The most appropriate choice for function and domain and range of a function will be given by -
Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}
Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}
What is a function and domain and range of a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is the domain of the function and the values obtained on substituting the values of domain in the function is the range of the function.
y = [tex]\frac{x -5}{2x + 4}\\[/tex]
For domain of y
y is not defined if 2x +4 = 0
y is not defined if [tex]x = -\frac{1}{2}[/tex]
Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}
For range of y
let [tex]\frac{x -5}{2x + 4}\\[/tex] = z
[tex]x - 5 = z(2x +4)\\x - 5 = 2zx + 4z\\x - 2zx = 4z + 5\\x(1 - 2z) = 4z + 5\\x = \frac{4z + 5}{1 - 2z}[/tex]
If y = [tex]\frac{1}{2}[/tex]
[tex]\frac{x-5}{2x + 4} = \frac{1}{2}\\2x - 10 = 2x + 8\\-10 = 8\\[/tex]
Not possible
[tex]\frac{1}{2}[/tex] is not in the range of y
Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Which two transformations would map the blue pre-image to the red image?
d) reflection over x axis and translation 6 units right
<
Which table has a constant of proportionality between y and c of 3/4?
Answer:
answer Is A.............
Please help me solve this
On solving the expression 1/2 - 1/10 we get 2/5
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example - 5/9. Here, (5) is called numerator and (9) is called denominator.
Given is the following expression -
1/2 - 1/10
We have -
1/2 - 1/10
Multiplying the denominator and numerator in 1/2 by 5, we get -
5/10
Now, the expression becomes -
5/10 - 1/10
(5 - 1)/10
4/10
2/5
Therefore, on solving the expression 1/2 - 1/10 we get 2/5.
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Express your answer as a polynomial in standard form.
f(x) = 2x² + 3x + 12
g(x) = 5x - 6
Find: (gof)(x)
The answer as a polynomial in standard form is 50x² - 45x +66.
What are polynomials?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of a single indeterminate x polynomial. Sums of terms with the pattern k x n—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
g(x) = 5x - 6
So,
f(x) = 2(5x - 6)² + 3(5x - 6) + 12
= 2( 25x² + 36 - 60x ) + 15x - 18 + 12
= 50x² + 66 - 45x
= 50x² - 45x +66
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Solve the problem. Express your answer to the correct number of significant figures.
6.221 × 7.11 − 13.7 =
We need to know about significant figures to solve this question. The value of the expression is 30.53131
Significant figures are the number of digits in a value that contribute to the degree of accuracy of the value. In the given expression we have three decimal numbers that have different significant figures, we need to solve the expression to get the answer with the right number of significant numbers. When a number starts with zero, the zeros are not significant, when a decimal number ends with zero, the zeroes are not significant.
6.221x7.11-13.7=44.23131-13.7=30.53131
Therefore the solution of the expression is 30.53131
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can you please help me with my homework and I have a picture of it. 2 raised to the power 3
The power 3 means "multiplying 3 copies" of (in our case) 2 ;
[tex]2^3=2\times2\times2[/tex]which is equal to 8.
Answer:
8
Step-by-step explanation:
HELP please
Giving brainlyest
The equation of the line that contains (-4, 6) and (7, -5) in point slope form is y + 5 = - 1(x - 7).
How to represent equation in point slope form?The point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinates.Therefore, the equation of the line that contains (-4, 6) and (7, -5) can be found in point slope form as follows:
Hence,
m = -5 - 6 / 7 + 4
m = - 11 / 11
m = -1
Therefore, using (7, -5)
y + 5 = - 1(x - 7)
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2. Big TV prices Here are prices and screen sizes (in inches, measured diagonally) for 7 different sizes of one brand of LED HD television.47 Use technology to calculate the equation of the least- squares regression line relating y = price to x = screen size. Screen size Price 60 1000 55 800 50 700 47 600 42 430 39 400 32 300
The general formula for the least-squares regression is:
[tex]y=a+bx_i[/tex]Where
a represents the y-intercept
b represents the slope
To estimate the y-intercept and the slope of the regression line you have to apply the following formulas:
[tex]b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\lbrack\Sigma x^2-\frac{(\Sigma x)^2}{n}\rbrack}[/tex][tex]a=\bar{y}-b\bar{x}[/tex]First, calculate the sums and the means for both variables.
X= screen size
Y= price
n=7
[tex]\begin{gathered} \Sigma x=60+55+50+47+42+39+32 \\ \Sigma x=325 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2=60^2+55^2+50^2+47^2+42^2+39^2+32^2 \\ \Sigma x^2=15643 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{\Sigma x}{n} \\ \bar{x}=\frac{325}{7} \\ \bar{x}=46.43 \end{gathered}[/tex][tex]\begin{gathered} \Sigma y=1000+800+700+600+430+400+300 \\ \Sigma y=4230 \end{gathered}[/tex][tex]\begin{gathered} \bar{y}=\frac{\Sigma y}{n} \\ \bar{y}=\frac{4230}{7} \\ \bar{y}=604.29 \end{gathered}[/tex][tex]\begin{gathered} \Sigma xy=60\cdot1000+55\cdot800+50\cdot700+47\cdot600+42\cdot430+39\cdot400+32\cdot300 \\ \Sigma xy=210460 \end{gathered}[/tex]Calculate the slope of the line:
[tex]\begin{gathered} b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\Sigma x^2-\frac{(\Sigma x)^2}{n}} \\ b=\frac{210460-\frac{325\cdot4230}{7}}{15643-\frac{325^2}{7}} \\ b=\frac{210460-196392.85}{15643-15089.29} \\ b=\frac{14067.75}{553.71} \\ b=25.41 \end{gathered}[/tex]Once you have calculated the slope, you can calculate the y-intercept:
[tex]\begin{gathered} a=\bar{y}-b\bar{x} \\ a=604.29-25.41\cdot46.43 \\ a=604.29-1179.7863 \\ a=-575.23 \end{gathered}[/tex]The regression line for the price with respect to the screen size is:
[tex]y=-575.23+25.41x[/tex]Find the unknown value please helppp
Answer:
30
Step-by-step explanation:
To get from 15 to 5, you multiply 15 times 1/3, so do the reciprocal to get from x to 10. So, 10 times 3 is 30.
What is the monthly payment for a $4,000 two-year loan with an APR of 4%?
A loan calculator is an automated instrument that enables you to comprehend what your potential monthly loan payments and total loan cost might be. Online, you can find a variety of loan calculators, such as those for mortgages or other kinds of specialized loans.
What is the cost of a $4000 loan every month?The amount due each month is $4000.
Detailed explanation:
Given: $4168.79 in total interest has been paid for a loan with a two-year term at 4% interest compounded monthly.
Identify: What is the loan's monthly payment?
Answer: $4168.79 in total interest for a two-year loan compounded monthly.
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Angelica's bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the
bouquet is pink roses? There are 12 roses in a dozen.
O
O
O
5
12
12
517
775
Answer: 7/12
Step-by-step explanation:12/12-5/12=7/12
Kinsley is thinking of a secret number, she tells her brother the number she's thinking of is divisible by 3, then tells her friends it's divisible by 17, if Kinsley is telling the truth to both of them, what could be the number she is thinking of?
Answer:
51
Step-by-step explanation:
17 x 3 = 51. To check this answer, you can do
51 ÷ 17 = 3
51 ÷ 3 = 17
what is the answer to -3(4-5b+7)
Answer:
-33+15n
Step-by-step explanation:
You will have to first distribute the -3.
-3*4 is equal to -12
-3*-5b is equal to 15b Note: -*-=+
-3*7 is equal to -21
Once you get those numbers you will have a equation like this
-12+15b-21
Combine like terms and you will get -33+15n as you answer
Which equation is perpendicular to
5-10y=6
and passes through (2.1)
Answer: x=2
Step-by-step explanation: Because there is only one variable in this equation, it makes a straight line. so to get a line, just do x= blank, but you need a point to go through (2,1), so x-2 is your equation.
Please help mee,
It’s what I’m doing in technology class
Area of square with side = 4cm is : 16cm²
Area of rectangle with height = 2cm and width = 3cm is : 6cm²
Explanation :To find the area of square:
A square is a two-dimensional figure with equal-sized sides. Because all of the sides are equal, the area is length times width, which equals side side. As a result, the area of a square is side square.Area = a×a
= a²
To find the area of rectangle :
In the rectangle opposite sides are equal .The area of a rectangle is calculated once the length and width are known. A rectangle's area can be calculated by multiplying its length and width.Area = l x b
Given sides of square a = 4cm .
Area = a²
Area = 4²
= 16 cm²
Given sides of rectangle ,
l = 3cm
b = 2cm
Area = l × b
= 3 × 2
= 6 cm²
Area of square is 16 cm²
Area of rectangle is 6 cm²
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5.
Amelia buys 6 cans of beans for $1.50 each. She also buys a
pineapple. The total cost of the items is $12.30, What is the cost of
the pineapple?
The residents of a village want to paint a sign that shows the
The residents of a village want to paint a sign that shows the elevation of their village relative to the sea. Their altimeter shows +2,100 feet. What should their signboard read?
A.
2,100 feet above sea level
B.
2,100 feet below sea level
C.
-2,100 feet above sea level
D.
+2,100 feet below sea level
A. 2,100 feet above sea level
B. 2,100 feet below sea level
C. -2,100 feet above sea level
D. +2,100 feet below sea levelEXPLANATIONDepth above water levels refers to a location's peak just above ocean.
If indeed the height is positive (+) then the depth might well just above water level and if negative (-) therefore the depth will be lower than the water level.
help me a=1/7(b+c-d-d)
The simplified equation of the equation given as a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d
How to simplify the equation?From the question, the equation is given as
a=1/7(b+c-d-d)
Rewrite the above equation properly
So, we have the following representation
a = 1/7(b + c - d - d)
Evaluate the like terms in the above equation
So, we have the following equation
a = 1/7(b + c - 2d)
Open the brackets in the above equation
So, we have the following equation
a = 1/7 * b + 1/7 * c - 1/7 * 2d
Evaluate the products in the above equation
So, we have the following equation
a = b/7 + c/7 - 2/7d
The above equation cannot be further simplified
So, we leave it like that
Hence, the simplified equation of a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d
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Tim bought a pair of Zeus running shoes on sale that were marked down 25% to $60 what was the original price of the shoe
Tim bought a pair of running shoes marked 25% down at a price of $60
The formula to find the discount of an item on sale is
[tex]\text{ \% discount =}\frac{Discount\text{ price}}{\text{Original price}}\times100\text{\%}[/tex]Where
[tex]\begin{gathered} \text{Discount price = \$60} \\ \text{\% discount = 25\%} \end{gathered}[/tex]Let k represent the original price
Substitute the values into the formula above
[tex]\begin{gathered} 25=\frac{60}{k}\times100 \\ \text{Crossmultiply} \\ 25\times k=60\times100 \\ 25k=6000 \\ \text{Divide both sides by 25} \\ \frac{25k}{25}=\frac{6000}{25} \\ k=\text{\$240} \end{gathered}[/tex]Hence, the original price, k, of the pair of Zeus running shoes is $240
1. Kylie mowed Mr. Johnson's lawn for
4 weeks. Every week Mr. Johnson
paid Kylie $15.43. How much money
did Kylie earn after the four weeks?
$71.62
c. $60.72
b. $61.72
d. $70.62
Answer:
The answer is b. $61.72
Step-by-step explanation:
Since she mowed the lawn for 4 weeks, and each week Kylie earned $15.43, then 4 x 15.43 = $61.72 after 4 weeks.
If the odds against an event are 4:7, then the probability that the event will fail to occur is
The odds against an event is 4:7
Unfavourable elements for the event = 4
Favourable elements for the event = 7
Total = 4 + 7 = 11
Hence the probability that the event will fail = 4/11.
PLEASE HELP!! These two shapes are similar. True or False?
(Be sure to use the two rules of similarity to make your choice)
A- True, because the corresponding side lengths are proportional and the corresponding angles are congruent.
B- False, because the corresponding side lengths are congruent but the angles are not proportional.
C- False, because the corresponding side lengths are congruent but the angles are not proportional.
D- True, because the corresponding side lengths and corresponding angles are the same size.
Answer:
True, because the corresponding side lengths are proportional and the corresponding angles are congruent.
Step-by-step explanation:
The statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
The two triangles are shown in the picture.
As we know from the definition of a similar triangle, two triangles have the same shape, but it is not compulsory to have the same size.
The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
As we can see in the picture, the relevant angles are congruent and the corresponding side lengths are proportionate.
The triangles are similar.
Thus, the statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.
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for a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as a. small as that provided by the sample. b. large as that provided by the sample. c. small as that provided by the population. d. large as that provided by the population.
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic is at least as small as that provided by the sample.
Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Probabilistic analysis of events is called statistics.
The lower-tailed test is a one-tailed test in which the critical region of the distribution is one-sided (leftmost) and tests whether a sample is less than a specified value.
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If 6/7 of 28 is divided by 2/9 of 21, what is the quotient?
Answer: 5.150
Step-by-step explanation:
1. Multiply 28 by 6/7
2. Multiply 21 by 2/9
3. Divide 24 by 4.66
Pic below!! Find the surface area of a cube with side length of three meters.
Eva is making smoothies. Each smoothie uses scup of yogurt. How many
cups of yogurt does she need to make 4 smoothies? Express your answer in
simplest form.
Cups of yogurt she needs to make 4 smoothies is 20 cups
What is Fraction?
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
Given,
5cups of yogurt is used to make 1 smoothie
We have to find out that how cups of yogurt will it take to make 4 smoothies
1 smoothie = 1 x 5cups
4smoothies = 4 x 5cups
= 20 cups
Hence, 20 cups of yogurt is needed to make 4 smoothies
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The prime factor trees for 14 and 15 are
shown.
a) Write down the lowest common
multiple (LCM) of 14 and 15 as the
product of its prime factors.
b) Hence, work out the lowest common
multiple (LCM) of 14 and 15.
2
14
7
3
15
5
Answer:
14 = 2 * 7
15 = 3 * 5
LCM = 2 * 3 * 5 * 7 = 210
Parking for 4 hours costs $10. Parking for 5 hours costs $12. Is this a proportional relationship, and if so, what is the constant of the proportionality
No, this is not a proportional relationship.
Proportional relationships are relationships between two variables where their ratios are equivalent.
In this scenario the ratio between 4 hours and $10 parking cost comes out to be 10/4=2.5
But in the second case the ratio between 5 hours and $12 paring cost comes out to be 12/5=2.6
Since the ratios don't come out to be equal therefore this is not a proportional relationship .
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I need help please!!
The most appropriate choice for slope will be given by -
1) Initially, as x increases, y also increases
2) Slope of the graph between x = 3 and x = 5 is 2
3) Slope of the graph between x = 5 and x = 9 is -1
4) Greatest value of y is y = 4 and it occurs when x = 5
What is slope of a line?
Slope of a line is equal to the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, slope = tan [tex]\theta[/tex]
Suppose [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]be two points on a line then the slope of the line is calculated by the formula
slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here,
1) Initially, as x increases, y also increases
2) Slope of the graph between x = 3 and x = 5 = [tex]\frac{4 - 0}{5 - 3}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
3) Slope of the graph between x = 5 and x = 9 =
[tex]\frac{4 - 0}{5 - 9}\\-\frac{4}{4}\\-1[/tex]
4) Greatest value of y is y = 4 and it occurs when x = 5
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the sum of a number v and 6.2 is at least -4.7
Answer:
We are required to write an inequality for the expression and also solve it
The number y is at least 10.9
let
the unknown number = y
The sum of a number y and 6.2 = y + 6.2
y + 6.2 ≤ -4.7
y ≤ -4.7 - 6.2
y ≤ 10.9
Step-by-step explanation:
