Answer:
[tex]\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1[/tex]
Step-by-step explanation:
a) (x2 - 4)/(x + 2)
We can simply use factorization to solve the given question.
Here the first term will be numerator and second term will be denominator.
We will factorize the numerator.
So,
[tex]\frac{x^2-4}{x+2}[/tex]
Using formula, [tex]a^2+b^2 = (a+b)(a-b)[/tex]
[tex]\frac{x^2-4}{x+2}\\= \frac{(x^2)-(2)^2}{x+2}\\=\frac{(x+2)(x-2)}{x+2}\\= x-2[/tex]
b) (4x2 - 1) / (2x + 1)
We can simply use factorization to solve the given question.
Here the first term will be numerator and second term will be denominator.
We will factorize the numerator.
[tex]\frac{4x^2-1}{2x+1}[/tex]
Using formula, [tex]a^2+b^2 = (a+b)(a-b)[/tex]
[tex]= \frac{(2x)^2-(1)^2}{2x+1}\\=\frac{(2x+1)(2x-1)}{2x+1}\\= 2x-1[/tex]
Hence,
[tex]\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1[/tex]
Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.
Answer:
Tyson's account will have $ 133.90 more than Ariana's account.
Step-by-step explanation:
In Tyson's case, he invests $ 2,500 in an account whose interest rate is 5.75% and is compounded annually. In turn, Ariana invests the same amount and for the same interest, but this is not compounded.
Thus, Ariana, at the end of her 6 years, will have a total amount in her account of $ 3,362.5 (((2,500 x 5.75 / 100) x 6) + 2,500), of which $ 862.5 will correspond to the interest generated.
Instead, Tyson's investment interests will be consolidated annually. Thus, in 6 years, this investment will evolve as follows:
-Year 1 --- 2,500 x 1.0575 = 2,643.75
-Year 2 --- 2,643.75 x 1.0575 = 2,795.76
-Year 3 --- 2,795.76 x 1.0575 = 2,956.52
-Year 4 --- 2,956.52 x 1.0575 = 3,126.52
-Year 5 --- 3,126.52 x 1.0575 = 3,306.29
-Year 6 --- 3,306.29 x 1.0575 = 3,496.40
Thus, at the end of the 6 years, Tyson will have $ 3,496.40 in his account. Thus, Tyson's account will have $ 133.90 more than Ariana's account.
Line segments AD and BE intersect at C, and triangles ABC and DEC are formed. They have the following characteristics: ∠ACB and ∠DCE are vertical angles ∠B ≅ ∠E BC ≅ EC Which congruence theorem can be used to prove △ABC ≅ △DEC? HL ASA SSS SAS
Answer:
asa
Step-by-step explanation:
yas
∠ACB and ∠DCE are vertical angles.
∠B ≅ ∠E
BC ≅ EC
The congruence theorem that can be used to prove ΔABC and ΔDEC is ASA.
Option A is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangles:
ABC and DEC
The congruence theorem that is used to prove two triangles are:
ASA = angle side angle
SSS = side side side
SAS = side angle side
∠ACB and ∠DCE are vertical angles.
∠B ≅ ∠E
This means that angles B and C are congruent.
BC ≅ EC
This means that sides BC and EC are congruent.
From the given conditions we see that,
∠ACB and ∠DCE are vertical angles
This is an angle condition.
∠B ≅ ∠E
This is an angle condition.
BC ≅ EC
This is a side condition.
Thus,
The congruence theorem that can be used to prove ΔABC and ΔDEC is ASA.
Option A is the correct answer.
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pleaseee helpp meee
Answer:no
Step-by-step explanation:hope it helps
(02.03 MC) Triangle DOG was rotated to create triangle D'O'G''. Describe the transformation using details and degrees. (10 points) Triangles DOG and D prime, O prime, and G prime are shown. D is at negative 2, 1. O is at negative 3, 3. G is at 1, 1. D prime
Answer and Step-by-step explanation: Rotation is a "movement" of a geometric figure in order to transform one in another. In rotation, the shape and size of the figure is the same, so they are congruent.
A geometric figure can be rotated clockwise or counterclockwise and by different angles.
One way to recognized the angle of rotation is comparing the points of the figure and its rotated image.
On the figure below, triangle DOG has coordinates:
D (-2,1)
O (-3,3)
G (1,1)
And its image:
D' (2,-1)
O' (3,-3)
G' (-1,-1)
Comparing both set of coordinates, we observe:
D (-2,1) → D' (2,-1)
O (-3,3) → O' (3,-3)
G (1,1) → G' (-1,-1)
that the coordinates for ΔDOG and ΔD'O'G' are opposite to each other, i.e.:
(x, y) → (-x,-y)
rotating counterclockwise.
