Find the distance between the points (3,4) and (5,9). Leave in simplest radical form.

Answer:

[tex]\frac{53}{6}[/tex]

Step-by-step explanation:

[tex]\int\limits^4_3 {x^2-x} \, dx[/tex]

= [ [tex]\frac{x^3}{3}[/tex] - [tex]\frac{x^2}{2}[/tex] ] ← evaluate for upper limit - lower limit

= ( [tex]\frac{64}{3}[/tex] - [tex]\frac{16}{2}[/tex] ) - ( [tex]\frac{27}{3}[/tex] - [tex]\frac{9}{2}[/tex] )

= [tex]\frac{64}{3}[/tex] - 8 - 9 + [tex]\frac{9}{2}[/tex]

= [tex]\frac{155}{6}[/tex] - 17

= [tex]\frac{53}{6}[/tex]

Answer:

40°, 95°, 105°, and 160°

Step-by-step explanation:

Let the smallest angle be x.

Measures of the 3 angles can be expressed as:

[tex] x + 55 [/tex]

[tex] x + 65 [/tex]

[tex] x + 120 [/tex]

The sum of all angles in a quadrilateral = 360°.

Therefore, [tex] (x + 55) + (x + 65) + (x + 120) = 360 [/tex]

Solve for x

[tex] x + 55 + x + 65 + x + 120 = 360 [/tex]

[tex] 3x + 240 = 360 [/tex]

[tex] 3x + 240 - 240 = 360 - 240 [/tex]

[tex] 3x = 120 [/tex]

[tex] \frac{3x}{3} = \frac{120}{3} [/tex]

[tex] x = 40 [/tex]

The smallest angle = 40°

Plug in the value of x in the earlier stated expressions to find the measure of the other angles:

[tex] x + 55 = 40 + 55 = 95 [/tex]

[tex] x + 65 = 40 + 65 = 105 [/tex]

[tex] x + 120 = 40 + 120 = 160 [/tex]

Answer: (-9,18) , (1,8)  and (5,4)

Step-by-step explanation:

If  the x coordinate is -9 then plot it into the equation and solve for y.

y = -1(-9) + 0

y = 9 + 9

y = 18

Same for the second one plot in the value of x and solve for y

y= -1(1) + 9

y = -1 + 9

y = 8

Again same for the last one

y = -1(5) + 9

y = -5 + 9

y = 4

Answer

the length is 20 cm and breadth is 16cm

Step-by-step explanation:

let, 2(a+b)= 72( as its the formulae of circumference)

here a is the length and b is the breadth

now total area is ab

according to the question

a(b-6)= ab-120

or -6a= - 120

so length is 20 cm

now by putting the value in the 1st eq we get

2(a+b)=72

or(a+b)=36

or 20+b=36

so breadth is 16 cm.

length is 20cm and breadth is 16 cm

(u can verify that easily)

thank u

Answer:

3+2=5

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

The fact of x=11 makes the equation true as for if it didnt work correctly it wouldnt be true.

Answer:

The time it takes to earn an amount A with a given principal P invested for a time period t is t = (A/P - 1)/r

Step-by-step explanation:

In order to calculate the time it would take to earn a certain amount of interest on a principal amount in an investment with simple interest, we use the simple interest formula as follows;

A = P·(1  + r·t)

A = The final amount after the number of periods of investment

P = The principal or initial amount

r = The interest rate per period

t = The number of the time periods

Therefore, the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is fount by making t the subject  of the above equation, which is given as follows;

A/P = 1 + rt

rt = A/P - 1

t = (A/P - 1)/r

Therefore, the time it takes to earn an amount A with a given principal P invested for a time period t is given by t = (A/P - 1)/r.

Answer:

Step-by-step explanation:

1 + ( -5)     Adding a negative = subtracting:

= 1 - 5

= -4.

Think of these numbers as 'directed' numbers - the numbers depend on the direction.

If we have a thermometer and the temperature reads 1 degree and the temperature drops, the mercury travels down ( negative direction) by 5 units. . It goes down 1 degree to reach 0 then another 4 degrees to reach -4,

1 - 5 = -4.

=======================================================

The base of the carton is 5*8 = 40 square cm. The height of the milk is 12 cm, so the milk takes up 40*12 = 480 cubic cm of volume. Imagine a rectangular block with dimensions 5, 8 and 12. The volume would be 480.

The carton is placed on its side. Specifically the orange side is flat on the table (assume the table is level). This orange face has area 8*15 = 120 square cm. It multiplies with some height h, which is the height of the milk after moving the carton, to get the volume of the milk inside.

