For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
What is meant by inequality?The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:
A less than sign, such as a, denotes that an is greater than b.
Given inequality is:
|2x+7|+9 >18.
First we have to rearrange all the variables to the left side of the given equation:
Then,
|2x+7|>18-9
|2x+7|>9
2x+7>9 or 2x+7< -9
S0, x>1 or x< -8
Therefore, x< -8 or x>1
Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
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Jack is running on a treadmill at a speed of 7. 2 miles per hour a slim y equals total distance and x equals number of hours
Need help pls important!!!!!!!!
Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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If 9^x / 9^3 = 9^5 what is x
Answer:
since , 9^x / 9^3 = 9^5
and since there is a law for exponents that says if the bases of the exponent are equal and divided by each other we subtract the exponents
, so 9^x-3 = 9^5
then x-3 =5 , therefore the final answer will be X= 8 .
Simplify each ratio. Make sure to convert the units when needed
1,320 feet: 1 mile (Hint: There are 5,280 feet in one mile.)
The simplification of the ratio 1320 feet : 1 mile will be 1:4
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. The term ratio is a straight borrowing from the Latin word ratio. In Latin, ratio could imply everything from "reason" to "calculation" to "proportion," and it was this last meaning that was used to create the mathematical and English ratios.
Given taht we need to simplify the ratio 1320 feet : 1 mile
For simplifying ratios we need to convert the terms in same units
and we know that 1 mile = 5280 feet
So,
1320 feet : 1 mile can be written as 1320 feet : 5280 feet
The simplification wil be 1:4
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PLEASE HELP ASAP!!!!
Answer:
statements 2 and 3 are true
Step-by-step explanation:
using the rule of exponents
[tex]a^{0}[/tex] = 1
then
1 [tex]a^{0}[/tex]≠ a ← lie
2 [tex]x^{0}[/tex] = 1 ← true
3 [tex]5^{0}[/tex] = 1 ← true
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135. What was the total of his sales for that week?
The total of his sales for that week is $49,500.
Given :
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.
Let x be the total sales.
2135 = 2.5 % * 50000 + 3 % (x - 50000 )
= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )
1235 = 2.5 * 500 + 0.03x - 0.03 * 50000
1235 = 1250 + 0.03x - 1500
0.03x = 1235 - 1250 + 1500
0.03x = -15 + 1500
0.03x = 1485
multiply by 100 on both sides
0.03x * 100 = 1485 * 100
3x = 148500
x = $49500
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The Scooter Company's total profit function is represented by -2x²+250x-2000.
Total profit of a company is the difference between total revenue and total cost.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Company earns a total revenue that can be determined by the function R(x) = 400x - 2x²
Each scooter cost $150 to produce, and the company has a fixed cost of $2,000.
Variable cost = Cost of each scooter × Number of scooter sold
Total cost = fixed cost + variable cost
= 2000 + (150×x)
Cost, C(x) = 2000 + 150x
Revenue, R(x) = 400x - 2x²
Total profit = Revenue - Cost
= 400x-2x²-(2000 + 150x)
= 400x-2x²-2000-150x
= -2x²+250x-2000
Therefore, the Scooter Company's total profit function is represented by -2x²+250x-2000.
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Ariana has 6 posters she wants to hang on the wall. How many different ways
can the posters be arranged in a row?
What are the values of x and y in the figure?
HELP LIKE WHAT ELSE DO I DO???? IT WONT LET ME PROOVE THAT LINES BA AND CD ARE PARALLEL
The triangles ABC and CDA are congruent by SAS criteria.
What are the criteria for congruent triangles?Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.
Given that,
In quadrilateral ABCD, AD = BC and AD ║BC.
Now, the given relation ΔABC ≅ ΔCDA can be proved as follows,
In ΔABC and ΔCDA, it is found as,
AC = AC (Common sides)
AD = BC (Given data)
And, ∠ACB = ∠DAC (Interior angles between parallel lines AD and BC)
Thus, ΔABC ≅ ΔCDA by SAS congruence criteria.
Hence, the given relation ΔABC ≅ ΔCDA is proved by SAS criteria.
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an
additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $256.00. On her second business trip she drove
200 miles in 3 days, and paid $159.00 for the rental. Find the daily fee, and find the mileage charge.
