The inequality 4/3|1/4x+3|<4 are Ox>-13 and x < -11 or Ox<-24 and x > 0
How do we determine the absolute values?We can begin by isolating the absolute value on one side of the inequality:
4/3|1/4x+3|<4
|1/4x+3|<3/2
We can then split this inequality into two cases, one for when 1/4x+3 is positive and one for when it is negative:
1/4x+3>0: 1/4x+3>3/2, so multiplying both sides by 4, we get x>-13 and x<-11
1/4x+3<0: 1/4x+3<-3/2, so multiplying both sides by -4, we get x<-24 and x>0
So, the solution is: Ox>-13 and x < -11 or Ox<-24 and x > 0
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ELECTRIC CAR For every hour x that Eva’s electric car charges, she can drive the car 7.5 miles. Eva needs to drive at least 60 miles tomorrow.
Part A
What inequality represents the situation in terms of x hours?
Multiple choice question.
A)
60x≥7.5
B)
7.5x≤60
C)
7.5x≥60
D)
60x≤7.5
The inequality that represents the situation in terms of x hours is; B: 7.5x ≤ 60
How to solve Inequality Word Problems?We are told that for every hour x that Eva’s electric car charges, she can drive the car 7.5 miles. Eva needs to drive at least 60 miles tomorrow.
Now, 7.5 miles represents the speed per hour and we know that formula for distance is;
distance = speed * time
Since she wants to drive at least 60 miles tomorrow, then it means the number of miles must be greater than or equal to 60. Thus, the inequality that models the given situation is;
7.5x ≤ 60
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The range of temperatures on a particular day could be described as |x-68|<=9. How many integer values are included in this range?
(1) There are 2b+1 integer solutions to the equation x-a=b. (2) and (2) There are 2b-1 integer solutions to the equation x-a = b.
what is integers ?Integers include 0 as well as positive and negative numbers that are indicated by minus signs. An equivalent positive number's additive reciprocal is a negative number. In mathematical notation, a group of integers is typically denoted by a bold Z or a bold "mathbb Z." An integer is a number that can be positive, negative, or zero and is not a fraction (pronounced IN-tuh-jer). An example of an integer is the number -5, 1, 5, 8, 97, and 3,043 Non-integer examples are 1.43, 1. 3/4, 3.14, and other numbers. A group of integers and their antipodes are known as integers. The set of integers excludes decimals and fractions.
given
This type of absolute value difficulty can be resolved by interpreting the expression x-a = b as indicating that the difference between x and an is at most b. Therefore, x is only 9 away from 68 if x-68 = 9. 68-9 = 59; 68+9 = 77. (77-59)+1 = 19 is the total number of integers from 59 to 77, inclusive.
A) Using the same meaning, x must be closer to -4 by no more than 8 than usual. -4-8 = -12; -4+8 = 4. The integer solutions range from -11 to 3 inclusive, or 15 numbers, because this is a rigorous inequality.
B) This one indicates that x is only three values away from five, ranging from three to seven.
(1) There are 2b+1 integer solutions to the equation x-a=b. (2) and (2) There are 2b-1 integer solutions to the equation x-a = b.
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4 (x + 3) = 3x + 2 + x
Answer:
No Solution
Step-by-step explanation:
4(x+3)=3x+2+x
4x+12=3x+2+x
4x+12=4x+2
0=-10
The equation has no solutions.
Hope this helped! :)
If 59 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?.
When 5/9 of the tank is filled in 2 minutes, then it will take 3.6 minutes to fill the entire tank.
The definition of a fraction is a fraction multiplied by another fraction, integer, or a group of variables. Given that the 5/9 tank fills in 2 minutes. The duration of this period in seconds is 60×5= 120 seconds.
So the time taken to fill a 1/9 tank is calculated as follows,
Time taken = 120/5
=24 seconds
The time taken to fill the 9/9 tank (full) is calculated by multiplying 24 seconds and 9, we get,
24×9 = 216 seconds
= 3.6 minutes.
Therefore, the required answer is 3.6 minutes.
The complete question is -
If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?
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Why is the formula for the area of a triangle 1 2BH?
The formula for the area of a triangle is 1/2bh. This formula can be derived from the area of a parallelogram.
