Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the inequality
-2x < 10
-6 < -2x
Part a) Is x = 0 a solution to both inequalities
FOR -2x < 10
substituting x = 0 in -2x < 10
-2x < 10
-3(0) < 10
0 < 10
TRUE!
Thus, x = 0 satisfies the inequality -2x < 10.
∴ x = 0 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 0 in -6 < -2x
-6 < -2x
-6 < -2(0)
-6 < 0
TRUE!
Thus, x = 0 satisfies the inequality -6 < -2x
∴ x = 0 is the solution to the inequality -6 < -2x
Conclusion:
x = 0 is a solution to both inequalites.
Part b) Is x = 4 a solution to both inequalities
FOR -2x < 10
substituting x = 4 in -2x < 10
-2x < 10
-3(4) < 10
-12 < 10
TRUE!
Thus, x = 4 satisfies the inequality -2x < 10.
∴ x = 4 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 4 in -6 < -2x
-6 < -2x
-6 < -2(4)
-6 < -8
FALSE!
Thus, x = 4 does not satisfiy the inequality -6 < -2x
∴ x = 4 is the NOT a solution to the inequality -6 < -2x.
Conclusion:
x = 4 is NOT a solution to both inequalites.
Part c) Find another value of x that is a solution to both inequalities.
solving -2x < 10
[tex]-2x\:<\:10[/tex]
Multiply both sides by -1 (reverses the inequality)
[tex]\left(-2x\right)\left(-1\right)>10\left(-1\right)[/tex]
Simplify
[tex]2x>-10[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}>\frac{-10}{2}[/tex]
[tex]x>-5[/tex]
[tex]-2x<10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}[/tex]
solving -6 < -2x
-6 < -2x
switch sides
[tex]-2x>-6[/tex]
Multiply both sides by -1 (reverses the inequality)
[tex]\left(-2x\right)\left(-1\right)<\left(-6\right)\left(-1\right)[/tex]
Simplify
[tex]2x<6[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{6}{2}[/tex]
[tex]x<3[/tex]
[tex]-6<-2x\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:3\right)\end{bmatrix}[/tex]
Thus, the two intervals:
[tex]\left(-\infty \:,\:3\right)[/tex]
[tex]\left(-5,\:\infty \:\right)[/tex]
The intersection of these two intervals would be the solution to both inequalities.
[tex]\left(-\infty \:,\:3\right)[/tex] and [tex]\left(-5,\:\infty \:\right)[/tex]
As x = 1 is included in both intervals.
so x = 1 would be another solution common to both inequalities.
SUBSTITUTING x = 1FOR -2x < 10
substituting x = 1 in -2x < 10
-2x < 10
-3(1) < 10
-3 < 10
TRUE!
Thus, x = 1 satisfies the inequality -2x < 10.
∴ x = 1 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 1 in -6 < -2x
-6 < -2x
-6 < -2(1)
-6 < -2
TRUE!
Thus, x = 1 satisfies the inequality -6 < -2x
∴ x = 1 is the solution to the inequality -6 < -2x.
Conclusion:
x = 1 is a solution common to both inequalites.
Related Questions
2+17x
i need help i can not find the answer
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Answer:
this question is not factorable with rational number so either trick question and the answer is no solution or it is typed wrong
Step-by-step explanation:
How are angle 4 and angle 5 related?
Answers
Answer:
C supplementary angles
Step-by-step explanation:
Reason: They Both Add Up To 180 Degrees
6th grade math !!!!!!!!!!!!!!!!
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Answer:
4th one
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
If a proportional relationship has a constant of proportionality of 6, what is a point that lies on the graph of
the line representing the relationship?
Answers
Answer:
(0,0) (1,6) (2,12)
Step-by-step explanation:
Proportional relationships are also known as direct variation, so I'll refer to it as DV.
The formula for finding DV is y=kx.
In this case, k=6, which is just y=6x. So, essentially..
(0,0) (1,6) (2,12) etc.
The points that lies on the graph of the line representing the relationship are (0, 0), (1, 60, and (2, 12).
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality. We can also express it as x is to y at times.
Given:
As, we know that the constant proportionality have
y= k x
where k is constant of proportionality.
We have given that constant of proportionality = 6
So, y= 6x
Now, when x=0
y=0
and, x=1
y= 6
and, x=2
y= 12
Hence, the points are (0, 0), (1, 60, and (2, 12).
Learn more about Constant of Proportionality here:
https://brainly.com/question/29126727
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Convert the following linear equations from slope form to standard form:
y=-3x+7
y = - 2/3x - 3/4
Answers
Answer:
3x+y=7
8x+12y=-9
Step-by-step explanation:
Select all tables that represent a proportional relationship between X and Y
Answers
Answer:
The 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.
