The value of x for the quadratic equation is 1.099 or -9.099 .
What is completing the square?
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
To solve ax²+bx+c=0 by completing the square:
1. Transform the equation so that the constant term, c , is alone on the right side.
2. If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .
3. Add the square of half the coefficient of the x -term, to both sides of the equation.
4. Factor the left side as the square of a binomial.
5. Take the square root of both sides. (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)
6. Solve for x .
According to the question
Quadratic equation by completing the square
x² + 8x = 10
As we will try to make complete square of left side
for that
we have to add to both sides of the equation
As
a = 1
2ab = 8
b = 4
x² + 8x + 4² = 10 + 4²
By using the identity ( )
(x + 4)² = 10 + 16
(x + 4)² = 26
x + 4 = ±
x + 4 = ± 5.099
x = 5.099 - 4
x = 1.099
or
x = -5.099 - 4
x = -9.099
Hence, The value of x for the quadratic equation is 1.099 or -9.099 .
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Given f(x) = 2 cos x, find the exact value of f (pi/6) in simplest form with a rational
denominator.
Using trigonometric functions, the value of 2 cos x is equals to √3.
What are trigonometric functions?One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The graphic shows these six trigonometric functions in respect to a right triangle.
Cos (π/6) = √3/2
So. f(x) = 2 cos x
⇒ f(x) = 2 cos(π/6)
⇒ f(x) = 2 × √3/2
f(x) = √3
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Fine the volume and surface area of the figure below
Answer:
1470 in³, 716 in²
Step-by-step explanation:
The figure is a cylinder, and it's volume can be found using the following formula:
Volume of cylinder
= area of circle base ×height
= πr²h
Identify the value of r and h:
From the diagram, the radius (r) is 6 in. while the height (h) is 13 in.
Using the formula,
volume of cylinder
= π(6²)(13)
= 468π
= 1470 in³ (3 s.f.)
The surface area of a cylinder is the total area of all its faces, i.e. the sum of the area of its two circular bases and its curved surface area.
Formula
Surface area of cylinder
= 2πr² +2πrh
Surface area of cylinder
= 2(π)(6²) +2(π)(6)(13)
= 72π +156π
= 228π
= 716 in² (3 s.f.)
Additional:
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A grocery store sells a bag of 6 oranges for $5.64. How much would it cost for 8
oranges?
The cost of 8 oranges is $7.52
How to find the cost of 8 oranges ?The first step is to find the cost of one orange
6 oranges cost 5.65
1 orange= 5.64/6
= 0.94
Therefore the cost of 8 oranges can be calculated as follows
= 0.94×8
= 7.52
Hence 8 oranges cost $7.52
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let f(x)=4x^2+5 and g(x)=2x-4. find f(x)+g(x)
Answer:
[tex]4x^2+2x+1[/tex]
Step-by-step explanation:
[tex]f(x)=4x^2+5\\g(x)=2x-4\\\\f(x)+g(x)=(4x^2+5)+(2x-4)\\\\4x^2+5+2x-4\\\\4x^2+2x+1[/tex]
√ 81 )^2 I can't figure this out. Sorry to bother anyone!
Answer: 81
Step-by-step explanation: The square root and the squared function cancel each other out
which set of mixed numbers has a difference less than 1
1 1/2-1 1/9
3 3/4-2 1/7
2 4/5-1 1/3
2 7/9- 1 1/3
Only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.
We have a set of mixed numbers.
We have to identify which set of mixed numbers has a difference less than 1.
What are Mixed Numbers ?A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Any mixed fraction can be converted into normal fraction using the formula -
[tex]X\frac{Y}{Z} =\frac{Z\times X+Y}{Z}[/tex]
According to the question -
Let us solve them one by one (for difference to be less than 1, the denominator should be less than numerator) -
A = [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] B = [tex]$3\frac{3}{4} - 2\frac{1}{7} = \frac{45}{28}[/tex]C = [tex]$2\frac{4}{5} - 1\frac{1}{3} = \frac{22}{15}[/tex]D = [tex]$2\frac{7}{9} - 1\frac{1}{3} = \frac{13}{9}[/tex]Hence, only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.
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Evaluate each.
a.
-4+|51|-4
b. -3•-8
C.
32 ÷ -2
Determine whether the sequence converges or diverges. if it converges, find the limit. if it diverges write none. a_n = (9 3 n**2)/(n 8 n**2)
According to the question, determine whether the given sequence converges or diverges.
The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]
Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]
Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].
Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].
What converges and diverges in limits?
When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.
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Determine whether each relation is a function. (3,9),(11,21),(121,34),(34,1),(23,45)
Domain - { 3, 11, 121, 34 , 23 , } is domain of each relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are the domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).Domain - { 3, 11, 121, 34 , 23 , }
Range - { 9, 21 , 34 , 1 , 45 }
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Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget.
PLEASE HELPPPP 3
The inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is x < 4
How to write and solve an equation which can be used to determine the number of gigabytes?The given parameters are
Flat cost = $58
Rate = $3 per gigabyte
Budget = Under $70
The equation is represented as:
Total cost = Flat cost + Rate * Number of gigabyte
So, we have
y = 58 + 3x
The budget is under 70
So, we have
58 + 3x < 70
Subtract 58 from both sides
So, we have
3x < 12
Divide both sides by 3
So, we have
x < 4
Hence. the inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is x < 4
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What is the property of 10+(-10)=0
How many ways can five of the nine us supreme court justices agree? (With solution)
(This is Combinations and Permutations)
The number of ways can five of the nine us supreme court justices agree is 3024 ways.
How to compute the value?The number of ways that five of the nine us supreme court justices agree will be calculated thus:
= 9! / 5!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)
= 3024
There'll be 3024 ways.
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betty worked at the golf course during the summer after 8th grade. after working for 2 weeks she added her earnings to the gifts she got for graduation and found she had $750. after four more weeks of work she had a total of 870$.
Plss help immidiatly
What does the y intercept represent in this situation?
Write the equation in slope intercept form
The y-intercept is the amount she got as gifts during her graduation.
The equation in slope intercept form is $630 + $60b
What does the y-intercept represent?The slope intercept form is used to write equations for equations for linear equations with two variables. The graph for a slope intercept form is a straight line.
The form for slope intercept form is: y = mx + b
Where:
y = y coordinatem = slopex = x coordinateb = y interceptThe y-intercept is the constant. It represents the point where the slope touches the y-axis.
The first step is to determine how much are earnings are and how much the gift is.
The equations that would be used to determine this are:
a +2b = 750 equation 1
a + 4b = 870 equation 2
Where:
a = gift
b = amount earned weekly while working on the golf course
Subtract equation 2 from equation 1: 2b = 120
Divide both sides of the equation by 4: b = $60
Substitute for b in equation 1
a + 2(60) = 750
a + 120 = 750
a = 750 - 120
a = 630
The y-intercept is $630.
The equation in slope intercept form is: $630 + $60w
Where w is the number of weeks that Betty works.
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Help me I’m so confused
The number of apples Chee bought is 2, and the number of peaches she bought is 8
Solving System of Linear Equations GraphicallyFrom the question, we are to determine the number of apples, x, and the number of peaches, y, that Chee bought
From the given information,
She bought $6 worth of apples and peaches
and
Each apple costs $1 and each peach costs $0.50
Then, we can write that
$1 × x + $0.50 × y = $6
x + 0.50y = 6
Also,
She bought 4 times as many peaches as apples
That is,
y = 4x
Now, we will solve the system of equations graphically
x + 0.50y = 6
y = 4x
From the graph, the solution to the system of equations is x = 2, y = 8.
Hence, the number of apples Chee bought is 2, and the number of peaches she bought is 8
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Bob is making a model of an ant for a play. Find the scale factor of the model if the ant is 1/2 inch long and the model is 1 foot long.
The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.
What exactly is a scale factor?The Scale Factor is employed to scale shapes in different dimensions. Geometry teaches us about numerous geometrical shapes in two and three dimensions. The scale factor is a metric considering similar figures that appear the same but have distinct scales or measures.
How do you calculate the scale factor?The basic formula for computing this same scale factor is, Scale factor = Dimension of the new shape x Dimension of the original shape If indeed the original figure is scaled up, then the formula is expressed as Scale factor = Larger figure dimensions /Smaller figure dimensions.
According to the given data:The size of the ant = 1/2 inch.
the model size is = 1 foot.
= 1 foot = 12 inch
The scale factor of the model = Larger figure dimensions ÷ Smaller figure dimensions.
= 12/.5
= 24 inch or 2 foot
The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.
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The area of rectangle A is bigger than the area of rectangle B
Work out the lowest possible integer value of x.
A=
2x-3
5 cm
B
3 cm
X+2
The lowest possible integer value of x is 3 such that (x ≥ 3).
What is referred as the inequalities?An inequality depicts the relationship between two non-equal values in such an algebraic expression. Inequality symbols can indicate that one of the two variables is greater than, greater or equal to, equal to some other value.For the given question;
The area of rectangle A is bigger than the area of rectangle B.
The sides of the rectangle A are 2x-3 and 5 cm.
Area = length×breadth
Area A = (2x - 3)(5)
Area A = 10x - 15
The sides of the rectangle B are x = 2 and 3 cm.
Area = length×breadth
Area B = (x + 2)3
Area B = 3x + 6
As area B > area B
Then,
10x - 15 ≥ 3x + 6
Solving the inequality;
10x - 3x ≥ 6 + 15
7x ≥ 21
x ≥ 3
Thus, the minimum value of the x is 3 to make the area A bigger than Area B.
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13. Compount Interest An initial deposit of $8500 is compounded continuously at an annual
percentage rate of 3.5%.
xmp+81
Find the number of years required for the investment to double. Round to the nearest whole
number. What is the amount after 10 years?
Use the formula: A = Pert
Answer:
It will take approximately 20 years for the investment to double. The amount after 10 years will be $17,033.
Step-by-step explanation:
Give me Brainliest if that helped! :)
Use square roots to solve the equation x2 = –100 over the complex numbers. Select any solutions that apply.
The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.
What is a complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,
where a, and b are real numbers and i is an imaginary number.
We have been given the equation of complex numbers x² = -100
Using the square roots property to solve the above equation
⇒ x² = -100
⇒ x = √-100
⇒ x = √(-1×10×10)
∵ i² = - 1 or i = √-1
Here i is an imaginary number.
⇒ x = 10(√-1)
⇒ x = 10i
Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.
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Consider the functions f(x) = 4x² - x and g(x) = 2x + 5.
f • g(-3) =
g • f(-3) =
Answer:
[tex]{ \tt{f•g(x) = 4(2x + 5) {}^{2} }} \\ = { \tt{4(4 {x}^{2} + 20x + 25)}} \\ = { \tt{ {8x}^{2} + 80x + 100}} \\ \\ { \tt{f•g( - 3) = 8 {( - 3)}^{2} + 80( - 3) + 100 }} \\ { \tt{f•g( - 3) = 72 - 240 + 100}} \\ { \tt{f•g( - 3) = - 68}} \\ \\ \\ { \tt{g•f(x) = 2( {4x}^{2}) + 5 }} \\ { \tt{ = {8x}^{2} + 5 }} \\ { \tt{g•f( - 3) = 8 {( - 3)}^{2} + 5}} \\ { \tt{g•f( - 3) = 77}}[/tex]
Below are graphs of functions over the interval [-4, 4]. Find the following for each function:
The domain
Zeros of the function
Intervals where the function is positive and intervals where it is negative
The positive interval is (0,2) and the negative range is calculated as (-4,0) and (2,4).
A graph is used to show the relationship between variables on a coordinate plane.
The domain of the function is [-4,4].
The zeros are: -2,0 and 2.
The positive interval is between (0,2).
The range of negative values is (-4,0) to (2,4). This is the set of x values in the graph. The graph demonstrates that the x value is between -4 and 4.
Thus, the domain is [-4,4]. The zeros of the function: Where it crosses the x- axis. The graph touches the x-axis when it is at -2,0 and 2. As a result, the function has the following zeros:-2,0 and 2.
Positive interval:
On the graph, positive values range from x = 0 to x = 2.
Consequently, the positive interval is (0,2).
Negative duration:
This is the x values when the function gives a negative result.
The graph shows negative values from x = -4 to x = 0, then from x = 2 to x = 4.
The negative range is therefore (-4,0) and (2,4).
Hence, the positive interval is (0,2) and the negative range is (-4,0) and (2,4).
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Write each logarithmic expression as a single logarithm. log₃ y + 4 log₃ t
The given lograthimic expression log₃ y + 4 log₃ t can be written as log₃(yt^4).
According to the given question.
We have an logarithmic expression
log₃ y + 4 log₃ t
As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.
Also according to the product and power rule we know that
log(mn) = logm + logn
Thereofore, the given lograthimic expression log₃ y + 4 log₃ t can be written as
log₃ y + 4 log₃ t
= log₃ y + log₃ t ^4
= log₃(yt^4)
Hence, the given lograthimic expression log₃ y + 4 log₃ t can be written as log₃(yt^4).
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La edad de maria es igul al quintuple de la edad de daniel
Answer:
m = 5d
Step-by-step explanation:
m = 5d
The residents of a city voted on whether to raise property taxes. The ratio of yes votes 4 to 5 no votes was to . If there were 5364 total votes, how many no votes were there?
-3y + 2x = -7
8x - 3y = -1
Answer: If you're solving for the substitution method then your answer would be (1,3)
Step-by-step explanation:
Answer:
x = -4/5
y = 9/5
Step-by-step explanation:
-3y + 2x = -7
8x - 3y = -1
make one of the equations y=....
-3y + 2x = -7
-3y = -7 - 2x
y = (-7 - 2x)/3
now put (-7 - 2x)/3 where y is in the other equation
8x - 3y = -1
8x - 3((-7 - 2x)/3) = -1
8x - 1*(-7 - 2x) = -1
8x + 7 + 2x = -1
solve for x
8x + 7 + 2x = -1
8x+2x = -8
10x = -8
x = -8/10
x = -4/5
now put -8/10 in one of the equations to get what y is
-3y + 2x = -7
-3y + 2(-8/10) = -7
-3y - 16/10 = -7
-3y = -7 + 16/10
-3y = -70/10 + 16/10
-3y = -54/10
y = -54/10 * -1/3
y = 18/10
y = 9/5
You deposit $400 into a savings account that earns interest annually. the function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. what is the range of the function in the context of the problem? â„ [0, 400] [0, [infinity]) [400, [infinity])
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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a 12 pound can of lemonade cost 1.32 how much would a 16 ounce can of lemonade cost? please tell me the answer I need to get this right thx xo
Answer:
1.76.
Step-by-step explanation:
1.32 ÷ 12 = 0.11
16 x 0.11 = 1.76.
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Write the equation for each line. Use slope-intercept form. m = - 3/8 and the y -intercept is (0,12) .
The equation of the line in slope-intercept form with a slope of -3/8 and y-intercept of (0 , 12) is y = (-3/8)x + 12.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given that the slope of the line is -3/8 and the y-intercept is (0 , 12), write the equation of the line by simply plugging in its values.
y = mx + b
y = (-3/8)x + 12
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find the center and foci of the ellipse:
4x^2+9y^2+8x-36y+4=0
The center of the given ellipse is given as (-1, 2)
Center of the Ellipse
To find the center of the ellipse, we need to rearrange the equation into the standard equation of ellipse.
[tex]4x^2 + 9y^2 + 8x - 36y + 4 = 0\\\frac{(x+1)^2}{2} + \frac{(y-2)}{4} = 1[/tex]
The center of the ellipse is given as
[tex]center = (-1, 2)[/tex]
FociThe foci of the ellipse are the reference points in an ellipse and it helps to derive the equation of the ellipse. There are two foci for the ellipse i.e F1 and F2
[tex]F_1= (-1 + \sqrt{5}, 2)\\ F_2 = (-1, -\sqrt{5}, 2)[/tex]
The center of the given ellipse is (-1,2) while the foci are stated above.
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Determine the truth value of the following statement for the set of conditions. Explain your reasoning.
If you are over 18 years old, then you vote in all elections.
You are 21 years old and do not vote.
The given statement is not correct because anyone above 18 years can vote.
It is given that if you are over 18 years old, then you vote in all elections.
We have to determine the truth value , if you are 21 years old and do not vote.
What is the truth value ?
Truth value is the attribute which states that whether the statement is true or false.
As per the question ;
If you are over 18 years old , then you vote in all elections, and if you are 21 years old and do not vote.
The criteria to vote in the elections is to be over 18 years.
Here ;
21 years age is greater than 18 years criteria , that's why it is not possible that you can't vote if you are 21 years old.
The statement is not correct.
Thus , the given statement is not correct because anyone above 18 years can vote.
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A string is vibrating at 220 MHz and the wavelength of the waves on the string is 2.20m. Find the speed of these waves as they travel up and down the string
The wavelength of the waves on a string that is vibrating at 220 MHz is 2.20 m. These waves move at a 4840 rpm rate as they move up and down the string.
What is a wave length?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). According to the available data, the wavelength is more frequently expressed in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (VL), ultraviolet (UV), and gamma radiation ().
V=∧F
V=220×22
V=4840m/s
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