The age of Mark and Lynne’s house right now, given the number of years left till the mortgage is paid off is 4 years.
How to find the age of the house?Mark and Lynne’s house is currently aged such that in 20 years when the mortgage is paid off, it will be five times as old as it is now.
Assuming the age of the house right now is x, the age of the house can be shown in an equation as:
20 years = 5x
The age of the house now is therefore:
x = 20 / 5
x = 4 years
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PLEASE HELP! AND PLEASE ANSWER WITH WORK!
1) x+9=12
2) s-1=10
3) 3=z-11
4) 5+y=7
5) 8=2+q
6) 6=n-4
7)r-2=5
8)6=m+6
9)p+7=8
10)4+a=13
Answer:
1) x = 3,
2) s = 11,
3) z = 14,
4) y = 2,
5) q = 6,
6) n = 10,
7) r = 7,
8) m = 0,
9) p = 1,
10) a = 9.
Step-by-step explanation:
1) Subtract 9 from both sides to isolate x, the result is 3.
2) Add one to both sides to isolate s, the result is 11.
3) Add 11 to both sides to isolate z, the result is 14.
4) Subtract 5 from both sides to isolate y, the result is 2.
5) Subtract 2 from both sides to isolate q, the result is 6.
6) Add 4 to both sides to isolate n, the result is 10.
7) Add 2 to both sides to isolate r, the result is 7.
8) Subtract 6 from both sides to isolate m, the result is 0.
9) Subtract 7 from both sides to isolate p, the result is 1.
10) Subtract 4 from both sides to isolate a, the result is 9.
Answer:
..............................
Find the open intervals where the function graphed below is a) increasing, or b) decreasing. a) List any open interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Type your answer in interval notation.
Use a comma to separate answers as needed.)
B. The function is never increasing.
The function decreasing in the interval will be (-∞, 0) and the function increasing in the interval will be (0, ∞). The function is never increasing is false.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The function decreasing in the interval will be (-∞, 0) and the function increasing in the interval will be (0, ∞).
The function is never increasing is false.
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An inlet pipe can fill a pool in 12hours, while and outlet pipe can empty a pool in 14 hours. If both pipes are open, how long will it take to fill the pool?
____ hours
This is a proportions math problem.
It will take 84 hours to fill the pool.
What is work done?Work is the amount of energy transferred to an object by an external force when it is moved over a certain distance.
Given that, an inlet pipe can fill a pool in 12 hours, while and outlet pipe can empty a pool in 14 hours.
Work done by inlet pipe in 1 hour = 1/12
Work done by outlet pipe in 1 hour = 1/14
Let the pool be filled in x hours, so in hour it will fill = 1/x
1/12-1/14 = 1/x
x = 84
Hence, It will take 84 hours to fill the pool.
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An experiment consists of rolling a fair die (sides numbered 1, 2, 3, 4, 5, 6) and then tossing a coin (with faces Heads and Tails).
Let A be the event that the number rolled is a 3 or a 4.
Let B be the event that a heads is flipped.
Are events A and B independent? Why or why not?
The events A and B are independent events
How to determine the type of the event?The sections on the dice are given as
S = {1, 2, 3, 4, 5, 6}
These sections mean that:
n(3) = 1 and n(4) = 1
Recall that:
A be the event that the number rolled is a 3 or a 4.
So, we have
P(A) = P(3) + P(4)
This gives
P(A) = 1/6 + 1/6 = 1/3
Also, we have
Coin = {Head, Tail}
Where
B be the event that a head is flipped.
This means that
P(B) = 1/2
The occurrence of an event in event A does not hinder the occurrence of another occurrence in event B
This means that the events are independent event
i.e. they do not depend on each other
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In Morse code, symbols are represented by variable-length sequences of dots and dashes. (For example, A =:-, 1=-----/?="--) How many different symbols can be represented by sequences of eight or fewer dots and dashes? Use the method of Example 9.5.10 to answer the following questions. (a) How many 18-bit strings contain exactly eight 1's? The number of 18-bit strings that contain exactly eight 1's equals the number of ways to choose the positions for the l's in the string, namely, (b) How many 18-bit strings contain at least fifteen l's? (c) How many 18-bit strings contain at least one 17 (d) How many 18-bit strings contain at most one 1?
Answer:
Applying the product rule of exponents, (a²c)³ = .
What is the Product Rule of Exponents?
When multiplying two numbers with the same base, their powers/exponents would be added.
