Select the correct answer.
What is the solution to |x - 6| ≥ 5?
A. 1 ≤ x ≤ 11
B. -11 ≤ x ≤ 1
C. x ≥ 11 or x ≤ 1
D. x ≥ 1 or x ≤ -11
Answer:
C. x ≥ 11 or x ≤ 1
Step-by-step explanation:
x - 6 + 6 ≥ 5 + 6
x ≥ 11
x - 6 ≤ -5
x - 6 + 6 ≤ -5 + 6
x ≤ 1
Hope this helps! :)
A social security number contains nine digits, such as 273-41-2406. How many different social security numbers can be formed?
Answer: 5 more!
Step-by-step explanation:
Due to the lack of numbers your could do about 4 - 5 more security numbers!
Answer:
I think 81
Step-by-step explanation:
I'm not too sure since 9 x 9 is 81 but im not sureeee
67,000 rounded to the nearest ten thousand
When 67,000 is rounded to the nearest ten thousand then we get 70,000
When you round to the nearest 10 thousand. Find the number in the 10 thousand place, that would be the 6 in this case, now look at the number to the right of it, if that number is 5 or higher, then your 67,000 becomes 70,000.
If the number to the right of place value is lower than 5 then it would have been rounded to 60,000.
The digits in the thousands, hundreds, tens, and ones should be changed to 0 if the number is less than 5, but the other digits should remain the same. If it is 5 or more, increase the digit in the tens of thousands by 1 and replace the digits in the thousands, hundreds, tens, and ones with 0.
Hence the nearest round of to ten thousand is 70,000.
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Solve for the value of x in the given rational inequalities.
Answer:
see explanation
Step-by-step explanation:
1
1 + [tex]\frac{x-5}{2}[/tex] - [tex]\frac{x+3}{5}[/tex] ≤ 0
multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions
10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify
10 + 5x - 25 - 2x - 6 ≤ 0
3x - 21 ≤ 0 ( add 21 to both sides )
3x ≤ 21 ( divide both sides by 3 )
x ≤ 7
2
[tex]\frac{6x}{5}[/tex] - [tex]\frac{2}{3}[/tex] ≥ 4
multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions
18x - 10 ≥ 60 ( add 10 to both sides )
18x ≥ 70 ( divide both sides by 18 )
x ≥ [tex]\frac{70}{18}[/tex] , that is
x ≥ [tex]\frac{35}{9}[/tex]
3
[tex]\frac{x}{10}[/tex] - [tex]\frac{2}{8}[/tex] ≥ 1
multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions
4x - 10 ≥ 40 ( add 10 to both sides )
4x ≥ 50 ( divide both sides by 4 )
x ≥ [tex]\frac{50}{4}[/tex] , that is
x ≥ [tex]\frac{25}{2}[/tex]
Answer:
[tex]\textsf{1.} \quad x \leq 7[/tex]
[tex]\textsf{2.} \quad x \geq \dfrac{35}{9}[/tex]
[tex]\textsf{3.} \quad x \geq \dfrac{25}{2}[/tex]
Step-by-step explanation:
Question 1Given inequality:
[tex]1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0[/tex]
[tex]\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:[/tex]
[tex]\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}[/tex]
[tex]\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:[/tex]
[tex]\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}[/tex]
Cross multiply:
[tex]\implies 5(x-3)\leq 2(x+3)[/tex]
[tex]\implies 5x-15\leq 2x+6[/tex]
Subtract 2x from both sides:
[tex]\implies 5x-15-2x\leq 2x+6-2x[/tex]
[tex]\implies 3x-15\leq 6[/tex]
Add 15 to both sides:
[tex]\implies 3x-15+15\leq 6+15[/tex]
[tex]\implies 3x\leq 21[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}\leq \dfrac{21}{3}[/tex]
[tex]\implies x \leq 7[/tex]
---------------------------------------------------------------------------------------
Question 2Given inequality:
[tex]\dfrac{6x}{5}-\dfrac{2}{3} \geq 4[/tex]
[tex]\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:[/tex]
[tex]\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{14}{3}[/tex]
Cross multiply:
[tex]\implies 3(6x) \geq 14(5)[/tex]
[tex]\implies 18x \geq 70[/tex]
Divide both sides by 18:
[tex]\implies \dfrac{18x}{18} \geq \dfrac{70}{18}[/tex]
[tex]\implies x \geq \dfrac{70}{18}[/tex]
Reduce the fraction by dividing the numerator and the denominator by 2:
[tex]\implies x \geq \dfrac{70 \div 2}{18 \div 2}[/tex]
[tex]\implies x \geq \dfrac{35}{9}[/tex]
---------------------------------------------------------------------------------------
Question 3Given inequality:
[tex]\dfrac{x}{10}-\dfrac{2}{8} \geq 1[/tex]
[tex]\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:[/tex]
[tex]\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{10}{8}[/tex]
Cross multiply:
[tex]\implies 8(x) \geq 10(10)[/tex]
[tex]\implies 8x \geq 100[/tex]
Divide both sides by 8:
[tex]\implies \dfrac{8x}{8} \geq \dfrac{100}{8}[/tex]
[tex]\implies x \geq \dfrac{100}{8}[/tex]
Reduce the fraction by dividing the numerator and the denominator by 4:
[tex]\implies x \geq \dfrac{100 \div 4}{8 \div 4}[/tex]
[tex]\implies x \geq \dfrac{25}{2}[/tex]
Find the distance between the following two points: (3, 2) and (0, -4).
