write in slope-intercept form of the line that passes through the points (-2,-2) and (5,12)

To find slope we use the formula ~

[ Ratio of the difference of y - coordinates of the points and the difference of x - coordinates of the points ]

let's find the slope of line passing through the given points ~

I hope it helps ~

___________________________________

\(꧁ \: \: \large \rm{kaul} \: ꧂\)

As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.

In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),

And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.

Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.

Among our concerned triangles, ΔABC and ΔADC, already given that,

(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,

And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.

At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.

Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and  (ΔABC and ΔADC) can be proved to be congruent triangles.

To learn more about Triangles and Congruency, click on the link below.

https://brainly.com/question/2299572

#SPJ1

Answer:

The equation 31=2c-7 to determine the number of points Carlos scored in the last game.

Step-by-step explanation:

We are given with,(I think every number is repeating for 3 times. So, I took each number as once)

Fabio had 7 less than 2 times as many points as Carlos. And Fabio score 31 points.

Let Carlos scored in the last game as "C".

So, we can set up equation for Fabio had 7 less than 2 times Carlos as

Fabio= 2C-7

Like so for Fabio score 31 as

Fabio =31

So, substitute Fabio as 31 into the first equation, we get

31= 2c-7

So, the equation 31=2c-7 to determine the number of points Carlos scored in the last game.

The equation of the function g(x) is g(x) = (x -4)/(x + 8)

The complete question is given as:

if g(x + h) = (x + h - 4)/(x + h + 8), determine the function g(x)

So, we have:

The function is given as:

g(x + h) = (x + h -4)/(x + h + 8)

To determine the function g(x), we simply substitute x + h for x in the equation g(x + h) = (x + h -4)/(x + h + 8)

So, we have

g(x) = (x -4)/(x + 8)

The above equation cannot be further simplified

Hence, the equation of the function g(x) is g(x) = (x -4)/(x + 8)

Read more about functions at:

https://brainly.com/question/2328150

#SPJ1

Complete question

if g(x + h) = (x + h - 4)/(x + h + 8), determine the function g(x)

Answer:

a) 5x - 9 = 3x + 3

5x - 3x = 3 + 9

2x = 12

x = 12 / 2

x = 6

b) x + 6 = 34 - x

x + x = 34 - 6

2x = 28

x = 28 / 2

x = 14

\( \: (a)5x - 9 = 3x + 3 \\ 5x - 9 - 3x = 3 \\ 2x - 9 = 3 \\ 2x = 3 + 9 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6 \\ (b) \: x + 6 = 34 - x \\ x + 6 + x = 34 \\ 2x + 6 = 34 \\ 2x = 34 - 6 \\ 2x = 28 \\ x = \frac{28}{2} \\ x = 14\)

Answer:

y=7x/4-3

Step-by-step explanation:

We can use the formula y=mx+b. m=slope so y=7/4x+b. We know that the line intersects the point (0,-3) so we plug it in, x=0 and y=-3. -3=(7/4)*0+b. b=-3. Therefore, the equation is y=7x/4-3.

The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

Learn more about expected value here:

https://brainly.com/question/13749480

#SPJ11

Answer:

A

Step-by-step explanation

i = \(\sqrt{-1}\)

i² = (\(\sqrt{-1}\) )² = - 1

i³ = i² × i = - 1 × i = - i

\(i^{4}\) = i² × i² = - 1 × - 1 = 1 , then

\(i^{16}\)

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

= \((1)^{4}\)

= 1

Answer:39?

Step-by-step explanation:

By following the steps below, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is the following function -

y = 5 cos(2x + π/3) - 1

We have -

y = 5 cos(2x + π/3) - 1

We can sketch the function as follows -

Let y = cos(x)

       y = 5 cos(x)

        y = 5 cos(2x)

        y = 5 cos(2x + π/3). This will shift the graph along the negative

        [x] - axis by π/3.

Therefore, by following the steps above, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

To solve more questions on trigonometry, visit the link below-

https://brainly.com/question/27926943

#SPJ1

The amount luke made more than alexa is $3.91 .

What is simple interest ?

simple interest can be defined as the ratio of product of principal amount , rate and time and 100.

Luke investment,

This is compound interest so the future value formula will be used:

= Amount * ( 1 + rate) ^ no. of years

= 4,000 * ( 1 + 1.8%)³

= $4,219.91

Alexa investment:

Simple interest is calculated with the formula:

= Amount * ( 1 + rate * time)

= 4,000 * ( 1 + 1.8% * 3)

= $4,216

Amount Luke made more than Alexa:

= 4,219.91 - 4,216

= $3.91

Hence , The amount luke made more than alexa is $3.91 .

To learn more about simple interest form the given link.

https://brainly.com/question/25845758

#SPJ4

1. 135°

2. 108°

i am unsure about 3 & 4, i am sorry :(

Answer:

This (x - 5) represents the length of the rectangle.

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L * W.

Here, the width is x - 4 and the area is x^2 + x - 20.  Dividing the width (x - 4) into the area results in an expression for the length:

x - 4  /   x^2 + x - 20

Let's use synthetic division here.  It's a little faster than long division.

If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:

4   /   1    1    -20

              4     20

    --------------------

         1     5     0

This synthetic division results in a remainder of 0.  This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor.  From the coefficients 1 and 5 we can construct the other factor:  (x - 5).  This (x - 5) represents the length of the rectangle.

Answer:

46.6

Step-by-step explanation:

have a good day

Answer:

k = 1.75

Step-by-step explanation:

5 - 4k = -7

k = 1.75, because if you subtract 4 from both sides, you are left with 1.75 = -7.

Answer:

k = 3

Step-by-step explanation:

5 - 4k = - 7 ( subtract 5 from both sides )

- 4k = - 12 ( divide both sides by - 4 )

k = 3

Step-by-step explanation:

Number 1

180° = x + 70° + 55° + 30°

180° = x + 155°

x = 180° - 155°

x = 25°

Number 2

x° = 93°

y° = 47°

z° = 180° - 47° - 93°

z° = 180° - 140°

z° = 40°

#LearnWithEXO

The missing values are:

BC = 25, BN = 16, NC = 9, and AN = 12

Given:

AB = 20

AC = 15

Using the Pythagorean theorem in triangle ABC:

CB = √AC² + AB²

CB= √20² + 15²

CB= √625

CB= 25

Since, AN is altitude we have ΔNBA~ΔABC and ΔNAC~ΔABC

BN / AN = BA / CB

BN/ 20= 20/25

BN = 16

and, AN / BA = AC / CB

AN /20 = 15/ 25

AN = 12

Now, CN=  CB - BN

CN = 25- 16

CN= 9

BC^2 = 20^2 + 15^2

BC^2 = 400 + 225

Since ΔANC is a right triangle so

AN = √15²-12²

AN = √81

AN = 9

Learn more about Pythagoras theorem here:

https://brainly.com/question/3618957

#SPJ1

Answer:

the answer would be 6

Step-by-step explanation:

the way i got my answer is by adding on to the negative on the 2,-1 then i add 5 to the over all to get 1 plus 5 and get 6.

The distance between the two points (2,-1) and (2,5) is 6 units.

The distance between two points \((x_1,y_1),(x_2,y_2)\) is,

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

For given example,

Let \((x_1,y_1)=(2,-1),(x_2,y_2)=(2,5)\)

Let 'd' be the distance between two points (2,-1) and (2,5).

Using distance formula,

⇒ \(d=\sqrt{(2-2)^{2}+(5-(-1))^{2} }\)

⇒ \(d=\sqrt{(0)+(5+1)^{2} }\)

⇒ \(d=\sqrt{6^{2} }\)

⇒ \(d=6\) units.

Therefore, the distance between two points (2,-1) and (2,5) is 6 units.

Learn more about distance between two points here:

brainly.com/question/8792086

#SPJ2

The maximum percentage of individuals who own a bike is 21.5%.

Margin of error is the percentage points a researcher's value would differ from the real population's value. The maximum percentage is the sum of the margin of error and the true value.

The maximum percentage = margin of error + true value

(1/5) x 100 + 1.5% = 21.5%

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ4

Answer:

See image

Step-by-step explanation:

Plato

To find the area bounded by the parabola, the y-axis, and the given y-values, we need to integrate the absolute value of the curve's equation with respect to y.

The equation of the parabola is given as x = 8 + 2y - y².

To find the limits of integration, we need to determine the y-values at the points of intersection between the parabola and the y-axis, y = -1, and y = 3.

Setting x = 0 in the parabola equation, we get:

0 = 8 + 2y - y²

Rearranging the equation:

y² - 2y - 8 = 0

Factoring the quadratic equation:

(y - 4)(y + 2) = 0

Therefore, the points of intersection are y = 4 and y = -2.

To calculate the area, we integrate the absolute value of the equation of the parabola with respect to y from y = -2 to y = 4:

Area = ∫[from -2 to 4] |8 + 2y - y²| dy

Splitting the integral into two parts based on the intervals:

Area = ∫[from -2 to 0] -(8 + 2y - y²) dy + ∫[from 0 to 4] (8 + 2y - y²) dy

Simplifying the integrals:

Area = -∫[from -2 to 0] (y² - 2y - 8) dy + ∫[from 0 to 4] (y² - 2y - 8) dy

Integrating each term:

Area = [-1/3y³ + y² - 8y] from -2 to 0 + [1/3y³ - y² - 8y] from 0 to 4

Evaluating the definite integrals:

Area = [(-1/3(0)³ + (0)² - 8(0)) - (-1/3(-2)³ + (-2)² - 8(-2))] + [(1/3(4)³ - (4)² - 8(4)) - (1/3(0)³ - (0)² - 8(0))]

Simplifying further:

Area = [0 - (-16/3)] + [(64/3 - 16 - 32) - (0 - 0 - 0)]

Area = [16/3] + [(16/3) - 48/3]

Area = 16/3 - 32/3

Area = -16/3

The area bounded by the parabola, the y-axis, and the y-values y = -1 and y = 3 is -16/3 square units.

Therefore, the answer is D) 92/5 square units.

know more about absolute value: brainly.com/question/17360689

#SPJ11

The magnitude of the force that must be applied parallel to the plane is 92 N, under the condition that the box moves up the plane with an acceleration of 2 m/ s².

The force needed to move a box up an inclined plane can be evaluated as
Fp = W sin α = m ag sin α
Here
Fp = pulling force (N),
W = weight of the box (N),
α = angle of incline (degrees),
m = mass of the box (kg),
a = acceleration of the box (m/s²), and
g = acceleration due to gravity (9.8 m/s²).

For the given case, we possess a 25 kg box at rest on a 30 degree incline with a friction force of 50 N acting on it.
Now
We have to evaluate the weight of the box using
W = mg
= 25 kg x 9.8 m/s²
= 245 N.

Then, we have to calculate the force required to overcome friction using Ff = μFn where μ is the coefficient of friction and Fn is the normal force acting on the box. Since the box is at rest on an incline, Fn can be calculated as Fn = W cos α = 245 N cos(30°) ≈ 212 N. Therefore, Ff = μFn = 0.2 x 212 N ≈ 42 N.

Now we can evaluate the force applied to move the box up the incline utilizing
Fp = ma + Ff
Here,
a = desired acceleration
Ff = frictional force acting on the box.
Staging the values
Fp = ma + Ff
Fp = (25 kg)(2 m/s²) + 42 N
Fp ≈ 92 N

Hence, a force of approximately 92 N must be applied parallel to the plane so that the box moves up the plane with an acceleration of 2 m/s².
To learn more about acceleration
https://brainly.com/question/30595126
#SPJ4
The complete question is
A 25 kg box is at rest on a 30 degree incline. If the friction force is 50 N, what is the magnitude of the force that must be applied parallel to the plane so that the box moves up the plane with an acceleration of 2 m/ s²?

The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

Learn more about cartesian plane here:

https://brainly.com/question/32222840

#SPJ11

Answer:

dashed horizontal line through (0, −15) with shading above line

Step-by-step explanation:

Answer:

Dashed horizontal line

Step-by-step explanation:

If its multiple choice and you need help just add a comment

and if you need help with any other math homework assignment or anything just DM me on ig

-Stewart.lil2

sorry me and my friend have matching usernames bc (ion een kno but yea)

Answer:

Point

Step-by-step explanation:

To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

To know more about outlier refer here:

https://brainly.com/question/26958242#

#SPJ11

Answer:

2*22/7/27+1

Step-by-step explanation:

2*22/7*27+1

2*(594+1)/7

2*595/7

2*85

170 ans..

Answer:

Linear equations are basically equations for just a straight line.

I'm assuming you're asking for the definition of such equations.

A linear equation is an equation that can be plotted on a graph, and the line will show you all possible values of the equation.

Answer:

AAS

Explanation:

The angles come first in that triange and then the side

Answer:

48900

Step-by-step explanation:

Because the first hundred would be the 900