The excluded value of the function is x = -1
How to determine the excluded valueFrom the question, we have the following parameters that can be used in our computation:
The function
The definition of the function is given as
y = 2/(x + 1) + 1
Set the denominator to 0 to determine the excluded value
So, we have
x + 1 = 0
Evaluate the like terms
x = -1
Hence, the value that is excluded is x = -1
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2x-5/ x^2-6x-7< 1/x-3
The solution is x^2-5x+22<0.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
2x-5/ x^2-6x-7< 1/x-3,
so, we get,
⇒2x-5/x^2-7x+x-7 < 1/x-3
⇒2x-5/(x-7)(x+1) < 1/x-3
⇒2x-5 * x-3 < (x-7)(x+1)
⇒2x^2-11x+15 < x^2-6x-7
⇒x^2-5x+22<0
Hence, The solution is x^2-5x+22<0.
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Enter the common ratio for the geometric sequence below. 4 , 8 , 16 , . . .
Answer:
its ×2
Step-by-step explanation:
4×2 = 8
8×2=16
..............
How are the properties of exponents used when dividing a polynomial by a monomial?
Answer:
a couple different obes
Step-by-step explanation:
there are five
You made it onto the game show Let's Make a Deall You are chosen for the opportunity to win some cash! You are
presented with a bag that contains 5 $100 bills, 9 $20 bills, 17 $5 bills, and 42 $1 bills. (write probabilities in
simplified fraction / ratio form)
Wayne says you can draw three bills randomly from the bag for your prize (you keep each bill you draw). What is
the probability of winning $300?
Unfortunately, you draw three $1 bills! Wayne feels for you and says you can put two of the bills back into the bag
(replace the bills). What is the probability of winning $201?
Which expression is equivalent to
(3x^2 + 2x - 4) + (5x^2 - 4x + 5) ?
8x^2 + 6x + 9
8x^2 + 2x + 1
8x^2 - 2x + 1
8x^2 + 6x + 9
Answer:
8x^2-2x+1
explaniationfirst remove the bracket 3x^2+2x-4+5x^2-4x+5then collect like term3x^2+5x^2+2x-4x-4+5 then the answer will be 8x^2-2x+1 thank you!!!!!Prepare to analyze the data (step 1): identify and classify the variable(s) you will use. Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Gender Alcohol Height Cheat
Indicating whether the variable is relevant to the questions, and Identifying the variable as either categorical or quantitative.
Gender - Categorical and Nominal Alcohol - QuantitativeHeight - QuantitativeCheat - CategoricalRather than straightforward explanations. Anything may be measured using it. It can also do mathematical calculations, which is essential for data analysis.
To completely understand all of the facets of quantitative data, statistical analysis—the discipline of obtaining, analysing, and presenting enormous volumes of data to uncover patterns and trends—is used. This calls for quantitative analysis employing a wide variety of data.
Categorical data is data that may be arranged into groups or categories using names or labels.
The approach is based on algorithms that assess each component of a data collection individually, compare them to other individual data sets, and look for particular similarities.
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Complete question:
identify and classify the variable(s) you will use.Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Group of answer choices
Gender [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Alcohol [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Height [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Cheat [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitativeIs the function linear or nonlinear?
y = 3 x 2 + 7
Answer:
y= 13
Step-by-step explanation:
y+3x2+7
y=6+7
y=13
x y
0 13
1 13
linear
there are 'b' daffodil bulbs in a bag. i buy 4 bags, but 5 of the bulbs have gone bad and will not grow. if i still have 55 bulbs that will grow, calculate the number of bulbs in each bag.
WILL MARK BRAINLIEST !!! please help and show work !!
Find the equation of the line passing through (1,5) and parallel to y = 3x - 1.
Answer:
Step-by-step explanation:
Finding an equation of a line can be condensed into 2 easy steps. Step one is to establish the basic form of the equation, including it's slope.
1) Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero). We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3. Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:
y = 3x + b.
2) The second step is finding the value of b. We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5). Easy: just enter this point in the equation we have so far: y = 3x + b:
y = 3x + b
5 = 3*(1) + b for point (1,5)
b = 2
The equation becomes y = 3x + 2
See the attached graph. [Extra credit]
The lines are parallel, and the y-intercept for the second line (b) is (0,2).
Who knows the answer to this ?
Answer:
angle 1 is 28 degrees angle 2 is 62 degrees
DONT FORGET TO PUT THE DEGREES SIGN
Step-by-step explanation:
since it is a right angle, angle 1+ angle 2 is 90 degrees.
So,
2x+(x+48)=90
3x=90-48
3x=42
x=14
angle 1=28 angle 2=62
7-2 Enrichment
Multiplying Polynomials
An architect is preparing to design an office building. She creates a sketch of the basic shape of the structure and
the relative dimensions of each piece shown. The angles in the sketch are all right angles. Find the volume of the structure using each approach. Draw lines on the sketches and record your expressions.
1. Divide the structure into two different rectangular
prisms. Add the volumes of the two prisms to create
an expression for the total
Volume
2. Divide the structure into three different rectangular
prisms. Add the volumes of the three prisms to create
an expression for the total volume.
3. View the structure as one prism with 2 equal sized prisms. Find the volume of the large prism and subtract the volumes of the smaller pieces to find the expression for the total volume!!
Thanks for helping!! (We are learning polynomials right now, like (2+x)^2 for clarification for the problems!!!) :)
The volumes of the structure are:
1. (8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)
2. (8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)
3. (8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]
What is polynomial expressions?A polynomial expression is an algebraic expression consisting of variables and coefficients, and involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Examples include 2x^3 - 5x^2 + 3x + 1 and 4y^2 + 7y - 2.
1.We can divide the structure into two rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of the second prism are 12(8 + x)(3 + x). To find the total volume, we can add the volumes of the two prisms:
(8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)
2.We can also divide the structure into three rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(3 + x), the dimensions of the second prism are 12(8 + x)(3 + x), and the dimensions of the third prism are 12(6 + 3x)(3 + x). To find the total volume, we can add the volumes of the three prisms:
(8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)
3.We can view the structure as one large rectangular prism with two smaller rectangular prisms removed, as shown in the sketch. The dimensions of the large prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of each small prism are 12(8 + x)(3 + x). To find the total volume, we can subtract the volumes of the two small prisms from the volume of the large prism:
(8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]
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Tuga has 2⅔ pounds of sweet potatoes. She needs 40 ounces of sweet potatoes to make chili. Which statement explains if Tuga has enough sweet potatoes to
make chili? (1 pound = 16 ounces)
Answer:
Step-by-step explanation:
Convert pounds to ounces:
2[tex]\frac{2}{3}[/tex] = 2.667
2.667 lb x 16 oz/lb = 42.7 oz
42.7 > 40, therefore Tuga has enough sweet potatoes to make chili
Six percent commission on first $10,000. Eight percent commission over $10,000. Find the total graduated commission on $13,200.
An amount of $ 13,200 has a total comission of 856.
How to determine the total comission for an amount of money
Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:
C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)
C = 856
The graduate must pay a total comission of $ 856 for an amount of $ 13,200.
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i need to find 2 standard form equations that represent the table.
We can find the two linear equations by using the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
For the first equation:
Using the first point (-2, 8), we have m = (y2 - y1) / (x2 - x1) = (-3 - 8) / (-2 - (-2)) = -11/0, which is undefined. This means the first line is a vertical line.
The equation can then be written as x = -2, since the x-coordinate is constant.
For the second equation:
Using the second point (-1, 4), we have m = (y2 - y1) / (x2 - x1) = (-2 - 4) / (-1 - (-2)) = -2.
The equation can then be written as y - 4 = -2(x + 1), or y = -2x - 2.
Thus, the system of linear equations is:
x = -2
y = -2x - 2
Written in standard form:
x + 0y = -2
-2x + y = -2
Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. But the early-bird special on Saturday morning offers 8 games for $30. How much more does glow-bowling cost per game? $ per game
The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. Then the rate is given as,
⇒ $22.50 / 5
⇒ $4.5 per game
But the early-bird special on Saturday morning offers 8 games for $30. Then the rate is given as,
⇒ $30 / 8
⇒ $3.75 per game
The difference is given as,
D = $4.5 - $3.75
D = $0.75 per game
The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.
