Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
What is the domain and range of a function?A domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
The curve points are
P₁ ( -1,5 , 0 ) Q ( 0. -2 ) and P₂ ( 1,5 , 0 )
We can see that P₁ and P₂ are symmetric around the y-axis, and point Q looks like a vertex so we can conclude the curve as
ax² + bx + c = y
The curve is a parabola
when x = 0
y = -2
then c = - 2
The equations we get,
a (-1.5)² + b (-1.5) + c = 0
2.25a - 1.5b - 2 = 0
a (1.5)² + b ( 1.5) + c = 0
2.25a + 1.5b -2 = 0
Adding these two equations
4.5a - 4 = 0
a = 4/4.5
The vertex is Q ( 0 , -2 )
x = - b/2a
0 = - b/ 9
b = 0
Therefore the equation of the function :
ax² + c = 0
(4/4.5) x² - 2 = 0
Therefore, Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
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Answer:
In a shorter explanation of what the guy above me is saying
The domain is all real numbers or A
The range is "all real numbers greater than or equal to –2" or B
Step-by-step explanation:
Which of the following is the correct factorization of the polynomial below?
p³ -343q³
A. (p-49q) (p² +7pq+49q²)
B. (p-7q) (p² +7pq+49q²)
C. (p² +7q) (p³ +49pq+7q²)
D. The polynomial is irreducible.
Answer:
B
Step-by-step explanation:
a difference of cubes factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
given
p³ - 343q³
= p³ - (7q)³ ← a difference of cubes , then
= (p - 7q)(p² + 7pq + 49q²) ← in factored form
is there anyone who understands this?
Answer:
The question was most likely asking for exponential form.(The list shows questions 16 through 20, not 1 through 5.)
b 1/6X Z/49 3/2m p/nj 2 + x/2can someone help me with this worksheet please!!!!
(1) The missing term in the sequence, a₁₂ = 0.8.
(2) The missing term in the sequence, a₈ = 102.5.
(3) The missing term in the sequence, a₈ = 111.
(4) The missing term in the sequence, a₁₂ = -19.
(5) The missing term in the sequence, a₁₂ = 94.
(6) The missing term in the sequence, a₆ = 40.
(7) The missing term in the sequence, a₃₆ = -52.
(8) The missing term in the sequence, a₂₁ = -58.
Missing term of the sequenceThe missing term in the sequence is determined as follows;
Tₙ = a + (n - 1)d
1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?T₄ = a + 3d
18.4 = a + 3d ---(1)
T₅ = a + 4d
16.2 = a + 4d ---(2)
subtract (1) from (2)
-2.2 = d
18.4 = a + 3(-2.2)
a = 25
a₁₂ = a + 11d
a₁₂ = 25 + 11(-2.2)
a₁₂ = 0.8
2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?a₂ = a + d
57.5 = a + d -- (1)
a₅ = a + 4d
80 = a + 4d --- (2)
solve (1) and (2)
d = 7.5
a = 50
a₈ = a + 7d
a₈ = 50 + 7(7.5)
a₈ = 102.5
3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?a₁₀ = a + 9d
141 = a + 9d --- (1)
a₁₃ = a + 12d
186 = a + 12d --- (2)
Subtract (1) from (2)
d = 15
a = 6
a₈ = a + 7d
a₈ = 6 + 7(15)
a₈ = 111
4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?a₂₂ = a + 21d
-49 = a + 21d ---- (1)
a₂₅ = a + 24d
-58 = a + 24d --- (2)
subtract (1) from (2)
d = -3
a = 14
a₁₂ = a + 11d
a₁₂ = 14 + 11(-3)
a₁₂ = -19
5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?a₄ = a + 3d
-2 = a + 3d --- (1)
a₈ = a + 7d
46 = a + 7d ---- (2)
Subtract (1) from (2)
d = 12
a = -38
a₁₂ = a + 11d
a₁₂ = -38 + 11(12)
a₁₂ = 94
6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?a₉ = a + 8d
64 = a + 8d --- (1)
a₁₂ = a + 11d
88 = a + 11d --- (2)
Subtract (1) from (2)
d = 8
a = 0
a₆ = a + 5d
a₆ = 0 + 5(8)
a₆ = 40
7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?a₂₀ = a + 19d
-4 = a + 19d ---- (1)
a₂₃ = a + 22d
-13 = a + 22d --- (2)
Subtract (1) from (2)
d = -3
a = 53
a₃₆ = a + 35d
a₃₆ = 53 + 35(-3)
a₃₆ = -52
8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?a₂₈ = a + 27d
5 = a + 27d ---- (1)
a₃₃ = a + 32d
50 = a + 32d --- (2)
Subtract (1) from (2)
d = 9
a = -238
a₂₁ = a + 20d
a₂₁ = -238 + 20(9)
a₂₁ = -58
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 72.
