m = [tex]\frac{4}{25}[/tex] 0r m = [tex]-\frac{16}{15}[/tex]
|2m+3/5|=|1-3m/6|
Split into two equations
⇒[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex] or
⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]
[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex]
multiply both side of the equation by the common denominator
⇒2m × 30 + [tex]\frac{3 * 30}{5}[/tex] = 30 - [tex]\frac{3 m * 30}{6}[/tex]
⇒2m×30 + 18 = 30 -15m
⇒60 m + 18 = 30 -15m
⇒60m + 15m = 30 - 18
⇒75m = 12
⇒m = [tex]\frac{12}{75}[/tex]
⇒m = [tex]\frac{4}{25}[/tex]
[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]
reduce the fraction
⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{m}{2})[/tex]
remove brackets
⇒[tex]2m + \frac{3}{5} = - 1 + \frac{m}{2}[/tex]
multiply both side of the equation by the common denominator
⇒2m × 10 + [tex]\frac{3 * 10}{5}[/tex] = -10 + [tex]\frac{ m * 10}{2}[/tex]
⇒2m × 10 + 6 = -10 + 5m
⇒20 m + 6 = - 10 + 5m
⇒20m - 5m = - 10 -6
⇒15m = -16
⇒m = [tex]-\frac{16}{15}[/tex]
we get,
m = [tex]\frac{4}{25}[/tex] 0r m = [tex]-\frac{16}{15}[/tex]
Equations with fractions involve solving equations where the unknown variable is part of the numerator and/or the denominator of the fraction.
To solve equations with fractions we need to work out what the value of the unknown variable. We solve equations by using the “balancing method” by applying the inverse operation to both sides of the equation.
The inverse operation of addition is subtraction.
The inverse operation of subtraction is addition.
The inverse operation of multiplication is division.
The inverse operation of division is multiplication.
How to solve equations with fractions
In order to solve equations with fraction:
Identify the operations that are being applied to the unknown variable.
Apply the inverse operations, one at a time, to both sides of the equation.
Write the final answer, checking that it is correct.
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Which of the following equations have an infinite solution set?
The equation has infinite solutions is the last option:
6(x - 1) = 2*(3x - 3)
Which equation has an infinite solution set?Any equation in which we can remove the variable has infinite solutions (because it does not depend on the value of x) only if the equation is true.
Let's look at the fourth equation:
6(x - 1) = 2*(3x - 3)
If we expand both sides, we will get:
6x - 6 = 2*3x - 2*3
6x - 6 = 6x - 6
So we have the exact same thing in both sides, if we remove 6x - 6 in both sides we will get:
0 = 0
Then this equation has infinite solutions.
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Solve the equation
sec x=√2 in the interval 0≤x≤2π
[tex]\displaystyle\\Answer:\ x=\frac{\pi }{4} \ \ \ \ \ x=\frac{7\pi }{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\secx=\sqrt{2} \ \ \ \ 0\leq x\leq 2\pi \\\\\frac{1}{cosx} =\sqrt{2} \\\\cosx=\frac{1}{\sqrt{2} } \\\\cosx=\frac{(1)(\sqrt{2)} }{(\sqrt{2})(\sqrt{2)} } \\\\cosx=\frac{\sqrt{2} }{2} \\\\x=\frac{\pi }{4} \\\\x=\frac{7\pi }{4}[/tex]
The product of two positive integers is always
Answer: positive
Step-by-step explanation: That's just how it works. It's an algerbra rule. Hope that helped. Have a nice day.
Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.
find the product of two numbers whose sum is 11 and diffrence is 3
Answer:
The numbers are 4 and 7
Step-by-step explanation:
To start, we can set up two equations.
x + y = 11 and x - y = 3
We now need to solve for one of these variables in terms of the other. I am choosing to solve for x, but either way will work. I'm using the second equation and solving for x by adding y to each side, which gives me
x = 3 + y
Now that I have a value for x, I can plug this into my first equation
3 + y + y = 11
Combining like terms gives me
3 + 2y = 11
Subtracting 3 from both sides leaves
2y = 8
And dividing by 2 to solve for y gets
y = 4
We now know one number, and to solve for the other we can plug our y value into either equation
x + 4 = 11
Subtracting 4 from both sides yields the x value
x = 7
So the two numbers are 4 and 7
10. The mass of planet Earth is about
5.98 x 1024 kilograms. How many significant
digits does this number contain?
The scientific notation has 3 significant digits.
What is a scenic notation?A significant number is the the numbers that are in in the coefficient of an expression in scientific notation, 5, 9 and 8 are the significant numbers.
Scientific notation is used in expressing large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, the number : 1 x 10² is equivalent to 100
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if 4n=3.60 what is the value of n
Answer:
0.9
Step-by-step explanation:
4n = 3.60
n = 3.60 / 4
n = 0.9
Answer: n = 0.9
Step-by-step explanation:
1. isolate the variable by dividing 4 from both sides
2. 3.60/4 = 0.9
a sporting event coordinator has 200 mini foam fingers. She gives 2 foam fingers to each student in attendance. there are 26 left. how many students are in attendance
PLEASE HELP!!!!
Translation using the rule
(x. y)-(x-5. y).
Answer:
P= (-12,0)
Q= (0,-8)
R= (-2,-16)
P'= (-17,0)
Q'= (-5,-8)
R'= (-7,-16)
Step-by-step explanation:
Assuming that each square is equal to one point, the shape is in quadrant 3, where all coordinates are negative.
Determine where each coordinate is for P, Q, and R; then move over each x coordinate by -5 (a.k.a. subtract 5).
This will give you your translation to P', Q', and R'.
Please let me know if I made any mistakes, and hope this helped!
What does |-5| + |7| equal?
Answer:
12
Step-by-step explanation:
absolute value basically makes numbers positive
Write each expression in simplest form. (-27x⁻⁹)¹/₃
The given expression can be written in its simplest form by using the rule of exponents.
There are three components to the given expression, there is a negative base term -27, there is a base term with negative exponent x^-9, and both base terms have a fractional exponent 1/3.
Solving the term with negative exponent, the rule dictates that a term with a negative exponent can be written as its reciprocal. As x^-n=1/x^n,
x^-9=1/x^9
Hence, the expression becomes (-27/x^9)^1/3
The fractional exponent is applied to both the base terms. As (x^n)^m=x^nm,
(-27/x^9)^¹/₃=(-27)^1/3/(x^9*1/3)
Solving the negative term, the rule dictates that when there is a negative term with an odd number power, the negative sign can be extracted from the expression.
Hence,
(-27)^1/3=-(27^1/3)
Further simplifying the term, we know that 3^3=27,
-(27^1/3)=-(3^3*1/3)
Multiplying the powers for the entire expression,
-(3^3*1/3)/(x^9*1/3)=-3^1/x^3=-3/x^3
The simplest form of the expression (-27x^-9)^¹/₃ is -3/x^3
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Students in Mr. Kendrick's class are divided into two groups for an activity. Students in group A must always tell the truth. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if he and Janeka are in group A or B, Jonah says, "We are both in Group B. " To which group does each student belong? Explain your reasoning
In the class of Mr. Kendrick's, Jonah is in Group B and Janeka is in Group A using the concept of Logical Reasoning.
As per the question statement, we are given that in Mr. Kendrick's class, students are divided into two groups for an activity. Students in group A must always tell the truth and correct info. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if Jonah and Janeka are in group A or B, Jonah says, "We are both in Group B. "
By their statement and using the concept of Logical Reasoning, we can conclude that Jonah is in Group B and Janeka is in Group A.
As Jonah said, "We are both in Group B. " and as both the students can't be in same group so Jonah lied and hence he is in group B and Janeka is in group A.
This is a classic example of Logical Reasoning.
Logical Reasoning: Working through a set of rules that govern a scenario is a method of problem-solving known as logical reasoning.
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do these ratios form a proportion? 5:10 11:14
Answer: no
Step-by-step explanation:
A = 7, B = 13 and C = 6 then D = 11.1428571429. 3. A = 28, B = 34 and D =15 then C= 12.3529411765. 4. A = 13, B = 15, C = 2 and D = 33 then 13: 15
Write the following inequality in slope-intercept form. 4x+y≤ – 15
The following inequality in slope-intercept form.
y≤-4x-15
Slope intercept form is y=mx+ c
m= slope c= y interceptSo, inequality 4x+y≤ – 15 is written as y≤-4x-15with , m= slope =-4c= y intercept= -15what is a coordinate in geometry?
Coordinates are two numbers (Cartesian coordinates), or every so often a letter and a range of, that discover a particular point on a grid, called a coordinate aircraft. A coordinate aircraft has 4 quadrants and two axes: the x axis (horizontal) and y axis (vertical).
what is coordinate geometry instance?
In coordinate geometry, lines are parallel if their slopes (m) are equal. for instance: the line y = ½ x - 1 is parallel to the line y = ½ x + 1 due to the fact their slopes are both the identical.
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İfadesinin en sade şekli aşağıdakilerden hangisidir?
Answer:
A
Step-by-step explanation:
1. Given the similar polygons, use proportion to find the value of each variable.
Triangles JKL~NML
JK=40. NM=16
KL=X. ML=14
LJ=45. LN= Y
The similar polygons, use proportion to find the value of each variable.
x= 40, y = 18
[tex]\frac{JK}{NM}[/tex] = [tex]\frac{KL}{ML}[/tex] = [tex]\frac{LJ}{LN}[/tex]
[tex]\frac{40}{16}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{45}{y}[/tex]
40*16 = 16*x
x= 40
40*y = 45*16
y = 18
In geometry, a polygon may be a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the 2 together, could also be called a polygon.The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices (singular: vertex) or corners. the inside of a solid polygon is sometimes called its body. An n-gon may be a polygon with n sides; for example, a triangle may be a 3-gon.
A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of straightforward polygons and they often define a polygon accordingly. A polygonal boundary could also be allowed to cross over itself, creating star polygons and other self-intersecting polygons.
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Yuson must complete a certain number of hours of community service. she does 2 hours of service each day. after 8 days, yuson has completed half of her required community service.
Answer:
i don't know what the question is but the total amount of comunity service she must do is 32 hours
Step-by-step explanation:
2 x 8 = 16 16 x 2 or 16 + 16 = 32 thus she must complete 32 hours of comunity service and she has already completed 16 hours of comunity service so she has 16 hours left to complete.
hope this helped = )
Can real numbers be instantly rational number
Answer:
A real number is a number that can take any value on the number line. They can be any of the rational and irrational numbers. Rational number is a number that can be expressed in the form of a fraction but with a non-zero denominator.
PLEASE HELP ME! Find the percent of change when 40 is increased to 83. If necessary, round your answer to the nearest tenth.
51.8% increase
51.8% decrease
107.5% increase
107.5% decrease
The percent of change when 40 is increased to 83 to the nearest tenth is: C. 107.5% increase.
The types of percentage.In Mathematics, there are two main types of percentage and these include the following:
Percentage decreasePercentage increaseMathematically, percentage increase can be calculated by using this formula:
Percentage increase = [Final value - Initial value]/Initial value × 100
Substituting the given parameters into the formula, we have;
Percentage increase = [83 - 40]/40 × 100
Percentage increase = 43/40 × 100
Percentage increase = 1.075 × 100
Percentage increase = 107.5%.
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which is the most accurate way to estimate 32% of 64
Answer:
32% of 200 is 64.
Step-by-step explanation:
A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable? ( W is the weight of the mobiles).
The inequality that gat can be used to show the mobiles that are tolerable is w - 8 <= 0.3.
How to illustrate the information?It should be noted that from the information, the
mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces.
Therefore, the mobiles are tolerable with an inequality will be:
w - 8 <= 0.3.
where w = weight of the mobiles.
In conclusion, the mobiles are tolerable with an inequality will be w - 8 <= 0.3.
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A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable with an inequality. ( W is the weight of the mobiles).
Deepa needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4.25 hours and charged her $167
for parts. The total was $655.75. Write and solve an equation which can be used to
determine 2, the cost of the labor per hour.
Answer:115
Step-by-step explanation:
(4.25x) + 167= 117.35
⚡️PLEASE HELP-URGENT⚡️
I only need help with 34.. but I. So confused and I need to go to bed
-12
----- = -4 that's the key to the operation so -4x 3
3
I dont know how to do his please help!
Without knowing what the dropdown list shows for reasons, it's hard to pinpoint exactly what is expected here.
Angle ACD is congruent to angle BCD because they are corresponding angles between the congruent triangles ∆ACD and ∆BCD.
The triangle congruency is due to angle-angle-side (AAS) similarity:
• angles A and B are congruent - this is given
• angles CDB and CDA are congruent right angles - this is implied by the given detail that CD and AB are perpendicular
• the leg CD is common to both triangles, and CD is of course congruent to itself (reflexive property)
So angles ACD and BCD are congruent, which means they have the same measure, so by definition of angle bisector, CD bisects angle ACB.
QED
35 x dash x 37 = 10,360 what can be said about the number in the box
Answer:
The missing number is 8
Step-by-step explanation:
[tex]10,360 \div 37 \div 35 = 8[/tex]
Find the 96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
arithmetic sequence 1, -12, -25, .. .1,−12,−25
an arithmetic sequence can be written as
a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d
nth tern of an arithmetic sequence is
aₙ= a+ (n-1)d
a= first term of an arithmetic sequence
d = common difference of an arithmetic sequence
n = number of terms in an arithmetic sequence
So in the above arithmetic sequence
a= 1
d= -13
n= 96
a₉₆= 1+ (96-1)(-13)
= 1- (95)13
= 1- 1235
= -1234
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
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Bill and Ted plan to buy a ps4 for $299.00. Games for the system cost $60 each. They plan to buy one console to share. If bill and Ted buy 1 console and 3 games, how much will they spend total?
Answer:
$459
Step-by-step explanation:
60x3=180
$299+180=$459
6 in.
4 in.
6 in. Math
It is an isosceles triangle.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
There are mainly three types of triangles:
Equilateral triangle
A triangle with three equal-length sides is said to be equilateral, matching what might also be referred as as a "regular" triangle. Because all three sides of an isosceles triangle are equal, an equilateral triangle is a particular case of an isosceles triangle. There are three equal sides to an equilateral triangle.
Isosceles triangle
A triangle with two equal sides is said to be isosceles.
Scalene triangle
A scalene triangle is a triangle wherein all 3 facets have distinct lengths. Also the angles of a scalene triangle have distinct measures. Some proper triangles may be a scalene triangle while the alternative angles or the legs aren't congruent.
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Simplify the expression.
-1- 2/3(6/7-3/7n)
[Mathematical Situation]
Simplify the expression.
[tex]-1-\frac{2}{3} (\frac{6}{7}-\frac{3}{7}n)[/tex]
Solution:
[tex]-\frac{11}{7}+\frac{2n}{7}[/tex]
Hope this helps!
The simplified expression is -1 - 4/7 + (2/7)n.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
-1 - 2/3 (6/7 - (3/7)n)
Distributive operation.
= -1 - 2/3 x 6/7 + 2/3 x (3/7)n
= -1 - 4/7 + (2/7)n
Thus,
The simplified expression is -1 - 4/7 + (2/7)n.
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ction T...
Show instructions
Question 4 (25 points)
Charley wants to start taking golf lessons. There is a one-time fee of $45 to sign up, then it costs $80 per month. a) Write an equation to model
this problem. b) What will be the total cost after 7 months?
a
d
C = 45m +80; The total cost will be $395 after 7 months.
C = 80m + 45; The total cost will be $605 after 7 months.
C = 45m +80; The total cost will be $125 after 7 months.
C = 80m + 45; The total cost will be $125 after 7 months.
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Question 4 of 20 | Page 4 of 20
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Find the value of y if M is the midpoint of LN. LM=9y-4 MN=6y+5 LN?
The value of y for which M is the mid-point of LN is equal to 3 and the numerical length of LN is 46 units.
What is Mid - point of a line?The mid - point of a line is the point which divides it into two equal parts of same length.
Given in the question is a line segment LN such that M is its mid - point. From the question, we can write -
LM = 9y - 4
MN = 6y + 5
According to the question, M is the midpoint of LN, therefore -
LM = MN
9y - 4 = 6y + 5
9y - 6y = 9
3y = 9
y = 3
So, the length of LN will be -
LN = LN + MN = 9 x 3 - 4 + 6 x 3 + 5 = 23 + 23 = 46 units
Therefore, the value of y is equal to 3 and the numerical length of LN is 46 units.
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