explain the difference between a vertex and an edge?

Given :

The equation below can be used to determine I (simple interest) on a loan as follows :

\(I=Prt\) ...(1)

P is principal, r the rate of the loan,  t is the length of the loan in years.

We need to find the equation to solve in terms of r. We can find the value of P.

Dividing both sides of equation (1) by rt. So,

\(\dfrac{I}{rt}=\dfrac{Prt}{rt}\\\\P=\dfrac{I}{rt}\)

So, P can be solved as : \(P=\dfrac{I}{rt}\).

Answer:

this example of a box whisker plot

Step-by-step explanation:

try to input your numbers

From the image given, if angle 1 is congruent with angle 7 (which we see is obviously not a possibility unless the figure formed by the intersection of the parallel lines is a perfect square), we need to decide on which option is the correct one:

So, since the fact that the lines being parallel cannot be enough to guarantee that the two angles are equal, we select the last option: none.

The individual values contained in an array are known as elements.

An array is a data structure that allows you to store multiple values of the same data type in a single variable. Each value within the array is assigned a unique index or position, starting from 0 for the first element. These elements can be accessed and manipulated using their respective indices.

By organizing related data into an array, it becomes easier to perform operations on the entire set of values or access specific elements based on their positions. Elements in an array can be of any data type, such as numbers, characters, or objects, depending on the programming language used.

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Answer:

2.5 hours

Step-by-step explanation:

4 - 1.5 = 2.5

You must subtract 1.5 from the amount of hours he plays piano, which is 4. This is because he spends 1.5 hours less playing drums than he does playing piano.

Answer:

the answer is 53

Step-by-step explanation:

Answer:

area of the figure: 29.92 m²

formula's:

solving steps:

area of rectangle + area of sector

5.5 * 4 + 30/360 * π(5.5)²

22 + 7.919

29.92 m²

Answer:

Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.

Rectangle

Area of a rectangle = width × length

                                = 4 × 5.5

                                = 22 m²

Sector

\(\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}\)

                     \(=\dfrac{30 \cdot\pi\cdot5.5^2}{360}\)

                     \(=\dfrac{121}{48}\pi \textsf{ m}^2\)

Total area

total area = area of rectangle + area of sector

                \(=22 +\dfrac{121}{48}\pi\)

                = 29.91943148...

                = 29.9 m² (nearest tenth)

according to question the simplified expression is (w + 4) / (w - 5).

To simplify the expression (w^2 + 2w - 24) / (w^2 + w - 30) + 8 / (w - 5), we need to first factor the two quadratic expressions in the numerator and denominator of the first term:

w^2 + w - 30 = (w - 5)(w + 6)

w^2 + 2w - 24 = (w + 6)(w - 4)

So, the first term simplifies to:

(w + 6)(w - 4) / (w - 5)(w + 6) = (w - 4) / (w - 5)

Now, we can rewrite the entire expression as:

(w - 4) / (w - 5) + 8 / (w - 5)

To combine the two fractions, we need to find a common denominator, which is (w - 5). Then, we can add the numerators:

[(w - 4) + 8] / (w - 5) = (w + 4) / (w - 5)

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The labelled parts of the graph is added as an attacment

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

The graph

The graph is a quadratic graph and we can label them using the following keys

Using the above as a guide, we have the following points

Minimum = (0.5, -2.5)

x-intercepts = (2, 0) and (-1, 0)

y-intercept = (0, -2)

See attachment for the labelled graph

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Answer:

10 : 7

Step-by-step explanation:

Deleting 56 songs leaves 136 - 56 = 80 songs, thus

ratio of songs kept : songs deleted = 80 : 56 ( divide both parts by 8 )

80 : 56 = 10 : 7 ← in simplest form

Roman's equation is correct.

What is an equation?

An equation is composed of two expressions joined by an equals sign. The phrases on each side of the equals sign are referred to as the equation's "bottom left" and "top part." The right hemisphere of an equation is frequently considered to be zero. Assuming that this does not limit the generality, it is possible to implement this by subtracting the right-hand side from both sides. The most frequent sort of equation is a polynomial equation, which has two polynomial sides. A scale into which weights are inserted is akin to an equation. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal.

given equations,

Allie's equation is y = 2x - 8

Roman's equation is y = -2x + 8

Roman's equation matches the given graph, so his equation is correct.

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The y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a

Given the coordinate points on a line as  (p , a) and ( p , − a )

Determine the slope

Slope = -a-a/p-p

Slope = infinity

If the value p is zero, hence the coordinate points will become (0, a) and (0, -a)

Since the y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a

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Answer:

x = 10

Step-by-step explanation:

AB=CB

So,

2x+17 = 4x-3

Answer:

Divide

Step-by-step explanation:

If you divide them then you get 2.5

Answer:

Kilometers per hour is often used for car speeds. One hour at this speed moves you 100 km

Step-by-step explanation:

i have a headache sorry if wrong

Answer:ion know

Step-by-step explanation:

The difference between exponential and quadratic function is variable exponent and base, shape of graph, y-intercept and rate of change of function of both.

The most basic difference evident in the equation is exponential function has variable exponent while quadratic function has base as variable. In this equation, the variable exponent is x written as power 1.03. The quadratic function has base x written with exponent 2. The exponential and quadratic function differ in exponential and parabolic growth.

Also, the rate of change in exponential function will increase with x. The quadratic function will alter according to the value x. The y-intercept is 2 for stated exponential function and 0 for given quadratic function f(x) = 2x².

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Answer:

(i), (ii) and (v) are the linear pairs in the following angles.

Step-by-step explanation:

Linear pair refers to adjacent supplementary angles whose sum = 180 degrees

Hope this helps!

Please mark as brainliest

Step-by-step explanation:

d is the answer hope it will help u

After a dilation with a scale factor of 1/2, the new vertices of the triangle are A'(3,1), B'(-1,0), and C'(-2,1). The dilated triangle is a smaller version of the original triangle, maintaining the same shape and proportions.

To draw the image of the triangle after a dilation with a scale factor of 1/2, we need to calculate the new coordinates of each vertex. Here's a detailed human-generated answer without plagiarism:

Given vertices:

A(6, 2)

B(-2, 0)

C(-4, 2)

Dilation with scale factor of 1/2:

To dilate the triangle, we will multiply the x and y coordinates of each vertex by the scale factor (1/2).

New coordinates calculation:

A'(x, y) = (1/2 × 6, 1/2 × 2) = (3, 1)

B'(x, y) = (1/2 × -2, 1/2 × 0) = (-1, 0)

C'(x, y) = (1/2 × -4, 1/2 × 2) = (-2, 1)

New coordinates:

A'(3, 1)

B'(-1, 0)

C'(-2, 1)

Now, let's plot the original triangle and the image after dilation:

Original Triangle:

A(6, 2)

B(-2, 0)

C(-4, 2)

Dilated Triangle:

A'(3, 1)

B'(-1, 0)

C'(-2, 1)

Here's the graphical representation of the original triangle (solid lines) and the dilated triangle (dashed lines):

In the diagram, the original triangle is represented by solid lines (connecting vertices A, B, and C), and the dilated triangle is represented by dashed lines (connecting vertices A', B', and C'). The dilation with a scale factor of 1/2 has resulted in the triangle being reduced in size by half.

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The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

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The equation of hyperboloid of one sheet: \(\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1\) which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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The length of AB, given that OC is perpendicular to AB is B. 13.4 units.

In a circle the length of the chord is bisected by the perpendicular joining the center. This chord is divided into two parts by the circle's chords' perpendicular distances from the circle's center.

We can therefore see that OC bisects Ab which means that AC is equal to CB.

Since AC is 6. 7 units, the value of AB would be:

= 6. 7 + 6. 7

= 13. 4 units

In conclusion, the value of AB would be 13. 4 units.

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The inverse function of f(x) = 4x is:

f⁻¹(x) =  (1/4)*x

So the correct option is the fourth one.

For any function f(x) we define the inverse f⁻¹(x) such that:

f(f⁻¹(x))  =x

f⁻¹(f(x)) = x

In this case we have f(x) = 4*x

Then the inverse is also a linear function:

f⁻¹(x) = a*x + b

Using the rules for inverses we get:

f⁻¹(f(x)) = a*f(x) + b = a*(4x) + b = x

a*(4x) + b = x

Then we have b = 0

a*4x  = x

a*4 = x/x

a*4 = 1

a = 1/4

The inverse is:

f⁻¹(x) =  (1/4)*x

The correct option is the last one.

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Let the first number be x and y be the second.

Then we habe:

I) x - 4 = 2y

II) x*y = 30

We can rewrite equation I as:

x = 2y + 4

Applying this result on equation II, we have:

(2y + 4)*y = 30

2y² + 4y = 30

2y² + 4y - 30 = 0

y² + 2y - 15 = 0

The second root is negative and don't satisfy equations I and II, then we can discard it.

Replacing y with 5 in equation I, we have:

x - 4 = 2*5

x = 2*5 + 4

x = 14

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Answer: To determine how much money Amber had in her account at the end, we need to subtract the total amount she withdrew from her initial balance.

Amber withdrew $36 each month for 6 months, so the total amount she withdrew is:

Total withdrawal = $36/month * 6 months = $216

To calculate the remaining balance, we subtract the total withdrawal from her initial balance:

Remaining balance = Initial balance - Total withdrawal

= $350 - $216

= $134

Therefore, at the end, Amber had $134 remaining in her account.

\(v = \frac{4}{3} \times \pi \times ({ \frac{8}{2} })^{3} \\ \)

\(v = \frac{4}{3} \times 3 \times {4}^{3} \\ \)

\(v = {4}^{4} \)

\(v = {2}^{8} \)

\(v = 256 \: \: {cm}^{3} \)