Answer:
First part: 64 and 46
Second part, 10, 12, 14, 16.
Step-by-step explanation:
First number has his first digit A, and second digit B, ie it can be written as 10A+B. Second number becomes then 10B+A.
Add them together, the sum becomes 11A + 11B = 110. (or A+B = 10 by dividing by 11).
Subtract them from each other, and you get 9A-9B = 18 (or dividing by 9 A-B=2)
At this point it's easy to find the solution A=6, B=4 which makes the two numbers 64 and 46.
Callthe first number of the chain 2x, the second 2x+2, third is 2x+4, fourth is 2x+6. Add them together, you get 8x +2+4+6= 8x+ 12=92 which easily solves for x = 10 and the four numbers are 10, 12, 14, 16.
Your school's talent show will feature 10 solo acts and 2 ensemble acts. The show will last 98 minutes. The 5 solo performers judged best will give a repeat performance at a second 63 minute show, which will also feature the 2 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b).
Solo acts are 7 minutes long and ensemble acts are 14 minutes long.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From the given data let us form the system of equations
10x+2y=98
5x+2y=63
To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.
Subtract both the equations
10x+2y-5x-2y=98-63
5x=35
Divide both sides by 5
x=7
Now plug in x value in any of the equation
70+2y=98
2y=98-70
2y=28
Divide both sides by 2
y=14
Hence, Solo acts are 7 minutes long and ensemble acts are 14 minutes long.
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Find the equation of the line perpendicular to y=-1/2x-5 that passes through the point (2,7) Write this line in slope-line intercept
Answer:
y = 2x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x - 5 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (2, 7 ) into the partial equation
7 = 4 + c ⇒ c = 7 - 4 = 3
y = 2x + 3 ← equation of perpendicular line
What is the break down of 300,000 15-year mortgage fixed-rate 4.4% with a 20% down payment with the credit union?
The monthly payment for the $300,000 mortgage, of 15 years, with a 4.4% interest rate and 20% down payment is given as follows:
$1,823.79.
What is the monthly payment formula?The monthly payment formula is given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are given as follows:
P is the initial amount.r is the interest rate.n is the number of payments.The down payment is of 20%, hence the amount subject to interest is given as follows:
P = 0.8 x 300,000 = 240,000.
The remaining parameters have the values given as follows:
r = 0.044, n = 15 x 12 = 180.
Hence:
r/12 = 0.044/12 = 0.003667.
Then the monthly payment is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 240000\frac{0.003667(1.003667)^{180}}{(1.003667)^{180} - 1}[/tex]
A = $1,823.79.
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Solve the system of equations by the addition method.
3x + 4y = 1
6x + 8y = 0
Using the addition method to solve the given system of equations, It can't be solved because these are the set of parallel lines.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination methodtake first equation multiply it by 2 and subtract second equation from it,
We can't solve for any values,
This is because our equations are parallel in nature.
They never intersect each other.
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Predict the cost of a meal for a family of four between $60 and $100. Be sure to include dollars and cents.
The cost of the meal if a family has a 25% off coupon for a family of four between $60 and $100 is between $45 and $75.
What will be the cost of the meal if a family has a 25% off coupon for a family of four between $60 and $100?A 25% off coupon is a discount price.
The cost of the meal if a family has a 25% off coupon for a family of four between $60 and $100 is calculated as follows:
For a $60 meal:
Cost of meal = $60 - 25% * $60
Cost of meal = $60 - $15
Cost of meal = $45
For a $100 meal:
Cost of meal = $100 - 25% * $100
Cost of meal = $100 - $25
Cost of meal = $75
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Complete question:
Predict the cost of a meal for a family of four between $60 and $100. Be sure to include dollars and cents.
Part A: If the family has a 25% off coupon, calculate the new price of the meal. Show all work or explain your steps. (6 points)
PLEASE HELP!!!
Use this information for questions 9 to 11.
Question 9: What is ∠2? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Question 10: What is ∠4? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Question 11: With the given information and what you are able to determine, can you conclude that a ll b? If they are not parallel, explain why they are not. If they are parallel, what theorem can be used to prove them parallel? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Step-by-step explanation:
p and q are parallel.
let's first only look at a and it's intersections with p and q.
based on the rules of intersecting lines (the angles of intersecting lines are the same in both sides of any of the lines, they are only left-right mirrored) and then parallel lines at that (the intersecting angles of a line with parallel lines are the same with every parallel line, otherwise they are not parallel).
angle 2 = angle 5 = angle 10 = angle 13
therefore,
8x + 14 = 10x - 10
14 = 2x - 10
24 = 2x
x = 24/2 = 12
angle 2 = 8×11 + 14 = 88 + 14 = 102°
because of the same rules of intersecting lines and parallel lines. it is also clear that
angle 4 = angle 7 = angle 12 = angle 15
therefore,
13y + 19 = 15y + 5
19 = 2y + 5
14 = 2y
y = 14/2 = 7
angle 4 = 13y + 19 = 13×7 + 19 = 91 + 19 = 110°
if a and b would be parallel too, then the principle of the same angles would be true not only top-down (as for the pervious 2 problems) but also left-right.
and then angle 2 would be equal to angle 4.
but they are not.
although the difference is small, it means a and b will intersect somewhere.
and they are therefore not parallel.
A bird takes off from the ground and flies up at a rate of 4 ft per second. A leaf drops from a tree from a height of 21ft
and floats to the ground at a rate of 3 ft per second.
a. Write a system of equations to model this situation.
Step-by-step explanation:
To model this situation, we can set up two equations: one for the bird and one for the leaf.
For the bird, we can let t be the time in seconds and h be the height of the bird in feet. We know that the bird flies up at a rate of 4 feet per second, so we can write the equation:
h = 4t
This equation represents the height of the bird at any given time t.
For the leaf, we can also let t be the time in seconds and h be the height of the leaf in feet. We know that the leaf drops from a height of 21 feet and floats to the ground at a rate of 3 feet per second, so we can write the equation:
h = 21 - 3t
This equation represents the height of the leaf at any given time t.
Together, these two equations form a system of equations that can be used to model the situation.
Data shown in a frequency table could be displayed in which of the following graphs?
line graph
line plot
bar graph
stem-and-leaf plot
(MULTIPLE CHOICE, PICK MORE THAN ONE ANSWER!!!!!)
The data that is shown in a frequency table can be displayed in:
line graphbar graphWhich type of graphs can display data from frequency tables ?There are several types of graphs that can be used to display data from frequency tables, including bar graphs, line graphs, and histograms. Bar graphs are a type of graph that use bars to represent different categories or groups of data, with the height of the bars representing the frequency of each category.
Line graphs are a type of graph that use a series of connected points to show trends or changes in data over time, with the height of the points representing the frequency of the data.
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Find the equation of the exponential function
In the solid figure below, what is the volume of the top section of the figure? 20 cm 3 10 cm 3 9 cm 3 40 cm 3
The volume of the top section of the figure is 16 cm³.
What is the volume?The volume of a body is a three - dimensional region, enclosed by a two - dimensional curve. Mathematically, we can write volume as → Vₙ = ∫∫∫(V{x, y, z}dx dy dz.The volume of cuboid is given by → V = l x b x hGiven is the solid cuboidal figure as shown in the image.
The volume of the top cuboidal figure will be -
V = L x B x H
V = 2 x 2 x 4
V = 4 x 4
V = 16 cm³
Therefore, the volume of the top section of the figure is 16 cm³.
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OB Susan's Lawn Care $20 Number of Hours Worked 2 3 7 Amount Charged (dollars) 48 11 72 168 Amount Charged (dollars) 1 2 3 4 5 6 Number of Hours Worked What is the difference between Susan's and Jim's lawn-care businesses in the amounts they charge for 10 hours of work? OA. $16 264 140 120 100 80 60 40 20 0 Jim's Lawn Care Jim charges for lawn Previous Next →
Jim's and Susan's lawn care businesses charge different rates for a 10-hour shift; the difference is $40.
How should a number be read?The groupings of numbers include ones, tens, scores, tens, millions, and so forth. Ones, tens, or hundreds are the three subgroups that make up each group. When printing or reading a huge number, start with both the largest group on the left and work your way right.
work done = force × distance. W = F s. When the amount of work (W) is expressed in joules.
