Answer:
(a) 2000 mL
(b) 70 mL, 30 mL
(c) No
Step-by-step explanation:
Given that Artesia is a 70% acid solution, and Borromeo is a 20% acid solution.
(a) Let x mL of Artesia is added to 500 mL of Borromeo to produce a 60% acid solution.
So, 70% of x + 20% of 500 = 60% of (x+500)
[tex]\Rightarrow 0.7 \times x + 0.2 \times 500 = 0.6 \times (x+500) \\\\\ \Rightarrow 0.7 \times x + 0.2 \times 500 = 0.6 \times x+0.6 \times500\\\\ \Rightarrow 0.7 \times x -0.6 \times x= 0.6 \times500- 0.2 \times 500 \\\\ \Rightarrow (0.7-0.6) \times x = (0.6-0.2) \times500\\\\\Rightarrow 0.1 \times x = 0.4 \times500\\\\[/tex]
[tex]\Rightarrow x = (0.4 \times500)/0.1=2000[/tex] mL.
(b) Let x mL of Artesia and y mL be combined in order to form a 100 mL solution having 55% acid solution.
So, x+y=100\Rightarrow y= 100-x
And, 70% of x + 20% of y = 55% of (100)\\\\
[tex]\Rightarrow 0.7 \times x + 0.2 \times (100-x) = 0.55 \times 100\\\\\Rightarrow 0.7 \times x + 0.2 \times 100- 0.2 \times x = 0.55 \times 100\\\\\Rightarrow 0.7 \times x -0.2 \times x= 0.55 \times100- 0.2 \times 100 \\\\\Rightarrow (0.7-0.2) \times x = (0.55-0.2) \times100\\\\\Rightarrow 0.5 \times x = 0.35 \times100\\\\[/tex]
[tex]\Rightarrow x = (0.35 \times100)/0.5=70[/tex] mL.
and y= 100-x= 100-70=30 mL.
(c) Let x mL of Artesia and y mL of Borromeo be combined in order to make 80% acid solution.
And, 70% of x + 20% of y = 80% of (x+y)
[tex]\Rightarrow 0.7 \times x + 0.2 \times y= 0.8 \times (x+y)\\\\\Rightarrow 0.7 \times x + 0.2 \times y = 0.8 \times x +0.8 \times y\\\\\Rightarrow (0.7-0.8) \times x = (0.8-0.2) \times y\\\\\Rightarrow -0.1 \times x = 0.6 \times y \\\\\Rightarrow \frac {x}{y} = -6 \\\\[/tex]
As x and y are amount of Artesia and Borromeo, so x>0 and y>0
[tex]\Rightarrow x/y >0[/tex], so the negative value of x/y is not possible.
Ad the negative value of x/y is not so x/y=-6 is not possible, hence, any combination of Artesia and Borromeo that is 80% acid solution is not possible.
Write a quadratic equation with the given transformations from the parent function y = x2
4) Reflect over x-axis, shift to the left 5 units, shift up 7 units
5) Vertical stretch by a factor of 4, shift down 11 units
6) Vertical compression by a factor of, reflect over x-axis, shift to the right 2 units, shift up 3 units.
Answer:
4
Step-by-step explanation:
By Using the Transformations of the parabola
[tex]y = -(x+5)^2+7\\y=4x^{2} +7\\y = -(x-2)^2+3[/tex]
Vertical Translation move the graph vertically - up or down[tex]y = x^2+ k[/tex]
Horizontal Translation move the graph horizontally - left or right[tex]y = (x - h)^2[/tex]
Reflection in x-axis
flip the graph over the x-axis, (negates the y-values of the coordinates)[tex]y = -(x^2)[/tex]
Reflection in y-axis
flip the graph over the y-axis,(negates the x-values of the coordinates)[tex]y = (-x)^2[/tex]
Stretch or Compress Verticallystretches away from the x-axis or compresses toward the x-axis
[tex]y = a .x^2[/tex]
| a | > 1 is a stretch;
0 < | a | <1 is a compression
Stretch or Compress Horizontallystretches away from the y-axis or compresses toward the y-axis
[tex]y=\frac{1}{a} x^{2}[/tex]
| a | > 1 is a compression by factor of 1/a;
0 < | a | <1 is a stretch by factor of 1/a
Now, we have [tex]y=x^2[/tex]
4). Reflect over x-axis, shift to the left 5 units, shift up 7 units
[tex]y = -(x+5)^2+7[/tex]
5) Vertical stretch by a factor of 4, shift down 11 units
[tex]y=4 x^{2} +7[/tex]
6) Vertical compression by a factor of, reflect over x-axis, shift to the right 2 units, shift up 3 units.
[tex]y=-(x-2)^{2} +3[/tex]
Learn more:https://brainly.com/question/20369546
I don't understand this
Answer:
y=2/3x+3
Step-by-step explanation:
First, you would use the point slope formula : y₂-y₁/x₂-x₁
(5--3)/(3--9)
=8/12
=2/3
Then you would plug it back into the equation along with one of the points. Ex:
-3=2/3(-9)+b
-3=-6+b
3=b
So in conclusion, the formula would come out to y=2/3x+3
Hope this helps! :)
A triangle has interior angle measures of 5s, 3s - 9°, and 45°, what is the value of s?
Answer:
s = 18
Step-by-step explanation:
Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select three that apply.
Each pair of vertical angles is congruent.
Each pair of corresponding angles is congruent.
Each pair of supplementary angles is congruent.
Each pair of alternate interior angles is congruent.
Answer:
Step-by-step explanation:
Each pair of vertically opposite angles are equal. If you mean vertical angles as in 90 degrees, you should qualify the question
Each pair of alternate interior angles is congruent (think it should be are congruent).
Each pair of corresponding angles is congruent
if you use synthetic division for this polynomial: 3x^5-12x^4+12x^3+30x^2-39x-42. What would the answer be?
Answer : x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14
Explanation :
(3x^5-12x^4+12x^3+30x^2-39x-42)/3 = x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14
EASY QUESTION!!Example 3:
A soccer ball will not move until a player kicks it.
Group of answer choices
Newton's 1st Law
Newton's 2nd Law
Newton's 3rd Law
Give evidence or explain your reasoning for your answer to example #3:
Answer:
this is Newton's first law
Step-by-step explanation:
the soccer ball when kicked keep going forward until friction a person or another object like a wall stops it when the soccer ball is resting non-moving on the ground or stay like that until someone kicks it or another Force acts upon it
An amusement park charges a $12 parking fee plus 25 per person. What is the total cost for 32 people?
Answer:
The total amount for 32 people is 15.36
Step-by-step explanation:
we know that for 25 people is $12 so we need to find how much it would be for one person. you would need to divide $12 / 25. from this you would get 0.48, so for one person it's 48 cents. next you're going to subtract 25 from 32, this leaves you with seven people who aren't in a group of 25. you then multiply 7 × this equals to 3.36, add 3.36 to $12 and you'll get your total 15.36.
an object travels at 20 m/s for 20 seconds. how far has it traveled?
Answer:
400 meters
Step-by-step explanation:
So it goes 20 meters every second. So you would multiply that by 20 seconds to get 400 meters.
Shel bought a $6,000 desk based on her income she can only afford to pay 600 per month The charge on the unpaid balance is 2% each month Calculate the balance outstanding at the end of month 2
Answer:
$5,030.40
Step-by-step explanation:
The balance outstanding at the end of any month is the due amount after adjusting for interest and loan repayment amount. The amount outstanding can be calculated as:
First month
Due amount = $6,000
Interest at 2% = $6,000*2% = $120
Loan repayment = $600
Reduction in balance = $600 - $120 = $480
Balance remaining = $6,000 - $480 = $5,520
Second month
Due amount = $5,520
Interest at 2% = $5,520*2% = $110.4
Loan repayment = $600
Reduction in balance = $600 - $110.4 = $489.60
Balance remaining = $5,520 - $489.60 = $5030.40
Hence, the balance outstanding at the end of month 2 is $5,030.40
Just part A please as soonnn as possible I need help!!! Thanks!
Answer: -1 ≤ x ≤ 4.
Step-by-step explanation: To solve this problem, we first add 7 to the inequality: -4 ≤ 4x ≤ 16. Then we divide the entire equation by 4 to get -1 ≤ x ≤ 4.
9 = -d + 17
A.-2
B.8
C.10
D.-8
Question in picture solve
Answer:
x= 13.5
Step-by-step explanation:
f(x) = 2x + 9
f(x) = 36
Set the 2 equations equal to each other;
2x + 9 = 36
Subtract 9 from both sides;
2x = 27
Divide both sides by 2;
x = 13.5
Check:
f(x) = 2x + 9
f(13.5) = 2(13.5) + 9= 27 + 9 = 36
The highest elevation in a small country occurs on a mountain 1232 meters above sea level, while the lowest elevation in the same country occurs at -27 meters (below sea level). What is the difference in elevation between the highest and lowest points?
Answer: 1259 meters
Step-by-step explanation:
Highest elevation = 1232 meters
Lowest elevation = -27 meters
The difference in elevation between the highest and lowest points will be:
= 1232 - (-27)
= 1232 + 27
= 1259 meters
Note that (-) × (-) = +
Find the slope of the line that passes through the given two points:
(1,4) and (3,7)
m =
PLEASE HELP I DONT UNDERSTAND THIS
Answer: 3/2
Step-by-step explanation:
To find slope you use the formula: m= y2-y1/x2-x1
So plugging stuff in it’s (7-4)/(3-1)
This comes out to be 3/2
Which means when graphing you go up 3 and right 2
let f(x)= p+ 8/x-q. the line x=4 is a vertical asymptote to the graph of f. what is the value of q and p, if the y intercept is (0,4)?
Answer:
The value of q and p is 4 and -24 respectively.
Step-by-step explanation:
Being [tex]f(x)=\frac{p+8}{x-q}[/tex] , the line x=4 is a vertical asymptote to the graph of f(x). The line r is an asymptote of a function if the graph of the function is infinitely close to the line r. That is, an asymptote is a line to which a function approaches indefinitely, without ever touching it.
Being a rational function that which can be expressed as the quotient of two polynomials, a vertical asymptote occurs when the denominator is 0, that is, where the function is not defined. In this case:
x - q= 0
Solving:
x= q
Being the line x=4 the vertical asymptote, then
4=q
Then the function f (x) is:
[tex]f(x)=y=\frac{p+8}{x-4}[/tex]
The y intercept is (0,4). This is, x= 0 and y=4. Replacing:
[tex]4=\frac{p+8}{0-4}[/tex]
Solving:
[tex]4=\frac{p+8}{-4}[/tex]
4*(-4)= p+8
-16= p+8
-16 - 8= p
-24= p
The value of q and p is 4 and -24 respectively.
prove that 1 + cos 2A / sin 2A=CotA
Answer:
I assume that there are parentheses missing from the question and that it should be
Prove that 1 + sin 2A + cos 2A ---------------------------------------------- = cot A
1+sin2A−cos 2A
Use sin 2 A= 2 sin A cos A and
cos 2 A = 1−2 sin 2 A and cos 2 A = 2 cos A−1
y= -2(x-3)(x-2) to standard form
answer plss. will mark the first correct answer as brainliest!!
n is an integer.
Write the values of n such that -15 < 3n<6
Answer:
(-1,-2, -3, -4)
Step-by-step explanation:
-15 < 3n <6
-15 < 3 (-1,-2, -3, -4) <6
3 • -1 = -3
3 • -2 = -6
3 • -3= - 9
3 • -4 = -12
so all these answer still make -15 the lowest value and 6 the highest value.
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
i really need help!!!! i need answer to c:
Answer:
76.3
Step-by-step explanation:
Answer:
C = 75°
Step-by-step explanation:
The interior angles of a triangle will always add up to 180°, so all we have to do is find the missing variable.
To do this, we first add up the two angles we do know.
—> 65 + 40 = 105
Now that we have the total of the other two angles, simply subtract 105 from 180.
—> 180 - 105 = 75
We now have our answer!
What do you have to increase a number by to change it's place value
Answer:
Build more buildings
Step-by-step explanation:
Answer:
change by a tenth to hundredth to thousandth to the millionth
Step-by-step explanation:
Will give brainiest
Surds
Step by step explanation please on this question
Make sure to use Surds
Answer:
3
Step-by-step explanation:
You need to multiple 3 by 3 because 3 has an exponent. That makes the 3 into a 9. the square root of 9 is 3 so the answer is 3
f (x)=−8x− 4 cual es la pendiente y y el coeficiente de posición f (x )= (6x− 12) : 3 cual es la pendiente y y el coeficiente de posición AYUDA PORFA
The translation of the given question is
f (x) = - 8x− 4 what is the slope y and the position coefficient f (x) = (6x− 12): 3 what is the slope y and the position coefficient
Answer:
We need to determine slope and position coefficient which is the intercept.
f (x) = - 8x− 4 we know that f(x) is y
slope intercept form of the line
y = -8x -4
slope = -8
intercept = -4
similarly
f (x) = 6x− 12
y = 6x -12
slope =6
intercept = -12
A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the two pieces of equipment?
Because Five-thirds greater-than three-halves, the slope of the climbing equipment at the gym is greater.
Because Five-thirds less-than three-halves, the slope of the climbing equipment at the playground is greater.
Because Three-fifths greater-than two-thirds, the slope of the climbing equipment at the gym is greater.
Because Three-fifths less-than two-thirds, the slope of the climbing equipment at the playground is greater.
Answer:
I think its D but I'm not that sure about it.
Step-by-step explanation:
Because three fifths less than two thirds, the slope of te climbing equipment at the playground is greater.
Answer:
A)
Step-by-step explanation:
A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally.
Therefore its slope = length of the equipment vertically / length of equipment horizontally
= 6/4 = 3/2 = 1.5
And, A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.
Therefore slope, = 10/6 = 5/3=1.67 (approx)
Since, >
Therefore, Five-thirds greater-than three-halves, the slope of the climbing equipment at the gym is greater
(I finished the quiz and got it correct, it is A.)
true or false, x =4 is a critical point to this inequality
x²-4 / x²+9x+20 is greater than/equal to 0
Answer:
true
Step-by-step explanation:
x²-4/x²+9x+20 >=0
cross multiplying the equation we have,
(x²-4/x²+9x+20)*x²+9x+20 >= 0*x²+9x+20
= x²-4>=0
x²>=4
taking the square root of both sides, we have:
√x²>= √4
x >=2
Cameron has a bag of 50 gumdrops. There are 15 peach, 20 strawberry, 5 cherry, and 10 watermelon. Without looking, he picks a gumdrop, looks at it and puts it back, then chooses another without looking. What is the probability he will choose strawberry both times?
Selina has $50. She wants to buy some donuts which cost $2.80 each. How many donuts can she buy?
Answer:
50/2.80= 17
17 dounuts
If the table below represents a propornal relationship, what number will go
in the empty box?
Notes (pages)
8
Time (hours)
16
18
20
9
10
11. Helpp
Since the box represents a proportional relationship, the empty box would be = 22.
What is a proportional relationship between two variables?When proportional relationship exists between two variables, it means that a particular value would be times with one variable to give the next compared variable.
For example, using the figures given above;
8 pages of notes = 16hours
1 page = 16/8 = 2 hours
Therefore, each page should be times by two to give the number of hours.
Learn more about multiplication here:
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Find the slope of the line passing through the given points using the slope formula. Describe the slope as positive, negative, zero, or undefined.
(−7, −18) and (−7, −4)
Answer:
Undifined
Step-by-step explanation:
Lin knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to a gallon, but cannot decide if she should multiply 6 by 4 or divide 6 by 4 to find her answer. What should she do? Explain or show your reasoning.
Given:
There are 4 quarts in a gallon.
She wants to convert 6 quarts to a gallon.
To find:
Whether she should multiply 6 by 4 or divide 6 by 4 to find her answer.
Solution:
We have,
[tex]4\text{ quarts}=1\text{ gallon}[/tex]
[tex]1\text{ quarts}=\dfrac{1}{4}\text{ gallon}[/tex]
[tex]6\text{ quarts}=\dfrac{6}{4}\text{ gallon}[/tex]
Here, 6 quarts is equal to [tex]\dfrac{6}{4}[/tex] gallon. It means we need to multiply 6 by 4 in [tex]4\text{ quarts}=1\text{ gallon}[/tex] to find the answer.