Answer:
Vertical asymptotes: x=-9 and x=3
Slant asymptote: y=5x-1
Step-by-step explanation:
Given
f(x)=(5x^3+29x^2-140x+21)/(x^2+6x-27)
For vertical asymptote, the denominator is put equal to zero,so
x^2+6x-27=0
Factorizing
x^2+9x-3x-27=0
x(x+9)-3(x+9)=0
(x+9)(x-3)=0
So,
x=-9 ;x=3
As the degree of the numerator is greater than the denominator the function will not have horizontal asymptote but it will have a slant asymptote which will be calculated by long division.
After dividing 5x^3+29x^2-140x+21 by x^2+6x-27 we get
Quotient: 5x-1
Remainder: x-6
We only need the quotient for the slant asymptote,
So the slant asymptote is y = 5x -1 ..
Answer:
Vertical asymptotes: x=-9 and x=3
Slant asymptote: y=5x-1
Step-by-step explanation:
Which set of numbers contains only multiplies of 12
12, 16, 20, 24
1, 2, 12, 24
2, 3, 8, 12
12, 24, 36, 48
Answer:
D.
Step-by-step explanation:
A multiple is a number that can be divided by another number without a remainder. These are all multiples of 12 because they can all be divided by another number without a remainder.
A circle with 50 meter of the circumference what is the diameter
Answer:
25 meters
Step-by-step explanation:
Answer: 15.9155
is you answer and if it dont include the .9155 just choose 15 or 16 if its there
Step-by-step explanation:
What quadratic has roots x=8 and x= -5
x^2+3x-40
X squared minus 3X -40
X squared +13 X +40
X squared -13 X +40
Answer:
So the correct option is X squared -3 X +40
Step-by-step explanation:
If a polynomial has roots x=8 and x=-5, then we know that the factorized form is:
(x-8)(x+5)
So, to find the polynomial we need to expand the polynomials:
(x-8)(x+5) = (x^2 +5x - 8x + 40) = x^2 -3x + 40
what is the answer to this question -1⁄4 a − 4 = 4
Answer:
The correct answer is: a= -32
Please Help!!! :C
One computer desk is located at (7, 2) on the map. Another is located at (7, -8). How many feet separate the two computer desks? Explain or show how you got your answer.
Answer:
-6
Step-by-step explanation:
Elizabeth buys a circular rug with a lace border. The lace is 12.56 feet long.
What is the diameter of the rug? Round to the nearest whole number. (Use 3.14 for pi.)
Answer:
The diameter of the rug is [tex]4\ ft[/tex]
Step-by-step explanation:
we know that
The circumference of a circle (circular rug) is equal to
[tex]C=\pi D[/tex]
where
D is the diameter of the circle
In this problem we have
[tex]C=12.56\ ft[/tex]
substitute in the formula and solve for D
[tex]12.56=(3.14)D[/tex]
[tex]D=12.56/(3.14)=4\ ft[/tex]
How is 1.35 x 10 -5 written in standard notation?
Answer:
0.0000135
Step-by-step explanation:
Draw the angle below in standard position. -3pi/4
First of all, the negative sign means that we will turn clockwise.
Since [tex]\frac{\pi}{4}[/tex] is half a quarter, we have:
[tex]-\frac{\pi}{4}[/tex] brings you at half of quadrant IV[tex]-\frac{2\pi}{4}[/tex] brings you on the negative side of the y axis[tex]-\frac{3\pi}{4}[/tex] brings you at half of quadrant IIISo, option A is correct.
To draw the angle -3pi/4 in standard position, we measure 135 degrees clockwise from the positive x-axis.
Explanation:To draw the angle below in standard position, -3pi/4, you begin from the positive x-axis (which is usually referred rightward).
In standard position, positive angles are measured counterclockwise and negative angles are measured clockwise. Since we're dealing with a negative angle of -3pi/4, we will measure this clockwise.
The angle -3pi/4 corresponds to 135 degrees (because -3pi/4 is -3 * 180 degrees/2 = -135 degrees). You would measure 135 degrees clockwise from the positive x-axis to draw this angle in standard position.
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Please help!!!! 15, 17, 21
Explanation:
15. x = 148°, z = 32°
In a parallelogram, adjacent angles are supplementary, so must add to 180°. That also means opposite angles are congruent.
___
17. x = 8, y = -3
The diagonals bisect each other, so ...
2x -4 = 12
x = (12 +4)/2 = 8
and ...
y +10 = 7
y = 7 -10 = -3
__
21. The diagonals of a parallelogram bisect each other, so their point of intersection is their midpoint. The midpoint of WY can be computed as ...
P = (W+Y)/2 = ((-3, 5) +(3, 1))/2 = (0, 6)/2 = (0, 3)
The diagonals intersect at (0, 3).
Which expression is equivalent to sqrt 900f^6/100g^4
Answer:
3f³/g²
Step-by-step explanation:
√(900f^6/100g^4) =√(9f^6/g^4)=3f³/g²
Answer:
[tex][3f^{3}g^{-2}][/tex]
Step-by-step explanation:
The given expression is [tex]\sqrt{\frac{900f^{6} }{100g^{4}}}[/tex]
We can rewrite the expression as [tex]\sqrt{\frac{(30f^{3})^{2}}{(10g^{2})^{2}}}[/tex]
Now we can remove the radical of the expression = [tex]\frac{30f^{3} }{10g^{2} }[/tex]
= [tex][\frac{3f^{3} }{g^{2}}][/tex]
= [tex][3f^{3}g^{-2}][/tex]
= [tex][3f^{3}g^{-2}][/tex] is the answer.
If jay Berry put the $100.00 in a savings account that earned 12% interest every month. How much would he have in one year? 10 pts
How much would he have in five years?
Answer: Alright get ready for a long explanation
he would have 820.00$ in his savings account after the 5 years
Step-by-step explanation:
if he earns 12% interest then you would have to multiply 100 by the 12/100 which is .12 in decimal form.
100 TIMES .12 = $12.00
because we are doing this in months you need to multiply the amount he makes per month by the amount of months that the 100 dollars is in the bank account.
Alright so now that thats over, he makes 12 dollars every month
thers 12 months in a year, so you would have to do 12 (the number of moths) times 5 (the amount of years) that equals 60.
60 TIMES the amount he makes per month ($12) equals $720.00
LASTLY! add the amount he made to the original amount and you get the answer of $820.00
i hope this helps :)
Can somebody teach me inscribed angles! My 40 question summarize on circles in geometry is today and I need help on everything!
Inscribed angles are pretty easy, they're always half the corresponding central angle. The arc measure are always of central angles.
1. We're told to arc is 62 degrees so the inscribed angle is half,
WXY = 31 degrees.
2. Here we're told the inscribed angle is 113 degrees so the arc is double,
DGF=226 degrees
3. Angles which subtend a diameter are always right angles.
PQR = 90 degrees
4. If we draw DC we see it's a radius too, so DC=DB and we have an isosceles triangle so DCB=47 degrees so BDC=180-47-47=86. The central angle is the arc measure so
BC=86 degrees
5. Angle JNK=53 degrees and angles NJK=NKJ because we have an isosceles triangle, two sides radii. So NKJ=(180-53)/2.
Similarly NKL=(180-65)/2
So angle JKL=NKJ+NKL=180 - (65+53)/2 = 180 - 118/2 = 121 degrees
I better leave the rest for you.
An inscribed angle is formed by two secant lines intersecting on a circle's circumference and is half the measure of the central angle intercepting the same arc. Fundamental theorems like the Pythagorean theorem and mnemonic SOHCAHTOA are important in geometry, especially when dealing with circles and triangles.
Explanation:An inscribed angle is formed when two secant lines of a circle intersect on the circle's circumference. The value of an inscribed angle is always half the measure of the central angle that intercepts the same arc.
This is a foundational concept in geometry that is often linked to other geometric properties and theorems, such as the relationship between angles and arcs, and the behavior of angles within and outside of circles.
Knowing how to work with inscribed angles is crucial, particularly when dealing with problems involving circles.
For example, if you know the measure of the central angle, you can easily find the inscribed angle by dividing the central angle by 2. Recall other basic geometrical facts, such as the Pythagorean theorem, which states that in a right triangle, a² + b² = c² (where c is the hypotenuse), and the mnemonic SOHCAHTOA which helps remember the relationships of sides and angles in right triangles.
To help visualize these concepts, sketching triangles and remembering that the angles of a triangle sum up to 180 degrees can be helpful. Plane geometry forms the basis for understanding these principles, which is essential in tackling more advanced problems in circles and other geometric figures.
Landry is opening two savings accounts. He is opening the first account with an initial deposit of $500. The account will compound continuously each year at a rate of 3%.
He is opening the second account with an initial deposit of $300. The account will compound continuously each year at a rate of 5%.
Landry would like to know how long it will take for the balance of the two accounts to be equal.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
Answer:
Never. (Not viable)
Step-by-step explanation:
3% of 500=15
5% of 300=15
Since both of them would get $15 a year, then they would stay the same amount apart. For example, when the first account reached 515 dollars, the second one would be at 315 dollars. Thus, they'd always be 200 dollars apart.
However!
Since it is a compound interest, and if there is the original 7% a year, the formula we'll use for this is the simple interest formula, or:
I=Pxrxt
Where:
P is the principal amount, $500.00.
r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.
t is the time involved, 5....year(s) time periods.
So, t is 5....year time periods.
To find the simple interest, we multiply 500 × 0.03 × 5 to get that:
The interest is: $75.00
Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),
or 500.00 + 75.00 = 575.00. For example:
If you borrowed the $500.00, you would now owe $575.00
If you loaned someone $500.00, you would now be due $575.00
If owned something, like a $500.00 bond, it would be worth $575.00 now.
You want to calculate the interest on $300 at 5% interest per year after 5 year(s).
The formula we'll use for this is the simple interest formula, or:
I=Pxrxt
Where:
P is the principal amount, $300.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 5....year(s) time periods.
So, t is 5....year time periods.
To find the simple interest, we multiply 300 × 0.05 × 5 to get that:
The interest is: $75.00
Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),
or 300.00 + 75.00 = 375.00. For example:
If you borrowed the $300.00, you would now owe $375.00
If you loaned someone $300.00, you would now be due $375.00
If owned something, like a $300.00 bond, it would be worth $375.00 now.
Answer: there is only one solution and it is viable . ( answer on PLATO)
Step-by-step explanation:
A pair of jeans that normally cost $20 is 30% off. What is the price of the jeans
$12
$14
$15
$16
Answer:
$14
Step-by-step explanation:
20*0.3 0.3 is 30%
20*0.3=6
20-6=14
The answer is 14.
Explanation
Multiply 20 by .3
You get 6
Subtract 20 from 6 and u get 14.
What do you get when you tip a fortune teller
Final answer:
Tipping a fortune teller involves giving them a gratuity as a gesture of appreciation for their service.
Explanation:
When you tip a fortune teller, you are giving them a gratuity or extra money as a gesture of appreciation for their service. Tipping is a common practice in various service industries, including fortune-telling. It is a way to show gratitude for the insights or entertainment provided by the fortune teller.
g(x) = -x2 + x. Find g(-10).
It's subsitution.
-(-10)^2 + (-10) --) -(100) + (-10) --) -100 - 10 --) -110.
g(-10) = -110
Answer:
-110
Step-by-step explanation:
g(x) = -x^2 + x
g(-10) = -(-10)^2 + (-10)
g(-10) = -100 - 10
g(-10) = -110
I have no clue help!?
Answer:
Corresponding angles theorem.
Step-by-step explanation:
The corresponding angles theorem states that corresponding angles are congruent.
Pretty much means that every other angle is congruent if two lines are parallel and a line traverses them.
Answer: angle 2 and angle 6 are both corresponding angles
Step-by-step explanation:
If the two angles are matching corners, they are corresponding to one another. Hope this helps and have a good day:)
FIRST CORRECT ANSWER GETS BRAINLIEST
Find the slope of the line.
A. –3
B. 3
C. –1/3
D. 1/3
Answer:
A. -3Step-by-step explanation:
Look at the first picture.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 4) and (2, 1). Substitute:
[tex]m=\dfrac{1-4}{2-1}=\dfrac{-3}{1}=-3[/tex]
Look at the second picture.
The slope m:
[tex]m=\dfrac{rise}{run}[/tex]
[tex]rise=-3\\run=1[/tex]
Substitute:
[tex]m=\dfrac{-3}{1}=-3[/tex]
Just need to know how to solve
Answer:
so where the points are on the triangles is where you would go side to side and up and down
Step-by-step explanation:
Find the lengths of the sides:
BA = 4, this would be y1
BC = 6, this would be x1
CD = 2, this would be y2
DE = 3, this would be x2
The slope is the Y over X
Slope of ABC = 4 / 6
Slope of CDE = 2 / 3
Answer A equals both of those:
6-2 / 9-3 = 4/6
8-6 = 12-9 = 2/3
Janes age is 5 years less than 3 times her brothers age. Janes age is 11 minus her brothers age. How old is Jane?
You did not specify the brother's age, so I make a expression, b as the variable.
(3b + 5) - 11
Now do that with the brother age instead of the variable.
(3b + 5) - 11 = 3
you first add 3 and 5 which equals 8 ten you subtract 11 and 8 which equals 3, so jane is 3 years old
Help me please
a34=
1
3
8
ANSWER
[tex]a_{34} = 8[/tex]
EXPLANATION
The given matrix is a 4 by 4 matrix.
The entry in the intersection of the first third row and the fourth column is denoted
[tex]a_{34}[/tex]
This entry is 8.
Check the attachment for how we got the 8.
Therefore
[tex]a_{34} = 8[/tex]
Brainliest + Points! Please explain
A(n) _______________ is a mapping that does not change the size of the original figure.
A.
isometry
B.
mapping
C.
image
D.
preimage
Answer A isometry
Step-by-step explanation:
Isometry is a mapping that does not change the size of the original figure. Isometry can be things like translation and rotation, both of which don't change size or shape!
Hope this helps!
Identify the features of the graph
Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
The graph represent a vertical parabola open up
The vertex is the minimum value of the parabola
The vertex is the point (3,-4)
The x-intercepts are the points (1,0) and (5,0)
The x-intercepts are the values of x when the value of y is equal to zero
The y-intercept is the point (0,5)
The y-intercept is the value of y when the value of x is equal to zero
The domain is the interval -----> (-∞,∞) All real numbers
The range is the interval -----> [-4, ∞) All real numbers greater than or equal to -4
see the attached figure to better understand the problem
Answer:
Solution 5,0
Vertex 3,-4
Y-intercept 0,5
Step-by-step explanation:
Just finished on math nation
Eloise got the following scores on the first five quizzes of the semester: 6,9,7,8,9. There is one more quiz left. What score must Eloise get on the last quiz to have a mean quiz score of 8? Explain how you found your answer
Answer:
9
Step-by-step explanation:
when u add her past five scored together, you get 39. your equation would be
39 + x
------------- = 8
6
you multiply both sides by 6 and get
39+x = 48
subtract 39 from both sides to get 9
what relationship has a zero slope
Answer:
the far left table
In Mathematics, a zero slope represents a horizontal line that can be defined by the equation y = C, where C is a constant, showing no relationship between changes in x and y.
Explanation:In Mathematics, when discussing about slopes, a zero slope signifies that there is no change in y for any change in x. This results in a straight horizontal line when graphed. A real-life example might be that if you were walking on a flat road, the slope of that road is zero because your altitude isn't changing no matter how far you walk horizontally.
The relationship involved in a zero slope scenario can be defined by the equation y = C, where C is a constant. This means that y will remain constant despite any changes in x.
The equation of a line with zero slope can be declared as y = b, where b is the y-intercept. This shows no correlation between x and y as x varies but y remains constant.
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What is the sum of the arithmetic sequence 8, 14, 20 ..., if there are 22 terms?
Answer: I'm pretty sure its 1562
Answer:
The sum of 22 terms of given AP = 1562
Step-by-step explanation:
Formula:-
Sum of n terms of AP,
Sₙ= (n/2)[2a + (n - 1)d]
To find the sum of 22 terms
Here. a = 8, d = 6 and n = 22
Sₙ= (n/2)[2a + (n - 1)d]
S₂₂ = (22/2)[2*8 + (22 - 1)*6]
= 11[16 + 126] = 11 * 142 = 1562
Which statements describe the solutions to (√x-2)-4=x-6? Check all that apply.
There are no true solutions to the radical equation.
x = 2 is an extraneous solution.
x = 3 is a true solution.
There is only 1 true solution to the equation.
The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.
Answer:
x = 3 is a true solution.
The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.
Step-by-step explanation:
Given in the question an equation,
√(x-2) - 4 = x - 6
√(x-2) = x - 6 + 4
√(x-2) = x -2
Take square on both sides of the equation
√(x-2)² = (x -2)²
x - 2 = x² - 4x + 4
0 = x² - 4x - x + 4 + 2
0 = x² - 5x + 6
a = 1
b = -5
c = 6
x = -b±√(b²-4ac) / 2a
x = -(-5)±√(5²-4(1)(6)) / 2(1)
x = 5 ± √1 / 2
x = 5 + 1 / 2 or 5 - 1 /2
x = 3 or x = 2
Plug value of x in the radical equation:
x=3√(3-2)-4=3-6
√1 -4 = -3
1 - 4 = -3
-3 = -3
x=2
√(2-2)-4=2-6
0 - 4 = -4
-4 = -4
Answer:
C. x = 3 is a true solution.
E. The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.
Step-by-step explanation:
A youth soccer association raised $5145 in fund-raising projects. There were expenses of $777 that had to be paid first, with the balance of the money divided evenly among the 14 teams. How much did each team receive?
Answer:
Each team recieved $312
Step-by-step explanation:
You will take $5145 - 777 = 4368 which is the balance
4368 of the balance ÷ 14 teams =312
each team received $312
After paying the expenses of $777 from the fund-raising total of $5145, $4368 was left. When this amount was divided evenly amongst 14 soccer teams, each team received $312.
Explanation:To solve the problem, we first need to subtract the expenses from the total fund-raising amount. This gives us $5145 - $777 = $4368.
After the expenses are taken into consideration, the remaining money is divided evenly among the 14 soccer teams. This is calculated by taking the remaining money and dividing it by the number of teams, $4368 ÷ 14 = $312.
So, each team will receive $312 after all the expenses are paid.
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1000+2008747295828492
Answer:
2,008,747,295,829,492
Step-by-step explanation:
2008747295829492= 1000 + 2008747295828492
If s= 1 over 2 and A = 12s^2, What is the value of A, in square units
(Input whole numbers only)
ANSWER
3 square units
EXPLANATION
The given formula is
[tex]A=12s^2[/tex]
But
[tex] s = \frac{1}{2} [/tex]
We substitute the value of s into the formula to get;
[tex]A=12( \frac{1}{2} )^2[/tex]
[tex]A=12 \times \frac{1}{4}[/tex]
[tex]A=3 {units}^{2} [/tex]
The value of A in square units is
3