Answer: Add 315 gallons of 70% antifreeze to 90 gallons of 25% antifreeze to make a 60% mixture.
You need to end up a mixture that is 60% antifreeze.
You have 90 gallons of 25% antifreeze, which means it has .25*90 = 22.5 gallons of pure antifreeze mixed with a solvent (probably water).
.
You will add 'x' gallons of 70% antifreeze to make the 60% mixture.
So, at the conclusion, you will have (90+x) gallons 60% 'pure' antifreeze. That can be shown with the equation:
.
.25*90 + .7*x = .6*(90+x)
.
Multiply by 100 to eliminate fractions.
.
25*90 + 70x = 60(90 +x)
.
2250 + 70x = 5400 + 60x
.
10x = 5400 -2250
.
10x = 3150
.
x = 315 gallons of 70% antifreeze.
.
How much will you end up having on hand?
90 + 315 = 405 gallons
.
If it is 60% antifreeze, how much 'pure' antifreeze will be in the mixture?
.6*405 = 243
.
In the original 90 gallons, you have 22.5 gallons of pure antifreeze.
In the additional 315 gallons, you have .7*315 = 220.5 gallons.
22.5+220.5 = 243 gallons
Step-by-step explanation:
Hope this helps,
Have a great day
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The relationship between each proportion of antifreeze can be used to form an equation.
The number of 90% antifreeze that must be added is 490 gallons.
The question is incomplete. So, I will use the following details to answer the question
[tex]Av ai la bl e = 70[/tex] gallons of 10% antifreeze
[tex]x \to[/tex] gallons of 90% antifreeze
[tex]Total = x + 70[/tex] --- after mixing the solution; to get a 80% solution
The equation is then represented as:
[tex]70 \times 10\% + x \times 90\% = (x + 70) \times 80\%[/tex]
[tex]7 + 0.9x = 0.8x + 56[/tex]
Collect like terms
[tex]0.9x - 0.8x = 56 - 7[/tex]
[tex]0.1x = 49[/tex]
Divide by 0.1
[tex]x = \frac{49}{0.1}[/tex]
[tex]x = 490[/tex]
Hence, 490 gallons of 90% antifreeze must be added.
Read more about equations at:
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Answer:
2x + 7y and 7g + 3h
Step-by-step explanation:
(a)
3x + 5y - x + 2y ← collect like terms
= (3x - x) + (5y + 2y)
= 2x + 7y
(b)
3g + 5h + 4g - 2h ← collect like terms
= (3g + 4g) + (5h - 2h)
= 7g + 3h
Answer:
A) 2x + 7y
B) 7g + 3h
Step-by-step explanation:
A) 3x + 5y - x +2y =
3x - x = 2x
5y + 2y = 7y ans: 2x + 7y
B) 3g + 5h +4g - 2h =
3g + 4g = 7g
5h - 2h = 3h ans: 7g + 3h
I think of a number. When I add 12 and subtract 8, I get
15. What is that number?
Answer:
11?
Step-by-step explanation:
Hope I'm right! (:
Answer:
11
Step-by-step explanation:
15 + 8 = 23
23 - 12 = 11
hope it's right
Do the bois got me? Please bois
Answer:
the 2
second one
Step-by-step explanation:
Answer:
DFA BFC
Step-by-step explanation:
Nike paid Leslie a quarterly dividend check for $900. Leslie owns 400
share of Nike. What was the quarterly dividend for one share of Nike? *
Answer:
Step-by-step explanation:
:(
Is the Point on the Line?
Answer:
yes.
Step-by-step explanation:
The eqation of the line is y=1/2x+3 so when we plug in x as 20 y is equal to 13
Answer:
Yes it is on the line becuase if you find the slope of the line which is 1/2. We can just use rise over run from there. So we know 1 is y and 2 is x Becuase slope is written in y/x. And we can fins slope by just calculating the rise over run or suing the formula y2-y1/x2-x1. So the last pont shown on the line is (10,8) so we can add 1 to the y or in this case 8 and add 2 to the x or in this case 10. You’ll get (12,9). We know this works becuase if you find the slope of (12,9) and (10, 8), you’ll get 1/2 again which is the same slope so we know it’s right. Now we just add using the same slope to the now new point. We add 1 to 9 and add 2 to 12. (14,10). Still, if you find the slope, it’ll still be 1/2. Now keep repeating that and you’ll get (20, 13) eventually. And we can check by calculating the slope. (20,13) and (10,8), you could use any point on the coordinate plane/ and you’ll get 1/2. A easier way could just be calculating the slope first and you’ll get 1/2 from any two points and then use any two points to calculate the slope for (20,13). It’ll still be the same thing.
