The value of x for which the function f(x)=g(x)-2 is x = 1 and 2
What is a function?
A function can be defined as an equation, expression, rule or law showing the relationship between two variables.
These variables are;
The dependent variableThe independent variableThe functions are given as;
f:x > x^2-2x-1 g:x > x-1For the function (x)=g(x)-2
Substitute the values, we get;
x² -2x - 1 = x - 1 - 2
collect like terms
x² - 2x - x = -3 + 1
add or subtract like terms
x² -3x + 2 = 0
x² - 2x - x + 2 = 0
(x² -2x) - (x + 2) = 0
x(x -2) - 1(x - 2) = 0
Then,
x = 1 and 2
Hence, the values are 1 and 2
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3. Find the volume of the child's toy shown below. Use 3.14 for π Round all answers to 1 decimal place.
Volume of the top solid: ________
Volume of the bottom solid: _________
Volume of the entire toy: _________
The total volume of the toy is 497.4192cm³ with 340.3392 cm³ being the volume of the top solid and 157.08 cm³ being the volume of the bottom solid.
What is volume?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas.
While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.
So, the volume of the cone:
V = πr²h/3
Now, invert values:
V = π5²*13/3
V = 340.3392 cm³
The similar, volume of a cylinder:
πr²h
Now, insert values as follows:
πr²h
π5²2
V = 157.08 cm³
Total volume: 340.3392 cm³+157.08 cm³ = 497.4192cm³
Therefore, the total volume of the toy is 497.4192cm³ with 340.3392 cm³ being the volume of the top solid and 157.08 cm³ being the volume of the bottom solid.
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The number of CD's sold since April 8 at a music store can be
modeled by the function N(d) = 12d +35 and the price per
CD can be modeled by P(d) = 0.3d2 - d+5, where d is
the number of days since April 8.
of revenue
According to this model, what is the total amount of rev
generated by the store's CD sales on April 18?
The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.Markup on selling price is 27 %.
How do you calculate markup on selling price?The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage.
Below, you'll find various possible formats for the markup formula or equation.
The selling price given as = $ 15
The cost per CD is = $ 11
The total profit = Selling price - Cost
Total profit per CD = $ 15 - $ 11
Total profit per CD = $ 4
The markup on selling price is calculated as - Total profit ÷ Selling price × 100
Markup on selling price = $ 4 ÷ $ 15 × 100 =26.6666 % or 27 %.
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The equation, A = 5,000(1 + 0.025t) represents the amount of money earned on a savings account with 2.5% annual simple interest. At the end of the investment period, the account balance is $5,875. How many years is the investment period? 1 year 4 years 7 years 9 years
The number of years in the investment period, given the account balance and the simple interest, is C. 7 years.
How to find the investment period ?To find the investment period, you can use the equation given on the account balance after a number of years, with " t " representing that number of years. And with simple interest,
With the formula being A = 5,000 x ( 1 + 0.025 t ), the investment period would be :
5, 875 = 5,000 x ( 1 + 0.025 t )
5, 875 = 5, 000 + 125 t
125 t = 5, 875 - 5, 000
125 t = 875
t = 875 / 125
t = 7 years
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WILL MARK BRAINLIEST! please help with easy geometry problem!! :) and give explanation and steps too
Therefore , the solution to the given problem of triangle comes out to be x =20 degree and y = 20 degree.
Defining a triangleIn a plane, any three points can be joined to form triangles, that have 3 components and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.
Here,
Given : 140 degree
Since it is a scalar triangle
two sides will have equal angle,
Thus ,
x=y
=> x+ x + 140 =180
=> 2x = 180-140
=> 2x =40
=> x =20
Therefore , the solution to the given problem of triangle comes out to be
x =20 degree and y = 20 degree.
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the solid below is made from cubes.
find its volume
Answer:
96
Step-by-step explanation:
Stephan and John are reading the same book. Stephan reads 7 pages a day and is on page 22. John reads 9 pages a day and is on page 10. How many days until Stephan and John are on the same page? What page will they be on?
