Use any method to solve the equation. If necessary, round to the nearest hundredth.
9x2 − 21 = 0
4.58, –4.58
3, –3
0.65, –0.65
1.53, –1.53
Answers
9x² − 21 = 0
using a graph tool
see the attached figure
the solution is
x=-1.528----> -1.53
x=1.528----> 1.53
Answer:
[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]9x^{2}-21=0[/tex]
To solve this equation, we just have to isolate the variable, because the quadratic expression has only one variable, the linear term is not present. So
[tex]9x^{2} =21\\x^{2} =\frac{21}{9}[/tex]
Now, we apply a square root, to have the variable complete isolated
[tex]\sqrt{x^{2} }=\sqrt{\frac{21}{9} } \\x=\±1.53[/tex]
Remember that all square roots have two results, one positive and one negative.
Therefore, the solutions for this equation are
[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]
Related Questions
hello can you please help me posted picture of question
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If Disc > 0, the function has two distinct roots
If Disc = 0, the function has repeated roots
If Disc < 0, the function has complex roots
The turning away of the function indicates a repeated root at that point.
Thus, the given quadratic equation has a repeated root at x = 2. So the discriminant of the function is zero.
Therefore, the correct answer is option B
Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?
Number on cube:1,2,3,4,5,6
Number of times event occurs:3,6,1,5,3,2
A.0.2
B.0.3
C.0.6
D.0.83
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[tex] \frac{4}{20} = 0.2[/tex]
The answer is A.
Lucia is not yet 80 years old. each of her sons has as many sons as brothers. the combined number of lucias sons and grandsons equals her age, and her oldest grandson is 29. how old is lucia? place your numerical answer in the corresponding answer blank.
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Hey can you please help me posted picture of question
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In given case, Karen has to find the probability of a number greater than 4 which can appear when a die is rolled. The possible outcomes in this case are 2 i.e. 5 and 6
Since, the number of possible outcomes is more than 1, the event is a compound event.
So answer is true
Miss Nelson Has a rectangular flower box that is 5 ft long 2 ft tall she wants the width of the box to be no more than 5 ft if the width is a whole number what are the possible volumes for the flower box
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please help me :)))))
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Answer: 5*sqrt(2pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi
Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"
============================================================
Part b)
Answer: 3*sqrt(3pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi
Note: the same issue comes up as before in part a)
============================================================
Part c)
Answer: sqrt(19pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi
The radius can be found by taking the square root of A divided by pi under the root sign.
Formula
r = sqrt(A / pi)
r = sqrt(A * pi/( pi * p)i)
the root of pi^2 is pi
r = sqrt(A * pi)/pi
Problem A
r = √(50 * π) / π <<<< answer
Comment
For each problem, all you need do is put in the given areas in A B C. I don't know what your input will do with the square root sign; you can write sqrt(50 * pi) / pi
B
r = √(27*π) / π
C
r = √(19* π) / π
Which of these shows 8 + 3m rewritten using the commutative property of addition? 8m + 3 8 − 3m 3m − 8 3m + 8
Answers
Reason:
★Commutative Property★
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.
For addition, the rule is:
"a + b = b + a"
Hope this helps!
Answer:(3m+8)
Step-by-step explanation:
hello can you please help me posted picture of question
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[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Explanation:
For the first given equation, we will need to isolate the x². This can be done as follows:
x² + y² = 25
x² + y² - y² = 25 - y²
x² = 25 - y² ..................> I
For the second given equation:
We will remove every x² and substitute with its equivalence from I as follows:
[tex] \frac{x^2}{16} + \frac{y^2}{9} = 1[/tex]
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Hope this helps :)
It is the c)25-y^2-y^2 by 16-9 = 1
There are 2,000 eligible voters in a precinct. 548 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 548 surveyed, 474 said they would vote for the democratic incumbent. using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the democratic incumbent?
Answers
Point estimate, p = 474/548 = 0.865 or 86.5%
Z at 0.99 confidence coefficient = 2.58
Confidence limits = p +/- Z*Sqrt [p(1-p)/n] = 0.865 +/- 2.58 Sqrt [0.865(1-0865)/548] = 0.865 +/- 0.0378 = (0.8272,0.9028) or (82.72%,90.28)
(-8,7),(-9,-5) write in Ax+By=C
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After the hairdresser Jenny had 27 centimeters cut off her hair how many decimeters of hair did jenny have cut off
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Answer:
2.7 dm
Step-by-step explanation:
You want to know the number of decimeters in 27 centimeters.
SI PrefixesThe SI prefix "deci-" means 1/10.
The SI prefix "centi-" means 1/100.
This tells you that 10 cm = 1 dm.
27 cm = (27 cm) × (1 dm)/(10 cm) = 2.7 dm
Jenny had 2.7 dm of hair cut off.
17.5% as a fraction in simplest form?
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The function F(x) = log0.5 x is increasing. The answer is B. False. Just finished taking the quiz I had guessed.
A. True
B. False
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Answer:
The statement is false
B is correct
Step-by-step explanation:
Given: [tex]f(x)=\log_{0.5}x[/tex]
Increasing function.
Log function:
[tex]y=\log_ax[/tex]
If 0<a<1 then y is decreasing function.
If a>1 then y is increasing function.
Now, we compare the given function
[tex]\log_ax\rightarrow \log_{0.5}x[/tex]
a=0.5
0.5<1
If 0<a<1 then y is decreasing function.
Therefore, f(x) is decreasing. But we are given f(x) is increasing.
Hence, The statement is false
5.
Find the present value of the annuity.
Amount Per Payment: $6,225
Payment at End of Each: Quarter
Number of Years: 6
Interest Rate: 8%
Compounded: Quarterly
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where
[tex]PV[/tex] is the present value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of payments per year
[tex]t[/tex] is the number of years
We know for our problem that [tex]P=6225[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{8}{100} [/tex]
[tex]r=0.08[/tex]
Since the interest is compounded quarterly, it is compounded 4 times per year, so [tex]n=4[/tex]. Similarly, since the payment is made at the end of each quarter, it is made 4 times per year; therefore, [tex]k=4[/tex].
Lets replace the values in our formula:
[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{(-kt)} }{ \frac{r}{n} }] [/tex]
[tex]PV=6225[ \frac{1-(1+ \frac{0.08}{4})^{(-(4)(6)} }{ \frac{0.08}{4} }] [/tex]
[tex]PV=117739.19[/tex]
We can conclude that the present value of the annuity is $117,739.19
A homeowner plants two flowerbeds around his garage. What is the total area he will have planted. Round to nearest tenth.
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Heong cut a slice of birthday cake. The slice formed the angle shown. What is the measure of the angle shown?
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One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint?
A) (−4, −6)
B)(−8, −4)
C)(10, 5)
D)(−8, 4)
Answers
The ratio of sugar to flour is 2:3. If there are 6 cups of sugar, how many cups of flour are there
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cross multiply
5x=2x1
simplify
5x=2
divide each side by 5 to find x
x=2/5
2/5 or 0.4 cups of flour are needed
answer= 2/5
Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?
Answers
c + m = 270
After 1/3 of cupcakes are sold (leaving 2c/3) and 18 more muffins are baked (m + 18), there are twice as many cupcakes as muffins:
2c/3 = 2(m + 18)
2c/3 = 2m + 36
c = 3m + 54
Substituting into the original equation:
3m + 54 + m = 270
4m = 216
m = 54 muffins
c = 3(54) + 54 = 216 cupcakes
The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Answers
3,14*7=21.98
21.98*6=131,88≈132
The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Solution:
Radius of cylindrical soup can= 3.5 cm
Height of cylindrical soup can= 6 cm
Area of cylinder =2πrh
So, Area of label of cylindrical soup can=2πrh
Plugging in the value of r and h in the formula
Area of label=2*π*3.5*6
Multiplying the constants, we get
Area=2*π*21
Area=42π
Plugging in the value of π
Area=42*[tex]\frac{22}{7}[/tex]
Multiplying the numerators
Area=[tex]\frac{924}{7}[/tex]
Area=132 sq.cm
Answer: Option (C)
Area of label= 132 sq. cm
The problem is in the picture
Answers
Answer:
∠1 and ∠2,
∠3 and ∠4,
∠5 and ∠6
Explanation:
Supplementary angles are angles opposite each other that share the same line that is being dissected by a perpendicular line. The sum of their angles will always equal 180 degrees.
Angles 1 and 2 are an example of such supplementary angles. They share the horizontal line but are being dissected by descending line which creates their angles.
Angles 3 and 4 are more of the same. They share the somewhat-vertical line and are dissected by a different descending line that created them.
Lastly, Angles 5 and 6 are also supplementary angles. They share the somewhat-vertical line and are dissected by the horizontal line, resulting in their angles.
Angles 7 and 8 are not supplementary angles. Rather, they are vertically-opposite angles, or vertical angle pairs, two angles lying opposite each other existing at the point where two lines intersect. These angles have the same exact measurement and their sum will never equal 180 degrees.
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]
Answers
The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.
Answer:
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
Step-by-step explanation:
To find the absolute extrema values of [tex]f(x) = 6x^3 - 9x^2 - 108x + 6[/tex] on the closed interval [−3, 4] you must:
1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.
[tex]\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108[/tex]
[tex]18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3[/tex]
2. Evaluate f(x) at all the critical values and also at the two values -3 and 4
[tex]\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right[/tex]
3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.
Therefore,
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
Identify the figure shown and find its surface area. Explain how you found your answer.
Answers
To find the surface area you need to first find the areas of the triangles, then the square, in the end you have to add them together.
Since we know the area of a triangle is 1/2bh we know that one if the triangle in the figure is
9*16/2=72(in^2)
there are four of these so we multiply it by 4
4*72=288(in^2 aka squared inches)
Then we need to find the area of the square. side * side=9*9=81 (in^2)
Add them together we get the surface area.
288+81=369 (in^2)
What is the vertex of the quadratic y=-2x^2-4x-5
Answers
We will need to complete square to write the equation in the vertex form.
y=-2(x²+2x)-5
y=-2(x²+2x+1)-5+2
y=-2(x+1)² - 3
Vertex (-1,-3)
Answer:
(-1,-3)
Step-by-step explanation:
I just took the test, and I got 100%!!!
Which of the following holds about 800 milliliters o f water?
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The hyperbola (x-5)^2/7 - (y+3)^2/9 = 1 is shifted to the right by 4 units and upward by 3 units. the new center of the hyperbola is
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(5, -3) +(4, 3) = (9, 0)
Answer:
( 9 ,0)
Step-by-step explanation:
Given : [tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex] is shifted to the right by 4 units and upward by 3 units
To find : New center of the hyperbola .
Solution : We have given
[tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex]
Center of hyperbola is ( 5 , -3)
By the transformation rule f(x) →→ f(x -h) + k it mean f(x) is shifted to right by h unit and k unit up.
Then Center of hyperbola is shifted to the right by 4 units and upward by 3 units.
( 5 , -3) →→ (5 + 4 , -3 + 3
( 5 , -3) →→ ( 9 ,0)
Therefore, new center is ( 9 ,0).
Find the length of AB , given that DB is a median of the triangle and AC = 24.
Answers
Answer:
AB = 12 units
Step-by-step explanation:
We are given the following information in the question:
DB is the median of the triangle.
AC = 24 units
Property of median of a triangle:
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.Thus, a median divides the side of triangle in two equal parts.Thus, DB divides AC in two equal parts.
Thus, we could say:
AB = BC
We have to find the length of AB.
[tex]\text{AB} = \displaystyle\frac{AC}{2} = \frac{24}{2} = 12\text{ units}[/tex]
Thus, AB is 12 units.
11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball?
Answers
[tex] |\Omega|=25\cdot24=600\\
|A|=11\cdot14+14\cdot13=154+182=336\\\\
P(A)=\dfrac{336}{600}=\dfrac{14}{25}=56\% [/tex]
solve the system of equations 5x-2y=88 3x+4y=58 show all work
Answers
5x - 2y = 88
3x + 4y = 58
Multiplying the 1st equation by 2, we get the new set of equations as:
10x - 4y = 176
3x + 4y = 58
Adding the two equations, we get:
10x - 4y + 3x + 4y = 176 + 58
13x =234
x = 18
Using the value of x in 1st equation, we get:
5(18) - 2y = 88
- 2y = 88 -5(18)
-2y = -2
y = 1
So, the solution of the equation is (18, 1)
[tex]3x+4\cdot(2.5x-44)=58\\3x+10x-176=58\\13x-176=58\ \ \ |\text{add 176 to both sides}\\13x=234\ \ \ \ |\text{divide both sides by 13}\\x=18\\\\\text{substitute value of x to the equation}\ 1^o\\\\y=2.5\cdot18-44=45-44=1\\\\Answer:\ \boxed{\left\{\begin{array}{ccc}x=18\\y=1\end{array}\right}[/tex]
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. find the probability that the number drawn is a multiple of 77 or a multiple of 4.
Answers
Multiples of 77: 1, 7, 11
Multiples of 4: 1, 2, 4
Therefore, multiples of 77 or 4 are: 1, 2, 4, 7, 11 = 5 numbers
P (multiples of 7 or 4) = 5/25 = 1/5 = 0.2