y-intercept: (0,4)
x-intercept: (8,0)
Y-intercept:
I made x=0
[tex]0+2y=8\\[/tex]
divide by 2 on both sides
[tex]y=4[/tex]
x-intercept
I made y=0
[tex]x+2(0)=8\\x=8[/tex]
the sum of the perimeter of two squares is 40cm while the sum of the area is 58cm². Find length the side of the square.
[tex]a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}[/tex]
[tex]\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}[/tex]
The sides of the squares will be 3 and 7.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
Area of square = Side²
The perimeter of the square = 4× side
Length of diagonal of square = √(2) × side
Let's say the side of the first square is a while the second is b
Now,
the sum of the perimeter of two squares is 40cm
4a + 4b = 40
a + b = 10
Now,
The Sum of the area is 58cm²
So,
a² + b² = 58
By substituting,
a² + (10 - a)² = 58
a² - 10a + 21 = 0
a² - 7a - 3a + 21 =0
a(a - 7) - 3(a - 7) = 0
(a-3)(a - 7) = 0
a = 3 ,7
Corresponding to 3 and 7
b = 10 - 3 = 7 and b = 10 - 7 = 3.
Hence "The sides of the squares will be 3 and 7".
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WILL MARK AS BRAINLIEST IF CORRECT!
What is the distance between (0,0) and (3,4)
a. 5
b. 4
c. 3
d. 2
Answer:
Your answer is A:5
Why is math important “?
Answer:
Without math, how would we know how to count seconds minutes, etc.?
Math is extremely important for knowing how to do simple things like cooking, you need to know for how much time to put something in the oven or microwave or stove. Those are just the basics. There is a lot more stuff out there that math is used for.
If you want to get a job, you have to know about math. Without math, you will be unable to get a job. Every single job you can get requires math. Even working in a grocery store, you need math. Whether we like it or not, you will have to learn math or you'll end up homeless and without a job.
What is the hypothesis of the following conditional statement: If a quadrilateral has 4 right angles, then the quadrilateral is a rectangle.
f a quadrilateral has 4 right angles.
A quadrilateral has 4 right angles.
Then the quadrilateral is a rectangle.
The quadrilateral is a rectangle.
The hypothesis of the conditional statement given is a quadrilateral has 4 right angles.
This is the 'If' part of the 'If P then Q' structure of a conditional statement.
Explanation:In a conditional statement in logic, the statement is usually given in the form 'If P then Q'. Here, 'P' is called the Hypothesis, and 'Q' is the Conclusion. In the statement 'If a quadrilateral has 4 right angles, then the quadrilateral is a rectangle', the Hypothesis (P) is a quadrilateral has 4 right angles. So, to answer your question, the hypothesis of this conditional statement is that a quadrilateral has 4 right angles.
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Can someone help with the first question
he table shows the total cost for different numbers of jackets. Number of Jackets 2 5 7 Total Cost ($) 46.50 116.25 162.75 What is the cost of 3 jackets?
Answer:
$69.75
Step-by-step explanation:
2 jackets cost $46.50 and 5 jackets cost $116.25
The different between 5 and 2 is 3.
So the cost of 3 jackets would be =$116.25 - $46.50
= $69.75
A store sells four 1 1/8-pound ears of corn in a package for $3.59. The expression 3.59p represents the cost of the corn for a number of packages. What does the variable p represent? PLZZ HELPP
a. The number of ears of corn purchased
b. The cost of one package of corn
c. The number of packages of corn purchased
d. The cost of one ear of corn
Answer:
c. The number of packages of corn purchased.
Step-by-step explanation:
We have been given that a store sells four 1 1/8-pound ears of corn in a package for $3.59. The expression [tex]3.59p[/tex] represents the cost of the corn for a number of packages.
Since the cost of each package of corn is $3.59 and [tex]3.59p[/tex] represents the cost of 'p' packages of the corn. So 'p' represents the number of packages of corn purchased.
Upon looking at our given choices, we can see that option C is the correct choice.
Write an expression equivalent to the one below
5(x + 6)-2x + 9
Answer:
5x+30-2x+9
Step-by-step explanation:
first you have to do the ''distributive property'' then you will get 5x+30-2x+9
Question
Write an expression equivalent to the one below
5(x + 6)-2x + 9
Answer:
2x + 10 + 29 + xStep-by-step explanation:
5(x + 6)-2x + 9 =
5x + 30 - 2x + 9 =
3x + 39
----------------------------
2x + 10 + 29 + x =
3x + 39
At the start of the 20th century,there were about 100,000 tigers in the wild.In 2014 there were about 3,200.What percent did the population decrease
The population decreased 96.8%.
Initial value = 100,000
Final value = 3,200
The percentage decrease is
= (Final value - initial value) * 100% /initial value
= [tex]\frac{\left(3200-100000\right)}{100000}\cdot100 \%[/tex]
= −96.8%
Negative sign because of decrease.
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PLEASE HELPPP!!!
WILL GIVE THE BRAINLEST!!!
Answer:
5.) Proportionality is 3/1 or 3 simplified
b x 3 = pb= boxesp= pens in box6.) Proportionality is 1/6
m ÷ 6 = pm = muffinsp= pack(s) of muffinsStep-by-step explanation:
You would take the first column (or in this case row (pens and packs) and place the 2nd row under it in fraction form.
5.) 3/1 = 36.) 1/6 = 1/6That would be your proportion
Then you would (in place of numbers) use letters to symbolize in the equation
5.) p = pens: b= boxes6.) m= muffins; p= packThen create an equation to figure out how to get the correct numbers.
1 box holds 3 pens so:5.) b x 3 = pCheck: 2 boxes x 3 pens per box = 6 pens (check table) Correct!6 muffins in 1 pack so:6.) m ÷ 6 = p12 muffins ÷ 6 muffins in per box = 2 packs (check table) Correct!The bowling club at your school had a car wash last week.
They washed 72 cars in 6.5 hours.
About how many cars did they wash per hour?
Answer:
This is approximately 11 cars per hour
Step-by-step explanation:
We want to find the the cars per hour so we will divide cars/ hour
72 cars/6.5 hours
11.07692308 cars per hour
This is approximately 11 cars per hour
Answer:
11.08 cars per hour Please give brainliest.
Step-by-step explanation:
72 ÷ 6.5 = 11.076 = 11.08 cars per hour
What are the zeros of the quadratic function f(x)=8x2-16x-15
Answer:
x = 2.696, x = -0.696
Step-by-step explanation:
We are given the following function of x and we are to find the zeros for the given quadratic function:
[tex]f(x)= 8x^2-16x-15[/tex]
To find its zeros, we will use the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values in the formula where [tex]a=8[/tex], [tex]b=-16[/tex] and [tex]c=-15[/tex].
[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4(8)(-15)} }{2(8)}[/tex]
[tex]x=\frac{16+-\sqrt{736} }{16}[/tex]
[tex]x=\frac{16+27.13}{16}[/tex] , [tex]x=\frac{16-27.13}{16}[/tex]
[tex]x = 2.696[/tex] , [tex]x=-0.696[/tex]
Therefore, the solutions are 2.696 and -0.696.
Answer: c on edge
Step-by-step explanation:
x=1-square root 23/8 and x=1+square root 7
mrs tran mowed 1/4 of the lawn. her son mowed 2/5 of it. who mowed more. how much of the lawn still need to be mowed
Answer:
Her son mowed more and 7/20 need to be mowed
Step-by-step explanation:
1/4 x 5 = 5/20 - Mrs Tran
2/5 x 4 = 8/20 - her son
20/20 - 13/20 = 7/20 needs to be finished
A pet store runs two different training programs. The first program charges a $35 membership fee and $5 for each class. The second program does not have a membership fee, but charges $10 for each class. For how many classes will the programs cost the same? The variable c represents the number of classes and t represents the total cost. Which equations create the system to represent the scenario? Check all that apply.
t = c + 35
t = 5c
t = 5c + 35
t = 10c
t = 10c + 35
Answer:
Step-by-step explanation:
the answer is
t=5c+35
t=10c
i just did this problem and got it right.
To represent the scenario of two training programs with different costs, we can use the equations t = c + 35 and t = 5c.
Explanation:In this scenario, we have two different training programs at a pet store. The first program charges a $35 membership fee and $5 for each class.
The second program does not have a membership fee, but charges $10 for each class. We want to find out for how many classes the total cost will be the same for both programs.
To create the system of equations, we can use the variable c to represent the number of classes and t to represent the total cost. The equations that represent the scenario are:
t = c + 35
t = 5c
Roger Ratkin has three employees who earn $500, $550, and $700, respectively. How much does Roger owe for the first 12 weeks for SUTA and FUTA? Assume a SUTA rate of 5.3% and a FUTA rate of .8%.
The answer explains how to calculate the SUTA and FUTA amounts owed by Roger Ratkin for the first 12 weeks for his employees' wages.
Explanation:State Unemployment Tax Act (SUTA) and Federal Unemployment Tax Act (FUTA)
Calculate SUTA amount: ($500 + $550 + $700) * 5.3% * 12 weeks = $744.Calculate FUTA amount: ($500 + $550 + $700) * .8% * 12 weeks = $55.20.Therefore, Roger owes a total of $799.20 for SUTA and FUTA for the first 12 weeks for his three employees.The graph shows a proportional relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes (x).
PLS HELP ASAP! WILL GIVE BRAINLIEST TO CORRECT ANSWER!
Answer:
0.33 Km/Min
Step-by-step explanation:
What is the solution to the system of equations shown below? Be sure to list your solution as an ordered pair in the form (x,y)
On the graph, the solution to the system of equations is the point of intersection (the point where the lines meet)
So the solution is (-4, 3)
Answer:
The solution for the system is [tex](-4,3)[/tex], that is, [tex]x=-4[/tex] and [tex]y=3[/tex].
Step-by-step explanation:
The solution of a system of equations can be find by using different methods, one of them is the graphic method, which is the one aplied to this problem.
When we use the graphic method to solve a system of equations, the interception point of both line represents the solution of such system.
Therefore, in this case, the solution for the system is [tex](-4,3)[/tex], that is, [tex]x=-4[/tex] and [tex]y=3[/tex].
The ages of Anjali and Aditya are in the ratio 3: 4.Eight years later sum
of their ages will be 44 years. What are their present ages
Answer:
12 years and 16 years
Step-by-step explanation:
their ages are in the ratio 3 : 4
let Anjali = 3x and Aditya = 4x ← present ages
In 8 years then
Anjali = 3x + 8 and Aditya = 4x + 8, hence
3x + 8 + 4x + 8 = 44 ← sum of their ages in 8 years
7x + 16 = 44 ( subtract 16 from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Anjali is 3x = 3 × 4 = 12 years old and Aditya = 4x = 4 × 4 = 16 years old
Plz help me answer A and B
For both questions, you essentially use the equation r = d/t
a. 34/7 = about 4.86 dollars per hour
b. 4/10 = 0.40 dollars per pound.
Estimate the sum or difference. Use the benchmarks,0, 1/2, and 1.
23/40- 11/30
A.0
B.1
C.1/2
Answer:
A. 0
Step-by-step explanation:
23/40 is approximately 1/2.
11/30 is approximately 1/2.
Sine 1/2 - 1/2 = 0, then 23/40 - 11/30 is approximately 0.
By converting the given fractions to a common denominator and performing subtraction, the result falls closest to the benchmark of 0. Hence, the estimated sum or difference of 23/40 and 11/30 is 0.
Explanation:The given problem is 23/40 - 11/30 and the student has to estimate the result using the benchmarks 0, 1/2, and 1.Steps to resolve the problem:
First, convert both fractions to a common denominator. The smallest number that both 40 and 30 divide into evenly is 120. Therefore, we multiply 23/40 by 3/3 to get 69/120, and 11/30 by 4/4 to get 44/120.Then, subtract the fractions: 69/120 - 44/120 = 25/120.Here, 25/120 is close to 1/4.The benchmark that is closest to 1/4 is 0. So, the estimated sum or difference would be 0.
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Solve. |x+5|>12 Help it would be great
Answer:
x < - 17 or x > 7
Step-by-step explanation:
Inequalities of the form | x | > a always have solutions of the form
x < - a or x > a
For | x + 5 | > 12, then
x + 5 < - 12 or x + 5 > 12 ( subtract 5 from both sides of the inequalities )
x < - 17 or x > 7
the grand prix cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket costs $7.75 and an adult ticket cost $10.25. if the cinema sold $1470 worth of tickets, which system of equations would be used to determine how many adult tickets, a, and how many child tickets, c, were sold?
The problem requires setting up a system of two equations: one representing the total number of tickets sold (c + a = 150) and the other representing the total revenue from ticket sales (7.75c + 10.25a = 1470). Solving this system will yield the number of adult and child tickets sold.
Explanation:To determine how many adult tickets, a, and child tickets, c, were sold by the Grand Prix Cinema, we need to establish a system of equations based on the given information:
The total number of tickets sold was 150: c + a = 150.The total revenue from tickets was $1470: 7.75c + 10.25a = 1470.These two equations can be used simultaneously to solve for the variables a (adult tickets) and c (child tickets). This problem is an example of a linear system of equations that can be solved by various methods such as substitution, elimination, or matrix operations.
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Which equation and solution represents each situation? Solutions may be rounded to the nearest tenth. What number is 74% of 58?
42.9
Step-by-step explanation:"74% of 58" translates to ...
... 74/100 × 58 = 42.92
Rounded to the nearest tenth, this is 42.9.
_____
Comment on translation
In this context, "of" means "times." Of course, % means /100, so ...
... 74% = 74/100 = 0.74
I used an RX savings card The prescription normally would be $11.00 With the free discount card I only paid $7.00. What was my percentage of savings using the free Rx savings card?
Answer:
=36.36 percent
Step-by-step explanation:
First we need to determine what you saved
11-7 = 4
You saved 4 dollars
Percentage of savings = savings /original price * 100
= 4/11 * 100
=36.36 percent
You saved $4.00 using an RX savings card on a prescription that originally cost $11.00. To find how much you saved in percentage terms, you divide the amount saved by the original cost and multiply by 100. In this case, you saved approximately 36.36%.
Explanation:You are asking about the percentage savings when using a free RX savings card. To get the savings percentage, you first need to know how much money you saved. In your case, you would have paid $11.00, but you only paid $7.00 with the RX savings card. That means you saved $11.00 - $7.00 = $4.00.
Next, to find the savings as a percentage, you divide the amount saved by the original cost, then multiply by 100 to get a percentage. Here's the calculation:
Savings Percentage = ($4.00 / $11.00) * 100
Doing the division first (4 ÷ 11 = 0.3636), then multiplying by 100, you saved approximately 36.36% with your RX savings card.
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buses on your route run every 8 minutes from 7:00 am to 11:00 am. you arrive at the bus stop at 8:19. how long will you wait for the bus?
a: 1 minutes
b: 3 minutes
c: 7 minutes
d: 8 minutes
Answer:
A: 1 Minute
Step-by-step explanation:
Buses start running at 7 and run every eight minutes. This means that:
Bus 1: 7:00 AM
Bus 2: 7:08 AM
Bus 3: 7:16 AM
Bus 4: 7:24 AM
Bus 5: 7:32 AM
Bus 6: 7:40 AM
Bus 7: 7:48 AM
Bus 8: 7:56 AM
Bus 9: 8:04 AM
Bus 10: 8:12 AM
Bus 11: 8:20 AM
The waiting time of the bus is 7 minutes,
To calculate the waiting time, we need to break down the time difference between your arrival (8:19 am) and the next bus arrival (scheduled to come every 8 minutes). Let's start by determining the time between 8:19 am and the next scheduled bus at 8:20 am. This is only 1 minute of waiting time.
However, you want to know how long you'll have to wait until the next bus after 8:20 am, which means we need to consider the remaining time until the next 8-minute interval. From 8:20 am to 8:24 am, the bus does not arrive yet, resulting in an additional 4 minutes of waiting time
=> (8:24 am - 8:20 am = 4 minutes).
Now, we have reached the second 8-minute interval from 8:24 am to 8:28 am. As you arrived at 8:19 am, you will have to wait for 5 more minutes
=> (8:28 am - 8:19 am = 7 minutes)
to catch the bus.
So, the Main Answer: c: 7 minutes.
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Help please ASAP!!! I’ll mark brainliest
Leo weighs 10 pounds of dog food at the pet store. The scale mistakenly lists the bag at 11.5 pounds
Answer:
percent error = 15%
Step-by-step explanation:
The following question is missing: What is the percent error?
percent error = (measure error/ actual weight)*100
where:
measure error = incorrect weight - correct weight = 11.5 - 10 = 1.5 pounds
percent error = (1.5/10)*100 = 15%
Solve for x. The polygons are similar
[tex]\frac{8x-2}{42}=\frac{63}{49}\\\frac{8x-2}{42}=\frac{9}{7}\\7(8x-2)=9\cdot42\ /:7\\8x-2=9\cdot6\\8x-2=54\\8x=54+2\\8x=56\ /:8\\x=7[/tex]
1. Two boats A and B depart from a port at the same time, travels to the north at 15 miles per hour, while B travels eastward at 20 mph. How fast boats are separated two hours after they left the port?
Answer:
50 mi
Step-by-step explanation:
Two hours after leaving port,
Boat A has travelled 30 mi north Boat B has travelled 40 mi east.The triangle formed by their tracks and the line joining their current positions is a right-angled triangle.
According to Pythagoras,
a² + b² = c²
30² + 40² = c²
900 + 1600 = c²
2500 = c²
√(2500) = c
c = 50 mi
The boats will be separated by 50 mi two hours after leaving port.
I am a two digit odd number less than fifty. The sum of my digits is seven and my root is 5. What number am I?
Answer: 25
Step-by-step explanation: