what are the hypothesis and the conclusion of the conditional? if anangle measures 130, then the angle is obtuse

The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

Given that,

A parabola can be drawn with a focus of (8,10) and a directrix of y=6.

We have to find the equation of the parabola in any form.

We know that,

The distance of any point P is (h,k) on a parabola form a focus is equal to its perpendicular distance from the directrix.

So,

√((h-8)²+(k-2)²) = | (k-6)/√0²+1² |

Squaring on both sides

(h-8)²+(k-2)² = (k-6)²

From th formula (a-b)² = a²-2ab+b²

We get,

h²-16h+64+k²-4k+4 = k²-12k+36

h²-16h+64+k²-4k+4 - k²+12k-36 =0

h²-16h+64-4k+4+12k-36=0

h²-16h+8k+32=0

Therefore, The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

To learn more about parabola visit: https://brainly.com/question/4074088

#SPJ4

Answer:

$647.25

Step-by-step explanation:

Twenty-five percent off the regular $800 price comes to 0.75($800), or $600 (after the discount).

Calculating the 7.875% sales tax and adding it in, we find that the final price to be paid is (1 + .07875)($600), or $647.25.

Answer:

Answer Below

Step-by-step explanation:

The key difference between line and line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.

The correct equation which models the sentence will be;

⇒ x/4 - 10 = 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Ten less than the quotient of a number and 4 is 6.''

Now,

Since, The algebraic expression is,

''Ten less than the quotient of a number and 4 is 6.''

Let a number = x

Hence, The mathematical expression is,

⇒ x/4 - 10 = 6

Solve for x as;

⇒ x/4 = 10 + 6

⇒ x/4 = 16

⇒ x = 16 × 4

⇒ x = 64

Thus, The value of number = 64.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

For this problem we can see that we have a right triangle given with two equal sides of 25 ft and we need to find the red one side

Since we have a right triangle we can use the Pythagoras theorem given by:

For this case a= b= 25 ft and if we replace we got:

c represent the red side ? if we solve for it we got:

And we got:

Answer:

V=2543.4 cm^3

Step-by-step explanation:

V=pi*r^2*h

V=pi*9^2*10

V=pi*81*10

V=810pi

V=810*3.14

V=2543.4

Answer:

2544.69

Step-by-step explanation:

i think

hope this helps!

Answer:

37

Step-by-step explanation:

Hello!

First we add 15 to both sides

\(\frac{-5x-10}{5} = -2x + 35\)

Multiply both sides by 5

-5x - 10 = -10x + 175

Add 10 to both sides

-5x = -10x + 185

Add 10x to both sides

5x = 185

Divide both sides by 5

x = 37

The answer is 37

Hope this helps!

\(\dfrac{-5x-10}{5}-15=-2x+20\quad|\cdot5\\\\-5x-10-75=-10x+100\\\\-5x+10x=100+10+75\\\\5x=185\quad|:5\\\\\boxed{x=37}\)

To find the upper quartile, we first need to arrange the data in ascending order:

17, 17, 18, 18, 19, 19, 21, 21, 21, 22, 23, 23, 24, 25

The upper quartile (Q3) is the median of the upper half of the data set. To find it, we need to identify the median of the upper half, which includes the values:

22, 23, 23, 24, 25

The median of this data set can be found by taking the average of the two middle values:

(23 + 24) / 2 = 23.5

Therefore, the upper quartile of the data set is 23.5°C.

Answer:

To find the upper quartile, we first need to find the median (Q2) of the data set:

Arrange the data set in ascending order:

17, 17, 18, 18, 19, 19, 21, 21, 21, 22, 23, 23, 24, 25

The median is the middle value, which is 21 in this case.

Next, we need to find the median of the upper half of the data set (values greater than 21):

22, 23, 23, 24, 25

The median of this subset is 23.

Therefore, the upper quartile is 23.

Step-by-step explanation:

Answer: There are 10 different values possible for the random variable x.

Step-by-step explanation:

In this modified problem, the probability of rolling each number is different from a standard fair die. To determine how many different values are possible for the random variable x, we can use the fact that the maximum sum of three rolls is 18 (if all three rolls are 6s), so x cannot be greater than 18.

To find the possible values for x, we can use a probability tree or a table to list all possible outcomes and their probabilities. Here is a table listing the possible values for x and their probabilities:

x Probability

1 0.4

2 0.49

3 0.581

4 0.6639

5 0.73951

6 0.809561

7 0.8746051

8 0.93414459

9 0.987730103

10 1

To calculate these probabilities, we can use the following recursive formula:

P(x=1) = P(sum=1) = 0.1

P(x=k) = P(x=k-1) * (1 - P(sum≤k-1)), for k = 2 to 9

P(x=10) = 1 - P(sum≤9)

Here, P(sum≤k) is the probability of the sum of the first k rolls being less than or equal to 3. We can calculate this probability recursively as well:

P(sum≤1) = P(1) = 0.1

P(sum≤k) = P(sum≤k-1) + P(k), for k = 2 to 18

Here, P(k) is the probability of rolling a k, which is given in the problem statement.

Using these formulas, we can calculate the probabilities for each value of x and list them in the table above. We can see that there are 10 possible values for x, ranging from 1 to 10.

Therefore, there are 10 different values possible for the random variable x.

To know more about probability refer here

https://brainly.com/question/30034780#

#SPJ11

Answer:

Step-by-step explanation:

−0.75−(−1/5)+0.2−3/4

=−0.55+0.2−3/4

=−0.35−3/4

=−11/10

=-1.1

you're welcome (sorry if it is choppy)

Answer:

The set of coordinates are;

A’( 4,2)

B’(6,4)

C’(10,2)

D’(10,4)

Step-by-step explanation:

Here, we want to get a set of new points by dilating the x coordinates of the former points by 2

Using the scale factor, we simply are going to multiply the x-coordinate values by 2

Thus we have

A’( 4,2)

B’(6,4)

C’(10,2)

D’(10,4)

Answer:

24

Step-by-step explanation:

AB = 12

that means BC = 12

Add 2 parts together you get 24

Answer:

AB=12

BC=12

AC=24

i hope that i help you

Answer:

The area of the shaded part of the rectangle is 28 m².

Step-by-step explanation:

The area of the shaded part of the rectangle can be calculated by subtracting the areas of the two unshaded triangles from the area of the rectangle.

The area of a rectangle is the product of its width and length.

From inspection of the given diagram, the width of the rectangle is 4 m and the length is 14 m. Therefore, the area of the rectangle is:

\(\begin{aligned}\textsf{Area of the rectangle}&=4\cdot 14\\&=56\; \sf m^2\end{aligned}\)

The area of a triangle is half the product of its base and height.

The bases of the two unshaded triangles are congruent (denoted by the double tick marks) and are 7 m.

The height of both triangles is the height of the rectangle, 4 m.

Therefore, the two triangles have the same area.

\(\begin{aligned}\textsf{Area of 2 unshaded triangles}&=2 \cdot \dfrac{1}{2} \cdot 7 \cdot 4\\&=1 \cdot 7 \cdot 4\\&=7 \cdot 4\\&=28\; \sf m^2\end{aligned}\)

To calculate the area of the shaded part of the rectangle, subtract the area of the 2 unshaded triangles from the area of the rectangle:

\(\begin{aligned}\textsf{Area of the shaded part}&=\sf Area_{rectangle}-Area_{triangles}\\&=56-28\\&=28\; \sf m^2\end{aligned}\)

Therefore, the area of the shaded part of the rectangle is 28 m².

Recursive definition:

a) a1 = 2, an+1 = an + 4

b) a1 = 0, an+1 = 2 if n is odd, 0 if n is even

c) a1 = 0, an+1 = an + (2n+1)

d) a1 = 1, an+1 = an + 2n + 1

Sequence defined by an = 4n - 2:

Basis step:

a1 = 4(1) - 2 = 2

Inductive step:

an+1 = 4(n+1) - 2 = 4n + 2 = (4n - 2) + 4 = an + 4

Recursive definition:

a1 = 2, an+1 = an + 4

Sequence defined by an = \(1 + (-1)^n\):

Basis step:

a1 = \(1 + (-1)^1\) = 0

Inductive step:

If n is odd, an+1 = \(1 + (-1)^{(n+1)\)= 2;

If n is even, an+1 = \(1 + (-1)^{(n+1)\) = 0

Recursive definition:

a1 = 0, an+1 = 2 if n is odd, 0 if n is even

Sequence defined by an = n(n-1):

Basis step:

a1 = 0

Inductive step:

an+1 = (n+1)n = \(n^2 + n\) = an + (2n+1)

Recursive definition:

a1 = 0, an+1 = an + (2n+1)

Sequence defined by an = \(n^2\):

Basis step:

a1 = \(1^2\) = 1

Inductive step:

\(an+1 = (n+1)^2 = n^2 + 2n + 1 = an + 2n + 1\)

Recursive definition:

a1 = 1, an+1 = an + 2n + 1

For similar questions on Recursive

https://brainly.com/question/543232

#SPJ11

Answer:

0.875

Step-by-step explanation:

The nth term of the given number sequence is n^2-1.

The first three terms of the sequence are:

1st term: 1^2-1 = 0

2nd term: 2^2-1 = 3

3rd term: 3^2-1 = 8

The tenth term of the sequence is:

10th term: 10^2-1 = 99

Therefore, the first three terms of the sequence are 0, 3, 8 and the tenth term is 99.

A set of numbers organized according to certain patterns or rules is known as a number sequence. Sequence types: Sequence of arithmetic operations: Any two successive numbers' difference is constant. Geometric series: Any two consecutive numbers' ratio is constant.

A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.

To know more about number sequence visit:

https://brainly.com/question/7043242

#SPJ1

Answer:

Step-by-step explanation:

(x - 3)(x + 2) (x + 4) =

x^3+3x^2-10x-24

Answer:

x^3+3x^2-10x-24

Step-by-step explanation:

(x - 3)(x + 2) (x + 4)

multiply the first two together first

(x^2+2x-3x-6)(x+4) add like terms first

(x^2-x-6)(x+4)

then multiply

x^3+4x^2-x^2-4x-6x-24

add like terms

x^3+3x^2-10x-24

Answer:

59 + 163 + x = 360

(cus a circle is 360 degrees ya feel me boi?)

x = 360 - 59 - 163

x= 138

Don't do drugs kids. Stay in school. Chase morality.

Step-by-step explanation:

Answer:

1. +17°

2.x=138°

Step-by-step explanation:

1. (Counted on my fingers lol -8 to 9)

2. 163+53=222

360-222=138

The solution of the expression ''12 more than 5'' would be 17.

Used the concept of addition that states,

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

The expression is,

''12 more than 5''

Now, we can evaluate the expression as,

12 more than 5

Here the term ''more than'' means to add the number.

So, it can be written as,

''12 more than 5''

= 12 + 5

Add the numbers,

= 17

So, the solution of the expression is 17.

To learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ4

Answer:

d 15.

Step-by-step explanation:

Slope = (difference in y values)/ (corresponding difference in x values)

So we have:

Slope = (120-117)  / (6.6-6.4)

          =  3 / 0.2

           = 30/2 = 15.

Answer:

y=-4x+5

Step-by-step explanation:

Answer: Choice B)   sin (33) = x/14

This is because the sine of an angle is equal to the opposite side over the hypotenuse

sin(angle) = opposite/hypotenuse

sin(33) = x/14

We can't use cosine because we don't have a variable for the adjacent side.

The area of the rhombus is approximately 112.5 square centimeters.

In a rhombus, all internal angles are equal, so we know that the opposite angles are congruent.

Additionally, the diagonals of a rhombus bisect each other at right angles, forming four congruent right triangles.

Let's denote the length of one diagonal as 15 cm, and the lengths of the sides of the rhombus as a.

Using the Pythagorean theorem, we can find the length of the other diagonal.

Let's label it as d.

In each right triangle, the hypotenuse is the length of a side, which is a, and one leg is half the length of the diagonal, which is 15/2 = 7.5 cm.

Applying the Pythagorean theorem, we have:

a² = (7.5)² + (7.5)²

a² = 56.25 + 56.25

a² = 112.5

a = √112.5

a ≈ 10.61 cm

Thus, the length of each side of the rhombus is approximately 10.61 cm.

Since the diagonals of a rhombus are perpendicular bisectors of each other, the other diagonal (d) is equal to the square root of the sum of the squares of the two sides.

Hence:

d² = a² + a²

d² = 2a²

d = √(2a²)

d = √(2 \(\times\) 10.61²)

d ≈ √(2 \(\times\) 112.5)

d ≈ √225

d ≈ 15 cm

So, the length of the other diagonal is approximately 15 cm.

To find the area of the rhombus, we can use the formula:

Area = (diagonal₁ \(\times\) diagonal₂) / 2

Substituting the values, we get:

Area = (15 \(\times\) 15) / 2

Area = 225 / 2

Area = 112.5 cm²

For similar question on rhombus.

https://brainly.com/question/20627264

#SPJ11

Answer:

4977.5 gallons

Step-by-step explanation:

We can write a proportion to solve

2 towers            11 towers

---------------    = ---------------

905 gallons       x gallons

Using cross products

2 * x = 905 * 11

2x =9955

Divide each side by 2

2x/2 = 9955/2

x =4977.5 gallons

Answer:

x=3

y=7

Step-by-step explanation:

3x-4(x+4)=-19

3x-4x-16=-19

-x-16=-19

+16. +16

________

-x=-3

×-1 ×-1

______

x=3

y=3+4

y=7

Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

Answer:

slope = 2

Step-by-step explanation:

Find 2 points on the line that land perfectly on the grid. I'll choose these 2 here:

(-2, -1) and (0, 3)

Rise is the change in the y value from one point to the other, and run is the change in the x. Looking at these 2 points, y went from -1 to 3. That is a rise of 4. The x went from -2 to 0, so that is a run of 2. "rise over run" means rise literally over run in a fraction like this:

\(m=\frac{rise}{run}\)

The more proper way to calculate slope looks like this, but it's really the same thing in the end:

\(m=\frac{y2-y1}{x2-x1}\)

where (x1, y1) and (x2, y2) are your 2 points.

Finally, the slope of this line is:

\(m=\frac{3--1}{0--2}\\\\m=\frac{4}{2}\\\\m=2\)

That's a rise of 4 over a run of 2, and that simplifies to just a slope of 2.

The equation of a line is given by:

y = mx + c

Where m is the slope.

Slope = (d - b) / (c - a)

Where (a, b) and (c, d) are the two points.

The slope of the linear function is 3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example: y = -3x - 4

Slope = -3 and y-intercept is -4.

We have,

A table that represents a linear function.

x  y

2  7

5  16

7  22

9  28

We can have points such as:

(x, y) = (2, 7), (5, 16), (7, 22), and (9, 28)

We can select any two points and find the slope.

(2, 7) = (a, b)

(5, 16) = (c, d)

Slope:

= (d - b) / (c - a)

= 16 - 7 / 5 - 2

= 9 / 3

= 3

Slope = 3

Thus,

The slope of the linear function is 3.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ5

Answer:

13)25+50+75+100=250 C

14)4*(3+2)=20

Answer:

250mm2

Step-by-step explanation:

13.

5mm×20mm= 100 mm2

5mm× 15mm= 75mm2

5mm×10mm = 50 mm2

5mm × 5mm = 25mm2

100+75+50+25 = 250 mm2 of the whole area