11. Show the following operation on a number line
(-7) + (-2) + (+6)
Hi
-7 - 2 + 6 = -9 + 6 = 6 - 9 = - 3
have a good day ;)
Krya is playing a card game. Black cards are worth points while red cards take points away. What is her score if she has a black 20-card and a red 42-card
Answer:
her score would be -22
Step-by-step explanation:
20-42=-22
Please Answer
This is due by tomorrow night and I need help
Answer:
AY = 16
IY = 9
FG = 30
PA = 24
Step-by-step explanation:
The centroid of the triangle divides each median at the ratio 1: 2 from the base
Let us solve the problem
In Δ AFT
∵ Y is the centroid
∵ AP, TI, and FG are medians
→ By using the rule above
∴ Y divides AP at ratio 1: 2 from the base FT
∴ AY = 2 YP
∵ YP = 8
∴ AY = 2(8)
∴ AY = 16
∵ PA = AY + YP
∴ AP = 16 + 8
∴ AP = 24
∵ Y divides TI at ratio 1: 2 from the base FA
∴ TY = 2 IY
∵ TY = 18
∴ 18 = 2
→ Divide both sides by 2
∴ 9 = IY
∴ IY = 9
∵ Y divides FG at ratio 1:2 from the base AT
∴ FY = 2 YG
∵ FY = 20
∴ 20 = 2 YG
→ Divide both sides by 2
∴ 10 = YG
∴ YG = 10
∵ FG = YG + FY
∴ FG = 10 + 20
∴ FG = 30
Cara and marcus shared a candy bar. The models are shaded to show the fraction of the candy bar each of them ate. What fraction of the candy bar did Cara and Marcus eat altogether?
Answer:
A. 11/12
Step-by-step explanation:
A. 11/12
B. 9/16
C. 1/12
D. 9/24
Cara = 8/12 candy bars
Marcus = 1/4 candy bars
What fraction of the candy bar did Cara and Marcus eat altogether?
Total candy bars = Cara + Marcus
= 8/12 + 1/4
= 8+3/12
= 11/12 candy bars
The correct answer is A. 11/12
Write an equation of the line in slope-intercept form given the slope is 2 and the y-intercept is -5.
Answer:
y=2x-5
Step-by-step explanation:
The Crazy 80s Baby Jr. Decides to make a Crazy Cake for dessert. The cake uses eggs and potatoes in a ratio of 2:5. If she uses 6 eggs, how many potatoes will she need?
Answer:
When
eggs = 6, Potatoes = 15
Step-by-step explanation:
Ratio of egg to potatoes
Egg : potatoes
2 : 5
If she uses 6 eggs, how many potatoes will she need?
Eggs = 6
Potatoes = x
2 : 5 = 6 : x
2 / 5 = 6 / x
Cross product
2 * x = 5 * 6
2x = 30
x = 30 / 2
x = 15
When
eggs = 6, Potatoes = 15
Find the zeros
f(x)=(x+3)( x-2)
g(x)=(2x-3)(x+4)
h(x)=(-2x+4)(x+1)
P(x)=3(x+3)(2x-1)
Answer:10
Step-by-step explanation:
Passes through (8,8) and (10,9)
Plz help need answer ASAP
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
Assuming you require the equation of the line.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 8) and (x₂, y₂ ) = (10, 9)
m = [tex]\frac{9-8}{10-8}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 8) , then
8 = 4 + c ⇒ c = 8 - 4 = 4
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
(a-b)-(4a+3c)-(c-2a) full process please
Answer:
-a - b - 4c
Step-by-step explanation:
(a - b) - (4a + 3c) - (c - 2a) = a - b - 4a - 3c - c + 2a
= a - 4a + 2a - b - 3c - c {Combine like terms}
= -a - b - 4c
asaps
In which number is the value represented by the digit 9 equal to 1 of the value
represented by the digit 9 in the number 73,951?
Answer:
The number is 83,194
Step-by-step explanation:
The value of 9 in the given number is 900
So
out of all the options, we want a number in which the value of 9 there is 1/10 of 900 which is 90
The correct answer here is 83,194
What is the measure of an interior angle of a regular 99-gon?
Answer:
17460°
I hope it will be useful.
Credit card A has an APR of 27.2% and an annual fee of $96, while credit card B has an APR of 30.3% and no annual fee. All else being equal, which of these equations can be used to solve the principal P for which the cards offer the same deal over the course of a year
Answer: D. P * (1 + 0.272/12)¹² + 96 = P * (1 + 0.303/12)¹²
Step-by-step explanation:
Credit Card A deal over the course of a year:
Payments are done per month so values need to be converted to monthly figures.
APR per month = 27.2%/12
Period = 1 year * 12 months = 12
= P * (1 + 27.2%/12)¹² + 96
Credit Card B deal over a year
= P * (1 + 30.3%/12)¹²
The Principal that will enable both cards to offer the same deal will therefore be:
P * (1 + 27.2%/12)¹² + 96 = P * (1 + 30.3%/12)¹²
a circle with a radius 3 centimeters is cut from square piece of felt. the side of the felt square are 8 centimeters long. How much felt is left over? use 3.14 for (pie symbol). show your work.
Answer:
There are [tex]35.74\ cm^2[/tex] of felt left over.
Step-by-step explanation:
The side of the felt square is 8 cm. A circle of radius 3 cm is cut from the square piece of felt.
The portion of felt leftover is the difference between the area of the square and the area of the circle.
The area of the square is:
[tex]A_s=(8\ cm)^2=64\ cm^2[/tex]
The area of the circle is:
[tex]A_c=\pi(3\ cm)^2=3.14*9\ cm^2[/tex]
[tex]A_c=28.26\ cm^2[/tex]
The remaining area of the piece of felt is:
[tex]A=64\ cm^2-28.26\ cm^2[/tex]
[tex]A=35.74\ cm^2[/tex]
There are [tex]35.74\ cm^2[/tex] of felt left over.
Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Sı.
. CBFG is a rectangle of area S2.
• ADEB is a right trapezoid of area S3.
1) Express S1, S2 and S3 in terms of x.
2) Let S = S1 + S2 -S3.
Answer:
1) S1 = 4·x² - 12·x + 9
S2 = 12·x² - 26·x + 12
S3 = 6·x² - 5·x - 6
2) S = 10·x² - 33·x + 27
Step-by-step explanation:
The length x in cm > 1.5
Segment AB = 2·x - 3, segment BC = 4·x - 6, segment AD = 2·x + 3 and segment BE = 4·x + 1
1) a) The area of the right triangle ABC = S1 = 1/2 × Base × Height
The base of the triangle ABC = Segment BC = 4·x - 6
The height of the triangle ABC = Segment AB = 2·x - 3
Therefore, The area of the triangle ABC = S1 = 1/2 × (4·x - 6) × (2·x - 3) = 1/2 × (8·x² - 12·x - 12·x + 18) = 4·x² - 12·x + 9
S1 = 4·x² - 12·x + 9
b) The area of the rectangle CBFG = S2 = Base × Height
The base of the rectangle CBFG = BC = 4·x - 6
The height of the rectangle CBFG = BF = 3·x - 2
The area of the rectangle CBFG = S2 =(4·x - 6) × (3·x - 2) = 12·x² - 8·x - 18·x + 12
The area of the rectangle CBFG = S2 = 12·x² - 26·x + 12
S2 = 12·x² - 26·x + 12
c) The area of the trapezoid ADEB = S3 = 1/2 × (Long side + Short side) × The height of the trapezoid ADEB
The long side of the trapezoid ADEB = BE = 4·x + 1
The short side of the trapezoid ADEB = AD = 2·x + 3
The height of the trapezoid ADEB = AB = 2·x - 3
The area of the trapezoid ADEB = S3 = 1/2 × (4·x + 1 + 2·x + 3) × (2·x - 3) = 6·x² - 9·x + 4·x - 6
∴ The area of the trapezoid ADEB = S3 = 6·x² - 5·x - 6
S3 = 6·x² - 5·x - 6
2) S = S1 + S2 - S3 = 4·x² - 12·x + 9 + 12·x² - 26·x + 12 - (6·x² - 5·x - 6) = 10·x² - 33·x + 27
please find what number x is
Step-by-step explanation:
Hey there!
Given;
The triangle is a right angled triangle, whose one side is 26 and another side is X. It has also one angle that is 41°.
Now, taking reference angle as angle 41°. We get;
Perpendicular= 26
Base = X
and Reference angle = 41°.
We know that the ratio of tan is p/b. So, let's use this ratio.
[tex] \tan(41°) = \frac{26}{x} [/tex]
[tex]0.869 \times x = 26[/tex]
[tex]x = \frac{26}{0.869} [/tex]
Therefore, The value of x is 29.90.
Hope it helps...
Which expression is equivalent to (4x^3)(2x)^-4
1/4x
4/x
8/x
128/x
Of course ima do 100 points, but sadly that means you only get 50 for answering.
Answer:
1/4x
4/x
128/x
Step-by-step explanation:
Brainliest pls Hit the thank you button
What is equivalent expression to 2a
Answer:
2a
Step-by-step explanation:
up at the top is the answer
can someone please help me with this question? please!
Answer:
22º
Step-by-step explanation:
You purchase 3 action figures per week. You have 27 action figures, which is 60% of the total number of action figures you need to complete your collection. How many weeks until your collection is complete?
Answer:
27/.6=45 total in collection
45-27=18
18/3 per week=6 weeks
Step-by-step explanation:
The number of weeks until your collection is complete should be 6 weeks.
Calculation of the number of weeks:Since You purchase 3 action figures per week. You have 27 action figures, which is 60% of the total number of action
So here total collection should be
[tex]27\div 0.60[/tex] = 45
Now the number of weeks should be
[tex]= (45 - 27) \div 3[/tex]
= 6
hence, The number of weeks until your collection is complete should be 6 weeks.
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Third time posting. Explain it too
Answer:
D. x-5 / x+4
Step-by-step explanation:
(-3x³ +9x² +30x) / (-3x³ -18x² - 24x)
=-3x (x²-3x-10) / -3x(x²+6x+8)
=-3x(x+2)(x-5) / -3x(x+2)(x+4)
=x-5 / x+4
Answer:
oooooooof
Step-by-step explanation:
It takes 5 men 12 days ro complete a job how many days does it take 3 men to complete the job
Answer:
5=12
3=? then Criss cross it and you will get 12*3 divided by 5 then you get 7.2
so the answer will be 7 days
9. What is the value to x in the inequality -4(6 + 5x) - 7 < - 9(2x+ 3)
Answer:
x [tex]\geq[/tex] -2
Step-by-step explanation:
Remove parentheses and distribute -4 and -9, calculate the difference, move the variable and constant, collect like terms. ( -2x [tex]\leq[/tex] 4), and divide both sides, and you'll end with -2.
Answer:
x > -2 (last choice)
Step-by-step explanation:
Using the distributive property multiple -4 to both integers
-24 - 20x - 7 < -18x - 27
-31 - 20x < -18x - 27
Add 27 on both sides
-4 - 20x < -18x
Add 20x on both sides
-4 < 2x
Divide each side by 2
x > -2
Help? I'm in Algebra and I'm the most unintelligent person that you can know and please comprehend that
9515 1404 393
Answer:
2×5×11 = 110
Step-by-step explanation:
The factors are separated by the × (multiplication) sign. Common factors are numbers that are factors of both products.
It can be useful to list the factors in order of size, for easier comparison.
1st product:
2 × 3² × 5² × 11 × 17
2nd product:
2 × 5 × 7 × 11² × 13²
Ignoring exponents (for the moment), the numbers that appear in both products are 2, 5, 11. (I've highlighted them so you can see them more easily.)
Now, we consider the exponents. We want to determine the lowest exponent of each of these factors.
2 has the same exponent in both products: 1
5 has exponents of 2 and 1. The least of these is 1.
11 has exponents of 1 and 2. The least of these is 1.
So, the greatest common factor (GCF) is ...
2¹ × 5¹ × 11¹ = 2×5×11 = 110 . . . . greatest common factor
(Comment on answer format: the given numbers are shown as a product of factors. It is not clear whether the desired answer format should match, or should have the value multiplied out. We have shown both ways.)
_____
Check
If we factor out the "greatest common factor," the given products can be written as ...
(2×5×11) × (3² × 5 × 17)
(2×5×11) × (7 × 11 × 13²)
You will notice that the right factors of each of these products have nothing in common. So, we have found the greatest common factor.
If using the method of completing the square to solve the quadratic equation x^2+8x-4=0 which number would have to be added to "complete the square"?
I need the answer ASAP. Please help. Thank you
x^2 + 8x - 4 = 0
(x^2 + 8x + 8/2^2) - 4 - 8/2^2 = 0
(x^2 + 8x + 16) - 4 - 16 = 0
(x^2 + 8x + 16) - 20 = 0
(x + 4)(x + 4) - 20 = 0
The number that is to be added to complete the square is 8/2^2, or 16.
5x + 3y = 27 and y = 2x – 2
Answer: 48
Step-by-step explanation:
-10x+6y=54 then + it to each other
-6x-6y=-6
-16x=48