Amanda was observing insects in a terrarium in her school's science lab. She noticed there were a number of ants
and a number of spiders in the terrarium. She decided to count the number of legs there were all together on all
of the ants and spiders in the terrarium. You can assume that each ant had six legs and each spider had eight legs.
Let a represent the number of ants, and let s represent the number of spiders.
Question # 1: Write an expression using a and s that represents the total number of
legs in the terrarium. Circle the letter of the best answer.
(A) a+s
(B) 6(s+a)
(C) 6a +8s
(D) 8a + 6s
Question #2: What does each term in the expression represent?

Answer:

Varies, see below

Step-by-step explanation:

We need to find the number of math problems per minute. To do that, we divide 40/32 to find that she completes 1.25 problems per minute.

Or, on the flippity flop, we can find the number of minutes per math problem. So we would do 32/40 to get  0.8 minutes per math problem.

Choose the one according to your needs.

Answer:

p = 9/55

Step-by-step explanation:

2/3p + 3p = 3/5.

2/3p + 9/3p = 3/5

11/3p = 3/5

Divided both sides by 11/3

p = 9/55

If you can, please give me a Brainliest, thank you!

Answer:

56.25

Step-by-step explanation:

Answer:

The number of batches of cookies required for your dad to bake is 6.33 batches.

Number of people at the party = 38

Number of cookies each would have = 4

Total number of cookies needed = Number of people at the party × Number of cookies each would have

= 152 cookies

Number of cookies baked per batch = 24

Equate the number of batches to the number of cookies baked.

Let x = number of batches required

1 : 24 = x : 152

1/24 = x / 152

cross product

1 × 152 = 24 × x

152 = 24x

divide both sides by 24

x = 152 / 24

x = 6.33 batches

Therefore, your dad should bake 6.33 batches of cookies for everyone at the party.

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Answer:

91

Step-by-step explanation:

89+89+89+92+x / 5= 90

359+x / 5= 90 (multiply by 5 both sides)

359+x =450 (subtract 359 from both sides)

X= 91

Statement: 5(x+6)=x+38 is x=2

We are given the equation 5(x+6)=x+38. We can solve this equation by isolating x on one side of the equation. To do this, we will first subtract x from both sides of the equation. This will leave us with 5x+30=38. We can then subtract 30 from both sides of the equation to isolate the x terms. This leaves us with 5x=8. We can then divide both sides of the equation by 5 to isolate x. This gives us x=2.

Therefore, if 5(x+6)=x+38, then x=2.

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The Given Statement is  true reason is the value in the left-hand side is equal to the value in the right-hand side. it shows proof that 5(x+6) = x+38 for x =2.

Here we have to understand what is an equation because in question we have given an equation.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

2x - 5 and 13 are expressions in this case.

These two expressions are joined together by the sign "=".

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Here we have given an equation

5(x+6) = x+38  we have to proof for x = 2.

LHS 5(x+6) = 5(2+6) = 5*8 = 40

RHS x+38 = 2+38 = 40

So the given statement is true because LHS = RHS.

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Answer:

Step-by-step explanation:

The equation 45x + 55x = 350 could be used to solve the following problem:

Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?

Answer:

∛x

Step-by-step explanation:

Replace x with y and then solve

[tex]y=x^3\\x=y^3\\\sqrt[3]{x} = y[/tex]

Answer:

7/60

Step-by-step explanation:

solution

(x*y) + z

(1/3*-2/5) + 1/4

-2/15 + 1/4

LCM 60

-8 + 15/60

7/60

Answer:

7/60

Step-by-step explanation:

Looking at the numbers:

x = 1/3

y = -2/5

z = 1/4

We can simply add them into the equation:
(x × y) + z

(1/3 × -2/5) + 1/4 =?

1/3 × -2/5 ≅ -0.1333333 or [tex]\frac{-1333333}{10000000}[/tex]

-0.1333333 + 1/4 = 0.1166667 or [tex]\frac{7}{60}[/tex]

Answer:

x = 30

Step-by-step explanation:

3x + 1 + 89 = 180

3x + 90 = 180

3x = 90

x = 30

3(30) + 1 = 91

91 + 89 = 180

Answer:

Step-by-step explanation:

3x + 1 + 89 = 180

3x = 180 - 1 - 89

3x = 90

x = 90 : 3

x = 30°

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

3 x 30 + 1 + 89 = 180

90 + 90 = 180

180 = 180

To draw a line segment, Gather your drawing materials and decide on the starting and ending points of your line segment. Place your pen or pencil on the starting point and use a ruler to guide it to the ending point, drawing a continuous, straight line and Lift the pen or pencil from the paper to complete the line segment.

To draw a line segment, follow these steps:

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Answer: B. 12cm^2.

