Answer:
Grace will be 32 years old in 2027.
Answer: she will be 32 years old.
Step-by-step explanation:
Use the number line to find the difference of-3(-1.5).
Answer:
=4.5
Step-by-step explanation:
the rule is
positive - negative changes to positive + positive so
3- (-1.5) changes to 3 + 1.5 which equals 4.5
How do you translate coordinate points on a graph?
The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
As given in the question,
Let us consider original coordinate point on a given graph be ( x ,y ).
Translation represents the change in the linear displacement or the location without changing the shape and size.
Shift of the point may be horizontally or vertically.
Let 'h' and 'k' be the horizontal and vertical shift.
If the horizontal shift is right then it is represented by x + h
If the horizontal shift is left then it is represented by x - h
If the vertical shift is up then it is represented by y +k
If the vertical shift is down then it is represented by y - k.
Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
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Using a number line, find both the intersection and the union of the following
intervals:
(-3,∞) and (4,∞)
The answer choice which represents a number line for the intersection of the given intervals is; (4, ∞).
The answer choice which represents a number line for the union of the given intervals is; (-3, ∞).
What is the number line representation of the intersection and union of the given intervals?It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.
Since the given intervals are; (-3, ∞) and (4, ∞)
It follows that the intersection of both intervals is the interval; (4, ∞).
Also, the interval which represents the union of both intervals is; (-3, ∞).
Hence, the image which represents both scenarios is attached.
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A pronto lube garage charges £25 to lube any vehicle. Other work adds about €6000 per month to the
revenue. It costs pronto lube £6 in materials to service cars. Monthly operating expenses are €23,500.
2.1). Write an expression for net profit for C cars.
2.2). If the number of cars serviced in a particular month is 3000, find the profit
2.3). If the number of car serviced in a particular month is 900, then the garage got a
profit. True / false.
Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.
What is the equation?A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.
Here,
For C no of cars
=> Profit = total earning in a month - Expense in a month
=> (25-6)C - (23500-6000)
=> P = 19C-17500
If 3000 cars serviced then,
=> Profit = 19(3000)-17500
=> Profit = 39500
If no of cars received in particular month is 900 then profit or loss
=>Profit = 19(900)-17500
=> Profit = -400
That is loss.
Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.
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Solve the inequality n - 4/7> - 2/3
Answer:
N > -2/21
Step-by-step explanation:
Move -4/7 to the other side
n - 4/7 > - 2/3
n > - 2/3 + 4/7
Find a common denominator
n > - 14/21 + 12/21
Add
n > - 2/21
c) Mr. Gurung had Rs 3300. He purchased 5 kg of rice at Rs 70 per kg, 2 packets of oil at Rs 125 per packet and he gave Rs 2500 to his wife. If he divided the remaining sum between his son and daughter equally, find the share of each of them.
Answer:
Intial money=Rs 3300
final money=3300-(70×5)-(2×125)-2500
=3300-350-250-2500
=3300-3100=RS 200
Now,
share of each of them= 200/2=Rs100
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On a assembly line, 2 parts can be made per minute. There are 8 parts already made. To determine how many more minutes (x) it will take to make y total parts, the equation y=2x + 8 is written. What is the description of a solution to this problem?
The description for the problem involving the linear function is given as follows:
The time it will take to make a total of 20 parts is of 6 minutes.
How to interpret this problem in the context of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial value.In this problem, the function is defined as follows:
y = 2x + 8.
In which the variables are given as follows:
x is the time in minutes.y is the number of pieces made.Hence the time needed to make 20 pieces is given as follows:
20 = 2x + 8
2x = 12
x = 12/2
x = 6 minutes.
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I don’t know this question
Help me
Answer: Probably negative 69
the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
The value of the length will be 17920cm.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³.
The value of the length will be:
= 7 / (7 +5+2) × 35840
= 7/14 × 35840
= 17920cm
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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³. Find the value of the length
solve for x: 2 < x + 4 < 4
Answer: −2<x<0
Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0
What are logarithms used for?
Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:
What are functions?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What are exponential function?The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
They are used for:
Solving exponential equationsCompressing dataMeasuring the Richness of a signalComparing quantitiesSolving problems in physics and engineeringIn finance, it is used for financial modelings, such as the Black-Scholes model for pricing optionsIn computer science, it is used for information theory in the analysis of algorithms, complexity theory, and data compression.To learn more about exponential visit:
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LESSON 12-1 Properties of Translations Practice and Problem Solving : A / B
We found that translations have the following three properties: line segments are taken to line segments of the same length;
angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.
Properties of Translations
- Distance Where the lengths of the segments stay the same.
-Angle Measures These remain the same.
-Parallelism Where the parallel lines will stay parallel.
-Collinearity The points will stay on the same line.
-Orientation The order of the letters will stay the same.
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WZ and XR are diameters of circle C. The diagram is not drawn to scale.
Circle C is shown.
Radii are drawn from point C to point R at the right, point Z at the upper right, point Y at the upper left, point X at the left, and point W at the lower left.
Angle Y C Z measures 112 degrees.
Angle X C W measures 63 degrees.
Points X, C, and R are all on the horizontal diameter of the circle.
What is the measure of convex arc upper Z upper W upper X?
A. 355º
B. 5º
C. 292º
D. 243º
The measure of convex arc upper Z is 243⁰ Option D
How to find the measure of the angle?We should be aware that a convex angle is the angles that are irregular in nature
Assume that the radius of the given circle is r.
The central angle of the lower arc ZWX = 41+180 = 221⁰
Note that then central angle of the upper arc ZWX = 360- 221⁰
This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰
Recall that Lenght of arc = A/360 *2*π*r
Where A is the angle made by the radii, r= radius of the circle
Arc length of upper ZWX:
Arc length of upper ZWX = 139π/180*r
Arc length of upper ZWX = 139πr/180
The lenght is (139*22)/ 180*7
= 3058/2360
= 245⁰
In conclusion the measure of the convex upper is 245⁰
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Questions:
1. What did you do to the numerators? What did you do too to the denominators?
2. Did you find like terms among the collected terms of the numerator? What did you do
to terms?
3. What factoring techniques did you apply?
4. How did you simplify your sum?
The answers to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
What is numerator and denominator?In a fraction, the number above the line is the numerator.
For instance, the numerator of the fraction 3/5 is 3.
A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.
So, we have the equation:
2x² + x/2x - 2 + x - 4/ 2x - 2
Now, answering questions taking the above-given equation into consideration:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
(3) We complete the square, but we can also use the straightforward factoring approach.
(4) We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.
Therefore, the answer to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
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In ΔSTU, = 670 inche, u = 630 inche and ∠U=67°. Find all poible value of ∠S, to the nearet degree
The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 10
and DC = 4, what is the length of AD?
AC = 25 units is the length of AD.
A right triangle is divided into three equal halves by the height of the hypotenuseThe Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.
Length of BC = 10 units
Length of DC = 4 units
We will use geometric mean theorem in the given right triangle to get the length of side AC.
[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]
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Don and Ana are driving to their vacation destination. Upon entering the freeway they began driving at a constant rate of 60 miles an hour. Don noticed that 3 hours into the trip they were 650 miles from the destination.
How far from their destination will they be 3. 7 hours since entering the freeway?
How far from their destination were they 2. 3 hours since entering the freeway?
Please help quick
Distance between them and their destination after 3.7 hours since entering the freeway is 608 miles and the distance between them and their destination after 2.3 hours since entering the freeway is 692 miles.
We know that the relationship between speed, distance, and time is given as,
Speed = distance/time
Speed = 60 miles an hour
Time = 3 hours
We know that Don and Ana are travelling at a constant speed and they are travelling for 3 hours.
Distance = speed × time
Distance = 60 × 3
Distance = 180 miles
Thus, the distance travelled by them in 3 hours is 180 miles.
We know that Don and Ana are travelling on the freeway for the past 3 hours and they are still 650 miles away, therefore,
Total Distance from their destination
= Distance travelled by them in 3 hours + 650 miles
= 180 miles + 650 miles
= 830 miles
Thus, the distance travelled by then is 830 miles.
Now, the distance between them and their destination after 3.7 hours since entering the freeway,
Distance travelled by them = speed x 3.7 = 60 x 3.7 = 222 miles
Distance between them and the destination
= Total Distance from their destination - Distance travelled by them
= 830 miles - 222 miles
= 608 miles
Therefore, they are 608 miles far from their destination.
And, Distance between them and their destination after 2.3 hours since entering the freeway,
Distance travelled by them = speed x 2.3 = 60 x 2.3 = 138 miles
Distance between them and the destination
= Total Distance from their destination - Distance travelled by them
= 830 miles - 138 miles
= 692 miles
Therefore, they are 692 miles far from their destination.
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Activity
Luna I made the 3. 8 x 105 kilometers trip to the moon in 2. 16 x 10 minutes. In this activity, you will determine the average speed of Luna!
using division
Part A
Write an expression for the speed of Luna I In kilometers/minute. Represent this expression as a quotient of two numbers expressed in scientific
notation.
The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.
To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.
It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.
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What is an inverse variation graph called?
The graph of the inverse variation equation is called a rectangular hyperbola.
A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.
An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.
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what is an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]
Write 63 521. 769 correct to the nearest hundred
Find a polynomial which when added to the polynomial 3x^2+3x-1, is equaivelant to the following expressions: 1
The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:
P = 2 - 3x² -3x.P = -2 -x² -3xP = 6 -2x -3x².What is a Polynomial?This is referred to as algebraic expressions that consist of variables and coefficients.
For 1; it is calculated as:
3x²+3x-1 + P = 1.
P = 2 - 3x² -3x.
For 2x²-3, it is calculated as:
3x²+3x-1 + P = 2x²-3
P = -2 -x² -3x
For x +5; it is calculated as:
3x²+3x-1 + P = x +5
P = 6 -2x -3x².
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The full question is:
Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5
domain and range of f(x)=|x|
The domain and range of f(x) = |x| is
Domain: all real numbers
range: positive real numbers
What are absolute values?The distance of a number from a number line's origin is referred to as the absolute value of that number. Its representation is |x|, which establishes the size of any integer 'x'.
Any integer's absolute value, regardless of its sign, will be one of the real numbers, whether it is positive or negative. The modulus of x, which is represented by two vertical lines |x|, is a mathematical concept.
Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value.
Since absolute value can be zero the range is all positive numbers
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Select the correct answer.
Which statement about this system of equations is true?
A. The system has no solution.
B. The system has a unique solution at (0,6).
C. The system has a unique solution at (0,-4).
D. The system has infinitely many solutions.
The statement that is true on the system of equations is that A. The system has no solution.
Why is there no solution ?There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.
A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.
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What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a _____.
An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.
What does the phrase "in contradiction" mean?a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.
What is an illustration of contradiction?A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."
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Help.....ASP Please help right now
The triangle with side lengths given in the question can be classified as a scalene triangle.
What is a scalene triangle?A scalene triangle is a type of triangle in which none of its three given length of sides are equal. It can be differentiated from other types with respect to this property.
A triangle is a plane shape which can be described by three sides and three measure of internal angles. Some other types of triangle are: equilateral, obtuse, isosceles etc. The sum of all internal angles of a triangle is 180^o
Considering the given length of sides in the question, it can be proven the the only type of triangle that can be formed is a scalene triangle. Therefore, the triangle can be classified as a scalene triangle.
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I’d love you he help for all of it but i’ll take what I can get
Answer:
Parallelogram formula- 1/2 x base xheight
Step-by-step explanation:
HELP PLEASE 10 POINTS!
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
Answer for the given problem,
a. Percentage of 160 in number 40 is, 400%
b. The number for which 40 is 160% of that number is, 25
c. The number which is 40% of 160 is, 64
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
a. present quantity = 160
whole quantity = 40
Percentage = 400 %
b. present quantity = 40
Percentage = 160
Whole quantity = 25
c. whole quantity = 160
Percentage = 40%
Present quantity = 64
Hence, Answers are respectively, 400%, 25, 64
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How to find the height of an isosceles triangle when only base is given?
It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.
The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.
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