What is the equation of a line written in slope-intercept form with a slope of 4 that passes through the point (-3, -3)?
a) Factor f(x)=−4x^4+26x^3−50x^2+16x+24 fully. Include a full solution - include details similar to the sample solution above. (Include all of your attempts in finding a factor.) b) Determine all real solutions to the following polynomial equations: x^3+2x^2−5x−6=0 0=5x^3−17x^2+21x−6
By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.
Find all real solutions to the polynomial equations \(x³+2x ²-5x-6=0\) and \(5x³-17x²+21x-6=0\).Checking for Rational Roots
Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).
The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.
By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).
Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:
-4x⁴ + 26x³ - 50x² + 16x + 24 = (x + 2)(-4x³ + 18x² - 16x + 12)Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).
Attempt 2: Factoring by Grouping
Rearranging the terms, we have:
-4x³ + 18x² - 16x + 12 = (-4x^3 + 18x²) + (-16x + 12) = 2x²(-2x + 9) - 4(-4x + 3)Factoring out common factors, we obtain:
-4x³+ 18x² - 16x + 12 = 2x²(-2x + 9) - 4(-4x + 3) = 2x²(-2x + 9) - 4(3 - 4x) = 2x²(-2x + 9) + 4(4x - 3)Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:
2x²(-2x + 9) + 4(4x - 3) = 2x² (-2x + 9) + 4(4x - 3) = 2x²(-2x + 9) + 4(4x - 3) = 2x²(-2x + 9) + 4(4x - 3) = (2x² + 4)(-2x + 9)Therefore, the fully factored form of \(f(x) = -4x⁴ + 26x³ - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).
Solutions to the polynomial equations:
\(x³ ³ + 2x² - 5x - 6 = 0\)Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +
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Answer.::::::::::::::::::::::::
Answer:
C
Step-by-step explanation:
Answer:
C) There are infinitely many solutions since -5=-5 is a true statement.
Step-by-step explanation:
costs that do not change with output are called __________ costs. group of answer choices marginal average fixed variable
Costs that do not change with output are called fixed costs.
Hence the correct option is D.
Fixed costs are the costs that does not change when output gets changed. Fixed cost is also known as overhead cost. For example, insurance, rent, profit, depreciation, and normal cost.
Fixed costs are indirect costs and must be paid irrespective of the level of production, that is, these costs can be incurred even when the level of production is zero. The best example for this is rent of the factory and payment on the lease for the equipment of the factory must be paid even if the level of production is zero.
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the difference of place values of the digit 3 in 53,230
in in the previous activity you solved a system of equations representing the carnival admissions using the elimination method in this activity you will solve the same system using substitution then you'll compare your solution with the solution you obtained in the previous activity by using the elimination method
the two equations from the previous activity are given below
k + a = 500 (1)
3K + 10A equals 3,600 (2)
which equation has at least one of its variables with a 1 as it's coefficient?
Answer:
The value of a=300 and value of k=200
If you solve the above system of equations by elimination method, you will get the same values of a and k.
In Equation 1 \(k+a=500\) both variables k has 1 as their coefficient.
Step-by-step explanation:
We need to solve the system of equations using substitution method
The equation are:
\(k + a = 500--eq(1)\\3k + 10a = 3,600 --eq(2)\)
For substitution method, we find value of k from equation 1 and put in equation 2
\(From \ eq(1) \ we \ get\\k=500-a\)
Putting it in eq(2)
\(3k+10a=3600\\Put \ k=500-a\\3(500-a)+10a=3600\\1500-3a+10a=3600\\7a=3600-1500\\7a=2100\\a=\frac{2100}{7}\\a=300\)
So, we get value of a = 300
Now finding value of k by putting value of a in equation \(k=500-a\)
\(k=500-a\\Putting \ a \ =500\\k=500-300\\k=200\)
So, we get value of k =200
The value of a=300 and value of k=200
If you solve the above system of equations by elimination method, you will get the same values of a and k.
In Equation 1 \(k+a=500\) both variables k has 1 as their coefficient.
