Answer:
Set notation: { x ∈ ℝ | -25 < x < 30 }
Interval notation: (-25, 30)
Step-by-step explanation:
In set notation,
"x ∈ ℝ" means "x is an element of all real numbers"
you then write the restrictions after that, which would be "-25 < x < 30"
this gives you { x ∈ ℝ | -25 < x < 30 },
"x is an element of all real numbers, such that x is larger than -25 and less than 30"
In interval notation, it is written as (-25, 30). The parentheses mean that the interval does not include the numbers -25 or 30.
If the interval does include those numbers, i.e. if it was "-25 ≤ x ≤ 30" instead of "-25 < x < 30" you would use brackets instead of parentheses,
giving you {-25, 30}.
2 pounds of dried fruit spit among 7 friends
While on a beach vacation, Tasha makes a scale drawing of points of interest between two
piers. On her drawing, 2 cm represents 0.5 mi. The piers are 12 cm apart on Tasha's drawing.
What is the actual distance between the two piers?
(I need this answered by August 25th.)
Answer:
The distance between the two piers is 3 miles.
Step-by-step explanation:
If in Tasha's drawing 2cm represents 0.5 miles between the two piers, and the distance between the two piers in Tasha's drawing is 12cm.
The answer is found by the rule of three:
2 cm : 0.5 miles
12 cm : X
X = (12 * 0.5) / 2
X = 3 miles.
The distance between the two piers is actually 3 miles.
Sara created the poster shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 28 cm, and the width is labeled as width equal to 32 cm. What would be the dimensions of the poster at fraction 1 over 4 times its current size? Length = 7 cm, width = 8 cm Length = 24 cm, width = 28 cm Length = 32 cm, width = 36 cm Length = 112 cm, width = 128 cm
Answer:
The answer is D. Length = 9, width = 6cm
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Kenny ueses 1/16 of the bottle of syrup every scoop of ice cream he eats how many scoops of ice cream had he ate if he had uesd 2 3/4 bottald of chocolate syrup
Answer:
[tex]\huge\boxed{Answer=>44}[/tex]
Steps:
If you do the steps correctly, the answer should be 44 ice cream scoops.
(Short way to do this problem/question)
Information given:
1. He uses 1/16 of the bottle of syrup(Every scoop of icecream he eats)
2. The question wants us to find, if he had ate 2 3/4 bottle of chocolate syrup.. how many scoops did he eat.
The steps are::::
1/16 = 16 (scoops of icecream)
Now, if we do 16 times 2 3/4 we would get...
44.
Hence, the answer is 44 scoops of icecream.
Find the total surface area. A. 192 cm² B. 197 cm² C. 109 cm² D. 216 cm²
Answer:
D) 216cm²
Step-by-step explanation:
Triangles: a=1/bh
a=1/2(6)(8)
a=24 (2 of them)
Base: 6x7=42
Back: 8x7=56
Front Rectangle: 7x10=70
24+24+42+56+70=216cm²
Using the numbers and symbols, solve 7x = 42
Answer:
you currently have the value of x × 7, you need to divide it by 7 to find the value of x.
42 ÷ 7 = 6
Step-by-step explanation:
Determine whether the given value is a sample statistic or a population parameter. A researcher examines the records of all the registered voters in one city and finds that 43% are registered Democrats. Group of answer choices
Answer: Population parameter
Step-by-step explanation: The parameter can be defined as a numerical value used to describe an entire population. The population describes all the entire values or members belonging to a particular group. Hence, numerical values which are used to explain the characteristic of the population is called the population parameter. Sample statistics on the other hand are numerical values associated statistical properties of a sample which is a subset of a certain population.
In the instance given above, 43% represents the population parameter which describes the percentage number of Democratic voters out of the entire population of voters in the city.
Can someone help me with this please I need it by today
Answer:
9 I THINK
Step-by-step explanation:
77 minus 14 equals 63 and 63 divided by 7 equals 9
The solution to -12 + n = -15 is n = 3. true or false
Answer:
False
Step-by-step explanation:
Step 1: Write out equation
-12 + n = -15
Step 2: Add 12 on both sides
n = -3
So our answer is -3 and not 3.
