7.5+k=10 7.5+k-7.5=10-7.5 step 1 k=2.5 step 2

A 40% sugar solution is added to an 85% sugar solution to create 1800 mL of a 60% solution. How much of each solution is used? (

denis-greek [22]

Answer:

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

Step-by-step explanation:

Let the

Number of ml of 40% sugar = x

Number of ml of 85% sugar used = y

From the above question, our system of equations is given as:

x + y = 1800mL ....... Equation 1

x = 1800 - y

40% × x + 85% × y = 60% × 1800mL

0.4x + 0.85y = 1080.... Equation 2

We substitute 1800 - y for x in Equation 2

0.4(1800 - y) + 0.85y = 1080

720 - 0.4y + 0.85y = 1080

- 0.4y + 0.85y = 1080 - 720

0.45y = 360

y = 360/0.45

y = 800mL

Solving for x

x = 1800 - y

x = 1800 - 800

x = 1000mL

Therefore,

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

4 0

2 years ago

Find the value of each variable

aniked [119]

Answer:

Answer d)

$a= 10*\sqrt{3}$ $b=5*\sqrt{3}$ , $c=15$ , and $d=5$

Step-by-step explanation:

Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".

So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

$b=10*sin(60^o)= 10*\frac{\sqrt{3} }{2} = 5*\sqrt{3}$

where we use the fact that the sine of 60 degrees can be written as: $\frac{\sqrt{3} }{2}$

We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

$d=10*cos(60^o)=10* \frac{1}{2} = 5$

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

$sin(30^o)= \frac{b}{a} \\a=\frac{b}{sin(30)} \\a=\frac{5*\sqrt{3} }{\frac{1}{2} } \\a= 10*\sqrt{3}$

where we used the value of the sine function of 30 degrees as one half: $\frac{1}{2}$

Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

$c=10*\sqrt{3} * cos(30^o)=10*\sqrt{3} *\frac{\sqrt{3} }{2} \\c= 5*3=15$

Therefore, our answer agrees with the values shown in option d)

6 0

2 years ago

Traveling math word problem - thank you! :)

Anni [7]

We are given:

car and train leave at the same time

average velocity of car = 50 miles/hour

average velocity of train = 70 miles/hour

train arrives 2 hours early

Assuming variables and making equations!

let the time taken by the train = t hours

since the car arrived late, it took more time as compared to the train

time taken by the car = t + 2 hours

since the distance from Pasadena to Sacramento doesn't change, both the vehicles covered the same distance, d

Distance travelled by the car:

d = 50 $\frac{miles}{hour}$ * (t+2) hours [distance = velocity * time]

d = 50(t+2) miles

rewriting in terms of t

$t = \frac{d-100}{50}$

Distance travelled by the train:

d = 70 $\frac{miles}{hour}$ * t hours

d = 70t miles

rewriting in terms of t

$t = \frac{d}{70}$

now we have two expressions for t, both of which are equal because t is just the time taken by the train

Finding the distance:

$t = \frac{d-100}{50}$

$t = \frac{d}{70}$

because t is the same:

$\frac{d-100}{50} = \frac{d}{70}$

$\frac{d-100}{5} = \frac{d}{7}$

7(d - 100) = 5(d)

7d - 700 = 5d

(7d - 5d) - 700 = 0 [subtracting 5d from both sides]

2d = 700 [adding 700 on both sides]

d = 350 miles [dividing both sides by 2]

The distance between Pasadena and Sacramento is 350 miles!

7 0

2 years ago

Pls Help god bless you

True [87]

Jus go a thru z and you’ll be fine

8 0

2 years ago

Read 2 more answers

Answer for: -10 = 10 = 7m. m = •0 •7 •10 •11

wel

Answer:

Ok so your answer should be m = 0

Step-by-step explanation:

the explanation is to Rewrite the equation as − 10 +7 m = − 10 .− 10 + 7 m = − 10

Move all terms not containing m

to the right side of the equation.

7 m = 0

Divide each term by 7

and simplify.

m = 0

i hope this can help

5 0

3 years ago