Answers
Answer:
x = - 16, x = 9
Step-by-step explanation:
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
Ignore the "A" ^
v² + 7v - 144 = 0
a = 1, b = 7, c = - 144
[tex]x=\frac{-7±\sqrt{7^{2} -4(1)(-144)} }{2(1)}[/tex]
[tex]x=\frac{-7±\sqrt{49 +576} }{2}[/tex]
[tex]x=\frac{-7±\sqrt{625} }{2}[/tex]
[tex]x=\frac{-7+25}{2}[/tex] and [tex]x=\frac{-7-25}{2}[/tex]
[tex]x=\frac{18}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex]
x = 9 and x = - 16
Related Questions
What is the area of the parallelogram?
Answers
Area = Base x Height
Base = 8 cm
Height is the perpendicular distance between the base. 6 cm is not the height, but we can use 6 cm and the angle 60 to find the height. See the picture attached with.
The height x is the perpendicular side of the triangle as shown in figure and 6 is the hypotenuse.
So,we can write
cos 60 = x/6
⇒
x = 6 * cos 60 = 3 cm
So, now we can write:
Area of parallelogram = 8 x 3 = 24 cm²
or A = base*lateral side /cos(theta)
A = 8 * 6 / cos(60) = 96cm^2
The area of the parallelogram is 96 sq.cm
If the areas of two rhombi are equal, are the perimeters sometimes, always or never equal. explain your answer – you can use examples with actual numbers to do so.equalif the areas of two rhombi are equal
Answers
The area of a rhombus = length of base * altitude. To keep the area the same we would have to keep the same base and move the opposite side so its parallel to the base. But doing this will lengthen the other 2 sides of the figure so its no longer a rhombus.
The perimeters of two rhombi with equal areas are sometimes equal, but not always.
Let's consider the formula for the area of a rhombus, which is given by [tex]\( A = \frac{1}{2} \times d_1 \times d_2 \), where \( d_1 \) and \( d_2 \)[/tex] are the lengths of the diagonals. For the perimeter P, we have [tex]\( P = 4 \times s \)[/tex], where s is the length of one side of the rhombus.
For two rhombi to have equal areas, the product of their diagonals must be the same. That is, if we have two rhombi with diagonals [tex]\( (d_1, d_2) \) and \( (d_1', d_2') \), then \( d_1 \times d_2 = d_1' \times d_2' \)[/tex].
However, the perimeter depends only on the length of one side, s, and not on the diagonals. Therefore, two rhombi with the same area can have different side lengths and thus different perimeters.
Let's consider an example:
Rhombus 1:
[tex]- Diagonals \( d_1 = 8 \) units and \( d_2 = 4 \) units[/tex]
[tex]- Area \( A = \frac{1}{2} \times 8 \times 4 = 16 \) square units[/tex]
[tex]- Side length \( s \), using the Pythagorean theorem (since the diagonals bisect each other at right angles), is \( s = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} \) units[/tex]
[tex]- Perimeter \( P = 4 \times s = 4 \times \sqrt{20} \) units[/tex]
Rhombus 2:
[tex]- Diagonals \( d_1' = 10 \) units and \( d_2' = 3.2 \) units[/tex]
[tex]- Area \( A' = \frac{1}{2} \times 10 \times 3.2 = 16 \) square units (equal to the area of Rhombus 1)[/tex]
[tex]- Side length \( s' \), using the Pythagorean theorem, is \( s' = \sqrt{1.6^2 + 2.56^2} = \sqrt{2.56 + 6.5536} = \sqrt{9.1136} \) units[/tex]
[tex]- Perimeter \( P' = 4 \times s' = 4 \times \sqrt{9.1136} \) units[/tex]
Comparing the perimeters:
[tex]- \( P = 4 \times \sqrt{20} \approx 4 \times 4.472 = 17.888 \) units[/tex]
[tex]- \( P' = 4 \times \sqrt{9.1136} \approx 4 \times 3.0188 = 12.0752 \) units[/tex]
Clearly, the perimeters are not equal, even though the areas are the same.
However, it is possible for two rhombi with equal areas to have equal perimeters if their side lengths are the same. For instance, if Rhombus 1 and Rhombus 2 both had side lengths of s = s' = 4 units, then their perimeters would both be P = P' = [tex]4 \times 4 = 16 \)[/tex] units, regardless of the lengths of their diagonals, as long as the diagonals satisfy the area condition [tex]\( d_1 \times d_2 = d_1' \times d_2' \)[/tex].
In conclusion, the perimeters of two rhombi with equal areas can sometimes be equal, specifically when the side lengths are the same, but they are not always equal, as demonstrated by the example above.
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?
Answers
Let: 1st number = x
2nd number = x - 4
3rd number = 4x
x + (x-4) + 4x = 62
6x - 4 = 62
6x = 62 + 4
6x = 66
x = 11 ---> 1st number
x - 4 = 11 - 4
= 7 ---> 2nd number
4x = 4(11)
= 44 ---> 3rd number
Find the values of b such that the function has the given maximum value. f(x) = −x2 + bx − 14; Maximum value: 86
Answers
[tex]y_{max}\ \text{is in the vertex of the parabola}.[/tex]
[tex]\text{The coordinates of the vertex of the parabola}\ f(x)=ax^2+bx+c:\\\\V\left(\dfrac{-b}{2a};\ \dfrac{-(b^2-4ac)}{4a}\right)[/tex]
[tex]\text{We have:}\\\\f(x)=-x^2+bx-14\to a=-1;\ b=b;\ c=-14[/tex]
[tex]\text{Substitute:}\\\\\dfrac{-\left(b^2-4\cdot(-1)\cdot(-14)\right)}{4\cdot(-1)}=86\\\\\dfrac{b^2-56}{4}=86\ \ \ \ |\cdot4\\\\b^2-56=344\ \ \ \ |+56\\\\b^2=400\to b=\pm\sqrt{400}\\\\b=-20\ \vee\ b=20[/tex]
Answer: b = -20 or b = 20.
To find the value of 'b' that gives the maximum value of 86 for the function f(x) = -x² + bx - 14, substitute the x-coordinate of the vertex (-b/2a) into the function, equate it with 86 and solve for 'b'.
Explanation:To find the values of b for which the quadratic function f(x) = -x² + bx - 14; Maximum value: 86 holds true, we need to utilize the properties of quadratic functions. In a quadratic function in the form f(x) = ax² + bx + c, the maximum value occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a.
Given that our quadratic is a maximum (opens downwards since a=-1), the y-coordinate of the vertex, which is our maximum value, is 86. Substituting these into our function, we get f(-b/2a) = 86, replacing a=-1, this reduces to -b²/4 -14 = 86. Simplifying this equation will give you the value of b.
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Find the determinant of G
Answers
where the letters are: a and b is the top row and c and d is the bottom row
so ad = 12*2 and cb = -6*0
12x2 = 24
-6x0 =0
24-0 = 24
the determinant = 24
If an airplane travels 15 miles in 2 minutes what is the speed in miles per hour
Answers
1 hour = 60 minutes
60 ÷ 2 = 30
30 × 15 = 450
Answer = 450 miles in 1 hour
Hope this helped :)
can you please help me on this worksheet and try to show the work
Answers
180° = π radians
13. (105°)*(π radians)/180° = 7π/12 radians
14. 5π/6 radians * 180°/(π radians) = 150°
15. (The geometry shown cannot actually exist. The total of subtended arcs on any linked sprockets must be 360°.)
a.
The arc length on the smaller sprocket is (12 in)*(160/360) = 5 1/3 in.
The arc length on the larger sprocket is (20 in)*(185/360) = 10 5/18 in.
The total chain length is 5 6/18 +10 + 10 5/18 + 10 = 35 11/18 in. Rounded to the nearest tenth inch, the chain length is 10.3 inches.
b.