Step-by-step explanation:

To find the area of the shape, you need to count the number of squares inside it and then multiply that number by the area of a single square. If each grey square is 1cm by 1cm, then the area of a single square is 1cm x 1cm = 1cm^2. If you count the squares inside the shape, you will see that there are 12 squares. Therefore, the total area of the shape is 12cm^2. The correct answer is therefore B. 12cm^2.

Answer: Pablo 45   josh 15  Melissa 6

Step-by-step explanation: 15 • 3 + 15 + 6 = 66

Answer:

a^4

Step-by-step explanation:

a^7 / a^3 = a^(7-3) = a^4

The solution to the equation 3 x 2 − 12 d − 2 is 1/3.

Solving the equation for d because the value of d would be the required solution to this equation:

Now

 3 x 2 − 12 d − 2  = 0

  6     -  12 d   - 2  =  0

Sitting the constant terms to the right side of the equation while keeping the term with d to the left-hand side of the equation:

Now

   -12d   =  -6 + 2

     -12d =  -4

     d = -4/-12

       d=  1/3

After solving the given equation for d, the solution of the equation is determined to be 1/3.

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The coefficient of y in the expression -2x² * y² * z is 0

From the question, we have the following parameters that can be used in our computation:

An algebraic expression

The algebraic expression is given as

- 2x ^ 2 * y ^ 2 * z

Express the exponents as proper subscripts

So, we have the following representation

-2x² * y² * z

There is no term in the expression with the variable y

Instead, the term has a y² as its variable

This means that the coefficient of y is 0

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Answer:

-20x^2 -6x

Step-by-step explanation:

I don't want to explain the whole thing, but here's a pic.

There are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.

We shall derive and solve the system of equations as follows:

homework questions corrected per week;

10x + 20y + 30z = 2100...(1)

number of homework papers corrected per week;

x + y + z = 100...(2)

x = number of students in the math class

y = number of students in the English class

z = number of students in the history class.

since the maths and English classes have the same number of students then x = y and: equations (1) and (2) becomes;

10x + 20x + 30z = 2100

30x + 30z = 2100

30(x + z) = 2100 {divide through by 30}

x + z = 70...(3)

x + x + z = 100

2x + z = 100...(4)

Subtract equation (3) from (4) to eliminate z

2x + z - x - z = 100 - 70

x = 30

Now we will substitute this value of x back into the equation (4) such that;

2(30) + z = 100

60 + z = 100

z = 100 - 30 {subtract 60 from both sides}

z = 40

So there are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.

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Answer:

Step-by-step explanation:

16 = 20% of x

20% = 1/5

So...

16 = 1/5 of x

16 = 1/5*x

Multiply both sides by 5...

80 = x

There are 80 questions on the test.

Please mark brainliest.

the sum of 4.06 x 10¹⁹ and 5.034 x 10¹⁷ is 4.11034 x 10¹⁹ (option b)

to add 4.06 x 10¹⁹ and 5.034 x10¹⁷ following steps are to be followed

4.06 x 10¹⁹ can be written as 406x10¹⁷

taking 10¹⁷ common from 406x10¹⁷ and 5.034 x10¹⁷ (406x10¹⁷ +5.034 x10¹⁷)  it will be 411.034 x 10¹⁷

or we can write it as 4.11034 x 10¹⁹

therefore, the sum of 4.06 x 10¹⁹ and 5.034 x 10¹⁷ is 4.11034 x 10¹⁹

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Answer:

9

Step-by-step explanation:

Answer:

Use PEMDAS, answer is 9

Step-by-step explanation:

Monique can make 5 Vase with 4 Daisies and 5 Roses in each.

The greatest number among all the common factors of the given numbers is the HCF (Highest Common Factor) of two numbers.

For example, the HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36.

Given:

Daisies = 20

Roses = 25

Monique obviously wants to use all the flowers so she does not any left over. She needs to find a number which divides into 20 and 25,

So, the HCF of 16 and 24, which is 5.

Factors of 20 = 2, 4, 5, 10, 20.

Factors of 25 = 5, 25

So, She will be able to make 5 bouquets.

and, Each bouquet will have 4 Daisies and  5 Roses.

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The Complete Table that missing in the table is

Flower Type Number

Daisies 20

Roses 25

The reasons for each statement about the given triangle are as follows:

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Given, A triangle PWZ in that base ∠1 and ∠2 are same and the distance between W and Z from X and Y are the same where XY is the base of another triangle inside the ΔPWZ.

For ΔPWZ

We know PWZ is an isosceles triangle since its two angles are the same.

thus another ΔPXY is on the same base of ΔPWZ and also at the same distance from its point Hence, these triangles are congruent triangles.

Looking at that perspective, we can say that ∠1 and ∠2 are pairs of alternate angles and are congruent.

∠1 ≅ ∠2

The same with ∠3 and ∠4.