It will be Susan's Charge for ten hours.
= 168 + 72 $
= 240 $
while Jim Charges was for 10 hours
= 120 + 80 $
= 200$
The rates Susan and Jim charge during 10 hours of labor in their respective lawn care businesses are as follows:
= 240 - 200 $
= 40$
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11. Given f(x) = -2/5x +4, which statement is true of the inverse function f-¹(x)?
1) f-¹(x) is a line with slope 5/2
2) f-¹(x) is a line with slope 2/5
3) f-¹(x) passes through the point (6,-5)
4) f¹(x) has a y-intercept at (0,-4).
f-¹(x) is a line with slope -5/2. The correct option is 1.
What is the inverse of the function?The inverse of the function is calculated by replacing or interchanging the variables x and y with each other. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Given that the function is f(x) = -2/5x +4. The inverse function of the given function will be calculated as,
y = -2/5x + 4
x = -2/5y + 4
2/5y = -x + 4
y = -5 /2x + 4
f-¹(x) = -5/2x + 4
Hence, the slope of the inverse function is -5/2.
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A spinner has 10 sections numbered 1 to 10. Consider the events in the table.
Event A
Spin an odd number
Event B Spin a number greater than 5
Event C
Spin a 4
Event D Spin a multiple of 2
Which pairs of events are disjoint and cannot occur at the same time?
Select all that apply.
Events A and B
Events B and C
Events C and D
Events A and C
Events A and D
The pairs of events that are disjoint and cannot occur at the same time are:
Events A and CEvents A and DWhat are disjoint events?Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time.
For example, the results of a single coin flip, which can result in either heads or tails but not both is a disjoint event since both head and tail cannot appear.
Considering the events given:
Event A: Spin an odd number
Event B: Spin a number greater than 5
Event C: Spin a 4
Event D: Spin a multiple of 2
Event A and Event C are disjoint because one cannot spin an odd number and a 4 since it is an even number.
Event A and Event D are disjoint because one cannot spin an odd number and a multople of 2 since it will an even number.
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Write in standard form if needed, then classify the polynomial.
25-9m^2 -m + 4m^3
The polynomial in the standard form is 4m³ - 9m² - m + 25. Then the polynomial is a cubic polynomial.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The polynomial is given below.
⇒ 25 - 9m² - m + 4m³
Convert the polynomial into its standard form. Then we have
⇒ 25 - 9m² - m + 4m³
⇒ 4m³ - 9m² - m + 25
The degree of the polynomial is 3. Then the polynomial is a cubic polynomial.
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ical Models with Applications - MA4072 A (Senior Math)
Online Content Active
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.
Online Content: Site 1
Explain the 2 different answers you can get when solving an equation and the variable is eliminated.
X D
A BIUS
X₂ x² =
Ω
I
English
T
Tutoring He
Senior Math Online Content Active ical Models with Applications - MA4072 A Click to read the online material. when an element is removed from the RHS or LHS.
What is the ways to different answers for solving an equation ?Think about a single-variable equation 2 x+5=4 x+3
If a variable is not dropped from either the LHS or the RHS, we obtain a different solution.
Put the variable on one side and the constant on the other.
[tex]$$\begin{aligned}& \rightarrow 4 x-2 x=5-3 \\& 2 x=2\end{aligned}$$[/tex]
on both sides, divide by two.
x=1
We will now only have constants, which may or may not be equal, if we remove the variables from both sides.
Now, suppose LHS if we drop inequality from one side.
4 x+3=5
4 x=5-3
[tex]$$\begin{aligned}& 4 \mathrm{x}=2 \\& x=\frac{2}{4} \\& =\frac{1}{2}\end{aligned}$$[/tex]
We eliminate inequity from the opposite side, or RHS.
[tex]$$\begin{aligned}& 5+2 x=3 \\& 2 x=3-5 \\& 2 x=-2\end{aligned}$$[/tex]
By dividing by 2, x equals -1 on both sides. As a result, we have three different solutions when no variable is dropped from any side; and when a variable is dropped from either the LHS or the RHS.
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Keisha is going to the airport. It is 5:31 PM right now. Keisha's flight will depart in 3 hours 48 minutes. What is the departure time of her flight?
Answer:
9:37
Step-by-step explanation:
right!
Answer:
8:19
Step-by-step explanation:
There is 1/3 gallon of water in a 3-gallon container. What fraction of the container is filled?
1. Write a multiplication equation and a division equation to represent the situation.
Answer: One-third of a gallon divided by 3 gallons equals one-ninth.
Step-by-step explanation: 1/3 / 3/1 = 1/3 x 1/3 = 1/9
Ravi scored 18 marks out of 25 in a maths unit test. What is the percentage of marks scored by him.
The percentage of the marks scored by Ravi is 72%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Ravi scored 18 marks out of 25 in a maths unit test. The percentage of the marks will be calculated as,
Percentage = ( Marks obtained / total marks ) x 100
Percentage = ( 18 / 25 ) x 100
Percentage = 0.72 x 100
Percentage = 72%
Hence, the percentage will be 72%.
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help pls basic polygons
The values of x and y in polygon D is 95 and 85, and the value of x and y in polygon E is 85 and 95
What is polygon?In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).
Given:
The polygon D having measure of an angle is 70°, 100°, 105°,
The polygon E has angles 100°, 95°, 70°
Calculate the value of x in the polygon D as shown below,
70 + 100 + 105 + y = 360
y = 360 - 275
y = 85
Hence, x = 180 - y (linear pair)
x = 180 - 85
x = 95
Calculate the value of x in the polygon E as shown below,
100 + 95 + 70 + y = 360
y = 360 - 265
y = 95
x = 180 - 95
x = 85
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I’ll give BRAINLIEST if correct
The total money remaining to be collected is given by -
R(x) = 8x² - 7x + 12.
What are expressions?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given is that the three friends collected some amount of money to buy the earphones. It is asked to find the amount of money still remaining to be collected.
The total cost of earphones are -
T(x) = 9x² - 3x + 4
The total money collected by the friends is -
C(x) = x² + x - 12 + 3x + 4
C(x) = x² + 4x - 8
Money still need to be collected -
R(x) = T(x) - C(x)
R(x) = 9x² - 3x + 4 - (x² + 4x - 8)
R(x) = 9x² - x² - 3x - 4x + 4 + 8
R(x) = 8x² - 7x + 12
Therefore, the total money remaining to be collected is given by -
R(x) = 8x² - 7x + 12.
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Estimate the quotient of 42.4 ÷ 7.28.
The quotient of the two decimal numbers 42.4 and 7.28 as required to be evaluated in the task content is; 5.82.
What is the quotient of the two decimal numbers as required to be determined?It follows from the task content that the quotient of the two decimal numbers given; 42.4 and 7.28 is required to be determined.
On this note, since the given division operation is;
42.4 ÷ 7.28
which may alternatively be written as; 42.4 / 7.28
By the use of a calculator; the quotient is therefore equal to;
= 5.824175824
However, when rounded to the nearest hundredth; we have;
= 5.82.
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Can you solve it to me?
Refer to the image uploaded, all the steps included
0.5 (-2 + 4d) -13 for d
Step-by-step explanation:
-13 x 4 = -52
-52 x 0.5 = -25
-2 x 0.5 = -1
-1 + -25 = -26
a). a car cost 34% more today than when it was sold. if the original cost of the car was $90000. find its price today.
b). during a sale, the price of a bicycle dropped from $160 to $125. what was the percentage decrease in price?
A) If the original cost of the car was $90000 and it now costs 34% more, the price has increased by 0.34*90000 = $30600. Therefore, the price today is 90000+30600 = $120600.
B) During the sale, the price of the bicycle dropped from $160 to $125, a difference of 160-125 = $35. This represents a decrease in price of 35/160 = 21.875%. Therefore, the percentage decrease in price is approximately 22%.
Math 5th grade
The table show the cost of a gym membership
The fee is 50$
Step-by-step explanation: The way I got this is by checking the differences between each month and finding out that each one is 30 and then I subtracted it from 80 and got 50$
4. The table below shows the number of basketball games and the total points scored by three
teammates.
Number of
Games Played
Total Points
Scored
Kiara 25 175
Cecilia 20 120
Kayleigh 15 105
a. Determine the ratio of total points scored to games played for each player.
b. Determine which two players’ points scored to games played ratios are proportional. Show
all work to justify your answer
The ratio of total points scored to games played for each player are Kiara 7:1, Cecilia = 6:1, and Kayleigh= 7:1. (b) The ratios of Kiara and Kayleigh are proportional
How to determine proportional ratio?You should know that two ratios are proportional to each other if they are equal. also, you should be aware that ratios show the number of times a number appears in another number when divided.
The parameters that will guide us to get these ratios are
Players Number of games Total points Ratios
Kiara 25 175 1:7
cecilia 20 120 1:6
Kayleigh 15 105 1:7
Therefore from the table shown above, the ratios of Kiara and Kayleigh are proportional with 1:7 respective.
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A friend proposes a game: Spin the spinner twice and if the sum is even, then you win. Let's say my spinner lands on 2 for the first spin, and then lands on 3 for the second spin.
My calculated sum would then be 5. However, if the sum is odd, then your friend wins. Is this a fair game?
The probability to know of it is a fair game depends on how the spinner is designed.
How to illustrate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.
It depends on how the spinner is designed and the probability of landing on each number. If the spinner is fair and each number is equally likely to be spun, then the probability of winning is 1/2, or 50%.
This means that over the long run, you would be expected to win half of the games you play. If you and your friend agree that these are the rules of the game and you both understand the probability of winning, then the game could be considered fair.
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Kathy has 5 red cards and 5 green cards. She shuffles the 10 cards and lays out 5 of the cards in a row in a random order. She will be happy if and only if all the red cards laid out are adjacent and all the green cards laid out are adjacent. For example, card orders RRGGG, GGGGR, or RRRRR will make Kathy happy, but RRRGR will not. The probability that Kathy will be happy is m/n where m and n are relatively prime positive integers. Find m +n
m+n = 8. The probability that Kathy will be happy is 3/8. This can be seen by counting the total number of possible arrangements of red and green cards that would make her happy (6). There are a total of 8 arrangements, so the probability is 3/8.
There are 6 possible arrangements of red and green cards that would make Kathy happy:
RRRRR, GGGGG, RRGGG, GGRRR, GRRRG, and RGGGR.
There are a total of 10 cards and 5 of them are laid out in a row, so the total number of arrangements is
10C5 = 10!/5!(10-5)!
= 10*9*8*7*6/5*4*3*2*1
= 10*9*8/5*4*3
= 8*9
= 72.
The probability that Kathy will be happy is the number of arrangements that make her happy (6) divided by the total number of arrangements (72). Therefore, the probability is
6/72
= 3/8.
Therefore, m+n = 8.
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Classify the equation 6(x+2)=(5x+7)
Answer:
x = -5
Step-by-step explanation:
6(x+2) = (5x+7)
6x + 12 = 5x + 7
x = -5
Find at least ten solutions to the linear equation 1/2x + y = 5, and plot the points on a coordinate plane. What shape is the graph of the linear equation taking?
The solutions of the linear equation is
x y
-8 9
-6 8
-4 7
-2 6
0 5
2 4
4 3
6 2
8 1
10 0
the graph is a straight-line graph
How to find the solutions of the linear equationThe solutions of the linear equation is the found by substituting an x value and solve for y
the given equation 1/2x + y = 5, rearranging the equation gives
y = 5 - 1/2 x
For x = -8, y = 5 - 1/2 * -8 = 9
For x = -6, y = 5 - 1/2 * -6 = 8
For x = -4, y = 5 - 1/2 * -4 = 7
For x = -2, y = 5 - 1/2 * -2 = 6
For x = 0, y = 5 - 1/2 * 0 = 5
For x = 2, y = 5 - 1/2 * 2 = 4
For x = 4, y = 5 - 1/2 * 4 = 3
For x = 6, y = 5 - 1/2 * 6 = 2
For x = 8, y = 5 - 1/2 * 8 = 1
For x = 10, y = 5 - 1/2 * 10 = 0
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