Answer:
x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17
/ = over
Step-by-step explanation:
a = 2, b=-9, c=8
x = −b±√b2−4ac/2a
x = −(−9)±√(−9)2−4(2)(8)/2(2)
x = 9±√17/4
x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17
Help with math work
Answers for different section are given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, given function;
f(x) = -x² - 4x + 6
1. If we take -1 common from the given function, we get
f(x) = -1 (x² + 4x - 6)
f(x) = -1 (x² + 4x) + 6
Thus, first block contains -1 and second block contains 4.
2. Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².
f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6
f(x) = -1 ( x² + 4x + 2²) +4 + 6
Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.
3. Then we factorize the bracket and simplify outside the bracket;
f(x) = -1 (x + 2)² + 10
Thus, first block contains -1, second block contains 2 and third block contains 10.
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What statement is true for f(x) = 3.2^x?
Answer:
Step-by-step explanation:
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
Answer:
[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]
Step-by-step explanation:
First off let's state the quadratic formula
Quadratic formula
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
For this question our quadratic equation is
[tex]x^2+20=2x[/tex]
Now before we can apply the quadratic formula we first have to set the equation equal to zero. We do this my moving everything to one side and setting it equal to zero.
In this case, we simply move the 2x to the other side making it negative and setting the equation equal to zero.
[tex]x^2-2x+20=0[/tex]
From here we plug in the values to the quadratic equation.
Now incase you don't know
[tex]a =[/tex] Coefficient of [tex]x^2[/tex] value
[tex]b=[/tex] Coefficient of [tex]x[/tex] value
[tex]c=[/tex] The Constant
Now plug in values
[tex]a=1[/tex]
[tex]b=-2[/tex]
[tex]c=20[/tex]
To get the values of x using the quadratic formula we have the plug in the values, we also have to both subtract and add the [tex]\sqrt{b^2-4ac}[/tex] to [tex]-b[/tex]
Plug in values into formula
[tex]\frac{2+\sqrt{(-2)^2-4(1)(20)} }{2(1)}[/tex]
[tex]\frac{2+\sqrt{-76} }{2}[/tex]
[tex]\frac{2+\sqrt{-1} *\sqrt{76} }{2}[/tex]
[tex]\frac{2+i *\sqrt{76} }{2}[/tex]
[tex]\frac{2+i *\sqrt{4(19)} }{2}[/tex]
[tex]\frac{2+i *\sqrt{2^2(19)} }{2}[/tex]
[tex]\frac{2+2i \sqrt{19} }{2}[/tex]
[tex]x=1+i\sqrt{19}[/tex]
Now repeat the steps except subtract from -b rather than add to it.
Final Answer
[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]
BTW
± = plus and minus
An object is attached to a spring that is stretched and released. The equation d= -8COS(pi/6 t) models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.
0 seconds
1.38 seconds
4.62 seconds
8 seconds
The time when the object will be 6 inches above the rest position is C. 4.62 seconds.
How to depict the information?From the information, the object is attached to a spring and is stretched and released.
The given model is given as:
d = -8 cos (π/6t)
In this case, it's important to plot the graph based on the model given. Therefore, the time when the object will be 6 inches above the rest position is 4.62 seconds.
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What is the solution to the equation startfraction 3 over m 3 endfraction minus startfraction m over 3 minus m endfraction = startfraction m squared 9 over m squared minus 9 endfraction?
The provided equation has no solution because the square of any number cannon is negative.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
Find a solution to the given equation
Please refer to the attached picture for the expression.
We have an expression:
[tex]\rm \dfrac{3}{\left(m+3\right)}-\dfrac{3}{\left(m-3\right)}=\dfrac{m^2+9}{\left(m^2-9\right)}[/tex]
3(m - 3) - 3(m + 3) = m² + 9
3m - 9 - 3m - 9 = m² + 9
m² ≠ -27
As the square of any number cannot is negative, so no solution to the provided equation.
Thus, the provided equation has no solution because the square of any number cannon is negative.
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Answer:
D = No Solution
Step-by-step explanation:
What is equivalent to 3(5-2i)?
Answer:
Step-by-step explanation:
One equivalent can be obtain by distributing multiplication with 3 over subtraction 5-2i
3(5-2i) =
3·5 -3·2·i =
15 -6i or -6i +15
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
Answer:
7m tall convert this into imperial measurement
6. Solve for x: please explain
Answer:
5
Step-by-step explanation:
the angles need to add up to 180
60 + 40 =100
180 - 100 =80
80 - 5 =75
75/15 =5
1. Kelsey spent 55 hours over 2 weeks working on a ELA project. She worked 32 hours the
Answer:
23
Step-by-step explanation:
If Kelsey spent 32 hours in the first week. We subtract 32 from 55. 55-32=23. That means she worked 23 hours in the second week.
Evaluate.
{3−[−4−(6+2)]}⋅(−5)
A−75
B−57
C−15
D−9
Step-by-step explanation:
please mark me as brainlest
What is the formula for capacity of a prism?
Answer:
The prism volume formula is B*h B (area of one end) =0.5*1000*566 = 283,000 mm 2 (area of a triangle) H (length/height of prism) = 1000 mm
Step-by-step explanation:
Answer:
Step-by-step explanation:
Any prism volume is equal to the area of the base (B) multiplied by the height of prism (H)
V = BH
Now, to find the area of the base you need this formula : B = 1/2 h(b1+b2), then multiply by the height of the prism.
A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?
Answer:
Step-by-step explanation:
số nữ là 65- 35= 30
vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13
A graph is shown below
what is the equation of the line in slope intercept form HELP ASAP
Answer:
y = -2x + 16
the y intercept is the y value at x = 0. On the graph there is a dot at 16 on x= 0, so the y intercept would be 16.
the only answer choice adding 16 sis y = -2x + 16
There are 7 pieces of pie over in the cafeteria. If 5 pieces are apple and 2 are cherry, what fraction of the remaining pieces are cherry?
Answer:
No
Step-by-step explanation
because 5+2=7 so I don't have a piece of cake left over
Find each difference.
(-6s² + 12s-8) - (3s² +8s - 6) =
O-9s² + 4s-14
O-9s² + 4s-2
O-9s² + 20s - 14
O-9s² +20s-2
DONE ✔
Answer: [tex]-9s^2 + 4s-2[/tex]
Step-by-step explanation:
[tex](-6s^2 +12s-8)-(3s^2 + 8s-6)\\\\=-6s^2 + 12s-8-3s^2 - 8s+6\\\\=\boxed{-9s^2 +4s-2}[/tex]
20 points!!
Flynn is playing with a toy that is tied to his hand by a string. The toy falls toward the floor then rises back toward Flynn's hand, and repeats this motion, following the path illustrated by given graph.
The function is h(t) = 7/4 cos π/3 t + 9/4,
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
As, h(t) = x cos π/3 t +y
when t= 0, h(t) = 4
when t= 3, h(t) = 0.5
So,
x cos π/3 *0 +y=4
x cos π/3 *3 +y=0.5
and, x+ y = 4, -x+ y =0.5
Now,
2y= 4.5
y= 9/4
and, x= 4-9/4= 7/4.
Hence, h(t) = 7/4 cos π/3 t + 9/4
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Answer:got it right
h(t)=1.75, cos(1/3), + 2.25
Step-by-step explanation:
Which inequality is shown on this graph?
The inequality which shows the graph is [tex]y\le\ 4x+2[/tex].
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
As, from the inequalities the graph is representing the fourth inequality.
The graph attached below show the graph corresponding to
[tex]y\le\ 4x+2[/tex] is shown.
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In AABC, what is the value of x?
Answer:
x = 6.5
Step-by-step explanation:
* since it's a triangle ALL the angles inside should give you 180° * Equate everything to 180°
8x + 10x - 10°+ 10x + 8° = 180°( sum of angles on a triangle)
28x - 2° = 180° * group like terms*
28x = 182°
x = 6.5
8y and y are like terms
true
or
false
Answer:
True
Step-by-step explanation:
Hope this helps :)
Which of the following is an example of why irrational numbers are not closed under addition?
√4+√4=2+2=4,
and 4 is not irrational
1/2+1/2=1, and 1 is not irrational
√10+(-√10) = 0, and 0 is not irrational
-3 +3 = 0, and 0 is not irrational
Answer:
√10 + (-√10) = 0, and 0 is not irrational
^ this one
4. Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 4
B. 5
C. 16
D. 12
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can start by dividing the inequality by 3 to get ...
8 -4x < 2(x -5)
And we can divide by 2 to simplify further to ...
4 -2x < x -5
Now, we can add 2x+5, which gives ...
9 < 3x
and then divide by 3 again:
3 < x
Therefore number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
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tan A + sin A/tan A-sin A
= sec A +1/sec A-1
We need to prove
[tex]\frac{\tan A+\sin A}{\tan A-\sin A}=\frac{\sec A+1}{\sec A-1}[/tex]
[tex]\text{LHS}=\frac{\tan A+\sin A}{\tan A-\sin A}\\\\=\frac{\frac{\sin A}{\cos A}+\sin A}{\frac{\sin A}{\cos A}-\sin A}\\\\=\frac{\sin A+\sin A \cos A}{\sin A-\sin A \cos A}\\\\=\frac{\sin A(1+\cos A)}{\sin A(1-\cos A)}\\\\=\frac{1+\cos A}{1-\cos A}\\\\=\frac{1+\frac{1}{\sec A}}{1-\frac{1}{\sec A}}\\\\=\frac{\sec A+1}{\sec A-1}\\\\ =\text{RHS}[/tex]
Round to the nearest tenth. B 63 142° 61 A C X x = [?]
The value of x in the triangle is 117.2 units
The missing image is attached with the answer.
What is an Equation?An equation is formed when two expression is equated by an equal sign to a constant , variable or an expression.
Cosine rule of Triangles is used and is given by
c² = a² + b² - 2ab cos C
Where a, b, c are the sides and C is the angle opposite side c.
from the given data in the figure
c = 63
a = 61 and
angle B is 142 degree
x² = 63² + 61² - 2(63)(61) * cos(142)
On solving
x = 117.2
The value of x in the triangle is 117.2 units
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Select the correct answer.
Consider the given functions.
A table with values of x and f of x is given along with a non-linear equation g of x equals 2 power x minus 5 and a graph solving the equation
Select the true statement regarding the end behavior of the functions.
Using limits, it is found that the true statement regarding the end behavior of the function is given by:
B. As the value of x increases, f is the only function to approach 0.
How to find the end behavior of a function?The end behavior of a function is given by the limit of the function as x goes to infinity.
In this problem, we have that:
[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex], as we can see from the table, when x increases, y decreases. [tex]\lim_{x \rightarrow \infty} g(x) = 2^{\infty} = \infty[/tex].[tex]\lim_{x \rightarrow \infty} h(x) = \infty[/tex], from the graph.Hence statement B is correct.
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What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?
Answer:
The squared root of 9 is 3
Why - Half of 9 is 3
Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.
5 Cubed is equal to 125
Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5
Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answer:
75 mm
Step-by-step explanation:
Pythagorean theorem:To find the hypotenuse, use Pythagorean theorem
Hypotenuse² = base² + altitude²
c² = 21² + 72²
= 441 + 5184
= 5625
[tex]\sf c = \sqrt{5625}[/tex]
[tex]= \sqrt{75*75}\\\\\boxed{\bf c = 75 \ mm}[/tex]
Which two numbers does √√61 lie between on a number line? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and Which two numbers does √√61 lie between on a number line ? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and 8.1
Answer:
B) 7.8 and 7.9
Step-by-step explanation:
Taking the square root of 61, we can conclude that the decimal form is 7.810, which falls between the range of 7.8 and 7.9
Answer:
√61 lie between 7.8 and 7.9
What is true about △ABC? Select three options
AB ⊥ AC
The triangle is a right triangle.
The triangle is an isosceles triangle.
The triangle is an equilateral triangle.
BC ∥ AC
Answer: Isosceles triangle
Step-by-step explanation: Two of the base sides are equal distance away. (Sides AB and AC)
What are all the solutions of x² + 3x -4 = 0? Multiple choice
A: -4
B:-2
C:-1
D:0
E:1
F:2
G:4
Answer :
A and E .
Step-by-step explanation:
