" increases one each year.
The function S(x) can be calculated like this:
[tex]S(x)=a*(1+i)^{x}[/tex]
Substituting constant values, we have
[tex]S(x)=42,000*(1+0.04)^{x}[/tex]
Simplifying, we have
[tex]S(x)=42,000*(1.04)^{x}[/tex]
Hope this helps!
What is the approximate value of a local maximum for the polynomial?
Answer:
2.4
Step-by-step explanation:
for the edge question the answer is actually 0.5
HELP in the image above please!
Answer:
D
Step-by-step explanation:
Using the section formula
x = [tex]\frac{5(-8)+8(7)}{5+8}[/tex] = [tex]\frac{-40+56}{13}[/tex] = [tex]\frac{16}{13}[/tex] ≈ 1.2
y = [tex]\frac{5(-9)+8(-2)}{5+8}[/tex] = [tex]\frac{-45-16}{13}[/tex] = [tex]\frac{-61}{13}[/tex] ≈ - 4.7
Coordinates are (1.2, - 4.7 ) → D
y varies directly as x. y =90 when x=6. find y when x=13
Answer:
195
Step-by-step explanation:
y varies directly with x means y=kx
k is a constant of proportionality (meaning no matter what the variable pair (x,y) is k will forever remain the same value)
we have while x=6, y=90
so plug in 90=k(6)
Solve for k: k=90/6=30/2=15
So no matter (x,y) you have the equation y=15x for this problem
Now what is y when x=13
plug in and find out
y=15(13)
y= 45+150= 195
If there are 6 cats 5 run away 10 came how many cats are there.
Originally there are 6 cats
5 run away so take 5 away from 6:
6 - 5 = 1
This means there is only one cat left, but now 10 more cats came:
1 + 10 = 11
There are 11 cats
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
11.
Step-by-step explanation:
6 - 5 + 10
= 11.
What is the product?
Answer:
2) -81t² +16
Step-by-step explanation:
(9t -4)(-9t -4) = (9t x -9t) + (9t x -4) + (-4 x -9t) + (-4 x -4)
= -81t² - 36t + 36t + 16
= -81t² + 16
Answer:
- 81t² + 16
Step-by-step explanation:
Simply expand the equation by factoring
(9t-4)(-9t-4) factor out negative sign
= -(9t - 4) (9t +4)
= -(9t + 4) (9t - 4) recall a² - b² = (a+b) (a-b)
= - [ (9t)² - 4²]
= - ( 81t² - 16)
= - 81t² + 16
15 points
7. You did not get enough sleep on Tuesday night.Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements.
If you have an income, then you must pay taxes.
If you have a job, then you have an income.
You work as a cashier in a convenience store.
You work as a cashier.
You have a job.
You must pay taxes.
You have an income.
Since you work as a cashier you must have a source of income, so you must pay taxes, because when you have an income you MUST pay taxes
Answer:
1)
Law of Detachment
If you have an income, then you must pay taxes.
You have an income.
You must pay taxes.
Law of Syllogism
If you have an income, then you must pay taxes.
If you must pay taxes, then you have a job.
If you have an income, then you have a job
2)
Law of Detachment
If you work as a cashier in a convenience store then you have a job.
You work as a cashier in a convenience store.
You have a job.
Law of Syllogism
If you work as as a cashier in a convenience store then you have a job
If you have a job then you must pay taxes
If you work as as a cashier in a convenience store then you must pay taxes
Step-by-step explanation:
To answer it properly we need to remind those Laws in Mathematical Logic.
The Law of Detachment says that if a Logical Implication and the second Statement is true, we can derive a true conclusion
1. If p→q (True)
2) p (True)
3) q (True)
On the other hand, The Law of Syllogism says:
1) If p→q (True)
2) If q→r (True)
Subsequently, we can conclude by derivation as true this Logical Implication:
3) If p→r (True)
-----
If you have an income, then you must pay taxes.
If you have a job, then you have an income.
Law of Detachment
If you have an income (p), then you must pay taxes. (q)
If you have a job(r), then you have an income.
1)If you have an income, then you must pay taxes. (T) If p→q (True)
2)You have an income (T) p (True)
3) You must pay taxes q (True)
Law of Syllogism
If you have an income (p), then you must pay taxes. (q) If p→q (True)
If you must pay taxes (q), then you have a job. (r) If q→r (True)
If you have an income (p), then you have a job (r) If p→r (True)
--
If you work as a cashier in a convenience store (p) then you have a job (q)
If you must pay taxes (r) then you have an income
Law of Detachment
If you work as a cashier in a convenience store (p) then you have a job (q) If p→q (True)
You work as a cashier in a convenience store (p) p (True)
You have a job (q) q (True)
Law of Syllogism
*If you work as as a cashier in a convenience store(p) then you have a job (q) If p→q (True)
*If you have a job (q) then you must pay taxes (r) If q→r (True)
If you work as as a cashier in a convenience store (p) then you must pay taxes (r) If p→r