10.3/0.5 ≈ 20.6 ≈ 21
The chain has about 21 links. (There are no "teeth" on a chain.)
1. The radius can be found by looking at the distance between the origin and the line 8x+6y-48=0. That distance is |-48|/√(8²+6²) = 4.8.
Since the radius of the circle is 4.8, so its circumference is ...
9.6π cm, about 30.159 cm.
2. s = rθ
s = (12 cm)(π/3 radians) = 4π cm
The length of arc AB is 4π cm, about 12.566 cm.
The length of a rectangle is 4 feet shorter than its width. the area of the rectangle is 42 square feet. find the length and width. round your answer to the nearest tenth of a foot
Answers
Length is [tex]\boldsymbol{4.4}[/tex] feets and width is equal to [tex]\boldsymbol{8.8}[/tex] feets.
Area of a rectangleThe area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.
A quadrilateral having four right angles is known as a rectangle.
Let [tex]\boldsymbol{w}[/tex] feets denotes width of a rectangle.
Length of a rectangle [tex]=\boldsymbol{w-4}[/tex] feets
Area of a rectangle [tex]=\boldsymbol{42}[/tex] square feet
Length [tex]\times[/tex] Width [tex]=42[/tex]
[tex]w(w-4)=42[/tex]
[tex]w^2-4w-42=0[/tex]
[tex]w=\frac{4\pm \sqrt{16+168}}{2}[/tex]
[tex]=2\pm \sqrt{46}[/tex]
As dimension can not be negative, [tex]2-\sqrt{46}[/tex] is rejected.
So,
[tex]w=2+ \sqrt{46}[/tex]
[tex]=\boldsymbol{8.8}[/tex] feets
Length [tex]=8.8-4[/tex]
[tex]=\boldsymbol{4.4}[/tex] feets
So, length is [tex]4.4[/tex] feets and width is equal to [tex]8.8[/tex] feets.
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Three added to eight times a number is the same as three times the value of two times the number minus one
Answers
How do I convert 2.4 x 10^21 formula units of magnesium hydroxide to grams?
Answers
Facts
1. As a formula unit, Magnesium Hydroxide has a chemical formula of Mg(OH)2
2. That means for every Magnesium, there are 2 oxygens and 2 hydrogens
3. The weights of these components are found on a periodic table. Since every periodic table is different, I'm going to approximate the results.
Mg = 24
O = 16
H = 1
4. One mole of anything has 6.02 * 10^23 (in this case) formula units associated with it.
Step One
Find the number of grams in 1 formula unit using the numbers from the periodic table.
1 Mg = 1 * 24 = 24
2 O = 2 * 16 = 32
2 H = 2 * 1 = 2
Total = 58 grams
So
1 mole of Mg(OH)2 = 58 grams
1 mole / 6.02 * 10 ^23 formula units = x mole / 2.4 * 10 ^ 21 formula units
Cross multiply
1 mole * 2.4 * 10^21 formula units = x mole * 6.02 * 10^23 formula units.
Divide both sides by 6.02 * 10^23
1 * 2.4 * 10^21 / 6.02 * 10 ^ 23 = x
x = 0.003987 moles
Now do this again for grams
1 mole / 58 grams = 0.003987 mole / x grams Cross multiply
1 mole * x = 0.003987 * 58 grams
x = 0.2232 grams <<<<< Answer
Simplify. x + 4.7 = −9.2 A. −13.9 B. 13.9 C. −12.9 D. 12.9
Answers
Isolate the x, subtract 4.7 from both sides
x + 4.7 = - 9.2
x + 4.7 (-4.7) = - 9.2 (-4.7)
x = -9.2 - 4.7
x = -13.9
-13.9, or A, is your answer
hope this helps
A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?
Answers
P (x) = - 3 (x-5) ^ 2 + 12
We derive the function to obtain the maximum.
We have then:
P (x) = - 6 (x-5)
We match zero:
-6 (x-5) = 0
We clear x:
x-5 = 0
x = 5
Answer:
the company should set a sock price of 5 $ to earn a maximum profit
To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.
Explanation:The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.
In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.
This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.
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PLEASE HELP! - Caitlyn recorded the height of each plant after she exposed each plant to a set amount of darkness daily. The scatterplot shows her results after 2 weeks of exposing each plant to the amount of darkness.
(Graph Below)
Which statement about the scatterplot is true?
A. The point (17, 12) could cause the description of the data set to be overstated.
B. The point (17, 12) could cause the description of the data set to be understated.
C. The point (17, 12) shows that there is no relationship between the number of hours of darkness and the height of the plant.
D. Although (17, 12) is an extreme value, it should be part of the description of the relationship between number of hours of darkness and the height of the plant.
Answers
Answer:
I think it's b, please correct me if I'm wrong.
Step-by-step explanation:
I'm taking the test rn so I hope its right.
Answer:
its b i just did it
Step-by-step explanation:
PLEASE SOMEONE I AM SO DESPERATE like actually crying
1. The equation of a parabola is given. y=−1/6x2+7x−80 What is the equation of the directrix of the parabola?
2. (y+2)^2= 129X-5)
What is the equation of the directrix of the parabola?
Answers
we have that
y=−1/6x2+7x−80
y= (−1/6)x^2+7x−80 multiply both sides by -6
-6y = x^2 - 42x + 480 subtract 480 from both sides
-6y - 480 = x^2 - 42x take (1/2) of 42 = 21.....square this = 441 and add to both sides
-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right
-6y - 39 = (x - 21)^2 factor the left side as
-6 (y + 39/6) = ( x - 21)^2 (1)
Using the form
4p (y - k) = ( x - h)^2 we can write (1) as
4 (-3/2)(y - (-39/6) ) = ( x - 21)^2
The vertex = ( h, k) = ( 21, -39/6) and p = -3/2
And the directrix is given by
y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =
-30/6 = - 5-------> y=-5
the answer Part 1) is
y=-5
Part 2) (y+2)^2= 129X-5
What is the equation of the directrix of the parabola?(y+2)²= 129X-5 -----> 129*(x-5/129)=(y+2)² (1)
Using the form
4p (x - h) = ( y - k)^2 we can write (1) as
4*(129/4)*(x-5/129)=(y+2)²
The vertex = ( h, k) = ( 5/129, -2) and p = 129/4
And the directrix is given by
x = h - p → x = 5/129 - (129/4) = (20-16641)/516-----> -16621/516
x=-32.21
the answer part 2) is
x=-32.21Please help with geometry
Answers
Anyone know the answer?
Answers
The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year.
An exponential function comes down from the positive infinity and passes through the points zero comma eighty-seven thousand. The graph is approaching the x-axis.
What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?
$90,000, and the graph would have a y-intercept at 20,000
$87,000, and the graph would have a y-intercept at 67,000
$87,000, and the graph would fall at a slower rate to the right
$87,000, and the graph would fall at a faster rate to the right
Answers
Answer:
I just took the test the answer is
Step-by-step explanation:
B. 87,000, and the graph would have a y-intercept at 67,000.
What is the best estimate for the sum of 3/8 and 1/12?
Answers
a boy flies a kite with a 100 foot long string. the angle of elevation of the string is 48 degrees. how high is the kite from the ground?
Answers
in a right triangle
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=hypotenuse*sin ∅
in this problem
angle ∅=48°
hypotenuse=100 ft
opposite side angle ∅=?----> height of the kite from the ground
opposite side angle ∅=100*sin 48°------> 74.31 ft
the answer is
74.31 ft
I need to answer three questions about y = x^(-2) on the interval [-4, -1/2]. I have attached my questions and my answers as screenshots:
Part 1 - ANSWER C
Part 2 - ANSWER A
Part 3 - ANSWER B
I am referring to each part in the order that I uploaded the screenshots. You will see that my answers are highlighted in blue. I like second opinions!
Answers
help me 15p for an answer and brainliest
help mme please
the true it is 20p
Answers
______________
Answer:
Option 4.
Step-by-step explanation:
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
Answers
1. 1
2. -1
3. 0
4. 1
5. 1 (x has been replaced by 1/x and the limiting value of x changed to 0)
How many distinct permutations are there of the letters of the word BOOKKEEPER?
There are __[blank]__ distinct permutations of the letters of the word BOOKKEEPER.
A group of 3 English majors, 2 anthropology majors, and 5
history majors are going out to dinner, where they will sit at a circular table. If students with the same major need to sit together, how many different ways can the students be seated around the table?
Answers
The group can be arranged in 8640 ways with all students of the same major together.
Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.
An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
[tex]\frac{n!}{n_1!\times n_2!\times ... \times n_k!} \\ \\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200[/tex]
Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.
Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.
This gives us 6(6*2*120) = 8640
The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.
Explanation:The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.
In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.
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quando o Ângulo de elevação do sol e de 70 a sombra de um edifício medes 20 cm calcule a altura do edifício
dados : sen 70=0,93 cos 70=0,3 e tg70=2,74?
Answers
tg 70 = x/(20 cm)
x = 20 cm * tg 70
x = 20 cm * 2,74
x = 54,8 cm
Resposta: A altura do edifício é 54,8 cm.
Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.
Answers
0 is the initial height, since you cannot hold one in your hand and safely set it off.
This will have a maximum; the firework will reach a highest point and fall back down. This is also evident from the equation; the negative in front of t² flips the parabola upside down, which gives it a maximum.
Rachel enjoys exercising outdoors. Today she walked5 2/3 miles in2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile
Answers
the answer to your question is
Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.
Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile
Answer:
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles or 5.67 miles in 2 2/3 hours or 2.67 hours.
Rachel’s unit walking rate in miles per hour is = [tex]\frac{5.67}{2.67}[/tex] = 2.125 miles per hour or 2 1/8 miles per hour.
Rachel’s unit walking rate in hours per mile = [tex]\frac{2.67}{5.67}[/tex] = 0.47 hours per mile.
For a circle with a radius of 6 feet, find the arc length of a central angle of 45 degrees
Answers
Arc Length, s = radius*theta where theta is in radians. First we need to convert theta from degrees to radians.
theta (radians) = 45 degrees * π radians / 180 degrees = 0.785 radians
radius = 6 ft
theta = 0.785 radians
s = arc length = 6 ft * 0.785 radians = 4.712 ft
PLEASE ANSWER QUICKLY! Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.
Answers
Correlation does not imply Causation.
This means if two variables are strongly related, it is not a must thing that one is causing any occurrence or change in the other variable. For example, before and during an occasion or an event people buy new clothes and celebrate by having different drinks. So there will be a strong correlation between buying new clothes and having drinks.
Thus this mean, having different drinks is causing people to buy new clothes? The answer is NO.
However, it is possible that if two variables are correlated on might be causing the other. For example, more hours of work will help the worker to earn more. So more work is causing the salary to grow. So more work is Causing an increase in salary? The answer is YES
Therefore, the answer to this question will be option A
the equation 3sinx+cos^2x=2 is solved below
Please help! Thanks!
Answers
3sin x+cos²x=2
3sin x+(1-sin²x)=2
-sin²x +3sin x=1
sin²x -3 sin x+1=0---------> up to here the procedure is correct
let
A=sin x
then
A²-3A+1=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(A²-3A)=-1Complete the square. Remember to balance the equation by adding the same constants to each side.
(A²-3A+2.25)=-1+2.25
Rewrite as perfect squares
(A-1.5)²=1.25(+/-)(A-1.5)=1.12
first solution
(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62
second solution
-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38
the answer is
the equation was factored incorrectly
Its is b. hope this halps
Choose the example that correctly shows the mean population density of a region.
A. 678 people per cubic meter
B. 678 cubic meter per number of people
C. 678 people per square mile
D. 678 square mile per people
Answers
The answer is C
- 678 per square mile