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
How do I get the result for 1/8 out of 40?
Answers
Answer:
5
Step-by-step explanation:
You divide your number by the denominator and then times it by the numerator
Step by step
You divide your number by the denominator and the time it by the numerator
Alvin is 9 years older than Elga. The sum of their ages is 81. What is Elga's age?
Answers
Answer:
elga is 32 and alvin is 49
The value of x² – 2yx + y² when x = 1, y = 2 is
Answers
The process
1-2(2x1)+(2)^2
[tex]x^2 - 2xy +y^2 = (x-y)^2 = (1-2)^2 = (-1)^2 =1[/tex]
The curve y= 1/3 x⁴ - 4x² -3x has a gradient of -3 at three points.
Find the coordinates of these points.
Answers
Answer:
[tex]\boxed{(0, 0), (\sqrt{6}, -12-3\sqrt{6}), (-\sqrt{6}, -12+3\sqrt{6})}[/tex]
Step-by-step explanation:
Step 1: Take the derivative of the function with respect to x
[tex]\frac{d}{dx} (\frac{1}{3}x^4-4x^2-3x)\\=\frac{d}{dx} (\frac{1}{3}x^4)-\frac{d}{dx}(4x^2)-\frac{d}{dx}(3x)\\=\frac{4}{3}x^3-8x-3[/tex]
Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,
Step 2: Set the derivative of the function equal to -3 and solve for x
[tex]\frac{4}{3}x^3-8x-3=-3\\\frac{4}{3}x^3-8x=0\\4x(\frac{1}{3}x^2-2)=0\\[/tex]
We can see that one solution is x=0.
The other 2 solutions are:
[tex]\frac{1}{3}x^2-2=0\\\frac{1}{3}x^2=2\\x^2=6\\x=\sqrt{6}, x=-\sqrt{6}[/tex]
Now that we found out the x value, we can plug it in back to the equation to find their respective y value:
x=0: y=0
x=sqrt(6): y=-12-3sqrt(6)
x=-sqrt(6): y=-12+3sqrt(6)
Hence we have our answer.
How to find the inverse of 3log3(x+3)+1. Its with a base of 3
Answers
Let [tex]f^{-1}(x)[/tex] be the inverse of
[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]
Then by definition of inverse function,
[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
Solve for the inverse :
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]
[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]
[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]
Which graph represents a linear function? (4 points)
A coordinate plane is shown with a curved line that starts in the bottom left area of the graph, passing through the point -1 comma -5, curving to pass through the y-axis at 2.5, then curving up again to pass through the point 1 comma 5
A coordinate plane is shown with a line passing through the x-axis at negative 2 and the y-axis at negative 6.
A coordinate plane is shown with a parabola graphed in an upward U shape. The bottom of the parabola touches the y-axis at -10 and curves upward on both sides
A coordinate plane is shown with a wavy line that sits on the x-axis and moves across the graph in even up and down waves.
Answers
Answer:
The second option
Step-by-step explanation:
Linear means a straight line.
Choices 1, 2, and 4 are wrong because they are either a parabola or wavy, and by definition of both of these terms, they are not straight and are therefore not linear.
Geologists collected some rock samples. Of the 12,000
grams of ore they collected, about 600 grams contain a
valuable mineral
What is the concentration of the mineral in the
sample?
5%
6%
50%
60%
Answers
Answer:
5%
Step-by-step explanation:
600 / 12000 = .05
Answer:
2 %
Step-by-step explanation:
An eight-person relay team completed a race in 96.8 seconds. On average, what was each runner's time?
Answers
Answer:
12.1
Step-by-step explanation:
Answer:
12.1 Seconds
Step-by-step explanation:
96.8/8=12.1
Please help me with this question and how to break even!
Answers
Answer:
The blogger needs at least 189subscribers to break even
6x + ____ = 10 Please find the blank.
Answers
Answer:
6x +4=10
I think this is answer
Find the area of the triangle
Please help me - I don't get how to do this.
