when factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten
Answers
Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
Related Questions
Maria is trying to solve -4 - 3 and thinks the answer is going to be negative. Is she correct?
Answers
Answer:
Yes
Step-by-step explanation:
(-4)-3= -7
By subtracting 3 from -4, the answer is -7 meaning Maria is correct.
-4-3=-7
What is the equation of the line that passes through the point (-6, -2) and has a
slope of -1/6?
Answers
Answer:
y=-1/6x-3
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/6(x-(-6))
y+2=-1/6(x+6)
y=-1/6x-6/6-2
y=-1/6x-1-2
y=-1/6x-3
Find a and b using the factor theorem.
\(f(x)=x^3+ax^2+bx-12\) has factor \((x-1), (x+1)\)
Answers
The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.
To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.
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intercept from the lines
Answers
Answer:
I mean tbh its pretty easy
The y intercept is: (0, 2.5)
The x-intercept is: (3.5,0)
just look at the graph lol but if im
wrong sorry
Write an equation that represents the line
Answers
Answer:
y = -2x - 3
Step-by-step explanation:
First, find slope (m) of the line using two points (0, -3) and (1, -5):
\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-3)}{1 - 0} = \frac{-2}{1} = -2 \)
The line intercepts the y-axis at y = -3. Therefore the y-intercept (b) of the line = -3.
To write the equation that represents the line, substitute m = -2, and b = -3 into y = mx + b.
Thus:
y = -2x + (-3)
y = -2x - 3
A real estate office pays its salespeople a weekly retainer of $220 plus commission of 2.5% for the first
$200 000 of the value of each property sold and 2% of each amount after that. Calculate the commission
received if the following houses are sold.
Answers
7- The commission for the sale of a $ 540,000 house was $ 12,020.
8- The commission for the sale of a $ 795,600 house was $ 17,132.
9- The commission during the 4 weeks of February was $ 24,690.
10- The commission during the 4 weeks was $ 27,754.
11- The house was worth $ 440,000.
Given that a real estate office pays its salespeople a weekly retainer of $ 220 plus commission of 2.5% for the first $ 200,000 of the value of each property sold and 2% of each amount after that, to determine the commission received if the following houses are sold, the following calculations must be performed:
7- a $ 540,000 house 540,000 - 200,000 = 340,000 220 + (200,000 x 0.025) + (340,000 x 0.02) = X 220 + 5000 + 6800 = X 12020 = X
8- a $ 795,600 house 795,600 - 200,000 = 595,600 220 + 5000 + (595,600 x 0.02) = X 5220 + 11912 = X 17132 = X
9- a $ 472,500 house and a $ 618,000 house 472,500 - 200,000 = 272,500 618,000 - 200,000 = 418,000 220 x 4 + 5000 + (272,500 x 0.02) + 5000 + (418,000 x 0.02) = X 880 + 10,000 + 5,450 + 8,360 = X 24,690 = X
10- a $ 384,000 unit, a $ 216,000 unit and a $ 593,700 house 384,000 - 200,000 = 184,000 216,000 - 200,000 = 16,000 593,700 - 200,000 = 393,700 880 + 5000 x 3 + (184,000 x 0.02) + (16,000 x 0.02) + (393,700 x 0.02) = X 15880 + 3680 + 320 + 7874 = X 27.754 = X
11- the value of a house whose commission is $ 9800 200,000 x 0.025 = 5000 9800 - 5000 = 4800 2 = 4800 100 = X 100 x 4800/2 = X 240,000 = X 240,000 + 200,000 = 440,000
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Graph the function. Identify whether or not the graph is a function
Answers
Answer:
No
Step-by-step explanation:
Because a vertical line can intersect the curve more than once, the graph does not represent a function.
Represent 2x + 3y = 6 by a graph. Write the coordinates of the point where it meets: (a) x-axis
Answers
The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.
To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Starting with the given equation, we isolate y to one side:
3y = -2x + 6
y = (-2/3)x + 2
Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).
To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.
Setting y = 0 in the equation, we have:
0 = (-2/3)x + 2
(-2/3)x = -2
x = (-2)(-3/2) = 3
Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.
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6x^2=-3x+1 to the nearest hundredth
Answers
The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
6x² = -3x + 1
To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:
6x² + 3x - 1 = 0
Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)
Here; a = 6, b = 3, and c = -1.
Let's substitute these values into the quadratic formula:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)
Therefore, the values of x are -0.73 and 0.23.
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Which function is graphed?
Answers
Answer: C.
Step-by-step explanation:
The function graphed is a piece-wise function.
A piece-wise function is a function where more than one formula is used to define the output over different pieces of the domain.
