Answer: f(x) will have vertical asymptotes at x=-2 and x=2 and horizontal asymptote at y=3.
Step-by-step explanation:
Given function: [tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]
The vertical asymptote occurs for those values of x which make function indeterminate or denominator 0.
i.e. [tex]x^2-4=0\Rightarrow\ x^2=4\Rightarrow\ x=\pm2[/tex]
Hence, f(x) will have vertical asymptotes at x=-2 and x=2.
To find the horizontal asymptote , we can see that the degree of numerator and denominator is same i.e. 2.
So, the graph will horizontal asymptote at [tex]y=\dfrac{\text{Coefficient of }x^2\text{ in numerator}}{\text{Coefficient of }x^2\text{ in denominator}}[/tex]
i.e. [tex]y=\dfrac{3}{1}=3[/tex]
Hence, f(x) will have horizontal asymptote at y=3.
Rose likes to water ski using her sister's boat. The boat takes 3 gallons of gas each hour to run. Gas costs $5 per gallon, how much money will she spend on gas to ski for 4 hours?
Answer:
$60
Step-by-step explanation:
Answer:
60$
Step-by-step explanation:
3 gallons per hr
multiply by 4
12gl per 4hrs
5 dl per gl
multiply by 12
60 dl per 12 gl
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Which is an equation of the line through (-1,-4) and parallel to the line 3x + y = 5?
Answer: y = -3x -7 or 3x + y = -7
Step-by-step explanation:
For two lines to be the same, they need to have the same slopes but different y-intercepts. First convert the equation 3x+y =5 into slope intercept form.
3x + y = 5 subtract 3x from both sides
-3x -3x
y = -3x + 5 in this case we know that the slope is -3 and the y-intercept is 5.
Now since they will have the same slope input the x and y coordinates and find the equation that will be parallel to it.
-4 = -3(-1) + b
-4 = 3 +b
-3 -3
b= -7
Since the y intercept is -7 the equation will be y = -3x -7 or 3x + y = -7
Equation of the line through (-1,-4) and parallel to the line 3x + y = 5 is
3x + y + 7 = 0
What is slope intercept form?The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis. Let us consider a straight line of slope 'm' and y-intercept 'b'. The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as:
y = mx + b.
Given, equation of line
3x + y = 5
y = -3x + 5
Comparing to y = mx+c
slope m = -3
slope of parallel lines are equal
∴ slope m' of the line which passes through (-1,-4) is -3
Equation of the line
y-(-4) = m'(x - (-1))
y + 4 = -3x - 3
y = -3x - 7
3x + y + 7 = 0
Hence, 3x + y + 7 = 0 is the equation of the line passing through (-1,-4) and parallel to 3x + y = 5.
Learn more about slope intercept form here:
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Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x
Answer:
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.
The discriminant is part of the quadratic formula. It is:
[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:
[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:
[tex]-4x^2+10x+8=0[/tex]
From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:
[tex]10^2-4(-4)(8)[/tex] which gives us a value of
100 - [4(-4)(8)] (don't forget orders of operation here!)
100 - (-128) = 100 + 128 = 228
This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking Last weekwalked 18 miles in 6 hours This week d = 2.5h Which statement must be true?
THIS IS THE COMPLETE QUESTION BELOW;
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.
Last week: walked 18 miles in 6 hours
This week: d = 2.5h
Which statement must be true?
A.This week, she walked a greater distance.
B. Last week, she walked a greater distance
C. This week, she walked at a faster pace.
D. Last week, she walked at a faster pace
Answer
OPTION B is correct
B)Last week, she walked a greater distance
Step-by-step explanation:
We were told Rosemary walks each week for exercise.
From the question,
✓d represented the distance walked
✓h represent the number of hours spent walking.
A)Last week: she walked 18 miles in 6 hours
Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)
= 3 miles per hour
B)This week: d = 2.5h
This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.
So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.
Therefore, OPTION B is correct, (Last week, she walked a greater distance)
Answer:
It's b
Step-by-step explanation:
Between which two integers on a number line does -√120 lie on?
Answer:
-11 and -10
Step-by-step explanation:
● -√120 = -1 × √120
● -√120 = -1 × 2√30
● 30 is close to 25 so √30 is close to five but greater than it.
