How do you solve inequalities in 7th grade?
Answers
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
Suppose we want to solve the inequality x + 3 > 2.
We can solve this by subtracting 3 from both sides:
x + 3 > 2
x > −1
So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.
Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.
To know more about inequality visit: brainly.com/question/28823603
#SPJ4
Related Questions
Rsm question please help!
Answers
The multiplication of the algebraic expressions gives x⁴ + 1.5x³ - 2x²
How to perform multiplication on algebraic expressions?An algebraic expression is an expression that consists of variables, constants, and a finite number of algebraic operations (such as addition, subtraction, multiplication, and division) e.g. 2x + 25
In order to perform the multiplication, you use expression outside the parenthesis to multiply the expressions inside the parenthesis one after the other. That is:
-0.5x²(-2x² - 3x + 4) = -2x²(-0.5x²) - 3x(-0.5x²) + 4(-0.5x²)
= 1x⁴ + 1.5x³ - 2x²
= x⁴ + 1.5x³ - 2x²
Learn more about algebraic expressions on:
https://brainly.com/question/4344214
#SPJ1
evaluate 27/32 × 16/27, give your answer in its simplest form
Answers
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{27}{32}[/tex] × [tex]\frac{16}{27}[/tex] ← cancel the 27 and 16, 32 by 16
= [tex]\frac{1}{2}[/tex]
To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Answers
Therefore ,the result is. It means that there exist 17 units between the two points supplied as the answer to the given distance problem.
Specify the distance.An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the quickest route a moving object can travel. We frequently take into account the concepts of range and displacement.
Here,
6 and -3 are given (2, -2)
Points (a, b) and (c, d) are now separated by
d= √(c-a)² + ( d- b) ²
d= √(-3+2)² + (2-6)² as a result.
=>d = √ 1 + 16 = √17
The distance between the two places is therefore 17 units.
the result is. It follows there are 17 units between the two points supplied as the answer to the given distance problem.
To know more about distance , visit
brainly.com/question/15172156
#SPJ1
Absolute value equations and inequalities.
Answers
An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.
What are absolute value equations and inequalities?The absolute number of a number a is written as |a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality |x|<2 represents the distance between x and 0 that is less than 2 Whereas the inequality |x|>2 represents the distance between x and 0 that is greater than 2.
You can write an absolute value inequality as a compound inequality.
$$\left | x \right |<2\: or
−2<x<2
This holds true for all absolute value inequalities.
|ax+ b| < c, where c>0
=−c < ax+ b < c
|ax+ b|> c, where c>0
=ax+ b <−corax+ b>c
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
To know more about absolute value equations and inequalities, check out:
https://brainly.com/question/1779337
#SPJ1
An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.
What are absolute value equations and inequalities?The absolute number of a number a is written as |a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality |x|<2 represents the distance between x and 0 that is less than 2 Whereas the inequality |x|>2 represents the distance between x and 0 that is greater than 2.
You can write an absolute value inequality as a compound inequality.
[tex]$$\left | x \right | < 2\[/tex]: or
−2<x<2
This holds true for all absolute value inequalities.
[tex]|ax+ b| < c, where c > 0\\=−c < ax+ b < c\\|ax+ b| > c, where c > 0\\=ax+ b < −corax+ b > c[/tex]
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
To know more about absolute value equations and inequalities, check out:
brainly.com/question/1779337
#SPJ1
HELP PLEASE ANOTHER ONE!
Answers
Answer:
(6.9)
Step-by-step explanation:
Suppose you are given the following rational function: y= 2x-4/x^2-4. What is the corresponding range value when the domain value is {4}?
Answers
Answer:
1/3
Step-by-step explanation:
The value of the range of the given function will be 1 / 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The solution of the given function will be:-
[tex]y =\dfrac{2x-4}{x^2-4}\\\\\\y=\dfrac{2\times 4 -4}{(4^2)-4}\\\\\\y=\dfrac{1}{3}[/tex]
Therefore the value of the range of the given function will be 1 / 3.
To know more about functions follow
https://brainly.com/question/2833285
#SPJ2
5. Which pair of angles represent corresponding angles?
Answers
Translate and solve: -5 times b is no less than 35.
Note: Write your solution in interval notation,
Answers
The solution in interval notation b ∈ (-∞ , -7)
-5 times b is no less than 35.
5b ≥ 35
n order to isolate the variable in this linear inequality, we need to get rid of the coefficient that multiplies it.
-[tex]\frac{5b}{5} = \frac{-35}{5}[/tex]
This can be accomplished if both sides are divided by .
Notice that the inequality sign has changed.
b ≤ -7
We need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
In our example, this is the common factor:5
b ∈ (-∞ , -7)
We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.
To know more about inequalities visit brainly.com/question/28823603
#SPJ4
6. Jenna wants to hang outdoor stringed lights on her house along the roof line
and horizontally across, connecting the ends of the roof line to create a triangle.
What is the approximate length, in feet, of lights that she needs to create one
triangle?
A. 48
B. 64
C. 80
D. 98
Answers
The approximate length, in feet, of lights that she needs to create one triangle is 64
This is an approximate estimate as the exact length would depend on the specific measurements of the roof line. However, if the roof line is a typical house roof and the string lights are hung horizontally across to connect the ends of the roof line, creating a triangle, the approximate length of lights needed would be the hypotenuse of the triangle (the longest side) which is equal to the square root of (leg 1^2 + leg 2^2).
A typical house roof is approximately 40 feet wide and 20 feet tall, which creates a right triangle with legs of 40 and 20. The hypotenuse of this triangle (the length of lights needed) would be approximately 64 feet (the square root of (40^2 + 20^2) = 64).
Learn more about geometry and measuring lengths here: https://brainly.com/question/1578168
#SPJ4
What are the AGI and taxable income? Responses $35,468 and $23,068 $35,468 and $23,068 $47,468 and $35,468 $47,468 and $35,468 $47,868 and $12,400 $47,868 and $12,400 $35,468 and $12,400 $35,468 and $12,400 Gross Income $35,468 Adjustments 0 1 Exemption $12,400 Deduction 0
Answers
The amount of GI is $35,468.
The amount of taxable income is $23,068.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Gross income = $35,468
Exemption = $12,400
Deduction = 0
Adjustment = 0
Taxable income.
= Gross income - Exemption
= 35,468 - 12,400
= $23068
Thus,
GI and taxable income are $35,468 and $23,068
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
answer this question for me.
Answers
The angle measure of m∠CAF = 23°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
The angle measures,
m∠EBG = 23°
m∠CAE = 52°
From the figure,
m∠EBG = m∠FAE = 23°
So, from the figure,
m∠CAE = m∠CAF + m∠FAE
Substituting the angle measures,
52 = m∠CAF + 23
m∠CAF = 52 - 23
m∠CAF = 22°
Therefore, 23° is the angle measure of m∠CAF.
To learn more about the angle measure;
brainly.com/question/14684647
#SPJ1
The drama club members want to buy 862 bags of popcorn to serve during the intermission of their play. If popcorn comes in cases of 24 bags, what is the minimum number of cases that they need?
Answers
Answer:36
Step-by-step explanation:
54 is 72% of what number?
Answers
This problem requires simple division in which we will be dividing 54 by 0.72:
54 / 0.72 = 75
This can be checked through calculation of 72% of 75, which can be started with by dividing 75 by 10 to find 10% of 75:
75 / 10 = 7.5, and we can divide again by 10 to find that 0.75 is 1% of 75.
Now that we have 1%, we multiply it by 72 to find that:
0.75 • 72% = 54
Therefore, 54 is 72% of 75.
Find the value
9 (2) 7
HELPPPP MEEEE I NEED THIS ASAP
Answers
Answer:
15/40 which is 3/8
Plug in the numbers into the variables then complete it which then gives you 3/8 simplified
Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.
Answers
Answer:
The answer is "[tex]cirtical\ points \ (x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]"
Step-by-step explanation:
Given:
[tex]g(x) = (x-e)^3e^{-(x-e)}[/tex]
Find critical points:
[tex]g(x) = (x-e)^3e^{(e-x)}[/tex]
differentiate the value with respect of x:
[tex]\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r} \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3][/tex]
critical points [tex]g'(x)=0[/tex]
[tex]\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3[/tex]
So,
The critical points of [tex](x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]
please help me out will give brainliest
Answers
Answer:
Step-by-step explanation:
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
Answer:
[tex]6(x-10)(x+9)[/tex]
Step-by-step explanation:
First, make A equal one by factoring out the greatest common factor, 6. This makes the new expression [tex]6(x^{2} +x-90)[/tex]. Then, factor the remaining polynomial by finding two numbers that multiply to -90 and add to 1. These two numbers are -10 and 9. So, add each term to x and then multiply to get the final answer, [tex]6(x-10)(x+9)[/tex].
Joy is solving a quadratic equation of the form a2+bx+c=0 where b
and care integers.
She correctly solves the equation to get a = 3 ± √/13
Work out the values of b and c.
(3 marks)
b=
=
Answers
To find the values of b and c, we can use the quadratic formula:
[tex]x = (-b ± \sqrt{ (b^2 - 4ac)}) / 2a[/tex] which will give us the value B = -6 & C = -4
What is a quadratic equation.A quadratic equation is a second-order polynomial equation in one variable using the formula [tex]x = ax2 + bx + c = 0[/tex] and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.
So the equation that she get is [tex]x^{2} -6x-4[/tex]
this means that x=3+√13 or 3-√13
which also equals to x=3+√13 & x-3-√13=0 and
x=3-√13
x-3+√13=0
which if you try to find the quadratic equation for this. you need to do it by this
(x-3+√13)(x-3-√13)
which will get you
To know more about quadratic equation visit:
brainly.com/question/30098550
#SPJ1
Is an absolute value graph increasing or decreasing?
Answers
The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).
Explain the nature of absolute value graph?When x< 0, you can see on the graph that there is a "open circle" at (0, 0).
This is owing to the fact that the points on y = x approach (0, 0) as that of the x-values reach 0, as we have already shown. Instead, the open circle was drawn since x must strictly be smaller than zero on just this stretch.A point at (0, 0) is filled in when x ≥ 0, which essentially "plugs" the hole represented either by open circle. Thus, we obtain:The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).The absolute minimum value of f is 0, and its relative minimum value is the same (0, 0). The relative maximum value of F is zero.Thus, due to the graph's indefinitely high y values, there is likewise no absolute maximum value for f.
To know more about the absolute value graph, here
https://brainly.com/question/14758059
#SPJ4
hey! please help i’ll give brainliest
Answers
Answer: A.
Step-by-step explanation: Think of present tense, past tense, future tense
Answer:
A
Step-by-step explanation:
i need to add 7/4 + 1/4 +5/3+ 1/3+1/2+1/2
Answers
Answer:
5
Step-by-step explanation:
[tex]\frac{7}{4}+\frac{1}{4}+\frac{5}{3}+\frac{1}{3}+\frac{1}{2}+\frac{1}{2}\\\\ =\frac{8}{4}+\frac{6}{3}+\frac{2}{2}\\ \\ =2+2+1\\ \\ =5[/tex]
PLEASE HELP I AM BEGGIN YOU EXTRA POINTS AND BRAINLIEST PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I dont know
Step-by-step explanation:
Answer:
9000 interest
Step-by-step explanation:
that is answer
For automobile safety, the maximum slope that a highway can have is 6%, or 0.06. A surveyor
measures the angle from one edge of the ravine to the other and determines that your bridge
should have a slope of 0.06.