For example, .
Given:
(a²c)³
Therefore:
(a²c)³ = (a²c)(a²c)(a²c)
(a²c)³ =
(a²c)³ =
Therefore, applying the product rule of exponents, (a²c)³ = .
Step-by-step explanation:
There are 2 rows of oranges on a table. Each row has 4 oranges. How many oranges are there in all?
Answer:
8
Step-by-step explanation:
2 rows with 4 oranges each -> 2*4 = 8
John started cooking at 5:46 PM and finished at 6:33 PM.
How long did it take him? Give your answer in minutes.
Answer:
i think 47 minutes
Step-by-step explanation:
hope this helps :)
Answer: 47 minutes
Step-by-step explanation:
There are 60 minutes in an hour, so: 60-46=14
If you add 14 minutes to the original time, then it will be 6:00pm, so that leaves the 33 minutes
Add: 14+33=47
13TAD
DATE:
I
Question &
A container of soft drink was shared
between four work teams of employers. The
first tam took ½ of the soft drink, the
second took of what was left, &
the remaining soft drink equally between
them. If there were originally 240L of soft
drink did the third team get?
A. 20
B. 40
C. 80
P. 160
E. None of these
Write the equation for this sequence where
a₁ = 8 and the common difference is 6
Answer:
[tex]a_{n}[/tex] = 8 + (n-1)6
Step-by-step explanation:
Kenneth drove 174.2 miles in 3 7/20 hours. What was his average speed?
Answer:
52 miles per hour
Step-by-step explanation:
You want to know Kenneth's average speed if he drove 174.2 miles in 3 7/20 hours.
SpeedSpeed is the ratio of distance to time:
speed = distance/time
speed = (174.2 mi)/(3 7/20 h) = 52 mi/h
Kenneth's average speed was 52 miles per hour.
Can someone help me?
On a Sunday in April, dog bite victims arrive at Carver Memorial Hospital at a historic rate of 0.6 victims per day. On a Sunday in April, what is the probability that exactly two dog bite victims will arrive?
The probability that exactly two dog bite victims will arrive is 0.099.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
Based on the information, the probability that exactly two dog bite victims will arrive will be:
P(x = 2) = e^(-06) (0.6)2 / 2!
= (0.549) × (0.36) / 2
= 0.099
The probability is 0.099.
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Please help identify the operations used to create equivalent systems of equations
1) The way we transform the simultaneous equation in system A to system B is;
1 * Equation [A1] → Equation [B1]
2 * Equation [A1] + Equation [B1] → Equation [B2]
2) The way we transform the simultaneous equation in system Bto system C is;
1 * Equation [B1] → Equation [C1]
-1/11 * Equation [B2] → Equation [C2]
How to solve simultaneous equations?We are given the system of simultaneous equations as;
System A;
-7x + 2y = 5 ----A1
3x - 4y = 23 ------A2
System B;
-7x + 2y = 5 -----B1
-11x = 33 ------B2
System C;
-7x + 2y = 5 ----A1
x = -3 ------A2
1) To find out the operation that transforms system A into system B, we need to analyze both equations and by careful observation, we see that;
When we multiply A1 by 2 and add to A2, the result will give us B2.
Let us check;
A1 * 2 = 2(-7x + 2y) = 2(5)
-14x + 4y = 10
Add to A2 to get;
-11x = 33
2) To find out the operation that transforms system B into system C, we need to analyze both equations and by careful observation, we see that;
When we multiply B2 by -1/11 and the result will give us C2.
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Find the sum:
(-2z to the power of 2 +4)+(8z to the power of 3 +6z to the power of 2 -12)
The sum of the given expression is (8z³ + 4z² - 8).
Given, an expression
(-2z² + 4) + (8z³ + 6z² - 12)
Now, we have to find the sum of the given expression,
On simplifying, we get
= (-2z² + 4)+(8z³ + 6z² - 12)
= -2z² + 4 + 8z³ + 6z² - 12
= 8z³ - 2z² + 6z² - 12 + 4
= 8z³ + 4z² - 8
So, (8z³ + 4z² - 8) is the sum of the given expression.
Hence, the sum of the given expression is (8z³ + 4z² - 8).
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A line has a slope of
-(6/5)
(a) What is the slope of the line parallel to it?
(b) What is the slope of the line perpendicular to it?
a) What is the slope of the line parallel to it?