Multiplying 5 by -2 gives -10
Multipluing √30 by -2 gives you a number that is close to -10 but smaller than it.
So -√120 lies between -11 and -10
I REALLY NEED HELP ASAP WITH THESE 3 QUESTIONS!!!!!!!!!
0. A submarine was at sea level and
then dove 752 ft. It then rose at a rate
of 12 ft. per minute. What was the
depth of the submarine after 8
minutes?
Also idk the equation so if u could help me out with that id be grateful
One equation you can use is y = -12x+752 and you plug in x = 8 to find y.
=================================================
Explanation:
x = number of minutes
y = depth of the submarine
Being at sea level means the depth is y = 0. Diving 752 ft below sea level means the depth is y = 752. It's tempting to make this negative since we're below sea level, but depth values are always positive. They are simply distances you are from the surface of the water. Negative distances are never possible. So this concept might be a bit tricky to get used to.
Possibly equally confusing is the fact that the "12 ft per minute" means the slope is -12. This is because the depth is getting smaller as the submarine gets closer to the surface (aka the sub is rising).
The equation is y = -12x+752. The equation is in the form y = mx+b with m = -12 as the slope and b = 752 as the y intercept. Note how the y intercept is the starting depth value.
From here, we plug in x = 8 to find where the sub is
y = -12x+752
y = -12*8+752
y = -96+752
y = 656
The submarine's depth after eight minutes is 656 feet
----------------------
An alternative equation to use is
y = 12x-752
which is very similar to the other one used earlier. All I did was flip the sign of each term. Now y represents the height of the sub. Negative y values indicate we're below the surface of the water. The slope being positive means the submarine is going upward. The negative y intercept indicates we're starting 752 feet below sea level. Plugging in x = 8 will lead to y = -656, which you'll need to make positive (since all depth values are positive).
As you can probably guess, the change from y = -12x+752 and y = 12x-752 is simply multiplying the right hand side by -1, which explains why the signs flip (and explains how the y value sign flips as well)
Solve for b.
ab+c=d
b=a+c/d
b= a/(c-d)
b = (d - c)/a
Answer:
[tex]b = \frac{(d-c)}{a}[/tex]
Step-by-step explanation:
ab + c = d
Subtract c from both sides
ab + c - c = d -c
ab = d - c
Divide both sides by 'a'
[tex]\frac{ab}{a}=\frac{d-c}{a}\\\\b = \frac{(d-c)}{a}[/tex]
Answer:
b = (d - c)/a
Step-by-step explanation:
just took this test
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Answer:
Step-by-step explanation:
Octagonal pyramid has 8 sloping faces and the base.
Total 9 faces.
Also 8 slope edges and 8 base edges
Total 16 edges.
It has 1 + 8
Total 9 vertices.
A Triangular prism has 5 faces and 9 edges.
Also 6 vertices.
Triangular pyramid has 4 faces, 4 vertices and 6 edges.
Note: The relation betseem faces, vertices and sdges in a polyhedron is given by Euler's formula:
T + V - E = 2
So we see, for an octagonal pyramid:
9 + 9 - 16 = 2.
Help !!! Thank you a lot!!
Answer:
E) 45
Step-by-step explanation:
Since b is 90 degrees, and lines CB and BA are equal (as seeen with the 2 lines across them) we can assume that this angle is 45 degrees, half or 90 degrees.
Angle C is also equal to angle A
Answer:
E
Step-by-step explanation:
Using the fact that the sum of angles in a triangle is 180 degrees, we can write the following equation to solve for 3x:
3x + 3x + 90 = 180
3x + 3x = 90
2 * 3x = 90
3x = 45°
Factorise using suitable identities (0.1x-0.2y)^2 plzzz help!!!!!
Answer:
0.1 exponent2 ( x − 2 y ) exponent 2
Step-by-step explanation:
The temperature dropped 15 degrees in an hour. If the starting temperature was 10 degrees, what was the final temperature?
Answer: If we're talking about the final temperature in 1 hour, then the final temperature would be -5 degrees. 10-15= -5.
Using the subtraction approach, the projected end temperature will be -5.
What is Algebra?Algebra is the study of graphic formulas, while logic is the application of those symbols.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.