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Find each exact value if 0
Tan (x - y) if csc x = 13/5 and cot y = 4/3
Using trigonometry formulas, the value of tan(x-y) = -16/63
What is trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
Given
cot y = 4/3
1/tan y = 4/3
Cross multiply
tan y = 3/4
Also since csc x = 13/5
1/sin x = 13/5
sin x = 5/13
Since sin x = opp/hyp
opp = 5
hyp = 13
Get the adjacent
hyp² = opp²+adj²
13² = 5²+adj²
adj² = 13² - 5²
adj² = 169 - 25
adj² = 144
adj = 12
cos x = adj/hyp
cos x = 12/13
tan x = sin x/ cos x
tan x = (5/13)/(12/13)
tan x = 5/13 * 13/12
tan x = 5/12
tan(x-y) = tan x - tan y/1 + tan x * tan y
tan(x-y) = (5/12 - 3/4) / 1 + (5/12) (3/4)
tan(x-y) = (5-9/12) / 1 + 5/16
tan(x-y) = -4/12/(21/16)
tan(x-y) = -1/3 * 16/21
tan(x-y) = -16/63
the value of tan(x-y) is -16/63
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Justice rents a car for a deposit of $50 and $20 a day. When he turns it in he owes $490. How many days did he have the car?
Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.
What do we mean by rent?Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc.
According to the information in the question:
Deposit = $50
Rent cost per day for the car = $20
Total amount that Justice has to pay = $490
∴ Total number of days that Justice kept the car = (490 - 50)/20
= 440/20
= 22 days
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The number of days did he have the car are 22.5 days.
Explain about rent.a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.
According to question:Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.
To find out how many days he had the car, we can set up an equation:
$50 + (number of days x $20) = $490.
Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.
So Justice had the car for approximately 22.5 days.
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Solve this problem:
㏒₅₄168=?
If:
a = ㏒₇12
b = ㏒₁₂24
Answer:
㏒₅₄168 = (1+ab)/(8a-5ab)
Step-by-step explanation:
You want ㏒₅₄168 written in terms of a and b, where ...
a = ㏒₇12b = ㏒₁₂24Log expressionsThe rules of logarithms are relevant here:
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]
In order to simplify the writing in what follows, we want to define ...
p = log(2)q = log(3)r = log(7)Now, we can write the equations ...
a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]
b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]
Using these, we can solve for p and q:
2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]
(3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]
Using your favorite solution method for linear equations, you find ...
p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)
q = (-ar(3 -2b)/(-1) = ar(3 -2b)
Desired logarithmSubstituting these expressions into ...
[tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]
__
Additional comment
The calculator confirms the result.
Stacy was a stay-at-home mom for most of her adult life. At age 46, she started working outside the home. Each year she earns the maximum number of Social Security credits. Until what age must she work to qualify to receive Social Security benefits when she retires?
The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years
What is the timeframe for Social Security benefits?Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.
To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.
Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.
If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.
Benefits may likely be taxed based on the specific income and tax return status.
She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.
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i need help
solve for a
x = 4
-- All angles of a triangle add up to 180° --
-- the inverse of a trianglenis equal to its opposite angle of intersection--
1) build equation
180° = 20° + (4 + 6x) + (32x + 4)
2) solve
180-20 = 4 + 6x + 32x + 4
160 = 8 + 38x
152 = 38x
152/38 = x
x = 4
verify
180 = 20 + (4 + 6x) + (32x + 4)
180 = 20 + (28) + (132)
180 = 180 so x = 4
ANSWER PLEASE 10 POINTS!!! EXPLANATION INCLUDED TOO PLS!
There are red tiles and blue tiles in a box. the ratio of red tiles to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
Ty!
r = red tiles
b = blue tiles
b = r + 12 , whatever "r" is, "b" is 12 more than that
[tex]\stackrel{red}{3}~~ : ~~\stackrel{blue}{5}\qquad \implies \cfrac{r}{b}=\cfrac{3}{5}\implies \cfrac{r}{r+12}=\cfrac{3}{5}\implies 5r=3r+36 \\\\\\ 2r=36\implies r=\cfrac{36}{2}\implies r=18[/tex]
Answer:
18
Step-by-step explanation:
Because there are 12 more blue tiles than red, that means that we can write the equation 3x + 12 = 5x. By simplifying, the equation is boiled down to 12=2x. By dividing, we see that x=6. This means that we can multiply 3 by 6 to get 18 red tiles. To check our answer, we just multiply 6 by 5 to get 30, and the ratio 18:30 is equivalent to 3:5. Also, 30-18=12, so this must be correct.
Find the area of the triangle below. Be sure to include the correct unit in your answer. 24 ft 6 ft 15 ft
Answer:
72 [tex]ft^{2}[/tex]
Step-by-step explanation:
a = 1/2(24)(6)
a = 72
A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet.
Which expression best represents the value of pi
In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is 43.96 feet/ 14 feet.
How can the value of pibe calculated?The concept that will be use here is Circumference. we were given Circumference of the circle as 43.96 feet
where the Diameter of the circle is 14 feet, then we can find the Circumference of the circle as( πd)
Then ( πd) = 43.96 feet
π= 43.96 feet/ 14 feet
Therefore, option C is correct.
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Sam's biweekly paycheck is $1500. 1/2 of his paycheck is used to pay bills. 1/5 of his paycheck is deposited into his savings account. The remainder of his paycheck is used for food and entertainment. How much money does Sam have available for food and entertainment?
[tex]\stackrel{\textit{for bills}}{1500\cdot \cfrac{1}{2}}~~ + ~~\stackrel{\textit{for savings}}{1500\cdot \cfrac{1}{5}}~~ + ~~\stackrel{\textit{food and ET}}{x}~~ = ~~\stackrel{total}{1500} \\\\\\ 750+300+x=1500\implies 1050+x=1500\implies x=450[/tex]
What is 6d greater than or equal to -84
Answer:
d ≥ - 14
Step-by-step explanation:
6d ≥ - 84
Divide by 6 both sides
6d/6 ≥ - 84/6
d ≥ - 14
35. Solve the equation and check your solution: -2(x + 2) = 5 - 2x
Answer:this equation is not right.so,it does not have any solutions
Step-by-step explanation:
because if we try to solve it we get,
-2x-4=5-2x
-4-5=-2x+2x
-9=0
so,this equation is not right.
Answer:
equation has no solution
Step-by-step explanation:
- 2(x + 2) = 5 - 2x ← distribute parenthesis on left side
- 2x - 4 = 5 - 2x ( add 4 to both sides )
- 2x = 9 - 2x ( add 2x to both sides )
0 = 9 ← false statement
this false statement indicates the equation has no solution
(35) MOVIE RENTALS The number of copies of a movie rented at a video kiosk decreased at a constant rate of 5 copies per week. The 6th week after the movie was released 4 copies were rented. How many copies were rented during the second week?
Answer:
25 copies rented
Step-by-step explanation:
r = r1 - 5t, t is time in weeks, r is the number of copies rented, r1 how many people were renting at the start
we know on the 6 weeks passed and 4 copies were rented
4 = r1 - 5(6)
4 = r1 - 30; add 30 on both sides
34 = r1
r = 34 - 5t now plug t = 2 in for this function
r = 34 - 5(2)
r = 35 - 10
r = 25 copies rented
what is the volume ?
so let's take a peek at the triangular pyramid, hmm it has a base of well, the base is a triangle, so we can say the triangle has a base of 10 and a height of 8, thus and area of (1/2)*10*8, and the pyramid has a height of 9.
[tex]\textit{Volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(10)(8)\\[1em] h=9 \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(10)(8) \right](9) \\\\\\ V=\cfrac{1}{3}(40)(9)\implies V=\cfrac{360}{3}\implies V=120~m^3[/tex]
2. There are 6 children that each want to eat half of a chocolate bar. If they buy a package of 4 chocolate bars, how many chocolate bars will be left over after they've eaten?
Answer:
1
Step-by-step explanation:
6 children that each want to eat half of a chocolate bar (0.5)
6 * 0.5 = 3 - chocolate bars will be eaten
They bought a package of 4 chocolate bars
4 - 3 = 1 - chocolate bar will be left
simplify
[tex]\frac{x^\frac{1}{5}x^\frac{2}{5} }{x^\frac{4}{5} }[/tex]
Answer:
Step-by-step explanation:
Since the base x is consistent with all terms of this complex fraction, all you need to do is add the two exponents found in the numerator and from that, subtract the exponent in the denominator.
This gives us x^(3/5) divided by x^(4/5), which is x^(-1/5). This gives 1/x^(1/5), which is 1 divided by the fifth root of x.