Answer: [tex]False[/tex]
The answer to this problem is [tex]n=-3[/tex]
To get -3 here is the work shown
Simplify both sides of the equation
[tex]n-12=-15[/tex]
Add 12 to both sides
[tex]n-12+12=-15+12\\n=-3[/tex]
Solve for x. A. 4 B. 3 C. 5 D. 7
Answer:
C. 5
Step-by-step explanation:
The product of distances to the near and far intercepts with the circle are the same for each line segment. In the case of the tangent, those distances are the same, so you have ...
6×6 = 4×(4+x)
36 = 16 +4x . . . . eliminate parentheses
9 = 4 + x . . . . . . .divide by 4; next, subtract 4
5 = x
Help plzz I think it is 1 or 2 ..... By The square root property, if k is a real number and x^2=k, then what is x equal to? 1. √k 2. =| √k 3. -√k 4. k^2
Answer:
[tex]\Large \boxed{2. \ x=\pm \sqrt{k}}[/tex]
Step-by-step explanation:
[tex]x^2 =k[/tex]
k is a real number.
We take the square root of both sides of the equation.
[tex]\sqrt{x^2 } =\pm \sqrt{k}[/tex]
Simplifying the equation.
[tex]x=\pm \sqrt{k}[/tex]
Answer:
x = ±√k
Step-by-step explanation:
If:
[tex]x^2 = k[/tex]
We'll take square root on both sides
=> [tex]\sqrt{x^2} = +/- \sqrt{k}[/tex]
=> x = ±√k
Can 8x be added to 56? Why or why not?
Use rich text?
Answer:
see below
Step-by-step explanation:
8x and 56 are not like terms
x is a variable and 56 is a constant
8x can be added to 56 but they cannot be combined together into one term
8x+56 cannot be combined because they are not like terms
If R is between A and D and
DR = 8 and DA = 15 then AR=
Answer:
7
Step-by-step explanation:
heres a model
A ----------R---------D
A ----?-----R----8---D
A----------15----------D
15 - 8 = 7
AR = 7
Julie and Kristen are the partners in a local sporting goods shop. They needed $51,000 to start the business. They invested in the ratio 5:12, respectively. a. How much money did each invest? b. What percent of the business was owned by Kristin? Round to the nearest tenth of a percent.c. If the business grows to $3,000,000, what percent of it will Julie own? Round to the nearest tenth of a percent.
Answer:
See below.
Step-by-step explanation:
They invested in a ratio of Julie:Kristen of 5:12.
5 + 12 = 17
Julie invested 5/17 of the amount, and Kristen invested 12/17 of the mount.
a.
Julie: 5/17 * $51,000 = $15,000
Kristen: 12/17 * $51,000 = $36,000
b.
Kristen owns 12/17 of the business.
As a percent, 12/17 = 12/17 * 100% = 70.6%
c.
The percent of the business each owns does not change with the amount the company is worth.
Kristen owns 70.6%, so Julie owns 100% - 70.6% = 29.4%
5
Type the correct answer in the box. Use numerals instead of words.
What value of x makes this equation true?
-6x + 3 = 45
x =
Answer:
45
Step-by-step explanation:
-6x = 45-3
-6x= 42
X = 42/-6
X= -7
if segment AB is 4 units, segment AD is 23 units, and segment CD is 12 units, what is the length of segment BC?
PLEASE HELP
Answer:
AD=23 because it is the same length as the top line. 12+4 is 16 and 23-16=7. X=7
Step-by-step explanation:
Complete the equation of the line through (3, -8) and (6, -4)
Answer:
we have,
y-y1=m(x-x1)
or, y+8=4/3(x-3)
or, 3y+24=4x-12
or, 4x +3y+36=0 is the required equation
Answer:4/3x–12.
Step-by-step explanation: I just did this on khan and got it wrong but I used hints to get the answer, so here you go.
Fug 20,5:45:45 PM Find the common ratio of the geometric sequence 19,95,475,-
Answer:
5
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
95/19 = 5
To verify take the third term and divide by the second term
475/95 = 5
The common ratio is 5
determine the inverse of f(x)=x-2 algebraically
Answer:
The answer is
f-¹(x) = x + 2Step-by-step explanation:
To find the inverse of f(x) equate f(x) to y
That's
y = f(x)
y = x - 2
Next interchange the terms.
That's x becomes y and y becomes x
We have
x = y - 2
Make y the subject
Send 2 to the left side of the equation
y = x + 2
We have the final answer as
f-¹(x) = x + 2Hope this helps you
Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a potential root of the polynomial?
Answer:
Zeroes : 1, 4 and -5.
Potential roots: [tex]\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20[/tex].
