1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ber [7]
3 years ago
6

A chemical company makes two brands of antifreeze. The first brand is 85% pure antifreeze, and the second brand is 90% pure anti

freeze. In order to obtain 50 gallons of a mixture that contains 50% pure antifreeze, how many gallons of EACH brand of antifreeze must be used?
Mathematics
1 answer:
AleksandrR [38]3 years ago
4 0

Answer:

Let +a+ = gallons of 55% antifreeze needed

Let +b+ = gallons of 95% antifreeze needed

-----------------------

(1) +a+%2B+b+=+160+

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

-----------------------------------

(2) +.55a+%2B+.95b+=+.85%2A160+

(2) +.55a+%2B+.95b+=+136+

(2) +55a+%2B+95b+=+13600+

(2) +11a+%2B+19b+=+2720+

----------------------------

Multiply both sides of (1) by +11+

and subtract (1) from (2)

(2) +11a+%2B+19b+=+2720+

(1) +-11a+-+11b+=+-1760+

---------------------------

 

+8b+=+960+

+b+=+120+

and

(1) +a+%2B+120+=+160+

(1) +a+=+40+

-------------------

40 gallons of 55% antifreeze are needed

120 gallons of 95% antifreeze are needed

--------------------------------------

check:

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

(2) +%28+.55%2A40+%2B+.95%2A120+%29+%2F+160+=+.85+

(2) +%28+22+%2B+114+%29+%2F+160+=+.85+

(2) +136+=+.85%2A160+

(2) +136+=+136+

OK

Step-by-step explanation:

You might be interested in
PLEASE HELP!!!!! What are the values of a and b? -7(x+3)=ax+b
Artist 52 [7]

Step-by-step explanation:

Hope dis helps you......

3 0
3 years ago
Annie's parents have offered her two different allowance options for her 10 week summer vacationAnnie's mom offers Annie an allo
vfiekz [6]
<h3>Annie's mom's offer is better because Annie will have more money at the end of weeks.</h3>

HOPE IT HELPS

PLEASE MARK ME BRAINLIEST ☺️

5 0
2 years ago
Read 2 more answers
During a field trip, 60 students are put into equal-sized groups. Use 60 ÷ 5 = 12 to answer this question. If 12 represents the
wel

Answer:

the groups

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
“encontrar la integral indefinida y verificar el resultado mediante derivación”
Oliga [24]

I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx

Haz la sustitución:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C

Para confirmar el resultado:

\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}

I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx

Sustituye:

y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx

\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C

(Te dejaré confirmar por ti mismo.)

I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx

Sustituye:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C

I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}

Sustituye:

u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}

\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C

Podemos hacer que esto se vea un poco mejor:

\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}

\implies I=-\dfrac{(t+1)^4}{4t^4}+C

4 0
3 years ago
PLEASE HELP ME OUT IF YOU CAN
ozzi

Answer:

D

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Which expression is equivalent to 15+80
    7·1 answer
  • What is the value of x in the equation x – y = 30, when y = 15?
    7·2 answers
  • What is the range of the data below? A box-and-whisker plot. The number line goes from 50 to 100. The whiskers range from 52 to
    13·1 answer
  • devon pays $24.95 for her roller skates.After that she pays$3.95 for each visit to the roller rink. What is the greatest number
    13·2 answers
  • 1/2x + 3/2x = 4x - 8
    8·2 answers
  • If f(x)=2x squared -x, find f (3)
    9·1 answer
  • Malik scores 24 goals in 8 soccer games. At that rate, how many goals will he sore in 15 games?
    12·1 answer
  • F(x)= 2x^3-10x^2+12x-12<br><br> Find critical points
    8·1 answer
  • In a survey, 75% of the people polled said they would vote in the upcoming election. How many people were polled if 375 said the
    7·2 answers
  • In 5 - 7 complete sentences, answer all of the following question. •Use this image to respond to the following prompt: •Is the s
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!