First lets look at the graph an identify the parts of this function:
We see that the first part of the function is a parabola, and from left to right, it starts from infinity and ends with a hole at (2, 8).
A hole is a single point where the graph is not defined and is indicated by an open circle.
The next part of the function starts with a closed circle at (2,2) and decreases at a rate of -1 (-1/1) to negative infinity.
With the graph broken down. lets identify which function in the answer choices is the graphed one.
From the given answer choices we see that all the functions have x^2 + 4 and -x + 4.
How ever each answer choice has different restrictions which can be further known as limits (calculus).
A limit is the value that a function approaches as the input approaches some value.
Lets look at each answer choices restrictions and compare it to the graph:
For answer choice A, x^2 + 4, it has a restriction where x must be less than or equal to two. In comparison to the graph we see that that function doesn't include two, hence its open circle (hole) at (2, 8). Meaning that x must be only less than two, as that part of the function is approaching two but never equaling two. This makes A. incorrect. For answer choice B, x^2 + 4, it has a restriction where x must be greater than or equal to two. This is completely incorrect when compared to the graph, as that part of the function is not greater than two nor does it equal two. This makes B. incorrect.For answer choice C, x^2 + 4, it has a restriction where x must be less than two. This is true with the given graph as that part of the function contains values that are all less than two and doesn't equal two. To make sure it is fully correct, we must check the second part of the function, -x + 4. That part of the function has a restriction where c must be greater than or equal to two. This is true with the given graph as that part of the function starts on a close circle at (2, 2), showing that two is included, and the x values continue to increase as the function goes to negative infinity.For answer choice D, x^2 + 4, it has a restriction where x must be greater than two. This incorrect as that part of the function is not greater than two. This makes D. incorrect.Candace received a 14% raise as part of a promotion with her work. Before the promotion she was earning $22.50 an hour. What is her new hourly wage?
A)$3.15. B)$26.35. C)$41.85. D)$25.65
Answers
Step-by-step explanation:
Traders have invested $ 100,000 in the Peace Garden Center to boost the capital Mogadishu and make a profit. looga farm income to make people come to the door to take the free tickets for different values $ 0.8 adults and 0.6 children. As many as 150 tickets were sold on Friday for $ 102. produce more child tickets than adult tickets?
Answer:
$25.65
which agrees with answer D
Step-by-step explanation:
14% of $22.50 is calculated using the decimal form (0.14) of the percent as shown below:
0.14 * 22.50 = 3.15
Then the new hourly wage will be this value added to the previous wage:
$22.50 + $3.15 = $25.65
which agrees with answer D
I REALLY REALLY REALLY NEED HELP PLS
Answers
The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.
What is Probability?Probability is measure of likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 indicates an impossible event and 1 indicates certain event
Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:
Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.
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Determine if the ordered pairs represent a direct variation or inverse variation.
{(1, 16), (2, 8), (4, 4)}
A. direct variation
B. inverse variation
Answers
Answer:
A direct variation
Step-by-step explanation:
Grandparents want to make a gift of $100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn: (a) 10.5% compounded continuously? (b) 11% compounded continuously? (c) Describe the effect that this slight change in the interest rate makes over the 20 years of this investment
Answers
Answer:
20
Step-by-step explanation:
20 yenara they hain aahe aahe
my answer is 20 i guess........
Please help me the grading period ends in an hour
Answers
2 60
3 32.7
(The equation for this is 360 / # of angles)
4 140
5 108
6 Trapezoid or quadrilateral
7 not sure sorry
8 square
9 not sure man
What is the solution to the equation squareroot 4t+5=3
Answers
Answer:
Step-by-step explanation:
√(4t+5) = 3
4t + 5 = 9
4t = 4
t = 1
Answer:
Step-by-step explanation:
Remark
This is a bit ambiguous. I'm going to take it to mean
√(4t + 5) = 3
Solution
√(4t + 5) = 3 Square both sides.
(√(4t + 5) )^2 = 3 ^2 If you square something and a √ is involved, sometimes squaring something will get rid of the√ sign. That's what happens here.
4t + 5 = 9 Subtract 5 from both sides.
4t + 5 - 5 = 9-5 Combine
4t = 4 Divide by 4
4t/4 = 4/4
t = 1
- 3х +Зу = 12
у=х+ 4
How many solutions are there
Answers
Answer:
Step-by-step explanation:
As given system of linear equations,
- 3х +Зу = 12у=х+ 4Hence taking 1st equation ,
-3x+3y=12
-3(x-y)=12 ( common -3 )
x-y=-4now take 2nd equation ,
y=x+4
y-x=4Now add these two equations, we get
x-y+ y- x=-4+4
0x+0y=0
so it have infinite many solution because for any value L.H.S =R.H.S PLS HELP ASAP! Given a cone with a height of 6 cm and a base diameter of 6 cm, what is the volume of the cone? Use 3.24 for π
π
Answers
Answer:
56.52 cm³
Step-by-step explanation:
\(\boxed{volume \: of \: cone = \frac{1}{3} \pi {r}^{2}h }\)
Diameter= 2 ×radius
Radius
= 6 ÷2
= 3cm
Height, h= 6cm
Volume of the cone
\( = \frac{1}{3} (3.14)( {3}^{2} )(6)\)
= 56.52 cm³
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
Answers
The number of Jim's model car is 48
How to determine the number of JIm's carFrom the question, we have the following parameters that can be used in our computation:
Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6
This means that
Jim : Terrence = 8 : 6
Also from the question, we have
Terrence owns 36 models cars
This means that
Terrence = 36
Substitute the known values in the above equation, so, we have the following representation
Jim : 36 = 8 : 6
Multiply by 6
Jim : 36 = 48 : 36
So, we have
Jim = 48
Hence, the number of car is 48
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In ΔMNO, m = 140 cm, n = 660 cm and o=640 cm. Find the measure of ∠N to the nearest 10th of a degree.
Answers
Answer:
92 is the right answer
Step-by-step explanation:
The measure for <N is 92.04 degree.
What is Cosine Rule?The square of the length of any one side of a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, multiplied by the cosine of the angle they are a part of.
We have,
m= 140 cm, n= 660 cm and o= 640 cm
Now, using Cosine rule
cos N = (m)² + (o)²- (n)²/ 2 mo
cos N= (140)² + (640)² - (640)² / 2(140)(640)
cos N= (196000 + 409600 - 435600)/ 179200
cos N= 0.03571
N= 92.04
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-3<-(w+3)+4w or -3>=-3(w-5)+6w
Answers
The solution to the compound inequality given as -3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w is w > -2 or w >= -6
How to solve the compound inequality?The compound inequality is given as:
-3<-(w+3)+4w or -3>=-3(w-5)+6w
Rewrite the compound inequality properly as follows
-3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w
Open the brackets in the above compound inequality expression
-3 < -w + 3 + 4w or -3 >= -3w + 15 + 6w
Evaluate the like terms in the above compound inequality expression
-6 < 3w or -18 >= 3w
Divide both sides of the above compound inequality expression by the coefficient of the variable terms
-2 < w or -6 >= w
Rewrite the inequality as:
w > -2 or w >= -6
Hence, the solution to the compound inequality given as -3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w is w > -2 or w >= -6
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PLZ HELP. DUE NOW!!!!!
Since every centipede that Ricky has seen has 30 legs, he concludes that all centipedes have 30 legs. Is Ricky correct? Explain.
a) Ricky is correct because inductive reasoning yields certain truths.
b) Ricky is not necessarily correct, as his premise does not support his conclusion.
c) Ricky is not necessarily correct, as inductive reasoning does not yield certain truths.
d) Ricky is correct because his conclusion is supported by the premise.
Answers
Answer:
a because centi means 100 so he was wrong from the start and ...how the heck did he count em
Step-by-step explanation:
Answer: Ricky is correct because his conclusion is supported by the premise.
Step-by-step explanation: "a previous statement or proposition from which another is inferred or follows as a conclusion." = PREMISE
HIS PREMISE LED TO AN INFERRED CONLUSION
consider the following probability distribution: 1 2 3 4 5 0.1 0.15 0.40 0.25 0.10 find (write it up to second decimal place).
Answers
The mean value is 1.19
x p(x) x*p(x) X^2p(x)
1 0.1 0.1 0.1
2 0.15 0.3 0.6
3 0.4 1.2 3.6
4 0.25 1 4
5 0.1 0.5 2.5
Sum 1 3.1 10.8
Mean =Σx * p(x)
u=3.1
Variance=σ^2
=Σx*p(x)-u^2
=10.8-(3.1)^2 =1 .19
A probability distribution is a frequency distribution that has been idealised. A frequency distribution is a description of a particular sample or dataset. It is the number of times each possible variable value appears in the dataset.
The probability of occurrence determines how many times a value appears in a sample. Probability is a number between 0 and 1 that indicates the likelihood of an event occurring:
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b) An integer, X, written as a product of its prime factors is a² × 7b+2
An integer, Y, written as a product of its prime factors is a³ × 7².
The highest common factor (HCF) of X and Y is 1225.
The lowest common multiple (LCM) of X and Y is 42875.
Find the value of X and the value of Y.
Answers
The value of integers X and Y are 8575 and 6125.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The set of integers is frequently represented by the letter Z in mathematical notation.So, a² from X and 7² from Y (We're solving for a)
Then,
a² from X and 7² from Y (solve for A)
a² 7² = 1225a² 49 = 1225a² = 25a = √25a = 5LCM of X and Y is 42875.
Let's take the biggest exponent as follows:
5³ 7ᵇ⁺² = 42875125 7ᵇ⁺² = 428757ᵇ⁺² = 343 (343 having the same root number 7)So, the value of X and Y:
7ᵇ⁺² = 7³ (Remove 7 just to have the exponents)b + 2 = 3b = 1Now,
X: 5² × 7³ = 8575Y: 5² × 7² = 6125Therefore, the value of integers X and Y are 8575 and 6125.
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What is the instantaneous rate of change y=sqrtx of at x = 2? Responses negative 1 over 2 negative 1 over 4 negative 1 none of these none of these
Answers
The instantaneous rate of change of y = √x at x = 2 is √2 / 2.
To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.
Taking the derivative of y = √x using the power rule for differentiation, we have:
dy/dx = (1/2) × x^(-1/2)
Now, substituting x = 2 into the derivative expression:
dy/dx = (1/2) × 2^(-1/2)
= (1/2) × √2
= √2 / 2
Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.
None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.
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What is the standard form for 4x10,000+8x1,000+2x100+3x10+6x1+7x1/10
choices
48,237.07
48,236.7
4,830.07
none of these
:)
Answers
Answer:
48,236.7
Step-by-step explanation:
40,000 + 8,000 + 200 + 30 + 6 + 7/10
7/10 can also be written .7
A survey of licensed drivers inquired about running red lights. One question asked, "Of every 10 motorists who run a red light, about how many do you think will be caught?" The mean result for 880 respondents was
¯x= 1.92. Suppose we know that σ = 1.83. Compute a 95% confidence interval for the mean opinion in the population of all licensed drivers. (Round your answer to the nearest hundredth.)
Answers
Answer: (0.79, 3.05 )
Step-by-step explanation:
Confidence interval for the population mean:
\(\overline{x}\pm z^c\dfrac{\sigma}{\sqrt{n}}\)
, where \(\overline{x}\) = Sample mean
\(\sigma\) = population standard deviation
n= sample size.
\(z^c\) = Critical z value for confidence interval c.
As per given:
n= 10
\(\overline{x}=1.92\)
\(\sigma=1.83\)
Critical z-value for 95% confidence = 1.96
A 95% confidence interval for the mean opinion in the population of all licensed drivers:-
\(1.92\pm (1.96)\dfrac{1.83}{\sqrt{10}}\\\\=1.92\pm1.134\\\\= (1.92-1.134,\ 1.92+1.134)\\\\\approx(0.79,\ 3.05 )\)
Hence, a 95% confidence interval for the mean opinion in the population of all licensed drivers = (0.79, 3.05)
Find the first five terms of the following sequence, starting with n=1.
Answers
Answer:
-2,1,6,13,22
Step-by-step explanation:
cn = n^2 -3
Let n=1
c1 = 1^2 -3 = 1-3 = -2
Let n=2
c2 = 2^2 -3 = 4-3 = 1
Let n=3
c3 = 3^2 -3 = 9-3 = 6
Let n=4
c4 = 4^2 -3 = 16-3 = 13
Let n=5
c5 = 5^2 -3 = 25-3 = 22
arrange the fractions in increasing order 2/1 1/2 4/4 9/12
Answers
Answer:
Step-by-step explanation:
\(\frac{2}{1} =\frac{24}{12} \rightarrow 4\)
\(\frac{1}{2} =\frac{6}{12}\rightarrow 1\)
\(\frac{4}{4} =\frac{12}{12} \rightarrow 3\)
\(\frac{9}{12} =\frac{9}{12} \rightarrow 2\)
In order: \(\frac{6}{12}, \frac{9}{12}, \frac{12}{12}, \frac{24}{12}\)
Solution: \(\frac{1}{2}, \frac{9}{12}, \frac{4}{4}, \frac{2}{1}\)
A farmer planted corn in two different fields. He planted 500 seeds of regular corn in Field A and 500 seeds of experimental corn in Field B. At
harvest time, more ears of corn had grown in Field A than in Field B. The farmer concluded that more corn grew in Field A because of the type
of corn planted.
Choose two other possible variables that could have caused more corn to grow in Field A.
Answers
Answer:
1. More pollination process in the regular corn planted in field A than that of field B.
2. Low pest and insect attack on corn planted in field A compared to that of B.
Step-by-step explanation:
1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.
Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.
2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.
Answer:
a,c, And gg gamer
Step-by-step explanation: