Answers
The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Find inequality ?Both equations and inequalities are mathematical phrases created by connecting two expressions.
The equal sign (=) in an equation denotes that the two expressions are regarded as equal.
In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
Given the inequality:
-3(4 – x) 6 < 9 – 2x
Solving the inequality:
(-12 + 3x)6 < 9 - 2x
-72 + 18x < 9 - 2x
20x < 81
x < 4.05
Therefore the solution to the inequality is (-∞, 4.05)
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Related Questions
A new car loan has a term of loan from 2 - 6 years and the interest rate is between 4% and 8%. what is the longest amount of time you could take to pay off the loan? what is the best interest rate you could get?
Answers
a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.
b) Based on the above, the best interest rate the borrower could get is 8%.
How is the interest rate determined?Many factors are considered in determining the interest rate for a loan.
Some of the factors include:
Loan TermLoan TypeCredit ScoreLoan AmountDown PaymentInterest rate type.We know that the longer the term of a loan, the higher the interest rate charged. This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.
Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.
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Solve the system of linear equations by graphing. Y=-3 and 6x +y=3
Answers
Where the two lines cross
Step by step
The two equations were graphed, see attached. The point where the two lines cross is the solution, ( 1, -3)
Please help me solve
Answers
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]
[tex](-6x^3 y^5 + 11x^3 y^2) \div (-2x^2 y^3)\implies \cfrac{-6x^3 y^5 + 11x^3 y^2}{-2x^2 y^3} \\\\\\ \cfrac{-6x^3 y^5}{-2x^2 y^3}+\cfrac{11x^3 y^2}{-2x^2 y^3}\implies \cfrac{-6}{-2}\cdot \cfrac{x^3 y^5}{x^2 y^3}+\cfrac{11}{-2}\cdot \cfrac{x^3 y^2}{x^2 y^3} \\\\\\ 3\cdot x^3 x^{-2}y^5 y^{-3}+\cfrac{11}{-2}\cdot \cfrac{x^3 x^{-2}}{y^3 y^{-2}}\implies 3x^{3-2}y^{5-3}-\cfrac{11}{2}\cdot \cfrac{x^{3-2}}{y^{3-2}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x y^2 -\cfrac{11x}{2y} \end{array}}~\hfill[/tex]
Rewrite the function f(x)=-4(x-4)^2+26 in the form f(x)=ax^2+bx+c
Answers
Step 1.
(x-4) ^2 = x^2 - 8x+ 16
Step 2.
(-4) x^2 - 8x+ 16
-4(x^2-8x+16) = -4x^2 + 32x - 64
Step 3.
-4x^2 + 32x - 64 + 26 = -4x^2 + 32x - 38
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Answers
Answer:
both are right
Step-by-step explanation:
2/5x = 14
multiply both sides by 5/2:
(5/2)(2/5)x = 14(5/2)
x = 70/2 = 35
However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
i dont understand this help
Answers
laucs ori nisiquiera estoy en universidad estoy en eseyo pe
Given A(0, a) and B(b, 0) , find coordinates of C so that the orthocenter of triangle ABC lies on the triangle.
Answers
The coordinate of the point C is (0, a)
How to determine the coordinates of point CFrom the question, we have the following parameters that can be used in our computation:
A = (0, a)
B = (b, 0)
As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.
This means that we start by calculating the equation of the altitude from B to line AC.
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the above as a guide, we have the following:
slope = (y₂ - y₁)/(x₂ - x₁)
This gives
m(BC) = (0 - 0)/(b - 0) = 0
y-intercept (c) = a
So the equation of the line BC is
y = 0 * x + a
y = a
For line AC, we have
m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.
This means that the equation of the line AC is
x = 0
The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)
At this stage, we have the coordinates of the points from lines AC and BC to be
(0, a) and (0, a)
Next, we calculate the C as follows
C = Midpoints of (0, a) and (0, a)
This gives
C = 1/2 * (0 + 0, a + a)
Evaluate
C = (0, a)
Hence, the coordinate of C is (0, a)
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answers
The equations that are true for x = –2 and x = 2 are:
x^2-4=0 and 4x^2 = 16
How can the equation be known?We can determine the equations that are true for x = –2 and x = 2 by testing the given options:
After testing the options option 1 ; x^2-4=0 putting x = 2 or -2 into the equation will give zero.
(2^)2-4=0
(-2)^2-4=0
Then option 4: 4x^2 = 16
4(2)^2 = 16
4(-2)^2 = 16
Therefore, option 1st and 4th are correct.
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coefficient: The number in BLANK of the variable within the BLANK BLANK
Answers
The blank spaces of the statement coefficient: The number in BLANK of the variable within the BLANK BLANK are, front, addition, subtraction.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
We know a coefficient is a constant value combined with a variable.
