Answer:
true
Step-by-step explanation:
Determine if x + 2 is a factor of p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8 and explain why.
Answer:
(x+2) is a factor of P(x)
Step-by-step explanation:
Determine if x + 2 is a factor of p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8
[tex]p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8[/tex]
To determine (x+2) is a factor , we set x+2=0 and solve for x
[tex]x+2=0 , x=-2[/tex]
then we replace x with -2 in p(x)
[tex]p(x) = x^4 + 3x^ 3 + 4x ^2 - 8[/tex]
[tex]p(-2) = (-2)^4 + 3(-2)^ 3 + 4(-2)^2 - 8[/tex]
[tex]p(-2) = 16-24+16- 8=0[/tex]
WE got p(-2)=0 , so (x+2) is a factor of P(x)
Which sequence is geometric and has 1/4 as it’s fifth term and 1/2 as common ratio is it A)...,1,1/2,1/4,1/8,...
B)...,1/4,1/2,1,2,...
C)...,1/72,1/36,1/18,1,9,
D)...,8,4,2,1,...
Answer:
Option A - [tex]......,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
Step-by-step explanation:
Given : A geometric has [tex]\frac{1}{4}[/tex] as its's fifth term and [tex]\frac{1}{2}[/tex] as common ratio.
To find : Which sequence is geometric ?
Solution :
The geometric sequence is defined as [tex]a,ar,ar^2,ar^3...[/tex]
where, a is the first term and r is the common ratio.
The nth term of the sequence is [tex]a_n=ar^{n-1}[/tex]
We have given, [tex]r=\frac{1}{2}[/tex] and [tex]a_5=\frac{1}{4}[/tex]
The 5'th term is
[tex]a_5=ar^{5-1}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{2})^{4}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{16})[/tex]
[tex]\frac{16}{4}=a[/tex]
[tex]a=4[/tex]
The sequence form is [tex]4,4(\frac{1}{2}),4(\frac{1}{2})^2,4(\frac{1}{2})^3,4(\frac{1}{2})^4,4(\frac{1}{2})^5...[/tex]
[tex]4,2,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
From the given sequence Option A matched with result.
Therefore, Option A is correct.
Jane bought 10 pears and 11 oranges for $10.05 the total cost of one pear and one orange was $0.94 how much did 1 pear and 1 orange cost
Please Send Help
The cost of one pear and one orange is $0.94.
Explanation:To find the cost of one pear and one orange, we need to set up an equation. Let's let x be the cost of one pear and y be the cost of one orange. We can set up two equations based on the given information:
10x + 11y = 10.05 (equation 1)x + y = 0.94 (equation 2)We can solve this system of equations by substitution or elimination. Let's use the substitution method. From equation 2, solve for x in terms of y:
x = 0.94 - y
Substitute this expression for x into equation 1:
10(0.94 - y) + 11y = 10.05
Distribute and simplify:
9.4 - 10y + 11y = 10.05
Combine like terms:
9.4 + y = 10.05
Subtract 9.4 from both sides:
y = 10.05 - 9.4
y = 0.65
Now substitute the value of y back into equation 2 to find x:
x + 0.65 = 0.94
Subtract 0.65 from both sides:
x = 0.94 - 0.65
x = 0.29
Therefore, the cost of one pear and one orange is $0.29 + $0.65 = $0.94.
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Kendra watched two movies. The first lasted 100 min. the second lasted 1 hour, 55 min. Which movie was longer? By how many min.?
What is the recursive rule for the sequence? −7.4, −21.2, −35, −48.8, −62.6
Answer:
[tex]a_n = a_{n-1}-13.8[/tex]
Step-by-step explanation:
The recursive rule for the arithmetic sequence is given by:
[tex]a_n = a_{n-1}+d[/tex] .....[1]
where, d is the common difference of two consecutive terms.
Given the sequence:
−7.4, −21.2, −35, −48.8, −62.6
This is an arithmetic sequence
Here, first term[tex](a_1)[/tex] = -7.4 and d = -13.8
Since,
-21.2+7.4 = -13.8,
-35+21.2 = -13.8 ans so on...
Substitute the given value in [1] we have;
[tex]a_n = a_{n-1}+(-13.8)[/tex]
⇒[tex]a_n = a_{n-1}-13.8[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = a_{n-1}-13.8[/tex] and [tex]a_1[/tex]= -7.4
The recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
What is the recursive rule?The recursive rule refers to the first term of the sequence and describe
the relation to the preceding term with the recursive equation.
The recursive formula for the arithmetic sequence is as follows
[tex]\rm a_{n} = a_{n-1} + d[/tex]
where [tex]\rm a_{n}[/tex] is the nth term and d is a common difference
The arithmetic sequence is given as
−7.4, −21.2, −35, −48.8, −62.6
[tex]\rm a_{1}[/tex] = -7.4 (first term)
d = -21.2+7.4 = -13.8,
d = -35+21.2 = -13.8
Substitute the given value, we get
[tex]\rm a_{n} = a_{n-1} + d[/tex]
[tex]\rm a_{n} = a_{n-1} -13.8[/tex]
Hence, the recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
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what is area
to count the inside of a shape
to count the out side of a shape
none of the above
Area refers to the amount of space inside a shape and is found by counting the inside of the shape. Therefore, the correct answer is option a.
"To count the inside of a shape": This means that when we calculate the area of a shape, we are determining the amount of space or surface area that is enclosed within the boundaries of that shape. In other words, it's the measurement of the total space covered by the shape, and it doesn't include the outer boundary or perimeter.
"To count the outside of a shape" is not an accurate definition for area. The outside of a shape is typically referred to as the perimeter or the circumference, and it represents the measurement of the boundary or the length of the outline of the shape.
"None of the above" is not the correct choice because the area is indeed about measuring the inside of a shape, as explained in the first option.
In summary, when we calculate the area of a shape, we are quantifying the space enclosed within the shape's boundary, not the space on the outside of it.
Therefore, the correct answer is option a.
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Carol payed 271$ to rent a car for 4 days. What was the rate, r, per day to rent the car
For which intervals is the function positive?
Select each correct answer.
(−6, −2)
[−8, −6)
(4, 8]
(−2, 4)
Positive is when the lines are above the X axis
in this graph it is positive from [−8, −6) and (−2, 4)
The function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]
A function is positive in intervals where the graph lies above the [tex]\boldsymbol{x-}[/tex]axis.
A function is negative in intervals where the graph lies below the [tex]\boldsymbol{x-}[/tex]axis.
In intervals [tex]\boldsymbol{(-6,-2),(4,8]}[/tex], the graph lies below the [tex]\boldsymbol{x-}[/tex] axis.
In intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex], the graph lies above the [tex]\boldsymbol{x-}[/tex] axis.
So, the function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]
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Find the missing value to the nearest hundredth cos___= 7/18
The missing value to the nearest hundredth using inverse trigonometric function is 67.11°
Let us say
Cos x = 7/18
x will be the inverse of cosine of (7/18)
What is an inverse trigonometric function?The inverse trigonometric functions are the inverse functions of the trigonometric functions and are used to obtain an angle from any of the angle's trigonometric ratios.
x = cos⁻¹ (7/18)
x = 67.11°
Hence, the missing value to the nearest hundredth is 67.11°.
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I have a math Brainliest reward
What is the value of p?
A. 45
B. 35
C. 55
D. 125
wouldn’t it be 35?
Answer:
35
Step-by-step explanation:
(sorry for bad image. I use OperaGX)
“Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?”
To solve the problem we will first name all the points given to us, and then we will find ∠O, and then we will find the value of x.
The value of x is 22°.
Given to us
∠OAB = 56°
Looking at the diagram below,
In ΔAOB
OA = OB = R, the radius of the circle O,
therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.
Thus, ∠OAB = ∠OBA = 56°
What is the sum of all the angles of a triangle?Sum of all the angles of a triangle = 180°
∠O + ∠AOB + ∠OBA = 180°
We know ∠AOB = ∠OBA, therefore,
∠O + 2(∠AOB) = 180°
∠O + 2(56°) = 180°
∠O = 68°,
In ΔOBC,
BC is the tangent to the circle O, therefore,
∠OBC = 90°
Sum of all the angles of a triangle = 180°
∠O + ∠OBC + ∠OCB = 180°
68° + 90° + ∠OCB = 180°
∠OCB = 180° - 68° - 90°
∠OCB = 22°
Hence, the value of x is 22°.
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Describe the translation in the figure from A to A’
Answer:
d
Step-by-step explanation:
Are lines of symmetry for any given polygon also diagonal?
Check my answer?
Given the proportion a/b = 8/15, which ratio completes the equivalent proportion a/8 = ?
My answer: 15/b
@KirbyLegs
Pre-calculus Help Please! Express the complex number in trigonometric form.
3
A. 3(cos 0° + i sin 0°)
B. 3(cos 90° + i sin 90°)
C. 3(cos 180° + i sin 180°)
D. 3(cos 270° + i sin 270°)
A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees.
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.
Answer:
It is D. 98.5
Step-by-step explanation:
Got it right on edge
Which of the following statements best describes the graph of x + y = 4?
It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.
If 2a+3b=12 and ab=6 find the value of 8a^3+27b^3
Evaluate e−12fe-\dfrac12f e− 2 1 f e, minus, start fraction, 1, divided by, 2, end fraction, f when e=15e=15 e=15 e, equals, 15 and f=2f=2 f=2 f, equals, 2 .
Answer:
the answer is 14
Step-by-step explanation:
If the value of e is 15 and f is 2. Then the value of the expression [e - (1/2)f] will be 14.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ e - (1/2)f
If the value of e is 15 and f is 2.
Then the value of the expression will be
⇒ e - (1/2)f
⇒ 15 - (1/2) x 2
⇒ 15 - 1
⇒ 14
Thus, the value of the expression will be 14.
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A rugby player passes the ball 7.75 m across the field, where it is caught at the same height as it left his hand. At what angle was the ball thrown if its initial speed was 12.0 m/s, assuming that the smaller of the two possible angles was used?
The smaller of the two possible angles used is;
θ = 15.92°.
We are given;
Range of pass; R = 7.75 m
Speed; u = 12 m/s
Formula for range is;
R = [u²sin (2θ)]/g
Where; θ is the angle at which the ball was thrown.
Thus;
7.75 = 12² × (sin(2θ))/9.8
(sin(2θ)) = (7.75 × 9.8)/12²
(sin(2θ)) = 0.5274
2θ = sin^(0.5274)
2θ = 31.83
θ = 31.83/2
θ = 15.92°
Now, if we assume that this angle is to the vertical, it means the angle to the horizontal is;
90 - 15.92 = 74.08°
In conclusion, the two possible angles are 15.92° and 74.08°.
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Question 8 (06.02 LC)
Which statement best describes the expression 2y ÷ 7?
A. 2 times y divided by 7
B. 7 divided by 2 times y
C. 7 times y divided by 2
D. 2 divided by 7 times y
Question 9 (06.06 LC)
Which algebraic property is used to rewrite 2(x + 3) as 2x + 6?
A. Distributive property
B. Associative property
C. Commutative property of addition
D. Commutative property of multiplication
Question 10 (06.02 LC)
Which of these is the algebraic expression for "5 times the sum of 2 and y?"
A. 5 ⋅ 2 + y
B. 2 + 5 ⋅ y
C. 2(5 + y)
D. 5(2 + y)
Answer:
A
Step-by-step explanation:
PLEASE HELPPPPPP
Photo necessities produces camera cases. They have found that the cost , c (x) of making x camera cases is a quadratic function in terms of x.
The company also discovered that it cost $45 to produce 3 camera cases $257 to produce 7 camera cases and $792 to produce 12 camera cases.
Find the total cost producing 1 camera case
The total cost producing 1 camera case is:
$ 11
Step-by-step explanation:Let the quadratic function be:
[tex]c(x)=ax^2+bx+c[/tex]
Now, c(3)=45
This means:
[tex]9a+3b+c=45------------(1)[/tex]
c(7)=257
This means that:
[tex]49a+7b+c=257----------------(2)[/tex]
and c(12)=792
This imply:
[tex]144a+12b+c=792-------------------(3)[/tex]
On subtracting first equation from second we get:
[tex]40a+4b=212------------(4)[/tex]
and on subtracting second equation from third we get:
[tex]95a+5b=535-----------(5)[/tex]
Now on multiplying equation (4) by 5 and equation (5) by 4 and subtracting both equation we get:
a=6
Putting value of a in equation (4) we get:
b= -7
and putting the value of a and b in equation (1) we get:
c=12
Hence, the cost function is:
[tex]c(x)=6x^2-7x+12[/tex]
Now, the cost of producing 1 camera will be the value of c(x) when x=1
i.e.
[tex]c(1)=6-7+12\\\\\\c(1)=11[/tex]
Hence, the answer is:
$ 11
A bike rental company rented out 6 bikes in its first month. The number of bikes it rented tripled each month.
What was the total number of bikes the company rented out for the first 6 months?
Answer:
Step-by-step explanation:
maya has 15 stickers . she places them on a page in rows of 5 . there are 2 flowers and 3 hearts in each row . how many hearts are on the page ? Draw to solve the problem . Write how many hearts are on the page
Please help!! I’ll mark you as brainliest
Why is the standard deviation preferable to the range as a measure of variation? select the correct answer below.
a. the standard deviation is preferable to the range as a measure of variation because the standard deviation takes into account all of the observations, whereas the range considers only the largest and smallest ones.
b. the standard deviation is preferable to the range as a measure of variation because the standard deviation is resistant to outliers, whereas the range is not.
c. the standard deviation is preferable to the range as a measure of variation because it is optimal when the median is used as the center of measure.
d. the standard deviation is preferable to the range as a measure of variation because the standard deviation is always smaller than the range?
Answer:
Option a is right.
Step-by-step explanation:
Both standard deviation and range are used as measures of dispersion. These show the deviations of the data within.
While range is maximum -minimum, the std deviation is the square root of variance and variance is the average of the sum of squares of each entry from the mean.
While range depends only on max and min the std deviation depends on each entry of the sample. Hence std deviation is a better measure.
a. the standard deviation is preferable to the range as a measure of variation because the standard deviation takes into account all of the observations, whereas the range considers only the largest and smallest ones.
Elizabeth has two gardens in her yard. The first garden is 8 feet long and 6 feet wide. The second garden is half the length of the first garden. the area of the second garden is twice the area of the first garden. What is the area of the second garden?
Answer:
the answer is B: 128 divided by 8 equals 16
Step-by-step explanation:I know this becasue to check ur answer after doing multiplication you must do division
multiplication-->division
division-->multiplication
subtraction-->addition
addition-->subtraction
What is the area of a square with sides that are 3 2/5 in long?
Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of one ball after t seconds is represented by the function f(t) = –After how many seconds does the ball return to the ground? Round to the hundredths place as needed.16t2 + 20t.