What are the two possible answers for the equation Ix/5I = 3?
Answers
Answer:
Either \(x = -15\) or \(x = 15\).
Step-by-step explanation:
\(|x| = \left\lbrace \begin{aligned} & x && \text{if $x \ge 0$} \\ & -x && \text{if $x < 0$}\end{aligned}\right.\).
Hence, there are two possibilities to consider:
Either \((x / 5) \ge 0\),Or \((x / 5) < 0\).If \((x / 5) \ge 0\), then \(|x / 5| = x / 5\).
Substitute into the original equation: \(x/ 5= 3\). Solve for \(x\): \(x = 15\).
Important: verify that the solution \(x = 15\) meet the assumption \((x / 5) \ge 0\). Indeed, \((x / 5) = (15 / 5) = 3\) and is indeed non-negative. Hence, the solution \(x = 15\!\) is valid.
On the other hand, if \((x / 5) < 0\), then \(|x / 5| = - x / 5\).
Substitute into the original equation: \((-x / 5) = 3\). Solve for \(x\): \(x = -15\).
Similarly, verify that the solution \(x= - 15\) satisfies the current assumption that \((x / 5) < 0\). Indeed, this assumption is met, and \(x = -15\) is also a valid solution.
Related Questions
Gym City charges a $30 sign-up fee, plus a monthly fee of $25. FitnessExpress charges a $20 sign-up fee, plus a monthly fee of $30. How muchmoney would Leslie save in a 6-month period by joining Gym City insteadof Fitness Express? PLSSSS
Answers
Answer:
$20
Step-by-step explanation:
Gym city fees are:
Sign up = 30
6 monthly sub = 6 x 25 = 150
Total fees = 30 + 150
FitnessExpress fees are:
Sign up = 20
6 monthly sub = 6 x 30 = 180
Total fees = 20 + 180 = 200
Therefore, the difference between the two is $20
Please help ill mark you the brainlist The scale on a map indicates that 1 cm represents 50 km. If two cities are 400 km apart, then how far apart would the cities be on this map?
Answers
Answer:
8 cm
Step-by-step explanation:
divide 400 by 50 which is 8.
There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?
Answers
In total, the number of greetings will be 1159.
Why do you use the term "numbers"?Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.
The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.
The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.
The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.
In total, the number of greetings will be 38 + 760 + 361 = 1159.
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According to experts the first 4 moves in a chess game can be played in 197299
totally different ways. If it takes 30 seconds to make one move, how long would it take one player to try every possible set of 4 moves ?
one player to try every possible set of 4 moves?
Answers
Answer:
5918970 seconds
Step-by-step explanation:
all you do is 30 x 197299
which is 5918970 seconds I believe
That's how long it would take one player to try every possible set of 4 moves.
or 2.25 months STRAIGHT
Chlorpheniramine 100 ml
Lidocaine 2 oz
Banana flavoring ½ tsp
Take 10 ml BID
How many days will this solution last?
Answers
The number of days that this solution will probably last would be = 8 days.
How to calculate the total number of days the solution will last?To calculate the number of days the solution will last the following is taken into consideration.
The parameters given which are not in ml should be converted to ml as follows;
2 Oz of Lidocaine to ml = 2×29.6=59.2ml
½tsp of banana flavouring;
= 1/2×4.92
= 2.5ml
Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml
But 2×10 = 1 day
20ml = 1 day
161.7ml = X
Make X the subject of formula;
X = 161.7/20
= 8.1
= 8 days.
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Write a real world situation the would represent -5 + -2 +3 = -4
Answers
Order of operation problem who two operations inside parentheses and two outside ( using all add, subtract, multiply and divide). I need examples
Answers
Here is one: PEMDAS
12- ( 6 + 3) - 19 x 1 divided by 1
I hope this helps
Please help I’m failing math.
Answers
Answer:
The point (5, -4) is a solution to the system because it satisfies both equations.
Step-by-step explanation:
4y = -3x - 1:
\(4(-4) = -3(5)-1\) \(-16=-15-1\) \(-16=-16\)2y = x - 13
\(2(-4)=5-13\) \(-8=-8\)Answer:
Look below
Step-by-step explanation:
Start by plugging (5, -4) into both equation:
\(4y=-3x-1\\4(-4)=-3(5)-1\\-16=-15-1\\-16=-16\rightarrow correct!\)
\(2y=x-13\\2(-4)=5-13\\-8=-8\rightarrow correct!\)
It is a solution because it satisfies both equations.
OR
It is a solution because it is the point of intersection of the two lines.
A state lotto has a prize that pays $900 each week for 20 years.
Find the total value of the prize: $
If the state can earn 5% interest on investments, how much money will they need to put into an account
now to cover the weekly prize payments?
Reminder: There are 52 weeks in a year.
Answers
The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
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Find the difference between -14w - 3 and 5w.
A -9 w - 3
B -19 w + 3
C -19 w - 3
D -22 w
Quick pls
Answers
Answer:
c
Step-by-step explanation:
cause -14w-3-(5w)
-14w-5w-3
-19w-3
Rachel has a bag of marbles. She added 6 marbles to the bag but then took out 8 marbles. The bag now has 14 marbles. How many marbles did Rachel have at the start? 12 marbles 16 marbles 22 marbles 28 marbles 22.
Answers
The equation formed is
x+6-8=14
As it is given that 6 marbles are add and took out 8 marbles.
\(undefined\)ill give brainless if you get right
Answers
Answer:
16%
Step-by-step explanation:
The temperature during a winter day was less than 8 degrees Fahrenheit. Digby wants to write an inequality for the temperature during the winter day. What constant should Digby use in the inequality?
Answers
The constant that will be used in Digby's linear inequality will be 8.
What are linear inequalities, exactly?
Inequality is a mathematical statement that states that neither side is equal. When a link causes a non-equal comparison between two expressions, an inequality develops. The inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.
The characters '<' and '>' denote severe inequalities, whereas " ≤ and ≥ " denote slack inequalities.
Now,
Given that The temperature during a winter day was less than 8 degrees Fahrenheit.
let x be the temperature in degree Fahrenheit
then the linear inequality to show the statement will be
x<8 where 8 is a constant
Hence,
The constant that will be used in Digby's linear inequality will be 8.
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Answer:
The awnser is 8.
Step-by-step explanation:
i just know<33
Find x (circle)
(Btw I don’t know if 5.6 is correct so just ignore that)
Answers
Answer:
A. 11.2
Step-by-step explanation:
But this has nothing to do with 5.6 × 2. Erase that! Lol.
You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.
The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.
The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.
The hypotenuse is 14.
Let's do some Pythagorean Theorem.
Leg^2+ leg^2=hypotenuse^2
you know,
a^2 + b^2 = c^2
fill in what we know.
8.4^2 + b^2 = 14^2
simplify.
70.56 + b^2 = 196
subtract 70.56
b^2 = 125.44
squareroot both sides
b = 11.2
Write these fractions in their simplest forms:
a)
15
20
8
b)
12
Answers
Answer:
a) 3/4
b)4/6 = 2/3
hope this helps u
pls mark me as brainiest :)
Landry purchased a vehicle for 4/5 of the sticker price of $22,550. He had to pay 7.75% sales tax. What was the amount of Landry's bill?
$16,641.90
b. $18,040.00
C. $18,214.76
d $19,438.10
Answers
Landry paid $18,040 for the vehicle, and the amount of sales tax that Landry had to pay is $1,397.90, thus the total amount of Landry's bill is $19,437.90 the correct option is (d).
The price Landry paid for the vehicle is \(\frac{4}{5}\) of the sticker price, which means he paid is:
= \(\frac{4}{5}\) x $22,550
= $18,040
To find the amount of sales tax, we need to multiply the price of the vehicle by the tax rate, which is 7.75% or 0.0775 as a decimal:
$18,040 x 0.0775 = $1,397.90
To find the total amount of Landry's bill, we add the price of the vehicle and the sales tax is:
$18,040 + $1,397.90
= $19,437.90
Therefore, Landry's bill was $19,437.90
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The complete question is:
Landry purchased a vehicle for 4/5 of the sticker price of $22,550. He had to pay 7.75% sales tax. What was the amount of Landry's bill?
a. $16,641.90
b. $18,040.00
c. $18,214.76
d. $19,437.90
Dado cot B = 0.57736, determina la medida del ángulo B.
Answers
The measure of angle B is approximately equal to 56.31 degrees, rounded to two decimal places.
What is a angle measure?An angle measure is a numerical value that represents the amount of rotation between two intersecting lines, line segments or rays. It is typically measured in degrees, although other units of measurement such as radians and grads may also be used. The size of an angle can range from 0 degrees (corresponding to no rotation or a straight line) to 360 degrees (corresponding to a full rotation). In geometry, angles are used to describe the relationships between lines and shapes, and are an important concept in fields such as trigonometry and calculus.
To find the measure of angle B given cot B = 0.57736, we can use the inverse tangent function.
The tangent of an angle is the ratio of the opposite side to the adjacent side,
So cot B = adjacent side / opposite side.
By taking the inverse tangent of both sides and substituting cot B for adjacent side / opposite side, we arrive at the equation
B = arctan(cot B).
Evaluating arctan(cot B) using a calculator gives us the measure of angle B as,
B = arctan(cot B) = 56.31° (rounded to two decimal places)
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The complete question is: "Given cot B = 0.57736, determine the measure of angle B".
Help with the slop for each one thanks
Answers
Answer:
13. zero slope
14. 1/2
15. undefined slope
16.-3/2 slope
solve for n.
1.) 7.26 × 0.22=n
2.) 17.92 × 0.64=n
3.) 7.65 × 0.65=n
4.) 36.20 × 0.05=n
5.) 31.86 × 0.92=n
Answers
Answer:
1.) 1.5972
2.) 11.4688
3.) 4.9725
4.) 1.81
5.) 29.3112
An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour. His income per job can be modeled using a linear function. The electrician works maximum of 20 hours on any job. What is the range of values for one job?
Answers
Answer:
The range of values from one job is between $50 and $650.
Step-by-step explanation:
An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.
This means that his earnings in a job can be modeled by the following function:
\(y = 30x + 50\)
The electrician works maximum of 20 hours on any job. What is the range of values for one job?
Minimum, he works 0 hours, and earns:
\(y(0) = 30(0) + 50 = 50\)
Maximum, he works 20 hours, and earns:
\(y(20) = 30(20) + 50 = 650\)
The range of values from one job is between $50 and $650.
Find the Horizontal or Vertical distance between the two points:
Answers
Answer:
5 units of vertical distance
Step-by-step explanation:
just count
f(x)
g(x)
=∣x∣
=∣x+9∣−5
We can think of
�
gg as a translated (shifted) version of
�
ff.
Complete the description of the transformation.
Use nonnegative numbers.
To get the function
�
gg, shift
�
ff
by
units and to the
by
units.
Answers
The function g( x ) is translated to the left by 9 units and down by 5 units.
Given data ,
Let the first function be represented as f ( x )
where the value of f ( x ) = | x |
Let the translated function be g ( x )
where the value of g ( x ) = | x + 9 | - 5
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
On translating to the left , f ( x + a )
So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |
Now , when the function is translated 5 units down , f ( x ) - 5
So , the translated function is g ( x ) = | x + 9 | - 5
Hence , the function is translated to the left by 9 and up by 5 units.
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Next O Quiz 6.2
10
Select the correct answer.
According to the Dietary Guidelines for American 2015, you should limit your fat intake to what percentage of your total calories?
OA. Less than 10%
OB. 25-35%
C.
OD.
45-55%
65-75%
Reset
Next
Answers
According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.
What is dietary guidelines?Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.
Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.
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-14 is less than or equal to x.
Question options:
-14 > x
-14 ≥ x
-14 ≤ x
-14 < x
Answers
Answer:
C
Step-by-step explanation:
This sign "≤" has both the less sign and the equal sign so it indicates that -14 is less than or equal to x.
Help quick please look at pic to solve
Answers
The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
Given the diagram of the hanger which one side has 10 + 5x and other side has 11.
To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.
Thus, the equation is 10 + 5x = 11.
Consider the equation 10 + 5x = 11
On subtracting 10 from each side gives,
5x = 1
Divide each side by 5 gives,
x = 1/5.
Hence, the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
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given: AB ≅AC and ∠BAD ≅ ∠CAD. Prove ∠DBC ≅ ∠DCB.
Answers
The given information is:
\(\begin{gathered} AB\cong AC \\ \angle BAD\cong\angle CAD \end{gathered}\)Now, the next statement is:
\(AD\cong AD\text{ }\)Reason: reflexive property
3. Statement:
\(\wedge BAD\cong\wedge CAD\)Reason: SAS congruence rule.
4. Statement:
\(BD\cong CD\)Reason: CPCTC - Corresponding parts of congruent triangles are congruent.
5. Statement:
\(\angle DBC\cong\angle\text{DCB}\)Reason: in a triangle, angles opposite of congruent sides are congruent.
translate the equation 49 is what percent of 66?
Answers
Answer:
49 ÷ 66 × 100= x
Step-by-step explanation:
please help
P (-∞ < z < ∞) =
Answers
The entire area is under the standard normal distribution curve, which is 1 by definition.
In other words, a typical normal random variable has a 100% chance of landing anywhere within its range of potential values (-∞ to +∞).
This makes sense since the area under the standard normal distribution curve, which is a continuous probability distribution, shows the likelihood that the random variable will take on any value within its range. Since the entire area under the curve is 1, the likelihood that any potential value for the random variable will occur is 1, or 100%.
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please help it's just homework
Answers
The circle graph shows the
number of votes received by each candidate during a
school election. Find the percent of students who voted
for the indicated candidate. (See Exploration 1, p. 247.)
10. Candidate A
11. Candidate B
12. Candidate C
Answers
Answer:
36%
Step-by-step explanation:
54/150=p/100
(150 comes from all of the numbers combined from the chart)
Do the math
150b=5400
divide both sides by 150
which gets you 36
just add the percentage
36%