For example, In 7x the coefficient of x is 7.
Given, A fill-in-the-blank statement,
coefficient: The number in BLANK of the variable within the BLANK BLANK.
Therefore,
coefficient: The number in front of the variable within the addition subtraction.
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Question 2(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length and g the line segment shown
!!!!please help me!!!!
Answers
The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
According to the graph -
The perpendicular measures 4 units.
The base measures 3 units.
To find the hypotenuse g apply the Pythagoras theorem -
(hypotenuse)^2=(base)^2+(perpendicular)^2
(g)^2=(3)^2+(4)^2
(g)^2=9+16
(g)^2=25
g=[tex]\sqrt{25}[/tex]
g=5
Therefore, line segment g measures 5 units.
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June is buying a sweater using a coupon offering a 30% discount on items over $99. If the discounted price is $91, how much was the original price of the sweater?
Answers
Answer: 130
Step-by-step explanation:
The original price of the sweater is $303.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.
The discounted price is $91
Let the original price of the sweater be x.
So, 30% of x=91
30/100 ×x=91
0.3x=91
x=91/0.3
x=$303
Therefore, the original price of the sweater is $303.
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Which of the following characteristics are true of all parallelograms? Select all that apply
Answers
Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram.
Parallel sides with two opposed pair?Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.The complete question is,
Which of the following attributes of a parallelogram leads to the conclusion that every square can be categorized as a parallelogram? Choose each option that applies.
four equal sides
two pairs of diametrically opposed equal angles
diagonals are cut in half.
two sets of parallel, opposed sides.
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How many pairs of potential clients can be randomly chosen from pool or eight candidates
Answers
There are 34 ways by which pairs of potential clients can be randomly chosen from pool or eight candidates.
What is combination?We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.
As such we would have the use of the formula for combination as follows;
C = n!/r!( n - r)!
C = 8!/2!(8 - 2)!
C = 8 * 7 * 6!/2! 61
C = 8 * 7/ 2 * 1
C = 28
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Which equation represents a linear function that has a slope of 4/5 and a y-intercept of -6?
○ y=-6x+4/5
O y=4/5x-6
O y=4/5x+6
Oy=6x+ 4/5
Answers
Answer: y= -6x+4/5
Step-by-step explanation: We will compare these equations with standard form y=mx+c where m is the slope of the line and c is the y-intercept.
for line y= -6x+4/5
on comparing with y= mx+c
we have m= -6 and c= 4/5.
So, the first option is correct.
A store is designing the space for rows of nested shopping carts
Answers
Which graph represents the solution to the following inequality? 3x - 2y ≥ 6
Answers
Answer:
First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
For:
x
=
0
(
3
⋅
0
)
+
2
y
=
6
0
+
2
y
=
6
2
y
=
6
2
y
2
=
6
2
y
=
3
or
(
0
,
3
)
For:
y
=
0
3
x
+
(
2
⋅
0
)
=
6
3
x
+
0
=
6
3
x
=
6
3
x
3
=
6
e
d
)
(
3
)
x
=
2
or
(
2
,
0
)
We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}
Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.
graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}
Step-by-step explanation:
In triangle JKL, angles J and L each measure 51° and JK = 18. Triangle PQR is similar to triangle JKL, where J corresponds to P, K corresponds to Q, and QR = 36. Which expression represents the length of segment PR?
Answers
Answer:
Step-by-step explanation:
Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:
(PR)/(JK) = (PQ)/(JL) = (36)/(18)
Cross multiplying and solving for PR, we find:
PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36
The rate of change increased by about _____ bass per a year. Round to the nearest tenth
Answers
From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65
What is Exponential FunctionAn exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.
In this problem, we have to calculate the rate of increase per year.
Data;
rate = 2%
P = 3000
The exponential growth can be calculated by;
A = P(1 + r)ⁿ
In year 1
A = 3000(1 + 0.02)¹
A = 3060
In year 4
A = 3000(1 + 0.02)⁴
A = 3247.3
a)
The average rate of change from year 1 to year 4 will be
A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1
A = 62.43
The average rate of change from year 1 to year 4 is 62.43
b)
The average rate of change from year 5 to year 8 is calculated as
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5
A = 67.57
C)
The rate of change increase can be calculated as;
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1
A =65
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pls help I have a hundred points for someone who answers
Answers
957÷3=319 this divide answer i hope help you
A hospital near a ski resort records the type of injuries treated during ski season and other seasons and other seasons over a year. the results shown in the table will help determine the medical staff that is required at different times of the year. according to the data in the table, what is the probability that a patient will need to be treated with a broken bone during ski season.
Answers
Answer:
The answer is C
Step-by-step explanation:
You have to divide both numerators then the denominater.
So, it would look like: 160 over 90 x 100 over 290
160x100=16 90x290=25 16/25
Work out 2/3 - 2/5 in its simplest form
Answers
Answer:
It is in its simplest form
Step-by-step explanation:
An online store charges $5 for shipping on all orders. They are having a sale on all t-shirts, $7 each! You and your friends are going to order some shirts. Write an expression that you could use to find the cost of the order.
Answers
Answer:
which one is correct about HRM?
The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.
In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.
By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.
For example, if 3 shirts are ordered, then x = 3 and the expression becomes:
7 * 3 + 5 = 26So the total cost of the order would be $26.
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An international company has 22400 employees in one country. If this represents 18.3 of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.
Answers
The total number of employees that this company would be said to have is given as 122424
How to solve for the number of employeesHow to solve for the number of employees in the company
We know that the number of employees in one country is 22400, and that this represents 18.3% of the company's employees in total.
We can use this information to set up a proportion to find the total number of employees in the company.
Employees in one country / Total employees = 18.3 / 100
22400 / X = 18.3/100
To find the total number of employees, we can cross-multiply and divide:
X = (22400 * 100) / 18.3
X = 122424
So the company has a total of 122424 employees.
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Please solve the ques below:
Answers
Answer:
510 miles
Step-by-step explanation:
A B
Rate 80 120
Time x x - 2
Distance
Distance = rate x time
A's distance
d = 80x
B's distance
d = 120(x -2)
The distances equal each other when B catches up to A. Set the equations equal to each other and solve for the time
80x = 120(x -2) Distribute the 120
80x = 120x - 240 Subtract 120x from both sides
-40x = -240 Divide both sides by -40
x = 6
After 6 hours, B caught up with A. Substitute 6 for t and find the distance. You can use A or B.
d= 80x
d = 80(6)
d = 480
We need to add another 30 miles to get to the next town.
480 + 30 = 510
In Circle O, mAB = 72. Find m
Answers
Check the picture below.
Please i have a question you can help me for answer.
The question is
Follow the construction program to build below the figure
° Draw a segment {ST} of length 9 cm.
°Draw the circle with center T and radius 4 cm
.
° Draw the circle with diameter {ST}
° The two circles intersect at A and B. Without measuring, give the length of the segments {TA} and {TB}:
Answers
The length of segments TA and TB are both 4 cm.
How to determine the diagram and the lengthsTo solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.
Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.
Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.
Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.
Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.
Therefore, the length of segments TA and TB are both 4 cm.
The figure is attached
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is 10/12 and 40/64 a proportion
Answers
Answer:
No, it is not a proportion
Step-by-step explanation:
10/12 and 40/64 is not a proportion since although the numerator is constant because when multiplied by 4, it gives us 40, however, when you multiply 4 by 12, you get 48, therefore, it is not a proportion since the changes in the value of a proportion must be constant in both the numerator and denominator.
Hope this helped! :D
Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price. f
Answers
p = 0.82 * 55
In this equation, p represents the new price after the discount has been applied, and 0.82 represents the percentage of the original price that remains after the discount has been applied (100% - 18% = 82%).
Solving this equation, we find that the new price, p, is equal to $45.90.
Note: This equation represents a discount, which means that the final price, p, will be less than the original price. If you want to represent a markdown (i.e., a price increase), you would use a value greater than 1 for the percentage factor (e.g., 1.18 for a markdown of 18%).
points A and B are shown on a coordinate plane
point A is at (-8, 6) point B is at (-2, -2)
What is the length of AB and the coordinates of its midpoint?
AB= __ units
the midpoint of AB is (_,_)
Answers
The length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).
What are the distance formula and midpoint of a segment?
The distance formula is a mathematical formula that can be used to determine the distance between two points in a coordinate plane. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
The midpoint of a segment is a point that is exactly in the middle of a line segment. Given the endpoints of the line segment, (x1, y1) and (x2, y2) the coordinates of the midpoint, (x, y) can be calculated using the following formulas:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
The given points are (-8, 6) and (-2, -2).
Given two points A(x1, y1) = (-8, 6) and B(x2, y2) = (-2, -2), we can use the distance formula to find the length of the line segment AB. The distance formula is:
[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\\\d= \sqrt{((-2) - (-8))^2 + ((-2) - (6))^2}\\\\d=\sqrt{36 + 64}\\\\d=\sqrt{100}\\\\d=10[/tex]
The length of AB would be 10.
To find the coordinates of the midpoint of AB, we can use the midpoint formula:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Plugging in the values for A and B, we get:
x = (-8 + (-2)) / 2 = -5
y = (6 + (-2)) / 2 = 2
The coordinates of the midpoint of AB are (-5, 2).
Hence, the length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).
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For polynomial function f, if f(3)=5 and f(5)=-2, what do we know about any roots of f(x)?
Answers
Answer:
There is a root between x=3 and x=5.
Step-by-step explanation:
Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.