Answers
When given a quadratic equation and we seek the vertex coordinates, we have to arrange such equation into its vertex form. The vertex form goes thus:
\(\begin{gathered} f(x)=a\mleft(x-h\mright)^2+k \\ \text{Vertex is at (h, k)} \end{gathered}\)If we put our equation in this form, we get:
\(\begin{gathered} f(x)=-2(x+3)^2-1 \\ ReArrangi\text{ng, we get:} \\ f(x)=-2(x-(-3))^2+(-1) \end{gathered}\)Therefore, our vertex, based on the general form is: (-3 , -1)
The domain of a function is the set into which all of the input of the function is constrained to fall, i.e, all the values of x that validates the function.
The domain is all real numbers
The range of a function is the set of outputs the function achieves when it is applied to its whole set of inputs. The set of the values of f(x) when the domain is applied.
The range is therefore:
\(y\le-1\)Third Option
Related Questions
Two buildings are 18 m part. The shorter building is 12 m high while the taller one is 19 m high. Find the distance, x m between the top of the buildings.
Answers
The distance between the tops of the buildings is 28.5 meters.
To find the distance between the top of the buildings, we can use the concept of similar triangles.
Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).
We can set up a proportion based on the similar triangles formed by the buildings:
a/c = b/x
Substituting the known values:
12/18 = 19/x
To find "x," we can cross-multiply and solve for "x":
12x = 18 * 19
12x = 342
x = 342/12
x = 28.5 m
Therefore, the distance between the tops of the buildings is 28.5 meters.
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Find the 45th term of the arithmetic sequence an = 2 + 4(n − 1).
Group of answer choices
182
178
145
264
Answers
Step-by-Step Explanation:
n = 45
Therefore, 2 + 4(n - 1)
Putting n = 45, we have
2 + 4(45 - 1)
= 2 + 4 × 44
= 2 + 176
= 178
Answer:
B) 178
Hope it helps.
If you have any query, feel free to ask.
An article which costs 17.50 is sold at a loss of 20%.what is the selling price.
Answers
Consider a medium with parameters € = 1.2 (10^-10 )F/m , n= 3(10^-3) H/m and sigma=0. Magnetic field intensity in the medium is given as R = 2cos (10^10t- 600x)äz Am.
Use Maxwell's equations to obtain the followings:
1) Magnetic flux density
These questions is circuit theory
Answers
Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:
\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),
where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).
In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:
\(\displaystyle \nabla \times \mathbf{H} =0\).
Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):
\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).
Using the curl identity and applying the chain rule, we can expand the expression:
\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:
\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Differentiating the cosine function with respect to \(\displaystyle x\):
\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):
\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).
Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:
\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).
Simplifying the equation:
\(\displaystyle \sin( 10^{10} t-600x) =0\).
The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):
\(\displaystyle 10^{10} t-600x =n\pi\),
where \(\displaystyle n\) is an integer. Rearranging the equation:
\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).
The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.
Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.
Thus, the correct expression for the magnetic flux density in the given medium is:
\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).
The rear windshield wiper of a car rotated 120 degrees,as shown. Find the area cleared by the wiper. 25inch,120 degrees, 14inch
Answers
The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.
The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.
The wiper's arm is represented by a line segment and has a length of 14 inches.
The wiper's blade is perpendicular to the arm and has a length of 25 inches.
Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.
As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.
The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.
In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.
Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.
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In a survey of 2,800 people who owned a certain type of car, 560 said they would buy that type of car again. what percent of the people surveyed were satisfied with the car?
Answers
20%
2800/560
= 0.2%
=20%
53/100-27/100 = ?????
Answers
Answer:
26/100
Step-by-step explanation:
53/100-27/100 = ?
53-27 = 26
26/100
Given: B is the midpoint of Line AD. Angle ABC and Angle DBC are right angles. Write a two column proof
Answers
Explanation:
We know that B is the midpoint of line AD, So, it divides AD into two equal parts, and then segment AB will be congruent to BD. Additionally, a segment is congruent to itself, so BC is congruent to BC.
Finally, we also know that Angle ABC and Angle DBC are right angles and in consequence, they are congruent.
Therefore, by SAS (Side - Angle - Side), the triangles ABC and DBC are congruent.
Answer:
Then, the two-column proof is:
Statement 1. B is the midpoint of AB
Reason 1. Given
Statement 2. AB ≅ BD
Reason 2. Definition of midpoint
Statement 3. ∠ABC and ∠DBC are right angles
Reason 3. Given
Statement 4. ∠ABC ≅ ∠DBC
Reason 4. Definition of congruence (they have the same measure)
Statement 5. BC ≅ BC
Reason 5. Reflexive property of congruence
Statement 6. ΔABC ≅ ΔDBC
Reason 6. SAS ( Side - Angle - Side)
Determine whether each function is linear or nonlinear. Function Linear Nonlinear {(–1, 2), (0, 3), (1, 4), (2, 5)} Linear – {(–1, 2), (0, 3), (1, 4), (2, 5)} Nonlinear – {(–1, 2), (0, 3), (1, 4), (2, 5)} {(–3, 9), (–2, 4), (3, 9), (4, 16)} Linear – {(–3, 9), (–2, 4), (3, 9), (4, 16)} Nonlinear – {(–3, 9), (–2, 4), (3, 9), (4, 16)} y = –14x + 9 Linear – y = –14 x + 9 Nonlinear – y = –14 x + 9 y = x Linear – y = x Nonlinear – y = x
Answers
A. {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.
B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.
C. y = –14x + 9 → Linear function
D. y = x → Linear function
What is a linear function?A linear function has a straight line as its graph. A linear function has the form shown below.
a + bx = y = f (x).
A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.
When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.
From the given choices;
A. {(–1, 2), (0, 3), (1, 4), (2, 5)}
Here, the absolute value of 1 is connected to more than one point, so non-linear function.
B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}
Here, the absolute value of 3 is connected to more than one point, so non-linear function.
C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.
D. y = x is a linear function.
Therefore, B and D are linear functions.
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what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)
Answers
⊰_________________________________________________________⊱
Answer:
The equation is-: y=3xStep-by-step explanation:
\(\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}\)
\(\pmb{\tt{done \ !!}}\)
⊱_________________________________________________________⊰
What is the total surface area of the prism? PLEASE HELP
94 sq. cm
82 sq. cm
Answers
Answer:
94 ft^2 (sq)
Step-by-step explanation:
Surface Area = 2×(4×3 + 4×5 + 3×5) = 94 feet^2(sq)
Please help with this problem thank you.
-8 + n = 62 What is n?
Answers
Answer:
n = 70
Step-by-step explanation:
-8 + n = 62
n = 70
36013063019zº10Find the values of x, y, and z. The diagram is not to scale.
Answers
The sum angles in a triangle is 180 degrees
In the first triangle where we have 36 degrees and 63 degrees
we have three angles
36 degrees , 63 degrees and x degrees
x + 36 + 63 = 180
x + 99 = 180
isolate x
x = 180 - 99
x = 81 degrees
to calculate z
interior altenate angles are equal
36 degrees is alternate to angle z
Therefore 36 degrees = z
z = 36 degrees
to get y
y + 36 + 13 = 180
y + 49 = 180
y = 180 - 49
y = 131 degrees
graph the equation.
H
-2
-1
0
2
4y + 16x = 28
Y
Ordered Pair
10
-5
10+
5
-S
-10-
Clear All
y
5
५
IC
Answers
The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation as 4y+16x=28 or y+4x=7
putting (1,3) in the equation we get 3+4×1=7
Similarly we can find the ordered pair as (2, -1) , (3,-5) , (4,-9)
Hence, The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
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What is the length of NP?
Answers
Answer:
\(c=\sqrt{174}\)
Step-by-step explanation:
First, find the length of MP. This can be done with the Pythagorean Theorem.
We can use x as angle MP.
a² + b² = c²
10²+ 7² = x²
100 + 49 = x²
x² = 149
Take the square root to get
x = √(149)
Now do the Pythagorean Theorem for Triangle MNP. We can again use x for angle NP.
a² + b² = c²
5² + √(149)² = c²
25 + 149 = c²
c² = 174
c = √(174)
quickly help 2//////////////////////////////////
Answers
Answer:
A. , C. ,
Step-by-step explanation:
Because perimeter is the area around. there are 4 sides, and two of them are same, and the other two are same. add the sides to get 6.
Answer:
Step-by-step explanation:
multiply each dimension by 2 (P=2W+2L). Only A and C add up to 6 (2+4)
Please tell me the question 11
Answers
Answer:
Step-by-step explanation:
Just find where both lines intersect. In this case, the two lines intersect at the point (2,4)
Contestants in a dance-a-thon rest for the same amount of time every hour. A couple rests for 28 minutes in 4 hours. How long did they rest in 5 hours?
