Divide f(x) by d(x). Your answer
should be in the following format:
f(x)
d(x)
R(x)
: Q(x) + d(x)
=
=
f(x) x42x³ + x² - 2x + 1
d(x)
x - 2
R(x) = [?]
So, the quotient is. [tex]Q(x) = x^3 - x^2 - x + 1/(x - 2)[/tex], and the remainder is. [tex]R(x) = 1.[/tex]Therefore, we can write:
[tex]f(x) / d(x) = Q(x) + R(x) / d(x)\\f(x) / d(x) = x^3 - x^2 - x + 1/(x - 2) + 1/(x - 2)[/tex].
What is algebraic division?Algebraic division is the process of dividing one algebraic expression by another. It involves applying the same rules of arithmetic division but with algebraic terms instead of numbers.
In algebraic division, the dividend, which is the expression being divided, is written on the top, while the divisor, which is the expression doing the dividing, is written below it. The division process involves finding how many times the divisor can fit into the dividend, and then subtracting that amount from the dividend. This process is repeated until there is no remainder left.
To divide [tex]f(x) = x^4 - 2x^3 + x^2 - 2x + 1[/tex] by[tex]d(x) = x - 2,[/tex] we can use long division as follows:
[tex]x^3 - x^2 - x + 1/ (x - 2)[/tex]
[tex]x - 2 | x^4 - 2x^3 + x^2 - 2x + 1[/tex]
[tex]-x^4 + 2x^3[/tex]
-----------
[tex]0 - x^2[/tex]
[tex]0 + x^2[/tex]
----------
[tex]- 2x[/tex]
[tex]+ 2x[/tex]
-----
1
1
-
0
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
blank 1. no
blank 2. not constant because it is a nonlinear function.
The slope of the curve ƒ(x) = x2 + 2 at x = 3 is _______.
6
9
3
0
Answer:
The slope of the curve ƒ(x) = x^2 + 2 at x = 3 can be found by taking the derivative of the function with respect to x and evaluating it at x = 3.
ƒ(x) = x^2 + 2
Taking the derivative:
ƒ'(x) = 2x
Substituting x = 3:
ƒ'(3) = 2(3) = 6
Therefore, the slope of the curve ƒ(x) = x^2 + 2 at x = 3 is 6.
Use the parallel lines cut by a transversal to answer a-b.
A. Find the value of x.
B. Find the measure of each marked angle.
Answer:
x = 8
Step-by-step explanation:
Parallel lines cut by a transversal.The angles in questions are alternate exterior angles and are congruent.We can write the following equation to find the value of x based on above mentioned information:
10x - 20 = 7x + 4
Transfer like terms to the same side of the equation10x - 7x = 20 + 4
Add/subtract3x = 24
Divide both sides by 3x = 8
To find each angle measure, replace x with 8:
10x - 20 would be 10 × 8 - 20 = 60
Since angles are congruent the other one also would be 60°.
You want to take out a $210,000 mortgage (home loan).The yearly interest rate on the loan is 6%, and the loan is for 30 years. How much will your monthly payment be?
Using the formula for calculating monthly mortgage payments, with a loan amount of $210,000, yearly rate of 6% and time period of 30 years, the monthly mortgage payment comes out to be approximately $1,259.81.
Explanation:The calculation that needs to be done here involves a formula related to annuities, which is what monthly mortgage payments are classified as. The formula used to calculate a monthly mortgage payment is:
[tex]M = P [r(1 + r)^n]/[(1 + r)^n - 1][/tex]
Where:
M = monthly mortgage payment
P = loan amount (present value)
r = monthly interest rate
n = total number of payments (or total number of periods)
Plugging our given values into the equation:
P = $210,000 (this is the loan amount)
r = 6/100/12 = 0.005 (this is the monthly interest rate)
n = 30 x 12 = 360 (this is the number of periods, ie the total number of monthly payments over 30 years)
By substituting these values, one can calculate that:
M = [tex]210,000[0.005(1 + 0.005)^3^6^0] / [(1 + 0.005)^3^6^0 - 1][/tex]
Calculating this, we get M ≈ $1,259.81
So, the monthly mortgage payment would be approximately $1,259.81.
