The function below contains ordered pairs of the form (x, y) -
f(x)={(6,5), (2, 3), (1,4)}
What is the range of the function?
Answer: [tex]\{4, 5, 6\}[/tex]
Step-by-step explanation:
The range of a function is the set of outputs (which is the set of [tex]y[/tex]-coordinates).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = negative one-half(x – 4) y – 1 = one-half(x – 4) y − 1 = 2(x − 4)
Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9
What is equation?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the formulas 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" between them.
Here,
If two lines have the same slope, they are considered to be parallel.
This will allow us to determine the equation for the line that is perpendicular to the graphed line and goes through the points (4, 1): y = -2*x + 9.
Let's try to locate the line as follows:
Finding the graphed line's slope is the first step towards locating the line.
Keep in mind that a generic statement is anything like:
y = a*x + b
where a represents the slope and b the y-intercept
If the line does indeed travel through the points (x1, y1) and (x2, y2), then the slope of that line can be expressed as follows:
[tex]m=\frac{y_{2}- y_{1}}{x_{2} -x_{1} }[/tex]
As seen below, the graphed line crosses (-3, 3) and (-2, 1). The slope will therefore be:
[tex]m=\frac{1- 3}{2 -(-3) }[/tex]
Since the parallel line's slope is likewise 2, it will look somewhat like this:
y = -2*x + c
Using the knowledge that this line passes through, we may determine the value of c. (4, 1).
Thus, y = 1 must exist when x = 4.
When we swap these out in the line equation, we get:
-2*4 + c = 1
-8 + c = 1
1 + 8 = c = 9
Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9
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Suppose you have two options from which to choose a pay raise for each of the next two years.
Option A: You received a $6,000 raise in year 1 and then 4% raise in year 2.
Option B: You receive a 4% raise for 1 year and then a $6,000 raise in year 2.
Which option will result in you making more money? Explain.
We see that under option B, you will make more money than under option A.
What is a percentage?
A relative value indicates the hundredth part of any quantity. One percent (symbolized 1%) is the hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
To compare the two options and determine which one will result in you making more money, we need to find the total amount of money you will make under each option.
Under option A, you will receive a $6,000 raise in year 1 and a 4% raise in year 2. Let's call your base salary S. After the first year, your salary will be S + $6,000. After the second year, your salary will be (S + $6,000) * 1.04 = S + $6,240.
Under option B, you will receive a 4% raise in year 1 and a $6,000 raise in year 2. After the first year, your salary will be S * 1.04 = S + $480. After the second year, your salary will be (S + $480) + $6,000 = S + $6,480.
Comparing the two options, we see that under option B, you will make more money than under option A. This is because option B includes a $6,000 raise in the second year, while option A includes a smaller 4% raise in the second year.
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8/3x+1/3x=3 1/3+ 7/3x
find value of x
An equation is a formula that expresses the equality of expressions, with the aid of using connecting them with the equals signal =. The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.
The required details for equation in given paragraph
The word equation and its cognates in different languages can also additionally have subtly extraordinary meanings; for example, in French an equation is described as containing one or more variables, whilst in English, any well-shaped formula which includes expressions associated with an equals signal is an equation. Solving an equation containing variables includes figuring out which values of the variables make the equality true. The variables for which the equation must be solved also are called unknowns, and the values of the unknowns that fulfill the equality are called solutions of the equation.
To find the value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x, we need to first get all of the terms with x on the same side of the equation.
We can start by moving the 3 1/3 to the right side of the equation by subtracting it from both sides:
8/3x + 1/3x - 3 1/3 = 7/3x - 3 1/3
Next, we can combine the coefficients of x on the left side of the equation:
(8/3 + 1/3) x = (7/3 - 3 1/3)
4/3 x = 4/3
Finally, we can divide both sides of the equation by 4/3 to find the value of x:
(4/3) x / (4/3) = (4/3) / (4/3)
x = 1
Therefore, The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.
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Answer:
x = 5
Step-by-step explanation:
8/3x+1/3x=3 1/3+ 7/3x
find value of x
8/3x + 1/3x = 3 1/3 + 7/3x
3x = 7/3x + 10/3
2/3x = 10/3
x = 5---------------------------
check8/3 x 5 + 1/3 x 5 = 3 1/3 + 7/3 x 5
15 = 15
the answer is good
A sales tax is charged on some items at a grocery store but not charged on others. When the
taxable items total t dollars and the non-taxable items total n dollars, the total bill is 1.06t +
n dollars. Malia went shopping yesterday. She spent $20 on taxable items and $8.20 on non-
taxable items.
How much was Malia's total grocery bill?
Answer:24.90
Step-by-step explanation: My brain
f(x) = 2(3)^x What are the coordinates of the y-intercept of the function? Enter your answer by filling in the boxes.
Answer: (0,2)
Step-by-step explanation:
to find the y intercept, solve for f(x) when x = 0
f(0) = 2(3)^0 = 2(1) = 2
therefore the coordinates of the y intercept are (0,2)
The Beta club sold hot pretzels as a fundraiser. The pretzels normally sold for $2.00, but near the end of the sale, the price was reduced by 25%. What was the new price for a hot pretzel?
Answer: The new price for a hot pretzel is 1.50
Step-by-step explanation: 200*75/100=150
HELP I WILL GIVE BRANLIEST IF CORRECT The steps to solving the expression the quantity of the sum of seven squared plus three divided by the absolute value of negative 0.5 end quantity minus 18.6 ÷ 6 are listed below.
Part A: Explain what the missing expression should be in Step 4. (6 points)
Part B: Explain what the missing expression should be in Step 6. (6 points)
Using the absolute value and PEMDAS order of operations, it is found that:
a) The missing expression for step 2 is: (36 + 2)/0.5 = − 14.8 ÷ 8.
b) The missing expression for step 6 is 76 - 1.85.
How to properly use mathematical operations?The absolute function is defined by:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
Thus, it usually measures the distance of a point x to the origin, hence |0.5| = |-0.5| = 0.5
In Step 2, we just have to apply the absolute value property to |-0.5|, and as such, the missing expression for step 2 is:
(36 + 2)/0.5 = − 14.8 ÷ 8.
For step 6, the division happens before the multiplication using PEMDAS order of operations and as such, the missing expression for step 6 is;
76 - 1.85.
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The missing steps are;
Step 1 the quantity of the sum of six squared plus two divided by the absolute value of negative 0.5 − 14.8 ÷ 8
Step 2
Step 3 the quantity of the sum of thirty six plus two divided by 0.5 − 14.8 ÷ 8
Step 4 the quantity thirty eight divided by 0.5 − 14.8 ÷ 8
Step 5 76 − 14.8 ÷ 8
Step 6
Step 7 74.15
Write an equation for the nth term of the sequence 12, 5, -2, -9,...
3. Given that x = 3 and y = 4, find the value of the following
expression (3x + 4y)^2 + (8x + 7y)² + 24xy
Answer: 3353
Let's solve this equation:
[(3)(3)+(4)(4)]2+[(8)(3)+(7)(4)]2+(2)(3)(4)
=(9+(4)(4))2+((8)(3)+(7)(4))2+(2)(3)(4)
=(9+16)2+((8)(3)+(7)(4))2+(2)(3)(4)
=252+((8)(3)+(7)(4))2+(2)(3)(4)
=625+((8)(3)+(7)(4))2+(2)(3)(4)
=625+(24+(7)(4))2+(2)(3)(4)
=625+(24+28)2+(2)(3)(4)
=625+522+(2)(3)(4)
=625+2704+(2)(3)(4)
=3329+(2)(3)(4)
=3329+(6)(4)
=3329+24
=3353
Hope this helps!!
A bag contains 10 balls.
4 are red and 6 are blue.
2 balls are taken from the bag at random without replacement.
a) Write down the probability that there are at least 2 red balls still in the bag. (1)
b) Write down the probability that there are at least 3 red balls still in the bag. (3)
Your final line must say, P(at least 3 red) = a/b where a and b are integers.
Feedback
Total marks: 4
Answer:
Step-by-step explanation:
a) since there are 4 red balls, at least 2 of them will ever remain in the bag
probability = 100% = 1
b) probability that 2 red balls are taken
4/10 x 3/9
2/5 x 1/3
2/15
15/15 - 2/15 = 13/15
P(at least 3 red) = 13/15
Which of the following equations have exactly one solution?
Choose all answers that apply:
(Choice A)
A
-5x+12=5x-5
(Choice B)
B
-5x+12=-5x-12
(Choice C)
C
-5x+12=5x+12
(Choice D)
D
-5x+12=-12x-12
Option A and D are appropriate.
What does the one solution mean?There is just one correct answer to some equations. There is only one value for the variable in these equations that causes the equation to be true. If you solve an equation and the result is a variable equal to a number, the problem has just one solution.
To date,
1) x has just one solution since -5x + 12 = 5x -5
-5x -5x = -5 -12
-10x = -17
x = 1.7
2) -5x+12=-5x-12 -5x + 5x = -12-12
0x (not possible)
3) -5x+12=5x+12 -5x + 5x = +12-12
0x ( not possible)
4) The equation -5x+12=-12x-12
-5x + 12x = -12 -12
7x = -24
x = -24/7, indicating that x has just one solution.
Option A and D thus have a single solution.
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If I had 24 assignment and had to get them done in 13 days how many assignments should I do I day
Answer:
2 per day
Step-by-step explanation:
S
Melissa wants to make a table representing the area of her vegetable garden for a variety of different
lengths of the tomato patch. She uses her area expression to create the table.
Complete the table by typing the correct answer in each box. Use numerals instead of words. Do not
round your decimal answers.
n
3
Length of Tomato Patch
(in feet)
Area of Vegetable Garden
(in square feet)
338
18. 38
ng
to
0
in
6. 5
42. 25
12. 13
147. 25
49
7
m
our
Dart B
hall nenners. Since the space
The appropriate numerical values to fill out Melissa's table using the area of the square are:
(A) 13√2 or 18.384776 ft.
(B) 42.25 square ft.
(C) 12.13466 ft.
(D) 49 square ft.
What is the area?The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.
Create a square on paper by using a pencil.
Two dimensions make it up.
A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
So, the area of the square:
A = x²
By changing the parameters in the formula, we obtain:
338 = x²
x = √338
x = √2 × √169
x = 13√2 or 18.384776 feet.
Following is row 2:
A = 6.5²
A = 42.25 square feet.
The following is row 3:
147.25 = x²
x = √147.25
x = 12.13466 feet.
Regarding row 4, we have:
A = 7²
A = 49 square feet.
Therefore, the appropriate numerical values to fill out Melissa's table using the area of the square are:
(A) 13√2 or 18.384776 ft.
(B) 42.25 square ft.
(C) 12.13466 ft.
(D) 49 square ft.
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Correct question:
Melissa wants to make a table representing the area of her vegetable garden for a variety of different lengths of the tomato patch. she uses her area expression to create the table. complete the table by typing the correct answer in each box. use numerals instead of words. do not round your decimal answers.
is 0.25 L less than or greater than 2,500 ML
Answer:
Equal to.
Step-by-step explanation:
there's 1000 ML in one L
so .25 x 1000 =
2500
which would mean they're equal
ashley was born on 06/10/1961. how many 8 digit codes could she make using the digits in her birthday
3360, 8 digit codes could she make using the digits in her birthday.
What is the 4 digit code?
A quick, thorough, and evidence-based method for diagnosing the full range of outcomes seen in people who have had prenatal alcohol exposure is the 4-Digit Code.
Given the date:
Birth date = 12/24/2002 06/10/1961
Number of digits = 8 = 8! = (8*7*6*5*4*3*2*1) = 40320
Repeated digits :
digit 6 = 2 times = 2! = 2*1 = 2
digit 1 = 3 times = 3! = 3*2*1 = 6
Therefore the number of 8 digit codes that can be formed is :
8! / (2! * 3!)
40320 / (2 * 6)
40320 / 12
= 3360
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What is 2 1/4 divided by 4????
1. 5/8
2. 1/10
3. 10
4. 1 3/5
Step-by-step explanation:
2 1/4 = 9/4
9/4 ÷ 4
9/4 x 1/4
9/16
so neither of these answers?
Find the difference between (5.5n^2 + 8-3) and (-3n^2-5)
How can -6.75 + -10.25 be expressed as the sum of its integer and decimal parts
-17 can be expressed as the sum of its integer and decimal parts.
-6.75+(-10.25)
Remove parentheses: (-a)=-a
=-6.75-10.25
Subtract the numbers: -6.75-10.25=-17
=-17
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
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A 12-ounce box of cereal costs $4.80. Which equation relates the price, p, to the weight, w, in ounces, of the cereal correctly?
Responses
The correct equation is [tex]P = 2.5w[/tex] .
What is cost and equation ?The average cost is the ratio of the total of cost of all the products to the total number of products.
The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
An equation says that two things are equal. It will have an equals sign "=" .
A 12-ounce box of cereal costs $4.80.
The price be 'P' and weight be 'w'.
$4.80 is the price of box with weight 12-ounce
i.e. 4.80P = 12w
Divide both side by 4.80
[tex]\frac{4.80P}{4.80} = \frac{12w}{4.80}[/tex]
[tex]P = 2.5w[/tex]
Therefore, the correct equation is [tex]P = 2.5w[/tex] .
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Is the triangle formed by joining the points A (1, 9), B (7, 1), and C (−5, 1) isosceles? Justify your answer.
A. Yes. AB=(1−1)2+(9−7)2−−−−−−−−−−−−−−−√; BC=(7−5)2+(1−1)2−−−−−−−−−−−−−−−√
B. Yes. AB=(1−7)2+(9−1)2−−−−−−−−−−−−−−−√; CA=(−5−1)2+(1−9)2−−−−−−−−−−−−−−−−√
C. No. BC=(7+5)2+(1−1)2−−−−−−−−−−−−−−−√; CA=(−5−1)2+(1−9)2−−−−−−−−−−−−−−−−√
D. No. BC=(7−5)2+(1−1)2−−−−−−−−−−−−−−−√; CA=(−5−1)2+(1−9)2−−−−−−−−−−−−−−−−√
Yes, the triangle formed by joining the points A (1, 9), B (7, 1), and C (−5, 1) isosceles
What are Triangles?Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object.
A polygon also includes a triangle.
Triangles have three sides.
Triangles have three sides. The sides of the triangle ABC are AB, BC, and CA.
The angle of a triangle is represented by the symbol and represents the angle created by any two of its sides.
Three angles make compose a triangle. The triangle ABC has the following three angles: ABC, BCA, and CAB. The names of these angles are B, C, and A, respectively.
The point of intersection of any two sides of a triangle is known as a vertex.
A triangle's vertex is the location where any two of its sides cross. The vertices of a triangle are three. The vertices of the triangle ABC are A, B, and C.
Hence, Yes, the triangle formed by joining the points A (1, 9), B (7, 1), and C (−5, 1) isosceles.
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y=3x + 1 if x =-2 then y=?
Answer:
Step-by-step explanation:
If x equals -2 then you multiply 3 times -2 which equals -6 then add 1. Your total then is -5. Y equals -5
Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y – 10 = –2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
How much did the bicycle cost?
Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.
What is an equation?
An equation is written in the form of variables and constants separated by the operation of multiplication and division.
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
According to the given question:
Hugo decided to pay $2 a week to his brother to buy a bicycle.
The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
To pay back to the brother he must owe no money which is y = 0.
∴ The weeks needed is,
0 - 10 = -2(x - 10).
- 10 = -2x + 20.
2x = 30.
x = 15.
He needs 15 weeks to pay back completely.
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Simplify
f(x) = 8x+5 find f(5)
Answer: To find the value of f(5), we need to substitute 5 for x in the expression f(x) = 8x+5. This gives us:
f(5) = 8*5+5 = 45
So, the value of f(5) is 45.
Which equation justifies why 73=3√7? (1 P
(73) - 7(6-0)-7
=7
O
O
° () .,(-4).
73
=7
(1)-(-)-
= 7
= 7
? (1 point)
Seven to the one third is the power all raised to the third of the power equals seven to the one of the third times three of power equals to seven.
What is power?Power is the amount that is the energy of to transferred or the converted per the unit.
Applying Power of a Power Property,
(X^a)^b= x^a×b
i.e. a power to the power, multiply by the exponents as
7^1/3 =√7
√7=7^1/3
We have given, seven to the one third power equals to the cube root of seven of
7^1/3=√7
√7= 7^1/3
Raise to the third power,
[7^1/3]^3
Applying the property ,
7^3/3=7^1 =7
i.e. seven to the one thirdly power all of the raised to the thirdly power equals to seven to the one of third times of three power equals to the seven.
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For the function f(x) = 2x +8, determine f(-3)
A) 2
B) 3
Answer:
2
Step-by-step explanation:
we replace x with -3
f(-3)=2(-3)+8
f(-3)=-6+8
f(-3)=2
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use distributive property to create an equivalent expression to 40+4x.
Answer:
4(10+x)
Step-by-step explanation:
find the gcf: 4
divide everything by the gcf: 4(10+x)
Answer:There are 3 answers 4(10+x), 4(10)+4(x), 40+4x
A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 3 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 18000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction.
The radius of the cylindrical base (and of the hemisphere) is ? ft.
(Rounding to the nearest tenth as needed.)
Answer:
The radius of the cylindrical base (and of the hemisphere) is 10.2 ft.
what is the probability of drawing two aces from a standard deck of cards, given that the first card is an ace? the cards are not returned to the deck.
1/34 is the probability of cards are not returned to the deck.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics is the study of events subject to probability.
A = the first card of ace.
B = Drawing two ace from a standard deck
P(AB) = ²C₄ / ²C₃₂
P(A) = ¹C₄ ¹C₅₁ / ²C₃₂
P(B/A) =P(AB)/P(A)
= ²C₄ / ²C₃₂ * ²C₃₂ / ¹C₄ ¹C₅₁
= ²C₄ /¹C₄ ¹C₅₁
= 1/2 * 17
= 1/34
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which expression is equal to (-2ab)^3 (-a^2b)
By using exponent, it can be calculated that
[tex](-2ab)^3 (-a^2b)[/tex] = [tex]8a^5b^4[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a .... \times a[/tex] (m times), a is the base and m is the index.
The laws of indices are
[tex]a^m \times a^n = a^{m + n}\\\\a^m\div a^n = a^{m - n}\\\\(ab)^m = a^mb^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}[/tex]
Now,
The given expression is
[tex](-2ab)^3 (-a^2b)[/tex] =
[tex](-8a^3b^3)(-a^2b)\\[/tex]
[tex]8a^{3+2}b^{3+1}[/tex]
[tex]8a^5b^4[/tex]
So, the expression [tex](-2ab)^3 (-a^2b)[/tex] is simplified [tex]8a^5b^4[/tex]
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