Joseph removes 5/8 gallons of white paint from a can. Then he adds 5/8 gallons of blue paint to the can.


Write and then evaluate a subtraction expression to find the overall increase or decrease in the amount of paint in the can.

Answer:

varies inversely as √t

Step-by-step explanation:

Answer:

a hexagon has three sides of length (2)+ in and other three side is equal to

the length of longest side

Step-by-step explanation:

The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

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If the approximated number is given as 6.3 Then the error interval of x is 6.24≤x≤6.35

A value or quantity that is nearly but not exactly correct.

The number is given as x.

So, we have:

x = 6.3

The smallest number that can be approximated to 6.3 is 6.25 (to 1 decimal place), while the largest number is 6.34

Given that there are possibilities of error, the lower and upper bound of the error interval would be:

6.25-0.01≤x≤6.34+0.01

6.24≤x≤6.35

Hence, the error interval of x is  6.24≤x≤6.35

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k, q, r, t are directly proportional to p and s is inversely proportional to p.

The inversely proportional property state that two values are opposite to each other. If there will increase in one value or quantity then the another quantity will automatically decrease with the same ratio and if one quantity will decrease then another will increase with that ratio.

Say if x and y are inversely proportional, then mathematically

x ∝ 1 / y

The directly proportional property state that two values are same to each other. If there will increase in one value or quantity then the another quantity will automatically increase with the same ratio and if one quantity will decrease then another will also decrease with that ratio.

Say if x and y are directly proportional, then mathematically

x ∝  y

In the given equation,

k, q, r, t are directly proportional to p and s is inversely proportional to p.

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Answer:

You draw the exact same shape but at a different scale

Step-by-step explanation:

You just draw it bigger.

The only option that is not viable to solve the systems of equations is:

D. Substitute y = 6/5x - 12 into the first equation

Given the systems of equations,

2x + y = 20 ----> equation 1

6x - 5y = 12 ----> equation 2

In order to solve the system of equations using the substitution method, rewrite 2x + y = 20:

2x + y - 2x = 20 - 2x

y = 20 - 2x

Or

2x = 20 - y

x = 10 - 1/2y

Or

6x - 5y = 12

-5y = -6x + 12

y = -6/5x - 12/5

or

6x = 12 + 5y

x = 2 + 5/6y

Therefore, the only option that is not viable to solve the systems of equations is:

D. Substitute y = 6/5x - 12 into the first equation

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The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.

We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.

For multiplication, the rule of exponents to be used is -

aᵇ×aⁿ = aᵇ⁺ⁿ

Rewriting the expression

Product = (p³)(2p² - 4p) (3p² - 1)

Performing multiplication of first two brackets -

Product = (p³ × 2p² - p³ × 4p) (3p² - 1)

Product = (2p⁵ - 4p⁴) (3p² - 1)

Further performing multiplication of product with third bracket -

Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)

Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴

Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.

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Answer:

C: 6p7 - 12p6 - 2p5 + 4p4

Step-by-step explanation:

Source: Trust me bro

X is between A and B, X is the midpoint of segment AB if and only if

AX = XB.

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

We have,

A_____X_____B

Given that X is ___________A and B, X is the midpoint of segment AB____________ AX= ______

We need to fill in the blanks.

X would be in between A and B.

X is a midpoint of segment AB if and only if AX = XB.

Thus,

X is between A and B, X is the midpoint of segment AB if and only if

AX= XB.

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 We write the expression in its simplest form and we are left with.

y²√3 + y - 6

  Before proceeding let's define an algebraic expression.

    An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

     The first thing we will do is to write the expression:

(√y-√3)(√y+2√3)

  Then we perform the multiplication, with the distributive property, which gives as a result

(y + 2√3y - √3y - 6)

y²√3 + y - 6

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The length of each side will be 14.8 inches approx.

It's given that an Octagon sign is drawn out of a square by cutting out triangles from its corners and the total length of the stop sign is 36 inches. We know that squares are Right Angled at each side so in the picture mentioned below, we apply Pythagoras' theorem to find an equation for the side of the sign.

                     =>  [tex]s^{2} = x^{2} + x^{2}[/tex]

                     =>  [tex]s^{2} = 2x^{2}[/tex]                  ----> Eq. 1

Also, it is a square. So, the measurement of length from side to side

                     => 2x + s = 36 inch      ----> Eq. 2

By solving Eq.1 we get s = (√2)(x), Putting this value in Eq.2

                    => s = 36 - 2x    =>    (√2)(x) = 36 - 2x

                    => x(2 + √2 ) = 36   =>  x = 36/(2+√2)

Putting this value of x in Eq.1 , s^2 = 2(x^2)

                   => s = √2.(x)       =>  s = √2 (36/(2 + √2)

                   => s = 14.8

Hence, the length of each side of the sign will be 14.81-inch approx.

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Answer:

1. 32/80  2. 9/3  3. 1/3  4. 12/4   5. 4/1  6. 3/6 or 1/2  7. 21/18  8.  24/15  9. 25/5  10. 7/21

Step-by-step explanation:

good fraction brain

The simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶

Given,

a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.

The expression : ( a⁻⁴ / 2 × b² )³

Simplify the expression :

( a⁻⁴ / 2 × b² )³

= a⁻⁴⁽³⁾ / 2³ ˣ b²⁽³⁾

= a⁻¹² / 2³ ˣ b⁶

= a⁻¹² / 8b⁶

Therefore, the simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶

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The proof of DE is parallel to BC in the given triangle is shown.

As per the given data in the question;

A, B and C are the vertices of a triangle.

Whereas,

D lies at the midpoint of AB.

E lies at  the midpoint of AC.

The mid piont formula is;

Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)

The coordinates of D is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and B (2,-2).

D = (4 + 2 / 2, 6 - 2 / 2)

D = (3, 2)

The coordinates of E is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and C (-2,-4)

E = (4 - 2 / 2, 6 - 4 / 2)

E = (1, 1)

Now, the slope is calculated by;

m of DE = (y₂ -  y₁)/(x₂ - x₁)

The slope of E is

m of DE = (1 - 2)/(1 - 3) = 1/3

Slope of BC

M of BC = (-4 + 2)/(-4 - 2)

M of BC = 1/2

As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.

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It follows that the least integer greater than log√₇ √50 is 3.

We have a logarithm function that is given to us.

Let x = log√₇ √50

We get that:√ 7 ˣ = √ 50

So, we must find an integer x, such that √ 7 ˣ > √ 50.

We know that √ 49 = 7

√ 7 ˣ > 7

7 ⁰°⁵ˣ  > √ 7

x / 2 > 1

x > 2

In this case, x = 3 will be the least integer to satisfy this inequality.

Therefore, it follows that the least integer greater than log√₇ √50 is 3.

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Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.

You may also hear the simplest form called "lowest term."

In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:

Expand the following:

(9×4 x sqrt(y)) ^(3/2)

9×4 = 36:

(36 x sqrt(y))^(3/2)

(36 x sqrt(y))^(3/2) = 36^(3/2) (x sqrt(y))^(3/2):

36^(3/2) (x sqrt(y))^(3/2)

36^(3/2) = 36^(2/2 + 1/2) = 36^(2/2)×sqrt(36):

36^(2/2) sqrt(36) (x sqrt(y))^(3/2)

2/2 = 1

Answer:

36 sqrt(36) (x sqrt(y))^(3/2).

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Answer:

14.5

Step-by-step explanation:

The equation that represent the statement "quotient of a number x and five is half the difference of the number and four" is x / 5 = 4 - 1/2x

x / 5 = 4 - 1/2x

x/5 + 1/2x = 4

(2x+5x) / 10 = 4

7/10x = 4

x = 4 ÷ 7/10

= 4 × 10/7

= 40/7

= 5.714285714285714

Approximately,

x = 5.7

Therefore, the value of x in the equation is approximately 5.7

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The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

The function definition is given as

f(n) = -4 +2n for n > 1

Start by calculating f(2), f(3) and f(4)

So, we have

f(2) = -4 +2(2)

f(2) = 0

f(3) = -4 +2(3)

f(3) = 2

f(4) = -4 +2(4)

f(4) = 4

In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2

So, we have

f(n) = f(n - 1) + 2

Also, we have

f(1) = -4 +2(1)

f(1) = -2

Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

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No extraneous solution to the equation:

The equation is:

[tex]x^{1/2}[/tex] - [tex](x- 5)^{1/2}[/tex] = 2

To know whether the equation has an extraneous solution first we need to find the value of x.

[tex]x^{1/2}[/tex] - 2 = [tex](x - 5)^{1/2}[/tex]

[tex]x^{1/2} - 2[/tex] = [tex](x - 5)^{1/2}[/tex]

Now squaring both sides of the equation we have:

[tex](x^{1/2} - 2)^{2}[/tex] = x - 5

x - 4[tex]x^{1/2}[/tex] + 4 = x -5

[tex]x^{1/2}[/tex] = -9/4

x = 81/16

Now we have to put the value of x in the equation.

[tex](81/16)^{1/2}[/tex] - [tex](81/16 - 5)^{1/2}[/tex] =2

9/4 - 1/4 =2

8/4 = 2

2 =2

Therefore we get to know that there is no extraneous solution to the equation.

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It should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance is -$25.

It should be noted that regarding a bank account, it should be noted that the withdrawal has to do with the amount of money that the person removes from the account.

It should be noted that deposit is an addition to the amount in the account while the withdrawal is the subtraction.

Therefore, should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance will be:

= -$55 + $30

= -$25.

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Step-by-step explanation:

[tex]23 - 7x = 3x + 8 \\ - 7x - 3x = 8 - 23 \\ - 10x = - 15 \\ - 10x = - 15 \\ - 10 \: \: \: \: \: \: \: \: \: \: \: \: - 10 \\ x = \frac{15}{10 \\ } \\ x = 1.5[/tex]

The value of the Equation 23 - 7x = 3x + 8 is x = 3.1

A mathematical statement that shows that two mathematical expressions are equal.

Given an equation, 23 - 7x = 3x + 8

7x + 3x = 23 + 8

10x = 31

x = 3.1

Hence, The value of the Equation 23 - 7x = 3x + 8 is x = 3.1

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Answer:

4

Step-by-step explanation:

18 - 2= 16

16/4=4

We can multiply 67 x 5 using distributive property and answer will be 335.

What is the distributive property of multiplication ?

The distributive property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

It is given that we have to multiply 67 x 5.

We can multiply the two numbers using the distributive property.

We know that , the distributive property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Distributive property is written in form : A × (B + C) = AB + AC

So , 67 x 5 can be written as : 5 × (60 + 7)

or

5 × (60 + 7)

= (5 × 60) + (5 × 7)

= 300 + 35

= 335

Therefore , we can multiply 67 x 5 using distributive property and answer will be 335.

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can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ?

Here, in the figure we can see a diagram with 3 lines and few points.

1.Name a line that contains point A is A point is an intersection point of 2 lines that are line "l" and line "n".

2.Name a line that contains point D is D point is an intersection point of 2 lines that are "n" and line "m".

3.What is the another name of line m is line BD, B and D point are on the line "m" so we can say as line BD.

4.what is the another name of line n is line AD, A and D points are on the line "n" so we can say as line AD.

5.Name a point not on line AC is there are two points that are not on line AC is D and E points.

6.  Name a point not on line BD is there are three points that are not on line BD is A,C and E points.

7.Name the intersection of AC and DB, B is the intersection of AC and DB.

8. Name the intersection of AD and AC, A is the intersection of AD and AC.

9. Name a point not on line l or line m is point E.

10.Name a point not on line n or line m is point E.

Intersection is nothing but a point where lines intersect is the intersection.

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This is a question from line segments part of geometry.

1. A line that contains point A is line l.

2. A line that contains point D is line n.

3. Another name for line m is line BD.

4. Another name for line n is line AD.

5. A point not on the line AC is the point D.

6. A point not on the line BD is the point A.

7. The intersection point of line AC and line DB is the point B.

8. The intersection point of line AC and line AD is the point A.

9. A point not on the line l or line n is the point E.

10. A point not on the line m or line n is the point D.

Geometry is a branch of mathematics that broadly deals with the measurement, characteristics, and connections of points, lines, angles, surfaces, and solids: the study of the characteristics of given elements that hold true even after being transformed in a certain way.

It is from line segments part of geometry.

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The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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The solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

– 25 ÷ – 13 – 35 × – 23

Evaluate the quotient

So, we have

– 25 ÷ – 13 – 35 × – 23 = 25/13 – 35 × – 23

Evaluate the product

So, we have

– 25 ÷ – 13 – 35 × – 23 = 25/13 + 805

Evaluate the sum

So, we have

– 25 ÷ – 13 – 35 × – 23 = 805 25/13

Divide the fraction

So, we have

– 25 ÷ – 13 – 35 × – 23 = 805 + 1 12/13

Evaluate the sum

So, we have

– 25 ÷ – 13 – 35 × – 23 = 806 12/13

Hence, the solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13

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