Step-by-step explanation:
The given equation is
[tex]x^3-21x=-20[/tex]
It can be written as
[tex]x^3+0x^2-21x+20=0[/tex]
Splitting the middle terms, we get
[tex]x^3-x^2+x^2-x-20x+20=0[/tex]
[tex]x^2(x-1)+x(x-1)-20(x-1)=0[/tex]
[tex](x-1)(x^2+x-20)=0[/tex]
Splitting the middle terms, we get
[tex](x-1)(x^2+5x-4x-20)=0[/tex]
[tex](x-1)(x(x+5)-4(x+5))=0[/tex]
[tex](x-1)(x+5)(x-4)=0[/tex]
Using zero product property, we get
[tex]x-1=0\Rightarrow x=1[/tex]
[tex]x-4=0\Rightarrow x=4[/tex]
[tex]x+5=0\Rightarrow x=-5[/tex]
Therefore, the zeroes of the equation are 1, 4 and -5.
According to rational root theorem, the potential root of the polynomial are
[tex]x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}[/tex]
Constant = 20
Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.
Leading coefficient= 1
Factors of leading coefficient ±1.
Therefore, the potential root of the polynomial are [tex]\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20[/tex].
A is the midpoint (3,6) and B is the midpoint (11,12).find the coordinates of midpoint of AB
Answer:
M(7,9)
Step-by-step explanation:
M(3+11/2, 6+12/2)
M(14/2, 18/2)
=M(7,9)
Answer:
(7,9)
The explanation is on the photo.
Hope it helps!
#MissionExam001
Solve for d. 4d-4= 5d -8
Answer:
d=4
Step-by-step explanation:
We are given the equation:
4d-4=5d-8
and asked to solve for d. In order to solve for d, we must isolate it on one side of the equation.
First, subtract 4d from both sides of the equation.
(4d-4d)-4=(5d-4d)-8
-4= (5d-4d)-8
-4= d-8
Next, add 8 to both sides of the equation.
(-4+8)=d-8+8
(-4+8)= d
4=d
Let's check our solution. Plug 4 in for d and solve.
4d-4=5d-8 (d=4)
4(4)-4=5(4)-8
Multiply 4 and 4.
16-4=5(4)-8
Subtract 4 from 16.
12= 5(4)-8
Multiply 5 and 4.
12= 20-8
Subtract 8 from 20.
12=12
The statement above is true, so we know our solution is correct.
The solution to the equation is d=4.
Answer:
It is 4
Step-by-step explanation:
KHAN
I need help to simplify this!!! Asap
Answer: The fraction [tex]\frac{7}{17}[/tex]
This can be written as 7/17 if you are using a computer keyboard.
====================================================
Explanation:
The two negatives next to each other basically cancel each other out to form a positive or a plus sign
We have
[tex]-\frac{9}{85} - \left(-\frac{44}{85}\right)[/tex]
turn into
[tex]-\frac{9}{85} +\frac{44}{85}[/tex]
From here, we add the fractions. To do this, we add the numerators and place the sum over the common denominator 85. This is only possible since both denominators are the same number.
[tex]-\frac{9}{85} +\frac{44}{85} = \frac{-9+44}{85} = \frac{35}{85}[/tex]
The last thing to do is to reduce this fraction as much as possible.
We see that 35 and 85 have 5 as a common factor. Divide each number by 5 to get...
35/5 = 785/5 = 17Therefore, [tex]\frac{35}{85} = \frac{7}{17}[/tex]
So overall,
[tex]-\frac{9}{85} - \left(-\frac{44}{85}\right) = \frac{7}{17}[/tex]
reduce the following rational expression to lowest terms if possible 12/16 Please answer me fast Will mark as a brainlist
Answer:
3/4
Step-by-step explanation:
Find the number that can be divided into both numbers.
12÷4 =3 16÷4=3
What is the value of 3 to the power 2 over 3 to the power 4
Greetings from Brasil...
From potentiation properties:
Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ
division of power of the same base: I repeat the base and subtract the exponents
In our case
3² ÷ 3⁴
3²⁻⁴
3⁻²We also know about another property: P⁻ⁿ = (1/Pⁿ) so
3⁻² = 1/3²
1/9Answer:
1/9
Step-by-step explanation:
hope i helped
Nathan is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 20° per minute after being turned on. What is the temperature of the oven 7 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answer:
205°
T(t) = 65°+20°t
Step-by-step explanation:
Let the temperature be T and time be t
The equation to determine the temperature T after t minutes is:
T(t) = 65° + 20°tFor t = 7 we get:
T(7) = 65° + 20°*7 = 65° + 140° = 205°4x + 5 = 25 x = 2 x = 5 x = 2 x = 7
Hi there!
