Let the coordinates of the pre-image which is point A be (x,y)
The point after the translation left 2 units and down 5 units is B(-8, -11)
To get the x coordinate
we were tolt that the point was move 2 units left
So this implies x = -8+2 = -6
To get the y coordinates, we wre told that the point was moved down 5 units
This implies y = -11+ 5 = -6
Therefore, the coordinates of the pre-image point A is (-6, -6)
what are the three terms and 4x - 2y + 3
Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]For her phone service, Mai pays a monthly fee of $19, and she pays an additional $0.04 per minute of use. The least she has been charged in a month is$70.28. What are the possible numbers of minutes she has used her phone in a month?
We have a phone service fee which can be divided in:
- A fixed fee of $19 per month.
- A variable fee of $0.04 per minute, so that the cost for m minutes is 0.04*m.
We can add the two fees to express the total cost in function of the minutes as:
[tex]C(m)=19+0.04m[/tex]For a month where the cost is C(m) = 70.28, we can calculate the minutes as:
[tex]\begin{gathered} C(m)=70.28 \\ 19+0.04m=70.28 \\ 0.04m=70.28-19 \\ 0.04m=51.28 \\ m=\frac{51.28}{0.04} \\ m=1282 \end{gathered}[/tex]Answer: if she pays at least $70.28, she has talked at least m = 1282 minutes per month.
Solve for x8x-11=6x-5Simplify your answer as much as possible
Solve the given equation for x as shown below
[tex]\begin{gathered} 8x-11=6x-5 \\ \Rightarrow8x-11-6x=6x-5-6x \\ \Rightarrow2x-11=-5 \\ \Rightarrow2x-11+11=-5+11 \\ \Rightarrow2x=6 \\ \Rightarrow\frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]Therefore, the solution to 8x-11=6x-5 is x=3.If Danica has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous,how long will it be? (Round your answers to three decimal places.)
ANSWER
EXPLANATION
a) To find the time it will take before he has $2400, we have to apply the formula for monthly compounded amount:
[tex]undefined[/tex]A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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f(x) = x2 + 1 g(x) = 5 – x
(f + g)(x) =
x to the power of 2 – x + 6
then (f – g)(x) =??
The function operation ( f - g )( x ) in the functions f(x) = x² + 1 and g(x) = 5 - x is x² + x - 4.
What is the function operation ( f - g )( x ) in the given functions?A function is simply a relationship that maps one input to one output. Each x-value can only have one y-value.
Given the data in the question;
f(x) = x² + 1g(x) = 5 - x( f - g )( x ) = ?To find ( f - g )( x ), replace the function designators in ( f - g ) with the actual functions.
( f - g )( x ) = f( x ) - g( x )
( f - g )( x ) = ( x² + 1 ) - ( 5 - x )
Remove the parenthesis using distributive property
( f - g )( x ) = ( x² + 1 ) - ( 5 - x )
( f - g )( x ) = x² + 1 - 5 + x
Collect and add like terms
( f - g )( x ) = x² + x + 1 - 5
( f - g )( x ) = x² + x - 4
Therefore, the function operation ( f - g )( x ) is x² + x - 4.
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The required function would be (f – g)(x) = x² + x - 4.
What is the function?A mathematical expression that defines the connection between two variables is considered a function.
The given functions following as
f(x) = x² + 1 and g(x) = 5 - x
We have to determine the function (f – g)(x).
(f – g)(x) = f(x) - g(x)
Substitute the values of functions f(x) = x² + 1 and g(x) = 5 - x in the function (f - g).
(f – g)(x) = (x² + 1) - (5 - x)
Open the parenthesis and apply the arithmetic operation,
(f – g)(x) = x² + 1 - 5 + x
Rearrange the terms likewise and combine them,
(f – g)(x) = x² + x + 1 - 5
Apply the subtraction operation to get
(f – g)(x) = x² + x - 4
Therefore, the required function would be (f – g)(x) = x² + x - 4.
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If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
The first three terms of an arithmetic sequence are as follows.3, -1, -5
We will take a look at how we go about with arithmatic progressions.
Arithmmetic sequences are caetgorized by the following two parameters:
[tex]\begin{gathered} a\text{ = First term} \\ d\text{ = common difference} \end{gathered}[/tex]Where,
[tex]\begin{gathered} \text{The value of the first term is called ( a )} \\ \text{The common difference between each and every successive value in a sequence is called ( d )} \end{gathered}[/tex]We are given the following arithmetic sequence:
[tex]3\text{ , -1 , -5 , }\ldots[/tex]Now we will try to determine the values of the two parameters ( a and d ) from the given sequence as follows:
[tex]\begin{gathered} a\text{ = 3 }(\text{ first term value )} \\ d\text{ = (-1 ) - ( 3 ) = (-5 ) - ( -1 ) = -4 ( common difference )} \end{gathered}[/tex]Now to determine the value of any term number ( n ) in an arithmetic sequence we use the following formula:
[tex]a_n\text{ = a + ( n - 1 )}\cdot d[/tex]Where,
[tex]n\text{ is the term number}[/tex]So if we plug in the values of arithmetic sequence parameters into the general equation above we get:
[tex]\textcolor{#FF7968}{a_n}\text{\textcolor{#FF7968}{ = 3 + ( n - 1 ) }}\textcolor{#FF7968}{\cdot}\text{\textcolor{#FF7968}{ ( -4 )}}[/tex]Now we are to determine the values of term numbers ( n = 4 ) and ( n = 5 ). We will evaluate the ( an ) for each term number as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 4}} \\ a_4\text{ = 3 + ( 4 - 1 )}\cdot(-4\text{ )} \\ a_4\text{ = 3 - 12} \\ \textcolor{#FF7968}{a_4}\text{\textcolor{#FF7968}{ = -9}} \\ \\ \text{\textcolor{#FF7968}{For n = 5}} \\ a_5\text{ = 3 + ( 5 - 1 )}\cdot(-4\text{ )} \\ a_5\text{ = 3 - 1}6 \\ \textcolor{#FF7968}{a_5}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{13} \end{gathered}[/tex]Hence, the next two consecutive numbers in the arithmetic sequence would be:
[tex]3\text{ , -1 , -5 ,}\text{\textcolor{#FF7968}{ -9}}\text{ , }\text{\textcolor{#FF7968}{-13}}[/tex]Subtract these polynomials.
(3x + 2x + 4) (x + 2x+ 1) =
=(3x2 + 2x + 4) - (x2 + 2x + 1)
Combine like terms
=(3x2-x2)+(2x-2x)+(4-1)
=2x2+0+3
The 2x terms cancel each other to 0
=2x2+3
C) 2x2+3 is the answer.
Hope this helps!
Answer:
15x^2+17x+4
Step-by-step explanation:
(3x+2x+4)(x+2x+1)
Combine 3x and 2x to get 5x.
(5x+4)(x+2x+1)
Combine x and 2x to get 3x.
(5x+4)(3x+1)
Apply the distributive property by multiplying each term of 5x+4 by each term of 3x+1.
15x ^2+5x+12x+4
Combine 5x and 12x to get 17x.
15x^2+17x+4
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Which equation represents a line which is perpendicular to the line y=-5/4x-4?A. 4y−5x=−4B. 5x+4y=−8C. 4x−5y=15D.4x+5y=40
The slope of a line, m, comes in the equation as the coefficient of x.
In the given equation, m= -5/4. Two perpendicular lines have slopes that are the negative reciprocals of each other.
So, the slope of the perpendicular line will be +4/5.
Between the given options, letter c will be:
4x-5y=15
-5y=15-4x (divided by -5)
y=4/5x-3
Letter C
Please help me I don’t know how to do this
We have a point (4,-9) it moves to (9,-14)
(4+x = 9, -9+y= -14)
x = 9-4
x = 5
y = -14 +9
y = -5
We are moving to the right 5 and down 5
We want to move the point (-9,-8) exactly the same way
(-9+5, -8-5)
(-4, -13)
(-4, -13)
Determine the value of k for which f(x) is continuous.
These are the conditions of the continuity in a function:
First, the value of x must have an image.
