Find the gradient of the line segment between the points (-5,2) and (4,3) give your answer in the simplest form

Answer: 4) The center is located at (1, 3), and the radius is 6

Step-by-step explanation:

Solve the general equation of the circle.

x^2 -2x +1+ y^2-6y+9= 26+1+9 (x-1)^2+(y-3)^2=36=6^2

Hence, the coordinates of the center (1,3) And the radius will be 6

The center is located at (1,3) and the radius is 6.

"The center is the point from which all of the points on the circle are the same distance."

"The radius is the exact distance from the center to any point on the circle."

We have

[tex]x^{2} -2x+y^{2}-6y = 26\\[/tex]

Add 1 and 9 on both sides of equation

⇒[tex]x^{2} -2x+1+y^{2}-6y+9 = 26+1+9[/tex]

⇒[tex](x-1)^{2} +(y-3)^{2}= 36[/tex]

⇒[tex](x-1)^{2}+(y-3)^{2}=6^{2}[/tex].......(1)

We know the Standard form of equation of the circle

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

By comparing the standard form and equation (1)

Center (h, k) = (1, 3) and radius is 6

Hence, The center is located at (1,3) and the radius is 6.

Learn more about circle here

https://brainly.com/question/13658927

#SPJ2

Using the Pythagorean Theorem, it is found that the length of the ladder needed to reach the window is given by:

a. 17.0 ft.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In this problem, the length of the ladder in feet is the hypotenuse, considering legs [tex]l_1 = 8, l_2 = 15[/tex].

Hence:

[tex]h^2 = 8^2 + 15^2[/tex]

[tex]h = \sqrt{8^2 + 15^2}[/tex]

h = 17.0 ft.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/26396675

#SPJ2

Answer:

12 months

Step-by-step explanation:

community gym = 50 + 50x

workout gym = 170 + 40x

you need to find out how many months it will take for them to be equal, so:

50+50x = 170+40x

solve for x

10x = 120

x = 12

after 12 months, they will cost the same

Answer:

[tex]A(w) = (40 - w) * w[/tex]

Step-by-step explanation:

Given

[tex]P = 80[/tex] ---- perimeter

Required

Write the area as a function of width

The perimeter of a rectangle is:

[tex]P =2(l + w)[/tex]

Where

[tex]l \to length\\ w \to width[/tex]

So, we have:

[tex]80 = 2*(l+w)[/tex]

Divide by 2

[tex]40 = l + w[/tex]

Make l the subject

[tex]l =40 - w[/tex]

The area of a rectangle is:

[tex]A = l * w[/tex]

Substitute: [tex]l =40 - w[/tex]

[tex]A = (40 - w) * w[/tex]

Hence, the function is:

[tex]A(w) = (40 - w) * w[/tex]

Answer:

258.3 sq inches

Step-by-step explanation:

Use the sphere surface area formula, SA = 4[tex]\pi[/tex]r²

The diameter is 9.07 inches, so the radius is 4.535 inches.

Plug in 3.14 as pi and 4.535 as r, and solve:

SA = 4[tex]\pi[/tex]r²

SA = 4(3.14)(4.535)²

SA = 258.3

So, the surface area is approximately 258.3 sq inches

Answer:

Y = +- √ x - 5

Step-by-step explanation:

1. write f (x) = x^2 +5 as an equation (y = x^2 + 5)

2. interchange the varibles (x = y^2 + 5)

3. Solve for Y

Answer:

Step-by-step explanation:

x^2+4x+3

we need to factorise this

So (x+1)(x+3)

X=-1 x=-3

Hope that helps.

Answer:

rational

Step-by-step explanation:

that is literally the definition of a rational number, just change the part where it says function to number and polynomial functions to number as well.

Answer:

48. option C : Substitution

49. Option D :  ( 3, 6)

Step-by-step explanation:

3x + y = 15       ------------- ( 1 )

      y = 2x  ------------------- ( 2 )

Substitute ( 2 ) in ( 1 ) :

3x + y = 15

3x + 2x = 15

5x = 15

[tex]x = \frac{15}{5} = 3[/tex]

Substitute x in ( 2 ) :

y = 2x

y = 2 × 3 = 6

The solution to the system of equation is ( 3 , 6 )  

Answer:

C and (3, 6 )

Step-by-step explanation:

(48)

Since given y = 2x the best method of solving is by substitution C

(49)

Given the 2 equations

3x + y = 15 → (1)

y = 2x → (2)

Substitute y = 2x into (1)

3x + 2x = 15

5x = 15 ( divide both sides by 5 )

x = 3

Substitute x = 3 into (2) and evaluate for y

y = 2x = 2 × 3 = 6

solution is (3, 6 )

Answer:

The answer is Option A

Step-by-step explanation:

Start by dividing 54 by 6 which will give you 9

then divide b² by b^5 which will give you b³ at the denominator

then a^8÷a^-4

using indices...

=a^8-(-4)

=a^12

at the numerator

put everything together and you'll have...

9a^12/b³

A. [tex] \frac{9 \: {a}^{12} }{ {b}^{3} }[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]54 {a}^{8} {b}^{2} \div 6 {a}^{ - 4} {b}^{5} [/tex]

To solve the expression in a simpler way, single out the like terms.

Now, we have

[tex] \frac{54}{6} . \frac{ {a}^{8} }{ {a}^{ - 4} } . \frac{ {b}^{2} }{ {b}^{5} } \\ \\ = 9 \: {a}^{8 - ( - 4)} {b}^{2 - 5} \\ \\ (∵ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} ) \\ \\ = 9 \: {a}^{8 + 4} {b}^{ - 3} \\ \\ = 9 \: {a}^{12} {b}^{ - 3} \\ \\ ( \: or \: ) \\ \\ = \frac{9 \: {a}^{12} }{ {b}^{3} } \\ \\ (∵ {a}^{ - m} = \frac{1}{ {a}^{m} } )[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

6x+30<102

0 ≤ x ≤ 12 gives all possible solutions for this problem.

Answer:

Your total would be 180 so with the extra you could donate or something like that

Step-by-step explanation:

I hope this helped:)

Answer:

<1

Step-by-step explanation:

Answer: [tex]17,649[/tex]

Step-by-step explanation:

Given

The radius of the cycle is [tex]r=63\ cm[/tex]

Distance traveled by Paul is [tex]68.89\ km[/tex]

Distance traveled by one complete revolution of wheel is equivalent to circumference of wheel i.e.

[tex]\Rightarrow 2\pi r\\\\\Rightarrow 2\times \dfrac{22}{7}\times 63\\\\\Rightarrow 396\ cm\ \text{or}\ \text{3.96}\ m[/tex]

No of revolution made by wheel

[tex]\Rightarrow n=\dfrac{69.89\times 1000}{3.96}\\\\\Rightarrow n=17,648.9899\approx 17,649[/tex]

Answer:

63 is the range of the following test scores.

Step-by-step explanation:

1. The largest number is 95.

2. The smallest number is 32.

3. The range is the difference between the largest and the smallest number.

4. Subtract 95 - 32 which equals 63.

5. 63 is the range of the following test scores.

Answer:

area=3.14 yd^2

Step-by-step explanation:

radius=diameter/2

=2/2

=1

area =π*r^2

=3.14&1

=3.14 yd^2

Answer:

3.14 yd^2

Step-by-step explanation:

First we need to find the radius

r = d/2 = 2/2 =1 yd

The area of a circle is given by

A = pi r^2

   = 3.14 ( 1)^2

   = 3.14 yd^2

Answer:

Answer Expert Verified

Given; prove; statements; and reasons. Explanation: The given is important information we are given at the beginning of the proof that we will use in constructing the proof. The "prove" is the statement we are trying to prove

Answer:

Sample Response: Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

Step-by-step explanation:

Have the day you deserve :)

Answer:

[tex]=7[/tex]

Step-by-step explanation:

18 - 18 ÷ 3 - 5 =

Divide 18 ÷ 3 first because you have to divide before subtracting.

18 - 6 - 5 =

12 - 5 =

= 7

Hope this helps

Answer:

7

Step-by-step explanation:

thanks for the pts

✌️❤️✌️

Answer:

20

Step-by-step explanation:

Let us represent the number as x. In a similar sense, half the number would be [tex]\frac{x}{2}[/tex]. We know that their sum is 30, so we can write the following equation:

[tex]x+\frac{x}{2} =30\\2x+x=60\\3x=60\\\fbox{x=20}[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

15,000 mm^3

Step-by-step explanation:

volume of the 2 stacked granola bars = volume of one granola bar x 2

volume of one granola bar = Volume of a prism = base area x height

5 x 55 x 30 x 2 = 15,000

Answer:

1/6

Step-by-step explanation:

We know that a die has 6 sides. What would be the probability to roll 1 of those sides? (to rephrase the question)

well. the probability to roll one of the sides on a 6 side dice is 1/6, 1 side on the 6 sided die.

Answer:

1/6

Step-by-step explanation:

There are six possible outcomes when rolling a die

1,2,3,4,5,6

P(rolling a 2) = number of outcomes that is a 2/ total outcomes

                     = 1/6

Answer:

Vase volume is 452.16 in³

Step-by-step explanation:

The question asks for the volume of a cylinder of radius r and height h.  The relevant formula is V = (pi)(r)^2*h

With h = 9 in and r = 4 in, that max volume (of water) is

V = (3.14)(4 in)^2*(9 in) = 452.`16 in³

Answer: -1/9

Step by step explanation:

The common difference of an arithmetic sequence can be found by picking 2 consecutive terms, and subtracting the second from the first. For example, if I chose the terms 2 and 1 8/9, I would find the common difference by:

1 8/9 - 2, which is equal to -1/9.

You can confirm this by picking another pair of consecutive terms. Let's pick 1 7/9 and 1 2/3:

1 2/3 - 1 7/9 = -1/9, as 1 2/3 = 1 6/9, so 1 6/9 - 1 7/9 = -1/9

Answer:

Animism

Step-by-step explanation:

Animism is often a major idea or thought which is developed in a child preooperational stage according to paiget's theory of cognitive development where a child's learning is driven and derived from by symbols. At this stage, a child often relates with their toys, and other inanimate objects they come across as though they were real, manipulating and transforming them to form different things including relating with these manipulated objects like they were living. This is because at this stage, a child cannot use cognitive or logic to make distinctions.

Answer:

x = -5

Step-by-step explanation:

25 - 3x = 40

3x = -15

x = - 5

Answer:

x = -5

Step-by-step explanation:

25 − 3x = 40

-3x = 15

x = -5

Answer:

a=70 vertically opp angles

b=80  linear pair

c=100   corresponding angles

d= 80 linear pair with c

e=  180 -a-d

=180-70-80

=30