Answer:
x=900/47, y=720/47
4x=5y == 3600/47 (top and bottom angle values)
3x+3y == 4860/47 (left and right angle values)
If you want the values in mixed number form, reply back.
Step-by-step explanation:
You can set this up in many different ways.
First, the inverse angles are always equal, so 4x=5y
Additionally, 2 sets of angles are supplementary, meaning they add up to 180 degrees; they are 4x+3x+3y=180 and 5y+3x+3y=180; both are equal
You could simplify the above two equations to get 7x+3y=180 and 3x+8y=180, meaning that 7x+3y=3x+8y, and 4x=5y
This simplifies to y=4x/5
Additionally, you could add the equations, meaning that 10x+11y=360, and y=4x/5
This gives you the answer:
x=900/47 and y=720/47.
You could check this by plugging the values into the equation, and if you do the math (which, I know, is kind of painful), you get the supposed values, so hooray!
Answer:
The angles measuring 4x and 5y measure: 3600/47
The other two angles measure: 4860/47
Step-by-step explanation:
The angles measuring 4x and 5y are vertical angles. Vertical angles are congruent, so we have one equation: 4x = 5y.
The angles measuring 5y and 3x + 3y form a linear pair. Angles in a linear pair are supplementary, so their measures add up to 180 degrees. That gives us a second equation: 3x + 3y + 5y = 180, or simply 3x + 8y = 180.
We have a system of two equations in two unknowns, so we can solve for x and y.
4x = 5y
3x + 8y = 180
We will use the substitution method.
Solve the first equation for x: x = 5y/4
Substitute 5y/4 for x in the second equation.
3(5y/4) + 8y = 180
15y/4 + 8y = 180
15y + 32y = 720
47y = 720
y = 720/47
Substitute y with 720/47 in the first original equation and solve for x.
4x = 5y
4x = 5(720/47)
4x = 3600/47
x = 900/47
The angles measuring 4x and 5y measure: 4x = 4(900/47) = 3600/47
The other two angles measure: 3x + 3y = 3(900/47) + 3(720/47) = 2700/47 + 2160/47 =4860/47
the square root of 2.4² +.7²
the square root of 2.4² +.7² is 2.89
A salad dressing recipe requires at least 8 oz of oil to be combined with some combination of vinegar and lemon juice in a 16 oz container. What inequality models this situation? Let x represent the number of ounces of vinegar and let y represent the number of ounces of lemon juice. Enter your answer in the box.
Let x represent the number of ounces of vinegar
Let y represent the number of ounces of lemon juice
Oil required = 8 oz
Container can hold = 16 oz
So the inequality equation will be :
[tex]x+y+8\geq16[/tex]
Answer:
This is the right answer ♡ hope it helps ;)
Step-by-step explanation:
what is 31% as a decimal
The answer is 0.31.
Change the percentage sign into a decimal and then move it two places to the left. Then add a zero in front of the decimal.
Hope this helps. =)
Gotcha!
If you put 31/100 and divide it you would get 0.31
Answer:0.31
Tip: if you need to find the decimal of a number just simply place it over 100 & divide!
Determine whether the equation 2x + y = 8 is linear. If so, graph the function.
It is linear because both variables have an exponent of 1. (FYI: one of the exponents can be 0 and still be a linear equation).
2x + y = 8
-2x -2x
y = -2x + 8 ⇒ slope (m) = -2 and y-intercept (b) = 8
plot the y-intercept (0, 8). then plot the next point by counting the rise over run from the y-intercept. count 2 units down and 1 unit to the right = (1, 6).
Answer:
It is linear because both variables have an exponent of 1.
Step-by-step explanation:
Julio cubes a number and then the cube root of the result.he ends up with 20.what number did Julio start with
[tex](\sqrt[3]{x^{3} }) = 20[/tex]
x = 20
Answer: 20
Jaime puts 3 oranges on each tray. How many oranges does he put on 5 trays?
Write the slope-intercept form of the equation for the line.
Write the slope-intercept form of the equation for the line.
Answer:
Y=Mx+b
Step-by-step explanation:
Yay
This section of a page from a telephone directory shows a column of 11 names in 1 inch. Each page has four 10-inch columns. Write an algebraic expression for the approximate number of names in p pages of the directory
.
number of names(p) = 4 columns * 10 inches per column * 11 names per inch * page
number of names(p) = 4*10*11*p = 440*p
The algebraic expression for the number of names in p pages is 440*p
The algebraic expression to estimate the total number of names in p pages of the telephone directory is 440p, where p represents the number of pages.
Explanation:To calculate the approximate number of names in p pages of the telephone directory, we start with the given information: there are 11 names in a 1-inch column.
Since each page has four 10-inch columns, first we calculate the number of names in one column by multiplying the number of names in 1 inch by its height in inches:
11 names/inch × 10 inches = 110 names/column
Then, to find the number in 4 columns per page we multiply by 4:
110 names/column × 4 columns = 440 names/page
Finally, to find the number in p pages, we use the algebraic expression:
440 names/page × p pages = 440p
This expression can be used to estimate the total number of names in p pages of the directory.
please include graph if you can thanks!
first function is f(x)= x+4
We make a table, plug in some numbers for x and find out y
x y= x+4
-4 0
3 7
Then graph the table using points (-4,0) and (3,7)
Second function is f(x)= 2x - 1
We make a table, plug in some numbers for x and find out y
x y= 2x - 1
3 5
6 11
Then graph the table using points (3,5) and (6,11)
The graph is uploaded below
Please help 33-40, thanks!
33. -8 belongs to:
Set of real numbers; all rational and irrational numbersSet of integers; positive and negative whole numbers34. 14 belongs to:
Set of natural numbers; all positive whole numbersSet of real numbers; all rational and irrational numbers35. 9.23 belongs to:
Set of real numbers; all rational and irrational numbers36. [tex]1\frac{5}{9}[/tex] belongs to:
Set of real numbers; all rational and irrational numbers37. Zero (0) belongs to:
Set of Integers; all positive and negative whole numbersSet of real numbers; all rational and irrational numbers38. -1 belongs to:
Set of integers; all positive and negative whole numbersSet of real numbers; all rational and irrational numbers39. 1/2 belongs to:
Set of real numbers; all rational and irrational numbers40. 0.3 where 3 is recurring belongs to:
Set of real numbers; all rational and irrational numbersCan anyone help me please
Another instance when you may face a cost-benefit analysis is if you frequently visit a café that serves coffee. Yes, this example is near and dear to my heart. Some cafés offer special refillable mugs in an effort to reduce waste. One such mug at a particular café costs $3.50 and holds 16 oz. of delicious coffee. Refills of this mug are $0.50. If you elect to forgo this refillable coffee mug, you can buy a disposable cup of coffee that only holds 12 oz. for $1.00. At what volume of coffee does buying the refillable mug become cost-effective?
Refillable mug:
Fixed cost is $3.50 including 16 oz of coffee
Each additional 16 oz of coffee cost $0.50
Disposable cup:
Cost is $1.00 per 12 oz of coffee
We can build up a table showing number of purchases, cost, and amount of coffee for each type of purchase until we see the refillable cup becoming cheaper.
Refillable Mug Disposable cup
Cost Amount Cost Amount
1 3.50 16 1.00 12
2 4.00 32 2.00 24
3 4.50 48 3.00 36
4 5.00 64 4.00 48
5 5.50 80 5.00 60
Notice that with 3 fill ups of the refillable cup, you have bought 48 oz of coffee for $4.50. With the disposable cup, the same 48 oz of coffee represent 4 cups, but at only $4.00, so up to the amount of 48 oz of coffee, you are better off buying the disposable cups.
When you spend $5.00, you can have 64 oz of coffee using the refillable cup or 60 oz of coffee using the disposable cup. When you spend $5.00 and up, then the refillable cup gives you the better price.
Answer: The refillable cup becomes cost effective at 64 oz.
F(x) = 3x + 4 for (-6)
If x = -6
Plug in -6 for x
f(x) = 3x + 4
f(-6) = 3(-6) + 4
Remember to follow PEMDAS. First, multiply
3 x -6 = -18
Finally, add
-18 + 4 = -14
f(-6) = -14
f(-6) = -14 is your answer
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~Rise Above the Ordinary, Senpai
adding and subtracting mixed numbers
you add and subtract
Some of the rules of adding and subtracting mixed numbers are:
1) Change the mixed numbers into improper fractions
2) Find common denominators. Remember that what you do to the denominator you also do to the numerator.
3) Subtract
4) Answer
hope this helps
what is the product of two more than a number and seven is thirteen
The answer is x = 15
The equation would be x + 2 = 17
The product of two more than a number and seven is thirteen when x = 13/7 - 2.
Explanation:The question is asking us to find the product of two more than a number and seven, given that the result is thirteen. Let's call the number x. The expression "two more than a number" can be written as (x + 2). The equation can then be written as (x + 2) * 7 = 13. To solve for x, we divide both sides of the equation by 7, giving us x + 2 = 13/7. Subtracting 2 from both sides, we get x = 13/7 - 2.
So, the solution is x = 13/7 - 2.
Learn more about Algebra here:https://brainly.com/question/32436021
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Which expression is equivalent to 2/7k(k-7)? Assume k=0.A. 2/7-k,B. 2/7-2/k,C. 2k/7-7,D. 2k/7k-2k
[tex]\dfrac{2}{7k}(k-7)\qquad|\text{use distributive property}\\\\=\left(\dfrac{2}{7k}\right)(k)-\left(\dfrac{2}{7k}\right)(7)=\dfrac{2}{7}-\dfrac{2}{k}[/tex]
what is 2.85 to the nearest tenth?
The answer is 2.9. You would round up since there is a 5
You round it up to 2.9
What is 5 8/12 as a mixed number in simplest form
Your fraction is in a mixed number. But if you wanted an improper fraction it would be 17/3 in simplest form.
John’s car gets 36 miles to one gallon of gas. How much gas will he use to travel 81 miles?
81 ÷ 36 = 2.25
John will use 2.25 gallons of gas to travel 81 miles
as my teacher was explaining this, i didn't have enough time to ask her how we got to $20.00. so how do i get to 20 if the markup is $7.50?
You got the twenty by adding the markup price and the original price.
decimal to fraction help
Y=1/2x
Y= 4x
Y= 1/4 x
Y= 2 x
It's a line in form y = mx.
Two points:
(0, 0) and (1, 4)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{1-0}{4-0}=\dfrac{1}{4}[/tex]
Answer: [tex]y=\dfrac{1}{4}x[/tex]
Plot the x- and y-intercepts to graph the equation.
y=−x−5
Answer:
What what the answer
Step-by-step explanation:
cause i neeed it ;~;
a movie was sold out for four straight days. If 535 tickets were sold each day, how many tickets were sold in all???
x-3y=7 and 2x-6y=12 solving by elimination
x-3y=7 2x-6y=12
You can multiply -2 in the first equation like this.
x+6y=7
2x-6y=12
Now you can eliminate 6y and -6y so cross them out and do x-2 which is -1 and 7-12 which is -5 -1/-5 would be .2
how do i write y=25x in function notation
N/3 ≤ 3
Solve the Inequality and show all work!
Answer:
n ≤ 9
Step-by-step explanation:
Step 1: Simplify both sides of the inequality
1/3n ≤ 3
Step 2: Multiply both sides by
3* (1/3n) ≤ (3)*(3)
n ≤ 9
Hope this helps :-)
A customer returned a light fixture to the store in exchange for a $52 light fixture and three gallons of paint at $29 each.He had to pay $112.How much had he paid for the first light fixture
$29 times 3 is $87
$112-$87 = $25
52-25= 35
The customer paid $35 for the first light fixture. I think.
The cost of the first light fixture is $27.
Given that, a customer returned a light fixture to the store in exchange for a $52 light fixture and three gallons of paint at $29 each.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the cost of first light fixture be x.
Now, x=52+3×29 - 112
=52+87 - 112
= 139 - 112
= 27
Therefore, the cost of the first light fixture is $27.
To learn more about an equation visit:
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how many pounds of premium coffee beans thats $9.50 pounds should be mixed with 2 pounds of supreme coffee thats $11.75 pounds to make the blend coffee that's 10.00 pounds
Answer:
We need to add 7 pounds of $9.5 premium coffee to make a blend of coffee that $10.
Step-by-step explanation:
Lets take the amount of $9.50 coffee added was [tex]x[/tex] pounds.
The requirement is that the value of 1 pound of resulting mixture of coffee to be $10.
We can use the weighted average value to find the value of the resulting mixture.
⇒[tex]\frac{(9.5*x)+(11.75*2)}{(x+2)} =10[/tex]
=[tex](9.5*x)+(23.5)=10(x+2)[/tex]
=[tex]9.5x+23.5=10x+20[/tex]
=[tex]3.5=0.5x[/tex]
=[tex]x=7[/tex]
So we need to add 7 pounds of $9.5 premium coffee to make a blend of coffee that $10.
7 pounds of premium coffee at $9.50 per pound should be mixed with 2 pounds of supreme coffee at $11.75 per pound to create a blend that costs $10.00 per pound. An equation is set up and solved to find the amount of premium coffee needed.
The student is asking how many pounds of premium coffee beans at $9.50 per pound should be mixed with 2 pounds of supreme coffee costing $11.75 per pound to create a coffee blend that costs $10.00 per pound. To solve this, we can set up an equation to represent the total cost of the coffee before and after mixing.
Let x be the number of pounds of premium coffee that we want to find. The cost for the premium coffee will then be x times $9.50. For the supreme coffee, we have 2 pounds at $11.75 per pound which gives us a total cost of $23.50. For the blend, we want the total pounds of coffee, which is x + 2 pounds, to be multiplied by the target price of $10.00 per pound.
The equation that represents the price point of the mixture is:
9.50x + 23.50 = 10.00(x + 2)
To find x, we solve the equation by distributing the $10.00 across x + 2 and moving all terms involving x to one side to isolate the variable:
9.50x + 23.50 = 10.00x + 20.00
Subtracting 9.50x from both sides:
23.50 = 0.50x + 20.00
Subtracting 20.00 from both sides gives us:
3.50 = 0.50x
Dividing both sides by 0.50 gives us the result:
x = 7 pounds
Therefore, 7 pounds of premium coffee at $9.50 per pound should be mixed with 2 pounds of supreme coffee at $11.75 per pound to obtain a blend that costs $10.00 per pound.
What are 3 fractions that have the same product as 30/64
15/32 - .4688 - 11.9063
I'm sorry what are you asking for??