Step-by-step explanation:
We know that when y varies directly with x, we get
y ∝ x
y = kx
k = y/x
where k is called the 'constant of proportionality'.
Given the table
x 0 5 10 15
y 2 17 32 47
Let us calculate the k value for all the points
FOR (0, 2)
k = y/x
substitute x = 0, and y = 2
k = 2 / 0 = ∞
FOR (5, 17)
k = y/x
substitute x = 5, and y = 17
k = 17/5
k = 3.4
FOR (10, 32)
k = y/x
substitute x = 10, and y = 32
k = 32/10
k = 16/5
k = 3.2
FOR (15, 47)
k = y/x
substitute x = 15, and y = 47
k = 47/15
k = 3.1
It is clear that the 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.
HELP ME PLEASE NEED HELP
Answers
Answer:
y = -3x - 6
Step-by-step explanation:
Which value of v makes 12 = 12 +
V – 8
a true statement?
2
Choose 1 answer:
А
v=8
B
v= 10
v= 12
D
v= 14
Answers
At an art auction, Geannina's painting sold for over $ 300 $300dollar sign, 300. Write an inequality that describes P PP, the price of Geannina's painting in do
Answers
Answer:
[tex]P > 300[/tex]
Step-by-step explanation:
Given
An art sold for over $300
Required
Represent as an inequality
Represent the price with p.
This implies that; P is over 300
In inequalities; the term "over" means greater than i.e. >
Hence:
P is over 300 is equivalent to [tex]P > 300[/tex]
How much more money is needed to make $10?
?
$5.95
$10
Answers
Sophie earns 6% interest from her bank. If she has $456 in the bank, how much interest will she earn?
Answers
Millie expected 20 friends to show up to her birthday party, but 24 attended. What was
her percent error? Round to the nearest percent.
Answers
Answer:
Her percent error was: ≈ 17% (whole percent)
Step-by-step explanation:
Given
Approximate value = 20 friends
Exact Value = 24 friends
To determine
Percent error
Using the formula to calculate the Percent error
Percent error = | Approximate Value| - Exact Value | / | Exact value | × 100
= | 20 - 24 | / | 24 | × 100
= | - 4 | / | 24 | × 100
Apply absolute value: |-a| = a, a>0
= 4/24 × 100
= 16.67 %
≈ 17% (whole percent)
Thus, her percent error was: ≈ 17% (whole percent)
Someone plz help me this is urgent!
Answers
Answer:
5^12
Step-by-step explanation:
When you have a power to the power, you multiply the powers. Since we have (5^3)^4, we can multiply the powers because we have a power to the power. Since 3 * 4 is equal to 12, we have 5^12. That means that 5^12 is the answer.
Answer:
1250
Step-by-step explanation:
5 times 5 times 5
Show work!!!!!!!!!!!!!!!!
Answers
Given the circumference of a circle is 8π centimeters, calculate the area of the circle in terms of π.
Answers
Answer:
16π cm²
Step-by-step explanation:
circumference = 2πr
Area = πr²
We need to determine r to calculate the area
2πr = 8π
Divide both sides of the equation by 2π to find r
r = 4
Now, we determine area.
area = πr² = π4² = 16πcm²
Answer:
[tex]\Large\boxed{\sf{16\pi\text{cm}^2}}[/tex]Step-by-step explanation:
The formula for the circumference of a circle can be used to solve this problem.
[tex]\underline{\text{CIRCLE OF A CIRCUMFERENCE FORMULA:}}[/tex]
[tex]:\Longrightarrow: \sf{C=2\pi r}[/tex]
[tex]\text{AREA:}= \sf{\pi r^2}[/tex]
[tex]\sf{2\pi r=8 \pi}[/tex]
You have to divide by 2 from both sides.
[tex]\sf{\dfrac{2\pi r }{2}=\dfrac{8\pi}{2} }[/tex]
Solve.
Divde the numbers from left to right.
8/2=4
r=4
[tex]\sf{\pi r^2=\pi4^2}[/tex]
Solve by exponents.
[tex]\sf{4^2=4*4=\boxed{\sf{16}}[/tex]
[tex]\Longrightarrow: \boxed{\sf{16\pi \text{cm}^2}}[/tex]
Therefore, the correct answer is 16πcm².I hope this helps. Let me know if you have any questions.
pls help!!
(don’t mind the circles on the numbers)
pls try them all, but ill be okay even if you just try one or however many.
