Answer:
x=-108117
Step-by-step explanation:
108105-2+1(2x+10)=1(x-4)
108113+2x=x-4
2x-x=-4-108113
x=-108117
A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width.
Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
A. Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. No part of the solution region is viable because the length and width cannot be negative.
C. The entire solution region is viable.
D. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.
The solution from the system of inequalities is (a). Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
The system of inequalityLet P represent the perimeter.
So, we have:
P ≤ 28 ---- i.e. perimeter not more than 28y ≥ (x - 2)²The perimeter is calculated using:
P = 2(x + y)
So, we have:
2(x + y) ≤ 28
y ≥ (x - 2)²
Next, we plot the system of inequalities (see attachment)
From the attached graph, we have some negative x values in the shaded region.
This means that not all solutions are viable
Hence, the true statement is (a)
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If the diameter of a circle is 14 inches, which of the following is the best approximation of the area of the circle?
Answer: 153.93791 inches³
Step-by-step explanation:
Area of a circle = pi * r²
Area of a circle = pi * 7²
Area of a circle = 3.14159 * 49
Area of a circle = 153.93791 inches³
We can't see you answer choices, so select the best answer choice that is closest to 153.93791 in³
Simplify 4 – 8 × 2. Question 9 options: A) –4 B) –8 C) –10 D) –12
Answer:
b
Step-by-step explanation:
4 - 8 = -4 times 2 = -8
Natalie invested $40,000 in an account paying an interest rate of 8 % compounded
continuously. Mackenzie invested $40,000 in an account paying an interest rate of
9 % compounded daily. After 20 years, how much more money would Mackenzie
have in her account than Natalie, to the nearest dollar?
%
Answer:
8000
Step-by-step explanation:
Natalie
Divide 40k by 2 to get 20k and divide 20k by 5 to get 4k we are at 10%
4k / 5 = 800 that means that every 2% is 800 now we multiply by 4x
To get 8% and we get 3200 and multiply by 20 representing the yrs
3200 x 20 = 64k + 40+ = 104k
Mackenzie
40k divide by 2 to get 50% 40k / 2 = 20k and now we divide by 5 to get 10% 20k / 5 = 4k now we divide by 10 to get the amount of each percents worth 4k / 10 = 400 we multiply by 9 to get the compounded interest
400 x 9 = 3600 multiply by 20 to get the compounded daily investment after 20yrs 3600 x 20 = 72k + 40k = 112k
112k - 104k = 8k
Round 2.486.3 to The hundred this place.
help me please i need help
Answer:
B. 11
Step-by-step explanation:
Hope this helps! ;-)
Answer:
11
Step-by-step explanation:
15-12/3
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
15-4 = 11
Please help surface area of a triangle
Answer:
A≈391.18
Step-by-step explanation:
The formula to find the surface area of a triangular prism is as follows:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
Plug in . .
A=ah+bh+ch+[tex]\frac{1}{2}[/tex][tex]\sqrt{ a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4}[/tex]
A = 6 * 20 + 6 * 20 + 6 * 20 + [tex]\frac{1}{2}[/tex] * [tex]\sqrt{64 + 2 * (6 * 6)2 + 2 * (6 * 6)2 - 64 + 2 *(6 * 6)2 * 64}[/tex]
A≈391.18
Answer:
391.2 square cm
Step-by-step explanation:
Surface area of triangular prisml = 20 cm
Base area = 15.6 square cm
[tex]\sf \boxed{\text{Surface area of triangular prism = Perimeter of base * l + 2*base area}}[/tex]
= (6+6+6)*20 + 2*15.6
= 18*20 + 31.2
= 360 +31.2
= 391.2 square cm
Find the surface area and volume of the figure below. Round your answers to the nearest tenth. (50 pts)
Answer:
Surface Area = 188.4 square yardsVolume = 216 cubic yardsStep-by-step explanation:
Finding the hypotenuse of the triangular side :
Applying Pythagorean theorem√6² + 6²√2 x 6²6√2Finding Surface Area :
Area (2 triangles) + Area (2 smaller rectangles) + Area (larger rectangle)2 x 1/2 x 6 x 6 + 2 x 12 x 6 + 12 x 6√236 + 144 + 6√2180 + 6√26 (30 + √2)6 (30 + 1.4)6 (31.4)188.4 square yardsFinding Volume :
1/2LWH1/2 x 12 x 6 x 66³216 cubic yardsWILL GIVE BRAINLIEST 25 POINTS
Congruent?
If so, what property?
Answer:
Yes, by ASA congruence.
Step-by-step explanation:
Solving :
∠DAB = ∠BCD (indicated in diagram)∠ADB = ∠DBC (indicated in diagram)BD = BD (common side)ΔABD ≅ ΔCDBHence, as 2 angles and a side of the triangles are equal, we can say they are congruent by ASA congruence.
[tex]\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's check if the two triangles are } [/tex][tex] \textbf{congruent} [/tex] ~
[tex] \large\textsf{Given information } [/tex]:
[tex] \textsf{Two angles of a triangle is equal to corresponding} [/tex] [tex] \textsf{two angles of another triangle, and they} [/tex][tex] \textsf{have one side in common (should be equal} [/tex][tex] \textsf{for both) } [/tex]
[tex] \textsf{So, after analyzing this information, we can } [/tex][tex] \textsf{conclude that the two triangles are congruent by} [/tex][tex] \textsf{AAS congruency criteria.} [/tex]
[tex] \texttt{[ since two angles are equal and one} [/tex][tex] \texttt{non included side is common/equal ]} [/tex]
NO LINKS!! Please help me with this graph. Part 2
[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (6, -7)
Take two points: (6, -7), (9, -5)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]
Join them to build the equation: [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]
Answer:
[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]
From inspection of the graph, the vertex of the transformed function is at (6, -7). Therefore, there has been a translation of:
6 units right7 units down[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]
[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]
The line goes through point (0, -3)
Substituting this point into the above equation to find [tex]a[/tex]:
[tex]\implies a|0-6|-7=-3[/tex]
[tex]\implies 6a=4[/tex]
[tex]\implies a=\dfrac{2}{3}[/tex]
Therefore,
[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Need help on this one please
if your 14 and you have a kid at 21 how old will your kid be when your 30
Answer:
Your kid will be 9 years old.
Step-by-step explanation:
It's not relevant, that you are 14 now.
Answer: 9
Step-by-step explanation: Regardless of if you are 14 or not, 30-21=9
Consider the line 9x+8y=-2.
Find the equation of the line that is parallel to this line and passes through the point (-3, 2).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 2).
Equation of parallel line:
Equation of perpendicular line:
Considering the definition of parallel and perpendicular line:
the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of parallel line in this caseIn this case, the line is 9x+8y=-2. Expressed in the form y = mx + b, you get:
8y= -2 - 9x
y= (-9x -2)÷ 8
y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex]
Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of -[tex]\frac{9}{8}[/tex] and has a form of: y= -[tex]\frac{9}{8}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= -[tex]\frac{9}{8}[/tex]× (-3) + b
2= [tex]\frac{27}{8}[/tex] + b
2- [tex]\frac{27}{8}[/tex]= b
- [tex]\frac{11}{8}[/tex]= b
Finally, the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].
Equation of perpendicular line in this caseThe line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex].
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -[tex]\frac{9}{8}[/tex]. So:
-[tex]\frac{9}{8}[/tex]× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-[tex]\frac{9}{8}[/tex])
slope perpendicular line= [tex]\frac{8}{9}[/tex]
So, the perpendicular line has a form of: y= [tex]\frac{8}{9}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= [tex]\frac{8}{9}[/tex]× (-3) + b
2= -[tex]\frac{8}{3}[/tex] + b
2+ [tex]\frac{8}{3}[/tex]= b
[tex]\frac{14}{3}[/tex]= b
Finally, the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].
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Find the fourth derivative of f(x)=3^x+ln(x)-108x. f(4)(x)=
[tex]f(x) = 3^x + \ln x -108 x\\\\f'(x) = 3^x \ln 3 + \dfrac 1x - 108\\\\f''(x) = 3^x \cdot 0+ \ln 3\cdot 3^x\cdot \ln (3)-x^{-1-1}-0= 3^x \cdot \ln^2 3 -x^{-2}\\ \\f'''(x) = 3^x \cdot 0 + \ln^2 (3) \cdot 3^x \cdot \ln (3) +2x^{-2-1} = 3^x \ln^3 (3)+2x^{-3}\\\\f''''(x) = 3^x \cdot 0 + \ln^3 (3) \cdot 3^x \ln(3) -3\cdot 2 x^{-3-1} = 3^x\ln^4 (3)-6x^{-4} \\\\\text{Hence the fourth derivative of f(x) is}~~ 3^x\ln^4 (3)-6x^{-4}.\\\\[/tex]
[tex]\textbf{Note:}\\\\\dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v\dfrac{du}{dx}\\\\\dfrac{d}{dx} \ln (x) = \dfrac 1x\\\\\dfrac{d}{dx} a^x = a^x \ln a\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} (\text{Constant}) = 0[/tex]
Solve by factoring y=4x^2-24x+36
Answer:
(x-3) (x-3)
Step-by-step explanation:
[tex]4x {}^{2} - 24x + 36 \\ dividing \: through \: by \: 4 \\ x {}^{2} - 6x { }^{} + 9 \\ two \: numbers \: such \: that \: when \: you \: add \: them \: they \: give \: you \: - 6 \: and \: when \: you \: multiply \: them \: they \: give \: 9 \\ the \: numbers \: are \: \: - 3 \: and \: - 3 \\ x {}^{2} - 3x - 3x + 9 \\ x( x - 3) - 3(x - 3) \\ (x - 3)(x - 3)[/tex]
Meghan’s bank account is charged $9.95 per month for an online newspaper subscription. How could you represent the change in her account balance after three months of charges?
·⎯.=
After three months, the change in her account balance is $.
A number line from negative 30 to 0, split into 3 equal sections of negative 9.95.
Convince Me!
Meghan’s bank account is charged 3 times. Without calculating, how can you determine whether this would be a negative or positive change to her account? Explain.
The expression for the amount of Meghan's newspaper for three months will be T = C - (9.95 x 3).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.
The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months.
T = C - (9.95 * 3)
The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.
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What’s the definition of decreasing function?
Answer:a function whose value decreases as the independent variable increases over a given range.
Step-by-step explanation:
Select the reason that best supports Statement 8 in the given proof.
A. Addition Property of Equality
B. Division Property of Equality
C. Substitution
D. Subtraction Property of Equality
Given: Ray BV bisects
Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Suppose that we're taking about
It means, we divide p into q equal parts.
And each part is of value p/q
Statement 7 is given below.
5x - 10 = 0
Then statement 8 is given by the division property of equality.
5x = 10
x = 10/5
x = 2
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Does anyone know how to do this Venn diagram question?
Answer:
[tex]\frac{8}{30}[/tex]
Step-by-step explanation:
Card(AUBUC)= Card(A)+card(B)+card(C)-Card (A∩B) -Card( A∩C)-Card(B∩C) +Card(A∩B∩C)
= 21 + 14 + 15 - 10 - 8 - 4 + 2
= 30
Then
Card(AUBUC) = 30
Card( A∩C) = 2 + 6 = 8
[tex]p\left( A\cap C\right) =\frac{card\left( A\cap C \right) }{card\left( A\cup B\cup C \right) }[/tex]
[tex]=\frac{8}{30}[/tex]
Which statement about the graphs is true?
O Graph A is a valid density curve because the part of
the graph from 2 to 6 is below the horizontal axis.
O Graph A is not a valid density curve because the
part of the graph from 1 to 2 is above the horizontal
axis.
O Graph B is not a valid density curve because part of
the horizontal axis has negative values.
O Graph B is a valid density curve because the curve
is above the horizontal axis, and the area under the
curve is 1.
The statement about the graphs is true is: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Statement about the graph that is trueGraph curve is above the horizontal axis.
Let determine the area under the curve using this formula
Base of left and right triangle
Left
Base = -3 - (-5)
Base= 2
Right
Base= 3 - (-3)
Base= 6
Right and left height
Height= 0.25
Hence:
Total area=(base× height)/2
Total area=[ (2×0.25)/2] + (6×0.25)/2
Total area=0.25+0.75
Total area=1
Therefore Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
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what is 747-329 equal
Answer:
418
Step-by-step explanation:
Solve for x. Round to the nearest tenth.
Answer:
x = 27.19
Step-by-step explanation:
Sin(54) =22/x
0.81=22/x
x0.81= 22
x = 27.19
b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.
3:7 =
3/7
3/7 = x/35
7x = 105
x = 15
answer : clara borrowed 15 books
I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.
Robert delivers papers every morning. On Sundays he has to deliver 61 papers and on each of the other days he only has to
deliver 44 papers. How many papers does Robert deliver each week?
A. 369
B. 325
C. 413
D. 427
Answer:
B. 325
Step-by-step explanation:
y = the total value of the amount of papers he has to deliver each week
44x + 61 = y
(7 days in a week - sunday = 6 days)
44(6) + 61 = y
264 + 61 = y
325 = y
meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
The probability that it will not rain on both Saturday and Sunday will be 0.2268.
How to calculate probability?From the information, meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
The probability that it will not rain on both Saturday and Sunday will be:
= (1 - 42%) × (1 - 54%)
= 0.58 × 0.46
= 0.2268
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PLEASE HELP!!! IMA DESPRATE!!!!!Use first and second differences to find the next three terms in the following sequence.
8, 11, 19, 35, 62,...
The next term of the given sequence using first and second differences is; 104
How to find the terms of a Sequence?We are given the sequence as;
8, 11, 19, 35, 62,.....
Thus, using the first and second differences, we have the sequence pattern as;
8 11 19 35 62 104
3 8 16 27 42
5 8 11 15
3 3 4
From the above pattern, we can see that the next term of the sequence is 104
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Select the correct vocabulary word from each drop-down menu to correctly complete the sentences.
A(n)
Choose...
is a chore, but it is not a game.
A(n)
Choose...
is a bond, but it is not a separation.
An ERRAND is a chore, but it is not a game and A CONNECTION is a bond, but it is not a separation.
What is Errand?An ERRAND is a chore, but it is not a game.
The correct vocabulary word from each drop-down menu that correctly complete the first sentences is errand.
What is Connection?A CONNECTION is a bond, but it is not a separation
The correct vocabulary word from each drop-down menu that correctly complete the second sentences is connection.
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In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Gabriella sets up a website where players can
buy and sell these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
27 visitors purchased no costume.
75 visitors purchased exactly one costume.
11 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
more than one costume as a fraction in simplest form.
Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113
How to find probability?
We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;
Number of visitors that purchased no costume = 27 visitors
Number of visitors that purchased exactly one costume = 75
Number of visitors that purchased more than one costume = 11
Total number of visitors = 27 + 75 + 11 = 113
Thus;
Probability that the next person will purchase more than one costume as a fraction in simplest form is;
P(purchase more than one costume) = 11/113
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Given that circumference of a circle is 44m. Calculate it's area
Answer:
Area=154.062 [tex]m^{2}[/tex]
Step-by-step explanation:
As Circumference of a circle is given by;
[tex]C=2\times \pi\times r[/tex]
As the circumference is 44m so we can calculate the value of r by using the above formula.
[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]
Now to Calculate the Area of a Circle.
As the area of a circle is,
[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]
Use the net to find the surface area of the regular pyramid.
A net includes four equilateral triangles. One triangle is shaded and it is a base. Each unshaded triangle shares a side with the shaded triangle. The shaded triangle has a side edge of 10 millimeters and area of base is 43.3 squared millimeters. The height of each unshaded triangle is 9 millimeters.
mm2
Answer: The surface area is 173.2 mm²
Step-by-step explanation: If the four triangles are equilateral and one of the sides is 10 then all the other sides must be 10 as well, meaning that the surface area of each triangle is 43.3 mm². That means that to find the surface area of the whole pyramid you must multiply 43.3 by 4 because there are 4 separate triangles.
43.3 × 4 = 173.2