Answer:
[tex]\huge\boxed{x = 5}[/tex]
4x + 5 = 25
Subtract 5 from both sides:
4x + 5 - 5 = 25 - 5
4x = 20
Divide both sides by 4:
4x/4 = 20/4
x = 5.
A car factory produces 100 cars in a day if C is the total number of cars produced in the days which equation represents the number of cars as a function of the number of days
Answer:
C = 100x
Step-by-step explanation:
We can create an equation where x represents the number of days.
C = 100x
This represents the situation, since 100 cars are made every day.
For example, in 2 days, 200 cars will be made since 100(2) = 200.
Write an equation parallel to the line determined by the points (15, -6) and (-3, 13), through: (4, 2)
Answer:
The answer is
[tex]y = - \frac{19}{18} x + \frac{76}{2} [/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
That's
Slope of the through points
(15, -6) and (-3, 13) is
[tex]m = \frac{13 - - 6}{ - 3 - 15} = - \frac{19}{18} [/tex]Since the lines are parallel their slope are also the same
So slope of parallel line = - 19/18
Equation of the line using point (4,2) and slope -19/18 is
[tex]y - 2 = - \frac{19}{18} (x - 4) \\ y - 2 = - \frac{19}{18} x + \frac{38}{9} \\ y = - \frac{19}{18} x + \frac{38}{9} + 2[/tex]We have the final answer as
[tex]y = - \frac{19}{18} x + \frac{76}{2} [/tex]Hope this helps you
Answer:y=-1.583x-8.332
Step-by-step explanation:
First find slope from two points (-6-13)/(15+3)=-1.583
Now line is parallel so the slope would be same for the other line passing through (4,2) now as the general equation of line is
y=mx+c
2=-1.583(4)+c
Solving for c equals to -8.332
So final equation is
y=1.583x-8.332
[tex] \frac{x^{3} }{x^{2} + 2x + 1 } [/tex]
How do I divide a monomial by a polynomial?
[tex]x^3=\boxed{x}\cdot x^2[/tex], and
[tex]\boxed{x}(x^2+2x+1)=x^3+2x^2+x[/tex]
Subtract this from [tex]x^3[/tex] to get a remainder of
[tex]x^3-(x^3+2x^2+x)=-2x^2-x[/tex]
[tex]-2x^2=\boxed{-2}\cdot x^2[/tex], and
[tex]\boxed{-2}(x^2+2x+1)=-2x^2-4x-2[/tex]
Subtract this from the previous remainder to get a new remainder of
[tex](-2x^2-x)-(-2x^2-4x-2)=3x+2[/tex]
[tex]3x[/tex] does not divide [tex]x^2[/tex], so we stop here.
What we've done is to write
[tex]\dfrac{x^3}{x^2+2x+1}=x-\dfrac{2x^2+x}{x^2+2x+1}[/tex]
then
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3x+2}{x^2+2x+1}[/tex]
and we stop here because the remainder term [tex](3x+2)[/tex] has a degree less than the degree of the denominator.
Alternatively, we can be a bit tricky and notice that
[tex]x^2+2x+1=(x+1)^2[/tex]
Now,
[tex](x+1)^3=x^3+3x^2+3x+1[/tex]
so that
[tex]\dfrac{x^3}{(x+1)^2}=\dfrac{(x+1)^3-(3x^2+3x+1)}{(x+1)^2}[/tex]
We can divide the first term by [tex](x+1)^2[/tex] easily to get
[tex]\dfrac{x^3}{(x+1)^2}=x+1-\dfrac{3x^2+3x+1}{(x+1)^2}[/tex]
Next,
[tex](x+1)^2=x^2+2x+1[/tex]
so that
[tex]\dfrac{x^3}{(x+1)^2}=x+1-\dfrac{3((x+1)^2-(2x+1))}{(x+1)^2}-\dfrac{3x+1}{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{(x+1)^2}=x+1-3+\dfrac{6x+3}{(x+1)^2}-\dfrac{3x+1}{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{(x+1)^2}=x-2+\dfrac{3x+2}{(x+1)^2}[/tex]
which is the same result as before.