Answers
Answer:
Option D: [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Step-by-step explanation:
GIven the following inequality statement:
[tex]\displaystyle\mathsf{7x\:+\:6\:\geq \:\frac{-x}{2}}[/tex]
Start by eliminating the fraction on the right-hand side.
Multiply both sides of the inequality statement by 2:
[tex]\displaystyle\mathsf{2(7x\:+\:6)\:\geq \:\bigg[\frac{-x}{2}\bigg](2)}[/tex]
2(7x + 6) ≥ -x
Next, distribute 2 into the terms inside the parenthesis:
14x + 12 ≥ -x
Subtract 12 from both sides:
14x + 12 - 12 ≥ -x - 12
14x ≥ -x - 12
Add x to both sides:
14x + x ≥ -x + x - 12
15x ≥ - 12
Divide both sides by 15 to isolate x:
[tex]\displaystyle\mathsf{\frac{15x}{15}\:=\:\frac{-12}{15}}[/tex]
[tex]\displaystyle\mathsf{x\geq -\frac{4}{5}}[/tex] or [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Therefore, the correct answer is Option D: [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Related Questions
The gas tank on a car holds 13.3 gallons. If the car goes 199.5 miles on a single tank, how many miles per gallon does the car get?
Answers
Answer:
292.6
Step-by-step explanation:
A
3
-2
-1
0
2
3
4
В.
The midpoint of AB = ([?],[ ])
Enter
Answers
Step-by-step explanation:
hope it will help you and please mark the answer as brillant please.
Harry read 1/3 of a book on Saturday and three force of the remainder on Sunday. If he still had 75 pages left how many pages were in the book?
Answers
You work backwards;
Since he read 3/4 of the remainder that would be 75 x 4 because 75 was left after 3/4. You would get 300. Then, you would do 300 / (1/3), this is getting the final thing, equals 900.
Hope this helps!
Hi need help for this maths question
Answers
a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have
[tex]\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}[/tex]
so both conditions are met and f(y) is indeed a PDF.
b) The probability P(Y > 4) is given by the integral,
[tex]\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}[/tex]
c) The mean is given by the integral,
[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy[/tex]
Integrate by parts, with
[tex]u = y \implies du = dy[/tex]
[tex]dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}[/tex]
Then
[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)[/tex]
[tex]\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy[/tex]
[tex]\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}[/tex]
Part 1 of 2
O Points
What are the lateral surface area and total surface area of a cylindrical oil storage tank that has a 44-ft diameter and 18-ft height?
The lateral surface area of the cylindrical oil storage tank is
(Round to one decimal place as needed.)
Answers
The Lateral Surface Area of the cylindrical oil storage tank is [tex]2486.9\text{ sq.ft}[/tex]
The Total Surface Area of the cylindrical oil storage tank is [tex]5526.4\text{ sq.ft}[/tex]
If the height and base radius of the cylindrical oil storage tank are represented by [tex]h[/tex] and [tex]r[/tex] respectively, then
The Lateral Surface Area, also known as the Curved Surface Area, of the cylindrical oil storage tank has the formula
[tex]L=2\pi rh[/tex]
The Total Surface Area of the cylindrical oil storage tank has the formula
[tex]T=2\pi rh+2\pi r^2\\T=2\pi r(h+r)[/tex]
The values for the height and base radius are [tex]18ft[/tex] and [tex]22ft[/tex] respectively.
Calculate the Lateral Surface Area
[tex]L=2\pi rh\\=2\times 3.14\times 22\times 18\\\approx 2486.9\text{ sq.ft}[/tex]
Calculate the Total Surface Area
[tex]T=2\pi r(h+r)\\=2\times 3.14\times22(18+22)\\=5526.4\text{ sq.ft}[/tex]
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There are two spheres; the radius of the big sphere is two times the radius of the small sphere. How many times larger is the volume of the big sphere compared to the small one?
Answers
The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.
The formula of the volume of a sphere is given below
⇒ Formula:
V = 4/3(πr³)................. Equation 1⇒ Where:
V = Volume of the spherer = radius of the sphereπ = constant called pieFrom the question, There are two spheres.
If the radius of the bigger sphere is two times the radius of the smaller sphere.
R = 2r⇒ Where
R = bigger radiusr = smaller radiusFor the bigger sphere
⇒ Substitute these values into equation 1
V = 4/3(π(2r)³)V = 4/3(π8r³)............. Equation 2For the smaller sphere,
V' = 4/3(πr³)............... Equation 3⇒ Comparing equation 2 and equation 3
V = 8V'Hence, The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.