Second, the lateral limits must be equal:
[tex]\lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)[/tex]Finally, the value of the limit must be equal to the image of x. This means that:
[tex]f(a)=\lim_{x\to a^}f(x)[/tex]In this case, we must find a value of k that can make the two lateral limits equal in x =3:
[tex]\lim_{x\to3^+}x^2+k=\lim_{x\to3^-}kx+5[/tex]We can solve these two limits easily by replacing the x with the value of 3
[tex]3^2+k=3k+5[/tex][tex]\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}[/tex]Finally, we can see that the answer is k=2.
I NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-9=-\dfrac{8}{3}(x-7)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define the given points:
(x₁, y₁) = (7, 9)(x₂, y₂) = (10, 1)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-9=-\dfrac{8}{3}(x-7)[/tex]
in a dog show there are 31 dogs competing in the terror group the top three dogs with we'll all wind crash price of $500 and moved on to complete for a place in the larger Best in Show competition how many ways can the top three dogs be determined if they are finishing position is not important
The selection of three dogs out of 31 dogs can be done in
[tex]31C3\text{ ways}[/tex]i.e.
[tex]\begin{gathered} =\frac{31!}{(31-3)!\times3!} \\ =\frac{31\times29\times28!}{28!\times3!} \\ =\frac{31\times29}{6} \\ =149.8 \\ \cong\text{ 150} \end{gathered}[/tex]Calculate the slope (2,-5) and (4,3)
Answer:
Slope = 4
Step-by-step explanation:
The slope of a line can be calculated using the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
From the question can put the points as:
(2, -5) as (x1, y1)
and
(4, 3) as (x2, y2)
Therefore, we can put in the values into the formula to solve for the slope.
[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]
10. A $152,000 home has an assessment rate of 52% and a tax rateof $48 per $1,000. Use the effective tax method to calculate theproperty tax .Hint: When you determine the effective tax rate, round the rateto three places.
Given
$152,000
52% assessment rate
$48 per $1,000
Procedure
First, let's calculate the assessment rate.
[tex]152000\cdot0.52=79040.0[/tex]Now let's calculate the taxes
[tex]79040.0\cdot\frac{48}{1000}=3793.92[/tex]Property taxes are equal to $3,793.92.
Instructions: Find the value of the trigonometric ratio. Makesure to simplify the fraction if needed.
sin C = 3/5
Explanation:Given:
CB = 32
AC = 40
AB = 24
To find:
sin C
To determine sinC, we will apply the sine ratio:
[tex]\begin{gathered} sin\text{ C = }\frac{opposite}{hypotenuse} \\ \\ oppoite\text{ =side opposite the angle = AB = 24} \\ hyp\text{ = 40} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ C}=\text{ }\frac{24}{40} \\ \\ sin\text{ C}=\text{ }\frac{3}{5} \end{gathered}[/tex]a person who weighs 145 pounds on Earth would weigh 47.2 pounds on Mercury. How much would a person weigh on Mercury if they weigh 135 pounds on Earth?
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
Weight of person on Earth = 145pounds
145 = mg
Weight of person on Mercury = 47.2pounds
47.2 = ma
145/47.2 = mg/ma
145/47.2 = g/a
a = 47.2g/145 .....1.
If weight of person on earth = 135pounds
135 = mg
m = 135/g .......2.
Then, Weight of person on Mercury = ma
using the above values of a and m we we get
= (135/g)x (47.2g/145 )
= 135 x 47.2 / 145
= 43.94 pounds
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
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Solve for a: a = 10.
a = , ,
Answer:
a=10 and a=-10
Step-by-step explanation: its absolute value
Solve 6 < x + 5 < 11
we have the following:
[tex]\begin{gathered} 6help meeeeeeeeee pleaseee !!!!!
The solution to the composite function is as follows;
(f + g)(x) = x² + 3x + 5(f - g)(x) = x² - 3x + 5(f. g)(x) = 3x³ + 15x(f / g)(x) = x² + 5 / 3xHow to solve composite function?The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
If we are given two functions, it is possible to create or generate a “new” function by composing one into the other.
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore,
f(x) = x² + 5
g(x) = 3x
Hence, the composite function can be solved as follows:
(f + g)(x) = f(x) + g(x) = x² + 5 + 3x = x² + 3x + 5
(f - g)(x) = f(x) - g(x) = x² + 5 - 3x = x² - 3x + 5
(f. g)(x) = f(x) . g(x) = (x² + 5)(3x) = 3x³ + 15x
(f / g)(x) = f(x) / g(x) = x² + 5 / 3x
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What is the opposite of the number −12?
A(-1/12
B(1/12
C(0
D(12
Answer: D(12)
Step-by-step explanation: To find the opposite it the number you would do -12= -12 x -1 = 12
I need help finding the exact perimeter. Special right triangles.
Answer:
The exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Explanation:
Given the square in the attached image.
The length of the diagonal is;
[tex]d=28[/tex]Let l represent the length of the sides;
[tex]\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=\frac{784}{2} \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}[/tex]The perimeter of a square can be calculated as;
[tex]\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}[/tex]Therefore, the exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Which values are solutions to the inequality below? Check all that applySqrt x>=9Choices are:-2, 82, 32, 180, 99, 63
We notice the following:
[tex]\begin{gathered} \sqrt[]{x}\ge9\ge0 \\ \Rightarrow \\ x\ge81 \end{gathered}[/tex]Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:
[tex]82,\text{ 180 and 99}[/tex]2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,
Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
Find the measurement of each subject. Assume that each figure is not drawn to scale.
To obtain the measure of segment AD, add the measurement of segment AC and segment CD.
[tex]AD=AC+CD=2\frac{3}{8}+1\frac{1}{4}[/tex]Rewrite the fraction part as similar fractions. Multiply the numerator and teh denominator of the second fraction by 2 to obtain 8 in the denominator.
[tex]\begin{gathered} AC+CD=2\frac{3}{8}+1\frac{1\cdot2}{4\cdot2} \\ =2\frac{3}{8}+1\frac{2}{8} \end{gathered}[/tex]Add the whole numbers, 2 and 1. Add the numerators, 3 and 2, and then copy the common denominator, which is 8.
[tex]\begin{gathered} AD=2\frac{3}{8}+1\frac{2}{8} \\ =3\frac{5}{8}_{} \end{gathered}[/tex]Therefore, the correct answer is the third option, 3 5/8 in.
Maria used a hundred chart to find a sum. She started at 57 then she moved down 3 rows and back 2 spaces which number did she land on
She landed on the number 25 on the hundred chart.
What is an 100 chart?
It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.
We are given that she was on 57th number
Then she moved down 3 rows
Each row contains 10 elements Hence we subtract 30 for 3 rows
57-30=27
Then also she took 2 steps back
Hence we again subtract 2 from 27
We get 27-2=25
Hence she is at 25th number
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HELP ASAP MATH PRE CALC
The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
The cube as a three dimensional shapes.A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.
From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.
So; H = (x) inches,
L = (30 - x)inches, and
W = (30 - x)inches.
Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
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QuestionGiven that cot(0)- 1 and 0 is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.Provide your answer below:sin (O)=
Given:
The trigonometric ratio is given as,
[tex]\cot \theta=-\frac{1}{2}[/tex]The value of θ lies in the second quadrant.
The objective is to find the value of sinθ.
Explanation:
The formula of cotθ is,
[tex]\cot \theta=\frac{\text{adjacent}}{\text{opposite}}=-\frac{1}{2}[/tex]Since, the value of θ lies in second quadrant, the triangle formed for cotθ will be,
Then, the value of x can be calculated as,
[tex]\begin{gathered} x^2=2^2+(-1)^2 \\ x=\sqrt[]{4+1} \\ x=\sqrt[]{5} \end{gathered}[/tex]To find the value of sinθ:
The value of sinθ can be calculated as,
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{2}{\sqrt[]{5}} \\ \sin \theta=\frac{2}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ \sin \theta=\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]Hence, the value of sinθ is (2√5)/5.
Dylan’s boat can carry 40 people across a river. Last month, 2504 people road on Dylan’s boat. What is the least number of trips that Dylan could have made across that river.
The required least number of trips that Dylan would have made across the river is 62.
Given that,
Dylan’s boat can carry 40 people across a river. Last month, 2504 people rode on Dylan’s boat. What is the least number of trips that Dylan could have made across that river is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Total people road = 2504
Maximum people can road at single trip = 40
Least number of trip = 2504 / 40
Least number of trip = 62
Thus, the required least number of trips that Dylan would have made across the river is 62.
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