Answers
Answer:
I've pretty much already solved this, in my discussion above:
| 3 | = 3
| –3 | = 3
So then x must be equal to 3 or equal to –3.
But how am I supposed to solve this if I don't already know the answer? I will use the positive / negative property of the absolute value to split the equation into two cases, and I will use the fact that the "minus" sign in the negative case indicates "the opposite sign", not "a negative number".
For example, if I have x = –6, then "–x " indicates "the opposite of x" or, in this case, –(–6) = +6, a positive number. The "minus" sign in "–x" just indicates that I am changing the sign on x. It does not indicate a negative number. This distinction is crucial!
Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might originally have been positive and might originally have been negative, I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases. For this exercise, these cases are as follows:
a. If the value of x was non-negative (that is, if it was positive or zero) to start with, then I can bring that value out of the absolute-value bars without changing its sign, giving me the equation x = 3.
b. If the value of x was negative to start with, then I can bring that value out of the absolute-value bars by changing the sign on x, giving me the equation –x = 3, which solves as x = –3.
Then my solution
Answer:
7 and [tex]\frac{16}{5}[/tex]
Step-by-step explanation:
(a)
Δ ABC and Δ ADE are similar thus the ratios of corresponding sides are equal
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{AC}{AE}[/tex] , substitute values
[tex]\frac{2}{4}[/tex] = [tex]\frac{x}{x+7}[/tex] ( cross- multiply )
4x = 2(x + 7) ← distribute
4x = 2x + 14 ( subtract 2x from both sides )
2x = 14 ( divide both sides by 2 )
x = 7
---------------------------------------------
(b)
Δ ABC and Δ CDF are similar thus ratios of corresponding sides are equal
[tex]\frac{AB}{CD}[/tex] = [tex]\frac{BC}{DF}[/tex] , substitute values
[tex]\frac{2}{5}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )
5x = 16 ( divide both sides by 5 )
x = [tex]\frac{16}{5}[/tex]
Related Questions
Total Price: The sales tax rate is 8%. If the sales tax on a 10-speed bicycle is $12, what is the purchase price? The purchase price is $ What is the total price? The total price is $ Get Help: Video eBook Points possible: 1
Answers
Answer:
Purchase Price = $150 and Total Price = $162
Step-by-step explanation:
Purchase price = Tax Amount / Tax Percentage (as decimal)
Purchase Price = $12 / .08
Purchase Price = $150
Total Price = Purchase Price + Tax
Total Price = 150 + 12 = $162
I hope this helps!
-The Business Man
The number 0.2 can be written as 2/10, so is it a rational number?
Answers
Answer:
yes it is
Step-by-step explanation:
Hope this helps✨
Is (1,9) a solution to this system of
equations?
y = x + 6
y = 2x + 7?
Answers
Answer:
No, the solution of the system is (-1,5)
iff(x) = (x - 3)2
for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3
Answers
Answer:
Option B. √x + 3
Step-by-step explanation:
f(x) = (x - 3)²
We can obtain the inverse f¯¹(x) of the above expression as follow:
f(x) = (x - 3)²
Replace f(x) with
f(x) = (x - 3)²
y = (x - 3)²
Next, interchange x and y
y = (x - 3)²
x = (y - 3)²
Make y the subject
x = (y - 3)²
Take the square root of both side
√x = y - 3
Add 3 to both side
√x + 3 = y - 3 +3
√x + 3 = y
y = √x + 3
Finally, replace y with f¯¹(x)
y = √x + 3
f¯¹(x) = √x + 3
Solve a combined inequality that is a conjunction of two linear equalities.
1.) solve for n. -1<9+n<17
2.) solve for x. -2<8x-12<_36
Answers
Answer:
-10 < n < 85/4 < x ≤ 6Step-by-step explanation:
1. Subtract 9:
-10 < n < 8
__
2. Add 12, then divide by 8:
10 < 8x ≤ 48
10/8 < x ≤ 6
5/4 < x ≤ 6 . . . . . with the fraction reduced
_____
The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...
-1 -9 < 9 +n -9 < 17 -9
This simplifies to the inequality we show above:
-10 < n < 8
If y = 3. what is 6y?
Answers
Your question has been heard loud and clear.
If y = 3 , then 6y = 6(3) = 18
Thank you
Andy painted 400 square feet in 3 hours. At that rate, how many cars could they wash in 7 hours? *
Answers
Answer:
It will take 5.4 hour to paint 720 square feet
Step-by-step explanation:
The question should be like this"Andy painted 400 square feet in 3 hours. How long would it take him to paint 720 square feet?"