Answer:
the daily fee is 37 and the mileage charge is .24 per mile.
Step-by-step explanation:
256 = 450x + 4b
159 = 200x + 3b
Multiple the top equations by -3 all the way through the bottom equations by 4 all the way through then add the equation together.
-768 = -1350x -12b
636 = 800x + 12b
-132 = -550x Divide both sides by -550
.24 = x This is the charge per mile.
Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.
256 = 450(.24) = 4b
256 = 108 + 4b Subtract 108 from both sides
148 = 4b Divide both sides by 4
37 = b This is the daily fee.
What is an algebraic expression for 16 more than the product of 43 and a number?
A: 16 − 43y
B: 43y(16)
C: 43y − 16
D: 43y + 16
The algebraic expression that can be represented by the statement is 43y + 16
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
16 more than the product of 43 and a number
Represent the variable with y
So, we have the following representation
16 more than the product of 43 and y
Express the product as an actual product
So, we have the following representation
16 more than 43y
more than as used here means addition
So, we have
43y + 16
Hence, the expression is (d) 43y + 16
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Answer: 43y + 16
Step-by-step explanation:
i did the test
Solve for x. 6 + |4x - 1| > 10 Graph the solution on the number line.
13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.Explanation:
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.
When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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HELP DUE TODAY THE 16TH OF DEC
Simplify fraction with 8 minus 4 times 3 in the numerator and the cube root of 8 plus 5 in the denominator.
twelve sevenths
negative twelve sevenths
four sevenths
negative four sevenths
Whats the scale factor of triangle PQR to triangle STU.
PR =8 SU=12
RQ=6 UT=9
QP=10 TS=15
The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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Describe a set of data in which it would be most appropriate to use the mode as the measure of central tendency.
Answer:
It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.
[tex]3(x+7)=7x-48[/tex] I can't solve this question can you help me please !!!
Therefore the value of x from the given equation comes out to be 13.5
What is equation?A statement proving the equality of two mathematical expressions is known as an equation. The equal sign (=) is used to represent an equation between two mathematical expressions. Anything that contains the equal sign is an equation, to put it simply. Examples of equations include x=7, 2x+5=7, etc.
Here,
The equation given is 3(x+2)=7x-48
thus we find the value of x from the given equation
=> 3(x+2)=7x-48
=> 3x+6=7x-48
=> 7x-48-3x-6=0
=> 4x-54=0
=> 4x=54
=> x=54/4
=> x=13.5
Therefore the value of x from the given equation comes out to be 13.5
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Molly wants to put a triangular fence around her garden. Use the diagram below to answer the questions.
Molly would need 43 feet of fencing to fence the triangular area.
What is Pythagorean theorem?
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
According to the given question:
We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilize Pythagoras theorem to our advantage to find out the third side.
In Δ ABC
AB² (base) + AC² (perpendicular) = BC² (hypotenuse)
Substituting the values of AB as 10 feet and BC as 18 feet
AC²= BC²- AB ²
∴AC²= 224
∴AC= 14.96 cm
Amount of fence required by molly would equal perimeter of the area.
⇒The perimeter of the area would equal AB+BC+AC
⇒Summing up the values of AB, AC and BC
Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet
Hence, Molly would require 43 feet of fencing.
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convert 5 centimeters into yards rounded to nearest hundredth
Answer:
.05 yd
Step-by-step explanation:
5/91.44=.05468066
THANK YOU AND HELP I’m VERY CONFUSED
Answer:
The first one is the answer
A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
Given that,
461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students. Sales of tickets totaled $1624.
We have to find the system of equations to model.
We know that,
We get,
a + s = 461
s = 461 -a
The student tickets sold = s × 3 = 3 × (461-a)
The adult tix sold = 4 a
Summed they total 1624
We get system of equations as
s = 461-a
3 (461-a) + 4a = 1624
1383 -3a +4a = 1624
a = 241
Then
s = 461 -a = 220
Therefore, The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
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Write ONE equivalent ratio for the following: 6 : 4
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Eliana and her friend Greta are each baking apple pies and tarts for a bake sale, using the
same recipes. Eliana baked 2 apple pies and 6 apple tarts, using a total of 38 apples. Greta
made 2 apple pies and 8 apple tarts, which used 46 apples. How many apples does each
dessert require?
An apple pie uses
Submit
apples and an apple tart requires
C
zoom
apples.
O
An apple pie requires 7 apples and an apple tart requires 4 apples
How to write a system of equations to describe a situation?To set up this problem, we can let p represent the number of apples needed for one pie and t represents the number of apples needed for one tart.
We can then set up the following system of equations to represent the information given in the problem:
2p + 6t = 38
2p + 8t = 46
To solve this system, we can subtract the first equation from the second to eliminate the p terms:
2p + 8t - 2p - 6t = 46 - 38
2t = 8
t = 4
Substituting this value back into the first equation, we get:
2p + 6(4) = 38
2p = 14
p = 7
Thus, an apple pie requires 7 apples and an apple tart requires 4 apples.
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Write 2/5 and 1/4 with the same denominator
Answer:
Make the denominators equal by L.C.M
--> 8/20 + 5/20
--> 13/20
Hello please perform indicated operation this with steps
(x+4)^2(x-2)
We can expand the given expression:
(x + 4)²*(x - 2)
To get the equivalent one:
x³ + 6x² - 32
How to perform the operation?Here we want to expand the given expression, which is:
(x + 4)²*(x - 2)
First remember the rule:
(a + b)² = a² + 2ab + b²
So we can rewrite the first factor as:
(x + 4)² = x² + 2*4*x + 4²
= x² + 8x + 16
Replacing that in our expression we get:
(x² + 8x + 16)*(x - 2)
Now we can expand that to get:
x²*x + x²*(-2) + (8x)*x + 8x*(-2) + 16*x + 16*(-2)
= x³ - 2x² + 8x² - 16x + 16x - 32
= x³ + 6x² - 32
That is the expression expanded.
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Dean is training for a 20 kilometre race. He wants to beat his personal best time of 3 hr 14 min 45 sec. If it takes him 9 minutes and 30 seconds to run one kilometre, will he beat his personal best? Calculate by how much will Dean beat/not beat his personal best time?
Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the personal best time of Dean be = A
Now , the value of A = 3 hours 14 minutes 45 seconds
And ,
The time taken by Dean to complete 1 km = 9 minutes 30 seconds
Now , the total distance of the race lap = 20 km
So , the equation will be
Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km
Substituting the values in the equation , we get
Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds
Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds
Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds
1 hour = 60 minutes
1 minute = 60 seconds
180 minutes = 3 hours
600 seconds = 10 minutes
So , the equation is
Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes
So , the value of B < value of A
Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes
Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
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Example An investor Saved #120,000 For 7 years in a bank which pays interest of 11½% per annum Calculate the a. Interest which accrued b balance if # 25,000 was withdrawn from the account (N 28,276) 00
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]
classify the polynomial 2x^3-5+9x^2
The category of the polynomial 2x³ - 5 + 9x² is a trinomial
How to determine the category of the expression?From the question, we have the following expression that can be used in our computation:
2x^3-5+9x^2
Rewrite this expression properly
So, we have the following representation
2x³ - 5 + 9x²
This expression can be further rewritten as
2x³ + 9x² - 5
The degree of a polynomial is the highest power of the polynomial
In this case, the degree of the above polynomial is 3
As a general rule, a trinomial is any polynomial that has a degree of 3
Hence, the expression is a trinomial
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if a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?
The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.
What is an unbiased estimator?In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.
Calculation:Consider a statistic.
"A statistic describes a portion of the target population".
"A parameter describes the whole population".
In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.
I.e., μ = E(x)
So, that statistic is said to be an unbiased estimator.
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Below are the steps to solve an equation:
Step 1: x 5+2=5
Step 2: x - 5] 5-2
Step 3: x 5 = 3
Which of the following is a correct next step to solve the equation? (1 point)
Ox+5=-3
O-x-5-3
Ox-5--3
Ox+5=3
Help me please before my assignment is due
Greta's current age is m + n years.
What is an expression?An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
In other words, algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation
Therefore, let's convert the word's expression to an algebraic expression.
Greta was m years old n years ago. Her age now is as follows:
n years ago Greta was m years old. This simply means n years ago Greta was m years old. Her current age will be the sum of her current age and the number of years ago.
Therefore,
(m + n) years
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