[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:
| 2 -7 8 -3
1 | 2 -5 3
| 2 -5 3 0
1 | 2 -3
2 -3 0
So the factorization is (x-1)² (2x-3)=0. So:
[tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:
| 1 -1 0 -4
2 | 2 2
1 2 2 0
So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.
[tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:
| 6 7 9 2
-2 | -12 10 -2
6 -5 1 0
So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:
[tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]
Which of the following is the correct graph of the solution to the inequality -13> -5x + 2 > -28?
Answer:
3 < x < 6
Step-by-step explanation:
1) Subtract 2 from the whole equation.
- 13 - 2 > -5x > -28 - 2
2) Simplify.
-15 > -5x > -30
3) Divide the whole equation by -5.
-15/-5 < x < -30/-5
4) Simplify.
3 < x < 6
please help what is…. 5-2?
that’s all the information ive been given and i don’t know how to solve it someone help please i beg
Answer:
3
Step-by-step explanation:
Solve the equation by factoring. 8x^2+10x-7=0
What is the solution set?
Answer:
[tex]x = - \frac{7}{4} \: \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]8 {x}^{2} + 14x - 4x - 7 = 0 \\ 2x(4x + 7) - (4x + 7) = 0 \\ (4x + 7)(2x - 1) = 0[/tex]
Answer:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
When factoring trinomials of the form ax² + bx + c:
multiply the leading coefficient and the last term.find the product factors that add to give you the coefficient of the middle term.rewrite the polynomial with those factors replacing the middle term.1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
4x + 7 = 02x - 1 = 0
Case 1:
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x = [tex]\bold{-\dfrac{7}{4}}[/tex]
Case 2:
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x = [tex]\bold{\dfrac{1}{2}}[/tex]
Solutions:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
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What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?
Answer:
(4, -8)
Step-by-step explanation:
The components of a vector are found by subtracting the tail from the head.
__
Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)
⇒ The component form is (4, -8), or maybe 4i -8j.
_____
Additional comment
There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.
(4,-8) is the answer
URGENT I don't know which one it is
A. Name the smallest angle and the largest angle of the following triangles: F 6 S 5 1. A J 5.03 7 5 G B H 5.1 2. D 4 3 E
Answer:
(smallest, largest) = (B, C), (D, E), (G, J)
Step-by-step explanation:
Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.
__
ΔABCThe shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.
smallest angle: Blargest angle: CΔDEFThe shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.
smallest angle: Dlargest angle: EΔGHJThe shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.
smallest angle: Glargest angle: J_____
Additional comment
Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.
what is the mean median and mode of 3,721,23,63,27,29,95 and 23?
Answer:
Mean: 123
Median: 28
Mode: 23
Step-by-step explanation:
give brainliest
Answer:
Mean = 123, Median = 28 , Mode = 23
Step-by-step explanation:
Mean is the average of all the numbers.
Mean = [tex]\frac{3+721+23+63+27+29+95+23}{8} \\= \frac{984}{8} \\= 123[/tex]
Median is the middle most value of the numbers when arranged in ascending order. (Average of the 2 middlemost numbers if there are even number of values.)
Arranged Values: 3,23,23,27,29,63,95,721
Median = [tex]\frac{27+29}{2} \\= \frac{56}{2} \\= 28[/tex]
Mode is the value that occurs the most in the numbers.
Mode = 23
In one country, approximately 144,000 of 900,00 residences are rentals. Determine the percentage of residences in the country that are rentals
The 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We are assuming:
Total number of residence in the country = 144,000
In which 900,00 residences are rentals.
Percentage of residences in the country that are rentals:
= (90000/144000)×100
= 0.625×100
= 62.5%
Thus, the 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.
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Why is it that when you convert 3/4 into a decimal it’s 0.75??
Answer:because it’s like a quarter
Step-by-step explanation:
A quarter is 25c, 25•3=75
find the measure of the indicated angle
?
82°
58⁰
__ degrees
If b=7 , what is the value of the expression 2(10-b)? A.4 B.6 C.24 D. 12
Answer:
B
Step-by-step explanation:
substitute b = 7 into the expression
2(10 - b)
= 2(10 - 7)
= 2(3)
= 6
Answer:
all you have to do is substitute
B. 6
Step-by-step explanation:
2(10-7)
2(3)
6
Sheryl has a basket of ripe apples and peaches. The number of apples in the basket is 12 more than twice the number of peaches. If there are
36 apples in the basket, how many peaches are in the basket?
Answer: 432
Step-by-step explanation:
12
x 36
--------
72
+ 36
-------
432
A minor-league hockey team had the following scores for the start of the season: 3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.
If the hockey team scores 9 goals in their next game, would the mean, median, or mode be more affected?
If the hockey team scores 9 goals in their next game, it means that; the mean would be the most affected.
How to find mean, median and mode?
We are given the data set as;
3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.
Let us rearrange in ascending order to get;
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6.
The mean = (0 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5 + 6)/12 = 3
Median = (3 + 3)/2 = 3
Mode = 1, 2, 3, 3, 5
Now, if they score 9 goals in their next game, it means that;
Mean = 45/13 = 3.46
Median = 3
Mode remains the same
Thus, mean will be the most affected.
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A box contains 60 raffle tickets. The tickets are numbered 1 to 60 inclusive. What is P(multiple of 12) when a ticket is drawn from the box?
Answer:
[tex]the \: probability \: is \: \frac{5}{60} \\ when \: simplified \: becomes \: \frac{1}{12} [/tex]
Step-by-step explanation:
The solution is in the image
Which option below demonstrates the correct interval notation for a
continuous set of all numbers between 5 and 6, including 5, but not including
6?
OA. (5,6]
OB. (5,6)
O C. [5, 6)
OD. (5, 6}
The correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.
What is interval notation?It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close bracket the close the brackets means the value is at the close bracket also included, and open bracket means the value at the open bracket does not include.
We have:
Continuous set of all numbers between 5 and 6, including 5, but not including 6.
From the above statement we can represent the number in the interval notation:
The numbers are between 5 and 6.
(5, 6)
As it is mentioned that 5 is included and 6 is not included, then:
[5, 6)
Thus, the correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.
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please solve it fast
This are function used to determine the term of a sequence. The second and the third term of the sequence is 6 and 18
Recursive functionsThis are function used to determine the term of a sequence. Given the following functions
an+1 = 3an
Given that a1 = 2
a2 = 3a1
a2 = 3(2)
a2 = 6
For the third term a3
a3 =3a2
a3 = 3(6)
a3 = 18
Hence the second and the third term of the sequence is 6 and 18
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Find the volume of a cone with a diameter of 10 yards and a height of 12 yards. round your answer to the nearest tenth.
Tom bought a computer for 15% off from the list price of p dollars. if the sales tax was 8%, how much did he pay for the computer including sales tax?
The amount paid for the computer including sales tax is 0.918p
How to determine the amount paid?The price paid is given as:
Price = p
A 15% off means that he pays 85%.
So, we have:
Amount = 85% * p = 0.85p
A sales tax of 8% means:
Total = 0.85p * (1 + 8%)
Evaluate the product
Total = 0.918p
Hence, the amount paid is 0.918p
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6. Multiply: (x – 4)(x + 5)
(a) x2 + 5x - 20,
(b) x2 - 4x - 20,
(c) x2 - x - 20,
(d) x2 + x - 20.
I don’t know how to do this question and my math teacher is not helpful
Answer:
i think its 4.7
Step-by-step explanation:
Answer:
AC is an enlargement of AE
scale factor = 11.7 ÷ 5.2 = 2.25
CD is an enlargement of AB
10.5 ÷ 2.25 = 4.666666...
= 4.7 (rounded to nearest tenth)
HELP with this please!!
[tex]~~~~\dfrac{12}{x^2 -49} \cdot \dfrac{x^2+9x+14}{9}\\\\\\=\dfrac{4}{x^2 -7^2}\cdot \dfrac{x^2 + 7x +2x +14}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)} \cdot \dfrac{x(x+7)+2(x+7)}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)}\cdot \dfrac{(x+7)(x+2)}{3}\\\\\\=\dfrac{4(x+2)}{3(x-7)}[/tex]
Answer:
[tex]\frac{4(x + 2)}{3(x - 7)}[/tex]
Step-by-step explanation:
Hello!
We can simplify this by factoring, and cross reducing.
Simplify[tex]\frac{12}{x^2 - 49} * \frac{x^2 + 9x + 14}{9}[/tex][tex]\frac{12}{(x+7)(x - 7)} * \frac{(x + 2)(x + 7)}{9}[/tex][tex]\frac{12(x + 2)}{9(x - 7)}[/tex][tex]\frac{4(x + 2)}{3(x - 7)}[/tex]The final simplified form is [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]
Given limit of f (x) = negative 4 as x approaches c and limit of g (x) = one-fifth as x approaches c. what is limit of left-bracket startfraction g (x) over f (x) endfraction right-bracket as x approaches c? negative startfraction 20 over 1 endfraction negative five-fourths negative four-fifths negative startfraction 1 over 20 endfraction
Since the limit of f(x) is non-zero, the limit distributes over the quotient and
[tex]\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}[/tex]
The angle marked a=92 degrees.
work out the angle marked x.
Answer:
x is 92 degrees
The lines x and a are parallel and congruent, meaning they are evenly proportioned and have the same length.
find the area of the circle if radius is 6 and there is only 3/4 of the circled
Answer:
84.8
Step-by-step explanation:
Begin by finding the total area of the circle. You have been given the radius.
A = πr²
A = π(6)²
A = 36π
A = 113
If there is only 3/4 of the circle, then multiply the entire area by 3/4 to find the final answer.
113 x 3/4 = 84.8
Write a linear equation in point-slope form for the line that goes through (-1,3) and (1, -9).
A. y- 3 = -6(x+1)
B. y+1=-6(x-3)
C. y-3= 6(x+1)
D. y + 1 = 2(x-3)
The correct answer is A. y - 3 = -6(x + 1) of the linear equation in point-slope form for the line that goes through (-1,3) and (1, -9).
To write the linear equation in point-slope form, we need to use the formula:
[tex]y - y_1 = m(x - x_1),[/tex]
where [tex](x_1, y_1)[/tex] represents one of the given points, and m represents the slope of the line.
Step 1: Find the slope (m):
[tex]m = \frac {(y_2 - y_1) }{(x_2 - x_1)}\\= \frac {(-9 - 3)} { (1 - (-1))}\=\frac {-12 } {2}= -6.[/tex]
Step 2: Choose one of the given points (-1, 3), and substitute its coordinates into the point-slope form:
[tex]y - 3 = -6(x - (-1)).[/tex]
Step 3: Simplify and rearrange the equation:
[tex]y - 3 = -6(x + 1)\\y - 3 = -6x - 6.[/tex]
Therefore, the correct equation is A. y - 3 = -6(x + 1).
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You save 25% on a $199 television. How much do you save?
Answer:
49.75$Step-by-step explanation:
You save 25% on a $199 television. How much do you save?
25% = 1/4
so
199 : 4 = 49.75$
Answer:
You save $49.75
Need help to proportion this question help please
Step-by-step explanation:
1. So first you have to cross multiple the two terms
2.Solve the algebraic equation
By dividing with 12 on both sides
(Note :That's a 32 in the picture sometimes i really write bad)
From a hot-air balloon, Brody measures a 39° angle of depression to a landmark
that's 532 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon's vertical distance above the ground is 430 feet.
What is the angle of depression?You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.
The angle from horizontal to the point where you stopped your head is called the angle of depression.
From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.
The angle of depression = 39°
The base = 532
We need to find the vertical distance consider perpendicular.
[tex]\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80[/tex]
Therefore, the balloon's vertical distance above the ground is 430.80 feet.
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Answer:
430.81
Step-by-step explanation:
hard way
What is the probability of drawing four queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.
3/20825
4/52
1/20825
3/52
The probability of drawing three queens from a standard deck of cards is 0.000162.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Total cards = 54
No. queens in a deck = 4
Probability of drawing a queen card = 4/54
Now that 1 queen has been taken, the no. of cards becomes = 53
and
no. of queens = 3
Probability of getting a queen again = (3/53)(4/54)
Two queens have already been removed.
No. of cards in the deck = 52
No. of queens in the deck = 2
Probability of drawing three queens
= (2/52)(3/53)(4/54)
= 0.000162 approximately
The probability of drawing three queens from a standard deck of cards is 0.000162.
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score distribution of the test result of 33 students in a science class containing 50 items