You need to find the length of your bridge if it has a slope of 0.06. This will tell you how much
pavement is needed for the bridge deck
4. Use the definition of slope to calculate the exact rise of the bridge, y (3 points: 2 points for
work, 1 point for the solution)
5. How long is the deck of the bridge? Show how you calculated r. (3 points: 2 points for work, 1
point for the solution)
Answers
Answer:
The change in y-axis with respect to change in x-axis is described as slope.
the slope is 0.06, rewrite it as a fraction
the base of the bridge is 50 and height of the bridge is 3, find the hypotenuse using the Pythagorean theorem to get the length of the bridge.
[tex] Length =\sqrt{3^{2}+50^{2}} =\sqrt{9+2500}} =\sqrt{2509}}
Length of the bridge is 50.08
A billiard ball starts 86\,\text{cm}86cm86, start text, c, m, end text from the corner pocket, as shown. The ball rolls 120\,\text{cm}120cm120, start text, c, m, end text in another direction, hits a rail, and rolls another 100\, \text{cm}100cm100, start text, c, m, end text into the pocket. What is the angle between the paths before and after the ball hits the rail? Do not round during your calculations. Round your final answer to the nearest degree.
Answers
Answer:
45 Degrees
Step-by-step explanation:
Khan Academy
Zendaya has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $269.88.
She buys 4 bicycle reflectors for $10.57 each and a pair of bike gloves for $17.76.
She plans to spend some or all of the money she has left to buy new biking outfits for $65.65 each.
Write and solve an inequality which can be used to determine
x
x, the number of outfits Zendaya can purchase while staying within her budget.
Plsss help!!
Answers
Answer:
269.88 +4(10.57) +17.76 +65.65x ≤ 540x ≤ 3.2; 3 outfits or lessStep-by-step explanation:
After spending $269.88, 4 times $10.57, and $17.76 of her $540 budget, you want to know how many (x) outfits Zendaya can buy at $65.65 each.
InequalityThe total of Zendaya's spending must be no more than her budget amount:
269.88 +4(10.57) +17.76 +65.65x ≤ 540
SolutionSimplifying the inequality gives ...
329.92 +65.65x ≤ 540
65.65x ≤ 210.08 . . . . . . . . . . subtract 329.92
x ≤ 3.2 . . . . . . . . . . . . . divide by 65.65
Zendaya can purchase up to 3 outfits while staying within her budget.
write as complete square root 3√5
Answers
3/6 divided by 5/6 because it’s on my revision list but I can’t work it out
Answers
A type of fish for your aquarium costs $5 each. You can spend no more than $30. How many of these
fish can you buy? Write an inequality to model the problem. Then solve the inequality to find the
number of fish.
Let f be the number of fish you can buy. Which inequality models the problem?
A. F+ 5 ≤ 30
B. 5f ≤ 30
C. 5f ≥ 30
D. F+5 ≥ 30
Answers
Answer:
B.
Step-by-step explanation:
5 * f (The number of fish) has to be less than or equal to $30
FIRST TO ANSWER GETS BRAINLIEST!! Melanie’s bank account balance is . She needs to pay $55 to her cell phone carrier and $80 to the landscaper. She also expects $250 from her sister to be added to her account.
(a) Write an expression Melanie can use to determine her bank account balance after paying these bills and receiving money from her sister.
(b) What is Melanie’s bank account balance after paying her bills and receiving money? Show any necessary work. Answer in a complete sentence.
Answers
Answer:
a 97- (55+80) +250
b Melanie has $212 left in her bank account.
Step-by-step explanation:
55 + 80 = 135
97 - 135 = -38
-38 +250 = 212
Input the correct values into the point-slope
formula.
y - [?] = [](x - [ ])
A. 3
A line is parallel to y = 3x - 2 and
intersects the point (3, 5).
C. -2
B. 5
D. 1/3
Answers
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 2 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes
then slope of parallel line is 3
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 3 and (a, b ) = (3, 5 ) , then
y - 5 = 3(x - 3) ← equation of parallel line in point- slope form