The distance between the 2 given points is √45.
What is the distance?Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending point. Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.So, the distance between (3, 2) and (0, -4) is:
The distance formula: D = √[(x₂ - x₁)² + (y₂ - y₁)²]Now, substitute the values in the formula and solve as follows:
D = √[(x₂ - x₁)² + (y₂ - y₁)²]D = √[(0 - 3)² + ((-4) - 2)²]D = √[(-3)² + (-6)²]D = √[9 + 36]D = √45Therefore, the distance between the 2 given points is √45.
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phythegorean theorem
Answer: 6.782
Step-by-step explanation:
how do I multiply 1 * 1
We have the following:
Multiplication is the product between two numbers, it is the number of times the number to be multiplied is repeated. In this case, it would be 1 time 1
[tex]1\cdot1=1[/tex]The answer is 1
Simplify to create an equivalent expression.
\qquad{5(10k+1)+2(2+8k)}5(10k+1)+2(2+8k)5, left parenthesis, 10, k, plus, 1, right parenthesis, plus, 2, left parenthesis, 2, plus, 8, k, right parenthesis
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
66k+966k+966, k, plus, 9
(Choice B)
B
64k+964k+964, k, plus, 9
(Choice C)
C
66k+5466k+5466, k, plus, 54
(Choice D)
D
64k-964k−964, k, minus, 9
URGENT!!!!
answer options:
cannot be determined
closer to point A
closer to point B
the same distance from both point a and b
Point M has the same distance from point A and point B (option d).
Given,
Line segment CD is the perpendicular bisector of line segment AB
AB ⊥ CD
Assume the conjecture that the set of points equidistant from A
and B is the perpendicular bisector of AB is true
Here, line segment CD intersect line segment AB at M
Then, M is the mid-point of line segment AB
So, the length of line AM = the length of line MB
That is, Point M has the same distance from both point A and point B.
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Anna buys ice cream and oranges at the store.
She pays a total of $59.53.
She pays a total of $6.49 for the ice cream.
She buys 8 bags of oranges that each cost the same amount.
Write and solve an equation which can be used to determine xx, how much each bag of oranges costs.
Algebraic equation - The cost of each bag of Oranges = $6.63
What is Algebraic equation ?
An algebraic equation, sometimes known as a polynomial equation, in mathematics is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers.
Let the cost one bag of oranges be x
Given,
Total amount she pays = $59.53
Total amount she pays for ice cream = $6.49
Since the total amount for 8 bag of oranges = 8x
Therefore, the equation of the following will be
8x + 6.49 = 59.53
Now by solving the equation we get the cost of each bag of oranges
8x = 59.53 - 6.49
8x = 53.04
x = 53.04 / 8
x = 6.63
Hence, The cost of each bag of oranges will be $6.63
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0.3(4+x)=4.5
Please help me out, I need this answer ASAP,
I give u 10 pts, thank u SOOO much :3
Answer: x=11
Step-by-step explanation:
Answer:
[tex] \sf \: x = 11[/tex]
Step-by-step explanation:
Given equation,
→ 0.3(4 + x) = 4.5
Now the value of x will be,
→ 0.3(4 + x) = 4.5
→ 1.2 + 0.3x = 4.5
→ 0.3x = 4.5 - 1.2
→ 0.3x = 3.3
[tex] \sf \rightarrow \: x = \frac{3.3}{0.3} [/tex]
→ [ x = 11 ]
Hence, the value of x is 11.