There was a missing data point in the Homework Grade. So I put a 74 to get 8 data points on each variable.
Put these data points in Excel. In the Data Analysis tab, scroll down and click on Regression. Input Y range for Test Grade and Input X range for Homework Grade.
y = -0.4x + 98.3
What is the correlation?
correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.
When you increase your homework score by 1 point, you lose 0.4 points on your test.
-0.4x + 98.3 = 74
→ -0.4x = -24.3
→ x = 60.75 ≈ 61
A student will earn a 61 on his/her homework if he/she earns a 74 on an exam.
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Convert 0.00001 to a power of 10
Answer:
10^(-5)
Step-by-step explanation:
1 x 10^(-5)
I hope it helps u dear! ^_^
The following diagram shows a 4-step process that begins with Operation 1 and ends with Operation 4.
Based on the operations and their times, the capacity of this process is 10 per hour and the action that would yield the greatest increase would be 2. increase operation 2 by 14%.
What is the capacity of the process?The capacity of the process is the least operation time in the process which is 10/ hr.
How can we get the greatest increase in process capacity?Check all the alternatives given. The alternative with the lowest capacity is best.
Increase operation 1 by 12%:
= 11 x (1 + 12%)
= 12.32 per hour
Increase operation 2 by 14%:
= 10 x (1 + 14%)
= 11.4 per hour
Increase operation 3 by 10%:
= 12 x (1 + 10%)
= 13.2 per hour
The best alternative is therefore to increase operation 2 by 14%.
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#18 please I’m not good at math at all
Answer:
The answer is in the picture.
Step-by-step explanation:
By hand, you can factor it. I did it on a website called Cymath.
Answer:
3x(y - 3)(y + 1)
Step-by-step explanation:
Factor 3x out of 3xy^2
Factor 3x out of -6xy
Factor 3x out of -9x
Factor 3x out of 3x(y^2)+3x(-2y)
Factor 3x out of 3x(y^2-2y) + 3x(-3)
HELP PLS! A kiddie pool is 9 feet long and 6 feet wide. Surrounding wach side of the kiddie pool is a cement walkway of uniform width. The combined area of the pool and walk way is 108 ft^2. Find the width of the walkway. Ill give brainliest too
I will answer this will within a few minutes
Elaina Kicks A Soccer Ball With An Initial Velocity Of
By using the motion equations, we conclude that she will make the goal.
Will she make the goal?
First, we know that the goal is 20ft away, and the position in x is given by:
[tex]x = 28*cos(58)*t[/tex]
Let's find the time in which the ball will travel these 20 ft.
[tex]20 = 28*cos(58)*t[/tex]
[tex](20)/(28*cos(58)) = t = 1.35[/tex]
So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.
The height equation is:
[tex]y = -16*t^2 +28*sin(58)*t[/tex]
Evaluating in t = 1.35 we get:
[tex]y = -16*(1.35)^2 +28*sin(58)*1.35\\\\y = 2.9[/tex]
And the goal is 5ft tall, so we can conclude that she will make the goal.
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After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?
well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]
Answer:
Answer is 7% sales Tax
Step-by-step explanation:
I first like to take one percent of the original value, in this case 1% of 600 is 6 dollars. I then multiply 6 by the number needed to get to 642, which is 107- you will always then subtract 100 from this number and you get 7%. This should work for other problems as well. This is probably not the best explanation btw
Let f(x)=20/5+6e^−0.1x What is (5)? Round your answer to 4 decimal places.
We can conclude that the function evaluated in x = 5 is equal to 2.3150
How to evaluate the function?Here we have the function:
[tex]f(x) = \frac{20}{5 + 6e^{-0.1x}}[/tex]
And we want to evaluate in x = 5, this just means to replace the x by a 5 in the given function:
We can evaluate this with a calculator (as doing it by hand is kinda hard), we will get:
[tex]f(5) = \frac{20}{5 + 6e^{-0.1*5}} = 2.3150[/tex]
So we can conclude that the function evaluated in x = 5 is equal to 2.3150.