The volume of the milk is 120h and it must be equal to 480 since the amount of milk has not changed as we moved the carton (assume there are no leaks)

So,

120h = 480

120h/120 = 480/120

h = 4

The height of the milk after moving the carton is 4 cm

It will be 25

Hope you get it right

Your question has been heard loud and clear.

First one (x+2i)(x-2i) = x^2+4

Second one (x-2+2i)(x-2-2i) = x^2-4x+8

Third one (x+1+i)(x+1-i) = x^2+2x+2

Thank you

Edit: Sorry for taking 15 minutes I was calculating lol

Answer:

$750 per year

Step-by-step explanation:

The farmer saves $250 in four months.  You need to find out how much he makes in a year.  There are 12 months in a year.  Multiply the amount he saves by 3.

$250 × 3 = $750

The farmer saves $750 per year.

Answer: $17.78; 26.67; 35.56

Step-by-step explanation:

Given the following information.:

Price of cab = $2 per mile , irrespective of the number of passengers.

Alice's destination = 20 miles

Ben's destination = 30 miles

Calvin's destination = 40 miles

If the three share a cab, the cab fee will be (cost per mile * number of miles of the farthest destination).

($2 * 40) = $80

Let price = a, for 20 miles

Ben's mile = 30 miles = 1.5 times Alice's miles, then Ben's pay = (1.5a)

Calvin's mile = 40 miles = 2 times Alice's miles, then Calvin's pay = (2a)

Thus,

a + 1.5a + 2a = $80

4.5a = $80

a = $80 / 4. 5

a = $17.78

Ben's pay = 1.5a = $26.67

Calvin's pay = 2a = $35.56

Answer:

1,243,206x

Step-by-step explanation:

Combine like terms:

[tex]28x +25x +23x+23x+45x+1234890x+6389x+1783x\\\\=\boxed{1243206x}[/tex]

The expression can no longer be simplified.

Answer:

The one that does not belong has a different number of dimensions.

Step-by-step explanation:

Given list consists of:

Three of them have one dimension but the plane has two dimensions,

therefore the plane in the list does not belong with the other three.

So correct answer choice is:

Answer:

x=15

Step-by-step explanation:

5x= 75 (divide)

75/5= 15

Answer: There is only one step to solve this equation; we use inverse operations to isolate the x by dividing 5 on both sides. We divide because 5 is being multiplied by x, and the inverse operation for multiplication is division.

5x/5 = x

75/5 = 15

The equation now looks like:

x = 15

x is equal to 15. This is your answer.

Answer:

12

Step-by-step explanation:

use the distance formula

(1-1)^2 + (6- (-6))^2

0+12^2

take the sqrt of 144

12

Answer:

12

Step-by-step explanation:

→To solve this, you need to use the distance formula:

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

→Plug in the numbers accordingly:

[tex]d=\sqrt{(1-1)^2+(6+6)^2}[/tex]

[tex]d=\sqrt{(0)^2 + (12)^2}[/tex]

[tex]d=\sqrt{144}[/tex]

→Take the square root of 144:

[tex]d=12[/tex]

Answer:

The answer is "[tex]\bold{i=0.05311 \ \ and \ \ x= \$ 2934.4670}[/tex]"

Step-by-step explanation:

2-year interest is:

[tex]\to (x)i + x(1 + i)i=320.......(i)[/tex]

The price of the discount is :

[tex]\to x(\frac{i}{1+i})=148......(ii)[/tex]

by mixing (ii) in (i), we get:    

[tex]\to 148(1+i)+148(1+i)^2=320 \\\\\to (i+1)(i+2)= \frac{320}{148} \\\\\to i = 0.05311 \\[/tex]

[tex]\to[/tex] [tex]x= 148(\frac{i+1}{i}) \\\\[/tex]

[tex]= 148(0.054311)+ \frac{1}{(0.005311)}\\\\ =$2934.4670[/tex]

The Interest rate of annual impact:  

i=0.05311  

x=$ 2934.4670

Answer:

113

Step-by-step explanation:

127 - 2(3+4)

127 - 2(7)

127-14

113

Answer:

[tex] a=\pm 4[/tex]

Step-by-step explanation:

[tex] M^2= \begin{bmatrix} a^2 +1 & 0 \\ 0 & a^2+1 \end{bmatrix} =17 \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\\[/tex]

Equate the terms to get:

$a^2+1=17$

$\implies a^2=16 \implies a= \pm 4$

Answer:

k = [tex]\frac{25}{12}[/tex]

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log([tex]\frac{x}{y}[/tex] )

log a = log b ⇒ a = b

Given

logk - log(k - 2) = log25, then

log ([tex]\frac{k}{k-2}[/tex] ) = log25, thus

[tex]\frac{k}{k-2}[/tex] = 25 ( multiply both sides by (k - 2)

25(k - 2) = k

25k - 50 = k ( subtract k from both sides )

24k - 50 = 0 ( add 50 to both sides )

24k = 50 ( divide both sides by 24 )

k = [tex]\frac{50}{24}[/tex] = [tex]\frac{25}{12}[/tex]

Answer:

Option D is correct answer.

Step-by-step explanation:

Hey, there!

Before finding a,b,c, you remember the formula of quadratic equation,

[tex]a {x}^{2} + bx + c = 0[/tex]

Where, "a" represents thecoefficient of, x^2 "b" represents the coefficient of y and "c" is a numerical value.

So, the value of a,b,c in this equation "-2x^2+4x-3=0" is:

a= -2

b= 4

and c= -3.

Hope it helps...

Answer:

D

Step-by-step explanation:

EDGE 2021

Answer:

Step-by-step explanation:

3x + 2 = 7(3 - x)

3x + 2 = 21 - 7x

3x + 7x = 21 - 2

10x = 19

 x = 1.9

[tex]26-x-4 = 26 - 1.9 -4 = 20.1[/tex]

Answer:

Step-by-step explanation:

Lin after 1 year has 300+2*300/100=300+6=306  $

     after 2 years has 306+2*306/100=306+6.12=312.12$

150-15*150/100=150-22.5=127.5 $ the price for the bicycle

The value after 20 years is $ 723.514

Solution:

Formula for Amount compounded annually is as follows:  

Where,

"A" is the total amount

"p" is the principal sum

"r" is the rate of interest

"n" is the number of years

From given question,

p = $ 300

r = 4.5 %

n = 20 years

Substituting the values we get,

Thus value after 20 years is $ 723.514

PART 2)

2. Given data

Cost of bicycle = $150

Depreciation = 15%

Firstly let us calculate 15% of $150

(15/100)*150 =0.15*150

= $22.5

Since the value depreciated

We will minus the the depression from the initial amount

New amount = 150-22.5=

$127.5

Step-by-step explanation:

( 4+ 2 ) = ( 2 - ( 6-6) * 6 )

8 = 2

6

follow me and Mark as brainlist ❤️

Answer:

Step-by-step explanation:

6 min/4 hole = 1.5 min per hole

9/1.5 = 6 holes

It can be concluded that 6 holes were made.

Hope this helped,

Kavitha

Answer:

6 holes

Step-by-step explanation:

Answer: Approximately  7 hours

Step-by-step explanation:

Divide the total number of miles by the miles traveled per hour to find out how long it will take you to go from New York to Paris.

3636 / 520 = 6.99  

which is approximately 7 hours

===========================================

Explanation:

Multiply both sides by 2 to clear out the fraction

y = (1/2)x+4

2y = 2[ (1/2)x + 4 ]

2y = 2*(1/2)x + 2*4

2y = x + 8

Then move the x term over to the left side

2y = x+8

2y-x = 8

-x+2y = 8

Optionally we can multiply both sides by -1

-x+2y = 8

-1*(-x+2y) = -1*8

x-2y = -8

This is in standard form Ax+By = C with A = 1, B = -2, C = -8

The reason why I multiplied both sides by -1 was to make A > 0 which is what some textbooks use as convention. Of course -x+2y = 8 is equally valid too.

Hi there! :)

Answer:

[tex]\huge\boxed{x = -1}[/tex]

Given:

AC = 22

BC = x + 14

AB + x + 10

AC is equivalent to AB + BC, therefore:

AC = AB + BC

Substitute in the expressions:

22 = (x + 10) + (x + 14)

Combine like terms:

22 = 2x + 24

Subtract 24 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

Given : AC = 22, BC = x + 14, and AB = x + 10.

[tex]\rule{130}1[/tex]

Solution :

[tex]:\implies\sf AB + BC = AC\:\:\:\:\Bigg\lgroup \bf{Segment\: addition\: postulate}\Bigg\rgroup \\\\\\:\implies\sf (x + 10) + (x + 14) = 22\:\:\:\:\Bigg\lgroup \bf{Substitution}\Bigg\rgroup\\\\\\:\implies\sf 2x + 24 = 22\:\:\:\:\Bigg\lgroup \bf{Simplify\:(added\:like\:term)}\Bigg\rgroup\\\\\\:\implies\sf 2x = -2\\\\\\:\implies\sf x = \dfrac{-2}{2}\\\\\\:\implies\underline{\boxed{\pink{\sf x = -1}}} [/tex]