Answer:
x = 7 is a solution
x = -2 is an extraneous solution
^ CORRECT ANSWER
Step-by-step explanation:
The rational equation is solved and the solutions are 7 and the extraneous solution is x = -2
What is rational function equation?A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
Let the rational equation be represented as A
Now , the value of A is
( 3 / ( x²+5x+6 ) ) + ( ( x-1) / (x+2) ) = 7 / (x+3) be equation (1)
On simplifying , we get
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
So , multiplying both sides by ( x²+5x+6 ) , we get
3 + x² + 2x - 3 = 7x + 14 be equation (2)
On further simplification , we get
x² - 5x - 14 = 0
On factorizing the equation , we get
x² - 7x + 2x - 14 = 0
Taking the common factors , we get
x ( x - 7 ) + 2 ( x - 7 ) = 0
( x + 2 ) ( x - 7 ) = 0
So , the two solutions of x are x = 7 and x = -2
Hence , the solutions of rational equation are x = 7 and x = -2
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Please help
Honestly cant understand
Pls help I’ll give crown
Answer:
B
Step-by-step explanation:
because area of prism = L×W×H
so
[tex] \frac{3}{4} \times \frac{5}{2} \times \frac{5}{4} [/tex]
answer is 75/32
hope this make sense:)
Answer:
Hi there uwu The answer is 75/32, also explained by the other answerer!
Step-by-step explanation:
Evaluate b^2 c^-1 for b = 8 and c = -4.
A. -16
B. 1/16
C. 16
D. 256
Answer:
-16
Step-by-step explanation:
b^2 c^-1
We know that c^-1 can also we written as 1/ c
b^2 / c
Let b =8 and c = -4
8^2 / (-4)
64 / -4
-16
in the diagram below P(x:y)is a point in the third quadrant. ROP=B and 17 cos B is equal to -15 calculate the values of x and y and r
you showed no diagram or any picture / screenshot
The rectangle below has an area of x2 - 16 square meters and a width of x + 4 meters.
What expression represents the length of the rectangle?
x +4
Length
x2 - 16
Length
meters
Answer:
Length = x - 4 meters
Step-by-step explanation:
Area of a rectangle = length × width
Area of a rectangle = x² - 16
width of the rectangle = x + 4 meters.
Length of the rectangle = ?
Recall:
Difference of two perfect square x² - 16 = (x + 4)(x - 4)
Area of a rectangle = length × width
(x + 4)(x - 4) = length * x + 4
Length = (x + 4)(x - 4) ÷ x + 4
Length = x - 4 meters
Which is an equation of a direct proportion? CLEAR CHECK y=8x y=12x+4 y=12x y=4x−4
Answer:
[tex]y=8x, \\y=12x[/tex]
Step-by-step explanation:
Proportional functions can be written as [tex]y=kx[/tex], where [tex]k[/tex] is some constant of proportional. Since directly proportional functions always pass through the origin, the y-intercept must be 0 (no additional number before or after [tex]x[/tex] term). The only answers that fit this format are:
[tex]\rightarrow \boxed{y=8x}\\\rightarrow \boxed{y=12x}[/tex]
Answer: Y=8x
Step-by-step explanation:
a) Write down the exact value of tan 60' b) Find the value of h in this triangle, h= c) Write down the exact area of this triangle, h 60° 43
Step-by-step explanation:
maybe this can help you with your problem
a) The exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b) The value of h in the given triangle is √3.
c) The area of the given triangle is 24[tex]\sqrt{3}[/tex].
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
What is the value of tan 60 degrees?The value of tan 60 degree is [tex]\sqrt{3}[/tex].
What is the formula for area of a triangle?[tex]Area = \frac{1}{2}bh[/tex]
Where,
b is the base of the triangle.
h is the height of the triangle.
a) Since, the value of tan60 degree is [tex]\sqrt{3}[/tex].
Hence, the exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b). According to the given question, we have a right angled triangle in which
The length of the adjacent side w.r.t angle 60 degrees is [tex]4\sqrt{3}[/tex].
And, the length of the opposite side w.r.t angle 60 degrees is h.
Therefore, the value of h in the given triangle is given by
[tex]tan60 = \frac{h}{4\sqrt{3} }[/tex]
⇒[tex]\sqrt{3} =\frac{h}{4\sqrt{3} }[/tex] (because tan60=√3)
⇒[tex]h=4\sqrt{3} \sqrt{3}[/tex]
⇒[tex]h = 12[/tex]
Hence, the value of h in the given triangle is √3.
c) For the given triangle
Length of base = 4[tex]\sqrt{3}[/tex] unit.
And, the height of the given triangle is 12 unit.
The area of the given triangle is given by
[tex]Area = \frac{1}{2} (4\sqrt{3} )(12)[/tex]
⇒[tex]Area =24\sqrt{3}[/tex]
Hence, the area of the given triangle is 24[tex]\sqrt{3}[/tex].
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Jacob wants to enlarge a 4 in. By 6 in. Photo so that the longer side will be 14 in. How long will the shorter side be? (MUST SHOW WORK) HINT: Refer to your notes on Scale Drawings.
Answer: 9.3 in.
Step-by-step explanation:
Jacob wants to enlarge the larger side of the photo which is the 6 in. part, to becomes 14 in.
This means that Jacob wants to increase the larger side by a scale factor of:
= Length of enlarged picture / Length of original
= 14 / 6
= 2.33
2.33 is therefore the scale factor.
The shorter side will also increase by this same scale factor:
= 4 * 2.33
= 9.3 in.
How do I this math problem? If tan8 theta = cot 7 theta then theta =?
Given:
[tex]\tan 8\theta =\cot 7\theta[/tex]
To find:
The value of [tex]\theta[/tex].
Solution:
We have,
[tex]\tan 8\theta =\cot 7\theta[/tex]
We know that, [tex]\cot \theta =\tan (90^\circ -\theta)[/tex].
Using the trigonometric property, we get
[tex]\tan 8\theta =\tan (90^\circ -7\theta)[/tex]
On comparing both sides, we get
[tex]8\theta =90^\circ -7\theta[/tex]
[tex]8\theta +7\theta=90^\circ [/tex]
[tex]15\theta=90^\circ [/tex]
Divide both sides by 15.
[tex]\theta=\dfrac{90^\circ}{15}[/tex]
[tex]\theta=6^\circ[/tex]
Therefore, the value of [tex]\theta[/tex] is 6 degrees.
What’s the answer for this
155/18 x 2
Step-by-step explanation:
[tex] \tt{} \frac{155}{18} \times 2[/tex]
[tex]\tt{} \frac{155}{9} [/tex]
[tex]\tt{}17 \frac{2}{9} \\ \\ \\ [/tex]
A glass is 1/3 full then 40cm3 of orange juice is poured in the glass is now 5/7 full what is the total volume of the glass
Answer:
1/3 x + 40 = 5/7 x
7x +(21)(40) = 15x
21*40 = 8x
x = 105cm3
Step-by-step explanation:
Helpppp i need this quick im taking a timed test!!!
Answer: c
Step-by-step explanation:
Answer:c
Step-by-step explanation: it makes the most sense
The value of a boat is depreciating at a rate of 9% per year. In 2006,
the boat was worth $17,800. Find the worth of the boat in 2013.
Write an exponential decay function for this situation. Graph the
function and state its domain and range. What does the y-intercept
represent in the context of the problem?
Answer:
Hello yes indeed I am here now vote me brainliest.
Step-by-step explanation:
Why you ask? well first I want it even though I did not do anything to help him/her even though, it is funny. :)
Bruce and Krista are going to buy a new furniture set for their living room. They want to buy a couch, a coffee table, and a recliner. They have narrowed it down so that they are choosing between 4 couches, 5 coffee tables, and 9 recliners. How many different combinations are possible?
Answer:
180
Step-by-step explanation:
to work out all possibilities you multiple the amount of options.
4x5x9=180
Can anybody help me with this one ??
HURRRRRYYYYY!!! This Stem-and-Leaf Plot shows the number of students in each of the cooking classes held at the local recreation center last week. What are the values of the following statistics? NO LINKKKKKKKKKKKSSSSS!!!! WILL GIVE BRAINLIEST!
Range =
Median =
Mode =
Answer:
4 im correct I don't care i used my brain and guessed
Step-by-step explanation:
Answer:
the range is 16 mode is 5 and median is 11
Step-by-step explanation:
u can cheat if u exit out of the assignment and then keep trying
Simon makes 30 cakes.
He gives 1/5 of the cakes to sali.
He gives 10% of the cakes to Jane.
What fraction of the 30 cakes does he have left?
Answer:
1/5 of 30 = 6 hes left with 24
10% of 24 = 2.4 hes left with 21.6
he has 21.6/30 left
Multiply number of cakes by 1/5 and 10%
Sali = 30 x 1/5 = 20/5 = 6 cakes
Jane = 30 x 10% = 30 x 0.10 = 3 cakes
Total he kept = 30-6-3 = 21 cakes left
Solve for x. Enter the solutions from least to greatest. Round to two decimal places. (x+7)^2 - 11 = 0
Answer:
lesser x = -10.32
greater x = -3.68
Step-by-step explanation:
can someone help please??
Answer:
The scores in order from least likely to most likely is 8, 3, 4, and 5.
Step-by-step explanation:
1. Calculate the probability of the spinner adding up to 1, 2, 3, 4, .... 8
You will get:
2 (1/16)
3 (2/16)
4 (3/16)
5 (4/16)
6 (3/16)
7 (2/16)
8 (1/16)
2. Given the scores from the problem, the probability of each number is 3 (2/16), 4 (3/16), 5 (4/16), and 8 (1/16).
3. With this, we can determine the scores in order from least likely to most likely is 8, 3, 4, and 5.
Choose the function whose graph is given by:
+1
2
x
+-1
- -2
-4
O
A. y= 4sin(x+1) - 2
B.y= 6sin(x+1) - 2
c. y= 4cos(x- 1) +2
D. y= 4sin(x-1) - 2
Your answer would be y=4sin(x+1)-2. That would be A.
The required function is y = 3 sin (x -2) + 1.
What is Function?A relation between a collection of inputs and outputs is known as a function.
A mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).
From the graph that is provided to us we observe that,
when x=2
then f(x)=1
Here, from the function y = 3 sin (x -2) + 1
So, when x=2
we get: y=1
Also, all the other points are satisfied.
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What are the coordinates of the point on the directed line segment from (- 3, - 9) to (4, 5) that partitions the segment into a ratio of 5 to 2?
Answer:
(2,1)
Step-by-step explanation:
the best way to figure it out is with a graph
(-3,-9) to (4,5)
for the x
-3 to 4 is exactly 7 points away so you should count 5 over and stop.
for the y
-9 to 5 is exactly 14 points away so you should count in twos and stop at 5 sets of 2
hope this helps <3
Math help please help thanks
Answer:
62
Step-by-step explanation:
Draw a line from the bottom of the 4 foot line straight across (horizontally) until it hits the vertical line on your left.
The two lines (the one you drew and the left vertical line) meet at right angles.
The upper figure is a rectangle.
Area = L * W
L = 5
W = 4
Area = 5 * 4
Area = 20
Now the bottom rectangle can be found the same way.
Area = L * W
L = 14
W = 3
Area = 14 * 3
Area = 42
The total area = 42 + 20
Total area = 62.
The comment was correct.
For tran appreciate it
The trip odometer reading will be between 378.3 km and 378.4 km. Nominally, it will read 378.3 km.
Can U pls help with this number in the sequence
Answer:
First one:
1², 2², 3² and so on (Square of 1,2,3,4,5,6,7.....)
Second one:
2, 13, 26, 41...
add 11, add 13, add 15 (add increasing odd numbers, beginning from 11)
Third one:
4, 14, 29, 49
+10, +15, +20 and so on (add the multiple of 5,beginning from 10)
Fourth one:
1, 8, 27, 64
1³, 2³, 3³, 4³ and so on(cube of 1,2,3,4,5,6,7.....)
Brainliest please
the dishes have been cleaned by us into active voice
Answer:
the dishes sparkled after we washed them.
Step-by-step explanation:
What’s is the answer for
5x + 15=
What is x equivalent to?
The question and multiple choice answers are in the image. Hope you can help!
Answer:
answer b, SAS rule
Step-by-step explanation:
The ASA rule states that: If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
Pls help I’ll give crown
Answer:
C) (0,5)and(-4,5)
Step-by-step explanation:
Please use the following image for the next 7 questions. Keep in mind that because XY is tangent to circle M, XM and XM form a right angle.
XM = 11 and YM = 36.
What is the area of circle M?
What is the circumference of circle M?
Find the length of XY .
Find the measure of angle M.
Find the area of triangle XYM.
Find the area of the minor sector that has been created as part of triangle XYM.
Find the arc length of the minor arc from point X to the point where YM intersects with the circle.
Step-by-step explanation:
• the area of circle M = 3.14×11² = 379.94
• the circumference of circle M =
2×3.14×11 = 69.08
• XY =√36²-11²=√1296-121=√1175=34.28
• L M = cos~¹ 11/36 = cos~¹0.3055 = 72.21°
• the area of triangle XY = ½×11×34.28
= 188.54
• the area of minor sector
= 72.21/360 × 379.94 = 76.20
• the minor arc from point X to
the point where YM intersects
withthe circle
= 72.21/360 × 69.08 = 13.86
need help again still struggling
Answer:
0.111111...
Step-by-step explanation:
Hi,
this function is stating that for any x the f is 9(3)^x.
SO if x was -4 it would be 9(3)^-4
Following order of operations we calculate the exponent first.
the answer is 0.1111111...