Identify equations, expressions, and inequalities
Identify whether each phrase is an expression, equation, or inequality.
HUH PLEASE HELP
Answer:
the middle one goes to the top, top one goes to the middle and bottom stays there
Step-by-step explanation:
6x+5=23
Explain the steps used to solve
Answer:
x = 3
Step-by-step explanation:
Step 1:
6x + 5 = 23
Step 2:
6x = 18
Answer:
x = 3
Hope This Helps :)
Angles a and b are...?
Choose all answers that apply?
a) Complementary
b) Vertical
c) Supplementary
d) None of the above
Answer:
vertical
Vertically opposite angles make a up a 360 degree angle
Answer:
b) Vertical
Step-by-step explanation:
When two lines intersect, 4 angles are formed. Two non-adjacent angles with no common inside points are called vertical angles.
Answer: b) Vertical
if p(x) is the taylor series for f centered at 0, then p( x - 1 ) is the taylor series for f centered at 1. True or False
True. If p(x) is the Taylor series for f centered at 0, then p(x-1) is not the Taylor series for f centered at 1. Instead, to obtain the Taylor series for f centered at 1, you would need to compute a new series with the center shifted to 1.
True. Shifting the center of a Taylor series by adding or subtracting a constant simply results in a new Taylor series centered at the shifted point. In this case, we are shifting the center from 0 to 1 by replacing x with (x-1) in the Taylor series for f, resulting in p(x-1).
In mathematics, the Taylor series or Taylor expansion of a function is an infinite number of points defined by the function at one point. For most ordinary functions, the partial function and its Taylor series are equal at point. The first n + 1 terms of the Taylor series form an n-order polynomial called the nth-order Taylor polynomial function. Taylor polynomials are generally approximate for functions that get better as n increases. Taylor's theorem provides a quantitative estimate of the resulting error using this approach. If the series of Taylor functions converge, the sum is the limit of an infinite number of Taylor polynomials.
A function can diverge from the equation of the Taylor series even if the Taylor series converges. A function is the definition of a point x if it is equal to the sum of the Taylor series over an open interval (or opening in the complex plane) containing x. This means that transactions are resolved anywhere on the clock (or disk).
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Which of the following shows the correct solution steps and solution to
7x – 4 = –18?
A.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
2
2
7
x
7
=
−
2
2
7
x
=
−
2
2
7
7x−4
7x−4+4
7x
7
7x
x
=−18
=−18+4
=−22
=
7
−22
=
7
−22
B.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
1
4
7
x
−
7
=
−
1
4
−
7
x
=
2
7x−4
7x−4+4
7x
−7
7x
x
=−18
=−18+4
=−14
=
−7
−14
=2
C.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
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−
1
4
7
x
7
=
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4
7
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=
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2
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7x−4+4
7x
7
7x
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=−18
=−18+4
=−14
=
7
−14
=−2
D.
7
x
−
4
=
−
1
8
7
x
−
4
−
4
=
−
1
8
−
4
7
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7
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4
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=
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2
7x−4
7x−4−4
7x
7
7x
x
=−18
=−18−4
=−14
=
7
−14
=−2
Answer:
Simplify 7\times -47×−4 to -28−28.
-28=-18
−28=−18
2 Since -28=-18−28=−18 is false, there is no solution.
No Solution
pls help asap
i am awarding brainliest to correct answer
The sum of two consecutive odd integers is -8.what are the integers
Answer:
- 3 and - 5
Step-by-step explanation:
1) 2x + 1 (a number times two = even number. Even number + 1 = odd number)
2) 2x + 3
2x+1+2x+3= -8
4x +4 = - 8
4x = -8 -4
x = -12/4
x = - 3
Tina went out to eat and her bill was $24.75.
She wants to leave the waiter a 20% tip. How
much more money will be added to her bill
once she included the tip?
Answer:
your awnser should be. 24.75 + 20% = $29.70
so the amount added to her bill is $4.95
Answer:
the bill will be 4.95 more than the original cost without the 20% tip.
Step-by-step explanation:
cost before tip: 4.75
cost after 20% tip: 29.70 or 30.00 (rounded)
Which description of a figure and its image match the transformation described by (x,y) → (2x, 2y + 1)?
The figure and its image are similar, but not congruent, and the image has been translated 1 unit up.
The figure and its image are similar, but not congruent, and the image has been translated 1 unit to the right.
The figure and its image are congruent and the image has been translated 1 unit up.
The figure and its image are congruent and the image has been translated 1 unit to the right.
Answer:
you will first extend what you know about coordinate transformations to rotations of two-dimensional figures by 90°, 180°,
Step-by-step explanation:
if T=1/4 A^3B make A the subject of formula
Step-by-step explanation:
A³B = 4T
A³=4T/B
A = cbrt 4T/B. or
³√(4T/B)
hope this helps.
The product of 2 consecutive even integers is 528 find the value of each integers
Answer :-
Value of two integers are 22 and 24Step-by-step explanation:
Given :-
The product of 2 consecutive even integers is 528To Find :-
Value of each integersSolution :-
Let one integer be xother integer be x + 2According to question,
Product of two integers = 528↠ (x)(x + 2) = 528
↠ x² + 2x = 528
↠ x² + 2x - 528 = 0
↠ x² + 24x - 22x - 528 = 0
↠ x(x + 24) - 22 (x + 24) = 0
↠ (x + 24) (x - 22) = 0
↠ x = -24 or 22
Hence,
1st integer = 222nd Integer = 22 + 2 = 24Value of two integers are 22 and 24
Step-by-step explanation:
It is given that, The product of 2 consecutive even integers is 528 and we have to find the value of each integers.
So, Let us assume the 1st consecutive even integer as y and the 2nd as (y + 2)Now, As it is stated in the question that the product of 2 consecutive even integers is 528, So
\( \\ { \longrightarrow \qquad{ \pmb{ \sf { y(y + 2) = 528 }}}} \: \: \\ \\\)
\({ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y = 528 }}}} \: \: \\ \\\)
Subtracting both sides by 528 we get :
\( \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 528 - 528 }}}} \: \: \\ \\\)
\({ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 0 }}}} \: \: \\ \\\)
We have to find two numbers such that,
\( \\ { \longrightarrow \qquad{ \pmb{ \sf { p + q= 24 }}}} \: \: \\ \\\)
\({ \longrightarrow \qquad{ \pmb{ \sf { p \times q= 528 }}}} \: \: \\ \\\)
The two numbers are 24 and 22. So,
\( \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + (-22y) + 24y - 528= 0 }}}} \\ \\ \)
\({ \longrightarrow \qquad{ \pmb{ \sf { {y}(y -22) + 24(y - 22)= 0 }}}} \\ \\ \)
\({ \longrightarrow \qquad{ \pmb{ \sf { (y -22) (y + 24)= 0 }}}} \\ \\ \)
Whether, the value of y is (-24) or 22.\( \: \)
So, The first consecutive even integer is 22.
Now,
\( \\ { \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=y \:+2 \: }}}} \\ \\ \)
\({ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=2 2+2 \: }}}} \\ \\ \)
\({ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=24 }}}} \\ \\ \)
Therefore,
The value of each integer is 22 and 24.A rock was thrown from the top of a building. The distance, in feet, between the rock and the ground t seconds after it is thrown is represented by d=-16t squared -4t+382. How long after the rock is thrown is it 370 feet from the ground
Answer:
Step-by-step explanation:
ERROR ANALYSIS 2
Solving Equations
Look at the students working below. Identify and explain the error that was
made when working the problem. Once completed re-work the problem
correctly in the space provided.
Identity & explain the error
WORKING
Sore the equation -
x-7-4
5
X5 XS
Re-work the problem
x-7-4
+7 +7
x=11
how the level of measurement and the number of levels of your independent variable help you choose between these options.
The level of measurement and number of levels of your independent variable will determine which statistical test is most appropriate for your data analysis.
T-test: The t-test is typically used to compare the means of two independent groups on a continuous variable. It is appropriate when your independent variable has only two levels and your dependent variable is measured at the interval or ratio level.
Product moment correlation: This is a measure of the strength and direction of the linear relationship between two continuous variables. It is appropriate when both variables are measured at the interval or ratio level.
Chi-square test: The chi-square test is used to test for association between two categorical variables. It is appropriate when both variables are measured at the nominal level.
One-way ANOVA: This test is used to compare the means of three or more independent groups on a continuous variable. It is appropriate when your independent variable has three or more levels and your dependent variable is measured at the interval or ratio level.
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Complete Question:
How the level of measurement and the number of levels of your independent variable help you choose between these options.
a) T test
b) Product moment correlation
c) Chi square
d) One way ANOVA
The figure shows a triangle with an exterior angle at each vertex.
8yº
1419
127°
What is the value of y?
Answer: y=11
Step-by-step explanation:
its right trust me pls
In a factory, eggs are packaged in groups of 12 per box.How many full boxes of eggs can the factory make with 2321 eggs?
A prism is completely filled with 1120 cubes that have edge lengths of 12 in.
What is the volume of the prism?
Enter your answer in the box.
in³
PLZ help
Find the volume of 1 cube.
Volume of a cube is sidelength^3
Volume of a cube = 12^3 = 1,728 cubic inches.
Now multiply the volume of a cube by the number of cubes:
1,728 x 1120 = 1,935,360 cubic inches.
The volume of the box is 1,935,360 cubic inches.
Answer:
140
Step-by-step explanation:
what is 3⁵÷3⁷ using indicies?
Answer:
9
Step-by-step explanation
First you multiply 3 five times, then you multiply 3 seven times and you divide the results of each multiplication
Answer:
0.111111111111111
Step-by-step explanation:
=> 3⁵÷3⁷
Note 3⁵ means multiplying 3 five times
And 3⁷ means multiplying 3 7 times
=> 3×3×3×3×3÷3×3×3×3×3×3×3
multiply the values and then divide
=> 243÷2,187
divide 243 by 2187
=> 0.111111111111111
Last week the team ran 21 1/2 miles total. this week the track coach had the team run 5 1/2 miles on monday and 4 3/4 miles on tuesday. the next three days the team averaged 6 miles a day
Help pls !!! Find the measure of the side indicated. Simplify your answer and write it as a whole number
Check the picture below.
1/4 + 1/4= please help me solve
Answer:
Step-by-step explanation:
1/4 + 1/4+ 2/4
Simplify to 1/2 you can also get 0.50
Joe had 21 pennies, but then he lost 11 pennies. His friend gave him 5 more pennies. How many pennies does Joe have now?
Answer:
15 pennies
Step-by-step explanation:
lost means subtract and gave him means add
21 -11 +5
15
Answer:
15 pennies
Step-by-step explanation:
You can start by saying that after losing 11 pennies from his original amount it is 21-11, which equals to 10.
THen the question says that his friend gives him an additional 5 pennies, which is shown by 10+5=15
THerefore, all you had to do was use the information given and add or subtract the number of pennies from the original.
Answer: 15 pennies
Hope this helped
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
Several trials are performed with the results shown in the table. What is the experimental probability of randomly drawing a green marble?
| Red | Blue | Green |
| 10 | 12 | 28 |
a. 48%
b. 24%
c. 28%
d. 56%
The experimental probability of randomly drawing a green marble is 56%
How to determine the experimental probability of randomly drawing a green marble?The table of values is given as:
| Red | Blue | Green |
| 10 | 12 | 28 |
So, we have
P(Green) = Green/Total
This gives
P(Green) = 28/(10 + 12 + 28)
Evaluate
P(Green) = 56%
Hence, the experimental probability of randomly drawing a green marble is 56%
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If g(x) = x2 + 2, find g(3). (2 points)
Оа
9
Ob
8
Ос
11
Od
6