Parallel lines will never intersect, meaning they have equivalent slopes, so the answer to this part is -(6/5).
b) What is the slope of the line perpendicular to it?
Perpendicular lines will intersect, creating a 90-degree angle, meaning all values in the graphs have been flipped. Thus, the slope of any perpendicular line is the negative reciprocal of the given slope (-1/x). The negative reciprocal of -(6/5) is 5/6, so that is the answer.
If the impedance of a resistor in a circuit is Z_(1)=2+9i ohms and the impedance of a second resistor is Z_(2)=7-i ohms, find the total impedance of the two resistors when they are placed in series (the sum of the two impedances ).
PLEASE HELP
The total impedance is 9+8i ohm.
From the question, we have
Z1= 2+9i
Z2= 7-i
we know,
total impedance in series,
Ztotal = Z1+Z2
= 2+9i+7-i
= 9+8i
The total impedance is 9+8i ohm.
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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Order from least to greatest 26/5,5.277,5.28,5 1/6
Step-by-step explanation:
1/6, 5,26/5,5.277,5.28
Which of these equations are true? Select TWO correct answers. Answer A −8×3=24 B −4+3=1 C 15−(−2)=−13 D −5 ×7=−35 E −10 + −10 = −20
Answer:
option D and E
Step-by-step explanation:
-5 × 7 = -35-10 + -10 = -20Select the correct answer
Two objects are moving along separate Inear paths where each path is described by position, d, and time, t The variable df is measured in meters,
and the variable f is measured in seconds. The equation describing the graph of the position of the first object with respect to time is d-25 22
The graph of the position of the second object is a parallel Ine passing through (-0, d-1). What is the equation of the second graph?
OA d-25t+1
OB. dt 25
OCd-04 1
OD. d=25+32
um All rights reserved
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Next
The slope intercept form of equation of second graph is
d = 2.5t + 1
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is 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, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The equation describing the graph of the position of the first object with respect to time is d=2.5t+2.2.
Now, we need to find the equation of line parallel to d = 2.5t + 2.2 and passing through t = 0, d = 1
Slope of line d = 2.5t + 2.2 is 2.5
Slope of line parallel to d = 2.5t + 2.2 is 2.5
The line passes through t = 0, d = 1
Equation of second graph =
d - 1 = 2.5(t - 0)
d = 2.5t + 1
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
The slope is [tex]\frac{-3}{5}[/tex]
Step-by-step explanation:
You know the slope is negative if you start on the left side and move right along the line. You are moving down hill. Down hill is a negative slope.
Standard form of line that passes through (6.-1) and it parallel to the line represented by 8x + 3Y= 15
The standard form equation for a line passing through the point (6, -1) and parallel to the line denoted by 8x + 3y = 15 is 8x + 3y = 45.
The standard form equation
ax + by = c
Here a, b, and c are constants and therefore use the slope-intercept form.
y = mx + c .... (1)
where m is the slope, b = y-intercept
8x + 3y = 15
3y = -8x + 15
y = -8 / 3 x + 5
Slope (m) = - 8 / 3
It passes through a line that has points (6, -1)
Let's find b by putting the value of m = - 8/3, x = 6, and y = -1 in equation (1).
-1 = - 8 / 3 (6) + c
-1 = -48 / 3 + c
-1 = -16 + c
c = -1 + 16
c = 15
Therefore,
y = - 8 / 3 x + 15
8 / 3 x + y = 15
=> 8x + 3y = 45
8x + 3y = 45 is the standard form of the line that passes through (6,-1) and is parallel to the line represented by 8x + 3y= 15.
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Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha’s songs were played on 2 more commercials than movies, and her total earnings on the royalties from all the commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha’s songs were played. Define the variables that you use to write the system
The equations that Nakeishia can use to determine the number of commercials and the number of movies on which Nakeisha’s songs were played include:
30m + 110(m + 2) = 760
How to illustrate the information?Let the movies be represented by m
Since Nakeisha’s songs were played on 2 more commercials than movies, this will be m + 2.
Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. This will be:
30m + 110(m + 2) = 760
This represents the equation.
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Explain how you can find the y-intercept of a function when given an equation of a graph.
The y-intercept of a function is the value of y when x = 0, which is represented as the value of b in the slope-intercept equation y = mx + b. b is the y-intercept.
What is the Y-intercept of a Function?If an equation of graph that represents a function is given in slope-intercept form as y = mx + b, the value of b in the function is the value of the y-intercept of the y-intercept.
The y-intercept of the function is the same as the value of y when the value of x is 0, or the point where the line of the function intercepts the y-axis on a given graph that represents the function.
For example, if we are given the equation of a graph that represents a function as, y = 3x + 4, the y-intercept of the function would be 4.
In summary, the y-intercept of the function is the value of b in the equation of the function that is expressed as y = mx + b in slope-intercept form.
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Identity the property of equality that was used for each step
Addition property
Subtraction property
Multiplication property
Division property
Transitive property
Symmetric property
Substitution property
Reflexive property
Distributive property
The following properties of equality are used to solve the given equation:
division property, multiplication property, addition property, Subtraction Property, distributive property
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Equation:
2((2/5) x+8)=4(14-(1/5)x)
1. The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal .
2((2/5) x+8)/2=4(14-(1/5)x)/2
(2/5) x+8=2(14-(1/5)x)
2. multiplying a quantity by the sum of two or more terms is the same as adding together the products of the original quantity and each term
(2/5) x+8=28-(2/5) x
3. when the same quantity is added to both sides of an equation, it produces an equivalent equation
(2/5) x +(2/5) x+8=(2/5) x+28-(2/5) x = 28
4. The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount
(4x)/5+8-8=28-8=20
5. The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
*5(4x)/5= 20*5
4x=100
6. The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal .
4x/4=100/4
x=25
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
1. Corresponding angles
2. Alternate Interior angles
Find the x-intercept and y-intercept of the line???
The x-intercept of the line is x = -2,and the y-intercept of the line is y = -6.
Determining the x-intercept and the y-intercept of a lineFrom the question, we are to determine the x-intercept and y-intercept of the line.
The x-intercept of a line is the point where y = 0
and
The y-intercept of a line is the point where x = 0
The equation for the line is
6x + 2y = -12
To determine the x-intercept, substitute y = 0 in the equation
6x + 2y = -12
6x + 2(0) = -12
6x + 0 = -12
6x = -12
Divide both sides by 6
6x/6 = -12/6
x = -2
Hence, the x-intercept is x = -2
To determine the y-intercept, substitute x = 0 in the equation
6x + 2y = -12
6(0) + 2y = -12
0 + 2y = -12
2y = -12
Divide both sides by 2
2y/2 = -12/2
y = -6
Hence, the y-intercept is y = -6
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original amount: 100 new amount:140
Answer:
100 + 40
Step-by-step explanation:
to get from 100 to 140 you have to add 40 to 100
Find (-3/4+5/9) + 7/4
Answer:
[tex]\frac{14}{9}[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Question 11 of 21
If you apply the changes below to the absolute value parent function, f(x) = Ixl,
which of these is the equation of the new function?
• Shift 5 units to the right.
• Shift 4 units down.
A. g(x)=|x+4| -5
B. g(x)=Ix-5| -4
C. g(x)= |x + 5| -4
D. g(x) = |x-4| -5
SUBMIT
The required function after shifting its origin will be g(x) = |x + 5| - 4
So, the answer is option C.
What is Shifting of Origin?To move the origin's coordinates to (h, k):
Get the new equation by changing x and y in the given equation to (x-h) and (y-k), respectively.
Given functions f(x) = |x| or y = |x| in this case
Shift now five units to the left. x is changed to x - (-5) = x + 5.
Shift four units down, and y becomes y -(-4) = y + 4.
After shifting, the equation is now
y - k = |x - h|
y = |x -h| + k
y = |x - (-5)| +(-4) (-4)
g(x) = |x+5|-4
As a result, the necessary function will be g(x) = |x + 5| - 4 after changing its origin.
Option C is the correct response.
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two mountain peaks are known to be 25 kilometers apart. a person located at a vista point such that a right angle is spanned when he looks from one peak to the other is told that the distances from the vista point to each peak differ by 5 kilometers. how far is the vista point from each mountain peak?
Pythagoras was a philosopher and a teacher. Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides: a2+b2=c2.
Explain about the Right angle?
An angle with a measure of exactly 90 degrees (or /2) is referred to as a right angle. The proper angles are frequently demonstrated in everyday life. For instance, the edges of the cardboard or the corner of a book.
The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A point is surrounded by four right angles. According to our definition of a degree, a "complete turn" around a point is 360°, making each right angle one-fourth of that, or 90°.
One mountain it should be 30 Kilometers and other mountain should be 40 kilometers
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Please help as soon as possible! Thank you so much!
