Solve |P| > 3. a{-3, 3}
b.{P|-3 < P < 3}
c.{P|P < -3 or P > 3}
(c)
given the inequality | P | > a then the solution is always of the form
P < - a or P > a
for | P | > 3 , then
P < - 3 or P > 3
Solve the equation. -3x + 1 + 10x = x + 4
Answer:
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Step-by-step explanation:
Solving the equation mean finding the value of x
Equation given is:
[tex]-3x+1+10x=x+4[/tex]
Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.
[tex]-3x+10x-x=4-1[/tex]
Now simplify values with x and the numbers.
[tex]6x=3[/tex]
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Therefore [tex]x=[tex]\frac{1}{2}[/tex][/tex]
x = [tex]\frac{1}{2}[/tex]
simplify the left side by collecting like terms
7x + 1 = x + 4 ( subtract x from both sides )
6x + 1 = 4 ( subtract 1 from both sides )
6x = 3 ( divide both sides by 6 )
x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
An employment agency specializing in temporary construction help pays heavy equipment operators $ 122 per day and general laborers $ 93 per day. If thirty dash four people were hired and the payroll was $ 3771 comma how many heavy equipment operators were employed? How many laborers?
If all were general laborers, the payroll would be 93·34 = 3162 per day. The payroll is actually 3771 -3162 = 609 more than that.
Each equipment operator makes 29 more than a laborer, so there must be ...
... 609/29 = 21 heavy equipment operators
and 34 -21 = 13 general laborers
_____
If you write an equation for the number of heavy equipment operators (h), you get the same result in the same way. 34-h is the number of laborers
... 122h + 93(34 -h) = 3771 . . . equation for total daily payroll
... 29h + 3162 = 3771 . . . . . . simplify
... 29h = 609 . . . . . . . . . . . . . subtract 3162
... h = 609/29 = 21 . . . . . . . . divide by 29
Two large topping pizzas cost $25.00. what is the constant of proportionality (k)?
which of the following demonstrate closure in a polynomial? Select all that apply: A.(x^2+2) (x-1) B.(x^2+2) over (X -1) C.(x+1) plus (X^2-3X -2) D.(X +5)-(3X +6) E.4/8x
Any arithmetic operation on polynomials except division* will result in a polynomial. Appropriate choices are ...
A. (x^2+2) (x-1)
C. (x+1) plus (X^2-3X -2)
D. (X +5)-(3X +6)
E. (4/8)x . . . . . but not if you mean 4/(8x)
_____
* For division, the result may be a polynomial. In the specific example given here for B, it is not.
The term closure in mathematics refers to the property of a set, in this case, polynomials, where doing certain operations (addition, subtraction, multiplication) with any numbers from the set always yields a number within the set. The options demonstrating closure in a polynomial are A, C, D, E, all but option B, which implies division.
Explanation:The term 'closure' in mathematics refers to the property of a set under an operation where the operation performed on any numbers in the set always produces a number that is also in that set. In the case of polynomials, the operations could be addition, subtraction, or multiplication.
The expressions that demonstrate closure in a polynomial for addition, subtraction, and multiplication are all but option B. Option B, '(x^2+2) over (X -1)', isn't representative of closure in a polynomial as it implies a division operation. Polynomial closure doesn't include division because it can produce numbers outside the original set.
So, the correct answers are A.(x^2+2) (x-1), C.(x+1) plus (X^2-3X -2), D.(X +5)-(3X +6) and E.4/8x as they illustrate closure by either multiplication of two polynomials, addition of two polynomials, or subtraction of two polynomials.
Learn more about Closure in Polynomials here:https://brainly.com/question/3205290
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please help, need answer fast!
What is the simplified expression for -3(2x - y) + 2y + 2(x + y)
a. 8x + y
b. y - 4x
c. 7y - 4x
d. -4x - y
Hey there!!!
Given equation :
... - 3 ( 2x - y ) + 2y + 2 ( x + y )
... -6x + 3y + 2y + 2x + 2y
... -6x + 5y + 2x + 2y
... -4x + 7y
( or )
... 7y - 4x
Hope helps!
E-mails do not require professionalism; it's acceptable to be informal. True False
I could REALLY use some help on this. I just cant seem to get it.(please help me)
Write an equation for the line parallel to the given line that contains C.
C (3, 6); y= -2 x + 7
y = - 2x + 12
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - 2x + 7 is in this form with slope m = - 2
Parallel lines have equal slopes, thus
y = - 2x + c is the partial equation.
To find c, substitute (3, 6 ) into the partial equation
6 = - 6 + c ⇒ c = 6 + 6 = 12
y = - 2x + 12 ← equation of parallel line
Bank robbers leave the bank with the bounty. The cops get alerted right away, but it takes them 4 minutes before they start in hot pursuit. The police station is 10 miles down the road from the bank in the direction opposite to that in which the robbers are heading. If the robbers travel at 96 mph how fast must the cops go to catch them before they reach the state line 55 miles away
In 4 minutes, 1/15 hour, the robbers have a (96 mi/h)·(1/15 h) = 6.4 mile head start.
The cops must travel 65 miles in the time the robbers travel 48.6 miles. Hence their speed must be 65/48.6 times that of the robbers, or about
... 65/48.6×96 mi/h ≈ 128.4 mi/h
_____
The chase will be over after (55 mi)/(96 mi/h) = 34 minutes 22.5 seconds from the time of the robbery. The cops will have to cover the 65 miles in less than 30:22.5 minutes, or about 0.50625 hours.
The cops' speed then is 65 miles/(0.50625 hour) ≈ 128.39506... mi/h
he is right do not look down here to be sure so go with his answer
A generator runs for 2 1/2 h and uses 4 3/8 gal of fuel. How many gallons of fuel did the generator use each hour? Enter your answer as a mixed number in simplest form in the box.
1 [tex]\frac{3}{4}[/tex] gallons per gour
divide number of gallons used by running time
4 [tex]\frac{3}{8}[/tex]÷ 2 [tex]\frac{1}{2}[/tex]
change mixed numbers to improper fractions
[tex]\frac{35}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]
leave the first fraction, change division to multiplication, turn the second fraction upside down
= [tex]\frac{35}{8}[/tex] × [tex]\frac{2}{5}[/tex]
= ( 35 × 2 ) / (8 × 5 ) = [tex]\frac{7}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex]
plz help asp!!!What is the relationship between 9.125×10−3 and 9.125×102 ?
The exponents differ by 5, meaning the numbers differ by a factor of 10⁵.
9.125×10² = 100,000×9.125×10⁻³
The latter is 100,000 times the former
Which of the following statements are true?
All square matrices are diagonal matrices.
All diagonal matrices are square matrices.
The size of any square matrix is m x m, where m is a positive integer.
All coefficient matrices are square matrices.
The statements that are true are:
All diagonal matrices are square matrices. The size of any square matrix is m x m, where m is a positive integer.The following information should be considered;
All square matrices should not be diagonal matrices. All coefficient matrices should not be square matrices.Therefore, the above two options should be considered true statement.Learn more: https://brainly.com/question/1301963?referrer=searchResults
Answer: B & C
Step-by-step explanation:
on edge
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
(−2,−3)
(3, 1)
(1, 3)
(3, 2)
pleaseeeee help i will give brainliest
Answer:
(1, 3)
Step-by-step explanation:
The first number of each pair is the x-coordinate, the horizontal location of the point.
The end points of the graphed line segment are (1, 3) and (-3, -2). It looks like the answer choices are intended to see if you can tell what order the coordinates are expressed in.
The appropriate choice is (1, 3), the upper right end point.
write an equation of the line in point slope form that passes through (-16, 8) and (4,-2)
a.) y-8=-1/2(x+16)
b.) y-8=1/2(x-16)
c.) y+8=2(x+16)
d.) y+8=-(x-16)
When the reference point is used in the point-slope form of the equation, the equation should evaluate to ...
... 0 = 0
This is only true for point (-16, 8) using the equation of selection a).
Happily, we also find that point (4, -2) satisfies the equation.
... -2-8 = -1/2(4+16)
... -10 = -1/2(20) . . . . true
The appropriate choice is ...
... a.) y-8 = -1/2(x+16)
!HELP!
Three is a zero of the equation x^3−4x^2−3x+18=0.
Which factored form is equivalent to the equation?
A (x+2)(x−3)^2=0
B (x−2)(x−3)^2=0
C (x+2)(x−√3)(x+√3)=0
D (x−2)(x−3)(x+3)=0
x^3−4x^2−3x+18=0
(x - 3)^2 (x + 2) = 0
Choice B
A
since x = 3 is a zero then (x - 3) is a factor
dividing x³ - 4x² - 3x + 18 by (x - 3) gives
x³ - 4x² - 3x + 18 = (x - 3)(x² - x - 6 ) = 0,
(x - 3)(x - 3 )(x + 2 ) = 0
(x + 2 )(x - 3)² = 0 → A
Center(-2,4) radius=6
(x + 2 )² + (y - 4)² = 36 ← is the equation of the circle
the equation of a circle in standard form is (x - a)² + (y - b)² = r²
where (a, b) are the coordinates of the centre and r is the radius
here (a, b ) =(- 2, 4) and r = 6
(x + 2)² + ( y - 4 )² = 36
What is the solution of sqrt1-3x=x+3
x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
Please help!!! The last one. Word answer
Often, variability is most usefully expressed in the same units as the original data. That's what standard deviation (square root of variance) does. In situations where that is the case, the variance is useful only for getting to the value of standard deviation.
6.
2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin
We need to find the triangle bounded by the y-axis the line [tex]f(x)=9-\frac{6}{7}x[/tex] and the line perpendicular to it that passes through the origin.
This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:
Therefore, this line is the blue one and is written as:
[tex]f(x)=\frac{7}{6}x[/tex]
To find [tex]y(t)[/tex] we need to find the slope and y-intercept. So, taking two points:
[tex]P_{1}(15,150) \ and \ P_{2}(25,450) \\ \\m=\frac{450-150}{25-15}=30[/tex]
So:
[tex]Using \ P_{1}(15,150) \\\\y=30t+b\\\\150=30(15)+b \therefore b=-300 \\\\\boxed{y(t)=30t-300}[/tex]
The y-intercept is [tex]b=-300[/tex] and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.
The x-intercept can be found when y=0 (year 1980), that is:
[tex]y(t)=30t-300 \\\\0=30t-300 \therefore t=10[/tex]
This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.
The slope of this function is [tex]m=30[/tex]
This value tells you that the profit increases $30.000 each year.
Hello,
Please, see the attached files.
Thanks.
Bill draws a regular octagon with the perimeter of 32 units.He picks a vertex of the octagon and draws two line segments through the interior of the octagon on each different opposite vertex.His line segments divide the octagon into three quadrilaterals.what does the shape look like ?
The quadrilaterals are two congruent isosceles trap ezoids and a kite.
a mattress store charges 7% sales tax and a $50 delivery fee. The delivery fee is not subject to sales tax. The following functions represent the situation F(a)=1.07a and g (b)= b+50
Solve for g (f (a)).
Answer: [tex]g(f(a))=1.07a+50[/tex]
Step-by-step explanation:
The given functions are: [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]
[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].
Thus, [tex]g(f(a))= g(1.07a)[/tex]
Now replacing [tex]b[/tex] as [tex]1.07a[/tex] into the given function of [tex]g(b)[/tex], we will get......
[tex]g(1.07a)= 1.07a+50[/tex]
So, [tex]g(f(a))=1.07a+50[/tex]
Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)
My answer was: y=0.5x+16.5
How can you tell by looking at the coordinates of the two triangles that Δ A'B'C' is a 180° rotation of Δ ABC? A) The coordinates cannot prove a 180° rotation. B) The y-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. C) The x-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. D) Both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC.
under a rotation about the origin of 180°
a point (x, y ) → (- x, - y )
hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC
Answer:
Its D
Step-by-step explanation:
Both coordinates have opposite signs.
In LaToya’s school
3
8
of the students have a blood type of O+, and
1
12
of the students have a blood type of O–. What fraction of the students in LaToya’s school has a blood type of O+ or O–?
[tex]\frac{11}{24}[/tex]
combine the fractions of each type by adding them
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{12}[/tex]
Before we can add the fractions we require them to have the same denominator
To achieve this we require the lowest common multiple (LCM ) of 8 and 12
The LCM of 8 and 12 is 24
To change the denominators , multiply the numerator/ denominator by the appropriate value
[tex]\frac{3}{8}[/tex] = [tex]\frac{3(3)}{8(3)}[/tex] = [tex]\frac{9}{24}[/tex]
[tex]\frac{1}{12}[/tex] = [tex]\frac{1(2)}{12(2)}[/tex] = [tex]\frac{2}{24}[/tex]
Add the numerators leaving the denominator as it is
= [tex]\frac{9+2}{24}[/tex] = [tex]\frac{11}{24}[/tex]
Answer:111/24
Step-by-step explanation:
A small company had a profit of -$528 in January. If it continues to have the same profit for each month for four months, what will be the companies total profit for four months?
$2112 you just have to do 528 x 4 = 2112
The company's total profit over four months, if sustaining a consistent loss of $528 per month, would be -$2,112.
If a small company had a profit of -$528 in January, and it continues to make the same profit (which is really a loss) each month for four months, we can calculate the total profit (total loss in this case) for those four months by multiplying the monthly profit by four.
So, the calculation would be:
Monthly Profit x Number of Months = Total Profit
(-$528) x 4 = -$2,112
Therefore, the company's total profit after four months would be -$2,112. This means the company would have a loss of $2,112 total over those four months.
find the sum of (2x^2 +4x-9) +(3x^2-2x+10) please show work
You can eliminate parentheses and combine like terms.
(2x^2 +4x-9) +(3x^2-2x+10)
= 2x^2 +4x-9 +3x^2-2x+10 . . . . . nothing needs to be distributed, so we can simply drop the parentheses
= x^2(2 +3) +x(4 -2) +(-9 +10) . . . group like terms
= 5x^2 +2x +1
Jared has taken out a loan for his car. His monthly payments amount to $650. If his loan is for 36 months, and he paid a down payment of $400, what is the total cost of the car for Jared? A. $15,050 B. $23,800 C. $28,300
B! 650 x 36 +400 = 23,800!
Answer:
$23800.
Step-by-step explanation:
Monthly payment of loan of a car = $650
His loan is for 36 months
So, Total payment of 36 months = [tex]36 \times 650[/tex]
= [tex]23400[/tex]
He paid the down payment of amount $400
So, Total cost of the car = [tex]23400+400[/tex]
= [tex]23800[/tex]
Hence the total cost of the car for Jared is $23800.
So, Option B is correct.
Need some help please.
In the smaller triangle, the corresponding side is 3 times the base length. Since these triangles are similar, the same ratio holds.
... n = 3×5
... n = 15
Jacob tapes down a piece of red tape on a basketball court. The piece of tape is 3/5 yard long. He wants to divide it into sections that are each 1/10 yard long. How many sections will the piece of tape be divided into? 30 points if u answer
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Answer:
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Step-by-step explanation:
Marie is cleaning her clothes out of the closet in her spare bedroom. She started with 650 of her items in the closet. She has been able to continually decrease the number of her items in the closet at a rate of one-half per month. Her brother, Dustin, has started putting 5 items of his clothing in the closet each month as Marie cleans it out. Marie wants to know how many months it will take before the number of items Dustin adds will be equal to the number of her items in the closet.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
Wording is everything. Here, there are some issues. "... at the rate of 1/2 per month" can be interpreted to mean that at the end of the first month, there are 649 1/2 items in Marie's closet (decreased by 1/2 from 650).
"The number of items Dustin adds" could mean 5 items, the number he adds each month. The wording should specify the time period or whether we're talking about the total number Dustin has added.
We assume your description means that the number of items in Marie's closet at the end of each month is 1/2 what it was at the beginning. (As opposed to decreasing by 1/2 item each month.) We assume we're interested in the total number of items of Dustin's that are in the closet.
Marie's quantity can be modeled by ...
... m = 650·(1/2)^t . . . . . t = time in months
Dustin's quantity can be modeled by ...
... d = 5t
There will be one solution for d=m, at about t = 4.8. At that point, Dustin will have added about 24 items, which will be the number Marie is down to.
There is a viable solution for d=m at about t = 4.8.
Answer:
D. there is only one solution, and it is viable
Step-by-step explanation: