Answer:
Option a is correct
Step-by-step explanation:
Given: [tex]3x^4+x^2-1[/tex]
To find: roots of the equation
Solution:
A number x is a root of an equation if it satisfies the equation. It is a real root if it is also a real number.
[tex]3x^4+x^2-1[/tex]
Take [tex]y=x^2[/tex]
[tex]3x^4+x^2-1=3y^2+y-1[/tex]
For an equation of the form [tex]ay^2+by+c=0[/tex], roots are given by [tex]y=\frac{-1\pm \sqrt{1+12}}{6}[/tex]
So,
[tex]x^2=\frac{-1\pm \sqrt{1+12}}{6}=\frac{-1\pm \sqrt{13}}{6}\\x=\pm \sqrt{\left ( \frac{-1\pm \sqrt{13}}{6} \right )}[/tex]
Real zeroes:
[tex]x=\pm \sqrt{\left ( \frac{-1+\sqrt{13}}{6} \right )}\\=\pm \sqrt{\left ( \frac{-1+ 3.61}{6} \right )}\\=\pm \sqrt{\left ( \frac{2.61}{6} \right )} \\=\pm \sqrt{0.44}\\=\pm 0.7[/tex]
Answer:a. -0.7, 0.7
Step-by-step explanation:
Here are the first five terms of an arithmetic sequence. 4 9 14 19 24 Find, in terms of n, an expression for the nth term of this sequence
Answer:
The nth term can be represented by;
Tn = 5n- 1
Step-by-step explanation:
In this question, we are concerned with finding an expression in terms of n for then the term of the sequence.
Mathematically, the nth term of a sequence Tn can be represented by the formula;
Tn = a + (n-1)d
where a is the first term in the sequence which is 4 , and d is the common difference which is the difference between 2 consecutive terms which is 9-4= 5
our n is n, since we do not know the number of terms we are finding for
Plugging these values, we have;
Tn = 4 + (n-1)5
Tn = 4 + 5n -5
Tn = 5n- 1
The area of a rectangle is 36 sg in and the length of the rectangle is 9 in Which equation could be used to find the width of the
rectangle?
Answer:
Step-by-step explanation:
[tex]Width=\frac{Area}{length}\\\\=\frac{36}{9}\\\\[/tex]
= 4 inches
Answer:
9×W=36 or 36÷9=W
Step-by-step explanation:
to find the area of a figure you multiply L×W in this situation you only have length. soo find what times 9 = 36 or 36÷9 to find Width
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013. A line was fit to the data to model the relationship. Which of these linear equations best describes the given model?
Answer:
y=40x+800 and 1600
Step-by-step explanation:
Answer:
C and 1600
Step-by-step explanation:
If you are good at figuring out sequences in math please help! Rewarding more points!
Answer:
-62.5008
Step-by-step explanation:
Find the pattern first: -75/15 = -5
Find the first 7 terms: -3/-5, 3/25, -3/125, 3/625
Add: -62.5008
Answer:
-62.5008
Step-by-step explanation:
The terms form a geometric sequence with first term -75 and common ratio -1/5. The sum of n terms of such a sequence is...
Sn = a1(1 -r^n)/(1 -r)
For the values of a1, r, and n, this sum is ...
S7 = -75(1 -(-1/5)^7)/(1 -(-1/5)) = -75(1 +1/78125)/(1 +1/5)
= -75(13021/15625) = -62 313/625
= -62.5008
The sum of the first 7 terms of the sequence is -62.5008.
Rewrite the expression in the form 4^n4 n 4, start superscript, n, end superscript. (4^{6})(4^{-8})=(4 6 )(4 −8 )=(, 4, start superscript, 6, end superscript, ), (, 4, start superscript, minus, 8, end superscript, ), equals
To multiply powers with the same base, like (4^6)(4^-8), add the exponents to get 4^(6-8) = 4^-2. Converting the negative exponents gives us 1/4^2 or 1/16 as the simplified expression.
Explanation:To rewrite the expression in the form 4n4n, we use the rule that when multiplying two numbers with the same base, we add their exponents. So, (46)(4-8) = 4(6 + (-8)) = 4-2 = 1/42 = 1/16.
When multiplying powers with the same base, you simply add the exponents. In the expression (4^{6})(4^{-8}), we add the exponents 6 and -8. The rules of exponents tell us that 4^{6} \times 4^{-8} = 4^{6-8} = 4^{-2}. Negative exponents indicate the reciprocal of the base raised to the positive of that exponent. Therefore, 4^{-2} = \frac{1}{4^{2}} = \frac{1}{16}. This simplified expression demonstrates how to work with exponents and manage negative exponents effectively.
What is the value of s3 when: (infinite geometric series)
The value of S₃ is 65/9.
what is a geometric series?A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. S= a + ar + ar² + ar³+ . . .
a=start term r =common ratio
Given here, the nth term is 5(1/3)ⁿ⁻¹
therefore the sum of the first 3 terms of the geometric series is
S₃ = 5(1/3⁰) +5(1/3)¹+5(1/3)²
= 1+ 5/3 + 5/9
= 65/9
Hence the final answer is 65/9
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A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. A regular pentagon has an apothem with a length of 3 centimeters and a perimeter of 21.8 centimeters. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2
Answer:
C. [tex]32.7cm^{2}[/tex]
Step-by-step explanation:
Area = (Perimeter x apothem) / 2
Area = 21.8 x 3 / 2
Area = 65.4 / 2
Area = [tex]32.7cm^{2}[/tex]
C. The area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².
Area of the regular pentagonThe area of the regular pentagon is calculated as follows;
Area = aP/2
where;
a is apothem of the pentagonP is perimeter of the pentagonArea = (3 x 21.8)/2
Area = 32.7 cm²
Thus, the area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².
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Use the table of values to calculate the linear correlation coefficient r.
X Y
4 -5
53 -1
86 13
162 16
The linear correlation coefficient r is **1.2237445080439002**.
To calculate the linear correlation coefficient r, we can use the following formula:
[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]
where:
* [tex]\sum[/tex] is the sum of the values
* [tex]\bar x[/tex] is the mean of x
* [tex]\bar y[/tex] is the mean of y
First, we need to calculate the mean of x and y:
[tex]\bar x[/tex] = (4 + 53 + 86 + 162) / 4 = 71.25
[tex]\bar y[/tex] = (-5 - 1 + 13 + 16) / 4 = 5.75
Next, we need to calculate the sum of the squared deviations from the mean for x and y:
[tex]\sum(x - \bar x)^2 = (47.25^2 + 17.25^2 + 14.25^2 + 90.75^2) = 10148.5[/tex]
[tex]\sum(y - \bar y)^2 = (11.25^2 + 6.75^2 + 7.25^2 + 10.25^2) = 317.5[/tex]
Now, we can calculate the linear correlation coefficient r:
[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]
r = (47.25 * 11.25 + 17.25 * 6.75 + 14.25 * 7.25 + 90.75 * 10.25) / √(10148.5 * 317.5)
r = 1.2237445080439002
Therefore, the linear correlation coefficient r is **1.2237445080439002**.
This value indicates a strong positive correlation between x and y.
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Step 4: Factor the function to find the x-intercepts.
The x-intercepts are:
Answer:
(5,0) and (-1,0)
Step-by-step explanation:
f(x) = 3^x Find f(x) when x = 8.
Answer:
f(8) = 3^8 = 6561
Step-by-step explanation:
f(x) = 3^x
Let x =8
f(8) = 3^8
= 6561
Answer:
f(8) = 6561
Step-by-step explanation:
f(x) = 3^x Substitute x = 8
f(8) = 3^8 Simplify the exponent
f(8) = 6561
If you are good at determining sequences please help! (Show work)
Answer:
-62.5008
Step-by-step explanation:
the pattern here is dividing by -5, so just continue dividing by -5 starting on -3 and continuing 4 more times. record each number and then add them together using a calculator. you will get -62.5008
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answer:
C.
D.
E.
Step-by-step explanation:
The two options that yield the same value for 'x' as the equation 'Three-fifths (30 x minus 15) = 72' are '3 (6 x minus 3) = 72' and 'x = 4.5'. The confusion can be eliminated by simply breaking down and solving the initial equation for 'x', and then substituting the calculated value for 'x' into the optional equations.
Explanation:To discover which options yield the same value as 'Three-fifths (30 x minus 15) = 72', we first need to solve the given equation for 'x'. This can be done as follows:
Multiply both sides by 5/3 to get rid of the 3/5 in front of the bracket: (30 x minus 15) = 120,Add 15 to both sides to isolate 30x on the left side: 30x = 135,Finally, divide by 30: x = 4.5.Substitute x = 4.5 into each option:
For '18 x minus 15 = 72', 18(4.5) - 15 isn’t equal to 72, so this is not correct.For '50 x minus 25 = 72', 50(4.5) - 25 isn’t equal to 72, so this isn’t correct as well.For '18 x minus 9 = 72', 18(4.5) - 9 isn’t equal to 72 either, hence, it is also incorrect.For '3 (6 x minus 3) = 72', 3(6*4.5 - 3) equals to 72, so this is correct.For 'x = 4.5', this is obviously correct as it matches our calculated value.Therefore, '3 (6 x minus 3) = 72' and 'x = 4.5' provide the same value for x as the initial equation 'Three-fifths (30 x minus 15) = 72'.
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Plz answer for 20 pts
Answer to Problem 1: 5√3
Answer to Problem 2: 21√5
Answer:
[tex] 6) \: \: \sqrt{3} + 4 \sqrt{3} \: = \: 5\sqrt{3}[/tex]
[tex] 7) \: \: 3\sqrt{5}+ 6\sqrt{45} = 3\sqrt{5}+6\sqrt{9} \! \cdot \! \sqrt{5} [/tex]
[tex] = 3\sqrt{5} + 6\! \cdot \! 3 \! \cdot \! \sqrt{5}=3 \sqrt{5} + 18 \sqrt{5} = 21\sqrt{5} [/tex]
The area of the base of this rectangular prism is 6 in.². The height is 12 inches. What is the volume of the rectangular prism?
Answer:
72 in^3
Step-by-step explanation:
The volume is found by V=Bh meaning volume = area of the base * height
V = 6 * 12
V = 72
There are 22 fourth-grade students and 26 fifth-grade students who became cheerleaders. Each cheerleading group will have 8 members. Which equation can be used to find out how many groups can be made?
The number of groups of cheerleaders are 6 groups.
Given that, the number of students in grade 4 is 22 and the number of students in grade 5 is 26.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, each cheerleading group will have 8 members.
Let the number of groups be x.
Now, 22+26=48
So, x=48/8
= 6 groups
Therefore, the number of groups of cheerleaders are 6 groups.
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Final answer:
To find the number of cheerleading groups that can be made with 22 fourth-graders and 26 fifth-graders, we add the total number of students and divide by the group size (8). The equation is k = (22 + 26) / 8, which simplifies to k = 6, meaning 6 groups can be formed.
Explanation:
The question is asking how to calculate the total number of cheerleading groups that can be formed from a given number of fourth-grade and fifth-grade students. In this case, there are 22 fourth-grade students and 26 fifth-grade students, making a total of 48 students. Given that each group should have 8 members, the formula to find the number of groups is the total number of students divided by the number of members per group.
The equation to find the number of cheerleading groups (k) is:
k = Total number of students / Number of members per group
Thus, the equation is:
k = (22 + 26) / 8
When simplified, it gives:
k = 48 / 8
Which equals:
k = 6
Therefore, 6 cheerleading groups can be made.
find the equivalent expression: 12a+6b
1)6(6z+6b)
2)6(2a+b)
3)2(6a+4b)
4)2(10b+4b)
Answer:
2
Step-by-step explanation:
12a+6b
factor out 6
6(2a+b)
For a bookease, Tim wants 6 shelves
ench 284 inches long What total length
of shelving does he need?
Answer:
1704 inches
Step-by-step explanation:
Take the length of each shelf and multiply by the number of shelves
6* 284 =1704 inches
Answer:
1704 in
Step-by-step explanation:
4(sin3x-cos2x)=5(sinx-1)
Keiko uses 8.8 pints of white paint and blue paint to paint her bedroom walls. 4/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
1.76pints of blue paintStep-by-step explanation:
The total number of paint used = 8.8pints
If 4/5 of this amount is white paint, then the amount of white pint is expressed as;
[tex]= \frac{4}{5}*8.8\\= \frac{35.2}{5}\\[/tex]
= 7.04
This means the amount of white paint used is 7.04pints.
amount of blue paint used = Total amount of paint - amount of white paint
amount of blue white paint used = 8.8 - 7.04
amount of blue paint used = 1.76pints of paint
i'll give 30 points and brainlist
Answer:
100 degrees
Step-by-step explanation:
Arc QM = Arc QN = 130°
Arc MN = 360 - Arc QM - Arc QN
= 360 - 2(130)
= 360 - 260
= 100°
product of (2x+3)(2x+4)
Answer:
4x² + 14x + 12
Step-by-step explanation:
There are several different methods you can use to multiply binomials, but I will walk through the FOIL method.
First - Multiply the first terms of each binomial
2x · 2x
Outer - Multiply the outside terms of each binomial (the first term of the first binomial and the second term of the second binomial)
2x · 4
Inner - Multiply the inside terms of each binomial (the second term of the first binomial and the first term of the second binomial)
3 · 2x
Last - Multiply the last term of each binomial
3 · 4
Then you will add each product together to get the expression 4x² + 8x + 6x + 12. This is not our answer as we have to combine like terms to simplify.
After simplifying, 4x² + 14x + 12 will be the answer.
Johnny ate 200 jars of his fathers sugar if johnny got a warning from his papa (While T-posing and floating to him) every 10 jars, how many warnings did he get? (Sorreh I'm not a troll I'm just extremely dumb.)
Answer:
I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4
Step-by-step explanation:6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.
20
Step-by-step explanation:
200 divided by 10 equals 20
You get tired of the sand and head up to the amusment park you can purchase 20 ride tickets for $14 or 30 ride tickets for 22.50 which is the better deal
Answer:
20 ride tickets for $14 is a better deal
Step-by-step explanation:
Considering the two offers
The first deal which is 20 ride tickets for $14 is more advantageous because it offers $1.5 less compare to the second offer as 30 rides would require a sum of $21 for the first deal whereas 30 rides cost $22.50 for the second deal
If the diameter of a circle is 19.3, what is the circumference?
Answer:
60.6
Step-by-step explanation:
The formula for finding the circumference of a circle is C = 2πr
C is circumference, π is pi (we'll just us 3.14 here), and r is radius.
The radius is found by dividing the diameter in half.
19.3/2=9.65
So the equation should look like this:
C = 2(3.14)(9.65)
C = 60.602
C = 60.6
1. Which student correctly simplified the expression 5.2 + 3.6x – 8 + x?
To simplify the expression 5.2 + 3.6x - 8 + x, combine like terms to get -2.8 + 4.6x, which is the final simplified expression.
Explanation:The student's question involves simplifying the expression 5.2 + 3.6x – 8 + x. To simplify the given algebraic expression, combine like terms. Like terms in this expression are the constant terms (5.2 and -8) and the variable terms (3.6x and x).
First, add the constant terms together:
5.2 - 8 = -2.8
Then, combine the variable terms:
3.6x + x = (3.6 + 1)x = 4.6x
Now, put the constants and variable terms together to get the simplified expression:
-2.8 + 4.6x
To check if the simplified expression is reasonable, ensure that all like terms have been correctly combined. There is no further simplification possible, so this is the final answer.
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A polynomial that has a degree of 0 is called ___.
Answer:
constant or constant polynomial
Some call is the zero polynomial
Step-by-step explanation:
Let x be raised to the 0 power
x^0 = 1
This is constant
3x^0 = 3*1 = 3
This is still constant
Answer:
Constant
Step-by-step explanation:
Degree 0 means the highest power of the variable is 0, which also means there's only one term
(Because the powers have to non-negative integers, and 0 is the smallest)
Ax⁰ is the form of a degree-0 polynomial
x⁰ = 1
Ax⁰ = A
Which is a constant
Deanna has a balance of $324.55 in her checking account. She uses her debit card to pay$102.00 for a concert ticket. What is the balance in her checking account now? *
Answer:
$222.55
Step-by-step explanation:
Answer:
$222.55
Step-by-step explanation:
$324.55-$102.00
Find the value of x in the figure
Answer:
I am 99% sure it's [tex]x = 100[/tex]°, here's why (down)
Step-by-step explanation:
The total is 180°. When adding 57° + 23° = 80°. To get [tex]x[/tex], you have to subtract 80° from 180°. The difference is 100°, which is the answer of this problem.
Solve 28 + 7y =91
Y=.....
Answer:
[tex]y = 9[/tex]
Step-by-step explanation:
[tex]28 + 7y = 91 \\ 7y = 91 - 28 \\ 7y = 63 \\ \frac{7y}{7} = \frac{63}{7} \\ y = 9[/tex]
Answer:
Y=9
Step-by-step explanation:
28 + 7y =91
first subtract 28 from both sides
28-28+7y=91-28
7y= 63
then divide both sides by 7
7y/7=63/7
y=9
ANSWER CHECK
to see if the answer is correct substitute the answer you got for the variable
y=9
28 + 7(9)
multiply 7 and 9
7(9)=63
63+28= 91
Which is the measure of
A)93
B.113
C.138
D.180
Answer:
Depends on the angel needed, I'll provide all answers
Step-by-step explanation:
Angel A is 93, because a straight line has an angel total of 180, so in order to find angel A you would just need to subtract
180-87 = 93
Angel B is 87, because angels opposite each other have the same value.
The Angel without a character would be 93 for the same reason :3