The coordinates after a dilation of scale factor k = 4 are (-16, 48)
What are the coordinates of the image after the dilation?If we have a general point (x, y), and we apply a dilation of scale factor k and the center of dilation is the origin, then the coordinates of the image after the dilation are (k*x, k*y)
Here we start with the point (-4, 12), and we apply a dilation of scale factor 4 and the center is the origin, then the coordinates of the image are::
(-4*4, 12*4) = (-16, 48)
The coordinates after the dilation are (-16, 48).
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
An open circle is at 5 and a bold line starts at 5 and is pointing to the right. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -3(2x - 5) < 5(2 - x).
Here, -6x+15<10-5x
Add 5x on both the sides of an inequality, we get
-x+15<10
Subtract 15 on both the sides of an inequality, we get
-x<10-15
-x<-5
Multiply -1 on both the sides of an inequality, we get
x>5
Therefore, option B is the correct answer.
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FInd the simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate.
The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
P = $2800
T = 5 years
R = 2%
Now,
The formula for simple interest.
SI = PRT/100
Now,
SI = (2800 x 2 x 5) / 100
SI = 28 x 10
SI = $280
Thus,
Simple interest is $280.
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there are 14 desktops and 16 laptops what percent of the computers are laptops
Answer:
53.3%
Step-by-step explanation:
14 + 16 = 30
16/30 x 100 = 53.3% are laptops
A man walks due west for 4km. he then changes direction and walks on a bearing of 197 degrees until he is southwest of his starting point. how far is he to the then from his starting point
Step-by-step explanation:
To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,
c² = a² + b² - 2abcos(C)
In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.
Therefore, we can use the law of cosines to find the distance he traveled in the second leg:
c² = a² + b² - 2abcos(90)
c² = 4² + b²
c = √(4² + b²)
c = √(16 + b²)
We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.
So we can use the law of cosines to find the distance he traveled in the second leg:
b = √(c² + a² - 2ac cos (-163))
We can now plug in the values we know:
b = √(c² + 4² - 24c*cos(-163))
We can now solve for c:
c = √(b² + 16 - 8bc)
The man is then southwest of his starting point, so the distance from his starting point to the final point is c.
What is ths measure of z. 3
using the multiple linear regression model you developed in part (a), what is the predicted freshman gpa of bobby engle, a student who has been admitted to ruggles college with a 660 sat score on critical reading and at a 630 sat score on mathematics?
y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.
A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.
Score on critical reading = 660
Score on mathematics = 630
Intercept = -2.6717
Reading(x1) = 0.0043
Mathematics(x2) = 0.0045
Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.
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make x the subject for 8x+7=2y-1
How many teaspoons are there in 6 milliliters?
Answer:
70
Step-by-step explanation:
you divide the intergert and div8de its easy
Answer: 70
Step-by-step explanation:
Quadrilaterals Q and P are similar. What is the scale factor of the dilation that takes P to Q?
A. 3/5
B. 4/5
C. 5/4
D. 5/3
Answer:
C. 5/4
Step-by-step explanation:
Let s = the scale factor
4s = 5 divide both sides by 4
s = 5/4
2. Mai also got the expression 7x 1 and wrote her answer as 7x + (−1). Are the two
expressions equivalent? How do you know?
Answer:
Yes, the answers are equivalent.
Step-by-step explanation:
The answers are equivalent because when adding a positive to something it does not change the value of the number. So by adding the + in front of the -1 the value of -1 does not change in the equation.
Hope this helps!!
Need some help with this paper
well, it comes down to, if f(x) is indeed an inverse of g(x) and the other way around, then f( g(x) ) = x, and likewise g( f(x) ) = x, so let's check if f( g(x) =x
[tex]f(x)=3x+11\hspace{5em}g(x)=-\cfrac{1}{3}x-\cfrac{11}{3} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=3\left( -\cfrac{1}{3}x-\cfrac{11}{3} \right)+11 \\\\\\ f(~~g(x)~~)=-x-11+11\implies f(~~g(x)~~)=-x ~~ \bigotimes[/tex]
now, we could do a test by doing g( f(x) ), however we don't need to, since f( g(x) ) ≠ x, they're not inverse of each other.
mentum.com
Lxpre3310113, 1931
ial Expressions: Mastery Test
5
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
40+8+32+(15-7) × 2
Arrange the steps in the order in which they are performed.
3²
5+9
40+8
14+ 16
8x2
KNOW
15-7
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.
Given: 40/8 + 3² + (15 - 7) × 2
The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.
40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8
Then you evaluate exponential terms.
40/8 + 9 + 8 × 2 . . . . . 3² = 9
Next, multiply and divide from left to right. In this case, division comes before multiplication.
5 + 9 + 8 × 2 . . . . . divide 40/8 = 5
5 + 9 +16 . . . . . . multiply 8 × 2 = 16
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
The complete question is:
Using the order of operations, what are the steps for solving this expression?
40/8+3^2+(15-7)*2
Arrange the steps in the order in which they are performed.
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You are ask to solve 12x-18 =126
anna leaves her house on her bike traveling at an averge speed of 6 mph. an hour later, her mother sets out after her on the same road, traveling by car. how fast must she drive to reach anna in twn minutes
The mother must drive at a speed of 6 mph to reach Anna in ten minutes.
To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.
Let x be the speed of the mother's car in mph.
In one hour, Anna will have covered 6 miles.
In ten minutes, the mother will have covered x * 10/60 miles.
The total distance between them is 6 + x * 10/60 miles.
The mother must cover this distance in ten minutes, so:
x * 10/60 = 6 / (10/60)
x = 6 * (10/60) / (10/60)
x = 6 mph
Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.
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Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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Harper has $0.70 worth of nickels and dimes. She has 5 more nickels than dimes. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Harper has.? Determine three ways to have 5 more nickels than dimes
The number of nickels, x, and the number of dimes y that Harper has are;
8 nickels and 3 dimes
How to solve algebra word problems?From conversion of coins we know that;
1 nickel = $0.05
1 dime = $0.10
Thus, if she has 5 more nickels than dimes, then;
Let x = the number of dimes Harper has
Let x + 5 = the number of nickels Harper has
Thus;
$0.05(x + 5) + $0.10(x) = $0.70
0.05x + 0.25 + 0.10x = 0.70
0.15x = 0.70 - 0.25
0.15x = 0.45
x = 0.45/0.15
x = 3 dimes
Nickels = 8 nickels
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Answer questions 8 and 9.
Find the measure of an arc from the central angle.
By using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
What is the measure of an arc from the central angle?
The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.
In the given figure
by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 360° - 225° = 135°
In the second figure,
If m(arc KJH) = 312°
m∠1 = 360° - 312° = 48°
Hence, by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
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Please help ASAP!!!!!!!!!
The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."
Option A is correct.
What is slope of line?In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.
We are given equation as 4x-7y=62
First, let's write it in the slope-intercept form .In general, slope-intercept form is y=mx + b
where m is the slope
So, writing the equation in the form, we get
⇒-7y = 62-4x
⇒7y = 4x-62
⇒y = 4x/7-62/7
Now, matching the equation with the general form,
m = 4/7
Hence, the slope of the line represented by 4x-7y=62 is 4/7.
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What is the equation of the line that passes through the point (1, 8) and has a slope
of 1?
Answer:
y = x + 7
Step-by-step explanation:
Equation of line:[tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]
m = 1
(1 , 8) ; x₁ = 1 & y₁= 8;
y - 8 = 1*(x - 1)
y - 8 = x - 1
y = x - 1 + 8
y = x + 7
In a survey, a group of students were asked to name their favorite world language class. There were 25 students who chose "other" languages. How many students participated? french:42. 5% spanish:45 students participated
Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.
When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.
The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.
Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.
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Determine the solution to the following system of linear equations by inspecting the graph below. Enter the solution set as an ordered pair in the form (x,y). If there are no solutions, enter None and enter ALL if there are infinitely many solutions.
The solution set to the system of linear equations as an ordered pair is (3, -3).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
Note: Each interval on this graph represents 1 unit.
By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).
In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.
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necesito esto para hoy,porfavor x-3(x+5)=3x+10
No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.
¿Cómo resolver una ecuación algebraica?
En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:
3 · (x + 5) = 3 · x + 10
Segundo, halle la solución por propiedades algebraicas:
3 · x + 15 = 3 · x + 10
15 = 10 (CRASH!)
La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.
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can anyone help me with this?
$97.056 is the total interest accrued after the first month.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.
The cost of car = 19,725*(1.0475) = 20,661.9375
Down payment = 2,175
So balance amount, P= 20661.9375-2175 = 18,486.9375
So interest for the average rating of a new car = 6.30%
So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056
therefore, interest accrued after the first month is $97.056.
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In a group of 60 tudent, 25 play table tenni, 16 do wimming and 22 play cricket, 8 play table tenni and do wimming, 6 play cricket and do wimming, 5 play table tenni and cricket, and 12 tudent do not play any of thee game
12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12
A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.
25 play table tennis
16 do swimming
22 play cricket
8 play table tennis and do swimming
6 play cricket and do swimming
5 play table tennis and cricket
Find the number of students who do not play any of the games
Total number of students = 60
Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82
Number of students who do not play any of the games = 60 - 82 = 12
12 students do not play any of the games.
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Printing company purchases an ad- vanced color copier/printer for $113,000 After 7 years, the equipment will be obsolete and have no value.
Write a linear equation giving the value of the equipment in terms of the time t
A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.
The value of the colour printer is 117000 $ and machine has no value after 7 years.
As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.
Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t
Thus, the required linear equation is v = 117000 - 16714.3t.
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Brett has c more comic books in his collection than Erica does. Erica has 19 comic books in her collection. Write an expression that shows how many comic books Brett has in his collection.
The expression for the given conditions is Y=10+c
where Y=no. of books Brett has and c=no. of books Erica has.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given No. of books Erica has = 19
and Brett has c more comic books than Erica has
let Y=no. of books Brett has
Hence, the expression will be
Y=19+c
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Exercise 2. 5. 2: Proof by contrapositive of statements about integer division. About Prove each statement by contrapositive (a) If x and y are integers such that 3xy then 3x. Solution (b) For any integers x, y, and z, if x|y and xz, then x(y z). (c) If x and y are integers such that x > 1, and x divides y, then x(y 1)
The statements
(a) If x and y are integers such that 3xy then 3x.
(b) For any integers x, y, and z, if x y and xz, then x(y - z).
(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)
are proved.
The term integers in math is defined as are the collection of whole numbers and negative numbers.
Here we know that x and y are the integers,
Then it takes both positive and negative numbers.
Then we take y=1, then we apply it on the expression then we get,
=> 3x(1) = 3x.
Similarly here we have take that xy|z means xy is a factor of z,
Here we can say xym = z for some integer m.
=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.
Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.
Where in the third one, we can take x|y means there exists a constant is written as y = kx
Where as y|x means there exists a constant written as x = cy
When we compare these, then we get,
=> y = kx = kcy
Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1
Therefore y = kx becomes y = 1*x or y = x
Similarly x = cy becomes x = 1*y or x = y
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The volume of soda dispensed in a can during production is normally distributed with a mean of 358. 2 ml and a standard deviation of 1. 8 ml. The company does not want more than 2. 5% of all cans to be less than the volume on the label which is 355ml. Is the company meeting its goal? If not, what should the company do? (Show work)
To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
We can use the z-score formula to find the probability of cans having a volume less than 355 ml.
z-score = (355 - 358.2) / 1.8 = -1.78
Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372
The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.
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Tyson must complete 30 hours of community service. She does 2 hours each day. Write a liner equation to represent the hours Tyson has left after x days?
Tyson has (30-2x) hours left after x days .
Linear equation: What is it?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.
She works out for two hours per day for a total of x days.
She has thus worked for two hours.
She has 30 hours left to accomplish, of which she has already worked for two of them.
She now has 30 2 hours to finish the task.
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6.4% as a fraction in simplest form
Answer:32/5
Step-by-step explanation:
32/5
Answer:
Solution: 6.4% as a fraction is 32/5.
Step-by-step explanation: