A scientist measures 4.62 ml of a chemical into a beaker. \with a pipette, he carefully takes out 0.67 of the chemical. finally, he adds 1.25 ml of water into the beaker. how much liquid is in the beaker now?

Answer: y= 2/5x+12/5

Step-by-step explanation:

when you subtract 2x from both sides you get

-5y=-12-2x

and then you divide by -5 to get

y=-12-2x/-5

and you see that all the terms have negatives so you can just change them all to positives to get

y=12+2x/5

and then making the equation into y=mx+b format (which is prettier)

you get y=2/5x+12/5

yw

Step-by-step explanation:

2x - 5y= - 12

-2× -2x

0 -5y = -12 - 2x

÷-5y ÷-5y ÷-5y

y = 12/5 + 2x/5 or y = 2x/5 + 12/5

(its recommended to but the variable number in front)

By substitution, the solution of the system of equations, 3x - y = 5 and y = 4x + 2, is (-7 , -26).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Given two linear equations in x and y,

3x - y = 5     (equation 1)

y = 4x + 2     (equation 2)

Use substitution method since the second equation is already expressed in y in terms of x. Substitute the value of y to the first equation.

3x - y = 5     (equation 1)

3x - (4x + 2) = 5

3x - 4x - 2 = 5

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

3x - 4x - 2 = 5

3x - 4x = 5 + 2

-x = 7

x = -7

Substitute the value of x in the second equation and solve for y.

y = 4x + 2     (equation 2)

y = 4(-7) + 2

y = -28 + 2

y = -26

Hence, the solution of the given system of equations is (-7 , -26).

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Answer:

8.7

Hope this helps <3

Have a great day!

Answer:

18x+66=6(3x+11) square feet

Step-by-step explanation:

The expression for the total number of pies baked in the two years is 156 + d

Algebraic expressions can be defined as expressions composed of variables, terms, factors, coefficients and constants.

They  are also made up of mathematical operations such as division, addition, subtraction, multiplication, etc

From the information given, we have;

The expression is written as;

Total number of baked pies = 156 + d

Thus, the expression for the total number of pies baked in the two years is 156 + d

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The volume of the larger suitcase, a rectangular prism 85 centimeters long, is 168,539.1 cubic cm.

Solids of the same type that have proportional corresponding linear

measures are similar solids. In the case of similar rectangular prisms:

length of A / length  of B = width of A / width of B = height of A / height of B

Using this scale, if the larger suitcase is 85 centimeters long, and the smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep, then:

length of larger suitcase / length of smaller suitcase = 85 cm / 68 cm = 5/4

width of larger suitcase / width of smaller suitcase = 5/4

width of larger suitcase = 5/4 (47 cm)

width of larger suitcase = 58.75 cm

depth of larger suitcase / depth of smaller suitcase = 5/4

depth of larger suitcase = 5/4 (27 cm)

depth of larger suitcase = 33.75 cm

Solving for the volume of the larger suitcase using the formula for the volume of rectangular prism:

V = lwh

V = 85 cm (58.75 cm) (33.75 cm)

V = 168,539.0625 cubic cm

Rounding off to the nearest tenth.

V = 168,539.1 cubic cm

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The correct statements for the function are given as follows:

A. The domain for the function is all real values.

B. The range for the function is the set {-5}.

For this problem, the function assumes the value y = -5 for all real values of x, hence statements A and B are correct, while D is not.

The graph also represents a function, as each value of x is associated with only one value of y.

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For the equation (4 x + 7)° = (2 x + 5)°, we get the value of x as - 1.

We are given an equation as:

(4 x + 7)° = (2 x + 5)°

We need to solve this equation to find the value of the variable x.

We first will subtract 7 from both the sides:

4 x + 7 - 7 = 2 x + 5 - 7

4 x = 2 x - 2

Now Subtract 2 x from both the sides:

4 x - 2 x = 2 x - 2 - 2 x

2 x = - 2

Divide both sides by 2

2 x / 2 = - 2 / 2

x = - 1

Therefore, for the equation (4 x + 7)° = (2 x + 5)°, we get the value of x as - 1.

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Answer:

5

Hope this helps :)

Step-by-step explanation:

1. Solve by adding since a = 2 and b = 3.

2 + 3 = 5

Check:

5 - 3 = 2 ✓

Using the segment addition postulate, the values are:

a. y = 6

b. RS = 50

ST = 29

Based on the segment addition postulate, the following equation is true which we can use in finding the missing measures:

RS + ST = RT.

Given:

RS = 8y + 2,

ST = 4y + 5,

RT = 79.

a. Plug in the given values into RS + ST = RT:

8y + 2 + 4y + 5 = 79

12y + 7 = 79

12y = 79 - 7

12y = 72

y = 6

b. RS = 8y + 2 = 8(6) + 2

RS = 50

ST = 4y + 5 = 4(6) + 5

ST = 29

Thus, using the segment addition postulate, the values are:

a. y = 6

b. RS = 50

ST = 29

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Answer:

24 [tex]cm^{2}[/tex]

Step-by-step explanation:

a = [tex]\frac{bh}{2}[/tex]

We have the base, we need the height.  Use the Pythagorean Theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]6^{2}[/tex] + [tex]b^{2}[/tex] = [tex]10^{2}[/tex]

36 + [tex]b^{2}[/tex] = 100  Subtract 36 from both sides

[tex]b^{2}[/tex] = 64

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{64}[/tex]

b = 8

a = [tex]\frac{bh}{2}[/tex]

a =[tex]\frac{6x8}{2}[/tex] =[tex]\frac{48}{2}[/tex] = 24

The required value of y is 5/8.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant  of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx      —-- 1

Now, find k for given x = 4 and y = ½, we need to put these values in equation 1, i.e.

½ = k(4)

k = ⅛

Further calculate y for given x = 5 and constant of proportion, k = 1/8 i.e.

y = (⅛)(5)

y = 5/8

Hence, the required value of y is 5/8.

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Answer:

Step-by-step explanation:

350 * 40% = 140 (MATH)

350 * 10% = 35 (ENGLISH)

350 * 25% = 87.5 so about 88 (SCIENCE)

350 * 10% = 35 (MUSIC)

350 * 15% = 52.5 also about 53 (HISTORY)

Answer:

[tex]6/17[/tex]

Step-by-step explanation:

I assume you want the question in the picture solved as your written question is different but appears to be copied and pasted from the text.

1. When adding fractions the denominator (number on the bottom) must be the same between the two fractions, i.e. having a common denominator. In this case they are already the same, that is, 17 and 17. Just add the top numbers (numerators) together, and leave the denominator the same. So,

[tex]\frac{3}{17} +\frac{3}{17} =\frac{6}{17}[/tex]

Answer:

2; 11; 17; 23

Step-by-step explanation:

when you have an x you plug it in for the y

so

for the first one

you do

y = 3(1) - 1

y = 3 - 1

y = 2

that is the first one

you do this for the next 3 too

y = 3(4) - 1

y = 12 - 1

y = 11

y = 3(6) - 1

y = 18 - 1

y = 17

y = 3(8) - 1

y = 24 - 1

y = 23

those are your answer

Answer:

Manisha is 36 and Rahul is 6.

Step-by-step explanation:

Let m = Manisha's current age

Let r - Rahul's current age.

Today:

m = 6r

In for years:

m+ 4 = 4(r + 4) Distribute the 4

m + 4 = 4r + 16  Substitute in 6r for me

6r + 4 = 4r + 16  Subtraction 4r from both sides

2r + 4 = 16  Subtract 4 from both sides

2r = 12  Divide both sides by 2

r = 6  Rahul is 6  Plug 6 for r into either of the two original equations to find Manisha's age.

m = 6r

m = 6(6)

m = 36

Rahul's present age is 6 years, and Manisha's present age is 36 years.

