3.) What is the slope intercept form of the line graphed below?

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

PLATO

i got it correct :)

Darren makes $210.83 monthly payments over a period of 5 years. Therefore, option D is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$11,000, rate of interest =3% and time period = 5 years.

Now, S.I. =(11,000×3×5)/100

= $1650

Now, 11,000+1650 =$12650

In 5 years there are 60 months

So, 12650/60

= $210.83

Therefore, option D is the correct answer.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

#SPJ1

Answer:

The relation ship is both are opposites

Step-by-step explanation:

so what is factorising ???

factorizing is like this example : 4x+32 = 4(x+8)

so u take the expression make it factorized or shorter or in a way that you multiply them .

what is expanding well its the opposite

suck as  4(x+8)=4x+32

Answer:

y = 1, 9.

Step-by-step explanation:

They are the y values of the points of intersection of the 2 parabolas.

y = 1, 9.

The inverse of the function f(x)= x^2 is a function.

The equation of the function is

f(x)= x^2

Rewrite as:

y = x^2

Swap x and y

x = y^2

Make y the subject

\(y = \sqrt x\)

Rewrite as:

\(f^{-1}(x) = \sqrt x\)

So, the inverse of f(x)= x^2 is \(f^{-1}(x) = \sqrt x\)

See attachment for the graph

The inverse is a function.

This is so because it passes the vertical line test

Read more about inverse functions at:

https://brainly.com/question/2883051

#SPJ1

Answer:

\((x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}\)

Step-by-step explanation:

So, we know that the center of the circle is at (-6, -7/6).

To find the equation of our circle that is tangent to the x-axis, we just need to find the vertical distance from our center to the x-axis.

Our center is at (-6, -7/6). The vertical distance from this to the x-axis directly above will be (-6, 0).

So, find our distance by subtracting our x-values:

\(d=r=0-(-7/6)\)

Subtract:

\(d=r=7/6\)

So, our distance, which is also our radius, will be 7/6.

Now, we can use the standard form for a circle, which is:

\((x-h)^2+(y-k)^2=r^2\)

Where (h, k) is the center and r is the radius.

Substitute -6 for h, -7/6 for k, and 7/6 for r. This yields:

\((x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}\)

We can confirm by graphing (using a calculator):

Answer:

12 m

Step-by-step explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

\( \frac{AD}{EH} = \frac{2}{3} \)

\( \frac{8}{EH} = \frac{2}{3} \)

Cross multiply

\( 3*8 = 2*EH \)

\( 24 = 2*EH \)

Divide both sides by 2 to make EH the subject of formula

\( \frac{24}{2} = \frac{2*EH}{2} \)

\( 12 = EH \)

The length of side EH = 12 m

Step-by-step explanation:

We can solve for x using the properties of logarithms as follows:

log2 (5x - 2) = -2

2^(-2) = 5x - 2 (using the definition of logarithms)

1/4 = 5x - 2 (simplifying 2^(-2))

5x = 2 + 1/4 = 9/4

x = 9/20

Therefore, the solution to the equation log2 (5x - 2) = -2 is x = 9/20.

Answer:

b. mutually exclusive.

Step-by-step explanation:

The given description is an illustration of mutually exclusive events.

Take for instance, when you roll a die;

It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.

In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.

Answer:

2225 I think just do 685+1570

Answer:

b=2.5-7.50

Step-by-step explanation: so 5 party hats cost 50 cents, so times that by 5 to get 2.50, and then use the 7.50 and minus it.

Answer:

183.75 pounds

Step-by-step explanation:

divide 147 by a fourth then add your result onto 147 for your awnser

Answer:

6.1

Step-by-step explanation:

Because 4 is nowhere near 10 so the answer is 6.1

The correct equation that matches the given graph is y = cos(x) + 1.

To determine the equation that matches the given graph, we can observe the key features and points provided.

The waveform starts from the y-axis at 1 unit: This suggests that the function has a vertical shift of 1 unit upwards.

The waveform passes through (π, -1), (2π, 1), and (3π, -1): This indicates that the function oscillates between the values of -1 and 1 as x increases.

The waveform intercepts the x-axis at π/2, 3π/2, 5π/2, and 7π/2: This suggests that the function has zeros or x-intercepts at these values.

Based on these observations, the function can be represented as a cosine function.

The cosine function with a vertical shift of 1, oscillating between -1 and 1, and having zeros at π/2, 3π/2, 5π/2, and 7π/2 is:

y = cos(x) + 1

For similar questions on equation

https://brainly.com/question/17145398

#SPJ11

Answer: 6(x+7)° = 24(x-8)°

Step-by-step explanation:
We know that both angles are equal as they are alternate exterior angles.

6(x+7)=24(x-8)

6x+42=24x-192

6x -6x +42 +192 =24x -6x -192 +192

234 = 18x

18x/18 = 234/18

x = 13

And then for question B and C, you need to calculate the expression with x being equal to 13.

The rounded numbers for the given decimal numbers are 4, 8 and 9.

To change a number into an approximation having fewer significant digits, is called the rounding numbers.

For example :- Round off 15.4 to 15, round off 15.51 to 15.5 or to 16, round off 0.499 to 0, and round off 970,000 to 1 million.

Given are three decimal numbers, 3.896, 7.8143 and 9.3959 we are asked to round them to whole number.

The rule for rounding the numbers is :-

Example: 38 rounded to the nearest ten is 40.

Example: 33 rounded to the nearest ten is 30.

Therefore, in 3.896, the number after the decimal is 8 which is greater than 5 so rounding up we will get, 4

Similarly, 7.8143 = 8

And in 9.3959, the number after the decimal is 3 which is smaller than 5 so rounding down we will get, 9

Hence, the rounded numbers for the given decimal numbers are 4, 8 and 9.

Learn more about rounding numbers, click;

https://brainly.com/question/5536190

#SPJ9

Answer:

2×2×2×2×3

Step-by-step explanation:

First, find the LCM of (16, 12).

This is equal to 48.

The prime factorisation of 48 is 2

^4 * 3 or 2*2*2*2*3.

Answer:

\(d = 33\)

Step-by-step explanation:

Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d = \sqrt{(13-13)^2+(-14-19)^2}\)

\(d = \sqrt{(0)^2+(-33)^2}\)

\(d = \sqrt{(-33)^2}\)

\(d = 33\)

Answer:

the distance between the two points is 33 units.

Step-by-step explanation:

because the two points have the same x value, we only need to consider the y values.

find the difference to solve for the distance.

\(19-(-14)\\19+14\\33\)

the answer is 33 units.

hope this helps :)

The amount that a student would pay in interest on a $1,500 loan for 2 years is $161.70

What is simple interest?

Under simple interest loan arrangement, the same amount of interest is paid every year for the entire duration of the loan as the interest is determined as the loan principal multiplied by interest rate as well as multiplied by the loan duration expressed in years as indicated below:

I=PRT

I=the interest on the Stafford loans in dollars=unknown

P=Stafford loans principal=$1500

R=annual rate of interest on the loan=5.39%

T=the loan period in years=2

I=$1500*5.39%*2

I=$161.70

Over the period of 2 years, the interest on the student's loan is $161.70

Find out more about simple interest on:https://brainly.com/question/25845758

#SPJ1

Answer:25-10=15

Step-by-step explanation:

25-10

Answer:

D) \(-\frac{3}{5}\)

Step-by-step explanation:

Given

\(tan\theta=-2,\:\frac{\pi}{2}<\theta<\pi\\cos(2\theta)=?\)

Use identities

\(cos(2\theta)=\frac{1-tan^2\theta}{1+tan^2\theta}\\\\cos(2\theta)=\frac{1-(-2)^2}{1+(-2)^2}\\\\cos(2\theta)=\frac{1-4}{1+4}\\ \\cos(2\theta)=-\frac{3}{5}\)

The polygon shown in the figure is the Rhombus.

What is a polygon?

A polygon is a closed figure made up of three or more line segments connected end to end.

Regular polygons have all side the same and that apothem bisects the side in two parts, (provable by symmetry).

A square is always a rectangle, parallelogram, rhombus and quadrilateral but its reverse statement may or may not be true.

A rhombus is a parallelogram but all sides of the same length.

An exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.

Hence the answer is the polygon shown in the figure is Rhombus.

To learn more about regular polygon click here https://brainly.com/question/1592456

#SPJ4

Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

Learn more about the measures of central tendency at https://brainly.com/question/28101345.

#SPJ1

Answer:

a triangle

Step-by-step explanation:

the definition of a triangle is a shape with 3 sides and the shape that is shown has 3 sides.

On solving the provided question, we can say that by linear equation If The Grant is thinking of two numbers, they are 13 and 26.

A linear equatiοn is one that has the form y = mx+b in algebra. B is the slοpe, and m is the y-intercept. It's usual to refer tο the previous clause as a "linear equation with twο variables" because y and x are variables. The twο-variable linear equations knοwn as bivariate linear equations.

There are several instances οf linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred tο as being linear when an equation has the fοrm y = mx+b, where m stands for the slοpe and b for the y-intercept. When an equatiοn has the formula y = mx+b, with m denοting the slope and b the y-intercept, it is referred tο as being linear.

x be the first number and y be the secοnd number:

x = 2y

x + y = 39

Plug x = 2y in the other equation:

2y + y = 39

3y = 39

y = 13

x = 26

If The Grant is thinking of two numbers, they are 13 and 26. He claims that the total of the two numbers is 39 and that one of the numbers is double the other.

To know more about linear equation visit:

brainly.com/question/11897796

#SPJ1

To know the function has inverse or not, draw the graph of the function. If the graph is not intersecting the horizontal line more than once, then the function has inverse.

The function is is defined as the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable other variable will be dependent variables. The function that consist off variables and numbers.

First draw the graph of the function using the values. If the graph is not intersecting the horizonal line of the graph then its a one to one function and the function has inverse

Therefore, if the graph of the function is not intersecting the horizontal line more than once, then the function has inverse

Learn more about function here

brainly.com/question/12721934

#SPJ4

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

Answer: 1

Step-by-step explanation: