Two tanks hold a total of 61 gallons of a toxic solvent. One tank holds 4 gallons more than twice the amount in the other. How many gallons does each tank hold?

[tex]\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}[/tex]

Answer:

y=-x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-2))/(3-1)

m=(-4+2)/2

m=-2/2

m=-1

y-y1=m(x-x1)

y-(-2)=-1(x-1)

y+2=-x+1

y=-x+1-2

y=-x-1

A function is an expression that defines a relationship between an independent variable and a dependent variable.

The number of bacteria colonies after 2 hours is 220.

It is an expression that defines a relationship between an independent variable and a dependent variable.

We have,

P(t) = 4t² + 27t + 150

Where t = time

P(t) = population of a slowly growing bacteria colony after a particular time

The growth rate after 2 hours:

P(2) = 4 x (2)² + 27 x 2 + 150

P (2) = 16 + 54 + 150

P (2) = 220

Thus the number of bacteria colonies after 2 hours is 220.

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Answer:

5/1

10/2

15/3

20/4

25/5

30/6

35/7

Step-by-step explanation:

There are 6 numbers on a standard die and. 5 of the numbers are less than 6.

The probability would be 5/6

Answer:

7.25 + S ≤ 32

Step-by-step explanation:

Our initial value is 7.25, and that is to watch the movie. Next, the absolute max he can spend is 32, or he would have negative money, which he cannot have. Therefore, we use the ≤ sign and point it as 32, to show that it must be less than or equal to our total of 32. Then, we can represent the money they spend on shopping with s

Answer : =

Step - by - step explanation :

6 3/6 -- simplest form --> 6 1/2

6 6/12 -- simplest form --> 6 1/2

Answer:

first of all take LCM OF THE denominator and solve it as shown

[tex]2x-3y = 7~~~....(i)\\\\y = 3x -7~~~....(ii)\\\\\\\text{Substitute}~ y = 3x -7~ \text{in equation (i):}\\\\\\2x-3(3x-7) = 7\\\\\implies 2x -9x + 21 =7\\\\\implies -7x = 7 -21\\\\\implies -7x = -14\\\\\implies x = \dfrac{-14}{-7} = 2\\\\\\\text{Substitute x = 2 in equation (ii):}\\\\y=3(2) -7 = 6 -7 = -1\\\\\\\text{Hence (x,y) =(2,-1)}[/tex]

Answer:

His son is 3 years old.

Step-by-step explanation:

33 years old ... 3 less than ....  =  36

36/12  =  3

Answer:

x-intercept: 4

y-intercept: -4

Step-by-step explanation:

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Answer:

Below in bold.

Step-by-step explanation:

Using the point-slope form of a straight line equation:

y - y1 = m(x - x1)

y - (-1)) = -2/5(x - -10)

y + 1 = -2/5(x + 10)

y  + 1 = -2/5x - 4

y = -2/5x - 5.

In standard form this is:

2x + 5y = -25.

Answer:

0.6

Step-by-step explanation:

3/5=0.6

Using the least common factor, it is found that she will do all the three activities again on the same day again in 48 days.

To find how many days it takes so that she will do all the three activities again on the same days, we have to find the least common factor of 4, 6 and 16.

It is done factoring them using prime factors, then:

4 - 6 - 16|2

2 - 3 - 8|2

1 - 3 - 4|2

1 - 3 - 2|2

1 - 3 - 1|3

1 - 1 - 1

Hence:

lcm(4,6,8) = 2x2x2x2x3 = 48

She will do all the three activities again on the same day again in 48 days.

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Answer:

3/16

Step-by-step explanation:

3/4÷4=3/16

Since there are 4 people, not 3, divide the remaining pizza by 4.

[tex]39+\dfrac 15 w \\\\=39+\dfrac 15 \left(-\dfrac 12 \right)\\\\\\=39 - \dfrac 1{10}\\\\\\=\dfrac{389}{10}\\\\\\=38\dfrac{9}{10}[/tex]

Answer:

Answer B- 1034

7% annual rate is 70. divide by 52 (total amount of weeks in a year) =1.35. 1.35 × 25=33.75 rounded up 34. 1000+34=1034

Answer:

Use a website called desmos and type in y=-3/4(x+4)-2

Step-by-step explanation:

1) isolate y by subtracting 2 on both sides

y=-3/4(x+4)-2

Answer:

Clue: two points : (0,-5)   ( 4 , -8)

Step-by-step explanation:

Look at the graph.