Since coordinates are opposite and rotation is counterclockwise, ΔD'O'G' is rotated by 180° related to ΔDOG.
Determine if y=5/4x +1 and y=5/4x-7 are parallel, perpendicular, or neither
Answer:
they are parallel
Step-by-step explanation:
they have the same slope
The lines represents the parallel line.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y=5/4x +1 and y=5/4x-7
4y= 5x+ 4 and 4y= 5x-7
Now, [tex]a_1[/tex]= 4, [tex]b_1[/tex]= 5, [tex]c_1[/tex]= 4
[tex]a_2[/tex]= 4, [tex]b_2[/tex]= 5, [tex]c_2[/tex]= -7
Now, on comparing the ratio we have
[tex]a_1[/tex]/[tex]a_2[/tex] = [tex]b_1[/tex]/ [tex]b_2[/tex] ≠ [tex]c_1[/tex]/ [tex]c_2[/tex]
Hence, the lines represents the parallel line.
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PLEASE HELP ME WITH THIS!! THANK YOU!!!
What do unit pricing and unit rate have in common?
Answer :When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. When prices are expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, they are called unit prices.
Step-by-step explanation:
I need help with this math question
Calc BC Problem. No random answers plz
Answer:
Part A)
[tex]f(1)=2, \; f^{-1}(1)=0, \; f^\prime(1)=1.4, \; (f^{-1})^\prime(1)=\frac{10}{7}[/tex]
Part B)
[tex]y=\frac{5}{14}x+\frac{4}{7}[/tex]
Step-by-step explanation:
Please refer to the table of values.
Part A)
A. 1)
We want to find f(1).
According to the table, when x=1, f(x)=2.
Hence, f(1)=2.
A. 2)
We want to find f⁻¹(1).
Notice that when x=0, f(x)=1.
So, f(0)=1.
Then by definition of inverses, f⁻¹(1)=0.
A. 3)
We want to find f’(1).
According to the table, when x=1, f’(x)=1.4.
Hence, f’(1)=1.4.
A. 4)
We will need to do some calculus.
Let g(x) equal to f⁻¹(x). Then by the definition of inverses:
[tex]f(g(x))=x[/tex]
Take the derivative of both sides with respect to x. On the left, this will require the chain rule. Therefore:
[tex]f^\prime(g(x))\cdot g^\prime(x)=1[/tex]
Solve for g’(x):
[tex]g^\prime(x)=\frac{1}{f^\prime(g(x))}[/tex]
Substituting back f⁻¹(x) for g(x) yields:
[tex](f^{-1})^\prime(x)=\frac{1}{f^\prime({f^{-1}(x)})}[/tex]
Therefore:
[tex](f^{-1})^\prime(1)=\frac{1}{f^\prime({f^{-1}(1)})}[/tex]
We already determined previously that f⁻¹(1) is 0. Therefore:
[tex](f^{-1})^\prime(1)=\frac{1}{f^\prime(0)}[/tex]
According to the table, f’(0) is 0.7. So:
[tex](f^{-1})^\prime(1)=\frac{1}{0.7}=\frac{10}{7}[/tex]
Hence, (f⁻¹)’(1)=10/7.
Part B)
We want to find the equation of the tangent line of y=f⁻¹(x) at x=4.
First, let’s determine the points. Since f(2)=4, this means that f⁻¹(4)=2.
Hence, our point is (4, 2).
We will now need to find our slope. This will be the derivative at x=4. Therefore:
[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime({f^{-1}(4)})}[/tex]
We know that f⁻¹(4)=2. So:
[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime(2)}[/tex]
Evaluate:
[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime(2)}=\frac{1}{2.8}=\frac{10}{28}=\frac{5}{14}[/tex]
Now, we can use the point slope form. Our point is (4, 2) and our slope at that point is 5/14.
So:
[tex]y-2=\frac{5}{14}(x-4)[/tex]
Solve for y:
[tex]y-2=\frac{5}{14}x-\frac{20}{14}[/tex]
Adding 2 to both sides yields:
[tex]y=\frac{5}{14}x-\frac{20}{14}+\frac{28}{14}[/tex]
Hence, our equation is:
[tex]y=\frac{5}{14}x+\frac{4}{7}[/tex]
What is the coefficient in this expression?
14y - 7
7
y
14
-
Answer:
The answer is C. 14
Step-by-step explanation:
Help quick please help
Answer:
Step-by-step explanation:
14h + 400 ≥ 2500
14h ≥ 2100
h ≥ 150
150 is minimum number of hours Ahmed must to work to meet his goal.
The pair of points (6, y) and (10, -1) lie on a line with a slope of 1/4. What is the value of y?
!!!
Answer quick will mark Brainliest!
30 POINTS!!!!
Find the constant of proportionality (r). Using the value for r, enter an equation that will calculate the cost (y) of x movie tickets in the form of y = rx.
Answer:
constant property of the proportionally proportionate rrrr is ryx
The relation between the cost (y) of x movie tickets is y= 8.5 x.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total. According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Number of Tickets Cost
2 $17.00
3 $25.50
4 $34.00
5 $42.50
As, y=rx
r= y/x
r= 17/2
r= 8.5
again, r= 34/4
r= 8.5
Hence, the relation is y= 8.5 x.
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help please, ive been cutting for a long time and i cant break the habit, no one will give me a straight answer. Ive lived a live full on pain, my cutting is just one of those things. i dont know when im cutting until i see the blood on the floor. I just need some help, hotlines are not an option and counseling is not possible because of my position in the military. anything helps.
Answer:
do you have any people who could make you happy from where you are?
Answer:
I've been through this too.
I know it's hard. I know there are many things that trigger your cutting. I noticed you said you live on your pain. I did too. One way I coped was instead of cutting myself, I would have a rubber band on my self and snap the rubber band to my wrist when I felt like cutting. This helped a lot, and I still do it to this day. Please trust me, when you look back at yourself in the future you won't believe you did that to your beautiful body. Please trust me on this one. <3
Andrew is showing his work in simplifying −4.5 + 4.2 + 5.6 − 7.3. Identify any errors in his work or in his reasoning. Step Work Reasoning −4.5 + 4.2 + 5.6 − 7.3 Original problem 1 −4.5 + 4.2 + 5.6 + (−7.3) Additive inverse 2 −4.5 + (−7.3) + 4.2 + 5.6 Commutative property 3 [−4.5 + (−7.3)] + (4.2 + 5.6) Associative property 4 −11.8 + 9.8 Simplify 5 −21.6 Simplify (5 points) Step 1: He wrote −7.3 incorrectly as + (−7.3). Step 2: He identified changing the order of the numbers as the commutative property, which is incorrect. Step 3: He identified changing the grouping of the numbers as the associative property, which is incorrect. Step 5: He simplified incorrectly. WHICH IS INNCORECCT MARKING RIGHT ANSWER AS BRAINLIEST IF THWY AINT BRAINLYIEST TDAT MEEN THEY SUS WROGN
Answer:
it is the last one ( HE SIMPLYFIED INCORECCT)
Step-by-step explanation:
i took the test
Angle BAD is __________ angle ABD *
Angle BAD is equal angle ABD
David earned $9.00 an hour at his job. He received a 6% pay increase. How
much does he now make per hour.
0.54
0 9.54
8.46
09.06
What is the slope of the line that passes through (3, 5) and (-2, 6)?
Answer:
0.2
Step-by-step explanation:
θ =
arctan( ΔY ) + 180°
ΔX
= 168.69006752598°
ΔX = -2 – 3 = -5
ΔY = 6 – 5 = 1
Distance (d) = √ΔX2 + ΔY2 = √26 = 5.0990195135928
Equation of the line:
y = -0.2x + 5.6
or
y =
- 1 x
5
+ 28
5
When x=0, y = 5.6
When y=0, x = 28
Answer:
-0.2
Step-by-step explanation:
goodluck:)
Solve fast answer gets brain and its 30 points ty
Answer:
74
Step-by-step explanation:
Answer:
I need the points, thanks!!!
Step-by-step explanation:
helppp please will give brainliest
Answer:
y = -1/2x + 2
Step-by-step explanation:
Topic: Graphs and Functions
If you would like to venture further into mathematics, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
The image below shows two dilated figures with lines KO and K’O’ drawn. If the larger figure was dilated using a scale factor of 5, what relationship do lines KO and K’O’ have? (10 points)
Two dilated figures are shown. The smaller figure has a line drawn connecting KO and the larger figure has a line drawn connecting K prime O prime.
The relationship between lines KO and K’O’ is given as Line K'O' = 5*line KO
Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Reflection happens when it is reflected over a line as we see in a mirror. But here the two triangles are not looking as images on a line. Hence no reflection
Rotation is keeping the same shape but rotating through a certain angle.
Translation is not right because there is no vertical or horizontal shift to get new triangle.
Dilation is the increase or decrease in size of a figure by a scale factor.
The larger figure was dilated using a scale factor of 5
hence
Line K'O' = 5 * line KO
The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO
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The lengths of the sardines received by a certain cannery is normally distributed with mean 4.62 inches and a standard deviation 0.23 inch. What percentage of all these sardines is between 4.35 and 4.85 inches long?
Answer:
5.87
Step-by-step explanation:
easy
Step-by-step explanation:
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The Temperature is 50F. The temperature will decrease by 4F each hour. Let h be the numbers of hours.
When will the temperature below 32F
Write inequality for this equation.
C. and D. arrows are suppose to have lines under them.
A. 50 - 4h< 32
B. 50 + 4h < 32
C. 50 + 4h <_32
D. 50 - 4h <_ 32
Answer:
a. 50 - 4h < 32
Step-by-step explanation:
The question is "When will the temperature be below 32F?" so it can't be less than or equal to (≤), it has to be less than (<).
If the temperature is decreasing every hour you have to decrease 4 for each hour.
hope that helps!
What is M+12-10? Hurry
Answer:
The answer is M + 2, if thats wat ur asking for.
Step-by-step explanation:
Answer:
M+2
Step-by-step explanation:
M+12-10
Since there are only 12 and -10 that are the same you can add them together to get 2 and that is pretty much what you could do unless you find what M is.
Hope this helps!
An integer is 3 less than 5 times together. If the product of the two integers is 36, then find the integers
Step-by-step explanation:
An integer is 3 less than 5 times another. If the product of the two integers is 36, then the integers are: 3 and 12. Solution: x * (5x 3) 36; 5x2 - 3x = 36; 5x2 -3x 36 = 0; (5x + 12)(x - 3) = 0; x = -12/5 or x =3.
Elena bought 8 tokens for $4.40. At this rate:
How many tokens could she buy with $6.05?
tokens
How much do 19 tokens cost? $
Answer:
11,10.45
Step-by-step explanation:
4.4/8=0.55
6.05/0.55=11
11*0.55=0.45
Answer:
Read below
Step-by-step explanation:
I whole. 5. Elena bought 8 tokens for $4.40. At this rate: Next Page. Unit 3: Unit Rates and Percentages Lesson 10: What Are Percentages?
what is the perimeter of the shape
Answer:that is an s
Step-by-step explanation:
si quema cuh
What is it then please
a) because the denominators are the same add the numerators:
1 1/5 + 3 2/5 = 4 3/5
b) rewrite the fractions to have a common denominator:
1/2 = 3/6
1/3 = 2/6
Now subtract:
4 3/6 - 1 2/6 = 3 1/6
Answer:
6/5+30/5
=6/5+6
=36/5
b)9/2+4/3
=26/6
=13/3
Step-by-step explanation:
please help asap question four
Answer:
(-5, 17)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS Equality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
5x + 3y = 26
-2y = 6x - 4
Step 2: Rewrite systems
5x + 3y = 26
y = 2 - 3x
Step 3: Solve for x
Substitute: 5x + 3(2 - 3x) = 26Distribute 3: 5x + 6 - 9x = 26Combine like terms: -4x + 6 = 26Subtract 6 on both sides: -4x = 20Divide -4 on both sides: x = -5Step 4: Solve for y
Define: -2y = 6x - 4Substitute: -2y = 6(-5) - 4Multiply: -2y = -30 - 4Subtract: -2y = -34Isolate y: y = 17And we have our final answer!
What is the sign of −4ab when a>0 and b<0?
Answer:
A
Step-by-step explanation:
We have the expression:
[tex]-4ab[/tex]
And we want to find its sign given that a>0 and b<0.
Notice that the expression is already negative since we have -4.
a>0 means that a is positive. Therefore, we can ignore it since it won’t do anything.
b<0 means that b is negative. Therefore, we will have two negatives being multiplied together. Hence, this will make a positive.
Therefore, the sign of our expression will be positive.
We can see this with an example. Let a=1 (1>0) and let b=-1 (-1<0). Then:
[tex]-4(1)(-1)=4[/tex]
So, the sign is positive.
Hence, the answer is A.
Answer:
The answer is A
Step-by-step explanation:
khan said so