Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Select three options.
1 ≥ 2x
6x ≥ 3 + 8x – 4
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
Answers
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
The solution to the given inequality is;
6x≥3+4(2x-1)
6x≥3+8x-4
2x≤1
x≤(1/2)
The correct options are;
A)1 ≥ 2x
B)6x ≥ 3 + 8x – 4
C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).
Hence, options A, B, and C are correct.
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Answer:
A, B, C
Step-by-step explanation:
Related Questions
Which function is the result of vertically stretching f(x) = x ^ 2 - 7 by a factor of 2 and translating downward 5 units?
Answers
The function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)The given function f(x) is needed to be stretched vertically by a factor of 2, therefore, the function can be written as,
g(x) = 2(x² - 7) = 2x² - 14
Now, the function is needed to be translated by 5 units in the downward direction, therefore,
p(x) = g(x)-5 = 2x² - 14 -5
p(x) = 2x² - 19
Hence, the function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
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Rotate the given triangle 90 degrees
CLOCKWISE about the origin.
0
0
07
0
-
-3 -4
0 -3
[?]
Answers
The value is [tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
what is clockwise and counterclockwise?Clockwise Rotations (CW) mimic the path of a clock's hands.
Negative numbers are used to represent these rotations. Counterclockwise rotations (CCW) follow the path of a clock's hands in the opposite direction.
Now, rotating 90 degree clockwise we get
[tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
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Round 969.991 to the nearest whole number
Answers
Answer:
Round of 969.991
970
Rules of round off
1) If the digit is odd no. the no. will increase to 1
2) if it is even the no. will be same.
Sandhu lights a candle at 6 pm. It is 30 cm high. At 7pm, the candle is 27 cm high. At 8pm, it is 24cm high. a) How many cm does the candle burn down every hour? b) How high is the candle at 11 pm?
Answers
Your final answer: A) The candle burns down 3 centimeters every hour. B) At 11 pm, the candle is 15 centimeters high.
Simplify the expression –3(x 3)2 – 3 3x. what is the simplified expression in standard form?
Answers
[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression
The given expression is:
[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]
This is the standard form of the given expression.
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Can you answer the question
Answers
Step-by-step explanation:
Hi There! Let me help you :)
[tex] = 8.8.8.8.8.8.8[/tex]
[tex] = ( \text{there \: are \: 7 \:numbers \: eight })[/tex]
[tex] \: [/tex]
So we can rewrite the above equation to be like this.
[tex] = 8.8.8.8.8.8.8[/tex]
[tex] = 8.(1 + 1 + 1 + 1 + 1 + 1 +1)[/tex]
[tex] = 8.7[/tex]
Work out the values of a, b, c and d.
Answers
Step-by-step explanation:
The are two angles ie. 45 and 80 than find the third angle
80 will be vertically opposite and alternative angle to a
Follow the steps to find the
area of the shaded region.
Now, use the formula
below to calculate the
area of the triangle.
Triangle Area = bh
h = 10.0708 cm
Triangle Area = [?] cm²
Round to four decimal places.
14 cm
hi
46°
14 cm
Answers
The area of the triangle is given as: ≈ 70.50cm²
What is the explanation to the above solution?Area of shaded region = Area of the sector less Area of the Triangle.
This is represented as:
π r² (∅/360) - 1/2 x b x h
= π x 14² x (46/360) - (1/2) x 14 x 10.0708
= 78.6794 - 70.4956
= 8.1838 cm²
Hence, the area of the triangle is (1/2) x 14 x 10.0708
= 70.4956 cm²
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3x+2=0 i need the answer quick
Answers
Answer:
[tex]\huge\boxed{\sf x = -2/3}[/tex]
Step-by-step explanation:
Given equation:3x + 2 = 0
Subtract 2 to both sides
3x = 0 - 2
3x = -2
Divide 3 to both sides
x = -2/3
[tex]\rule[225]{225}{2}[/tex]
Mr. Thakuri deposited Rs.2,00,000 in her fixed account at a bank for 3 years. The bank pays her the simple interest at the rate of 10℅ p.a. How much net interest would she get if 5 % of interest in charged as income tax?
Answers
The net interest she would get on the amount deposited is $57,000.
What is the net interest?The net interest is the total interest earned less tax.
Interest = amount deposited x simple interest x time
200,000 x 0.1 x 3 = $60,000
Net interest = $60,000 x (1 - 0.05)
$60,000 x 0.95
$57,000
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The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answers
Answer:
15
Step-by-step explanation:
"one number is three more than twice the second number"
15 * 2 = 30
30 + 3 = 33
15 + 33 = 48
Answer:
15
Step-by-step explanation:
The key to most problems of this type is carefully translating the word problem into math ... an equation.
"The sum of two numbers is 48."
"Sum": Add
"two numbers": we'll need two numbers... let's call them x & y
"is": =
"48": 48
So, the first sentence means: [tex]x+y=48[/tex]
Note that we have two unknowns here. To solve for them, we'll need another equation... at least as many equations as unknowns (2 unknowns, needs 2 equations).
"If one number is three more than twice the second number..."
"one number": x
"is": =
"three more than": +3
"twice": 2*
"the second number": y
So, the second sentence introductory clause means: [tex]x=2y+3[/tex]
Systems of equationsWe have a system of equations. We need as many equations as we have unknowns. We currently have two equations, and two unknowns. Let's try to solve the system:
[tex]x+y=48[/tex]
[tex]x=2y+3[/tex]
There are two main methods to solve systems of equations: Substitution & Elimination
To use the Substitution Method, we'll need to isolate one of the variables in one of the equations, substitute, and solve.
To use the Elimination Method, we'll need to align like terms, find or build matching coefficients with opposite signs, add to eliminate, and solve.
Given that equation 2 already has x isolated, this system is already ready to use the Substitution method, so let's do that.
Solving a system with the Substitution Method[tex]x+y=48\\x=2y+3[/tex]
[tex](2y+3) + y = 48[/tex]
[tex]2y+3 + y = 48[/tex]
[tex]3y+3 = 48[/tex]
[tex]3y= 45[/tex]
[tex]y= 15[/tex]
To find x, substitute back into one of the equations: Equation 2 already has x isolated, so it will be easy to solve for x.
[tex]x=2(15)+3[/tex]
[tex]x=30+3[/tex]
[tex]x=33[/tex]
So the solution we found is x=33 and y=15.
Check to make sure it satisfies the original conditions:The sum of the numbers is 48:
[tex]x+y=(33)+(15)\\x+y=48[/tex]
One number is three more than twice the second number
[tex]x=2y+3[/tex]
[tex](33)\text{ ?=? }2(15)+3[/tex]
[tex]33=33[/tex]
Our answer satisfies all of the original conditions, so our answer works.
Answering the questionThe question finally asks, "...which of the following is the smaller number?"
Of the two numbers, the smaller number is 15.
Kimberly loves science and just subscribed to KiwiCo, a company that delivers STEAM kits to students to build and create
things at home! KiwiCo charges a subscription fee of $16.99 for each of its members. KiwiCo had 300 subscribers in March.
In April, 50 new people subscribed to KiwiCo, and 23 people canceled their subscriptions. How much more money did
KiwiCo earn from subscriptions in April?
Answers
The KiwiCo earn money from subscriptions in April would be $5555.73.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
KiwiCo charges a subscription fee of $16.99 for each of its members.
$16.99 per 1 person
KiwiCo had 300 subscribers in March.
In April, 50 new people subscribed to KiwiCo, and 23 people canceled their subscriptions.
300 + 50 = 350 - 23 = 327
So,
327×$16.99= 5555.73
Hence, The KiwiCo earn money from subscriptions in April would be $5555.73.
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How tall is the tree?
5ft
35°
-20ft-
[? ]ft
Answers
Answer:
19
Step-by-step explanation:
tan35=x/20
20tan35=x
x=14.0041507641942
x+5=19.0041507641942
Nearest foot is 19
A shop increases all their prices by 6%
A picture frame increases by £294
Find the new price of the picture frame.
Answers
Answer:
0riginal price = 4900
Step-by-step explanation:
294 = 6%
294/6 = 49 49 = 1%
49 x 100 = 4900
0riginal price = 4900
What are all the solutions of x² + 3x -4 = 0? Multiple choice
A: -4
B:-2
C:-1
D:0
E:1
F:2
G:4
Answers
Answer :
A and E .
Step-by-step explanation:
a) Copy a segment using the construction tool. Insert a screenshot of the construction here.
Alternatively, construct a segment and copy it by hand using a compass and straightedge. Leave
all circle and arc markings.
Answers
We need to understand circles and colinear points in order to use the building tool to create a circle.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Draw arcs such that they all bisect one another at a point, which will be the center of the circle, starting with three non-colinear points (points A, B, and C).
Additionally, the radius will match the distance between the arcs' centers and their correspondingly drawn arcs.
Hence we need to understand circles and colinear points in order to use the building tool to create a circle.
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giving 20 points out for this question!
Answers
Answer: £20 doubling at the end of each year for 5 years
From the question, Stephen would want to select one option which gives the highest amount of profit. I mean, even if you were to select one, you would obviously try calculating all the 4 choices to see which one makes you earn the most money. Now let's conduct the workout and see which one will earn us the most £ in 5 years:
Option 1:
[tex](500*\frac{5}{100} ) + 500 ---- > 1yr\\= 25 + 500 \\ = 525\\\\(525*\frac{5}{100} ) + 525 ----- > 2yrs\\= 26.25 + 525\\= 551.25\\\\(551.25 * \frac{5}{100}) + 551.25 - - - > 3yrs\\ = 27.563 + 551.25\\= 578.813\\\\(578.813 * \frac{5}{100}) + 578.813 - - > 4 yrs\\ = 28.941 + 578.813\\ = 607.754 \\\\(607.754 * \frac{5}{100}) + 607.754 - - > 5 yrs\\ = 30.388 + 607.754\\ = 638.142 \\[/tex]
ans: £ 638.142
Option 2:
[tex]1 year = 12 months\\5 years : 5*12 = 60 months\\\\10*60 = 600[/tex]
ans: £ 600
Option 3:
[tex](550*\frac{3}{100}) + 550 - - - - > 1yr\\= 16.5 + 550\\= 566.5 \\\\(566.5 * \frac{3}{100}) + 566.5 - - - > 2 yrs\\ = 16.995 + 566.5\\= 583.495\\\\(583.495 * \frac{3}{100}) + 583.495 - - > 3 yrs\\ =17.505 + 583.495\\= 601\\\\(601 * \frac{3}{100}) + 601 - - - - - - > 4 yrs\\= 18.03 + 601\\= 619.03\\\\( 619.03* \frac{3}{100}) + 619.03 - - - - > 5 yrs\\= 18.571 + 619.03\\= 637.601[/tex]
ans: £ 637.601
Option 4:
[tex]20*2= 40 - - - - > 1yr\\40 * 2= 80 - - -- > 2 yrs\\80*2 = 160 - - - > 3 yrs\\160*2 = 320 - - - > 4 yrs\\320*2= 640 - - - > 5yrs[/tex]
ans: £ 640
Out of all the calculated answers, you can see that option 4 has the highest amount. So that's it. By the way, I might do some incorrections in some calculations because I am not good at long maths, but yes i hope I did it all right!
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
What is the value of x in the figure below? In this diagram, ABD ~ CAD.
Answers
Answer:
[tex] \sqrt{30} [/tex]
Step-by-step explanation:
altitude rule
10 / x = x / 3
x^2 = 30
x = sqrt(30)
15-
4
3+
2H
11
-5-4-3-2-1₁
Mark this and return
2345
-3-
2 3 4 5 x
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
Answers
The question was incomplete. Below you will find the missing graph image.
The range contain all the real numbers greater than or equal to –3 .
Range of function : The set of outputs of a function is called range of that function. Range of a function is also called co-domain of the function.
Example : If f(x) = x² is the function with domain as all real numbers, then the range of that function is the set of all non-negative real numbers.
We have to find the range of the function on the graph.
We can see by the graph minimum value of y of function is -3 and the graph continues to extend upward in the positive direction.
So, the range contain all the real numbers greater than or equal to –3 .
Therefore, the range contain all the real numbers greater than or equal to –3 .