Please show your work - I really need to understand this
Answers
Answer:
Step-by-step explanation:
1. Pythagorean theorem: a^2+b^2=c^2
Note that the hypotenuse is 11 (for the second right triangle).
Find the length of the dotted line by doing 7^2+b^2=11^2
49+b^2=121, b=[tex]\sqrt{72\\}[/tex].
Now you can the area of the second right triangle: ([tex]\sqrt{72\\}[/tex](7))/2=29.7.
Find the length of the first right triangle:
Note that 9 is the hypotenuse; ([tex]\sqrt{72\\}[/tex])^2+b^2=9^2
=72+b^2=81
b=3.
([tex]\sqrt{72}[/tex])(3))/2=12.7
Help me please i really need it
Answers
Answer:
Step-by-step explanation:
RSB is a right angle
12. RSB is 90 degrees
13. A right angle is 90 degrees
H is between P and S
14. PS + PH = HS
15. Deductive Reasoning
68 is 40% of what number?A.17 B.136 C.170D.270
Answers
Answer:
C. 170
Step-by-step explanation:
68/4=17
17 is 10% of the unknown number
17 times 10 is 170
Answer:
C. 170Step-by-step explanation:
68 is 40% of what number?
A.17
B.136
C.170
D.270
68 : 40 * 100 = 170
Molly went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $1 per game. Sharon went Thursday, paying $2 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How much did each one spend?
Answers
Answer:
Molly played 4 games
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone.
Answers
Answer:
5 weeks
Step-by-step explanation:
75 w + 55 ≥ 400
75 w ≥ 345
15 w ≥ 69
w ≥ [tex]\frac{23}{5}[/tex] = 4.6 weeks ⇒ the minimum number of weeks Jordan must work is 5 weeks
simplify help me to do this
Answers
Answer:
204
Step-by-step explanation:
90-5 (9-5 (9- (14-12) 3 ) ÷5
▪︎ First we have to solve the ones in the brackets ___ ( 14-12 ) which is e equal to 2
90-5 (9-5 (9- 2×3 ) ÷5 "the 3 comes inside the bracket coz we solved the previous one"
▪︎then we have to solve ( 9-2×3 ) which is equal to 3 _____ is 3 because if we go in the BODMAS way it will be
( 2×3 =6) , then... (9-6=3)
▪︎at the same time we can subtract 9-5 because we are done with the first bracket ( 9-5=4 )
90-5 (4×3)÷5
▪︎at the same time we can subtract 90-5 as well coz we are done with the first bracket ( 90-5=85)
▪︎then we can multiply (4×3) coz it's in the brackets (4×3=12)
85×12÷5
▪︎so then we hv to multiply 85 by 12 , then the answer is 1020
1020÷5
▪︎then divide (1020÷5=204)
☆90-5 (9-5 (9- (14-12) 3 ) ÷5
=90-5(9-5(9-2×3)÷5
=90-5(4×3)÷5
=85×12÷5
=1020÷5
=204
hope this helps☆☆☆
( sorry fr the long answer )
Help please, help please
Answers
Answer:
i think the perimeter is 60
Step-by-step explanation:
9²+12² = x²
15 = x
perimeter = 15×4 = 60
what is the percent change of
30 to 90?
what is what is the percent change of 30 to 90?
Answers
Answer:
200% increase
Step-by-step explanation:
I need the anwser to this right now please
Answers
Answer:
b. 9
Step-by-step explanation:
2+9=11
11+11=22
22+6=28
(3+3)-28 = 22
that leaves the other side having to be 11 on each so
2+9= 11
First the first 4 term for 4n-5
Answers
Answer:
-1, 3, 7, 11
Step-by-step explanation:
First, let's find term 1. To find this term, we need to replace n with 1 - what is 4(1) - 5? Well, that's just 4 - 5, or -1. So, our first term is -1. Next, we'll find our second term. To do this, we'll replace n with 2. 4(2) = 8, and then 8 - 5 is equal to 3, so our second term is 3. Let's now find the third term by replacing n with the number 3. 4(3) - 5 is equal to 12 - 5, or 7. So, 7 is our third term. Finally, we'll find the fourth term. 4(4) is equal to 16, and 16 - 5 is equal to 11. So, the fourth and final term is equal to 11.
Hopefully that's helpful! :)
Step-by-step explanation:
Term 1: - 1
Term 2: 3
Term 3: 7
Term 4: 11
The rule is, where you see n, substitute with the position/term requested
First 4 terms are: - 1,3,7, 11
Dog slept 3 hours . If the dog snored 1/3 of an hour . How many times did he snore
Answers
Answer:
it depends how much the god snores within a certain time period
Pls confirm if right. If not pls help. Thx!
Answers
Yep, you are all good!
Answer:
yes you are correct
Step-by-step explanation:
what is the output of the function when the input is −3
Answers
It depends on the function. Please add a picture or type your function.
Write the equation in standard form.
y - 10=-2(x-8)
Answers
Answer:
2x + y = 26
Step-by-step explanation:
The standard form of a linear equation is A x + By = C.
Simplify -2(x - 8)
Multiply -2 by -8
y - 10 = -2x + 16
2x + y - 10 = 16
Add 10 to both sides.
Add 16 and 10
Answer= 2x + y = 26
there are 11 members on a board of directors.if they must firm a subcommittee of 5 members how many different subcommittees are possible
Answers
You see here, there are too many people in the government and all of this gets us no where. So, too many is the answer.
SOMEBODY HELP ME NO LINKS PLEASE
Answers
4.A counterexample can be used to show that a conjecture is false. Below are three
conjectures students made after visiting a zoo. Write a counterexample that shows that
conjecture is false.
a. There are always more elephants in a zoo than giraffes.
b. The oldest leatherback sea turtle in captivity is 33 years
old.
c. American bison are never over 6 feet tall.
Answers
Counterexamples are simply used to disprove conjectures.
(a) Elephants and Giraffes
This conjecture may or may not be true.
However, it can be disproved by the following counterexample
There are sometimes more elephants in a zoo than giraffes
The word "sometimes" disproves the original conjecture
(b) The oldest leatherback sea turtle
This conjecture is not true.
This is so because the oldest leatherback sea turtle in captivity is actually 400 years old.
So, the conjecture can be disproved by the following counterexample
The oldest leatherback sea turtle in captivity is 400 years old.
(c) American bison
This conjecture may or may not be true.
However, it can be disproved by the following counterexample
American bison are sometimes over 6 feet tall
The word "sometimes" disproves the original conjecture
Read more about conjectures and counterexamples at:
https://brainly.com/question/1619980
REI.C.6 Level 1
below.
2. A student is solving the system,
2x + 3y = 12
5x - 2y = 11
algebraically. Their work is shown below but is unfinished.
Continue where the student left off and solve the system.
2x + 3y = 12
5x - 2y = 11
=
2 (2x + 3y = 12)
3 (5x - 2y = 11)
4x + 6y = 24
15x – 6y = 33
-
Answers
Answer:
The solution is x = 3, y = 2.
Step-by-step explanation:
4x + 6y = 24
15x – 6y = 33 Add these 2 equations:
19x = 57
x = 57/19
x = 3. Now Substitute for x in the original equation:
2(3) + 3y = 12
3y = 12 - 6
2y = 6
y = 2.
The sum of two angles of a triangle is
110°. Calculate the third angle in
degrees.
Answers
Answer:
70
Step-by-step explanation:
the sum of all angles is 180°
so 180-110= 70
A company claims that their new bottle holds 40% more laundry soap.
If their original container held 53 fluid ounces of soap, how much does the new container hold?
plz show work too plz
Answers
Answer:
74.2
Step-by-step explanation:
53 x .4 = 21.2
21.2 + 53 = 74.2