The complete factorization of the given polynomial is (x² + 1)(x + 2).
Explanation:To factorize the polynomial [tex]x^3 + 2x^2 + x + 2[/tex], we first look for any common factors. In this case, we don't have any common factors, so we move on to factoring by grouping.
Unfortunately, this cubic polynomial does not factorize nicely into simpler terms using rational numbers. It would involve using heavy algebra and complex numbers to factor. Usually, for a cubic polynomial of this nature, a numerical method will be employed to find its roots.
We can group the terms as [tex]x^3 + 2x^2 + x + 2[/tex]). Taking out the common factors from each group, we get:
[tex]x^2[/tex](x + 2) + 1(x + 2).
Now, notice that we have a common binomial term (x + 2), so we can factor that out as well:
([tex]x^2[/tex] + 1)(x + 2).
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The legs of a right triangle are 4cm and x cm. The hypotenuse is (2x-1)cm. What is x?
Answer:
Step-by-step explanation:
(2x-1)²=x²+4²
4x²-4x+1=x²+16
3x²-4x-15=0
a=3 b=-4 c= -15
D=b²-4ac
=16-4*3*(-15)=196
x1=-b+√D/2a=4+14/6=3
x2=-b-√D/2a=4-14/6=-10/6=-5/3
Answer:
x = 3
Step-by-step explanation:
Using Pythagoras' theorem on the right triangle, then
(2x - 1)² = 4² + x² ← expand parenthesis on the left side and simplify
4x² - 4x + 1 = 16 + x² ( subtract 16 + x² from both sides )
3x² - 4x - 15 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 15 = - 45 and sum = - 4
The factors are - 9 and + 5
Use these factors to split the x- term
3x² - 9x + 5x - 15 = 0 ( factor the first/second and third/fourth terms )
3x(x - 3) + 5(x - 3) ← factor out (x - 3)
(x - 3)(3x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]
However, x must be greater than zero
Hence x = 3 cm
For a two way frequency tables the variables can be found...
A. in each cell
B. in the title of the table
C. along the rows and columns
Answer:
c
Step-by-step explanation:
Notice that there are two variables-- gender and preference-- this is where the two in two-way
Answer:
C)
Step-by-step explanation:
What is the value of a?
Answer options: 27.5, 90, 45, 50
Answer:
90°
Step-by-step explanation:
Arc a subtends and angle of 45° to the circumference of the circle
We know that;
An angle subtended by an arc to the center of a circle is twice the angle subtended by the same chord to the center of the circle.
Therefore, if arc a subtends and angle of 45° to the circumference of the circle then;
a will be = 45 × 2
= 90°
Mrs. McIntyre needs to buy pencils and erasers for her math class. The store is selling a box of pencils for $2 and a box of erasers for $1. She needs to buy four times as many pencils as erasers. If she can only spend $18, how many boxes of each will she buy?
Answer:
8 boxes of pencils and 2 boxes of erasers
Step-by-step explanation:
2 times 4 equals 8, which is the part where she needs to buy 4 times as many pencils as erasers.
8 times 2 is 16 and 1 times 2 is 2 add both 16 and 2 together and you get 18 so she spends all $18
simplify 16a^4 b^2 c
—————-
2abc
Answer:
[tex]\large\boxed{\dfrac{16a^4b^2c}{2abc}=8a^3b}[/tex]
Step-by-step explanation:
[tex]\dfrac{16a^4b^2c}{2abc}=\dfrac{16}{2}\cdot\dfrac{a^4}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{c}{c}=8a^3b[/tex]
x+y+2=0 graph the equation
Answer:
see the attachment for a graph
Step-by-step explanation:
A graphing calculator is a useful tool for this.
___
The x- and y-intercepts are -2, so you can plot those points and draw the line through them.
Given the system below:
ƒ(x) = 2x
g(x) = 2x
Which value(s) of x make ƒ(x) = g(x) a true statement? If necessary, you may choose more than one answer.
0
1
2
3
4
Answer:
B) x = 1
C) x = 4
Step-by-step explanation:
Given:
f(x) = 2x
g(x) = 2^x
We have to find at what value of x, the above two functions are equal in value.
Now we have to check with the each options.
When x = 0, f(0) = 2(0) = 0 ; g(0) = 2^0 = 1 [Anything power 0, is 1]
When x = 1, f(1) = 2(1) = 2 ; g(1) = 2^1 = 2.
when x = 2, f(2) = 2(2) = 4; g(2) = 2^2 = 4
when x = 3, f(3) = 2(3) = 6, g(3) = 2^3 = 8
when x = 4, f(4) = 2(4) = 8, g(4) = 2^4 = 16
The two functions are equal in value when x = 1 and x = 2.
Final answer:
The value(s) of x for which the equation f(x) = 2x and g(x) = 2ˣ are equal are x = 1 and x = 2, as those are the points where the two functions have the same value.
Explanation:
The student seems to be asking for which value(s) of x the equations f(x) = 2x and g(x) = 2ˣ are equal. To find the solution, we need to identify the point where the two functions intersect, by setting them equal to each other and solving for x.
So we set up the equation 2x = 2ˣ and look for solutions. At first glance, it seems there are two obvious solutions:
When x = 1, f(x) = 2 x 1 = 2 and g(x) = 2¹ = 2, so the statement f(x) = g(x) is true.
When x = 0, f(x) = 2 x 0 = 0 and g(x) = 2⁰ = 1, so the statement f(x) = g(x) is not true.
Testing the other provided options similarly, you'll find that:
For x = 2, f(x) = 4 and g(x) = 4, hence f(x) = g(x) is true.
For x = 3, f(x) = 6 and g(x) = 8, hence f(x) = g(x) is not true.
For x = 4, f(x) = 8 and g(x) = 16, hence f(x) = g(x) is not true.
The correct answers are x = 1 and x = 2, where the equation f(x) = g(x) holds true.
What is the best first step to solve 2x - 4 = -2. ???
first you have to add the -4 to the -2 and you get 2. so 2x=2 then you divide 2 by 2x and get x=1
Zach walked his dog for 7/8 hour. They spent 1/2 of the time at the beach. How much time did Zach and his dog spend at the beach?
Answer: [tex]\frac{7}{16}hour[/tex]
Step-by-step explanation:
You know that the total time was: 7/8 hour
You also know that they spent 1/2 of the time at the beach.
Therefore, to calculate the time Zach and his dog spend at the beach (which you can call x) , you must multiply both fractions (7/8 and 1/2).
Then, you obtain the following result:
[tex]x=\frac{7}{8}hour*\frac{1}{2}\\\\x=\frac{7}{16}hour[/tex]
Zach and his dog spent 7/16 of an hour at the beach. This was calculated by multiplying the total walking time of 7/8 of an hour by 1/2, which represents the proportion of the total time spent at the beach.
Explanation:The question is asking for the amount of time that Zach and his dog spent at the beach. We know that they spent 1/2 of their total walking time, which was 7/8 hour, at the beach. To find this, we simply need to multiply those two fractions together. Multiply the numerators (top numbers) together to get the numerator of the product, and multiply the denominators (bottom numbers) together to get the denominator of the product. 1 * 7 equals 7, and 2 * 8 equals 16, so the product is 7/16 of an hour. This is the amount of time they spent at the beach.
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combine like terms. 42y + 22y
Answer:64y
Step-by-step explanation:42+22 then just put the y at the end
which mean absolute deviation would be more consistent 4.2 or 8.5?
8.5 would be more consistent
Answer:
4.2 would be more consistent.
Step-by-step explanation:
( sorry the picture isn’t that good ) Find the area of the unfolded box bottom. Show your work. ( 30 in. on top 5 in. in the corners 20 in. on the sides )
Answer:
1100 in²
Step-by-step explanation:
Find the area of the boxes separately and add them
Solve the word problem. Round your final result to the nearest hundredth.
A pattern for Miata’s new carpet design contains circles, semicircles, and quarter-circles. All circular shapes have a radius of 8 cm. What is the area of a pattern that contains 1 circle, 4 semicircles, and 8 quarter-circles? There should be four answers
Area of circle: _____
Area of semicircles: _____
Area of quarter-circles: _____
Total area of pattern: _____
Area of semicircles
Area of semicircles =
Area of circle =
Area of quarter-circles =
Total area of pattern
Area of quarter-circles
Area of circle
Total area of pattern
The area of the pattern is calculated by finding the area of the circle, semicircles, and quarter-circles separately and then adding them together. The area of the pattern is approximately 1005.31 cm^2.
Explanation:To find the area of the pattern, we need to calculate the area of the circle, semicircles, and quarter-circles separately. The area of a circle is found using the formula A = πr^2, where r is the radius. So, the area of the circle is A = π(8)^2 = 64π cm^2. The area of a semicircle is half the area of a circle, so it is 32π cm^2. The area of a quarter-circle is a quarter of the area of a circle, which is 16π cm^2. To find the total area of the pattern, we add the areas of the circle, semicircles, and quarter-circles: 64π + 4(32π) + 8(16π) = 64π + 128π + 128π = 320π cm^2. Rounding to the nearest hundredth, the total area of the pattern is approximately 1005.31 cm^2.
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Finding the areas of the circles, semicircles, and quarter-circles separately and combining them together yields the pattern's overall area. The pattern's estimated area is 1005.31 cm^2.
To determine the area of the pattern, individual areas of the circle, semicircles, and quarter-circles are computed separately.
Utilizing the formula
A = πr^2
for a circle with a radius (r) of 8 cm, the circle's area is 64π cm^2.
The semicircles, constituting half the circle's area, total 32π cm^2 each.
Quarter-circles, representing a quarter of the circle's area, contribute 16π cm^2 each.
Combining these, the pattern's total area is calculated as 64π + 4(32π) + 8(16π) = 320π cm^2.
Rounded to the nearest hundredth, the total area is approximately 1005.31 cm^2.
This comprehensive approach ensures the accurate summation of all constituent shapes within the intricate pattern.
The length of a rectangle is 5 centimeters less than twice its width. Its area is 42 square centimeters. Find the dimensions of the rectangle.
The width is
and the length is
Answer:
width=6cm, lenth is 7cm
Step-by-step explanation:
Let width of rectangle be x cm
Twice width=2x cm
length=2x-5 cm
Area of the rectangle= L× W =42cm²
(2x-5) × x =42
x(2x-5)=42
2x²-5x-42=0
solving the quadratic equation
x=6cm
width=6cm
length= (2×6)- 5 =7cm
Which expression is equivalent to the expression below? g+g+g+g+g+g
Answer:
6g
Step-by-step explanation:
add all G's
The equivalent expression of g + g + g + g + g + g is 6g
How to determine the equivalent expression?The expression is given as:
g + g + g + g + g + g
Factor out g
g + g + g + g + g + g = g(1 + 1 + 1 + 1 + 1 +1)
Evaluate the sum
g + g + g + g + g + g = g * 6
Evaluate the product
g + g + g + g + g + g = 6g
Hence, the equivalent expression of g + g + g + g + g + g is 6g
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seth finds the slant height of a square pyramid with a base length of 6cm and a height of 7 CM to be approximately 9.2 cm. what mistake did Seth make in finding the slant height of the square pyramid
please help asap
Answer:
He used formula C).
Step-by-step explanation:
The correct formula for the slant height is given by
x^2 = 3^2 + 7^2
x = 7.62 cm.
To get 9.2 he must have used
x^2 = 6^2 + 7^2 = 85
as √85 = about 9.2.
Answer:
the green at the top means i got it right
Step-by-step explanation:
7x + 2(x-5) =46
Solve for x using distribution.
Answer:
X=56/9
Step-by-step explanation:
7x+2(x-5)46
7x+2x-10=46
9x-10=46
9x=46+10
9x=56
The stack consists of five rows of boxes that are all the same size. If another row is added to the bottom of the stack, how many boxes will be in the row?
Answer:
6 rows
Step-by-step explanation:
How many boxes will be in the row ?
5+1=6
five rows
one more added to that same row
add u get six
Answer:
6 boxes.
Step-by-step explanation:
If another row is added to the bottom of the stack, how many boxes will be in the row. The stack consists of five rows of boxes that are all the same size.
5 + 1 = 6 boxes.
u + xy, for u = 18, x = 10, and y = 8
Answer:
98
Step-by-step explanation:
Substitute the given values into the expression
u + xy
= 18 + (10 × 8 ) ← multiply before adding
= 18 + 80
= 98
f(t)=3-2t.2t+t write in standard form
The answer is: [tex]f(t)=-4t^{2}+t+3[/tex]
Why?Since we are given a quadratic function, we need to write it using the standard form of quadratic function (parabola).
The given function is:
[tex]f(t)=3-2t.2t=+t[/tex]
The standard form of a parabola is:
[tex]f(t)=a^{2}+bx+c[/tex]
Where,
a is equal to the quadratic variable coefficient
b is equal to the linear variable coefficient
c is the constant number
So, writing the function in the standard form will be:
[tex]f(t)=3-2t*2t+t=3-4t^{2}+t=-4t^{2}+t+3[/tex]
[tex]f(t)=-4t^{2}+t+3[/tex]
Where,
[tex]a=-4\\b=1\\c=3[/tex]
Have a nice day!
omg this has been killing me and idk how to do it , help please? will mark BRAINLIEST TOO (Show work too ) plz :,)
Figure 1: find the surface area: [(3 x 2 1/4) x 2] for the top and bottom. [(4 1/2 x 2 1/4)x 2] for the left and right squares. [(3 x 4 1/2) x 2] for the front and back. Which should be 20 1/4 + 27 + 13 1/2 = 60 3/4 m. The area is 4 1/2 x 3 x 2 1/4 = 30 3/4 m.
PLEAS HELP!
What is the length of the unknown leg in the right triangle?
Answers on second image.
Answer:
The answer is 15 m.
Step-by-step explanation:
Answer:
b = 15
Step-by-step explanation:
Using Pythagoras' theorem on the right triangle, that is
20² + b² = 25²
400 + b² = 625 ( subtract 400 from both sides )
b² = 225 ( take the square root of both sides )
b = [tex]\sqrt{225}[/tex] = 15
PLZ HURRY IT'S URGENT!!!
What is 0.04 written as a percent? A. 0.4% B. 0.04% C. 4% D. 40%
Answer:
C. 4%
Step-by-step explanation:
find the product (b-2at^2)(3b-3at^2)
Answer: [tex]3b^2-9bat^2+6a^2t^4[/tex]
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- Apply the Distributive property.
- Remember that, according the exponents properties, when you multiply two powers with equal base, you must add the exponents.
- Add the like terms.
Therefore, you obtain that the product is the following:
[tex](b-2at^2)(3b-3at^2)=3b^2-3bat^2-6bat^2+6a^2t^4=3b^2-9bat^2+6a^2t^4[/tex]
A set of data has a normal distribution with a mean of 49 and a standard deviation of 8. Find the percent of data within the following interval. from 33 to 65.
Answer:
95 percent
Step-by-step explanation:
The empirical rule states that approximately 95% of observations will fall within 2 standard deviations of the mean if the population is approximately symmetrical(normal) in distribution.
The interval from 33 to 65 falls within 2 standard deviations of the mean;
49-2(8) = 33
49+2(8) = 65
Thus, 95 percent of data will fall within the interval from 33 to 65
What is the value of X
If x=6 and y=3 is 9_______________________________________
Answer:
x = 2
Step-by-step explanation:
The product of the external part times the entire secant of one secant is equal to the external part times the entire secant of the other secant, that is
(x + 4)(x + 5) = (x + 1)(x + 12) ← distribute factors on both sides
x² + 9x + 20 = x² + 13x + 12 ( subtract x² from both sides )
9x + 20 = 13x + 12 ( subtract 13x from both sides )
- 4x + 20 = 12 ( subtract 20 from both sides )
- 4x = - 8 ( divide both sides by - 4 )
x = 2
Let f(x) = 7x^2-5x+3 and g(x) = 2x^2+4x-6
Part A: f(x)+g(x)
Part B:f(x)-g(x)
Part C: g(x)-f(x)
Answer:
Part A : 9x^2 - x - 3
Part B : 5x^2 - 9x + 9
Part C : -5x^2 + 9x - 9
Assume that, as a newspaper reporter, you must graph data showing that LED light bulbs are more environmentally friendly than traditional light bulbs. Given that the environment is important to everyone, is it ethical to construct a graph that exaggerates the environmental benefits?
No, it is not important that people buy LED light bulbs.
Yes, the environment is important to everyone.
Yes, it is important to make sure that people buy LED light bulbs.
No, results should be presented in a fair and objective manner.
no. No results should be presented in a fair and objective manner.
Answer:
Assume that, as a newspaper reporter, you must graph data showing that LED light bulbs are more environmentally friendly than traditional light bulbs. Given that the environment is important to everyone, is it ethical to construct a graph that exaggerates the environmental benefits?
No, it is not important that people buy LED light bulbs.
Yes, the environment is important to everyone.
Yes, it is important to make sure that people buy LED light bulbs.
No, results should be presented in a fair and objective manner.
Step-by-step explanation:
It is not ethical at all to lie and exaggerate things, but to be objective and say things as they really are.
The answer is: No, the results must be presented in a fair and objective manner.
Gavin drove 85 miles on 10 gallons of gas.How many miles can gavin drive on 25 gallons of gas?
Answer:
212.5
Step-by-step explanation:
10=85
212.5=25
Gavin can drive 8.5 miles with 1 gallon of gas. Therefore, he can drive 212.5 miles with 25 gallons of gas.
Explanation:The question asks how many miles Gavin can drive on 25 gallons of gas, given that he has driven 85 miles on 10 gallons of gas. This requires the use of proportions to calculate. First, you find out how many miles Gavin can drive on 1 gallon of gas, which is 85 miles / 10 gallons = 8.5 miles/gallon. Then, using this value, we can multiply it by 25 gallons to get the total miles Gavin can drive on 25 gallons, which is 8.5 miles/gallon * 25 gallons = 212.5 miles. Therefore, Gavin can drive 212.5 miles on 25 gallons of gas.
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True or false? A circle could be circumscribed about the quadrilateral below
Answer:
Yes
Step-by-step explanation:
A circle can be circumscribed around the four vertices of a quadrilateral if and only if,
both pair of opposite angles inscribed in the quadrilateral are supplementary to each other. By supplementary to each other we mean that their sum is equal to 180°.
In this case we have opposite interior angles supplementary to each other hence we can circumscribe a circle around it. Such Quadrilateral are called cyclic quadrilateral.
Answer:
The answer is True
Step-by-step explanation:
I just got it correct.