what is Vivian's new account balance?

proper scientific notation: 3.6 x 10⁻⁵

standard form: 0.000036

The length of the diagonal of the Triangle is 14.86 units

What is Diagonal?

When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

Given,

Area of Rectangle = 110square units

Length = 11units

Breadth = ?

Area of Rectangle = length x breadth

Breadth = Area of Rectangle / length

Breadth = 110 / 11

Breadth = 10units

Length of diagonal (Pythagoras Theorem)

H^2 = P^2 + B^2

H^2 = (11)^2 + (10)^2

H^2 = 121 + 100

H^2 = 221

H = [tex]\sqrt{221}[/tex]

H = 14.86 units

Hence, The length of its diagonal is 14.86 units

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In a equation as above:

a is the leading coefficient

n is the degree

For the given equation:

By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

So, the values in the blank will be:

Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

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Remember that

The y-intercept is the value of y when the value of x=0

In this problem

we have the equation

y=7x^2+4

For x=0

substitute

y=7(0)^2+4

y=4

The product of the given expression is 1,30,200.

Given expression:-

(−310)(4.2)(−100)

We have to find the solution of the given expression by using either the commutative property or the associative property.

We will use the associative property of multiplication to find the product.

(−310)(4.2)(−100) = (-310)*(4.2*(-100)) = (-310)*(-420) = 1,30,200

Associative property

The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.

Hence,

(a*b)*c = a*(b*c) , where a, b and, c are real numbers.

Commutative property

Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Answer:)0.3 I Think

Step-by-step explanation:

1.8/6

The answer is:

10.8 cm

Explanation:

6 × 1.8 = 10.8

- firstly, remove the decimal point

- Secondly, multiply regularly 6 by 18

- You'll get 108 as an answer

- Take back the decimal point one to the left because you took it one to the right before, so you will have to do the inverse of the previous action

Good luck

Answer:

Step-by-step explanation:

1 T shirt = 28.14

There are 2 methods this can be done.

Method `1

Adding 3 times

28.14 + 28.14 + 28.14 = $84.42

Method 2

Multiplying 28.14 by 3

28.14 times 3 = $84.42

Therefore answer is 84.42

The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.

Given a line 13x + 18y=108, this slope intercept form can be written as,

3x + 18y = 108

18y = 108 - 3x

y = (108 /18) - (3/18)x.

y = (6) - 1x/6.

y = -(1/6)x + 6.

∴ The slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).

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Area = 300 ft^2

Formula

Area = length of a side x length of a side

Substitution

300 = length of a side ^2

The length of a side is between 17 and 18

Answer:

The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].

Step-by-step explanation:

Step 1: Assume your variable

Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].

Step 2: Create an equation

The formula for the area of a square is:

[tex]\text{Area}=\text{Side}^{2}[/tex]

We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:

[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]

Step 3: Solve the equation

Using the formula for the area of a square, we came to find an equation:

[tex]x^{2}=300[/tex]

Now, let's find the value of [tex]x[/tex]:

[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]

The length of the side of the square is approximately [tex]17.32[/tex] feet.

As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].

The equation relating to A to B is A = 45 + b and the amount is $66.

An equation is used to show the relationship between the variables that are illustrated.

In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.

Let the books be represented as b. The equation will be:.

A = 45 + 1b

A = 45 + b

where A = amount earned.

The amount earned when 21 books are sold will be:

A = 45 + b

A = 45 + 21

A = 66

The amount is $66.

This illustrates the concept of equations.

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Answer:

-8x + (3x - 12)

Step-by-step explanation:

f(x) · g(x)

(-x + 3) · (x - 4)

(-2x · 4x) + (3x - 12)

-8x + (3x - 12)

Pls mark brainliest

The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 68.52 units².

The volume of a cylinder is calculated as:

= πr²h

In this case, the volume is given as 18 units³. The computed height is 0.637 units.

The surface area will be:

= 2πr² + 2πrh

= 2(3.14 × 3²) + (2 × 3.14 × 3 × 0.637)

= 56.52 + 12

= 68.52 units²

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Answer:

Step-by-step explanation:
Slope is gradient which is, change in y
                                              change in x
so, on the graph, change in y = 10-2.5 = 7.5
                              change in x = 5-0 =5
so, gradient is, 7.5/5
                     = 3/2

A C E

Those are the answers

Answer:

Step-by-step explanation:

A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]

A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.

The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;

let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]

The multiplication product is therefore;

[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]

The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5

Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]

The multiplication problem is therefore;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]

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The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

Given,

A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)

To find the coordinates of the vertices of each figure after a reflection over the given axis.

Now, According to the question:

We should know that:

You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)

(x, y) reflected over the y axis = (-x, y)

(x, y) rotated 90 degrees around the origin = (y, -x)

(x, y) rotated 180 degrees around the origin = (-x, -y)

(x, y) rotated 270 degrees around the origin = (-x, y)

So here's our set of points.

A(2,3) , B(4,-5), and C(-1,2)

Here's those points reflected over the x axis.

A' (2, -3) B' (4, 5) and C' (-1, -2)

Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

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Answer:

The number is 40.