∠3 ≅ ∠4

Therefore, As a result, according to the ASA Theorem, the Triangles are congruent. The two angles and the side they encompass are comparable.

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Using the diameter given, the volume of the sphere is 14137.17cm³

The volume of a sphere is a measurement of how much space it takes up. It is calculated using the following formula and represents the volume of the sphere:

v = 4/3 * π * r³

Where: r is the radius of the sphere, which is the distance from the sphere's center to its surface, and π is a mathematical constant roughly equal to 3.14.

The formula is based on the observation that a sphere's volume is two thirds that of a cylinder with the same radius and height.

The volume of a sphere is directly proportional to the cube of the radius, which is a crucial point to remember.

In the problem, the diameter given is 30cm, we can calculate the radius from this.

radius = diameter / 2

radius = 30 / 2

radius = 15cm

We can plug in the values to calculate the volume of this sphere;

v = 4/3πr³

v = 4/3(3.14)(15)³

v = 14137.17cm³

The volume is 14137.17cm³

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The local linear approximation of f(x) 2In(x) at x = 2 is y = x - 2 + log (4).

As per the given data, the function f(x) is given by:

f(x)=2 log (x) at x = 2

Here we have to determine the linear approximation of f(x).

A linear approximation is a mathematical phrase that describes using a linear function to approximate a general function.

We know the linear form of the function is

y = f(a) + f'(a) ( x - a )

Here, a = 2

Therefore y = f(2) + f'(2) (x - 2) . . . (1)

Now, f(2) = 2 log (2)

= log [tex](2)^2[/tex]

= log (4)

Again, f'(x) =[tex]\frac{d}{d x}[f(x)][/tex]

[tex]=\frac{d}{d x}(2 \log (x)) \\[/tex]

f'(x) = [tex]2 \cdot \frac{1}{x}=\frac{2}{x} \\[/tex]

Therefore f'(2) = [tex]\frac{2}{2}[/tex] = 1

Plug in the values of f(2) and f'(2) in equation (1) we get,

y = log (4) + 1(x - 2)

y = x - 2 + log (4) (which is the linear approximation of f(x))

Therefore option (b) is correct

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You can form two different types of quadrilaterals from the given sticks of 8cm,8cm,5cm,5cm.

A quadrilateral is a polygon with four sides and four angles. Quadrilaterals are two-dimensional shapes, meaning they exist on a flat surface and have length and width, but no depth. Some examples of quadrilaterals include rectangles, squares, parallelograms, and trapezoids.

You can form two different types of quadrilaterals using four sticks of 8cm, 8cm, 5cm, and 5cm in length such as a rectangle of the two 8cm sticks as the length and the two 5cm sticks as the width to create a rectangle, and you can also form a parallelogram by using the two 8cm sticks as the length, and the other two 5cm sticks as the width.

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Your question seems incomplete, but I assume the complete question was:

"How many types of quadrilaterals can be formed using these sticks of 8cm, 8cm, 5cm, 5cm?"

x=3 is the solution of equation 2x-3=3 which represent the line parallel to y axis such that x coordinate is always 3

In mathematics, an axis is a line that is used to take or indicate measurements. The coordinate plane's x and y axes are two of its most important axes. The x-axis is represented by a horizontal number line, and the y-axis by a vertical number line. The perpendicular intersection of these two axes yields the coordinate plane. The x-axis and y-axis are also known as the ordinate and abscissa, respectively.

in the question we have:

⇒ 2x - 3 = 3

⇒ 2x = 6

⇒ x = 3

which represent a line parallel to y axis where x is always equal to 3 .To plot graph take any y such that point is (3, y) .

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People hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

Theories of human labor motivation and management include Theory X and Theory Y.

They were invented by Douglas McGregor in the 1950s while he was a faculty member at the MIT Sloan School of Management, and they underwent further development in the 1960s.

Consider work a natural part of life, and come up with creative solutions for workplace issues.

According to Theory X, individuals despise their jobs, desire to escape them, and detest having to be accountable.

According to Theory Y, people are self-driven and enjoy having responsibilities placed on them.

Therefore, people hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

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the equation for line will be y = (5/4)x + 13.

What is the slope of line?

Determine the slope of the line using the slope formula given two line-side coordinates. The formula m=(y2-y1)/ describes the slope as the proportion of the change in y values to the change in x values (x2-x1). The coordinates of the first point represent x1 and y1 respectively. At x2, y2, and their respective locations are the second points. It doesn't matter which point you choose to rank as the first and which as the second.

Knowing that formula two, which is used to determine the slope of a line connecting two points, is

The line passes through (-4, 8) so,

8 = (5/4)(-4) + c

8 = -5 + c

c = 13

c = 13

The equation of a line is y = (5/4)x + 13

Hence the equation for line will be y = (5/4)x + 13.

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