30 points please help asap!!
Which statement describes a reflection?
A.
A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
B.
A reflection moves points a specified distance along a line perpendicular to a specified line.
C.
A reflection moves points a specified distance along a line parallel to a specified line.
D.
A reflection occurs when an object moves in a circular arc around a point.
Answer:
A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
Hope this helps! :)
Help needed for trigonometry !!!
Answer:
k = 53.13°
Step-by-step explanation:
[tex]{ tan (k) = \dfrac{\text{side opposite k}}{\text{side adjacent k}}}[/tex]
[tex]= \dfrac{35}{JK}\\\\\textrm{Since JK is a right triangle, by the Pythagorean theorem }\\JK = \sqrt{IK^2 - IJ^2}}\\\\= \sqrt{35^2 - 28^2}\\\\\\ =\sqrt{1225 - 784}\\\\= \sqrt{441}\\\\= 21[/tex]
[tex]\tan(k) = \dfrac{28}{21} = 1.333\\\\k = \tan^{-1}(1.333)\\\\= 53.13^\circ[/tex]
URGENT!!!!!
math assignment(not to be confused with assessment) that I need help with
Answer: DF
Step-by-step explanation:
What is the answer???
Answer:
f = 90 + 32
= 122° (exterior angle)
What is the y-intercept of the online given by the equation below
y= -10x+14
Answer:
y - intercept = 14
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 = - 10x + 14 ← is in slope- intercept form
with y- intercept c = 14
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. There were 4 more large boxes
shipped than small boxes and the total weight of all boxes was 1750 pounds. Write a
system of equations that could be used to determine the number of small boxes
shipped and the number of large boxes shipped. Define the variables that you use to
write the system.
The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:
50x+80y=1750
y = x+4 ,
where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
We have:
Weight of small box of paper = 50 pounds
Weight of large box of paper = 80 pounds
Total weight of boxes = 1750 pounds
Let us consider that the number of small boxes of papers be x.
The number of large boxes of papers be y.
Then, according to question
50x+80y=1750
y = x+4
Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.
where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.
two members of the math competition team solve 13 problems in 1 hour. If all team members solve problems at the same rate how many tema members are needed to solve 39 problems in 1 hour
In a case whereby two members of the math competition team solve at the rate 13 problems in 1 hour, the members that are needed to solve 39 problems in 1 hour is 6 member of the team.
How can the rate be calculated?Since two members solve 13 problems in 1 hour, which implies that
2 members= 13 problem/ hr
Then if we want to calculate the number of the team that will be able to solve the problem at the rate of 39 problems in 1 hour, we can represent the number required as X.
Then X = 39 problems/hr.
2 members= 13 problem/ hr
Then in this case we can cross multiply as follows:
13 problem/ hr * X = 39 problems/hr * 2
Then we can make X the subject of the formular as X =( 78 /13)
= 6 member of the team.
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1.50 x 10 ^5 / 5.0 x 10^1 in scientific notation
(Please help me I will give you extra points and the crown)
What is the special angle pair relationship between <1 and <3
Answer:
These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Step-by-step explanation:
What is the domain of the following function:
A.) x is all real numbers.
B.) –1 ≤ x ≤ 0
C.) x > 0
D.) –1 ≤ x ≤ 1
-1 is the domain of the following
what is the answer???????
Answer: Where P is.
Step-by-step explanation
Quadrilateral QRST is shown. Two students each perform a different reflection on
the original figure.
Use the drop-down menus to give the coordinates of point T' after each reflection
When Ramona reflect the original figure over the x-axis, the coordinate of point T' will be (-2, -4). When Elias reflect the original figure over the y-axis, the coordinate of point T' will be (2, 4).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Mathematics, a reflection over the x-axis is given by this transformation rule:
(x, y) → (x, -y)
Point T = (-2, 4) → Point T' = (-2, -4)
In Geometry, a reflection over the y-axis of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, the coordinates of point T' after a reflection over the y-axis is as follows:
Point T = (-2, 4) → Point T' = (-(-2), 4) = (2, 4)
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Which of the following lists of ordered pairs is a function?
A.) (1, 2), (1, –2), (3, 2), (3, 4)
B.) (0, 2), (2, 3), (0, –2), (4, 1)
C.) (1, 6), (2, 7), (4, 9), (0, 5)
D.) (2, 4), (0, 2), (2, –4), (5, 3)
Answer: d
Step-by-step explanation:
im new at this but i am pretty sure it would be d
What is 2x-8=34?
please answer quickly
Answer: x=21
Step-by-step explanation:
2x-8=34 (change the -8 into a positive since it doesn't have a variable)
34+8=42 (divide 34 by 2)
42/2=21
Check your answer
2 x 21 = 42
42-8=34
x=21
The scale of a map of Pennsylvania is 1 inch: 25 miles. The actual distance from Ambridge to Pittsburgh is 20 miles. What is the distance on the map?
Step-by-step explanation:
1 inch = 25 miles
or as ratio
1 inch : 25 miles
1 : 25 or 1/25
a ratio is nothing else than a fraction (just with special meaning, but the handling, calculation, transformation and simplification is the same).
the checked distance is 20 miles.
so, we need to transform the ratio (in the same way as we transform fractions) to show 20 instead of 25 in the denominator.
25 × f = 20
f = 20/25 = 4/5
remember, we need to multiply 1/25 by f/f to keep the original value of the ratio unchanged.
1/25 × 4/5/4/5 = (4/5)/(25×4/5) = (4/5)/20
so, the distance on the map is 4/5 in.
7) G is the midpoint of FH. If FG-70 what is the mFH?
A. 35 B. 140
C. 105
D. 100
Answer:
A
Step-by-step explanation:
Jason has $3,561.05 in credit card debt. The annual interest rate on the unpaid balance is 18.2% compounded monthly. If Jason wants to pay off his credit card debt in 2 years, what is his monthly payment, assuming he makes no additional purchases on this card? (Suggestion: Use the formula for the present value of an ordinary annuity. Round your answer to the nearest cent.)
The monthly payment of Jason with no additional charge is found as $1,556.53.
What is meant by the compound interest?Compound interest is investment determined just on initial principal plus all previous periods' accumulated interest.A power of interest compounding is the ability to generate "interest on interest."Interest could be compounded at any time, from continuously to daily to annually.Compounding accelerates the growth of money.The formula for the calculation of the compound interest is;
CI = A - P
A = P(1 + r/100n)∧nt
Where,
CI = compound interestA = total amount after given timeP = principal amountT = total time in yearsn = number of time interest compoundedr = rate of interest in %The given values are;
P = $3,561.05 T = 2 yearsn = 12×2 = 24 times.R = 18.2%Put the values in the formula;
CI = $3,561.05(1 + 18.2/24×100)∧24×2 - $3,561.05
Simplifying;
CI = $3,561.05×1.43 - $3,561.05
CI = $5117.58 - $3,561.05
CI = $1,556.53
Thus, the monthly payment of with no additional charge is found as $1,556.53.
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The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?
X y
5 2
10 3
15 4
20 5
The rate of change of y with respect to x for this linear function is 1/5 or 0.2
What is a linear function?A linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
How to calculate the average rate of change?Mathematically, the average rate of change (slope) of a linear function can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Average rate of change = (3 - 2)/(10 - 5) = (4 - 3)(15 - 10)
Average rate of change = 1/5 or 0.2
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Suppose that an individual has a body fat percentage of 14.4% and weighs 148 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
An individual has a body fat percentage of 14.4% and weighs 148 pounds,
total pounds of her weight is made up of fat is 21.3pounds (nearest tenth).
As given in the question,
Total weight of an individual =148pounds
Percentage of her weight made up of fat = 14.4%
Pounds of her weight is made up of fat = 14.4% of 148
= ( 14.4 / 100 ) × 148
= 21.3 pounds (nearest tenth)
Therefore, an individual has a body fat percentage of 14.4% and weighs 148 pounds, total pounds of her weight is made up of fat is 21.3pounds(nearest tenth).
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