Answer:

A. 52%

B. 36%

C. 16%

D. 4%

Step-by-step explanation:

13/25 people have freckles.

9/25 people have Blonde or red hair.

4/25 people have freckles and brown hair.

1/25 people have freckles and red hair.

Divide the fractions to get the percentages.

The probabilities are A. 52%, B. 56%, C. 16% and D. 4%

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Alan collects data about the students in his class. he records their hair colour and whether they have freckles,

P(E) = (Number of favourable outcomes) ÷ (Sample space).

There are total 25 students in data,

A) Students having freckles = 13

P(freckles) = 13/25% = 52%

B) Students having blonde or red hair = 14

P(blonde hair or red hair) = 14/25% = 56%

C) Students having freckles and brown hair = 4

P(freckles and brown hair) = 4/25% = 16%

D) Students with no freckles and red hair = 1

P(no freckles and red hair) = 4/25% = 4%

Hence, a. P(freckles) = 52%

b. P(blonde hair or red hair) = 56%

c. P(freckles and brown hair) = 16%

d. P(no freckles | red hair) = 4%

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Answer:

Given,

2,3,4,8,10

ex=2+3+4+8+10+x

=27+x

mean=6

no of data=5

now,

mean = ex/n

or,6=27+x/5

or,5×6=27+x

or,30=27+x

or,30-27=x

3=x

Answer: A number with the same absolute value of 23 is -23.

Explanation: The absolute value of a number is how far it is from zero, and the absolute value of a number is always positive, unless the number is 0, in which case the absolute value is neutral, and the absolute value is 0.

Examples: 6 is 6 away from zero, so the absolute value of 6 is 6.

−6 is 6 away from zero, so the absolute value of −6 is 6.

The number that has the same absolute as 23 is -23.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

An absolute number x is denoted by |x|

If x = -x,

|-x| = x

Now,

|23| = 23

|-23| = 23

So,

-23 has the same absolute value as 23.

Thus,

-23 is the number.

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7 x 27               189

              =    -------------------

9 x 1                     9

Answer:

The sum of 8 and 1 is 9.

lol

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

I took the test this is it

Counterexamples are simply used to disprove conjectures.

(a) Elephants and Giraffes

This conjecture may or may not be true.

However, it can be disproved by the following counterexample

There are sometimes more elephants in a zoo than giraffes

The word "sometimes" disproves the original conjecture

(b) The oldest leatherback sea turtle

This conjecture is not true.

This is so because the oldest leatherback sea turtle in captivity is actually 400 years old.

So, the conjecture can be disproved by the following counterexample

The oldest leatherback sea turtle in captivity is 400 years old.

(c) American bison

This conjecture may or may not be true.

However, it can be disproved by the following counterexample

American bison are sometimes over 6 feet tall

The word "sometimes" disproves the original conjecture

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Answer:

Option (C) is correct, the dimensions of the brand name television = 32 inches by 64 inches.

Step-by-step explanation:

Given :  The generic version was based on the brand name and was three eighths the size of the brand name and both are similar.

The dimensions of the generic television set = 12 inches by 24 inches

Let the dimensions of brand name be x by y such that

three eighth of x=12 inches

and three eighth of y=24 inches

Therefore, the dimensions of the brand name television = 32 inches by 64 inches.

Hence option (C) is correct.

Answer:b=5

Step-by-step explanation:

The value of B for the given expression is B = (2 - 3C) / 5.

An expression in mathematics is a grouping of one or more numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, division, and exponentiation) that illustrates a relationship or calculation.

Parentheses, braces, and other grouping symbols that specify the sequence in which operations should be carried out are also permitted in expressions.

To solve for B, we need to isolate B on one side of the equation.

15B + 9C = 6

Subtract 9C from both sides:

15B = 6 - 9C

Divide both sides by 15:

B = (6 - 9C) / 15

Simplifying the right side gives:

B = (2 - 3C) / 5

Therefore, B = (2 - 3C) / 5.

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Answer:

D). 0.1x+99=149.30

How many songs Tyna Bought:

503 songs

Step-by-step explanation:

Since the membership fee is 99 you don't have to pay for it again

(Until next year that is)

Now it states that every download cost 10 cents or $0.1

So we don't know how many she will buy so we can replace that unknown value with x

So the equation is

0.1x+99=149.30

To solve this you first subtract 99 on both sides:

Which will result in

0.1x=50.3

Divide 0.1 on both sides

So Tyna bought 503 songs

(HOLY THAT IS A LOT OF SONGS)

Hope this Helps!