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What is another way to write the absolute value inequality p ≤ 12? O-12≤p≤ 12 O-122p≤12 O-12 ≤por p≤ 12 -122P or p≤ 12 958 What is another way to write the absolute value inequality p ≤ 12 ? O - 12≤p≤ 12 O - 122p≤12 O - 12 ≤por p≤ 12 -122P or p≤ 12 958
Answers
Answer:
-12 ≤ p ≤ 12
Step-by-step explanation:
If the absolute value inequality is
|p| ≤ 12,
then the answer is
-12 ≤ p ≤ 12
Partially factored form: f(x) = (x − 3)(x 3)(x2− 4x 5) use the quadratic formula to identify the zeroes of x2 − 4x 5. x =
Answers
Answer:
2 ± i
Step-by-step explanation:
by 5, I assume you mean +5
x² - 4x + 5 = 0
x = (-b±(√(b²-4ac)) / 2a
x = (4 ± (√(16 - 20)) / 2
x = (4 ± (√(-4)) / 2
√-4 = √4√-1 which is 2i
x = (4 ± 2i) / 2
x = 2 ± i
Clare has a recipe for yellow cake. She uses 9 1/3 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups for flour.
Which of these equations represent the relationship between c and f ?
A. c = 7/3f
B. c = 3/16f
C. c = 16/3f
D. c = 3/7f
Answers
The correct answer is option A which is the equations which represent relationship between c and f is c = 7 / 3f.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
Given that:-
Clare has a recipe for yellow cake. She uses 9 1/3 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups for flour.From the given data we can see that the amount of flour required is [tex]9\dfrac{1}{3}\[/tex] Cups or [tex]\dfrac{28}{3}[/tex] Cups for making 4 cakes.
So the expression will be written as:-
[tex]9\dfrac{1}{3}f = 4c[/tex]
[tex]\dfrac{28}{3\\}f = 4c[/tex]
[tex]c = \dfrac{28}{3\times 4}f[/tex]
c = [tex]\dfrac{7}{3}[/tex]f
Therefore the correct answer is option A which is the equation that represents the relationship between c and f is c = 7 / 3f.
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Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Answers
Mikaela's team's score is 8.33
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Viktoria's team's score = 7
According to question,
= 2+ 7*2 = 16
so, Mikaela team score= 16/3+3= 8.33
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What is the answer for the question down below
Answers
Answer:
This is the ray BAStep-by-step explanation:
Ray can be defined as a part of a line that has a fixed starting point but no end point.
The starting point is B and on its way to infinity, it passes through point A.
Correct sign is
[tex]\huge\boxed{\overrightarrow{BA}}[/tex]
What is the discriminant of the quadratic equation 2x² - x - 3=0?
A. -25
B. 25
C. -23
D. 23
Answers
The given quadratic equation is
[tex]2 {x}^{2} - x - 3 = 0[/tex]
comparing with
[tex] {ax}^{2} + bx + c = 0[/tex]
We get ,
[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]
formula :
[tex]D = {b}^{2} - 4ac \\ \\ D = {( - 1)}^{2} - 4 \times 2 \times ( - 3) \\ \\ D = 1 - ( - 24) \\ \\D = 1 + 24 \\ \\D = 25.[/tex]
Discriminant of given quadratic equation is 25 .
option (B) 25 ✔
Jack have 34 toy cars, Mike says he have 3 times more than Jack's toy cars. How many toy cars does Mike have?
Answers
Answer:102
Step-by-step explanation:
34 x 3 = 102
Answer:
102
Step-by-step explanation:
Since Jack has 34 toy cars and Mike has 3 times more than Jack's toys, we should multiply 34 with 3 to get the answer.
34 * 3 = 102
So, this means that Mike has 102 toy cars.\
Hope this helps :)
Can someone please help me
Answers
Which angle refers to the same angle as \angle DAC∠DACangle, D, A, C?
Answers
Answer:
Option
Step-by-step explanation: The way tell what the answer is are the similar lines. The single yellow line helps indicate that it's a similar angle.
Let a be a matrix with 4 columns. What are the possible values for rank(a)?
Answers
The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?
The possible values for rank A = 2
What is a vector space?A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.
From the information given:
If v,w be the vectors in a [tex]\mathbb{R}[/tex]where;
A = matrix with 4 columns v, w, 2v+w, v-w, which are non-independent vectors.However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).
We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.
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Please help
(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Answers
Answer:
V = 4*8
V= 32
(x+x) * (x+x) = 2x * 2x = 4x^2