Answers
Answer: 35. The equation would be y = 17/2x
Answer:
32) yes, linear
33) no
34) yes
Step-by-step explanation:
32) if you look at the difference in the y-values and the difference of the x-values you will see that they all equal 3; for example, 24/8, 21/7, 18/6
33) following same method as for #32, there is not a consistent ratio of change between x-and-y values
34) yes, constant ratio is 10
Can someone please help me out
Answers
B= -1,-1
C= 3,4
D= 1,4
What is the measure of Zx?
Angles are not necessarily drawn to scale.
B
20
35
A-
C
What is the measure of x?
Answers
Answer:
x = 145
Step-by-step explanation:
x and 35 are adjacent angles and are supplementary, sum to 180° , then
x + 35 = 180 ( subtract 35 from both sides )
x = 145
at school, 460 of the students walk to school.
The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
Answers
Answer:
460/100 X 5 = 23
23 bike to school xx
f(x)= (x-1)(x(x+1)+2x) find all rational zeros
Answers
Answer:
x = 0, x = 1, x = - 3
Step-by-step explanation:
To find the zeros, let f(x) = 0 , that is
(x - 1)(x(x + 1) + 2x) = 0 ← distribute and simplify parenthesis
(x - 1)(x² + x + 2x) = 0
(x - 1)(x² + 3x) = 0 ← factor out x from the second parenthesis
x(x - 1)(x + 3) = 0
Equate each factor to zero and solve for x
x = 0
x - 1 = 0 ⇒ x = 1
x + 3 = 0 ⇒ x = - 3
what is the length of AC
Answers
Answer:
12 units
Step-by-step explanation:
[tex]\sin 30\degree = \frac{AC}{BC} \\ \\ \frac{1}{2} = \frac{AC}{24} \\ \\ 2AC = 24 \\ \\ AC = \frac{24}{2} \\ \\ AC = 12 \: units[/tex]
5x to the second power-13x +6
guys answer only
Answers
Answer:
-138
Step-by-step explanation:
What is the value of c in the equation below?
2 Superscript negative 4 Baseline times 2 squared = a Superscript b Baseline = c
Answers
Answer:
c
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
Chris plays basketball every 2 days and football every 5 days. The last day he played both sports on the same day was on June 13th. What is the next day in June that he will play both basketball and football on the same day?
Answers
Answer:
They will both occur on the 28th of june.
Step-by-step explanation:
This will happen bc you are trying to find same multiples of the two numbers
2 x 5 = 15
3 x 5 = 15
add 15 to 13 and you will get your date.
(geomatry) Pleasee help I'll give brainest and thanks :)
Also please don't answer if you don't know!! Thanks in advance
Answers
Answer:
JML=142 degrees
Step-by-step explanation:
This shape is a rhombus, as all 4 sides are equal, but the angle measures are not. One of the properties of a rhombus is that opposite angles are congruent, and adjacent angles are supplementary. Only the second one is important. Since angles KLM and angle JML are supplementary, the equation KLM+JML=180 can be used. KLM is then substituted by the given angle measure, 38 degrees, to get an equation such as JML+38=180. Now, to solve for JML, 38 must be subtracted from both sides of the equation, which leaves teh answer of JML=142.
**IF ANYONE IS AN EXPERT IN MATH PLEASE HELP.**
i’ve figured out the answer to this problem but i have to check which i dont know how. Could anyone please help me on this? how do you check your answer?
Answers
To check you're answer just fill in 18.7 for h in the original problem.
Function: Yes or no
{(-3,4),(-2,5),(0,0),(-2,5),(4,8)}
Answers
Answer:
Yes.
Step-by-step explanation:
Every input has a specific output.
ima say yes but I may not be correct if somebody else answers chose them and let me be your last chose ;-;
Line a passed through points (-2,1) and (2,9). Which is parallel to line a?
Answers
Answer:
D
Step-by-step explanation:
Line A's slope: 9-1/2+2 = 8/4 = 2
y = 2x+b
y = 2x-5
If the slope of 2 lines are equal, then the lines are parallel.
Please help me with this math problem, 20 points!
Answers
Answer:
The first one
Step-by-step explanation:
The price of a notebook was $3.60 yesterday. Today, the price fell to $3.10. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answers
Answer:
13.9%
Step-by-step explanation:
First, we find the amount of decrease.
$3.60 - $3.10 = $0.50
The price decreased $0.50.
Now we find what percent $0.50 is of $3.60.
percent = part/whole * 100%
percent = $0.50/$3.60 * 100%
percent = 0.13888 * 100% = 13.9%
Answer: 13.9%