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Triangle ABC is given.%0D%0A%0D%0A%0D%0A%0D%0AIf cos(A) = , what is sin(B)?
Without further context about the triangle and the lengths of its sides, it is not possible to solve for sin(B) using just the given information about cos(A).
34x23 =r (mod13)
please help asap !!
Answer:
To solve 34x23 ≡ r (mod 13), we can first calculate the product 34x23 = 782. Next, we need to find the remainder when 782 is divided by 13. To do this, we can divide 782 by 13 and find the remainder: 782 ÷ 13 = 60 remainder 2 Therefore, 782 is equivalent to 2 (mod 13). So, the solution to the original equation is r ≡ 2 (mod 13).
6. Anna solved three problems on her math test. One of them was incorrect. Circle the problem that was solved incorrectly and find the correct answer.
32° 122°
B
4 . 10
83.2° X° A
83.2+74.1+×=180 157.3 +×= 180
x = 22.70
X
W 1420
M
X°
329 1089
142.7°
42+36.08+×= 180 78.08 +×= 180 ×= 101.92°
32 +×= 108 ×= 76°
It seems that the problem solved incorrectly is the one represented by letter A, which is trying to find the missing angle in a triangle. The correct answer is 74.1°, which can be obtained by subtracting the sum of the other two given angles (83.2° and 22.7°) from 180°.
The problem that Anna solved incorrectly is the last one: 32 + x = 108. The correct answer should be x = 76, not x = 108.
Explanation:In this math problem, Anna seems to be solving for unknown angles in several triangle problems. An important principle here is that the sum of the angles in a triangle always adds up to 180 degrees. Looking at the problems she solved:
83.2 + 74.1 + x = 180: The correct answer for x here is 22.7 degrees, and Anna solved it correctly.42 + 36.08 + x = 180: The correct answer for x here is 101.92 degrees, and Anna also solved this correctly.32 + x = 108: Misstep appears here. If we subtract 32 from both sides of the equation, the correct answer for x should be 76 degrees. However, Anna seems to have calculated x = 108, which is incorrect.So, the problem that was solved incorrectly is the last one: 32 + x = 108.
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Point A is located at (-2,-5) and Point B is locatged at (6, 3). Point C partitions line segment
AB such that ratio AC:CB is 1:3
As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .
what is coordinates ?A point together in two-dimensional plane can be found using coordinates, which are pairs of numbers. Each point is represented by an ordered pair of absolute values (x,y), where x represents the horizontal coordinate and y represents the vertical coordinate, in the Cartesian geometry. The x-axis is the horizontal axis, while the y-axis is the vertical axis. The origin is the intersection of the two axes and bears the following coordinates: (0,0). A point's coordinates might be plus, negative, or zero depending on where it is in relation to the axes and the origin.
given
We may use the section formula to determine the coordinates of point C, which divides line segment AB in a ratio of 1:3.
Let point C's coordinates be (x, y). Next, we have
x = [(3/4) * (-2)] + [(1/4) * 6] = -3/2
y = [(3/4) * (-5)] + [(1/4) * 3] = -21/4
As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .
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A plane ascends at a 28°
angle. When it reaches an altitude of 250 feet, how much ground distance has it covered? Round your answer to the nearest tenth.
(HINT: DRAW THE PICTURE)
Ground distance covered is ft.
(50 points)
According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
What is trigonometry?
The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.
The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.
There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).
The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
To draw a diagram of the situation:
[tex]tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft[/tex]
Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
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Margo borrows $700, agreeing to pay it back with 3% annual interest after 17 months. How much interest will she pay? Round your answer to the nearest cent, if necessary.
To calculate the interest that Margo will pay, we first need to determine how much interest she will accrue over the 17-month period.
We can use the formula:
Interest = Principal x Rate x Time
Where:
Principal is the amount borrowed, which is $700 in this case.
Rate is the annual interest rate, which is 3% or 0.03 as a decimal.
Time is the time period expressed in years, which is 17/12 or 1.4167 years in this case (since there are 12 months in a year).
Therefore, the interest that Margo will pay can be calculated as:
Interest = $700 x 0.03 x 1.4167
Interest = $29.75
So Margo will pay $29.75 in interest. Rounded to the nearest cent, the answer is $29.8.
Could someone please explain how to answer this question. I think its 66 but im not sure.
asap I have 2 minutes
Answer:
6
Step-by-Step Explanation:
if you were to move the bottom triangle to the top, it would make the parallelogram a perfect rectangle.
the area is 60 units^2.
area=length*width
and the one side is 10. 60/10 =6 so 6 units is the answer
Which of the following is the distance between the two points shown?
4 Ty
3
(-3.5, 0)
-3
-2
4
O5 units
O-5 units
O2 units
O-2 units
-1
2
0
1
-1
-3
-2
7
(1.5,0)
2
1
3
X₂
4
The distance between the points (-3.5, 0), and (1.5, 0), shown on the coordinate plane, obtained using the distance formula; is 5 units
The correct option is; 5 units
What is the distance formula?The distance formula is a formula that can be used to calculate the distance between the points (x₁, y₁), and (x₂, y₂) on the coordinate plane using the following equation;
d = √((x₂ - x₁)² + (y₂ - y₁)²).
The distance between the points (-3.5, 0), and (1.5, 0), on the graph can be obtained using the distance formula which is; d = √((x₂ - x₁)² + (y₂ - y₁)²
Where;
(x₁, y₁) = (-3.5, 0)
(x₂, y₂) = (1.5, 0), we get;
d = √((1.5 – (-3.5))² – (0 – 0)²) = 5
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y=100(0.96)^x is an equation that can be used to represent the purchasing power of $100 after x years of inflation. what is the rate of inflation used to make this calculation?
Evaluate 16/4 +56-(3+4-1)
Answer:
54
Step-by-step explanation:
16/4 + 56 - (3 + 4 - 1)
= 16/4 + 56 - (6)
= 4 + 56 - (6)
= 4 + 56 - 6
= 60 - 6
= 54
So, the answer is 54 !
If you can, please give me a Brainliest; thank you!
[tex] \sf \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]
[tex] \: [/tex]
[tex] \sf \cancel \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]
[tex] \: [/tex]
[tex] \sf \: 4 + 56 - (3 + 4 - 1)[/tex]
[tex] \: [/tex]
[tex] \sf \: 60 - (3 + 4 - 1)[/tex]
[tex] \: [/tex]
[tex] \sf \: 60 - (3 + 3)[/tex]
[tex] \: [/tex]
[tex] \sf \: 60 - 6[/tex]
[tex] \: [/tex]
[tex] \sf \fbox{ \: \sf \blue{ 54 }\: \: }[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps!:)
hELP PLEASEE
(Q005) How does the Missouri Compromise reflect the strong sense of nationalism Americans felt for their country in the early 1800s?
What details can we learn from John Quincy Adams's diary entry? Use quotes directly from the primary source.
Answer: The Missouri Compromise of 1820 was a landmark agreement in American history that temporarily resolved the issue of slavery in the western territories. The compromise was driven by a sense of nationalism among Americans in the early 1800s, who were concerned about preserving the unity of the country and avoiding the outbreak of civil war.
The Missouri Compromise reflected this sense of nationalism by seeking to maintain a balance of power between the slave states and the free states. The compromise allowed Missouri to enter the Union as a slave state, but it also admitted Maine as a free state, and prohibited slavery in any new states formed north of the 36°30′ parallel. By preserving this balance of power, the Missouri Compromise helped to ease tensions between the North and the South, and prevent the outbreak of civil war for several decades.
John Quincy Adams's diary entry provides some insights into the political climate of the time, and the debates surrounding the Missouri Compromise. In his diary entry of February 24, 1820, Adams writes:
"The Missouri question still hangs over us like a black cloud. The ground of the controversy is evidently an apprehension of the preponderance of power in the Union, which by some is feared to be passing from the South to the North."
This quote suggests that there was a growing concern among some Southerners about the balance of power in the Union, and that this concern was driving the debates over the Missouri Compromise. Adams goes on to describe the debates in Congress, noting that "the debates upon the Missouri question are exceedingly able, ingenious, and eloquent." He also provides some insights into the strategies being used by different sides of the debate, noting that "the argument for restriction upon Missouri, is that it will preserve the balance of power in the Union; that the balance of power is a fundamental principle of the Constitution; and that this principle is essential to the preservation of the Union."
These quotes suggest that the Missouri Compromise was a highly contentious issue, and that the debates surrounding it were marked by a strong sense of nationalism among both supporters and opponents of the compromise. The compromise ultimately reflected a desire among Americans to maintain the unity and stability of the country, even as it grappled with the divisive issue of slavery.
Step-by-step explanation:
The tables represent hat sizes measured in inches for two softball teams.
Pelicans
20 20 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Seahawks
21 21 21
23.5 23.5 23.5
23.5 23.5 23.5
22.5 22.5 22.5
23 23 23
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Pelicans; they have a larger mean value of about 22 inches
Seahawks; they have a larger mean value of about 23 inches
Pelicans; they have a larger median value of 22 inches
Seahawks; they have a larger median value of 23 inches
The team that has the largest overall size hat for their players is the Seahawks; they have a larger mean value of about 23 inches. The correct option is b.
What is the mean and median?The two most frequently used measures of center are mean and median. When we compare the mean numbers for the Pelicans and Seahawks, we can see that the Pelicans have a mean of roughly 22 inches and the Seahawks have a mean of roughly 23 inches.
Nevertheless, when the data is skewed or contains outliers, the mean may not be the best approximation of the center because the mean can be altered by extreme values or outliers. Thus, we also need to compare the median values. The median is the midway value in the ordered set of data.
Thus, the correct option is b, Seahawks; they have a larger mean value of about 23 inches.
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Answer:
Step-by-step explanation:
the right answer is b 23 inches seahawkS BRAINLIST and verified answer wanted
p+aw=b make w the subject of the formula
Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.
First, we can subtract "P" from both sides of the equation to get:
aw = b - P
Next, we can divide both sides of the equation by "a" to get:
w = (b - P) / a
Therefore, the solution is:
w = (b - P) / a
Step-by-step explanation:
convert to slope intercept form ( y=mx+b)
2x+5y=0
Original Equation:
2x + 5y = 0
Explanation:
The slope intercept form is y = mx + b, so first we have to get x onto the other side, to do that, we subtract 2x from both sides and end up getting:
5y = - 2x
Now we divide both sides by 5 to isolate y
[tex]y = -\frac{2}{5} x[/tex]
That's our equation!
(Hopefully that helps, and if you can later, please give me brainliest)
For problems 11 and 12, find the area of the figure. Round your answer to the nearest tenth, if necessary. (2 points each)
The area of the triangle is 4.64 square meters and that of the trapezoid is 61.6 square inches.
What is a triangle?A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides.
What is a trapezoid?A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.
Equation:The formula for the area of a triangle is:
A = (1/2) * b * h
where b is the base of the triangle and h is the height of the triangle.
Substituting the given values, we get:
A = (1/2) * 2.9 m * 3.2 m
A = 4.64 square meters
Therefore, the area of the triangle is 4.64 square meters.
The formula for the area of a trapezoid is:
A = (a + b) * h / 2
where a and b are the lengths of the parallel bases, and h is the height of the trapezoid.
Substituting the given values, we get:
A = (10 + 12) * 5.6 / 2
A = 22 * 2.8
A = 61.6 square inches
Therefore, the area of the trapezoid is 61.6 square inches.
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One integer is 6 times another. I f the product of the two integers is 54. Find the integers.
Answer:
integers 3 and 18
Step-by-step explanation:
What is −412−−√+75−−√
ANSWER: −−3√3
just took the test
Answer: [tex]-3\sqrt{3}[/tex]
This the expression [tex]-3\times\sqrt{3}[/tex] or "-3 times the square root of 3"
[tex]\rule{300}{1.5}[/tex]
Work Shown:
Factor each term inside the square root so that a perfect square is one of the pieces. Then break up the roots and simplify as shown below.
[tex]-4\sqrt{12}+\sqrt{75}[/tex]
[tex]-4\sqrt{4\times3} +\sqrt{25\times3}[/tex]
[tex]-4\sqrt{4} \times\sqrt{3} +\sqrt{25} \times\sqrt{3}[/tex]
[tex]-4\times2\times\sqrt{3} +5\times\sqrt{3}[/tex]
[tex]-8\sqrt{3}+5\sqrt{3}[/tex]
[tex](-8+5)\sqrt{3}[/tex]
[tex]\bold{-3\sqrt{3}}[/tex]
What are the zeros of the equation 2x^2+16x-96=0
Using quadratic equations, we can find the zeros of the equation are -4 and 12.
What is a quadratic equation?Quadratic equations are second-degree algebraic expressions because they have the form ax² + bx + c = 0. The word "quadratic" is derived from the Latin word "quadratus," which meaning "square," and alludes to the fact that the equation's variable x is squared. To put it another way, a "equation of degree 2" is a quadratic equation.
Given equation:
2x²-16x-96=0
Factor out of the terms on the left side:
2 × x² - 2 × 8x - 2 × 48 = 0
⇒ 2 (x² - 8x - 48) = 0
⇒ x² - 8x - 48 = 0
⇒ x² + 4x - 12x - 48 = 0
⇒ x (x+4) -12(x+4) = 0
⇒ (x+4) (x-12) = 0
⇒ x = -4 or x = 12.
Therefore, zeros of the equation are -4 and 12.
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HELPPPP!!!!!!!!
Median for Jamal:
Explain why the triangles are similar (state the theorem used to prove similarity) solve for x
Answer:
there is no image so i cannot solve your question.
Step-by-step explanation:
Geomatic sequance for this question
Answer:
a = 2
Step-by-step explanation:
Geometric series:
r = 3
n = 6
[tex]S_n=728[/tex]
[tex]\boxed{\bf S_n = \dfrac{a(r^n - 1)}{r- 1}}[/tex]
[tex]\dfrac{a*(3^6 - 1)}{3-1}=728\\\\ \dfrac{a * (729 -1)}{2}= 728\\\\ \dfrac{a * 728}{2} = 728[/tex]
[tex]a = 728 * \dfrac{2}{728}\\\\a = 2[/tex]
Which of the following is the *best* way to rewrite
44 x 50
so that the exact answer can be found mentally?
50 x 44
88 x 25
4.4 x 500
22 x 100
Answer:
22 * 100
Step-by-step explanation:
It would defintely be 22 * 100 because the other ones may be troubling to do mentally, especially 88 * 25. But with 22 * 100, you can easily get an answer of 2200.
Triangle D'E"F"is the image of triangle DEF after a sequence of
transformations. Which sequence of transformations could have been
applied?
De
1-
24
34
E
Dº
FE
OA. ADEF is translated 1 unit right, then rotated 90° clockwise about
the origin.
OB. ADEF is translated 2 units right, then rotated 90° clockwise about
the origin.
OC. ADEF is translated 2 units up, then rotated 90° clockwise about
the origin.
OD. ADEF is translated 2 units down, then rotated 90° clockwise about
the origin.
Answer:
oc
Step-by-step explanation:
A pole that is 3 m tall casts a shadow that is 1.55 m long. At the same time, a nearby tower casts a shadow that is 49.25 m long. How
tall is the tower? Round your answer to the nearest meter.
m
The tower is approximately 95 meters(m) tall.
What is a meter?
A meter is the basic unit of length in the International System of Units (SI). It is defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
What kind of unit is meter?
The meter is a unit of measurement for length or distance. It is commonly used in science, engineering, and daily life to measure the size or distance between objects.
According to the given information
Let's call the height of the tower h. We can use similar triangles to set up a proportion:
3 / 1.55 = h / 49.25
Simplifying this expression gives:
h = (3 * 49.25) / 1.55
h = 95.48
Rounding this answer to the nearest meter gives:
h ≈ *95 meters*.
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