Buying art supplies. Isabella is an artist who normally purchases her spray fixative in 6 2/3 ounce cans. If the economy size contains 1 2/5 as much spray, how many ounces will it contain?

In the replacement set, 9 is the solution to this equation 3 (n+7) = 48.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3 (n + 7) = 48

And, Replacement set: {8, 9, 10}

Now, We can solve the expression as;

⇒ 3 (n + 7) = 48

Divide by 3,

⇒ n + 7 = 48/3

⇒ n + 7 = 16

Subtract 7, we get;

⇒ n = 16 - 7

⇒ n = 9

Thus, The solution of the equation is, 9.

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the answer is D : 4

According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).

Let's call this other side "x".

We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.

Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.

We can also say that the area of the square and the rectangle is equal to 4 cm^2.

If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.

Solving for y, we get: y = 2 cm.

Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.

So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).

So the answer is D : 4

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a. The sum of 1/3+1/5= 8/15

b. The sum of 1/8+2/6 = 3/8

c. the sum of 8/9+11/12= 1 87/108

d. the sum of 1/7+5/8= 1 7/36

e. the sum of 1/4+2/4= 3/4

f. the sum of 1/2+3/9= 5/6

g. the sum of 1/10+1/4= 7/20

h. the sum of 3/11+11/12 = 1 25/132

Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.

a. 1/3 + 1/5 = (5+3)/15 = 8/15

b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8

c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108

d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36

e. 1/4+ 2/4 = (2+1)/4 = 3/4

f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6

g. 1/10+1/4 = (2+5)/20 = 7/20

h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132

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Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

Answer:

C (2)

Step-by-step explanation:

• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )

• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )

So √32 ÷ √8 is equal to 4√2 ÷ 2√2

And there √2 cancels for both

So what you're left with is 4 ÷ 2

And 4÷2 = 2

The solution to the equation 9(6^3x) - 13(6^3x) + 4(6^3x) = 0 is x = 0.

Generally, To solve the equation we try to get the values to be coherent by writing as

9(6^3x)-13*(6^3x)+4*(6^3x)=0

Therefore we solve the coefficients of the solution

To solve this equation, we can first distribute the constants in front of the parentheses:

9(6^3x) - 13(6^3x) + 4(6^3x) = 0

This simplifies to:

(9 - 13 + 4)(6^3x) = 0

Then, we can simplify the expression in the parentheses:

(0)(6^3x) = 0

This means that either (0) = 0 or (6^3x) = 0.

The second case is not possible, because the base of an exponent can't be zero. So, the only solution to this equation is x = 0.

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Answer:

[tex]\frac{25}{3x^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{125xy^{3} }{5x^{3}3y^{3} }[/tex] = [tex]\frac{25}{3x^{2} }[/tex]

125/5 = 15

[tex]\frac{xyyy}{xxxyyy}[/tex]  We can cancel out one x in the numerator and the denominator.  That leaves [tex]x^{2}[/tex] in the denominator.

We can cancel out the 3 y's in the numerator and the denominator and that leaves no y's

Answer:

A

Step-by-step explanation:

For an ideal gas : PV=RT

And the internal energy of an ideal gas:

E

in

​

=

2

3

​

RT

E

in

​

=

2

3

​

PV

V

E

in

​

​

=

2

3

​

P

Energy density (E)=

2

3

​

P

P=2/3E

(4x + 7)(3x-5) are the factors of trinomial 12x²-x-35

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given trinomial is 12x²-x-35

Break the expression into groups

(12x²+20x)+(-21x-35)

12x²+20x-21x-35=0

Now take the gcf of first two terms

4x(3x+5)-7(3x+5)=0

(4x-7)(3x+5)=0

Hence, (4x + 7)(3x-5) are the factors of trinomial 12x²-x-35

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The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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Answer:

Step-by-step explanation:

pass it then

The indicated operation 1/3 x 6/7 can be performed as 2/7.

The concept that will be used in this operation is the multiplication operation.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.

Given operation is  1/3 x 6/7

1/3 x 6/7

=[ (1 x 6)/(3 x 7) ]

= (6/21)

= 2/7

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check the correct question:

Perform the indicated operation. 1/3 x 6/7

The value of x = ±5.

What is Quadratic Equation?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x).

Method 1 :

⇒ 16x² - 400 = 0

⇒ 16x² = 400

⇒ x² = 400/16

⇒ x² = 25

⇒ x = ±5

Method 2 :

⇒ 16x² - 400 = 0

⇒ 16(x² - 25) = 0

⇒ x² - 25 = 0

⇒ x² = 25

⇒ x = ±5

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Completing the table with the appropriate percentage and decimals will be:

Fraction Decimal Percentage

1/4. 0.25. 25% of 1

1/10. 0.1. 10% of 1

3/4. 0.75. 75% of 1

1/5. 0.2. 20% of 1

3/2. 1.5. 150% of 1

7/5. 1.4. 140% of 1

It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:

= 1/10 × 100

= 10%

0.1 to fraction will be:

= 1/10

The percentage for 1/5 will be:

= 1/5 × 100

= 20%

1/5 to decimal will be:

= 1/5

= 0.2

The decimal 1.5 will give 150%

The fraction for 1.5 will be:

= 1.5 / 1

= 15 / 10

= 3/2

Also 3/4 as percentage will be:

= 3/4 × 100

= 75%

75% to decimal will be:

= 75 / 100

= 0.75

140% to fraction will be:

= 140 / 100

= 7 / 5.

The decimal for 140% will be:

= 140 / 100

= 1.4

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the solutions to the system of inequalities are (1,1) and (-2,3).

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2х + 3у > 2

3x + 5y > 1

for (1,1):

2+3 > 2 (true)

3+5 > 1 (true)

for (-2,-1)

-4-3 > 2 (false)

for (-2,3):

-4+9 >2 (true)

-6+15>1 (true)

for (7,-4):

14-12>2(false)

Hence, the solutions to the system of inequalities are (1,1) and (-2,3).

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==============================================

Work Shown:

C = 2pi*r

9pi = 2pi*r

r = (9pi)/(2pi)

r = 4.5

A = pi*r^2

A = pi*(4.5)^2

A = 20.25pi  square cm

------------------

Explanation:

The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.

Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2

Side notes:

The measure of the value of x in the expression for the angle (2·x + 1)°, obtained using vertical angles theorem is; x = 33°

Vertical angles are angles formed when two lines intersect. Vertical angles are the angles vertically opposite each other, formed by the intersection of the two lines.

Vertical angles theorem states that the vertical angles formed by the intersection of two straight lines are congruent.

The angles (2·x + 1)° and 67° are vertical angles. therefore;

(2·x + 1)° ≅ 67° (Vertical angles theorem)

(2·x + 1)° = 67°, by the definition of congruency

(2·x)° = 67° - 1° = 66°

x = 66° ÷ 2 = 33°

Therefore, plugging in the value of x = 33°, in the expression; (2·x + 1)° + 67°, we get;

(2·x + 1)° + 67° = (2 ×33 + 1)° + 67°

(2 ×33 + 1)° + 67° = 67° + 67° = 134°

The measure of the sum of the angles, (2 ×33 + 1)° and 67° is 134°

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When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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If each term in the sum a1+a2+a3...+an is  7 and the sum equals 350, C: 40 would be equal to n.

In equation form, it is:  

                  7s +  77t = 350

In this equation,

          s represents the number of 7's

          t represents the number of 77's

          thus, the number of terms i.e n = s + t =?

now solving the equation,

        7 (s + 11t) = 350

        7 (s + 11t) = 350

            s + 11t = 50

            s + 11t = 50

now, if  

       s=39     &      t =1  

then

         s + 11t = 50 -> 39 + 11 (1)  = 50

Since the number of terms n = s + t

        n = s + t

        n = 39 + 1

        n = 40

Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.

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The length in centimeters of AB is 125/360 x 42cm.

What is the circumference of the circle?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: The circumference of the circle is 42 centimeters

AB is an arc, the formula for calculating the length of an arc is given as

L = Ф/360 X 2πr

where Ф is the angle subtended by the arc, and 2πr is the circumference of the circle.

Substituting the given values into the formula, we have

L = 125/360 x 42

L = 14.5

Hence, the length in centimeters of AB is 125/360 x 42cm.

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Answer:

g(t) = 22(1.09)t

Step-by-step explanation:

formula is y = a(1 + r)t

staticbigideasmathcom

9647/15 is the long division on

Step-by-step explanation:

9647/15 = 643.1333333333

Using the given conditions and the value provided to us, The answer is Paolo sold 210 tickets in 3 days.

A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.

Word problems in mathematics are problems that are presented in a narrative format, rather than as a mathematical equation. They often describe a real-world situation, such as a person buying items at a store, and ask the student to use mathematical concepts to solve the problem. This can include concepts such as addition, subtraction, multiplication, division, fractions, and percentages. Word problems can be challenging for students because they require not only mathematical knowledge, but also the ability to understand and interpret the problem, and to translate the information given into mathematical equations.

On Tuesday, Paolo sold 3 * 21 = 63 tickets.

On Wednesday, he sold 2 * 63 = 126 tickets.

So in total, Paolo sold 21 + 63 + 126 = 210 tickets.

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Answer: Using the given conditions and the value provided to us, The answer is Paolo sold 210 tickets in 3 days.What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.What are word problems in mathematics?Word problems in mathematics are problems that are presented in a narrative format, rather than as a mathematical equation. They often describe a real-world situation, such as a person buying items at a store, and ask the student to use mathematical concepts to solve the problem. This can include concepts such as addition, subtraction, multiplication, division, fractions, and percentages. Word problems can be challenging for students because they require not only mathematical knowledge, but also the ability to understand and interpret the problem, and to translate the information given into mathematical equations.On Tuesday, Paolo sold 3 * 21 = 63 tickets.On Wednesday, he sold 2 * 63 = 126 tickets.So in total, Paolo sold 21 + 63 + 126 = 210 tickets.

Step-by-step explanation:

The number of quarts of soil in each pot will be 3.25 quarts.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil.

Then the number of quarts of soil in each pot will be given as,

⇒ 13 ÷ 4

⇒ 13 / 4

⇒ 3.25

The number of quarts of soil in each pot will be 3.25 quarts.

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The Equations  is b/4 + 2= 8 and b = 24.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Mathematical statements called expressions must contain at least two phrases including numbers, variables, or both, and they must be joined by an operator.

Given Two more than the quotient of a number and 4 is 8,

Let number be b

b/4 + 2= 8

b/4 = 8 -2

b/4 = 6

b = 24

Hence, two more than the quotient of a number is 24.

Hence the equation for phrase is b/4 + 2= 8 and b = 24.

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Given ,

To Find : The Surface Area of a Cylinder

First we need to find the radius

[tex]r = \frac{6}{2}\\r = 3[/tex]

Formula to find the SA of a cylinder

[tex]SA = 2\pi r(r+h)[/tex]

[tex]SA = 2X3.14X3(3+12)[/tex]

[tex]SA = 18.24(16)\\SA = 291.84cm^{2}[/tex]

When solving a system of two equations there are three possible outcomes for the solution of a system of three variables and two solutions for two variables.we can say that system of equation have infinite solutions.

There are three methods used to solve systems of equations graphing, substitution, and elimination. To solve a system by graphing you simply graph the given equations and find the point(s) where they all intersect.Solve the linear equation for the remaining variable.

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.

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