Step-by-step explanation:

Step 1: Assume your variables

Consider the 'number' to be [tex]x[/tex].

Step 2: Create an equation(s)

The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].

Representing this mathematically gives us:

[tex](\frac{2}{5}\times x) -9=7[/tex]

Step 3: Solve the equation

The equation we have is:

[tex](\frac{2}{5}\times x) -9=7[/tex]

So, let's solve it:

[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]

the relation is 3x + y = 3

so,

y = 3x - 3

the domain is the values of x

so, substitute with each value of {-2,2,4} at the last equation of y

when x = -2 , y = 3*-2 - 3 = -6 - 3 = -9

when x = 2 , y = 3 * 2 - 3 = 6 - 3 = 3

when x = 4 , y = 3 * 4 - 3 = 12 - 3 = 9

so, the range will be {-9 , 3 , 9}

The correct answer is option a. (-9,3,9)x

Given:

There are given the equation:

Explanation:

According to the question:

we need to find the factor of the given equation:

So,

From the equation:

Final answer:

Hence, the factor of the given equation is shown below:

I WILL USE THE LAWS OF EXPONENTS

[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]

AND

[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]

[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]

ATTACHED IS THE SOLUTION.

Answer:

i hope this one is good for you

Answer:

240 copies of the standard version.

Step-by-step explanation:

See attached worksheet.

Bonus:  Since 240 standard copies were downloaded, we know that 3 times that number is the number of high quality versions downloaded.

                    Copies      Size(MB)        Total MB

Standard       240              2.6                624

High               720              4.4               3168

Total (MB)                                               3792   {This matches the data]

The value of x according to the complete task content as given is; 5.

It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).

Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;

90° + 54° + 7x + 1° = 180°

7x = 180° - 90° - 54° - 1°

Evaluate the right side of the equation;

7x = 35°

Divide both sides by; 7;

x = 35°/7

x = 5.

Ultimately, the value of x according to the task content is; 5.

Remark:

The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.

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Answer:

Step-by-step explanation:

what 15/60 as a decimal?

so

15 : 60 =

0.25   (1/4 as a fraction)

Answer:

x = -3, 9

Explanation:

First, let us divide both sides of the equation by 10^x; this gives,

subtracting 27 from both sides gives

The left-hand side can be factored as

which gives us two further equations

Hence, the two solutions we get are x = 9 and x = -3.

To construct the graph of the hyperbola, the procedure is as follows:

The equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:

(y - y*)²/a² - (x - x*)²/b² = 1.

A vertical hyperbola opens up and down.

In this problem, the equation is:

(y + 2)²/36 - (x + 5)²/64 = 1.

Hence the center is:

(-5, 2).

The value of coefficient a is:

a² = 36 -> a = 6.

Then the vertices of the hyperbola are:

The slopes of the asymptotes of the parabola are given as follows:

±a/b.

Hence:

Since the asymptotes pass through the center, the equation is:

y - 2 = ± 3/4(x + 5).

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2(5 + X) - 1 = 3X + 9

Step 1: Expand the terms in the bracket

=> 2 x 5 + 2 x X - 1 = 3X + 9

=> 10 + 2X - 1 = 3X + 9

Step 2: collect like terms

=> 2X - 3X = -10 + 1 + 9

=> -X = 0

Answer:

Adult: $7

Student $3

Step-by-step explanation:

Hello!

We can use a system of linear equations to find the solution.

Let the price of adult tickets be x, and the price of student tickets are y.

The price of Day 1 can be represented by 6x + 14y = 84, and the second day can be represented by 12x + 7y = 105.

We can solve the system by graphing both equations on a coordinate plane and finding the point of intersection.

The point of intersection happens at x-coordinate 7 and y-coordinate 3. Recall that x is assigned to the price of adult tickets, and y is assigned to student tickets.

The price of adult tickets is $7, and the price of student tickets is $3.

Answer:  [tex](h\circ m)(2) = 6[/tex]

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

Explanation:

The notation [tex](h \circ m)(2)[/tex] refers to function composition

It's the same as writing [tex]h(m(2))[/tex]

According to

m = {(3,4), (2,-2), (-2,6), (5,8)}

We have m(2) = -2 since x = 2 leads to m(x) = -2

Then the output -2 is treated as the input of the outer function h(x)

Looking through

h = {(1,5), (-2,6), (4, -3), (6,9)}

shows that h(-2) = 6

Therefore, [tex]h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6[/tex]

Optionally we can write out a table like shown below.

The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.

The absolute value equation to represent the definition of betweenness is

AB + BC = AC ↔ B ∈ A,C  

Absolute value equation:

An absolute value equation is a function that contains an algebraic expression within absolute value symbols.

Given,

Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".

Here we need to find the absolute value function for this statement.

In order to find the absolute value equation,

First we have to identify the symbols for the terms mentioned in the statement they are,

between = ∈

if and only if = ↔

sum = +

Now, we have to divide the statement as two parts.

First one is, "c lie on the same line, then b is between a and c"

It can be written as,

B ∈ A,C

Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."

Which can be written as

AB + BC = AC

When we combine it, the we get the absolute value equation as,

B ∈ A,C ↔  AB +BC = AC

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