Use point slope form to write the equation of the lines that go through the given points in slope intercept form. 1. (-1,-3) and (1,5) 2. (-4,2) and (8,-1)

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

As we have given about the Euclidean and analytical geometry.

Without using any numerical measurements, we have investigated the connections between points, lines, and planes in Euclidean geometry.

In analytical geometry, we've looked at how the locations of points in a Cartesian coordinate system related to algebra and geometry.

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

If the Euclidean geometry can be more advantageous in particular circumstances

Example: If using terrain or building chart),

Thus, the analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

Learn more about the geometry here:

https://brainly.com/question/16836548

#SPJ1

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

C

Step-by-step explanation:

The sum of the angles is 90

2x + x = 90

3x = 90

x = 30

the angle ABC is 2x, so it means that is the double of x, so it is 60 degrees

Answer:

The circle graph does not represent a function because it doesn't pass the vertical line test.

Step-by-step explanation:

Answer:

7/8 is larger than 5/6

Step-by-step explanation:

If you divide the numerator by the denominator of each given fraction:

7/8 = 0.875

5/6 = 0.833

We can easily see that 0.875 > 0.833.

Therefore, 7/8 is larger than 5/6.

Answer:

7/8 is bigger than 5/6, I hope this helps :)

Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Answer:

2, 3, 6

Step-by-step explanation:

Simply try each value using long division.

2:

Since 5,238 ends in an even number, that automatically means it is divisible by 2.

5238/2=2619

Now for 3:

5238/3=1746 no remainder or decimal, so 3 also works

4:

You can either do long division again with 4, or you can see if 5238 divided by 2 (5238/2) is also divisible by 2. Since 2619 doesn't end in an even number, 4 is a no go.

Long division 5238/4=1309.5 decimal here, so 4 isn't an answer

5:

This is also very easy, simply check if the number ends in 0 or 5. Since 5,238 does not, 5 doesn't work either.

6:

You can do the same thing as with 4, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 2. Since 1746 ends in an even number, 6 also works.

Long division: 5238/6=873

9:

You can do the same thing as with 6, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 3.

1746/3=548 with a remainder of 2, which means 9 doesn't work

Long division: 5238/9=548.66 repeating

10:

Finally, 10 is another easy one. Simply check if the number ends in 0. 5,238 does not, so 10 doesn't work.

Answer:

32

Step-by-step explanation:

if u do pythagoras, sq root of 20^2-12^2=16

16x2=32

Answer:

polynomial have 7 side...

The addition of function f(x) = 3 · x² - 1 and function g(x) = x + 2 is equal to (f + g)(x) = 3 · x² + x + 1. (Correct choice: B)

New functions can be created by combining functions, the most common operations are listed below:

In this problem we must determine the expression that is the result of the addition of two functions, whose definition is shown below:

(f + g) (x) = f(x) + g(x)

First, use the definition of the addition of two functions:

(f + g)(x) = (3 · x² - 1) + (x + 2)

Second, simplify the algebraic expression:

(f + g)(x) = 3 · x² + x + 1

To learn more on addition of functions: https://brainly.com/question/15658887

#SPJ1

The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

To know more about x-axis visit

brainly.com/question/12032954

#SPJ1

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

Learn more on distance between two points here: https://brainly.com/question/7243416

#SPJ1

Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

\(\boxed {\boxed {\sf B. \ 324 \ cm^3}}\)

Step-by-step explanation:

The volume of a triangular prism is the product of the area of the triangular cross-section (B) and the height (h).

First, let's find the area of the triangular cross-section/the end of the triangle. The area of a triangle is:

\(B= \frac{1}{2} b*h\)

The base of the triangle base (not the prism) is 6 centimeters and the height is 9 centimeters.

\(B= \frac{1}{2} (6 \ cm)(9 \ cm)\)

Multiply the numbers in parentheses.

\(B= \frac{1}{2}(54 \ cm^2)\)

Multiply by 1/2 or divide by 2.

\(B= 27 \ cm^2\)

Now we know the area of the cross-section or base is 27 square inches. The height of the prism is 12 centimeters.

Substitute the values into the volume formula for a triangular prism.

\(V= 27 \ cm^2 * 12 \ cm\)

Multiply.

\(V= 324 \ cm^3\)

The volume of the prism is 324 cubic centimeters and choice B is correct.

The volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

The volume of a triangular prism is determined by multiplying the area of the triangular cross-section (B) by the height (h). In this case, the base (b) of the triangular cross-section is given as 6 centimeters, and the height (h) is given as 9 centimeters.

To find the area of the triangular cross-section (B), we can use the formula for the area of a triangle: B = (1/2) * base * height.

Substituting the values:

B = (1/2) * 6 * 9 = 27 square centimeters.

Next, we multiply the area of the cross-section (B) by the height (h) to find the volume (V) of the prism:

V = B * h = 27 * 12 = 324 cubic centimeters.

Therefore, the volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

To know more about triangular prism:

https://brainly.com/question/27102803

#SPJ6

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

Find out more on monthly payments at https://brainly.com/question/27926261

#SPJ1

Answer:

28

Step-by-step explanation:

To solve this, I would first add up the total of the numbers in the ratio.

9 + 7 + 2 = 18

Then, I would divide 72 by that number.

72/18 = 4.

Finally, I would multiply that quotient by 7 because 7 is the number in the ratio for B's.

4 x 7 = 28

Answer:

4

Step-by-step explanation:

-8 +12=4

there has to be 20 characters so thi is what I'm putting.

Answer:

4° that is how much degrees Indiana had.

Step-by-step explanation:

-8 + 12 = 4

Answer:

Jacob has more. $8,500,000 more.

Step-by-step explanation:

4.5 x 10^6 can be expressed as 4500000. and 1.3 x 10^7 can be expressed as 13000000. subtract, and you get %8,500,000

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

For similar question on distance.

https://brainly.com/question/26550516  

#SPJ8

Answer:

Number Students= 1,634

Step-by-step explanation:

Giving the following information:

In a survey at a local university, 62% of students say that they get less than the recommended eight hours of sleep per night.

Group= 4,300 students

To calculate the number of students that sleeps at least 8 hours, we need to use the following formula:

Students= 4,300*(1-0.62)

Students= 4,300*0.38

Students= 1,634

Answer:

Step-by-step explanation:

18 muffins for Millie,

18 muffins for August,

18 muffins for herself,

80 muffins for a church,

18+18+18+80 = 134 muffins in total

Answer:

c

Step-by-step explanation:

Answer: C.2304

Step-by-step explanation:

volume for a sphere formula: V=4/3πr^3

\(V=4/3\pi r^3=4/3*\pi *12^3=7238.23\\7238.23/\pi \\=2304\\\)

The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

To know more about the secant function visit:

brainly.com/question/16230804

#SPJ1

Answer:

Step-by-step explanation:

??????????????? What’s the question?!

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

The total weight change for the eight women was -24.

Step-by-step explanation:

In order to find the answer, you have to consider that average is calculated by dividing the total weight change by the number of women and you know that the average was they lost 3 pounds and there were 8 women:

Average= total weight change/number of women

-3=total weight change/8

total weight change=-3*8

total weight change=-24

According to this, the answer is that the total weight change for the eight women was -24.

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

For such more questions on translated

https://brainly.com/question/12861087

#SPJ8

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Yeah, your right the answer would be -39.1%

Answer:

360

Step-by-step explanation:

(1yd = 3ft) (1ft = 12in)

12 x 3 = 36

36 x 10 = 360

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

In accordance with the information presented in the statement, we find a parabola whose axis of symmetry is parallel to the y-axis. The location of the vertex is the midpoint of the segment between the focus and a point of the directrix.

V(x, y) = 0.5 · (- 3, 4) + 0.5 · (- 3, 2)

V(x, y) = (- 3, 3)

The distance between the focus with respect to the vertex (p) is:

D(x, y) = F(x, y) - V(x, y)

D(x, y) = (- 3, 2) - (- 3, 3)

D(x, y) = (0, - 1)

Which a distance equal to - 1.

The standard form of the equation of the parabola is based on this model:

4 · p · (y - k) = (x - h)²             (1)

Where (h, k) are the coordinates of the vertex.

If we know that (h, k) = (- 3, 3) and p = - 1, then the standard form of the equation of the parabola is:

- 4 · (y - 3) = (x + 3)²

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

The statement has typing and orthographical mistakes. Correct form is presented below:

What is the standard form of the equation of the parabola with a focus at (x, y) = (- 3, 2) and directrix at y = 4.

To learn more on parabolas: https://brainly.com/question/21685473

#SPJ1