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Show all work to multiply
(3+ square root -16) (5 – square root -25)
Answers
[tex]\left(3+\sqrt{-16} \right) \left(5-\sqrt{-25} \right)\\\\=\left(3+\sqrt{-1} \cdot \sqrt{16} \right) \left(5- \sqrt{-1} \cdot \sqrt{25} \right)\\\\=(3+4i)(5-5i)~~~~~~~~~~~~~~;\left[i=\sqrt{-1} \right]\\\\=15-15i + 20i - 20i^2\\\\=15+5i -20(-1)~~~~~~~~~~~~;[i^2 =-1]\\\\=15+5i +20\\\\=35+5i[/tex]
(3v^5-34v^4+79v^3+5v^2+21v+19)\(v-8)
Answers
Answer:
3 big guys
Step-by-step explanation:
Answer:
Step-by-step explanation:
we find by synthetic division.
v-8=0
v=8
8 | 3 -34 79 5 21 19
| - 24 -80 -8 -24 -24
|----------------------------------
3 -10 -1 -3 -3 |-5
Quotient:-3v^4-10v³-v²-3v-3
Remainder:- -5
y = x^2+5x-3
y-x=2
What is the solution of the linear-quadratic system of equations
Answers
Answer:
(-5,-3)
(1,3)
Step-by-step explanation:
Solving with substitution
Set both equations to y = ...
y = x^2 + 5x - 3
----------------
y - x =2
y = x + 2
----------------
Substitute one of the Y's with the other Y = equation.
x + 2 = x ^2 + 5x -3
Set one side to 0
0 = x^2 + 4x -5
x^2 + 4x - 5 = 0
Simplify by factoring
(x-1) (x+5)
Get your X values
x-1 = 0
x = 1
x+5 = 0
x = -5
Plug in each X into one of the equations to get your Y value.
1st X
y = x + 2
y = 1 + 2
y = 3
When X = 1, Y = 3
2nd X
y = x + 2
y = -5 + 2
y = -3
When X = - 5, Y = -3
Your answers are (1,3) and (-5,-3)
I need help solving this problem
Solve for X
Answers
Answer:
x = -7
Step-by-step explanation:
The 2 horizontal lines are parallel as given ion the problem.
The x + 97 angle is congruent to the right angle.
x + 97 = 90
x = -7
Should I write the answer as decimal or a whole number
Answers
x=y^2+4y+4 solve for y
Answers
Answer:
y=
x
−2
y=−
x
−2, x≥0
y=−
x−2, x≥0
Step-by-step explanation:
HELP
HOW AM I MEANT TO ANSWER THIS QUESTION I WOULD ASO LIKE ANSWER.
THX
100 points on the line
Answers
Answer:
x = 7 & y = 8
Step-by-step explanation:
We know that
Mean = Sum of terms/Total terms
=> Mean = 4 + 6 + x + y + 10/5
=> Mean = 20 + x + y/5
Now,
Median = (n + 1)/2
=> Median = (5 + 1)/2
=> Median = 6/3
=> Median = 3rd term = x
So,
x = 20 + x + y/5
x × 5 = 20 + x + y
5x = 20 + x + y
5x - x = 20 + y
4x = 20 + y
Since x and y are in order so,
Possible outcomes will be 7,8 & 9
(7,8) & (8,9) & (7,9)
Taking x = 7 and y = 8
4(7) = 20 + 8
28 = 28
Hence,
x = 7 and y = 8
Answer:
y=7 x=8
Step-by-step explanation: hope you do well in school
Hey , can you help me with this math equation ?
Answers
Define the following sequence recursively: 96, 48, 24, 12, ....
Select one:
a. f(1)=12 f(n−1)=2⋅f(n) n≥2
b. f(1)=12 f(n−1)=−12⋅f(n) n≥2
c. f(1)=96 f(n)=12⋅f(n−1) n≥2
d. f(1)=96 f(n)=2⋅f(n−1) n≥2
Answers
Answer:
I do not see that any of your options will work.
Step-by-step explanation:
a) and b) have a false first statement because f(1) = 96, not 12
c) would create the sequence 96, 1152, 13824
d.) would create the sequence 96, 192, 384. 768...
I believe the correct answer would be
f(1) = 96 f(n) = ½f(n-1) n ≥ 2
which could be either c) or d) if taking potential typographic errors into account. Recording a "2" or "12" where a "½" ought to be.
6x+3y=13 find the value
Answers
6x+3y=13
6x+3y-13=13--13
6x+3y-13=0
Which TWO identify the same sequence?
A) f(x) = 6x + 4 for x = {1, 2, 3, ...}
B) f(x) = 10x + 4 for x = {1, 2, 3, ...}
C) a1 = 6 and an + 1 = an + 4 for n = {1, 2, 3, ...}
D) a1 = 10 and an + 1 = an + 4 for n = {1, 2, 3, ...}
E) a1 = 10 and an + 1 = an + 6 for n = {1, 2, 3, ...}
Answers
The sequences A and E are the same sequences.
What is Sequence?Sequences are set of numbers where the numbers are arranged in a specific order. Some of the common types of sequences are Arithmetic sequences and Geometric sequences.
A) f(x) = 6x + 4 for x = {1, 2, 3, ....}
f(1) = 10, f(2) = 16, f(3) = 22, ....
B) f(x) = 10x + 4 for x = {1, 2, 3, ...}
f(1) = 14, f(2) = 24, f(3) = 34, ....
C) a₁ = 6 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}
a₁ = 6, a₂ = a₁ + 4 = 10, a₃ = a₂ + 4 = 14, ....
D) a₁ = 10 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}
a₁ = 10, a₂ = a₁ + 4 = 14, a₃ = a₂ + 4 = 18, .....
E) a₁ = 10 and aₙ₊₁ = aₙ + 6 for n = {1, 2, 3, ...}
a₁ = 10, a₂ = a₁ + 6 = 16, a₃ = a₂ + 1 = 22, ....
A and E are the same sequences with a common difference 6 and the first term 10.
Hence A and E have the same sequence 10, 16, 22, .....
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16,40 and 56 LCM
Solve please
Answers
Answer:
pic?
Step-by-step explanation:
send me the picture please
What is the third number in this sequence?
Answers
Step-by-step explanation:
x = the first number of the sequence
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
6x + 1 + 2 + 3 + 4 + 5 = 519
6x = 504
x = 84
so, the third number is x+2 = 84 + 2 = 86
What is the measurement of ADB?
A. 90
B. 95
C. 105
D. 145
Answers
Answer:
C)105
Step-by-step explanation:
sizde benim sorduğum soruları cevaplarsanız sevinirim doğru ve hızlı bir şekilde
A Quadrilateral ABCD is rotated 55° about point R to create quadrilateral A' B'C'D'. QUICK. PLEASE
Answers
Answer:
2.8
Step-by-step explanation:
Answer:
Step-by-step explanation:
2.8 units
Last year's computer models are discounted 20%. What was the original price to the nearest dollar of a computer that now costs $1,480?
Answers
Answer:
$1850Step-by-step explanation:
If the Original price was $ X , Then[tex]x - 0.20x \: = 1480[/tex]
[tex]0.8x = 1480[/tex]
[tex]x = 1480 \div 0.8[/tex]
So , X = 1850 dollars .Hope this helps you !!!I'm not sure if this is correct, but I got this
Last year’s computer models are discounted 20%. If a computer is on sale for $1,480, what is the original price of the computer rounded to the nearest dollar?
20% = 0.2
1,480 x 0.2 = 296
1,480 + 296 = 1,776
Answer: 1,776
Again, I don't know if this is correct, so don't be 100% sure with my response.
A rectangle has a perimeter of 270cm and its length is 2½cm times its width find its width
Answers
Answer:
Step-by-step explanation:
If you mean length is 2½ times its width not "2½cm times its width"
2(L + W) = 270
2(2.5W + W) = 270
2(3.5W) = 270
7W = 270
W = 38.5714285714...
W ≈ 38.57 cm
Answer:
Width = 38. 57 cm
Step-by-step explanation:
The perimeter of a Rectangle = 270 cm
Now,
Let's take x to be the width.
Length = 2½ = 5x/2
According to the formula,
The perimeter of a rectangle = 2 ( l + w )
270 = 2 ( 5x/2 + x )
270 = 5x + 2x
270 = 7x
x = 270/7
x = 38. 57 cm.
• The width of a rectangle is 38.57 cm
What's does A equal?
Answers
Answer:
x = 65
Step-by-step explanation:
2x + 2(2x-15) = 360
2x + 4x - 30 = 360
6x = 390
x = 65
Nick wants to buy a pair of shoes. The original cost of the shoes is $56.75, and the markup is 12 percent. How much will he have to pay for the shoes?
Answers
Answer:
Nick will have to pay $63.56 for the shoes.
Step-by-step explanation:
f the original cost of the shoes is $56.75 and the markup is 12% greater than the original price, the final price would be $63.56.
$56.75 • 0.12 = $6.81
$56.75 + $6.81 = $63.56
$56.75 + 12% = $63.56
Answer:
Nick will have to pay $63.56 for the shoes.
Points E, D, and H are the midpoints of the sides of ΔTUV. UV=82, TV=106, and HD= 82. Find HE.
Answers
Answer:
41
Step-by-step explanation:
53/106 = x/82 similar triangles
x=41
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs.
Let x be the calf's age and y be the weight.
a. Write an equation in slope-intercept form that represents the situation.
Answers
The equation in slope-intercept form that represents the situation is y = 3x + 12
A linear equation is on the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let x be the calf's age in month and y be the weight.
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs. Hence it can be represented by:
(2, 18) and (8, 36). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-18=\frac{36-18}{8-2}(x-2) \\\\y=3x+12[/tex]
The equation in slope-intercept form that represents the situation is y = 3x + 12
Find out more on linear equation at: brainly.com/question/14323743
Which of the following expressions has a "x" term with a coefficient of 1?
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that has a "x" term with a coefficient of 1 is the expression that has positive one in from of the term that has x in the expression.
Now, If all the options are observed, then it can be found that the second option has x term with leading coefficient as 1.
Hence, the correct option is B.
Learn more about Expression here:
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The perimeter of a rectangular field is 314 m.
If the width of the field is 72 m, what is its length?
Answers
Answer:
85m
Step-by-step explanation:
Perimeter of a rectangle = 2(l+b)
b=72m, l=?
perimeter =314m
314=2(l+72)
314/2= l+72
157=l+72
l=157-72
l=85m
Pls help fast i will mark brainlyest
Answers
Answer:
x = 20
Hope you could get an idea from here.
Doubt clarification - use comment section