Let's use the letters "M" for Manisha's current age and "R" for Rahul's.

Given information:

1. Manisha's age is 6 times Rahul's age: M = 6R

2. After 4 years, Manisha's age will be four times Rahul's age: M + 4 = 4(R + 4)

We have a system of two equations with two variables. We can use these equations to solve for their present ages.

Equation 1: M = 6R

Equation 2: M + 4 = 4(R + 4)

Substitute the value of M from Equation 1 into Equation 2:

6R + 4 = 4(R + 4)

Distribute the 4 on the right side:

6R + 4 = 4R + 16

Subtract 4R from both sides:

2R + 4 = 16

Subtract 4 from both sides:

2R = 12

Divide by 2:

R = 6

Now that we know Rahul's age (R = 6), we can find Manisha's age using Equation 1:

M = 6R = 6 × 6 = 36

So, Manisha is 36 years old and Rahul is 6 years old at the moment.

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According to the given statement;

Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35

Gross pay is the sum of a person's earnings during a specific time period before any deductions are made. The calculation of gross pay does not take into account deductions for employer-provided health insurance, retirement plans, or compulsory taxes and Medicare contributions. Since it does not reflect a person's take-home pay, the gross pay definition is different from the one for net pay.

According to the given value;

Dalton's gross pay = 576

his medicare tax rate = 1.45% = 0.0145

the tax on his medicare = 0.0145 x 576 = $8.35

Hence,Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35

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Answer:

B

Step-by-step explanation:

Let's start by evaluating each of the equations:

[tex]y\geq 2x+7[/tex]

To begin to understand this equation, first, graph line by replacing the inequality symbol with an equal sign:

The graph of this line is the first attached image at the bottom of this answer.

The inequality reads, y is greater than or equal to 2x + 7.

The "equal to" is very important. This means that the line [tex]y= 2x+7[/tex] is a solution to this problem, so the line is drawn as a SOLID line.

Because the inequality is GREATER than, that means that all values greater than the function are solutions! Thus the area  ABOVE the line is shaded. The second image attached below shows the shaded graph.

Now, let's look at the second equation:

[tex]y > -\frac{1}{3} x-2[/tex]

Start by replacing the inequality symbol with an equal sign and graphing the line. See the third image below for that line.

Now, THIS inequality is just GREATER than, not equal to. This means that the line that we just graphed, [tex]y = -\frac{1}{3} x-2[/tex] is NOT a solution to the equation! Therefore, the line is drawn as a dashed line. This means it is NOT included in the solution.

Again, since it is greater than, the area ABOVE the line is shaded. See the fourth image attached below to see the graph.

Now, let's combine these graphs! In the fifth image below, the blue represents [tex]y\geq 2x+7[/tex], and the red represents [tex]y > -\frac{1}{3} x-2[/tex].

The area where the red and blue overlap is the area to keep for the solution of this problem, since these equations represent a system of linear inequalities. I hope this helped!

The square root of (1/96) is the same as the square root of 1 divided by the square root of 96. You can divide the fraction inside the radical before or after you calculate the square root. The result will be the same.

Here we first calculate the square root of the numerator and the square root of the denominator separately, and then we divide the two:

[tex]\frac{\sqrt{1}}{\sqrt{96} }[/tex] ≈ [tex]\frac{1}{9.798}[/tex]  ≈  0.1021

Alternatively, we first divide 1 by 96 and then do the square root of the quotient:

[tex]\sqrt{1/96}[/tex] ≈ [tex]\sqrt{0.0104}[/tex] ≈ 0.1021

To calculate the square root of 1 divided by 96, you first take the square root of 1 and then divide that result by 96:

[tex]\frac{\sqrt{1}}{96} = \frac{1}{96}[/tex] ≈  0.0104

The solutions of the trigonometric equation are x₁ = π / 6 and x₂ = 5π / 3.

In this problem we find a trigonometric equation which has to be simplified and solved for x to find the family of solutions within the given interval:

csc x · tan x = 2√3 / 3

(1 / sin x) · (sin x / cos x) = 2√3 / 3

1 / cos x = 2√3 / 3

cos x = 3 / 2√3

cos x = √3 / 2

Then, by inverse trigonometric functions:

x₁ = π / 6, x₂ = 5π / 3

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Not all rhombus can be inscribed in a circle until the rhombus has four   90º angles which is a  square.

A rhombus can only be can be inscribed in a circle. basically  the opposite angles there  in the rhombus are congruent. if the opposite angles are not supplementary, that rhombus cannot be encircled,  while that rhombus had four  90º angles, which means if it is a square, as in general a rhombus has two diagonals that are not equal except square so the endpoints of the shorter diagonal would not be points on the circle.

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Answer: 25/12

Step-by-step explanation:

The number of Earths needed have a total mass of 1 googol kilograms is 1.67 x [tex]10^{75}[/tex].

Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.For example: 1 x 10² is equivalent to 100

A googol in scientific notation is 1 x [tex]10^{100}[/tex]

The number of Earths needed have a total mass of 1 googol kilograms =

(1 x [tex]10^{100}[/tex])  ÷ (5.972 ×[tex]10^{24}[/tex])

(1 ÷ 5.972) x ([tex]10^{100 - 24}[/tex])

0.16745 x [tex]10^{76}[/tex]

= 1.67 x [tex]10^{75}[/tex]

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Hi ~

* ˚ ✦ E x p l a n a t i o n : - * ˚ ✦

Combine multiplied terms into a single fraction.

[tex]\bold{(\frac{1}{2} \: a \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Multiply by 1.

[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Find common denominator.

[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Combine fractions with common denominator.

[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]

[tex]\bold{(\frac{a \: + \: 4}{2})^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Multiply the numbers.

[tex]\bold{(\frac{a \: + \: 2 \: ^. \: 2d}{2})^2}[/tex]

[tex]\bold{\frac{(a \: + \: 4d \: ^. \: 2d)}{2^2}^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Distribute exponent.

[tex]\bold{(\frac{a \: + \: 4d}{2}^2)}}[/tex]

[tex]\bold{\frac{(a \: + \: 4d)}{2}^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Evaluate the exponent.

[tex]\bold{\frac{(a \: + \: 4d)}{2^2}^2}}[/tex]

[tex]\bold{\frac{(a \: + \: 4d)}{4}^2}}[/tex]

Your answer would be is:

[tex]{\huge{\boxed{\bold{{\rightarrow{\frac{(a \: + \: 4d)}{4}^2}}}}[/tex]

Hope It Helps...

[tex]\textsc{Answer:}[/tex]

TheAestheticGirl

Answer:

Step-by-step explanation:

The solution of the equation 2/y + 1/2 = 5/2y is y = 1

In this question, we have been given an equation.

2/y + 1/2 = 5/2y

We need to find the solution of given equation.

⇒ 2/y + 1/2 = 5/2y

⇒ (4 + y)/2y = 5/2y

⇒ 4 + y = 5

⇒ y = 5 - 4

⇒ y = 1

We need to check above solution.

So, substitute y = 1 in given equation.

⇒ 2/y + 1/2 = 5/2y

⇒ 2/(1) + 1/2 = 5/2(1)

⇒ 2 + 1/2 = 5/2

⇒ 5/2 = 5/2

⇒ LHS = RHS

Therefore, the solution of the equation 2/y + 1/2 = 5/2y is y = 1

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Answer:

6 3/14

Step-by-step explanation:

[tex]4\:1/7 \div 2/3 = 29/7 \div 2/3\\= 29/7 \div 2/3\\= \frac{29*3}{7*2}\\= 87/14\\= 6\:3/14[/tex]