In 3 hours = 400 square feet is painted
1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]
To find time to paint 720 square feet multiply the above term by 720 as follows :
[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]
So, it will take 5.4 hour to paint 720 square feet.
Please help me with the question below
Answers
Answer:
She's 12 years old! i hope this helps you!
Step-by-step explanation:
August 22 3months later what day would it be
Answers
3 Months later would be November 22
why is 5.1 a rational number
Answers
Answer:
5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number
Step-by-step explanation:
Recall that a rational number is a number that can be written as the quotient of two integer numbers.
In particular the number 5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number.
2. Metcalf School has two third-grade rooms (A and B) and two fourth-grade rooms
(C and D). Together, rooms C and D have 46 students. Room A has 6 more students
than room D. Room B has 2 fewer students than room C. Room D has 22 students.
How many students are there altogether in rooms A and B?
Answers
Answer: 50 students
Step-by-step explanation: Room D has 22 students, so room A has 28 (22+6). If room D has 22 students, then room C has 24 students (46-22). Room B has 22 students (26-2). In total, rooms A and B will have 50 students (28+22)
The Tigers had twice as many hits as the yanks.Let x= number of hits by yanks.Then ?= number of hits by tigers
Answers
Answer:
2x
Step-by-step explanation:
Since the tigers hit 2 times the number of x you would get that the tigers hit 2 times x or 2x balls
Answer:
2x.
hope it helps u...
plz mark as brainliest...
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $28 monthly fee and charges an additional
$0.09 for each minute of calls. The second plan has no monthly fee but charges $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answers
Answer:
700 Minutes
Step-by-step explanation:
For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.
For the first phone plan, we have a base $28 and additional $0.09 per minute of call. This can be expressed as:
28 + 0.09x Where x is the number of minutes used
For the second phone plan, we have a flat $0.13 per minute of call. This can be expressed as:
0.13x Where x is the number of minutes used
To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.
28 + 0.09x = 0.13x
28 + 0.09x + -0.09x = 0.13x + -0.09x
28 = 0.04x
28 = (1/25)x
28 * 25 = (1/25)x * 25
28 * 25 = x
700 = x
Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.
Cheers.
Alana noticed that a number like 8 = 2 (i.e. ) has exactly four factors: 1, 2, 2 , and ! 2 . What other numbers are of this form have exactly four factors? Do all the perfect cubes have exactly four factors? Is it true that all numbers that have exactly four factors are perfect cubes?
Answers
Answer:
Step-by-step explanation:
Hello,
What other numbers are of this form have exactly four factors?
[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]
Do all the perfect cubes have exactly four factors?
[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
Thank you.
We know that any number can be decomposed as a product of prime numbers.
For example:
[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]
8 has four factors if we count the 1.
Now we need to answer some questions regarding this:
What other numbers are of this form have exactly four factors?
8 is a cube number.
Remember that all cube numbers X can be written as:
[tex]X = n\cdot n\cdot n \cdot 1[/tex]
Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.
But let's see the case:
[tex]8\cdot 8\cdot8= 512[/tex]
512 is a perfect cube, and if we decompose it we get:
[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]
So we found a perfect cube that has 10 factors.
This means that not all perfect cubes have exactly 4 factors.
Now, all numbers that have exactly four factors are perfect cubes?
This is also false, just let's create a counterexample.
[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]
the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.
If you want to learn more, you can read:
https://brainly.com/question/832797
Which number sentence shows the correct placement of the decimal point in the product based on the two factors A: 3.48 x 42.37 = 147.4476 B: 23.2 x 8.8 = 20.416 C: 0.39 x 7.2 = 28.08 D: 43.72 x 9.2 = 4,022.24 I NEED ANSWERS ASAP
Answers
Answer:
A
Step-by-step explanation:
Add the number of decimal places of the two numbers being multiplied to know the number of decimal places of the product.
A: 3.48 x 42.37 = 147.4476
2 decimal places + 2 decimal places = 4 decimal places
Only choice A is correct.
What’s is 2000+100.000
Answers
Answer:
2,100.000
Step-by-step explanation:
Answer:
2000+100.000=2100
Its simple just calculate it in a calculator...
Merlyn had 22 magic tricks to perform. He had completed 4/5 of them when the fire alarm sounded. How many magic tricks had he performed?
Answers
Answer:
Merlyn realizo 17,6 trucos de magia
Step-by-step explanatio:
Hizo 17,6 trucos de magia porque 22 dividido 5 es igual a 4,4 entonces despues haces 22 menos 4,4 da 17,6
What is the standard form equation of the line shown below?
5
4
3
2 +
o
+ +
3 4
2
5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-6
Answers
Consider the following time series: t12345 6 11 9 14 15 a. Construct a time series plot. What type of pattern exists in the data
Answers
Answer:
Kindly check explanation and attached picture
Step-by-step explanation:
Given the time-series data:
Time (x) : 1 - - 2 - - 3 - - - 4 - - - 5
Data (yt) :6 - - 11 - - 9 - - 14 - - 15
The pattern which exists within the data is a linear pattern which could be inferred through the observable decrement and Incremental change in the y values at a steady or constant rate with time. The second attachment shows the linear trend line of the data.
A woman making $3000 per month has her salary reduced by 20% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise. $ per month What percent change is this from the $3000 per month? %
Answers
Answer:
4%
Step-by-step explanation:
Since she first goes down 20% you would do 3000 times 20 which is 60000 and divided by 100 which is 600 and you would subtract 600 from 3000 which is 2400 and then you would multiply that by 30 which is 72000 and then you would divide by 100 which is 720 and add that to 2400 which is 3120 and to find the percent change from 3000 to 3120 you would subtract 3120 by 3000 which is 120 and you would divide that by 3000 which is 0.04 and multiply that by 100 which is 4 so the percent change would be 4%
Find the intercepts for this equation. x+2y=10
Answers
Answer:
Step-by-step explanation:
y= 0
x + 2(0) = 10
x = 10
(10, 0)
x = 0
0 + 2y = 10
2y = 10
y = 5
(0,5)
Solve the following linear equation. If a x is a fraction write as follows
-4/5
-6x+3=-21
X =
Answers
Answer:
x-5
Step-by-step explanation:
x=5
cause of the negt 6x and posstive 3 =21 so yeah that it for now so go for it head froce
$10.00 divided by 25
Answers
Explanation:
10/25 = 0.4$
Check:
25 x 0.4 = 10$
Therefore, 10$ divide by 25 is 0.4$
A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.
Answers
Answer: yes
Step-by-step explanation: 8^2+15^2=17^2 =289 and 17^2=289 ... 17 is the largest number so therefore its the largest side(c) .
equation- a+b=c
The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.
Answers
Answer:
7.5 seconds
Step-by-step explanation:
[tex]h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}[/tex]
Thus, the time required for the object to return to its point of departure is 7.5 seconds.
Solve equation. What is the solution set
-4(z-2)+4=21-(z-3)
Answers
Answer:
z=-75/17
Step-by-step explanation:
Expand this equation:
-4z+8+4=-21z-63
-4z+21z=-63-8-4
17z=-75
z=-75/17
What is the equation of the line that passes through the points (- 2, 3) and (4, 1)
Answers
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex]
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = ((- 2, 3) and (x₂, y₂ ) = (4, 1)
m = [tex]\frac{1-3}{4+2}[/tex] = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/tex] , thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3), then
3 = [tex]\frac{2}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex] ← equation of line
In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.
a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )
b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.
c. How would the manager of a chain of restaurants use the results of (a) and (b)?
Answers
Answer:
a
[tex]0.716 < p < 0.744[/tex]
b
[tex]0.3498 < p < 0.4089[/tex]
c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1003[/tex]
The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]
The number that complained about loud or distracting diners at other tables is [tex]q = 381[/tex]
Given that the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
The sample proportion is mathematically represented as
[tex]\r p = \frac{e}{n}[/tex]
=> [tex]\r p = \frac{732}{1003}[/tex]
=> [tex]\r p = 0.73[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]
[tex]E = 0.01402[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]
[tex]0.716 < p < 0.744[/tex]
Considering question b
The sample proportion is mathematically represented as
[tex]\r p = \frac{q}{n}[/tex]
=> [tex]\r p = \frac{381}{1003}[/tex]
=> [tex]\r p = 0.3799[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]
[tex]E = 0.0300[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]
[tex]0.3498 < p < 0.4089[/tex]
Simplify using like terms
1.7 + 8.23 -3.4 +4.7j
Answers
Step-by-step explanation:
Let's look at our expression:
[tex]1.7+8.23-3.4+4.7j[/tex]
The numbers without a variable at the end are like terms here. Let's add them up.
[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]
Then, let's add our answer, 6.53, to the term with a variable, 4.7j.
Our final answer: 6.53 + 4.7j
I hope this helps you!
Margaret is going to paint a wall that 'is 8 feet high and 15 feet long. How many square feet will she be covering with paint?
Answers
Answer:
120 ft²
Step-by-step explanation:
the question is asking for the area of the wall, which we have been given.
8 ft high by 15 ft wide.
Area of a rectangle is length multiplied by breadth.
so, the area is 8 * 15 = 120 ft²