Find the domain PLEASE HELP
The domain of this function is all the real numbers except - 7 / 3 and 23 / 3.
What is the domain of a function?
In accordance with function theory, the domain of a function is a set of x-values such that y-values exist. Herein we find that the given function is a rational function whose denominator includes an absolute value function. The numerator is a linear equation.
Therefore, the domain of the function is all real numbers except those x-values such that denominator is equal to zero. We need to solve the following expression in two cases:
|3 · x - 15| = 8
For x ≥ 5:
3 · x - 15 = 8
3 · x = 23
x = 23 / 3
For x < 5:
- 3 · x + 15 = 8
- 3 · x = - 7
x = - 7 / 3
Then, the domain of this function is all the real numbers except - 7 / 3 and 23 / 3.
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BD bisects AC at point E. if AE is 2x²- 8 and AC is 5x^2-25
find the length of EC
The length of EC will be 154 units.
We have the data that:
BD is the bisector of AC at point E.
This means that AE = EC
Also, AE + EC = AC
AE + AE = AC
2 AE = AC
Now,
AE = 2x² - 8 and AC is 5x² - 25
Substituting the values, we get that:
2 (2x² - 8) = 5x² - 25
4x² - 16 = 5x² - 25
5 x² - 4 x² = 25 - 16
x² = 9
x = 3 ( as length cannot be negative)
AE = EC = 2x² - 8
EC = 2 (9)² - 8
EC = 162 - 8
EC = 154 units.
Therefore, we get that, the length of EC will be 154 units.
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The difference of four times a number and seven is ten more than the number
The number is 5.67
Let the number be 'x'
The difference of four times a number and seven = 4x - 7
Ten more than the number = 10 + x
According to the condition given in the question,
The difference between four times a number and seven is equal to ten more than the number.
4x - 7 = 10 + x
4x - x = 10 + 7
3x = 17
x = 17/3 = 5.67
We can verify the answer,
Consider the LHS,
=> 4x - 7 = 4(5.67) - 7 = 22.68 - 7 = 15.68
Consider the RHS,
=> 10 + x = 5.67 + 10 = 15.67
Both LHS and RHS are equal.
Therefore the number that satisfies the given condition is 5.67
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describe a real world situation where you can apply finding the unit rate
The unit rate problem is discussed above and the unit rate of speed according to problem is 50 kilometers per hour.
What is the unit rate method ?
The unit rate method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The real world situation can be as follows ;
A police officer who believes you were speeding stops you. You say that it took you exactly seven hours to travel 350 kilometers across the state. To determine if you were over speeding, the policeman must perform the necessary calculations. He requires to find out the unit rate.
Let's solve it to find out that at what unit rate of speed you were travelling.
We know that unit rate meant we need to find out the distance we have travelled in 1 hour.
So,
Unit speed = 350 / 7 km per hour
or
Unit speed = 50 kilometers per hour
Police man will check with the limit of speed and if he find that you were not over speeding , then he would allow you to go further.
Therefore , the unit rate problem is discussed above and the unit rate of speed according to problem is 50 kilometers per hour.
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Only if you are sure, please :')
Answer:
Option D) 6.8 × 10⁻²
Answer:
D
Step-by-step explanation:
3x^2+7-6+1+3+7 add , sub, mult, what is the answer
Answer:
If just combining like terms: 3x^2 + 12
If solving for x: 2i, -2i
Step-by-step explanation: Combine like terms, so 3x^2 + 12 = 0; move the 12 to the other side by subtracting (3x^2 = -12), then divide both sides by 3, which gives x^2 = -4. Then get the square root of both sides to cancel out the power on the x. Since -4 is negative, use imaginary numbers, which makes x = 2i and x = -2i
Input
0
1
6
Output = Input x Itself + (-5) Output
95
59
76
We are given a table for input and output values and the relation between them.
Consider the table,
Input Output = Input × itself + (-5) Output
0
1
6
95
59
76
For Input = 0 :
Output = Input × itself + (-5)
Output = 0 × 0 - 5
Output = -5
Now, for Input = 1,
Output = Input x Itself + (-5)
Output = (1) × 1 + (-5)
Output = 1 - 5
Output = - 4
For Input = 6,
Output = Input x Itself + (-5)
Output = (6) × 6 + (-5)
Output = 36 - 5
Output = 31
For Output = 95,
Output = Input x Itself + (-5)
95 = (Input)²+ (-5)
95 + 5 = (Input)²
(Input)² = 100
Input = √100
Input = 10
For Output = 59,
Output = Input x Itself + (-5)
59 = (Input)²+ (-5)
59 + 5 = (Input)²
(Input)² = 64
Input = √64
Input = 8
For Output = 76,
Output = Input x Itself + (-5)
76 = (Input)²+ (-5)
76 + 5 = (Input)²
(Input)² = 81
Input = √81
Input = 9
Therefore the complete table will be:
Input Output = Input × itself + (-5) Output
0 Output = 0 × 0 + (-5) -5
1 Output = 1 × 1 + (-5) -4
6 Output = 6 × 6 + (-5) 31
10 95 = Input × itself + (-5) 95
8 59 = Input x Itself + (-5) 59
9 76 = Input x Itself + (-5) 76
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Let f(x) = [tex]3x\sqrt{2-4x}[/tex].
Find the equation of line tangent to the graph of f at x = -2.
Tangent line: y = ?
the linear equation tangent at x = -2 is:
y = 123.33*x + 226.74
How to find the equation of the tangent line?To get the slope of the line we need to evaluate the first derivative in x = -2, we get:
f'(x) = 3√(2 - 4x) + (-12/2)*3x*(2 - 4x)^(-1/2)
Evaluating in x = -2 we get:
f'(-2) = 3√(2 - 4*-2) + (-12/2)*3*-2*(2 - 4*-2)^(-1/2) = 123.33
Then the line is something like:
y = 123.33*x + b
And the line must pass through:
f(-2) = 3*(-2)*√(2 - 4*(-2)) = -18.97
So the line must pass through the point (-2, -18.97)
Replacing that in the linear equation:
-18.97 = 123.33*2 + b
-19.92 + 123.33*2 = b = 226.74
Then we conclude that the linear equation tangent at x = -2 is:
y = 123.33*x + 226.74
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Part C
Which investment would you choose if you were Sam or Julia?
In two to three sentences, state your choice of investment and the reasoning for your decision using concepts you've
learned in this lesson.
Answer:
i would choose investment A
Step-by-step explanation:
A is simply the best anwser choice
Answer:
If I were Sam, I would buy the bond with a 3% interest rate since selling at any time is not a priority. The bond would provide a steady income from the investment, which is what he his needing.If I were Julia, I would invest in the stock, which has long-term growth potential. This would allow her to sell the investment at any time in the future.
Step-by-step explanation:
SAMPLE ANSWER!!!
I. Resuelve el siguiente sistema por el método de eliminación
(7x - 3y = 27
5x + y = 35
[tex]5x+y=35 \implies 15x+3y=105 \\ \\ \implies (15x+3y)+(7x-3y)=105+27 \\ \\ 22x=132 \\ \\ \boxed{x=6} \implies 7(6)-3y=27 \\ \\ -3y=-15 \\ \\ \boxed{y=5}[/tex]
The following trial balance of Reese Corp. at December 31, 2014 has been properly adjusted except for the income tax expense adjustment. Reese Corp. Trial Balance December 31, 2014 Dr. Cr. Cash $ 775,000 Accounts receivable (net) 2,695,000 Inventory 2,085,000 Property, plant, and equipment (net) 7,566,000 Accounts payable and accrued liabilities $ 1,701,000 Income taxes payable 654,000 Deferred income tax liability 85,000 Common stock 2,350,000 Additional paid-in capital 3,680,000 Retained earnings, 1/1/14 3,450,000 Net sales and other revenues 13,560,000 Costs and expenses 11,180,000 Income tax expenses 1,179,000 $25,480,000 $25,480,000 07. The current assets total is: A. $6,080,000 C. $5,405,000 B. $5,555,000 D. $4,955,000
Based on the balances in Reese Corp's trial balance, the current assets total can be found to be B. $5,555,000
What is the total current assets?The total of the current assets can be found by the formula:
= Inventory + Accounts Receivable + Cash
Solving then gives:
= 775,000 + 2,695,000 + 2,085,000
= $5,555,000
In conclusion, the current assets for Reese Corp is $5,555,000 .
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−13,9,9,−13,5,−13,9
Calculate the value of the sample standard deviation. Round your answer to one decimal place.
Step-by-step explanation:
first we need the mean value. this is the sum of all data points divided by the number of data points :
(3×9 + 5 - 3×13)/7 = -7/7 = -1
next, for the standard deviation, we need to sum the squares of the differences of the data points to the mean value, divide that by the number of data points again, and then pull the square root :
(3(-13 - -1)² + 3(9 - -1)² + (5 - -1)²)/7 =
= (3×196 + 3×100 + 36)/7 = (588 + 300 + 36)/7 =
= 924/7 = 132
the standard deviation is now the square root of 132 :
sqrt(132) = 11.48912529... ≈ 11.5
so, yes, as we can see, the numbers vary/deviate rather strongly from the mean value.
please help
please hurry
Answer:
-22 I arrived as fast as I could
Simplify the expression
(-3m to the 2) x (-5m to the 7)
Explain your process and justify each step by naming the appropriate property.
Answer:
15m⁹
Step-by-step explanation:
-3m² × -5m⁷ multiply bases (-3×-5=15). when multiplying bases you add exponents (2+7=9)
= 15m⁹
please help with geometry problem
The value of the x in the given geometry figure is 108° .
When 2 lines ran into one another, then the other angles, shaped thanks to intersection are referred to as vertical angles or vertically opposite angles. A try of vertically opposite angles are invariably capable one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to one hundred eighty degrees.When 2 lines ran into, four angles are shaped. There are 2 pairs of distant angles. These pairs are referred to as vertical angles.Vertical angles are a try of non-adjacent angles shaped by the intersection of 2 straight lines. In straightforward words, vertical angles are set across from each other within the corners of the "X" shaped by 2 straight lines. they're conjointly referred to as vertically opposite angles as they're settled opposite to every alternative.The labelled diagram of the figure is given below.
From the figure , we can see that ∠OEA = ∠BOF as they are vertically opposite angles .
Hence ∠BOF = x
∠OFT and ∠BOF are linear pair , so on adding them , we will get sum 180°
∠OFT + ∠BOF = 180°
72° + x = 180°
x = 108°
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Answer:
x° = 22°
Step-by-step explanation:
You want the measure of the angle marked x° in the figure with two parallel lines and a "bent" transversal.
Remote interior anglesExtending the upward-sloping line in the figure as shown in the attachment results in a triangle against the top horizontal line.
The angle on the right side of that triangle corresponds to the one marked 50°, so has the same measure. It is one of two "remote interior angles" whose sum is the measure of the exterior angle marked 72°. The other "remote interior angle" making up that sum is the vertical angle to the one marked x°.
So, we have ...
x° +50° = 72°
x° = 22° . . . . . . . . subtract 50°
__
Additional comment
You can do a "sanity check" on this answer by considering some extreme cases. If the 72° angle is reduced to 50°, the top leg of the "72°" angle would be horizontal. That would effectively reduce x to 0. Similarly, if the 72° angle were made to be 180°, then the value of x would be supplementary to the 50° angle. In other words, x is the difference between the one marked 72° and 50°, or 22°.
Aubrey has 64 m of fencingEli has 44 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 120 square meters. Solve for the dimensions (length and width) of the field. to build a four-sided fence around a rectangular plot of land. The area of the land is 255 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the rectangular field with area 120 square meters is 10 meters by 12 meters.
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given perimeter of the rectangular plot is 44 meters.
let the length is x , and width = y
Therefore perimeter = 2 (x + y)
or, 2 (x + y) = 44
or, x + y = 22
or, y = 22 - x
Now the area of the field is given as 120 square meters.
Area of the fields in terms of x is given by:
x ( 22 - x ) = 22 x - x²
Therefore 22 x - x² = 120
or, x² -22x +120 = 0
or, x² - 10x - 12x + 120 = 0
or, x (x -10) -12(x-10)=0
or, (x-10)(x-12) = 0
Now either the value of x is 10m or the value of x is 12m
Therefore the dimensions of the rectangular field is 10 meters by 12 meters.
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Four brothers have ages that are consecutive even integers. From youngest to oldest, their names are Matt, Pat, Dave, and Dan. If Dan's age is 36 years less than twice Pat's age, then what are the ages of all four brothers?
Answer:
Matt is 38, Pat is 40, Dave is 42 and Dan is 44.
Step-by-step explanation:
Let Matt's age be x.
Then Pat is x + 2, Dave is x + 4 and Dan is x + 6.
Dan's age is 36 years less than twice Pat's age:
x + 6 = 2(x + 2) - 36Solve it for x:
x + 6 = 2x + 4 - 36x + 6 = 2x - 322x - x= 6 + 32x = 38So Matt is 38, Pat is 40, Dave is 42 and Dan is 44.
Multiply the numbers.
Answer:
[tex] \: \: \: \: \: { \rm{2 \: \: \: 3 \: \: \: 4}} \\ { \underline{ \times \: \: 0. \: \: 3 \: \: 5}} \\ { \rm{ 1 \: \: 1 \: \: 7\: \: 0}} \\ { \underline{ + 7\: \: 0\: \: 2 \: \: 0 }} \\ { \underline{ \: \boxed{ 8\: \: 1 \: .\: \: 9 \: \: 0}}}[/tex]
Answer: 81.9
Help me am I correct?
Answer: Yes
Step-by-step explanation:
All you had/have to do is 19-11 and get 8
Answer:
Yes, you're correct.
Step-by-step explanation:
Because since the bases are the same you can set the exponents equal. Then move the constant to the right hand side and it changes the sign. Then you calculate the difference. Finally you change the signs on both sides of the equation. x = 8
If the price of gas was on average $3.20 per gallon, and this was $1.43 cheaper than a year before, what is the percent of decrease in price? (Round to the nearest percent.)
Based on the current price of gas per gallon, and the fact that it was cheaper the year before, the percent decrease in price is 31%
How to find the percentage decrease?First, find the price of gas last year:
=Current price of gas + Decrease in price
= 3.20 + 1.43
= $4.63
The percent of decrease in price can be found by the formula:
= Change in gas price / Price of gas last year x 100%
= 1.43 / 4.63 x 100%
= 0.30885529157667386609071274298056 x 100%
= 31%
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Y= |x-1|-5 find points and graph
Step-by-step explanation:
(-4,0)
(0, -4)
(1, -5)
(6, 0)
A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
[tex]\stackrel{\textit{\LARGE sides}}{\cfrac{x}{2}+(x-5)+(x-2)~}~ = ~~13\implies \cfrac{x}{2}+2x-7=13 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{x}{2}+2x-7 \right)=2(13)}\implies x+4x-14=26\implies 5x-14=26 \\\\\\ 5x=40\implies x=\cfrac{40}{5}\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(8)}{2}\implies 4\hspace{5em}(8)-5\implies 3\hspace{5em}\underset{Longest}{(8)-2\implies 6}[/tex]
18 acres of land is for sale at $11001.
What is the cost per acre?
Answer in units of dollars/acre.
Answer:
$611.17 per acre
Step-by-step explanation:
11001 ÷ 18 = 611.16666...
So, the answer is an infinite decimal, so we round it to the nearest hundredth.
-29/36 - 3/4 equals to what?
Louisa made a purchase at her local convenience store for $6.65. She wanted to use up her change so she used
quarters and dimes to pay the clerk. If she used a total of 29 coins, how many fewer dimes than quarters did she
use?
Louisa used Number
fewer dimes.
Answer:
25 quarters and 4 dimes. Louisa used 21 more quarters than she did dimes.
Step-by-step explanation:
q=number of quarters
d=number of dimes
6.65=.25q+.10d 6.65 (the total) is equivalent to the amount of quarters times .25 (the value of a quarter) plus the amount of dimes times .10 (the value of a dime)
Now divide 6.65 by .25.
26 quarters can be used.
26 times .25 = 6.50
26 quarters is $6.50
29-26=3
3 times .10 = .30
.30+6.50=6.80
This is too much. Let's try taking off one quarter.
Now we have 25 quarters. .25 times 25 = 6.25
29-25=4 (This means there will be 4 dimes if she used 25 quarters, but let's see)
4 times .10 = .40
.40 + 6.25=6.65
6.65 is the total amount she had to pay, so we did it. Solving this showed us that she used 25 quarters and 4 dimes. This equals $6.65, the amount she paid, uses only quarters and dimes, and uses a total of 29 coins.
I hope this helps you! Please mark as Brainliest answer! I worked really hard to type all of this out for you.
True or False: If x > y, then |x| < |y|
Answer:
False
Step-by-step explanation:
This applies perfectly when x and y are negative.
What if both x and y are positive??
x=4, y=3.
4>3 which is true
but |4|<|3| = 4<3 ==> not true.
Hence, the answer is false
find the measures of the labeled angles :)
3x =
second answer =
simplified =
please help im struggling !! this is my last question :) ill mark brainliest
Answer: 54
Step-by-step explanation:
3x=72-x ==> 3x and 72-x are both congruent angles, so they're equal
3x+x=72-x+x
4x=72
x=18
3x=
3(18)=54 degrees
When the width of the map on his phone represents an actual distance of 400 feet, the length of Peninsula Park on his phone is 1.2 inches. Joshua changes the zoom on the map so that the width of the map on his phone represents an actual distance of 300 feet instead. What is the length of Peninsula park on his phone, in inches, on the new map?
Answer:
.9 inches
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{1.2}{400} = \frac{x}{300} [/tex]
[tex]400x = 360[/tex]
[tex]x = .9[/tex]
Rosa has 3 3/5 pounds of dough. She uses 3/4 of a pound for one large roll. How many large rolls could be made from rosa's dough
The number of large rolls that could be made from Rosa's dough is 4 numbers.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of large rolls that can be made from Rosa's dough, hence:
(3/4)x = 3 3/5
(3/4)x = 18/5
x = 4.8
The number of large rolls that could be made from Rosa's dough is 4 numbers.
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
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Find the unit rate.
1¹/2 =
4
[?]
1
Answer:
[tex]\frac{12}{4} = \frac{3}{1}[/tex]
Step-by-step explanation:
[tex]\frac{12\div4}{4\div4}=\frac{3}{1}[/tex]
Hope this helps!
Answer:
12 = 3
4 1
Step-by-step explanation:
hope the helps
