Answer:
320 ft^2
Step-by-step explanation:
if you know how to do this problem please let me know, thank you.
As per the question statement, we are given a mathematical expression [tex]|a+5| -1[/tex] is [tex]$\left[\begin{array}{cc}\text { Solution: } & -\infty < a < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
As this question involves a modulus function therefore let us suppose that [tex]b=|a+5|-1[/tex]
Find the absolute value vertex. In this case, the vertex for [tex]b=|a+5|-1[/tex] is [tex](-5,-1)[/tex]
Function range definition
The set of values of the dependent variable for which a function is defined
Domain of [tex]$|a-5|-1: \quad-\infty < a < \infty$[/tex]
Extreme Points of [tex]$|a-5|-1: \quad$[/tex] Minimum [tex]$(5,-1)$[/tex]
Find the range for the interval [tex]$-\infty < a < \infty: \quad-1 \leq f(x) < \infty$[/tex]
Combine the ranges of all domain intervals to obtain the function range [tex]$f(x) \geq-1$[/tex]
Axis interception points of [tex]$|a-5|-1: \quad X$[/tex]Intercepts: [tex]$(4,0),(6,0), Y$[/tex]Intercepts:[tex]$(0,4)$[/tex]
x - axis interception points of[tex]$|a-5|-1: \quad(4,0),(6,0)$[/tex]
y - axis interception point of [tex]$|a-5|-1: \quad(0,4)$[/tex]
X Intercepts: [tex]$(4,0),(6,0), Y$[/tex] Intercepts: [tex]$(0,4)$[/tex]
Asymptotes of [tex]$|a-5|-1$[/tex] : None
Vertical asymptotes of [tex]$|a-5|-1$[/tex] : None
Horizontal Asymptotes of [tex]$|a-5|-1$[/tex] : None
Extreme Points of[tex]$|a-5|-1$[/tex] : Minimum [tex]$(5,-1)$[/tex]
First Derivative Test definition
Suppose that [tex]$x=c$[/tex] is a critical point of [tex]$f(x)$[/tex] then,
If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of [tex]$x=c$[/tex] then $x=c$ is a local maximum.
If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of[tex]$x=c$[/tex] then $x=c$ is a local minimum.
If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex]
is neither a local maximum nor a local minimum.
[tex]f^{\prime}(a)=\frac{a-5}{a-5}$$[/tex]
Plug [tex]$a=5$[/tex] into [tex]$|a-5|-1: \quad-1$[/tex]
Minimum [tex]$(5,-1)$[/tex]
Absolute value vertex: The difference between two numbers; a number's positive value.Interval: A collection of values spanning two endpoints.To learn more about such Absolute value vertex:, click on the link given below:
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Vincent earns $892 on Monday and he earns $711 on Tuesday. How much total money does Vincent
earn?
Find rules for the tables below. State your rules in two different ways: (1) as a sentence; and (2) as a rule, using x for the input and y for the output. a. X 6 0 2 -3 1 Process y -3 9 -21 3 33 Rule: (1) X and Topic 3: Foundations of Y are Linear (2) relationship Y = 6x=3
Answer:6x+3
Step-by-step explanation:
I am stuglling please someone help me
76 degrees n 83 degrees it's div
30 points!!! But I need a 2 step problem with variables on both side and a fraction that equal 23
The equation of the two-step problem is 2x = x + 2/3
How to determine the two-step problem?The conditions are given as
Fraction = 2/3Variable on both sidesLet the variable in the equation be x
So, a possible equation is as follows
2x = x + 2/3
The solution to the equation is as follows
2x = x + 2/3
Subtract x from both sides
x = 2/3
Hence, the equation of the two-step problem is 2x = x + 2/3
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Hello! I'd really appreciate it if someone helped me solve this logarithm! It was my first class but the professor only showed the more simple versions :)
Answer:
(1/3)log(5) +(4/3)log(x) +log(y)
Step-by-step explanation:
You want the expanded form of the expression log(∛5·x^4·y^3).
Rules of logarithmsThe applicable rules of logarithms are ...
log(ab) = log(a) + log(b)
log(a^b) = b·log(a)
In addition to these, you need to know that a root is a fractional power: the cube root is the 1/3 power. Of course, the rules of powers tell you ...
(a^b)^c = a^(bc)
ApplicationYou can express the root as a fractional power before or after taking logs. Either way, you get the same result.
Before
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\log\left(5^{\frac{1}{3}}\cdot x^{\frac{4}{3}}y^{\frac{3}{3}}\right)=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
After
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\dfrac{1}{3}\log\left(5}\cdot x^{4}y^{3}}\right)=\dfrac{1}{3}\left(\log(5)+4\log(x)+3\log(y)\right)\\\\=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
__
Additional comment
Working a more complex problem is like working a simple problem, except it has more parts and may require the use of the rules more times. It may be tedious to keep track of all the parts, but it is not difficult.
Figurative language is different from literal language because _____.
A. it means exactly what it says
B.it is unclear
C.it contains meaning other than the actual word for word meaning
D.it is hard to define
Answer:
C i think
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
Answer A is the definition of literal language, while C is the definition of figurative. So, C is correct.
Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument? Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons.
"Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons." This is a Valid Argument
This is further explained below.
What is a Valid Argument?Generally, In the context of deductive reasoning, an argument is considered to be sound if and only if it can be expressed in a way that makes it logically impossible for all of the premises to be true while still leading to an incorrect conclusion.
In conclusion, This is a Valid Argument
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A square rug has an area of 35 square ft. What is the exact side length of the rug?
The exact side length of the rug is √35.
What is the area of parallelogram
Let take the area of length as =a
As per the given question
A square rug has an area=35 sq ft
Area is the quantity that measures the number of unit square
As we know
area of square= a^2
Square area formula: A = a²
As already given a^2=35
So a=√35
The exact side length of the rug is √35.
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HELP QUICK I WILL GIVE BRAINLIEST ANSWER! In the diagram, line m intersects line n. A two-column proof shows that vertical angles 21 and 23 are
congruent. What should be the statement and justification for step 3?
Answer:
Option A=============================
The missing statement is:
∠1 + ∠2 = 180°∠2 + ∠3 = 180°Justification is:
Angles that form a linear pair have measures that sum to 180°.All the other options have mismatching or wrong statements or justifications:
B) Wrong statement, the angles are not congruent.C) Wrong justification, angles are not vertical.D) Wrong justification, not matching the statement.In the diagram m∠ACB=25° and CE bisects ∠DCF. explain how to find m∠DCE
The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
We are given a ray diagram.
In the diagram, the measure of angles are given as:
∠ ACB = 25°
∠ ACG = 90°
We need to find the measure of angle ∠ DCE when CE bisects ∠ DCEF.
Now, we know that:
∠ BCG = ∠ DCF ( Vertically opposite angles.) … (1)
Now,
∠ BCG = ∠ ACB + ∠ ACG
∠ BCG = 25° + 90°
∠ BCG = 115° … (2)
∠ DCF = ∠ DCE + ∠ CEF
∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)
∠ DCF = 2 ∠ DCE … (3)
Now, put (2) and (3) in (1), we get that:
115° = 2 ∠ DCE
∠ DCE = 115 / 2°
∠ DCE = 57.5°
Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
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Use equivalent ratios to answer
If out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.
Given that out of 7 squares, 4 squares are in grey colour.
We are required to find the number of grey colour squares if there are 15 white squares by using equivalent ratios.
Equivalent ratios are basically the ratios that are the same when we compare them. Two or more ratios can be compared with each other to find whether they are equivalent or not.
Ratio of white squares in 7 total squares=3:4
Total number of squares if there are 15 white squares=15*7/3=35
Number of grey squares=35-15=20
Hence if out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.
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The probability of passing the math class of Professor Goodrum is 59%, the probability of passing Professor Cruise's physics
class is 26%, and the probability of passing both is 17%. What is the probability of passing one or the other?
(Give your answer as a whole percent number.)
probability of passing one or the other:
Answer:
51%
Step-by-step explanation:
Given P(passing math) = 59%, P(passing physics) = 26%, and P(passing both) = 17%, you want to find the probability of passing only one of the courses.
Probability relationsWe can record the given probabilities in a 2-way table (values shown in blue). The table is completed by making sure the totals add up (values shown in black).
The probability of passing one course and failing the other is the sum of the probabilities with a yellow background:
42% +9% = 51%
The probability of passing one or the other is 51%.
__
Additional comment
We can also get there using the relation ...
P(A+B) = P(A) +P(B) -P(AB)
The union of A and B also includes their overlap:
P(A+B) = P(AB') +P(A'B) +P(AB)
In other words, the probability of interest is ...
P(AB') +P(A'B) = P(A) +P(B) -2×P(AB) = 59% +26% -2(17%)
P(AB') +P(A'B) = 51%
how can you make the equation true?
111+222=
Answer: 111 + 222 = 333
If an employee at Tacos R US gets paid $11.50 per hour. Find his net pay if the
employee works 38 hours in that one week. Employee has a 10% federal tax rate. SS
tax is 6.2% and Medicare tax is 1.45%
the net pay (weekly) is $359.87
How to find the net pay?First, we know that the employee wins $11.50 per hour. The employee works 38 hours per week, then the weekly pay is:
38*$11.50 = $437
Now we need to discount the taxes:
There are 10% from federal tax, 6.2% from social services and 1.45% from medicare.
The total is:
10% + 6.2% + 1.45% = 17.65%
Then we need to discount a 17.65% of the weekly pay, we will get:
$437*(1 - 17.65%/100%) = $437*(1 - 0.1765) = $359.87
We conclude that the net pay (weekly) is $359.87
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What is: 14 - (-20) + (-13)
Answer:
21
Step-by-step explanation:
14 - (-20) + (-13) =
= 14 + 20 - 13
= 34 - 13
= 21
"The unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November." What is the relative change in the unemployment rate expressed as a percentage?
If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
Given,
The unemployment rate in February = 8.9%
The unemployment rate in November = 7.1%
The relative change in unemployment rate = [(unemployment rate in February - unemployment rate in November )÷ unemployment rate in November ] ×100
The relative change in unemployment rate= [tex](\frac{8.9-7.1}{7.1} )100[/tex]
=25.35%
Hence, If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
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HURRY IM TIMED Which benchmark fraction is closest to 9/10-3/10 A. 3/4 B. 1/2 C. 1/4 D. 4/4
Answer:
I am pretty sure it is a i think.
Step-by-step explanation:
just subtract the fractions and you will get 6\10 and the you will simplify and get 3\5. so 3\4 is closest to 3\5.
1.
destions. Show your wor
For a recent Broadway musical, orchestra main floor seats cost $148 each, and
balcony seats cost $65 each. A theatre group purchased 30 tickets for an upcoming
show in June. If the total cost of the 30 tickets was $2,614, how many of each type
of ticket did the theatre group buy?
Number of orchestra tickets
Number of balcony tickets
Answer:
Number of orchestra tickets = 8
Number of balcony tickets = 22
Step-by-step explanation:
Let the number of orchestra tickets be x and number of balcony tickets be y.
So, cost of x orchestra tickets = $148 × x = $148x
Cost of y balcony tickets = $65 × x = $65y
Also given, total number of tickets = 30
Cost of 30 tickets = $2,614
So, the system of equations that can ne formed is :
x + y = 30 ....eq 1
148x + 65y = 2614 ....eq 2
Multiplying eq 1 by 148 and subtracting eq 2 by it,
148x + 148y - 148x - 65y = 4440 - 2614
83y = 1826
y = 1826/83 = 22
Substituting y = 22 in eq 1,
x + 22 = 30
So, x = 30 - 22 = 8
Thus,
Number of orchestra tickets = 8
Number of balcony tickets = 22
An average middle-income family will spend $242,020 to raise a child born in 2004
from birth to age 17. The graph shows the percents spent for various categories. To
the nearest dollar, how much will be spent to provide housing for the child? Use the
graph to answer.
graph numbers-- housing 34%, food 17%, miscellaneous 11%, child care 11%, health care 7%, clothing 6%, transportation 14%
Work Shown:
34% of $242,020 = 0.34*242020 = 82,286.80
This rounds to 82,287 when rounding to the nearest whole number.
What is the equation of a line through the points (0, 9) and (3, 0)?
0-9
3-0 y=-3x + 9
Obecause m=
Obecause m=
Obecause m=
O because m=
0-9
3-0 y=-3x + 3
3-0
0-9;y=-
y=-x+9
3-0
1
0-9; X=-3x+3
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ -9 }{ 3 }\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-9=-3x\implies y=-3x+9[/tex]
Use the number line to answer the following 2 questions
Answer:
for first question the answer will be .. 5
Step-by-step explanation:
easily,
[tex] \frac{1}{5} \times 5 = 1 [/tex]
There are [tex]6\frac{1}{4}[/tex] groups of 1/5 in 5.
The simplified value of 5 ÷ 4/5 is also [tex]6\frac{1}{4}[/tex].
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
From the bar given above the number line, each group has subgroups of 4.
Therefore, The number of groups of (1/5) in 5 is [tex]6\frac{1}{4}[/tex] groups.
We know when a fraction is in the division we can reciprocate the fraction and the division changes to multiplication,
Therefore, 5 ÷ 4/5 = 5×5/4 = 25/4 = [tex]6\frac{1}{4}[/tex]
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At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
Child
Ava
Grayson
Mason
Tyler
Amount of
Trail Mix (oz)
15
14
10
17
The trail mix costs $4.50 per pound. How much will Mr.
Arnett pay for all the trail mix?
A cookie recipe requires 4 2/3 cups of flour. If a person only wanted to make 3/4 of a batch, how many cups of flour would they need? (Do not add the label)
[tex]\begin{array}{ccll} \stackrel{recipe}{batch}&\stackrel{recipe}{flour}\\ \cline{1-2} 1&4\frac{2}{3}\\[1em] \frac{3}{4}&f \end{array}\implies \cfrac{1}{ ~~ \frac{3}{4}~~ }~~ = ~~\cfrac{ ~~ 4\frac{2}{3} ~~ }{f}\implies \cfrac{4}{3}~~ = ~~\cfrac{ ~~ \frac{4\cdot 3+2}{3}~~ }{f}\implies \cfrac{4}{3}=\cfrac{ ~~ \frac{14}{3} ~~ }{f} \\\\\\ \cfrac{4}{3}=\cfrac{14}{3f}\implies 12f=42\implies f=\cfrac{42}{12}\implies f=\cfrac{7}{2}\implies f=3\frac{1}{2}[/tex]
what is the vertex of f(x)=x^2+10x+1
The vertex of f(x)=x²+10x+1 is found to be (-5,-24).
The Vertex of the quadratic equation f(x)=ax²+bx+c is (h,k) where
h=-b/2a and k=f(h).
In the given question
f(x)=x²+10x+1
On comparing with ax²+bx+c
we get a=1 , b=10 , c=1
So , h=-b/2a
h=-10/2(1)
h=-5 ...(i)
k=f(h)
Substituting the value of x=h in f(x) we get
k=(-5)²+10(-5)+1
k=25-50+1
k=-25+1
k=-24
Therefore , the vertex of f(x)=x²+10x+1 is (-5,-24).
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
The height of the density curve is 1/5
How to determine the height of the density curve?From the graph, we have the following parameter
Base = 5 units
As a general rule, the area under the density curve must have a value of 1
This means that
Area = 1
So, we have
Area = Base * Height
So, we have
1 = 5 * Height
Evaluate
Height = 1/5
Hence, the height of the density curve is 1/5
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During a science experiment Mary found the mass of two rocks to be 36.81 grams and 52.4 grams what is the total mass of these two rocks
Answer: 89.21g
Step-by-step explanation:
36.81g + 52.40g = 89.21g
Please help
(100 Points)
Answer:
Equation: (14.71-4.48) [divided by] 3 =x
"Answer x": 3.41
Explanation:
14.71-4.48=10.23
10.23/3 = 3.41
3.41
Robert buys last year's best-selling novel, in hardcover, for $22.40. This is with a 20% discount from the original price. What was the original price of the novel?
Answer:
$28.00
Step-by-step explanation:
Set up an equation:
$22.40 = y(1 - 0.20)
Solve the contents of the parentheses first:
$22.40 = y(0.80)
Divide by 0.80 on both sides to isolate y:
($22.40)/0.80 = y
Solve:
$22.40 / 0.80 = $28.00
what is the value of x?!?
please help!
Answer:
x = 25
Step-by-step explanation:
The given angles, x° and (6x+5)° form a linear pair. You want the value of x.
Linear pairTwo angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.
x° +(6x +5)° = 180°
7x +5 = 180 . . . . . . . . . divide by °, collect terms
7x = 175 . . . . . . . . . . subtract 5
x = 25 . . . . . . . . . . divide by 7
The value of x is 25.