A parallelogram is a four-sided shape with two pairs of parallel sides. To find the area of a parallelogram, you need to multiply the base, b, by the height, h. This will give you the area of the parallelogram, which is bh. To find the area of a triangle, you need to divide the area of a parallelogram by two since a triangle has only one set of parallel sides. Therefore, the formula for the area of a triangle is 1/2bh. To calculate the area of a triangle, you need to multiply the base by the height and then divide the result by two. For example, if the base of a triangle is 8 cm and the height is 4 cm, the area of the triangle is 1/2 × 8 × 4 = 16 cm2.
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Given the sequence 2 and one half comma 2 and one third comma 2 and one fourth comma and continues comma what is f (n)?.
From the sequence 2 [tex]\frac{1}{2}[/tex], 2 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{4}[/tex], ..., f(n) can be expressed as 2 + [tex]\frac{1}{(n+1)}[/tex] where n is the term number in the sequence. Hence, the correct answer is A.
Each term in the sequence is 2 plus a fraction where the denominator is one more than the term number. For example:
In the first term, n=1 and the fraction is [tex]\frac{1}{2}[/tex] In the second term, n=2 and the fraction is [tex]\frac{1}{3}[/tex]In general, the n-th term in the sequence will have the fraction [tex]\frac{1}{(n+1)}[/tex].
Therefore, the function f(n) that generates this sequence is 2 + [tex]\frac{1}{(n+1)}[/tex]. This function takes an input of n and outputs the corresponding term in the sequence.
This question should be written as:
Given the sequence 2 [tex]\frac{1}{2}[/tex], 2 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{4}[/tex], ...., what is f (n)?
A. 2 + [tex]\frac{1}{(n+1)}[/tex]B. 2 + [tex]\frac{1}{n}[/tex]C. n + [tex]\frac{1}{(n+1)}[/tex]D. 3 - [tex]\frac{1}{n}[/tex]The correct answer is A.
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Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs S2, and a piece of fudge costs $3. This system of inequalities models the scenario: 2x + 3y = 15 x+y²3 Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points) PLEASE PLEASE HELP ME I REALLY NEED THIS DONE RIGHT ILL GIVE BRAINLEST
The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.
what is inequality ?A interaction between two expressions like values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a link among two values that do not equal. Egality and inequality are different. The not equal symbol is typically used to indicate that two values are also not equal (). Different inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. Negative values are split or added on either side. Switch between the left and right.
given
Michael wants to spend his $15 on enough cupcakes and fudge to feed at least three siblings.
A cupcake costs $2 but a slice of fudge costs $3.
With this inequality approach, the following scenario is simulated:
2x + 3y ≤ 15
x + y ≥ 3
The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.
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What is the standard form for six cubed?
Answer: 2.16 x 10^2
Step-by-step explanation:
6^3 = 216
2.16 x 10^2
Tell whether the ratios form a proportion 56/20 24/10
Answer:
no it is not proportion
Step-by-step explanation:
you would have to divied 56/20 which will be 56/2 that is 28
and then 20/2 which is 10 so then it will be
28/10 and 24/10
London went shopping for a new video game because of a sale. The store was offering a 20% discount. If the price on the tag was $50, what would be the price after the discount but before tax, to the nearest dollar and cent?
I need help
Before tax, a new video game costs $10.00 in the store London visited
How to calculate a new video game's costThe calculations will be involving 100 because the question is a percentage problem and percent is a fraction of a hundred.
A 20% discount was being offered in the shop London visited. This is equal to 20%, and expressed as
= 20/100
= 0.20.
Discount factor: (1 - 0.2) = 0.8
The price of the video game will be multiplied by the discount factor to determine a new price.
The new video game's selling price before taxes is $50 * 0.2, which equals $10.
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At a hockey game, a vendor sold a combine of 125 sodas and hotdogs. The number of Sotos sold was 37 more than a number of hotdogs sold. find the number of sodas sold and the number of hotdogs sold.
So on solving the provided question, we can say that by equation, 122 sodas and 80 hot dogs
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
let x be of sodas sold
and let x - 42 be of hot dogs sold
so, the equation formed is
[tex]x+x-42=202\\2x = 244\\x=122\\[/tex]
122 sodas and 80 hot dogs
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Can you construct a triangle with sides 17 cm 7 cm 8 cm?
Answer:
In order to form a triangle, the sum of the length of two sides should be greater than the length of the third side. This is called the triangle inequality theorem.
Given the side lengths of 17 cm, 7 cm, and 8 cm, we can see that 17 cm is the longest side. To form a triangle, the sum of the other two sides (7 cm and 8 cm) should be greater than 17 cm.
7 cm + 8 cm = 15 cm which is less than 17 cm. Therefore, it is not possible to construct a triangle with sides 17 cm, 7 cm, and 8 cm.
Step-by-step explanation:
Answer:
No u cannot
Step-by-step explanation:
7+8 = 15 which is less than 17 meaning u cannot create a triangle with this
What is meant by value Mcq?
The combination of quality, efficiency, price, and service that guarantees the ultimate economy and satisfaction of the customer is referred to as value.
What's the MCQ's response?
A multiple choice (MC), objective response, or MCQ (multiple choice question) is a type of objective assessment in which participants are required to choose only the right responses from a list of options.
What does "value analysis" mean?
Value analysis (VA), often referred to as Value Engineering (VE) and Value Management (VM), is a methodical and function-based approach to enhancing the value of initiatives, projects, or processes. Alternative methods of achieving goals are found using a combination of analytical and creative strategies known as value analysis.
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A certain car averages 15 kilometers per liter of gasoline. How many meters can the car travel on one mililiter of gasoline
Answer: 250
Step-by-step explanation: :)
Answer: 250
Based on the given conditions, formulate:: 15 x 100 over 60
Simplify fraction(s): 5 x 50
Calculate the product or quotient: 250
Which is true about the solution to the system of inequalities shown?
ys-x-1
y≤-x-3
All values that satisfy y ≤
All values that satisfy y ≤
x − 1 are solutions.
x-3 are solutions.
-5-4-3-2-1.
77
The statement true about the system of inequalities solution is option A, all the values of satisfy y ≤ 1/3x -1.
What is system of inequalities?One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality's solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.
Given the graph of the system of inequalities we can see that the inequality y ≤ 1/3x -1, comprises of all the values under the blue shaded region. This region also includes the graph of the second inequality.
Hence, option A is correct as all the values of satisfy y ≤ 1/3x -1.
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What is the equation of the line that passes through (0, 3) and is perpendicular to y = 34x + 5?.
The equation of a line that is perpendicular to the line y = 34x + 5 and passes through the point (0, 3) is y = -34x + 3
The slope-intercept form of the equation of a line is y = mx + c, where
m is the slope of the line c is the y-intercept.The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. In this case, the original line has a slope of 34, so the slope of the line that is perpendicular to it is -1/34.
To find the y-intercept of the line, we can use the point (0,3) that the line passes through. Substituting the x and y values of this point into the equation of the line, we get 3 = -34(0) + c, which simplifies to c = 3.
So the equation of the line that is perpendicular to y = 34x + 5 and passes through (0, 3) is y = -1/34x + 3
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helppppppppppppp asappppppppppppp plssssssssss will give brainly
Solve for x. Round to the nearest tenth, if necessary.
The length of the hypotenuse of the right-angle triangle ΔCDE will be 9 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The triangle ΔCDE is a right-angle triangle. The angle ∠D is a right-angle triangle.
The length of the hypotenuse is given as,
sin 50° = 6.9 / x
0.766 = 6.9 / x
x = 6.9 / 0.766
x = 9.0073 ≈ 9 units
The length of the hypotenuse of the right-angle triangle ΔCDE will be 9 units.
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Find the value of tan D rounded to the nearest hundredth, if necessary.
The value of the angle tan(D) will be 53.13°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the sides of the triangle are BC = 32 and CD = 24.
The value of tan(D) is calculated as,
tan(D) = 32 / 24
D = tan⁻¹ (32 / 24 )
D = 53.13°
The value of angle D will be 53.13°.
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ASAP Please and thank you
Answer:
Obtuse
Step-by-step explanation:
The angle measures add to [tex]180^{\circ}[/tex], so a triangle can be formed.
Since one of the angles has a measure greater than [tex]90^{\circ}[/tex] but less than [tex]180^{\circ}[/tex], the triangle is obtuse.
What quadrant is ordered pair 4 3?
An ordered pair (x,y) represents a point on a coordinate plane, where x is the horizontal position and y is the vertical position. The quadrant in which this point lies can be determined by the signs of the x and y coordinates.
The quadrant that contains the point (4,3) is Quadrant 1. This is because both the x-coordinate (4) and y-coordinate (3) are positive, indicating that the point lies in the top-right region of the coordinate plane.
Brittany and Brooke were dress shopping for the school dance. Brittany tried on 6 dresses in 16 minutes. If Brooke tried on dresses at the same rate, how many dresses did she try on in 48 minutes?
Answer: 18
Step-by-step explanation: For every 16 minutes in those 48 minutes, she tried on 6 dresses. 16 goes into 48 three times. That means there are three pairs of 16 minutes. 3 (pairs of 16 minutes) x 6 (the number of dresses each time) is 18.
if f(x)=x^3+13x^2+44x+32 and f(-1)=0, then find all of the zeros of f(x) algebraically
just do the inverse boi
ok is the probability of the curriculum of an
Show your work
x+2y=-4
-4x-3y=16
x+2y=-4
-4x-3y=16
---------------------------------------------
stepbystep
−2y=4−x - 2 y = 4 - x by −2 - 2 .
How do you prove the change of base formula?
The change of base formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.
The change of base formula is a mathematical formula that allows you to convert a logarithm with one base to a logarithm with another base. The formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.
One way to prove this is to use the properties of logarithms:
log_b(x × y) = log_b(x) + log_b(y)log_b(xⁿ) = n × log_b(x)Using these properties, we can write log_b(x) as:
log_b(x) = log_b([tex]c^{(log_c(x))}[/tex])
log_b(x) = log_b([tex]c^{(log_c(x))}[/tex]) / log_b(c¹)
log_b(x) = log_c(x) / log_c(b)
Therefore, the change of base formula is proven.
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Help me solve this pls because i need to solve this fast help me
Answer:
See below
Step-by-step explanation:
When they are equivalent.....they are equal...so...set them equal
4x+5+x+9=9x+10 solve for x ....first simplify
5x + 14 = 9x+10 subtract 5x and 10 from both sides of the equation
4 = 4x
x = 1
Are infinite solutions zero?
There are an endless number of solutions to a system of m n linear homogeneous equations with m n fewer equations than unknowns. As a result, such a system always has both the zero solution and the nonzero solution.
What is infinite solution?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".
What is an infinite number?
There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.
The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.
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i accidentally clicked D but help pls
The equation for the parabola given is y=(x-2)^2+1.
What is parabola?
A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:
y^2 = 4ax
If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,
x^2 = 4ay
Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.
Now, To find the correct equation from the graph
we can check the equation by putting values
when x then y
2 1
3 2
4 5
As only equation in option C follows given values
Hence,
The equation for the parabola given is y=(x-2)^2+1
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How do you find the range of a function in class 11 maths?
The range of a function is the set of all the y-values that you get when you plug all of the possible x-values into the function. It is also called a co-domain of function.
To find the range of function write down the function as y=f(x). Find all the minimum to a maximum value of y that satisfies f(x). The values obtained are the range of function. Plot the range on the graph.
For example, if you want to find the range of f(x) = 3x^2 + 6x -2. The lowest y-coordinate is at the vertex, -5, and the values for set y expand infinitely above this point. This means that the range of the function is y={-5, R}
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Which of the following is not a way to determine whether a relation is a function?
That which is not a way to determine whether a relation is a function is this:
D. Determine if the relations’ graph forms a line.
How can one determine whether a relation is a function?One notable way of determining if a relation is a function is whether an input results in a single output. A function is easily identified by the ability to generate a single output when a single input is inserted.
While the input value is the domain, the output translates to the range. Checking whether the relation's graph forms a line is not a viable way of determining whether a relation is a function.
Options:
A.
Use the vertical line test on a graph of the relation.
B.
Check to see if each input maps to only one output.
C.
There should be no duplicated x-coordinates in the ordered pair set.
D.
Determine if the relations’ graph forms a line.
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