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Write the prime factorization of 10
Answer:
2|10
5|5
1
Prime factors of 10 are 2*5
how many prime number are between 2 and 22
Answer:
8
Step-by-step explanation:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 easily get rid of all the even numbers except 2 and then look at the numbers to see if they can be divisible by anything but 1 and its self. then you will get the answers 2, 3, 5, 7, 11, 13, 17, and 19
what is two significant digit for 59.3506494?
Answer:
59
Step-by-step explanation:
Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.
4 The angle of elevation of point P from point Q is 40°. PQ = 45 km. How high is point P above the level of point Q?
Answer: [tex]45\sin 40^{\circ} \approx 28.925[/tex] km
Step-by-step explanation:
[tex]\sin 40^{\circ}=\frac{x}{45} \\ \\ x=45 \sin 40^{\circ} \approx 28.925[/tex]
The height of point P above the level of point Q is given by trigonometric relations h = 34.7 km
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let's call the height of point P above the level of point Q as h.
We know that the angle of elevation of point P from point Q is 40°, which means that the angle between the horizontal line passing through Q and the line segment connecting Q and P is 40°.
We also know that PQ = 45 km, which represents the distance between Q and P.
Using trigonometry, we can set up the following equation:
tan(40°) = h / 45
Solving for h, we get:
h = 45 x tan(40°) ≈ 34.7 km
Therefore, point P is approximately 34.7 km above the level of point Q
Hence , the height is h = 34.7 km
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Cooper just started a running plan where he runs 8 miles the first week and then
increases the number of miles he runs by 5% each week. If he keeps up this plan for
21 weeks, how many total miles would Cooper have run, to the nearest whole
number?
Cooper ran 286 miles in 21 weeks.
solve this quadratic inequalitie with detailed full explanation
X2≤16
x square less than or equal to 16
[tex]x^2\leq16\\x\leq 4 \wedge x\geq -4\\x\in\langle-4,4\rangle[/tex]
different approach:
[tex]x^2\leq16\\x^2-16\leq0\\(x-4)(x+4)\leq0[/tex]
see attachment
[tex]x\in\langle-4,4\rangle[/tex]
[tex]~~~~~~x^2 \leq 16\\\\\implies -\sqrt{16} \leq x\leq \sqrt{16}\\\\\implies -4\leq x \leq 4\\\\\text{Interval notation:}~ [-4,4][/tex]
follow the steps to construct a diagram:
1:create points A, B, and C in order on a horizontal line with a distance of four units between successive points.
2:draw Circle with center that passes through b, and two tangents to the circle passing through C.
3:locate the points of intersection of the tangents with the circle, and labeled them D and E.
4: draw the radii AD and AE to create central angel EAD.
Take a screenshot of your construction, and paste it below.
Answer:
a=3=8
Step-by-step explanation:
there is none
The construction forms a diagram consisting of a circle, two tangents, and a central angle EAD as shown in the attached figure.
Construction is a topic that requires drawing a required shape, line, and figure with constructing tools. The appropriate steps should be taken so as to complete the required figure.
In the given question, the circumference of the required circle passes through points A and C. And the radius of the circle with center B is 4 units so its diameter is 8 units. Then joining the points D and E to A, creates a central angle EAD.
Following the appropriate steps, the required diagram for the construction is as given in the attachment to this question.
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In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
The complete figure is attached with the answer below.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.
Cos(x)= Base / Hypotenuse
Cos(x) = ( 4.3 / 6.7 )
(x) = Cos⁻¹ ( 4.3 / 6.7)
Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
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Answer:
The answer is A
Step-by-step explanation:
Just took the test
Rewrite using the Distributive Property and GCF 13+36
Answer:
Step-by-step explanation:
13 and 36 have no common factor except 1.
Perhaps you meant that the 13 should be 12. In that case
GCF
12 = 2*2*336 = 2*2 *3 * 3The greatest common factor is 2 * 2 * 3
If there is a number that is not bolded, it is what is left behind inside the backets the distributive property creates.
Answer: 12(1 + 3)
Note: the 1 is part of the answer inside the brackets when one of the numbers inside the brackets and the GCF are the same
Solve the following inequality algebraically:
-2 less-than x/3 + 1 less than 5
a.
Negative 9 greater-than x greater-than 12
b.
Negative 9 less-than x less-than 12
c.
Negative 2 less-than x less-than 5
d.
Negative 2 greater-than x greater-than 5
Answer:
d
Step-by-step explanation:
What is the measure of each interior angle of a regular octagon?
45º
60º
120º
135º
Answer:
135 degrees
Step-by-step explanation:
Just took the test...
Answer:
135 degrees
Step-by-step explanation:
180 (n - 2)
180 (8 - 2)
180(6)
1080 divided by 8
135 is your answer.
The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003
9=28
when 834 nine=365 and 7
Answer:
The answer is C
Step-by-step explanation:
good job on quiz i got a 15/15 but keep up 3´5
Answer:
i got a 0/15 i didnt do it
Step-by-step explanation:
0000.7 C
Which number has the greatest value?
O 0.095
1.24
O 1.215
245
The number that has the greatest value is 245
How to determine the greatest number?The numbers are given as:
0.095, 1.24, 1.215 and 245
Rearrange the numbers in ascending order
0.095, 1.215, 1.24 and 245
The last number on the list is the greatest
Hence, the number that has the greatest value is 245
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answer asap giving max points and brainliest A projectile is launched at an angle of 30° and travels a distance of 400 meters. Gravitational acceleration equals 9.8 m/sec2 calculate the initial velocity.
answer choices:
67
87
57
Answer:
67 m/s
Step-by-step explanation:
Formula for range :
Range = u²sin2θ / gu = initial velocityθ = angle of launchg = gravitational accelerationSolving with the given values :
400 = u² x sin60° / 9.8u² x √3/2 = 3920u² = 7840/√3u² = 4526.4u = 67 m/s (approximately)Answer:
[tex]\sf u=67\:ms^{-1}[/tex]
Step-by-step explanation:
Assuming the distance traveled is the horizontal distance.
Horizontal Range Formula
[tex]\sf R=\dfrac{u^2 \sin 2\theta}{g}[/tex]
where:
R = horizontal rangeu = initial velocity[tex]\theta[/tex] = angle of initial velocityg = acceleration due to gravityGiven:
R = 400 m[tex]\theta[/tex] = 30°g = 9.8 m/s²Substituting the given values into the formula and solving for u:
[tex]\implies \sf 400=\dfrac{u^2 \sin 60^{\circ}}{9.8}[/tex]
[tex]\implies \sf 3920=u^2 \sin 60^{\circ}[/tex]
[tex]\implies \sf 3920=\left(\dfrac{\sqrt{3}}{2}\right)u^2[/tex]
[tex]\implies \sf u^2=\dfrac{7840}{\sqrt{3}}[/tex]
[tex]\implies \sf u=\sqrt{\left(\dfrac{7840}{\sqrt{3}} \right) }[/tex]
[tex]\implies \sf u=67.2787196...[/tex]
[tex]\implies \sf u=67\:ms^{-1}\:(nearest\:whole\:number)[/tex]
Question 1 of 10
Evaluate the following expression. Round your answer to two decimal places.
log79
A. 0.89
Step-by-step explanation:
log(79) = 1.897627091... ≈ 1.90
what's the answer to this
Step-by-step explanation:
the angle CDB is the supplementary angle to 9x+10 (angle ADC).
that means they stand together for 180°. as all angles around a single point on one side of a line are together always 180°.
and then, the sum of all angles in a triangle is always 180°.
so,
CDB + (4x + 10) + 50 = 180
CDB = 180 - (9x + 10) = 180 - 9x - 19 = 170 - 9x
therefore,
(170 - 9x) + (4x + 10) + 50 = 180
170 - 9x + 4x + 10 + 50 = 180
-5x = -50
5x = 50
x = 10
angle CDB = 170 - 9x = 170 - 90 = 80°
Una camioneta transportaba 3/4 de tonelada de arena para entregar a diferentes clientes. Si al primer cliente le dejo 1/3 de la carga que fracción de toneladas quedo en la camioneta
Rectangle ABCD has has vertices A(1,1), B (1,5), C(5,5) and D (5,1). Graph the rectangle and its translation (2,1). Then write the new vertices for both.
The rectangle and the translated rectangle have been plot and the image is attached.
What is a Rectangle ?A rectangle is a polygon with four sides , opposites sides of the polygon are equal and parallel.
To draw a Rectangle having vertices A(1,1), B (1,5), C(5,5) and D (5,1).
and a rectangle with translation (2,1)
After translation the new points are
A(3,2) ,B (3,6) , C(7,6) , D(7,2)
The rectangle and the translated rectangle have been plot and the image is attached.
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If 0 lies in the quadrant IV. What can be the value of cos 0 ?
Answer:
the value of cos 0 is 7
Step-by-step explanation:
because you have to times it twice
Answer:
Between 0 and 1
Step-by-step explanation:
Cos Θ is the x coordinate of the unit circle. The points of that circle in quadrant IV have an x coordinate of 0≤x≤1.