Answers
Answer:
4 hours divided into 28 minutes is 7 minutes per hour, om average.
So they rest for 35 minutes in within a 5 hour span
Step-by-step explanation:
If my answer satisfies, please leave a 5 star, and mark me as brainleist. Thank you!
Charles McCoy is a manager at a coffee shop, and he has to decide how many workers to hire. One worker can make 20 drinks that sell for $3 on average in one hour. A second worker can make another 18 drinks in one hour. The marginal benefit of each additional worker decreases by two drinks, with each additional hire. Given that workers are paid $15 per hour and have eight-hour shifts, how many employees should Charles hire for each hour?
Answers
Charles should hire 20 workers for each hour.
To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.
The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.
Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.
The marginal cost is $15/worker * 8 hours = $120.
The second worker has a marginal benefit of 18 drinks * $3/drink = $54.
The marginal cost is still $120.
For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.
Charles should hire workers as long as the marginal benefit is greater than the marginal cost.
Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.
Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.
To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:
$6 * n = $120
$n = 20
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Mort and George are 18 miles apart on a path when they start moving toward each other. Mort runs at a constant speed of 7 miles per hour, and George walks at a constant speed of 5 miles per hour. How long does it take until Mort and George meet?
Answers
Answer:
1 1/2 hours
Step-by-step explanation:
In one hour, the distance between them is reduced by 7+5 = 12 miles. At that rate, the 18 mile distance between them will be reduced to zero in ...
time = distance/speed
time = (18 mi)/(12 mi/h) = 3/2 h
It will take 1 1/2 hours until Mort and George meet.
Find the local maximum and local minimum
Answers
Answer:
Maximum= (-2,15)
Minimum= (2,-15)
Solve the equation by completing the square. Round your solutions to the nearest hundredth if necessary. x^2+2x=5
Answers
Answer: The correct answers are -3.45 and 1.45
Step-by-step explanation: The only problem you had was you rounded it to the tenths place instead of the hundredths place.
Sorry for getting back to you late.
What is 3.173 rounded to the nearest tenth
Answers
THE answer is 3.173≅3.2(nearest tenth)
The library is 10 kilometers south of Aaron's home. The school is 10 kilometers east of Aaron's home. How many
kilometers, to the nearest tenth of a kilometer, is the library from the school?
A 10.2 kilometers
C 14.1 kilometers
Answers
Answer:
20kilometers
Step-by-step explanation:
10kilometers home to library +10killometer home to school
d/-5 < -4 solve plz show work
Answers
Answer:
D<-20
Step-by-step explanation:
Multiply to remove the fraction, then set equal to 0 and solve.
HELP ASAP
50 POINTS.......
+BRAINLIEST
Answers
Answer:
The answer is $12 and Jackie washed 15 cars.
2. Jackie washed 15 cars
find the indicated side of the right triangle. 45 degrees, 45 degrees, 6, y, x, x = ?
Answers
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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nswer the following question the best you can.
8. Jon opened a package of candies and counted them. He found 60 candies in the 1.69 oz
package. Estimate the number of candies in a 1 lb (16 oz) bag. Explain your thinking in
arriving at this estimate.
Answers
Answer:
568 candies
Step-by-step explanation:
16 oz/ 1.69 oz.= 9.47 x 60 candies= 568.2= 568 candies.
Estimate the square root to the nearest (a) integer and (b) tenth.
46−−√
Answers
Using rounding concepts, it is found that the estimates of the square root of 46 are given as follows:
a) Rounded to the nearest integer, the square root of 46 is of 7.
b) Rounded to the nearest tenth, the square root of 46 is of 6.8.
How we round a number?To round a number to the nearest integer, we have to look at the tenths digit.To round a number to the nearest tenth, we have to look at the hundredths digit.If the digit we look is of 5 or greater, we round one to the rounded digit.Using a calculator, we have that the square root of 46 is of 6.78.
7 > 5, hence rounded to the nearest integer, the square root of 46 is of 7.8 > 5, hence rounded to the nearest tenth, the square root of 46 is of 6.8.More can be learned about rounding concepts at https://brainly.com/question/17248958
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How do I do this question: Six numbers have been left to the final door. Those numbers are: 6,2,3,3,2,2. Fill in the following blanks, and use those 6 digits to make the largest number possible. Enter that number (without the comma) to escape!
Answers
Answer:
633222
Step-by-step explanation:
just put them in order from biggest - smallest