The number of days until Stephen and John are on the same page would be 6 days
The page they would be on would be 64 pages
How to find the number of days ?Assuming that the number of days can be denoted as x, the equation for the number of pages that Stephen has read in total is:
= 22 + 7 x
The number of pages that John has read in total is:
= 10 + 9 x
To find the number of pages, equate these:
22 + 7 x = 10 + 9x
22 - 10 = 9x - 7 x
12 = 2 x
x = 12 / 2
x = 6 days
The page they would be on is:
= 10 + 9 x
= 10 + 9 ( 6 )
= 64 pages
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Felipe uploaded a funny viedo of his dog. The relationship between the elapsed time in days, d , since the viedo was first uploaded and the total number of views, v , that the viedo received is modeled by v=4^1.25d . Find the number of days it took Felipe's viedo to get 1024 views.
The number of days took to get the video of Felipe 1024 views is 4.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The relationship between the elapsed time in days, d, since the video was uploaded and the total number of views, v, that the video received is modeled by the equation,
v = 4^(1.25d)
We have to find d when v = 1024
1024 = 4^(1.25d)
We have the rule for exponents aᵇⁿ = (aᵇ)ⁿ
1024 = [tex](4^{1.25} )^d[/tex]
1024 = (5.6569)^d
Taking logarithms on both sides,
㏒ (1024) = ㏒ [(5.6569)^d]
We have the exponent rule for logarithm, ㏒ (aᵇ) = b ㏒ (a)
㏒ (1024) = d ㏒ (5.6569)
d = ㏒ (1024) / ㏒ (5.6569)
d = 4
Hence it took 4 days to for Felipe's video to get 1024 views.
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Is this SSS, ASA, SAS, or AAS? I’m pretty sure it’s either sss or sas because there are already two sides but I’m not sure!! Please help:,)
Therefore , the solution of the given problem of congruent comes out to be in this case we have two side equal and one side common so it is sss
What in mathematics is a congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
How does SSS work?SSS definitions. an autonomous government organization responsible for overseeing military conscription. Selective Service and Selective Service System are synonyms. independent agency kind. a federal agency that was established by a congressional act and is unrelated to the executive departments.
In this case we have two side equal and one side common so it is sss
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Which of the following represents a tragedy of the commons?
Plastic trash in the neighborhood park
Two hospitals for the town's residents
Leaves piled in a person's backyard
Plenty of food at a local market
Two hospitals for the town's residents represents a tragedy of the commons. Hence, option B is correct.
What is tragedy of the commons?The phrase "tragedy of the commons" describes a situation in which people who have access to a shared resource, also known as a common, act selfishly and ultimately deplete the resource. British author William Forster Lloyd initially conceived of this economic theory in 1833.
The Tragedy of the Commons, first proposed in 1968 by American ecologist Garret Hardin, is a scenario in which common environmental resources are overused, abused, and eventually exhausted, bringing risks to all parties concerned.
Thus, option B is correct.
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Gwen buys 3 identical pairs of shoes at store A. She pays $110.25 after the discount. What is the regular price of each pair?
The regular price of each pair of shoe is 36.75 dollars.
How to find the regular price of the pairs?Gwen buys 3 identical pairs of shoes at store A. She pays $110.25 after the discount.
The regular price of the each pair of shoe can be calculated as follows:
Therefore,
3 pairs of shoe = 110.25 dollars
1 pair of shoe = ?
cross multiply
Therefore,
regular price of a pair of shoe = 110.25 / 3
regular price of a pair of shoe = 36.75
Therefore, the regular price is 36.75 dollars.
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How many 5 card hands are possible with a 52-card deck?
How many 5-card hands are possible with a 52-card deck?
Answer:
Only 10, there will still be 2 cards left though.
