Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?
x(x2 – 5) + 6(x2 – 5)
x(x2 + 5) – 6(x2 + 5)
x2(x – 5) + 6(x – 5)
x2(x + 5) – 6(x + 5)
Answers
Answer:
D
Step-by-step explanation:
group them first :
( x3+5x2) and ( -6x-30)
then simply by gcf ( greatest common factor) :
x2(x+5) and -6(x+5)
and just add them together:
x2(x+5)-6(x+5)
bonus :
it can be written as (x2-6)(x+5)
The answer choice which shows how to determine the factors of the expression by grouping is; Choice D; x²(x + 5) – 6(x + 5)
Factorisation by groupingThe given expression is; x³ + 5x² – 6x – 30.
The expression is tetranomial, hence, by grouping into 2 terms each; we have;
(x³+ 5x²) (– 6x – 30)Ultimately, upon factorisation of each subunit of the expression, we have;
x²(x+5) -6(x+5)Read more on factorisation by grouping;
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Related Questions
The 7th grade basketball team has won 15 games out of the 20 games they have played this season. If they were to keep up this winning ratio, what is the probability they will win their next game?
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Answer: 3/4
Step-by-step explanation:
Help find the slope of the line. Please and thank you!
Answers
Answer:
There is no slope
Step-by-step explanation:
the end no slope, simple!!
Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)+7sin(θ)−5=0
Select all that apply:
2.57
1.37
1.05
2.35
0.58
1.88
Answers
Answer:θ ≈ 2.57 radians
θ ≈ 0.58 radians
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:
4sin^2(θ) + 7sin(θ) - 5 = 0
(4sin(θ) - 1)(sin(θ) + 5) = 0
Therefore, either:
4sin(θ) - 1 = 0
sin(θ) = 1/4
or:
sin(θ) + 5 = 0
sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)
So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:
θ = arcsin(1/4)
Using a calculator, we find:
θ ≈ 0.2531 or θ ≈ 2.8887
Therefore, in radians, the solutions for θ are approximately:
0.2531 (which is less than 2π)
2.8887 (which is greater than 2π)
So the only answer that satisfies 0 ≤ θ < 2π is:
What is the maximum value and what is the point the maximum value is at?
Answers
9514 1404 393
Answer:
z = 47 at (x, y) = (3, 8)
Step-by-step explanation:
In the attached graph, the inequalities are graphed as their opposites, so the feasible solution region is the white area of the graph. The dashed boundary lines are part of the feasible region. The vertex of the feasible region that is farthest from the origin is ...
(x, y) = (3, 8)
The value of z there is 5·3 +4·8 = 47.
The maximum value of z is 47 at the point (x, y) = (3, 8).
\( {x}^{4} - 12 \\ x - 2\)
find the quotient showing the long division process
Answers
![[tex] {x}^{4} - 12 \\ x - 2[/tex]find the quotient showing the long division process](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Vf6gMZY7eVb5TeD29fr9hcpTcVs27i1r.png)
pls help ill mark brainliest
Answers
Answer:
Step-by-step explanation:
since you are rotating the image it shows y k j and l so it would be 5.5
Following this rule, we will take all coordinates of triangle JKL and apply the rule to rotate the triangle 90° clockwise. We will do each point individually.
Point J to J’: (2, 2)——>(2, -2)
Point K to K’: (3, 5)——>(5, -3)
Point L to L’: (-1, 6)——>(6, 1)
To check, after graphing triangle J’K’L’, a segment can be constructed from the new points to the origin, and another segment can be constructed from the origin to the pre-image’s corresponding points. This should form a ray with a measurement of 90.° So, each corresponding point should be 90° clockwise about the origin.
Now, we must dilate the rotated triangle by a scale factor of k=1/2. To do this, each coordinate in triangle J’K’L’ must shrink by 1/2 f triangle JKL. We must shrink each x and y coordinate in every pair to create a proportional, similar figure. Therefore, dilating the figure by k=1/2 is equivalent to dilating the figure to half the size of the original.
Point J’ to 1/2(J’): (2, -2)——>(2/2, -2/2) = (1, -1)
*Note that one half times a number is the same as that number divided by half.*
Point K’ to 1/2(K’): (5, -3)——>(5/2, -3/2) = (2.5, -1.5)
Point L’ to 1/2(L’): (6, 1)——>(6/2, 1/2) = (3, .5)
So, the final triangle should have coordinates of (1, -1), (2.5, -1.5), and (3, .5)
The data points on the scatter plot below show the theater revenue and the rental revenue generated by each of 25 movies.
Answers
From the distribution of points on the graph, we see that the variables x-y follow a linear relation. The line that fits this distribution passes through the center of it:
Answer
Help&EXPLAIN
Don’t use for points or I’ll take it back and u will be reported
Answers
Answer:
103
Step-by-step explanation:
Every straight line's angle measurement is 180 degrees, so if one angle is 77 degrees, the other must be 103 degrees to equal 180. (77+103=180)
Hope this helps!
Evaluate the given expression for x=5
Answers
x² + 3x - 2
(5)² + 3 × 5- 2
25 + 15 - 2
40 - 2
38...
6X – 10y = 18
-6x + 5y = 12
solve by elimination
show your work
Answers
You can just cross out the Xs. Hope this helps.
Shannon wants to buy 4 coffee mugs for the lowest amount.a set of 4 mugs costs £12
Answers
i can help, but you need to write the whole question..
HELPPPPPPPP MEEEEEEEE
Answers
Answer:
5-9.5=5+(-9.5)
.................
the price of gasoline rose from $2.40 to $2.76 in one month. by whay precent fid the gas price rise?
Answers
Answer:
it increased by 15%
Step-by-step explanation:
im just omega smart
Whats 3/10 + 5/8 ?
I need some help!
Answers
Answer:
37/40
Step-by-step explanation:
1) \(\frac{3}{10}\) + \(\frac{5}{8}\)
2) Have a common denominator
So, multiply 3/10 by 4/4 and multiply 5/8 by 5/5
3) Now, you have \(\frac{12}{40} + \frac{25}{40}\)
4) 12 + 25 = 37 and you keep the denominator 40 since they're the same on both fractions.
5 ) 37/40
4x - (x - 5) + 3 = -1
Answers
Answer:
- 3
Step-by-step explanation:
Step 1:
4x - ( x - 5 ) + 3 = - 1
Step 2:
4x - x + 5 + 3 = - 1
Step 3:
3x + 8 = - 1
Step 4:
3x = - 9
Answer:
x = - 3
Hope This Helps :)
It's in the picture !
Answers
The position of √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.
What is Number line?A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.
Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.
The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.
If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:
To begin, determine the approximate square root values:
√17 is between 4 and 5, since 4² = 16 and 5² = 25.
√6 is between 2 and 3, since 2² = 4 and 3² = 9.
Place the number √17 closer to 5, between 4 and 5.
Place the number √6 between the numbers 2 and 3, closer to 2.
Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.
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Number line attached below,
At the beginning of a population study, a city had 370,000 people. Each year since, the population has grown by 6. Let be the number of years since start of the study. Let y be the city's population . Write an exponential function showing the relationship between y and
Answers
The exponential function that gives the relationship between y and t is:
\(y = 370000(1.06)^t\).
What is an exponential function?An increasing exponential function is modeled by:
\(A(t) = A(0)(1 + r)^t\)
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 370000, r = 0.06.
Hence the equation is:
\(y = A(0)(1 + r)^t\)
\(y = 370000(1 + 0.06)^t\)
\(y = 370000(1 .06)^t\)
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Triangle X(1, 6), Y(5, -2), Z(-5, -1) is mapped onto Δ
Δ
XʹYʹZʹ by a dilation with center (1, -2) and a scale factor of 3. Which function represents this dilation?
(x, y) → (1 + 3(x + 1), -2 + 3(y + 2))
(x, y) → (1 + 3(x - 1), -2 + 3(y - 2))
(x, y) → (1 + 3(x - 1), -2 + 3(y + 2))
(x, y) → (x + 3, y - 6)
30 points
Answers
On solving the provided question we can say that by herons formula, area of the triangle is, A = 2.828
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
the provided points are Triangle X(1, 6), Y(5, -2), Z(-5, -1)
by herons formula
A = \(\sqrt{s(s-a)(s-b)(s-c)}\)
s = a+b+c/3
s = 5+2+5+/3 =12/3 = 4
Area of the triangle is, A =
\(\sqrt{4(5-4)(4-2)(5-4)} \\A = \sqrt{4*1*2*1} \\A = \sqrt{8} \\A = 2\sqrt{2}\\ A = 2*1.414\\A = 2.828\)
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Answer:
2.828
Step-by-step explanation:
How far is the distance from sprinkler head to ?
The distance from sprinkler head B to C is?
.B (-14,-5)
C(-14, 7)
Answers
The distance between the points B and C is 12m
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7
therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)
d=√((0)² + 12²)
d=√144
d= 12m
therefore the distance between the points B and C is 12m.
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The dimensions of a rectangular Pyramid are shown in the diagram below what is the volume of the rectangular pyramid in cubic
Answers
Answer:
160 in³
Step-by-step explanation:
Volume of rectangular pyramid, V = (Length * width * height) / 3
Length = 10 in ; width = 8 in ; height = 6 in
V = (10 * 8 * 6) / 3
V = 160 in³
2radical3+3radical2
Rationalize the denominator (simplify)
(3-√2
Answers
Step-by-step explanation:
ucixidepchflgkckcudkchdkgldjcisifiic
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 10 percent annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. What will the value of each bond be if the going interest rate is 5 percent, 8 percent, and 12 percent?
Answers
Answer:
two bonds in his portfolio that have a face value of $1000 and pay an 11% annual coupon. Bond L matures in 12 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 6%, 8%, and 12%? An investor has two bonds in his portfolio that have a face value of $1,000 and pay
Step-by-step explanation:
PROBABILITY (Chapter 10)223EXERCISE 10B1 Jose surveyed the length of TV commercials in seconds.Estimate, to 3 decimal places, the probability that a randomlychosen TV commercial will last:a 20 to 39 secondsb more than a minutec between 20 and 59 seconds inclusive.Length Frequency0 - 19 1720 - 39 3840 - 59 1960+4
Answers
Solution:
The probability of an event is expressed as
\(Pr(\text{event)}=\frac{\text{Number of desired outcome}}{Number\text{ of possible outcome}}\)Given the survey as shown below:
a) Probability that the chosen TV commercial will last 20 to 39 seconds.
Thus,
\(\begin{gathered} Pr(20-39\text{ seconds)=}\frac{frequency\text{ of 20-30 seconds}}{total\text{ frequency}} \\ =\frac{38}{78} \\ =0.4871794872 \\ \therefore Pr(20-39\text{ seconds)}\approx0.487\text{ (3 decimal places)} \end{gathered}\)Hence, the probability that the chosen TV commercial will last 20 to 39 seconds is 0.487.
b) Probability that the chosen TV commercial will last more than a minute.
Thus,
\(\begin{gathered} Pr(\text{more than a minute)=Pr(60+)=}\frac{4}{78} \\ =0.05128205128 \\ \Rightarrow Pr(\text{more than a minute)}\approx0.051\text{ (3 decimal places)} \end{gathered}\)Hence, the probability that the chosen TV commercial will last more than a minute.is 0.051.
c) Probability that the chosen TV commercial will last between 20 and 59 seconds inclusive.
Thus,
\(\begin{gathered} Pr(20\text{ and 59 seconds inclusive)=Pr(20-39) and Pr(40-59)} \\ \text{where} \\ \text{Pr(20-39)=}\frac{38}{78} \\ \text{Pr(40-59)=}\frac{19}{78} \\ \text{thus,} \\ Pr(20\text{ and 59 seconds inclusive)=}\frac{38}{78}\times\frac{19}{78} \\ =\: 0.1186719264 \\ \Rightarrow Pr(20\text{ and 59 seconds inclusive)}\approx0.119\text{ (3 decimal places)} \end{gathered}\)Hence, the probability that the chosen TV commercial will last between 20 and 59 seconds inclusive is 0.119.
If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
C) 3 years
D) 308 years
Answers
Answer:
approx 32years so pick answer A
Step-by-step explanation:
22000x4=88000
22000x1.045^t
22000x1.045^31=84,104
22000x1.045^32=89,979
Quisssssssssss !!!!!
x + 5y - 7z + 10x - 6z + 10y - 14y = ?
Answers
\(\:\)
◇◆□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□◆◇
x + 5y + 7z + 10x - 6z + 10y - 14y
( x + 10x ) + ( 5y + 10y - 14y ) + ( 7z - 6z )
11x + y + z
◇◆□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□◆◇
\(\:\)
__________
\( \: \)
x + 5y - 7z + 10x - 6z + 10y - 14y = ?
= (1x + 10x) + (5y + 10y - 14y) + (-7z - 6z)
= 11x + y - 13z
Write the equation that is parallel to the question: y = -2/3x - 5 and goes through point: (6,-1)
Answers
Answer:
y = -2/3x + 3
Step-by-step explanation:
Parallel lines have the same slope so we already know
y = -2/3x + b
Solve for b using the point given
-1=-2/3(6)+b
-1+4=b
b=3
y = -2/3x + 3
Using a calculator or statistical software, find the linear regression line for the data in the table below.
Using the regression with the values rounded to the nearest hundredth, find the value of y at x=7. Round your answer to the nearest hundredth if necessary.
x y
0 2.83
1 3.33
2 6.99
3 8.01
4 7.62
5 7.66
Answers
Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.
To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.
Using the provided data, the linear regression line equation is:
\(\[ y = 1.3642x + 3.2324 \]\)
To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:
\(\[ y = 1.3642(7) + 3.2324 \]\)
Simplifying the equation, we get:
\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)
In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.
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A rectangular lot is 80 yards long and 50 yards wide.
Give the length and width of another rectangular lot that has the same perimeter but a larger area.
Answers
Answer:
55 Wide and 75 Long works.
Step-by-step explanation:
Since the Perimeter of the original is likely 80 + 80 +50 + 50 = 260 since it it a rectangular lot, 55 + 75 + 55 + 75 = 260 as well, meaning no change in perimeter. Now when we look at the area 80 x 50 = 4000, but
55 x 75 = 4125, leading to a larger plot
Two skateboarders start a race at the same time. Skateboarder A travels at a steady rate of 15 feet per second. Skateboarder B travels at a steady rate of 22 feet per second. After 4 minutes, how much farther will Skateboarder B have traveled? Explain your reasoning.
Answers
Answer:
Skateboarder B will have traveled 1,680 feet farther.
Step-by-step
Possible reasoning: There are 240 seconds in 4 minutes
If f(3) = 24, what is f-1 (24)?
Answers
Answer:
f=25
Step-by-step explanation:
24+1=25
25-1=24