Use the long division method to find the result when 2x^3-7x^2+17x-7 is divided by 2x-1.
Answers
Given the expression below
[tex]\frac{2x^3-7x^2+17x-7}{2x-1}[/tex]To divide the above expression using long division, we will follow the steps below:
Step 1: Arrange the indices of the polynomial in descending order. Replace the missing term(s) with 0.
Looking at the expression given, polynomials is already arranged in descending order, from degree 3 to 0, and there are no missing terms of x.
Step 2: Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient.
Looking at the expression given, it can be seen that
[tex]\begin{gathered} \text{dividend}=2x^3-7x^2+17x-7 \\ \text{divisor}=2x-1 \end{gathered}[/tex][tex]\frac{2x^3}{2x}=x^2[/tex]Step 3: Multiply the divisor by the first term of the quotient.
[tex]x^2(2x-1)=2x^3-x^2[/tex]Step 4: Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend. Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".
Step 5: Repeat step 2 – 4 to find the second term of the quotient.
[tex]\frac{-6x^2}{2x^2}=-3x[/tex][tex]-3x(2x-1)=-6x^2+3x[/tex]Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.
[tex]\frac{14x}{2x}=7[/tex][tex]7(2x-1)=14x-7[/tex]The quotients from the divisions gives
[tex]x^2-3x+7[/tex]Hence, the result of the division is as written below x² - 3x +7
Related Questions
Please Help!!!!! I will give brainliest and 5 stars!!!!
Answers
1. A system of linear functions cannot have only two or three solutions, the possible amounts are: Zero, One and Infinity.
2. This is not true because if the lines do not cross, the system has no solutions.
3. Substitution: Explicit variable, such as:
x = 3, y + 3x = 10.y = 2x + 4, 3x + 2y = 20.Elimination: Non-explicit variable, such as:
x + y = 2, 2x + 3y = 5.x - y = 10, 2x + 5y = 40.What are linear functions?Linear functions have the definition given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.A system of linear equations is composed by multiple equations, and the number of solutions is defined as follows:
Zero solutions: slopes are multiples and intercepts are not -> the functions do not intersect on the graph.One solution: different slope and intercepts -> the functions intersect once on the graph.Infinitely many solutions: slopes and intercepts are multiples, hence the functions are the same on the graph.There are two ways to solve the systems, given as follows:
Substitution: one of the variables has an explicit definition.Elimination: none of the variables has an explicit definition.More can be learned about linear functions at https://brainly.com/question/24808124
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can someone please help me with question 3 and question 5-7
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Question 5
The coordinate of C is (4,4)
If you dilate ABCD by a scale factor of 1/2, the coordinate of the image of C will be:
[tex]\begin{gathered} C^{\prime}(4\times\frac{1}{2},4\times\frac{1}{2}) \\ =(2,2) \end{gathered}[/tex]Question 6
The coordinate of A is (0,2)
If you dilate ABC by a scale factor of 2, the coordinate of the image of A will be:
[tex]\begin{gathered} A^{\prime}0\times2,2\times2) \\ =(0,4) \end{gathered}[/tex]Find the probability of having 2, 3, or 4successes in five trials of a binomialexperiment in which the probability ofsuccess is 40%.p=[?]%Round to the nearest tenth of a percent.
Answers
The probability of having 2, 3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40% is 0.6528.
We are given that:
The probability of the success is = 40%
P(S) = 0.40
Let the random variable be X :
Number of trials = 5 trials
X ≈ B(5, 0.40).
Now, we need to find the probability of having 2, 3, or 4successes in these five trials:
P(2 , 3 or 4 successes in five trials )
= P(X = 2) + P(X = 3) + P(X = 4)
= 0.3465 + 0.2304 + 0.0768
Adding the values:
= 0.6528.
Therefore, the probability of having 2, 3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40% is 0.6528.
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Write an equation in slope intercept form for the line that has a slope of 4/5 and passes through (0,7) Mark only one ovalY=7xY=7x-4/5Y=4/5x+7Y=-4/5x+7
Answers
Given:
The slope of the line is
[tex]m=\frac{4}{5}[/tex]Passes through the point
[tex](x,y)=(0,7)[/tex]Required:
To find equation in slope intercept form.
Explanation:
The general equation of slope intercept form is
[tex]y=mx+b[/tex]Where, m = slope
b = y-intercept.
Now,
[tex]y=\frac{4}{5}x+b[/tex]Here The line passes through the point (0,7), therefore the y-intercept is 7.
So,
[tex]y=\frac{4}{5}x+7[/tex]Final Answer:
[tex]y=\frac{4}{5}x+7[/tex]Triangle a is reflected in the x-axis to give triangle b traingle b is reflected in the y-axis to give triangle a describe fully the transformation that maps a onto c
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Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
Is a reflection over the x-axis positive or negative?Thus, we get the conclusion that when a point is mirrored along the x-axis, the x-coordinate stays constant while the y-coordinate deviates from zero. So, M' is the image of the point M (h, k) (h, -k). Guidelines for determining a point's x-axis reflection: I Maintain the x-coordinate, or abscissa.
Thus, the reflection in the x-xis:
The entire x-component is unaltered.
The sign of each y-component is changed from - to + and vice versa.
then, the reflection in the y-xis:
The entire y-component is unaltered.
Every x-component has its sign altered from - to + and vice versa.
Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
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solve for x perimeter of the rectangle is 100to x - 8 + x + 4 + 2x - 8 + x + 4 = 100 solve for x
Answers
The perimeter of rectangle is 100.
The formula for the perimeter of rectangle is
[tex]P=2(l+w)[/tex]The length of the rectangle is 2x-8 and width of the rectangle is x+4.
The perimeter is
[tex]100=2(2x-8+x+4)[/tex][tex]50=3x-4[/tex][tex]3x=54[/tex][tex]x=18[/tex]Hence the value of x is 18.
The length is
[tex]2\times18-8=36-8=28[/tex]The width is
[tex]18+4=22[/tex]The correct options are 22 and 28.
Find the ratio of the length of the longest side to the length of the shortest side. Write the ratio as a fraction in lowest terms.1.2 meters0.8 meter0.8 meter1.2 meters
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A ratio may be written as a:b or, in fraction form, a/b.
To obtain the ratio in fraction, divide the longest side by the shortest side. Thus, we get the following.
[tex]\frac{1.2}{0.8}[/tex]To determine the lowest term, eliminate the decimal point by multiplying the numerator and the denominator by 10.
[tex]\frac{1.2}{0.8}\cdot\frac{10}{10}=\frac{12}{8}[/tex]Divide the numerator and the denominator by the greatest common factor (GCF) of 12 and 8, which is 4.
[tex]\frac{12\div4}{8\div4}=\frac{3}{2}[/tex]Therefore, the ratio in fraction form is
[tex]\frac{3}{2}[/tex]Watch help video
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find out
the time at which the rocket will reach its max, to the nearest 100th of a second.
y = -16x² + 217x +96
Answers
The time at which the rocket will be at its maximum height, to the nearest 100th of a second is 14 seconds.
Define the term quadratic equation?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2.For the given value of launch of rocket.
Height of the rocket is y in feet.
Time after launch is x in seconds.
The quadratic equation of height is-
y = -16x² + 217x +96
For the maximum height,
Put y = 0.
0 = -16x² + 217x +96
The standard form of quadratic equation is-
ax² + bx + c = 0
On comparing.
a = -16
b = 217
c = 96
Solve equation by quadratic formula and find the roots,
x1 = 217 + √53233 / 32
x2 = 217 - √53233 / 32
Solve both-
x1 = 13.99 = 14 sec
x2 = -0.41 (neglecting negative value)
Thus, the time at which the rocket will reach its maximum height, to the nearest 100th of a second is 14 seconds.
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Question:Solve the formula I = Prt to find the principal, P, when I = $272.25, r = 2.2%, and t = 3 years.
Answers
Given in the question:
I = $272.25
r = r = 2.2%
t = 3 years
Let's re-equate the formula of Simple Interest to find P in terms of I, r, and t.
[tex]I\text{ = Prt }\rightarrow\text{ P = }\frac{I}{rt}[/tex]Let's plug in the values to find P.
[tex]P\text{ = }\frac{I}{rt}[/tex][tex]P\text{ = }\frac{272.25}{(\frac{2.2}{100})(3)}\text{ = }\frac{272.25}{(0.022)(3)}[/tex][tex]P\text{ = }\frac{272.25}{0.066}[/tex][tex]P\text{ = 4,125 = \$4,125}[/tex]Therefore, the Principal Amount is $4,125.
over the last 3 evenings 85 phone calls were received. the second evening she received 5 fewer calls than the first evening.The third evening she received 4 times as many calls how many did she receive each evening
Answers
a =20, b =15, c= 60
1) Writing this we have
1st evening: a
2nd evening: b
3rd evening: c
a +b+ c = 85
b=5 -a
c=4a
2) So rewriting this out as an expression we have:
a + b+ c = 85 Plug into that in terms of "a"
a + 5-a + 4a = 85 Combine like terms
4a +5 = 85 subtract 5 from both sides
4a = 80 Divide both sides by 4
a = 20
2.2) Plug into each formula:
b =a -5
b = 20 -5
b = 15
20+15 + c = 85 Add them up
35 +c = 85 Subtract 35 from both sides
c = 85 -35
c= 60
Or we could have done it:
c = 4b
c= 4* 15
c= 60
3) Hence, the answer is a =20, b =15, c= 60
Solve the polynomial equation by factoring and then using the zero product principal
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Given: The polynomial below
[tex]x^3+2x^2=9x+18[/tex]To Determine: The factored form of the equation using the zero product principle
Step 1: Put all the terms to the left hand side of the equation
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \end{gathered}[/tex]Step 2: Group the equation into and factorize
[tex]\begin{gathered} (x^3+2x^2)-(9x-18)=0 \\ x^2(x+2)-9(x+2)=0 \\ (x+2)(x^2-9)=0 \end{gathered}[/tex]Step 3: Expand the difference of two squares
[tex]\begin{gathered} a^2-b^2=(a-b)(a+b) \\ x^2-9^2=x^2-3^2=(x-3)(x+3) \end{gathered}[/tex]Step 4: Replace the difference of two squares with its equivalence
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \\ (x+2)(x^2-9)=0 \\ (x+2)(x-3)(x+3)=0 \end{gathered}[/tex]Step 5: Use the zero product principle to determine the solution set
[tex]\begin{gathered} (x+2)(x-3)(x+3)=0 \\ x+2=0,or,x-3=0,or,x+3=0 \\ x=-2,or,x=3,or,x=-3 \end{gathered}[/tex]Hence,
The factored form is (x + 2)(x - 3)(x + 3) = 0
The solution set is x = -2, 3, -3
By how much was the price counted?What was the percentage of the discount?
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1.
original price - price with discount = 22-13.26 = 8.74
2.
in order to know the percentage of the discount
first, we need to know the percentage pay
x=percentage pay
(22)(x)=13.26
x=13.26/22= 0.60
the percentage pay 60%
the percentage of the discount is
100%-60%=40%
the percentage of the discount is 40%
Write an equation for the line who passes through (-3,1) and (1,3)
Answers
Given:
Two points are given as (-3,1) and (1,3)
[tex]\begin{gathered} (x_1,y_1)=\left(-3,1\right) \\ (x_2,y_2)=\left(1,3\right) \end{gathered}[/tex]Required:
We want to write an equation which passes through the given points
Explanation:
First we need to find the slope of the required line
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-(-3)}=\frac{2}{4}=\frac{1}{2}[/tex]The equation of is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{x}{2}+\frac{3}{2} \\ \\ y=\frac{x}{2}+\frac{5}{2} \end{gathered}[/tex]Final answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]Answer:
Step-by-step explanation:
y= r/2 + 3/4
Jimmy wants to make a pentagonal push pop that is 3.25 inches long with a side length of 0.75 inches. Find the surface area of the push pop.
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We are asked to determine the surface area of the figure. To do taht we will add the areas of each of the surfaces of the figure. Since it is a pentagon, we will determine the lateral area of one of the surfaces and multiply the result by 5:
[tex]A_l=5sl[/tex]Where "s" is the side length and "l" is the longitude. Replacing the values:
[tex]A_l=5(0.75in)(3.25in)[/tex]Solving the operations:
[tex]A_l=12.19in^2[/tex]can someone please help me find the answer to the following?
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Using the Euler formula, we have:
F + V = E + 2 (F: faces, E:edges, V:vertices)
F + 12 = 18 + 2 (Replacing)
F + 12 = 20 (Adding)
F= 8 (Subtracting 12 from both sides of the equation)
The answer is 8.
Answer:
Step-by-step explanation:
1. This polyhedron has 8 faces.
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Points A,B,C are collinear. explain what iswrong with this picture. Use the linear pairtheorem in your explanation
Answers
SOLUTION
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
For instance
Consider the image given
The measure of the angles are
[tex]\begin{gathered} 129^0and41^0 \\ \text{Hence } \\ A=129^0 \\ B=41^0 \end{gathered}[/tex]The sum of the angles is
[tex]\begin{gathered} 129^0+41^0=170^0 \\ \text{Hence the angles are not linear pair since the summation is not 180 degr}ees\text{ } \end{gathered}[/tex]From the image,
we can see that the angles are not linear pair and hence did not follow the linear pair thorem
What is the best estimate for this sum 1/8+1/6=The sum will be close to?
Answers
The expression given is
[tex]\frac{1}{8}+\frac{1}{6}[/tex]The sum of the expression will be,
[tex]\frac{1}{8}+\frac{1}{6}=\frac{6+8}{48}=\frac{14}{48}=\frac{7}{24}[/tex]The sum will be
[tex]\frac{7}{24}[/tex]Triangle ABC has vertices (1,4), (5,6), and (3, 10). It is reflected across the y-axis, forming Triangle A’B’C’. What are the vertices of the new triangle?
Answers
Step 1:
First, write the rule for the transformation across the y-axis
The rule for a reflection over the y -axis is (x,y)→(−x,y).
Meaning value of y remains the same and you will multiply the coordinate of x by negative.
Step 2
Coordinates of pre-image
A = (1 , 4)
B = (5 , 6)
C = (3 , 10)
Step 3:
Find the coordinates of the image using the rule.
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
Final answer
The vertices of the new triangle is
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
Solve for Y2x + = 4a. y = 6x + 12b. y = -6x +12C. y= 6x - 12d. y = -6x - 12
Answers
You have the following equation:
2x + y/3 = 4
In order to solve for y, proceed as follow:
2x + y/3 = 4 subtract by 2x both sides
y/3 = 4 - 2x multiply by 3 both sides
y = 3(4 -2x) apply distribution property
y = 3(4) + 3(-2x)
y = 12 - 6x order the expression
y = -6x + 12
Hence the solution for y is:
y = -6x + 12
Jay Field's bank granted him a single-payment loan of $6,800. He agreed to repay the loan in 91 days at an ordinary interest rate of 4.25 percent. What is the maturity value of the loan?
Answers
Answer:
$6,872.05
Explanation:
The maturity value of the loan can be calculated as:
[tex]V=P(1+r\cdot t_{})[/tex]Where P is the initial amount, r is the interest rate as a decimal and t is the time in years.
4.25% is equivalent to: 4.25/100 = 0.0425
91 days are equivalent to 91/365 = 0.25 years
Then, the maturity value is equal to:
[tex]\begin{gathered} V=6800(1+0.0425\cdot0.25) \\ V=6800(1+0.011) \\ V=6800(1.011) \\ V=\text{ \$6,872.05} \end{gathered}[/tex]So, the maturity value of the loan is $6,872.05
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm. For a random sample of 134 adult males, the mean pulse rate is 70.1 bpm and the standard deviation is 10.9 bpm. Complete parts (a) and (b) below.
Answers
Part A. Express the original claim in symbolic form.
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm.
Therefore, the original claim in symbolic form is:
ANSWER:
[tex]\mu=68.9\text{ bpm}[/tex]Part B. Identify the null and alternative hypotheses.
[tex]\begin{gathered} H_0\colon\text{ }\mu=68.9\text{ bpm} \\ H_1\colon\mu\ne68.9\text{ bpm} \end{gathered}[/tex][tex]\begin{gathered} H_0\text{ or the null hypothesis will be based to our claim. We will test if the mean pulse} \\ \text{rate of an adult male is equal to 68.9 bpm.} \\ H_1\text{ or the alternative hypothesis is the one that contradicts the null hypothesis. That is } \\ \text{why our H}_a\text{ has the sign of not equal to (}\ne). \end{gathered}[/tex]
If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar.
Answers
If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar
the slope is
m=(17-24)/(15-25)
m=-7/-10
m=7/10
answer is slope is 7/10Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Letmidpoint (2,9), endpoint (1, -3)
Answers
Given this is a one of the endpoints of the segment:
[tex](1,-3)[/tex]You know that the midpoint is:
[tex](2,9)[/tex]By definition, the formula for finding the midpoint of a segment is:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
- The coordinates of the midpoint are:
[tex](x_m,y_m)[/tex]- And the coordinates of the endpoints are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_m=2 \\ y_m=9 \\ \\ x_1=1 \\ y_1=-3 \end{gathered}[/tex]Then, you can set up this equation to find the x-coordinate of the other endpoint:
[tex]2=\frac{1+x_2}{2}[/tex]Solving for:
[tex]x_2[/tex]You get:
[tex](2)(2)=1+x_2[/tex][tex]\begin{gathered} 4-1=x_2 \\ x_2=3 \end{gathered}[/tex]Set up the following equation to find the y-coordinate of the other endpoint:
[tex]9=\frac{-3+y_2}{2}[/tex][tex](9)(2)=-3+y_2[/tex][tex]\begin{gathered} 18+3=y_2 \\ y_2=21 \end{gathered}[/tex]Hence, the answer is:
[tex](3,21)[/tex]28 ft 20 it 18 ft Given x < 20, which COULD be the area of this trapezoid? 424 ft2 B) 460 +2 464 ft2 5042
Answers
Trapezoid area =(Base 1 + Base 2 )Height/2
If x= 20
then area = (28+18)/2 • √ ( 20^2 - 5^2)
. = 23 • √375
. = 445
If x< 20 ,area is
Answer is OPTION A ) 424 ft2
Determine if the following set is a function or not.
Answers
In an ordered pair (x,y), x represents the domain, and y is the range.
Gather up all of the domain, the domain is
{-10, -3, 4, 7, 12}
The range is
{-2, 3, 4, 3, 3} ----> {-2, 3, 4} (the same multiple sets counts as one)
A function can be defined as either one-to-one, or many-to-one BUT NOT one-to-many.
Draw a diagram representing the domain mapping to a range.
Based on the diagram, we have mappings of one-to-one [-10 maps to 2, 4 maps to 4, based on the ordered pair (-10,-2) and (4,4)],
and many-to-one [-3, 7, and 12 maps to 3, based on the ordered pair (-3,3), (7,3), and (12,3)]
Since there are no one-to-many mappings, we can conclude that the set is a function.
A 30-m-wide field is how many yard wide?The field is ____ yard wide.( Type a whole number or decimal. Round to three decimal places as needed.)
Answers
Given:
30 meter wide field
To determine the field in yards, we convert the given 30 meters into yards.
We must remember that:
1 meter = 1.0936 yards
So,
Therefore, the answer is 32.808 yards.
Evaluate the expression when c = -3/10 and x = -7/8c + 1/5xWrite your answer in simplest form.
Answers
Explanation:
if c = -3/10 and x = -7/8
by replacing them in the equation c + 1/5 * x, we get:
[tex]\frac{-3}{10}+\frac{1}{5}*\frac{-7}{8}\text{ = }\frac{-3}{10}-\frac{7}{40}=\frac{-3*4}{10\text{ * 4}}-\frac{7}{40}=\text{ }\frac{-12-7}{40}\text{ = }\frac{-19}{40}[/tex]Use the accompanying Venn Diagram, which shows the cardinality of each region,to answer the question below.How many elements belong to set B?
Answers
4 elements
Explanation
to find the number of elements that belong to set B, just count the elements inside the circle B
4 elements (3,5,2,9)
I hope this helps you
A 9-meter roll of blue ribbon costs $9.63. What is the unit price?
whats the unit price
Answers
$1.07 is the unit price
can you help me on the Rolling a 7 part
Answers
Rolling a 7
Total outcomes=6*6=36
favorable outcomes
1-6
2-5
3-4
4-3
5-2
6-1
tota favorable outcomes=6
so
The probability of rolling a 7 is equal to
P=6/36
simplify
P=1/6