Step-by-step explanation:
You're welcome.
the sumof the first two term of a g.p is 28 but the sum of the third and fourth term 252.find the second term of the g.p if the seventh term is 5103
S_ = a/(1 - r), where a denotes the first term and r denotes the common ratio, is the formula for calculating the sum of an infinite geometric progression.
What is Geometric Progression?If a series of phrases is called a geometric progression if each next term is created by multiplying each previous term by a fixed amount. (GP), while the common ratio refers to the constant value. As an illustration, a GP with the common ratio of 2 is 2, 4, 8, 16, 32, 64,...4 / 2 = 8 / 4 = 16 / 8 = 32 / 16 = 2.
Similarly,
A series of 1 through 5 and 1 through 16 is an example.1/2 / 1 = 1/4 / 1/2 = 1/8 / 1/4 = 1/16 / 1/8 = 1/2
The ratio is constant in the provided examples. Geometric Progressions are the name for such a series. G.P. is how it is shortened.When none of the terms in the sequence are zero, the constant r, often known as the common ratio, is used.A Sequence a1,a2,a3, ......,an,......... is a G.P, then ak + 1 / ak = r [k >1]The next step is to understand how to add GP when it has n words.To Learn more About geometric progression Refer To:
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The price of a technology stock has risen to $9.62 today. Yesterday's price was $9.55. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
0.73%
Step-by-step explanation:
First of all subtract the 2 values
9.62 − 9.55 = 0.07
then use this value and find the percentage from the original price which was 9.71 so 0.07/9.55 x 100
percentage increase is
0.73%
Tyrell is traveling to Chicago, Ilinois. He takes a cab service from the airport to his hotel.
The table shows the linear relationship between the number of miles the
Cab Fare
Number of Miles Total Fee
$15.00
5
$19.50
7
$22.50
10
$27.00
15
$34.50
What does the y-intercept mean in this situation?
O When the cab travels 0 miles, the total fee will be $1.50.
O When the cab travels 0 miles, the total fee will be $12.00.
O For every additional
mile the cab travels, the total fee increases by $1.50.
O For every additional mile the cab travels, the total fee increases by $12.00.
Y-intercept linear 12 shows that the total cost will be $12.00 when the taxi travels 0 miles.
How do you define a linear relationship?the connection between two variables that, when plotted on the coordinate plane, forms a straight line. The term "linear expression" refers to both the linear equation and the expression that depicts a linear relationship.
(2, 15), (5, 19.50), (7, 22.50), and (10, 27) are the coordinates (15, 34.50)
We will obtain a straight line if we plot the points on the XY coordinate system. The line crosses the Y axis at 12.00, as can be seen. As a result, the y-intercept is 12.00, and its coordinate is (0,12)
The y-intercept in this case is 12, which indicates that the total cost will be $12.00 even if the taxi travels 0 miles.
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1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval
-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.
On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
The factors of 5 are -
5and 1
as 5 = 5 X 1
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Which of the following is the product of the rational expressions shown
below?
2/x+1 • 5/3x
A. 5(x+1)/6x
B. 5/x^2+3
C. 10/3x+3
D. 10/3x^2+3x
Answer:
D. 10/3x^2+3x
Step-by-step explanation:
The product of the two rational expressions is:
(2/x+1) * (5/3x)
Multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:
(2*5) / (x+1) * (3x)
Which simplifies to:
10 / (x^2 + x)
So the correct answer is:
D. 10/3x^2+3x
Joey wants to buy several tickets to the next Jastin Timberlake concert. Each ticket will cost $150. Create a table of values to show the cost of buying up to 5 tickets. Show your work in the box
Ticket #1 ║ Ticket #2 ║ Ticket #3 ║ Ticket #4 ║ Ticket #5
$150 $300 $450 $600 $750
Step-by-step explanation:
The table shows tickets #1-5, but if you want to go up to tickets #6 and #7, then Ticket #6 would be $900, and Ticket #7 would be $1,050. Due to each ticket being equivalent to $150, you get your answer by adding 150 for each ticket or multiplying 150 × 7.
Determine the rate of change and initial value of the
linear function represented by the following scenario:
An airplane starts it's descent at an altitude (height) of
30,000 ft and descends at a rate of 2000 feet per
minute.
Answer:
13009 is the best answer for this question
What is the perimeter of trapezoid JKLM?
O√2+√5 units
O2+ √2+√5 units
O9+2√2 units
9+√2+√5 units
By applying pythagorean theorem and perimeter formula, The answer is D 9+[tex]\sqrt{2}[/tex] +[tex]\sqrt{5}[/tex]
What is pythagorean theorem?The Pythagorean theorem is a fundamental result in mathematics named after the ancient Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
What is perimeter?Perimeter is a measure of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The formula for perimeter depends on the shape. For example, the perimeter of a rectangle is twice the sum of its length and width, while the perimeter of a circle is equal to its circumference.
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Multiply. Write your answer as a decimal.
-0.05 × (-0.5)
The solution for the given decimal multiplication is 0.025.
What are decimal numbers and how do you multiply them?To multiply two decimal numbers, first multiply the values without the decimal points.
The digits in the factors that follow the decimal point should now be added together.
Following that, the dot should be placed in the product so that it has the same number of digits as the total number of factors.
If there are more decimal places than digits in the number, place zeroes immediately after the dot.
If there are more decimal places present compared to digits in the product, fill the decimal places with zeroes immediately after the dot.
For the given question, multiply -5 * -5 = 25
Now the total digits after the decimal point in factors are 3.
But there are only 2 digits in 25.
So fill the decimal place with a zero.
Therefore the product of given decimal numbers is 0.025.
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Determine the domain and range of the function:
The domain of the function is x ∈ [ -3, -∞) and range is {-3, -2, 1}.
What is domain and range?The set of allowable inputs, or all the x-values in the (x, y) points decided by the relation, is known as the domain of a relation (and, by extension, a function). All the y-values in the (x, y) points determined by the relation make up the range of a relation (and, by extension, a function).
Graphs can be used as a second method to define the domain and range of functions. A graph's domain is the entire set of input values represented on the x-axis because the term "domain" refers to the set of potential input values. The possible output values are displayed on the y-axis and make up the range.
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Question 9 of 10
What is the product of the following numbers? Use a scientific calculator to
find the answer.
5.56 x 104 x 2.43 x 106
A. 2.23 x 10-2
OB. 1.97 x 10²1
C. 1.35 × 1020
OD. 1.35 x 10¹1
The total energy, E, in joules of a metal cylinder with an angular velocity of w radians per second
and a height of h meters above the ground is given by the equation above. The height and
angular velocity are independent. Which of the following expressions is the energy due to the
angular velocity?
The energy due to the angular velocity is given by the expression: [tex]E = 1/2 * I * w^2[/tex], where I is the moment of inertia of the cylinder.
Inertia: What is it?Everyone uses inertia, although few people are familiar with it. Additionally, it touches on every thing or person at some time. It is also a state of repose or inaction.
Inertia at rest: Until and unless an external force greater than the inertial force is applied to the object, the inertia (opposing force) existent inside the item keeps the object at rest. A body in motion maintains its motion until and until an outside force (such brakes, friction, etc.) is applied to it.
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Jason is married and has one child. He also takes care of his dad. What
is the highest number of allowances can he claim?
Jason can claim a total of 3 allowances.
Number of allowances to be claimed
The number of allowances that Jason can claim on his taxes depends on the number of dependents that he has and the deductions that he is eligible for.
As a married person with one child and taking care of his dad, Jason can claim the highest number of allowances which is three. He can claim one allowance for himself, one for his child and one for his dad. Therefore, Jason can claim a total of 3 allowances.
It's important to note that the number of allowances is based on personal financial situation and this should be confirmed through IRS guidelines or tax professional.
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Suppose that this is not a complete graph of a particular function.instead,the function also has a local maximum at x=-4 what might be true about the function
The right answer is B, i.e., option c. It might be a polynomial of sixth degree with a negative leading coefficient.
what is function ?The study of mathematics covers numbers and associated variations, formulas and associated tissues, shapes with their locations, and locations where they might be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and results where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The function's negative leading coefficient
sixth-degree polynomial are determined by the local maximum,
which is x = -4. (x)
The right answer is B, i.e., option c. It might be a polynomial of sixth degree with a negative leading coefficient.
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Important
Given AABC ~ ADE F, determine the following information.
Determine the measure of LB. Show the work that leads to your answer.
Determine the length of EF. Show the work that leads to your answer.
Answer:
m∠B = 83°
EF = 10
Step-by-step explanation:
Two triangles are similar if their corresponding angles are the same size.
Therefore if ΔABC ~ ΔDEF then:
∠A ≅ ∠D = 24° ∠B ≅ ∠E∠C ≅ ∠F = 73°Interior angles of a triangle sum to 180°:
⇒ m∠A + m∠B + m∠C = 180°
⇒ 24° + m∠B + 73° = 180°
⇒ m∠B + 97° = 180°
⇒ m∠B = 83°
In similar triangles, corresponding sides are always in the same ratio.
Therefore if ΔABC ~ ΔDEF then:
⇒ AB : DE = BC : EF = CA : FD
⇒ 12 : DE = 8 : EF = 16 : 20
Therefore, to find the length of EF:
[tex]\implies \sf 8 : EF = 16 : 20[/tex]
[tex]\implies \sf \dfrac{8}{EF} = \dfrac{16}{20}[/tex]
[tex]\implies \sf 8 \cdot 20= 16 \cdot EF[/tex]
[tex]\implies \sf160= 16 \cdot EF[/tex]
[tex]\implies \sf EF=\dfrac{160}{16}[/tex]
[tex]\implies \sf EF=10[/tex]
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 68%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie from the batch would be likely. That is option A
What is probability?Probability is defined as the possibility of an outcome of an event which may likely or unlikely occur.
The batch contains the following content:
chocolate chip,(68%)oatmeal raisin, and sugar cookiesThe chocolate chip makes up 68% of the batch and this shows a higher quantity than other content. Therefore, likelihood of randomly selecting a chocolate chip cookie from the batch would be likely.
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what are the stpes to answer 9 - 3 7/8
The subtraction is equal to the mixed number below:
9 - (3 + 7/8) = 5 + 1/8
How to solve the subtraction?Here we want to solve the expression below:
9 - (3 + 7/8)
So we have a whole number and a mixed number.
First we can subtract the two whole numbers so we get:
9 - (3 + 7/8) = (9 - 3) - 7/8
= 6 - 7/8
Now, to have a mixed number the fraction needs to be positive, so we can write:
6 - 7/8 = 5 + 1 - 7/8
5 + 1 - 7/8 = 5 + 1/8
That is the answer.
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Lily received 50 postcards. 16% of them were from Thailand. After he received ostcards from Thailand, the percentage of Thailand postcard increased to 30%. How many Thailand postcards did he receive?
Answer:
Step-by-step explanation:
Final answer: Lily received 10 postcards from Thailand.
Explanation: Number of postcards=50
Percentage of postcards from thailand= 16
Number of postcards from Thailand= 16/100*50= 8
Now, he received some postcards from Thailand. Let the number of postcards received from Thailand be x. Therefore,
Number of postcards=50+x
Number of postcards from Thailand= 8+x
We know that the percentage of postcards from Thailand now is 30.
Therefore,
30=(8+x/50+x)*100
0.3(50+x)=8+x
15+0.3x=8+x
0.7x=7
x=10
Therefore, he received 10 postcards from Thailand.
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Jennifer has 256 beads stella has 3 times more beads tiah had104
beads
The total number of beads will be 1128 beads.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
In this case, Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads.
The total number of beads will be:
= 256 + (256 × 3) + 104
= 256 + 768 + 104
= 1128
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Complete question
Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads. What is the total number of beads?