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lyudmila [28]
2 years ago
5

if there are two containers of sugar solution, the first is 4% concentration and second is 8% concentration. how much of each sh

ould we combine to get 40 gallons of 5% concentrate solution​
Mathematics
1 answer:
Elina [12.6K]2 years ago
5 0

Answer:

<u>30 gallons solution 4% and 10 gallons solution 8%</u>

Step-by-step explanation:

<h3>x•4%+y•8%=40•5% </h3>

<em><u>4x+8y=40•5 and x+y=40</u></em>

x=40-y

4(40-y)+8y=200

160-4y+8y=200

4y=200-160

4y=40 => y=10 (gallons solution 8%)

=> x=40-10=30 (gallons solution 4%)

30 gallons solution 4% and 10 gallons solution 8%

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The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the smaller leg. How
dlinn [17]
For rigt triangle with legs legnth a and b and hypotnuse legnth c

a^2+b^2=c^2

we are given
larger leg is 3 longer than smaller leg
hypotnuse is 6 longer than smaller
find smaller

ok so

first pick a smaller leg
lets say b is smaller
longer leg is 3 more than shorter leg
a is 3 more than b
a=3+b
and

hypontuse is 6 more than shorter
c=6+b

sub 3+b for a and 6+b for c in oroiginal equation'

a^2+b^2=c^2
(3+b)^2+b^2=(6+b)^2
9+6b+b^2+b^2=36+12b+b^2
2b^2+6b^2+9=b^2+12b+36
minus (b^2+12b+36) from both sides
b^2-6b-27=0
factor
(b-9)(b+3)=0
set equal to zero

b-9=0
b=9

b+3=0
b=-3
fasle, legnths cannot be negative


answer is shorter side=9 cm


5 0
3 years ago
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0
3 years ago
ASAP TODAY MY B-DAY HELP ME AS A PRESNT PLZZZZZZZZZZZZZZZZZZZ7. The cost of a telephone call is $0.75 + $0.25 times the number o
katrin [286]

Answer:

0.75 + 0.25 = t

3 0
3 years ago
Here are two rectangles.
Sophie [7]

Answer:

AB=9.5\ cm

Step-by-step explanation:

step 1

Find the length side PQ

we know that

The area of rectangle PQRS is given by

A=(PQ)(QR)

A=66\ cm^2

so

66=(PQ)(QR)

substitute the value of QR

66=(PQ)(12)

solve for PQ

PQ=66/12\\PQ=5.5\ cm

step 2

Find the length side AB

we know that

The perimeter of rectangle ABCD is given by

P=2(AB+BC)

we have

P=30\ cm\\BC=PQ=5.5\ cm

substitute

30=2(AB+5.5)

solve for AB

15=AB+5.5\\AB=15-5.5\\AB=9.5\ cm

6 0
3 years ago
HELPPP ILL GIVE BRAINLIEST IF ITS RIGHT
Veseljchak [2.6K]

Answer:

Mixed Number: 4 191919/1,000,000

Fraction: 4191919/1,000,000

Step-by-step explanation:

5 0
2 years ago
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