You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression
What is an extraneous solution?
An extraneous solution is a solution that in obtained after completely solving an equation but it does not work in the original given equation.
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression (Option D).
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2.
janine is building a box with a height of 10 inches. the rectangular base of her box will have a perimeter of 72 inches.
select the equation where v represents the volume of the box and wrepresents the width of the base of the box.
a. v= -20w^2 + 720w
b. v=-10w^2 + 360w
c. v= -100w^2 +3,600w
d. v=-10w^2 + 720w
The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let w represent the width of the box and v represents the volume, hence:
2(w + length) = 72
Length = 36 - w
Volume = w(36 - w) * 10
Volume = 360w - 10w²
The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²
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Three multiplied by the sum of 4 and a number is the same as 18 more than the number. Find the number.
If n is "the Bumber," which equation could be used to solve for the number?
Answer:
3(4 + n) = n + 18
n = 3
Step-by-step explanation:
because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.
PLEASE HELP ME PICTURE BELOW!!!
Answer:
corographicia
Step-by-step explanation:
its the right answer
jeanne barrons has decided to buy a new car. it has a base price of
$21,276.00, options totaling $1,219.80 and a destination charge of $590.00.
while surfing the internet, she learned that the dealer's cost is
approximately 83% of the base price and 80% of the price of the options.
what should barrons estimate as the dealer's cost? (section 9-2) *
o a. $19,224.92
b. $17,659.09
c. $17,500.25
d. $19,430.84
Answer:
a. $19,224.92
Step-by-step explanation:
The dealer's cost will be the sum of the dealer's costs for the base car, its options, and the destination charge.
__
cost for base car = 0.83 × $21,276 = $17,659.08
cost for options = 0.80 × $1,219.80 = $975.84
cost for destination charge = $590.00
The sum of the dealer's costs is ...
$17,659.08 +975.84 +590.00 = $19,224.92
Barrons should estimate the dealer's cost to be $19,224.92.
Write the equation of the line that passes through (4, 2) and is parallel to the line y = 2x – 1.
Answer:
Step-by-step explanation:
We will look for a line that has the general form of y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).
A line parallel to y=2x-1 will have the same slope, 2.
We can write y = 2x + b for the new line. We need to find b. We can use the given point in this equation and solve for b:
y = 2x + b
2 = 2(4) + b for (4,2)
2 = 8 + b
x = -6
The parallel line to y=2x-1 that goes through point (4,2) is:
y = 2x-6
See the attached graph.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write the equation of the line that passes through (4, 2) and is parallel to y=2x-1.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Parallel lines have the same slope.Since the slope of the given line is 2, the slope of the line parallel to this one is also 2.
Now, figure out the y-intercept, c:y=2x+c
We're given a point: (4, 2).Where: 2 is the y-coordinate of the point, and 4 is the x-coordinate.
Now, substitute 2 for y and 4 for x:
[tex]\longmapsto\sf{2=2(4)+c}[/tex]
Simplify!
[tex]\longmapsto\sf{2=8+c}[/tex]
Subtract 8 from both sides of the equal sign:
[tex]\longmapsto\sf{2-8=c}[/tex]
[tex]\longmapsto\sf{-6=c}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
does someone mind helping me with this question? Thank you!
Please help! check attachment. This is grade 11 trigonometry
[tex]~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan B = \dfrac{AC}{BC}\\\\\\\implies \tan 40^{\circ} = \dfrac{10}{a}\\\\\\\implies a = \dfrac{10}{\tan 40^{\circ}}\\\\\\\implies a= 11.9~ m[/tex]
A weather forecast predicts that for each day from Monday to Friday this week, there is a $40\%$ chance of sun, a $25\%$ chance of getting 4 inches of rain, and a $35\%$ chance of getting 10 inches of rain. What is the expected value of the total number of inches of rain which will fall from Monday to Friday
Step-by-step explanation:
correct u know jsjsjsjsjajajaj shahha hshshs hsgshs hshshs hshshs hzhsvs hsvzvshsvss hshshs hshshs hshsh hshs
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
#1 evaluates to 2
#2 evaluates to 0
#3 evaluates to 10
#4 evaluates to 6
code is HIEA
Please I need HELP!!!!!!
Answer:
I just need points I don't know your answer
Step-by-step explanation:
At a basketball game, 45% of people attending were supporting the home team, while 55% were supporting the visiting team. If 1413 people attending the game supported the home team, what was the total number of people attending the game?
divide the number of people supporting the home team by the percentage supporting the home team.
1413/0.45 = 3140
total people = 3,140
The total number of people attending the basketball game was 3140.
Let's denote the total number of people attending the game as "T."
According to the information given, 45% of the people were supporting the home team. Therefore, the number of people supporting the home team can be calculated as 45% of the total number of people: 0.45 * T.
We are also told that 1413 people supported the home team. So, we can write the equation:
0.45 * T = 1413
Now, let's solve for the total number of people attending the game (T):
T = 1413 / 0.45
T = 3140
Therefore, the total number of people attending the basketball game was 3140.
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The band is raising money for their spring trip. they need to raise at
least $1500. earlier in the year, they made $575 on their annual fruit sale.
now they are selling donuts, where they will earn $5 profit for each box
of donuts they sell. which inequality could be used in order to
determine the number of boxes of donuts, d, they must sell in order to
meet their goal?
The inequality that can be used to determine the number of boxes of donuts, d, they must sell in order to meet their goal is $1500 ≥ $575 + $5d.
What is the inequality?Here are inequality signs and what they denote:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toTotal amount that needs to be raised ≥ amount made at the fruit sale + (profit per box x number of boxes)
$1500 ≥ $575 + $5d
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what is 2 1/4 - 5 2/3
Answer:
-41/12 or -3 5/12
Step-by-step explanation:
4*2 +1 = 9, 5 * 3 + 2 = 17
9/4 - 17/3
27/12 - 68/12
= -41/12 or -3 5/12
What is DE?
Enter your answer as a decimal in the box.
2/3 b + 5 =20 - b solve for b
Answer:
b = 9
Step-by-step explanation:
[tex]\frac{2}{3} b + 5 = 20-b\\\frac{2}{3} b+5+b=20-b+b\\\frac{5}{3} b+5=20\\\frac{5}{3} b+5-5=20-5\\\frac{5}{3}b=15\\b= 15*\frac{3}{5} \\b= 9[/tex]
Answer:
[tex]b = 9[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} b + 5 = 20 - b[/tex]
In order to solve for b, we must isolate the variable. We can start by subtracting 5 from both sides.
[tex]\frac{2}{3} b + 5 - 5 = 20 - b - 5[/tex]
Simplify.
[tex]\frac{2}{3} b = 15 - b[/tex]
Add b to both sides.
[tex]\frac{2}{3} b + b = 15 - b + b[/tex]
Simplify.
[tex]\frac{2}{3} b + b = 15[/tex]
Multiply everything by 3 to remove the fractions.
[tex]3(\frac{2}{3}b+b) = 3(15)[/tex]
Simplify.
2b + 3b = 45
Simplify.
5b = 45
Divide 5 from both sides.
5b ÷ 5 = 45 ÷ 5
Simplify.
b = 9
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https://brainly.com/question/633344https://brainly.com/question/1267151https://brainly.com/question/4207498Find the function of (0,6), (3,15.8) and (9.5,0)
The polynomic function that contains the points (0, 6), (3, 15.8) and (9.5, 0) is a quadratic function, whose model is y = -0.600 · x² + 5.066 · x + 6.
How to derive a polynomic function from given points
To determine the coefficients of a polynomic function we must know a set of distinct points, whose number is the same number of coefficients. In this case, we can derive a quadratic function, as quadratic functions have three coefficients:
y = a · x² + b · x + c (1)
Now we substitute x and y in (1) and solve the resulting system of linear equations:
c = 6
9 · a + 3 · b + c = 15.8
90.25 · a + 9.5 · b + c = 0
Whose solution is a ≈ -0.600, b ≈ 5.066 and c = 6.
Remark
The statement is incomplete. The complete form is shown below:
There is a polynomial function. Find the function of (0, 6), (3, 15.8) and (9.5, 0).
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Which is the graph of f(x) = 2(3)x?
Answer:
Step-by-step explanation:
Please Help I Don't Undertand.
If triangles AMN and ABC are similar, then
AM/AB = AN/AC
or
AM/(AM + MB) = AN/(AN + NC)
Check if this is true:
AM/AB = 21/(21 + 9) = 21/30 = 7/10
AN/AC = 14/(14 + 6) = 14/20 = 7/10
The angle at vertex A is common to both of the triangles.
Then by the side-angle-side (SAS) similarity theorem, the triangles are indeed similar.
Factor the algebraic expression.
18a+15
Answer: 3(6a+5)
We can confirm this by distributing the 3 back in
3*6a = 18a
3*5 = 15
So 3(6a+5) = 3*6a+3*5 = 18a+15
The process of factoring polynomials like this is basically using the distributive property in reverse.
Answer:
3(6a + 5)
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into 18a and 15?
It is 3.
2 - What is the highest degree of a that divides evenly into 18a and 15.
It is 1, since a s not in every term.
3 - Multiplying the results above,
The GCF is 3.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
3 (18a/3 + 15/3)
3) Simplify each term in parentheses.
3(6a + 5)
__•__=42
__+__=23
Can someone help me solve this?
Answer:
21 * 2 = 42
21 + 2 = 23
Step-by-step explanation:
well I know that 6 * 7 = 42 so I’m assuming that’s correct
Then 11 + 12 = 23 it could be the answer I’m not positive for this one though.
The first one should be correct.
Maybe try
21 * 2 = 42
21 + 2 = 23
X+17=38 which property is included in the justification for the steps used to solve the equation?
Looking at the problem statement, the question is asking for us to determine the justification for the steps that are used to help solve the equation. We are given the expression [tex]x + 17 = 38[/tex] to help achieve that goal.
Now that we know what we must do to finish this problem let us look how this equation can be solved. When the term solve the equation is used it refers to us solving for the unknown, in this case being the variable x. We can see that we have [tex]x + 17[/tex] on the left side and in order to solve the equation x must be alone so we would subtract 17 from both sides.
Subtract 17 from both sides
[tex]x + 17 = 38[/tex][tex]x + (17 - 17) = (38 - 17)[/tex][tex]x = (38 - 17)[/tex][tex]x = 21[/tex]Therefore, we know that we must subtract the same number from both sides and this justification is known as the Subtraction Property of Equality. This basically states that an equal value needs to be subtracted from both sides and it will become a new equation but with the same result.
Answer:
Subtraction Property of Equality
Step-by-step explanation:
Given: x + 17 = 38
Algebraic Properties:
Addition: If a = b, then a + c = b + c
Subtraction: If a = b, then a - c = b - c
Multiplication: If a = b, then ac = bc
Division: If a = b, then a ÷ c = b ÷ c
To solve this equation, we know that we need to isolate the variable x. To do this, we need to subtract 17 from both sides to isolate x.
This is also known as the subtraction property of equality, which states that when the same thing is subtracted from both sides of an equation, the equation will still be balanced.
Subtract 17 from both sides:
x + 17 - 17 = 38 - 17
⟹ x = 21
Therefore, the subtraction property of equality is included in the steps used to solve this equation.
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+)
Kirsten invested $1000 in an account at an annual-
interest rate of 3%. She made no deposits or
on the account for 5 years. The
withdrawals
interest was compounded annually. Find the
balance in the account, to the nearest cent, at the
end of 5 years.
Answer:
Kristen will have $1159.27 after 5 years
Step-by-step explanation:
trust in ya boy
Answer:
$ 1159.27
Step-by-step explanation:
1000 ( 1 + .03)^5 = 1159.27
Neena just earned her bachelor’s degree. based on her qualifications and desire for the highest pay scale, which career would she be best suited for? supply chain manager survey researchers logistic analyst marketing specialist
Based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.
Who is a supply chain manager?A supply chain manager ensures the movement of goods, from manufacturers and suppliers to the ultimate customer.
A supply chain manager oversees and manages the production flow:
Raw materials acquisitionProduction logisticsDelivery logistics.A supply chain manager requires the following skills:
Business ManagementLeadershipTransportationManufacturing production and processesCustomer servicePersonal relationshipsAnalytical skills.Thus, based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.
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Using graphing, what is the approximate solution of this equation? 3xˆ2-6x-4 = -2/x+3 + 1 A. x = .64
B. x = .33
C. x = .18
D. x = 2.60
Answer: c
Step-by-step explanation:
The required values on the graph, the solution is approximate x = -0.33.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To solve this equation, we can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
Approximating these values on the graph, we see that the solution is approximate x = -0.33.
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What is the (LCM) of 5/6 and2/5
Answer:
30
Step-by-step explanation:
[tex]\frac{5\cdot\frac{6}{6} }{2\cdot\frac{6}{6} } = \frac{25}{30}, \frac{12}{30}[/tex]
What is the range of the function y=3√x+8?
Answer:
The range will be (-∞,∞)
Step-by-step explanation:
Since there is no number that can make this function undefined or limited to a certain set of values, the range shall be infinite.
Which of the following statements is true concerning ABC below?
10
B
с
OA. ZA is the smallest angle.
OB. ZB is the largest angle.
C. Bis the smallest angle.
OD. ZA is the largest angle.
2
Answer:
see the attachment photo!
Graph y = |x| + 2
Please help
For the function y = |x| + 2, it shows a vertical translation of the parent function up by 2 units.
Graph of modulus of functionsThe parent function for the graph of the modulus is given as g(x) = |x|
For the function y = |x| + 2, it shows a vertical translation of the parent function up by 2 units.
For the graph, there will be s shift down the graph by 2 units from the graph of the parent function as shown;
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The height of the oak tree is 2.5 meters. what is the height of the oak tree in
inches?
(1 ft. 0.305 m)
show your work!
Answer:
98.4 inches
Step-by-step explanation:
1 meter is about 3.28 ft, meaning the oak tree is 8.2ft tall. (2.5*3.28)
1 foot is 12 inches, meaning the oak tree is 98.4 in tall. (8.2*12)
The height of the oak tree = 98.42 inches.
Given that,
The height of the oak tree is 2.5 meters
We have to find height of tree in inches.
Since we know that,
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Since we know that,
1 meter = 39.37
Then to find the height of oak tree in inches
Multiply 2.5 with 39.37
Therefore,
The height of the oak tree in inches = 2.5 x 39.37
= 98.42 inches
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what three consecutive odd integers have a sum of 64. show steps please
There are no such integers. Odd + odd = even, and adding odd to that makes it odd again. But 64 is even.
Put another way, let n be the smallest of the three integers. Then
n + (n + 2) + (n + 4) = 64
3n + 8 = 64
3n = 56
But 3 does not divide 56, so there is no integer solution for n.