In an hour, the temperature plummeted by 15 degrees. assuming that the initial temperature was 10 °.
Then the final temperature is given by subtracting the numbers 10 and 15.
Using the subtraction approach, the projected end temperature will be -5.
More about the Algebra link is given below.
https://brainly.com/question/953809
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How to do this question plz answer me step by step plzz
Answer:
4 cm
Step-by-step explanation:
At 12 cm depth, the depth is 12/15 = 4/5 of the height of the container.
When the container is tipped on its side, so its height is 5 cm, the depth will still be 4/5 of the height.
(4/5)(5 cm) = 4 cm
The depth will be 4 cm.
how many are 6 raised to 3 ???
Answer:
216
Step-by-step explanation:
When you say "6 raised to 3", it means you multiply 6, 3 times. Meaning:
6✖️6✖️6=216
Hope this helped!
Have a nice day:)
Enter a counterexample for the conclusion. If x is a prime number, then x + 1 is not a prime number. A counterexample is x = .
Answer:
x = 2
Step-by-step explanation:
If x is a prime number, then x + 1 is not a prime number.
A counterexample is x = 2.
x = 2
2 is prime
x + 1 = 2 + 1 = 3
3 is also prime
Help need work shown ASAP
Answer:
y = 2x + 1
Step-by-step explanation:
From the table attached,
x y Difference [tex][d=(y_2-y_1)][/tex]
-1 -1 -
0 1 1 - (-1) = 2
1 3 3 - 1 = 2
2 5 5 - 3 = 2
Since,there is a common difference 'd' = 2
Therefore, this table represents a linear equation.
Let the equation is,
y = mx + b
where 'm' is the slope and 'b' is the y-intercept.
Two points lying on the linear equation are (-1, -1) and (0, 1)
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{1+1}{0+1}[/tex]
m = 2
And y-intercept 'b' = 1 unit
Therefore, equation of the line will be,
y = 2x + 1
One day Shahed was playing with numbers. He wrote 15 fractions using all natural numbers from 1 to 30 exactly once- either as numerator or denominator. How many of these fractions, at most, are integers?
Answer:
30 i think because he has done numbers from 1 -30, which are all integers except for decimals...
A rectangle has a length of 12 m and a width of 400 cm. What is the perimeter of the rectangle?
Answer:
Perimeter = 32 meters
Step-by-step explanation:
1 meter = 1m = 100 cm = 100 centimeters
400cm = 400/100 = 4 meters
Rectangle Perimeter = 2(legth + width)
= 2(12 + 4)
= 2*16
= 32 meters
PLEASE HELP WILL MARK BRAINLIEST
Answer:
I believe the answer is 39.368, if we round that it makes it, 39.4
Step-by-step explanation:
Please answer now question
Answer:
1664 yd²Step-by-step explanation:
P = 2•(¹/₂•24•16) + 2•(20•20) + 24•20 = 384 + 800 + 480 = 1664 yd²
Help pls need work shown
Answer:
1.) P = 8g + 50
2.) Find the attached file for the graph.
Step-by-step explanation:
Let the profit = P
And g = good sold.
Given that each yo-yo sells for $8.00
The rate or the slope of the equation will be 8
Also, it is given that they must pay a clerk $50.00 a day to sell them. A flat rate of 50 dollars is an intercept of the equation.
Using the general linear equation of
Y = mX + C
The equation for the profit the store will make in a day will be.
P = 8g + 50
Please find the attached file for the graph
how do you work out 28.4 x 1.92
Answer:
54.528
Step-by-step explanation:
Please help.. I'm really stuck
Answer:
C. C only
Step-by-step explanation:
Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,
A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.
B. this also fails because a vertical line could pass through 2 points.
C. This passes because the vertical line doesn’t touch 2 points.
A machine fills 680 bottles in 5hours how many bottles will it fill in three hours?
Answer:
408 bottles
Step-by-step explanation:
the machine can fill 136 bottles in 1 hour, 136×3=408
Answer:
408
Step-by-step explanation:
680 bottles in 5 hours
in three hours:
1 hour =680/5=136
in three hours:it will be 136*3=408
Find the area of the shape shown below.
9.0
3.5
2
5
2.
units
Answer:
[tex] \boxed{42.5 \: {units}^{2} }[/tex]Step-by-step explanation:
The shape could be divided into a rectangle and a trapezoid ( bottom part )
Let's find the area of the given shape:
Area of the given shape = [tex] \mathsf{ (l \times b) + \frac{1}{2} (b1 + b2)h}[/tex]
plug the values
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 +9 - (5 + 2) \times 2}[/tex]
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 + 2)(2)}[/tex]
[tex] \mathsf{ = 31.5 + \frac{1}{2} \times 11 \times 2}[/tex]
[tex] \mathsf{ = 31.5 + 11}[/tex]
[tex] \mathsf{ = 42.5 \: {units}^{2} }[/tex]
Hope I helped!
Best regards!
-5y+6>26 does the inequality sign flip?
Answer:
Yes
Step-by-step explanation:
Answer:
y < -4
Step-by-step explanation:
-5y+6>26
subtract 6 from each side
-5y+6-6>26-6
-5y > 20
Divide each side by -5. remembering to flip the inequality
-5y/-5 < 20/-5
y < -4
3x - y = 0
2x - y = 1
What is the simplified sum of 3x/x-4 + x-3/2x
━━━━━━━☆☆━━━━━━━
▹ Answer
-1 - 1/2x
▹ Step-by-Step Explanation
3x ÷ x - 4 + x - 3 ÷ 2x
Divide and Rewrite:
3 * 1 - 4 + x - 3 ÷ 2 * x
Calculate:
3 - 4 + x - 3/2x
-1 + x - 3/2x
= -1 - 1/2x
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
Step-by-step explanation:
[tex]\frac{3x}{x-4}+\frac{x-3}{2x}[/tex]
Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:
[tex](\frac{2x}{2x}) \frac{3x}{x-4}+(\frac{x-4}{x-4}) \frac{x-3}{2x}[/tex]
Simplify:
[tex]\frac{6x^2}{2x(x-4)}+\frac{x^2-7x+12}{2x(x-4)} \\=\frac{7x^2-7x+12}{2x(x-4)}[/tex]
And this cannot be simplified further (you can also distribute the denominator if preferred).
BRAINLIEST, THANKS AND 5 STARS IF ANSWERED BOTH CORRECTLY. What is the 7th term in this geometric sequence? 3, 12, 48, 192.. ---------- What is the ratio (multiplier) of the following geometric sequence? 4, 2, 1, 0.5
Answer:
see below
Step-by-step explanation:
3, 12, 48, 192
We are multiplying by 4 each time (12/3 =4)
The 5th term
192 *4 =768
The 6th term
768 *4 =3072
The th term
3072 *4 =12288
To find the common ratio, take the second term and divide by the first
2/4 = 1/2
The common ratio is 1/2
Problem 1
Answer: 12288---------------------------
Explanation:
The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is
a(n) = a*(r)^(n-1)
a(n) = 3*(4)^(n-1)
Plug in n = 7 to get the seventh term
a(7) = 3*(4)^(7-1)
a(7) = 3*(4)^6
a(7) = 3*4096
a(7) = 12288
====================================================
Problem 2
Answer: 1/2 or 0.5----------------------
Explanation:
To find the common ratio, we pick any term but the first one and divide it over its previous term
r = common ratio
r = (second term)/(first term) = 2/4 = 1/2 = 0.5
r = (third term)/(second term) = 1/2 = 0.5
r = (fourth term)/(third term) = 0.5/1 = 0.5
Each term is cut in half to get the next one.
Find the area of the shaded region . RQ= 71.5 inches and PO=93.4 inches . Use 3.14 as necessary
Answer:
25,886.01 in²
Step-by-step explanation:
The area of shaded region = Area of the outter circle (the larger circle) - area of the inner circle (the smaller circle)
Area of a circle = πr²
Radius of larger circle = PO = 93.4 in
Area of the larger circle = 3.14*93.4² = 27,391.98 in²
Radius of smaller circle = PO - RQ = 93.4 - 71.5 = 21.9
Area of smaller circle = 3.14*21.9² = 1,505.97 in²
Area of shaded region = 27,391.98 - 1,505.97 = 25,886.01 in²
