Answer:
b is not a polynomial
Step-by-step explanation:
b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial
What is the least possible value of (x+4)(x+5)+[tex]\frac{10^{6} }{x(x+9)} ,[/tex] where x is a positive real number?
Answer choice: 2017, 2018, 2019, 2020, 2021
Explain in High School Mathematics terminology. Do not attempt if your not 98% sure
The least possible value of the expression is 2020
How to determine the value of the expression?The expression is given as:
[tex](x + 4)(x + 5) + \frac{10^6}{x(x + 9)}[/tex]
Next, we plot the expression on a graph (see attachment)
From the attached graph, the minimum value of the expression is 2020 under the domain of x > 0
Hence, the least possible value of the expression is 2020
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What is the solution to the equation startfraction negative 3 d over d squared minus 2 d minus 8 endfraction startfraction 3 over d minus 4 endfraction = startfraction negative 2 over d 2 endfraction?
Answer: C / d=1
Step-by-step explanation:
Just did it
Answer: C
Step-by-step explanation: Just took the quiz
Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for$25 off his entire purches at check out, so the tickets would him $215 before tax. what was the original price of each tickets?
The original price of each tickets is; $60 per ticket
What is the original Price?We are told that $215 is what it costs after the discount. Thus, we add the amount taken off, back on to get;
$215 + $25 = $240
Now, since he wants to buy 4 tickets, then we divide the amount above by 4 to get the cost of each individual ticket.
Original Cost of each individual ticket = 240/4 = $60
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What is the inverse of the function f(x) = 1/9x+2
Hello,
f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)
x = 9y - 18
⇒ f⁻¹(x) = 9x - 18
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
If we have a function, we can find its inverse if we do the
following-:
[tex]\tiny\bullet[/tex] replace f(x) with y.
[tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]
[tex]\tiny\bullet[/tex] switch the places of x and y
[tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]
[tex]\bullet[/tex] solve for y
[tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]
[tex]\boldsymbol{\sf{9x=y+18}}[/tex]
[tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]
[tex]\boldsymbol{\sf{y=9x-18}}}[/tex]
[tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
write the following linear equations into the standard form Ax+ by=c
DETERMINE the values of A,B and C.
Answer:
Step-by-step explanation:
1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5
2). 4x - y = 1 , A = 4 , B = - 1 , C = 1
3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3
4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3
5). 2x + y = 15 , A = 2 , B = 1 , C = 15
If A+B =45 then prove that
i) CotA.CotB-CotA-CotB=1
Answer:
Step-by-step explanation:
[tex]if A+B=45\\tan(A+B)=tan(45)\\\dfrac{tanA+tanB}{1-tanA.tanB}=1\\ \implies tanA+tanB=1-tanA.tanB\\\frac{1}{cotA}+\frac{1}{cotB}=1-\frac{1}{cotA}\frac{1}{cotB}, \{tanX=\dfrac{1}{cotX} \}\\ cotA+cotB=cotA.cotB-1\\cotA.cotB-cotA-cotB=1.[/tex]
2/5 (1/3x - 15/8) - 1/3(1/2 - 2/3x)
Your question presented was: [tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)[/tex]
Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.
Step 1.
[tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )[/tex] when distributed is [tex]\frac{2}{15} x - \frac{30}{40}[/tex]
Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.
Step 2.
[tex]\frac{-1}{5} + \frac{2}{9} x[/tex]
So..lets put the 2 parts of the equation together
[tex]\frac{2}{15} x - \frac{30}{40}[/tex] + [tex]\frac{-1}{5} + \frac{2}{9} x[/tex] can be simplified by getting the common denominator.
You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
[tex]\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}[/tex]
We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.
Now we combine.
Step 4.
[tex]\frac{16}{45}x-\frac{38}{40}[/tex]. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
[tex]\frac{16}{45}x-\frac{19}{20}[/tex]
I hope this helps you, heart if it helps.
Simplify the expression (startfraction 1 over 4 a b endfraction) superscript negative 2. assume a not-equals 0, b not-equals 0. negative startfraction 1 over 16 a squared b squared endfraction startfraction a squared b squared over 4 endfraction negative 16 a squared b squared 16 a squared b squared
Answer:
16a^2b^2
Step-by-step explanation:
An exponent that is over a whole entire fraction can be split up and put separately onto the numerator (top number) and denominator (bottom number) See image.
Then you can get rid of a negative exponent (make it positive) by moving the whole term across the fraction bar. The top moves to the bottom and the bottom moves to the top. See image.
In the term (4ab)^2, the exponent 2 can be passed out to the 4 and the a and the b. See image.
Answer: D
Step-by-step explanation:
Find the length of UC
Answer:
18
Step-by-step explanation:
Entire length =105 + 82 =187
subtract 22
subtract 96
subtract 51 result =18
Write each expression as a difference.
a+5
The equivalent expression of a + 5 is -(-a - 5)
How to rewrite the expression?The expression is given as:
a + 5
Multiply by 1
1 * (a + 5)
Express 1 as -1 * -1
-1 * -1 * (a + 5)
Open the bracket
-1 * (-a - 5)
This gives
-(-a - 5)
Hence, the equivalent expression of a + 5 is -(-a - 5)
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can anyone help me with this problem?
Answer:
a1
Step-by-step explanation:
Just add the numerators if both fractions to get: a + 1 = a1
Answer:
a+1
Step-by-step explanation:
Well if you have the same denominator, which in this case you do, it's equal to b, you can simply add the numerators. This gives you the expression [tex]\frac{a+1}{b}[/tex] so the numerator is a+1
Math 2 Of high school
Answer:
B. BC = 18 so ∆ABC ～ ∆DEF by SASStep-by-step explanation:
[tex] \bf \cfrac{AB}{DE} = \cfrac{BC}{EF} [/tex]
[tex] \bf \cfrac{15}{10} = \cfrac{BC}{12} [/tex][tex]\bf \cfrac{3}{2} = \cfrac{BC}{12} [/tex][tex]\bf BC = \cfrac{3}{2} \times 12 [/tex][tex]\bf 3 \times 6[/tex][tex]\bf BC = 18[/tex][tex] \bf \angle B = \angle \: E[/tex]So, ∆ABC ～ ∆DEF by SAS.
------------------------------------Under a certain transformation △ABC→△A′B′C′ such that AB≠A′B′. The triangles are:
Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease in the size of a figure by a scale factor.
Dilation does not preserve the size of a figure, it only preserves the shape and angle.
Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′
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| -4 + 5\2 | - (-x) =-3
Answer:
x = -4.5
Step-by-step explanation:
Solving the equation :
[tex]\left\vert -4+\frac{5}{2} \right\vert -\left( -x\right) =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-8}{2} +\frac{5}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-8+5}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-3}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \frac{3}{2} +x =-3[/tex]
[tex]\Longleftrightarrow x =-3-\frac{3}{2}[/tex]
[tex]\Longleftrightarrow x =-\frac{6}{2} -\frac{3}{2}[/tex]
[tex]\Longleftrightarrow x = -(\frac{6}{2} +\frac{3}{2} )[/tex]
[tex]\Longleftrightarrow x =-\frac{9}{2}[/tex]
[tex]\Longleftrightarrow x =-4.5[/tex]
The heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121. Find the interquartile range of the data set.
The interquartile range of the data set is 21.
Given that the heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121.
The interquartile range shows the extent of the middle half of the distribution. Quartiles segment any distribution, ordered from low to high, into four equal parts. The interquartile range (IQR) contains the second and third interquartile ranges, the central half of the dataset.
The value of quartile 1 is Q₁=90
The value of quartile 3 is Q₃=111
So, the interquartile range is
IQR=Q₃-Q₁
IQR=111-90
IQR=21
Hence, the interquartile range of the data set 83, 87, 90, 92, 93, 100, 104, 111, 115, 121 is 21.
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Find the coordinates of the circumcenter 0,0 4,0 4,-3
The coordinates of the circumcenter of triangle having coordinates of (0,0),(4,0),(4,-3) are (1,-17/6).
Given The coordinates of triangle are (0,0),(4,0),(4,-3).
Let the triangle be ABC.
Let the coordinates of the circumcenter be D(x, y).
We know that the length of circumcenter from the corner points are equal to each other.
In this way AD=BD=DC
AD=[tex]\sqrt{(x-0)^{2} +(y-0)^{2} }[/tex]
=[tex]\sqrt{x^{2} +y^{2} }[/tex]
DC=[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]
BD=[tex]\sqrt{(4-x)^{2} +(0-y)^{2} }[/tex]
=[tex]\sqrt{(4-x)^{2} +y^{2} }[/tex]
AD=DC
[tex]\sqrt{x^{2} +y^{2} }[/tex]==[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]
Squaring both sides we get
[tex]x^{2} +y^{2}=16+x^{2} -8x+9+3y+3y+y^{2}[/tex]
8x-6y=25--------------------1
DC=BD
[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} } =\sqrt{(4-x)^{2} +y^{2} }[/tex]
8x+6y=-9---------------------2
Solve equation 1 and 2
Add both equations
8x-6y+8x+6y=25-9
16x=16
x=1
put the value of x in 1
8x-6y=25
8*1-6y=25
-6y=25-8
y=-17/6
Hence the coordinates of circumcenter is (1,-17/6).
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Question 3 of 10 True or False? A circle could be circumscribed about the quadrilateral below.
95, 80, 85, 100
True, a circle can be circumscribed about the quadrilateral described in the task content.
What is the condition to circumscribe a circle about a quadrilateral?It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.
By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.
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I am not able to solve this question
Answer:
Choice A
Step-by-step explanation:
[tex] \rm \: a {}^{2} \cdot \{ a \ { {}^{ (\frac{2}{3}) } \}}^{ - 1} [/tex]x^-1 = 1/x[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]
Applying Distributive property;
[tex] \rm \: a {}^{2 \times \cfrac{2}{3} } [/tex][tex] \rm \: a {}^{ \cfrac{4}{3} } [/tex]Choice A is accurate.
Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.
What is the length of GF?
units
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,
AG / DG = 2/1
(19x+14)/(9x+20) = 2/1
19x + 14 = 18x + 40
19x - 18x = 40 - 14
x = 26
Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,
GF = DG = 9x+20
GF = DG = 9(26) + 20
GF = 254 units
Hence, the length of GF is 254 units.
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Answer: 26 units
Step-by-step explanation: Trust Me!!!
The answer is correct on Edge. I just got it right!
4. Write the trinomial represented by each rectangle of algebra tiles. Then, determine the
dimensions of each rectangle
The trinomial represented by the algebraic tiles is x^2 + 4x + 3
How to determine the trinomial?On the horizontal axis, we have:
1 row under the big square.
This represents x + 1
On the vertical axis, we have:
3 columns beside the big square.
This represents x + 3
So, we have:
(x + 1) * (x + 3)
Expand
(x + 1) * (x + 3) = x^2 + x + 3x + 3
Evaluate
(x + 1) * (x + 3) = x^2 + 4x + 3
Hence, the trinomial represented by the algebraic tiles is x^2 + 4x + 3
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Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
The graphs are attached in the attachment.
The equation for the trend line in the scatter plot will be Y= 5x-1.
Hence, option B is correct.
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find the equation of the line shown
i will put brainliest
2/x+3/y=9/x;4/x+9/y=21/xy(x=0,y=0)
The solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The complete question is:
Solve for x and y:
2/x+3/y=9/xy; and 4/x+9/y=21/xy x ≠ 0, y ≠ 0
We have two equations:
2/x+3/y=9/xy;
4/x+9/y=21/xy
Solving substitution method:
[tex]\rm \dfrac{4}{\dfrac{9-2y}{3}}+\dfrac{9}{y}=\dfrac{21}{\dfrac{9-2y}{3}y}[/tex]
y = 3
x = 1
Thus, the solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.
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A parabola with a vertex at (0,0) has a focus along the negative part of the x-axis.
Which could be the equation of the parabola?
y2 = x
y2 = –2x
x2 = 4y
x2 = –6y
The equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y. (Correct choice: D)
How to determine the best equation of the parabola based on given characteristics
In accordance with the statement, we find that the parabola has its vertex at the origin, therefore it is horizontal and its vertex constant (C) is negative as its focus is in the negative part of the x-axis. Therefore, the equation of the parabola in standard form has the following form:
x² = C · y, for C < 0. (1)
In consequence, the equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y.
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(1 + cos(x))(l — cos(x))
The expression given in the task content can be evaluated and simplified to be equal to; sin²(x).
What is the result of the product?It follows from the task content that the result of the product given is to be determined.
Hence, the multiplication is as follows;
1 -cos(x) +cos(x) -cos²(x).
1 -cos²(x).
However, since sin²(x) + cos2(x) = 1; it therefore follows that;
1 -cos²(x) = sin²(x)
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Two farmers bought a total of 230 cows and a year later found out that the first farmer had 10% more cows than in the beginning, whereas the second had 20% increase. The total number of cows at the end of the observed period was 263. How many cows did each have in the beginning?
In the beginning, they have 50 and 180 cows respectively.
How to find the total number of cows?The two farmers bought a total of 230 cows .
A year later the first farmer had 10% more cows than in the beginning.
Therefore,
let
x = number of cow he has initially.
A year later the percentage increase = 0.1x
whereas the second had 20% increase. Therefore,
let
y = number of cow he has initially.
A year later percentage increase = 0.2y
Hence,
x + y = 230
1.1x + 1.2y = 263
1.1x + 1.1y = 253
1.1x + 1.2y = 263
0.2y = 10
y = 10 / 0.2
y = 50
x = 230 - 50
x = 180
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A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the length of the pole, round o the nearest tenth.
a. 12.00 ft
b. 19.60 ft
c. 24.17 ft
d. 38.40 ft
NEED HELP ASAP
Answer:
19.6ft (nearest tenth)
Step-by-step explanation:
Please refer to the attached photo for better understanding.
Given Length of Wire = BC = 22ft
Given Distance from Grounded Wire to Base of Pole = AC = 10ft
Length of Pole = AB
We can use Pythagoras' Theorem to find Length of Pole, AB.
By Pythagoras' Theorem,
[tex]c^{2} =a^{2} +b^{2} \\BC^{2} =AB^{2} + AC^{2} \\22^{2} =AB^{2} +10^{2} \\484=AB^{2} +100\\AB^{2} =484-100\\AB=\sqrt{384} ft\\=19.6ft (nearest tenth)[/tex]
Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, descibe the new location of point F in relation to lines m and t.
The image of the figure under reflections in line m and then line t is shown below.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the square DEFG will be given in the figure.
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The total cost of owning a home for 6 years is $120,000. The
rent for a comparable home is $1500 per month. If you had invested the
down payment for the home, you could have earned $10,000 in interest.
After 6 years, how much more, in dollars, is the cost of owning compared
to the cost of renting?
After 6 years, the difference between owning the house and renting is $12,000.
What is the difference in owing and renting the house?
The first step is to determine the total cost of renting the house for six years.
Total cost of renting the house = rent per month x number of years x number of months in a year
1500 x 12 x 6 = $108,000
Difference = cost of owning - cost of renting
$120,000 - $108,000 = $12,000
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Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet
If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.
Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.
We know that speed is the distance covered by an object in a particular period of time.
Speed=distance/time.
It is expressed as kilometers per hour or miles per hour, etc.
If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.
Distance=45 miles.
Time =distance/speed
=45/30
=1.5
Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.
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