find the distance between points P(3, 4) and Q(4, -6) If necessary round to the nearest hundredth.

Answer:

x = ln9

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] = nlogx , lne = 1

Given

[tex]e^{x}[/tex] = 9 ( take the ln of both sides )

ln[tex]e^{x}[/tex] = ln9, thus

xlne = ln9, that is

x = ln9

The evaluation of the numeric expression is:

5(−6) = -30

A numeric expression is a mathematical statement that involves only numbers and one or more operation symbols.

Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.

We can evaluate 5(−6) as follow:

5(−6) = 5 * (-6)

        = -30

Learn more about numeric expression on:

https://brainly.com/question/4344214

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Answer:

SU = 70

Step-by-step explanation:

First, we need to find the value of x. Since M is the midpoint of SU, that means that SM = MU, therefore:

x + 15 = 4x - 45

15 = 3x - 45

60 = 3x

x = 20

We know that SU = SM + MU = (x + 15) + (4x - 45) = 5x - 30 and that x = 20 so SU = 5x - 30 = 5 * 20 - 30 = 100 - 30 = 70.

Answer:

x = [tex]-\frac{3}{b}[/tex]

x = -1

Step-by-step explanation:

The given equation is,

-2(bx - 5) = 16

Dividing by (-2) on both sides of the equation,

[tex]\frac{-2(bx-5)}{(-2)}=\frac{16}{(-2)}[/tex]

(bx - 5) = -8

By adding 5 on both the sides of the equation,

(bx - 5) + 5 = -8 + 5

bx = -3

Dividing by 'b' on both the sides of the equation,

[tex]\frac{bx}{b}=\frac{-3}{b}[/tex]

x = [tex]-\frac{3}{b}[/tex]

If b = 3,

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

x = -1

Answer:

The minimum sample size needed for each city  = 922

Step-by-step explanation:

From the information given:

the objective is to find the minimum sample size needed for each city so that the margin of error not to exceed 6%.

If we take a look at the question very well:

we are only given the confidence interval of 99% and the margin of error of 6%

we were not informed or given the value or estimate of any proportions>

so we assume that:

[tex]p_1 =q_ 1= p_2 = q_2 = 0.5[/tex]

At confidence interval of 0.99 , the level of significance = 1 - 0.99 = 0.01

The critical value for [tex]z_{\alpha/2} = z_{0.01 /2}[/tex]

= [tex]z_{0.005}[/tex] = 2.576

The minimum sample size needed can be calculated by using the formula :

[tex]n = \dfrac{z^2_{\alpha/2}}{E^2}(p_1q_1+p_2q_2)[/tex]

[tex]n = \dfrac{2.576^2}{0.06^2}((0.5 \times 0.5)+(0.5 \times 0.5))[/tex]

[tex]n = \dfrac{6.635776}{0.0036}(0.25+0.25)[/tex]

[tex]n =1843.271 \times (0.5)[/tex]

n = 921.63

n [tex]\simeq[/tex] 922

∴ The minimum sample size needed for each city  = 922

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)=-18

-18/-3=6

6*-1=-6

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)÷(-3)×(-1)

PEMDAS

Parentheses first

(-17+4+1-6)÷(-3)×(-1)

Add and subtract inside the left parentheses

(-18)÷(-3)×(-1)

Multiply and divide from left to right

6 * -1

-6

Answer:

here is a formulae

cos2A= 2cos square a -1

Step-by-step explanation:

as given cos A= 1/2 (a+1/a)

by simplifying

cosA =a²+1/2a

now by following the formulae

cos2A = 2cos²A-1

=2(a²+1/2a)² -1

=2(a⁴+2a²+1/4a²)-1

=a⁴+2a²+1/2a² -1

=a⁴+2a²+1-2a²/2a²

=a⁴+1/2a²

=1/2 (a⁴+1/a²)

=1/2(a⁴/a²+1/a²)

=1/2(a²+1/a²)

{proved}

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thank uuu

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity: cos 2A = 2cos²A - 1

Proof  LHS → RHS

Given:                                [tex]\cos A=\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)[/tex]

LHS:                                   cos 2A

Double Angle Identity:      2(cos²A) - 1

                                     [tex]=2\bigg(\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)^2\bigg)-1[/tex]

Simplify:                           [tex]2\bigg(\dfrac{1}{4}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)\bigg)-1[/tex]

                                     [tex]=\dfrac{1}{2}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+1+\dfrac{1}{2a^2}-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+\dfrac{1}{2a^2}[/tex]

Factor:                         [tex]=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)[/tex]

[tex]\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)\quad \checkmark[/tex]

Answer:

11) x=1 or x=3.

12) x=2/3 or x=-7.

Step-by-step explanation:

So we have two equations:

[tex]f(x)=3x(2x-6)\\f(x)=3x(x+7)-2(x+7)[/tex]

And we want to solve them. To do so, make each of them equal 0 and then solve for x:

11)

[tex]f(x)=3x(2x-6)\\0=3x(2x-6)[/tex]

Using the Zero Product Property, either one or both of the factor must be zero for this to be true. Therefore, make each factor equal to zero and solve:

[tex]3x=0 \text{ or } 2x-6=0[/tex]

Divide the left by 3. On the right, add 6 and then divide by 2:

[tex]x=0\text{ or } 2x=6\\x=0 \text{ or } x=3[/tex]

Therefore, the solutions to the first equation is:

x=1 or x=3.

12)

[tex]f(x)=3x(x+7)-2(x+7)[/tex]

First, use the distributive property to group the terms together. The equation is equivalent to:

[tex]f(x)=(3x-2)(x+7)[/tex]

Now, set the function to zero and solve:

[tex]0=(3x-2)(x+7)[/tex]

[tex](3x-2)=0 \text{ or } x+7=0\\3x=2 \text{ or } x=-7\\x=2/3 \text{ or } x=-7.[/tex]

Therefore, the answer is:

x=2/3 or x=-7.

Answer:

[tex]\large \boxed{{\bold{11.} \ x=0, \ x=3}} \\ \\ \large \boxed{{\bold{12.} \ x=-7, \ x=2/3}}[/tex]

Step-by-step explanation:

We will set the outputs of the functions to 0 and solve for x.

0 = 3x(2x - 6)

Set factors equal to 0.

First possibility:

3x = 0

x = 0

Second possibility:

2x - 6 = 0

2x = 6

x = 3

0=3x(x+7)-2(x+7)

Take (x+7) as a common factor.

0 = (3x-2)(x+7)

Set factors equal to 0.

First possibility:

x + 7 = 0

x = -7

Second possibility:

3x - 2 = 0

3x = 2

x = 2/3

Answer: 9

Step-by-step explanation:

plug in numbers to get 3+6

add them

boom

Answer:

D. 9

Step-by-step explanation:

Plug in 3 as x and -2 as y in the expression:

x - 3y

3 - 3(-2)

3 + 6

= 9

Answer:

Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.

Step-by-step explanation:

A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.

Answer:

x = 7.6°, so A = 18.8°

Step-by-step explanation:

What we need to know in order to utilize algebra is the total sum of all triangle's angle. It's 180°. So, we can write

25 + 17x - 1 + 3x - 4 = 180

20x + 28 = 180

20x = 152

x = 7.6°

Now what you need to do is substitute 7.6° into each expression 17x - 1 and 3x - 4.

Answer:

A,C, and D I believe.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given , value of b = -4

To find : ( - b )²

plug the value of b

⇒[tex] \sf{( - {( - 4))}^{2} }[/tex]

we know that ,

[tex] \sf{( - ) \times ( - ) = ( + )}[/tex]

⇒[tex] \sf{ {4}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{16}[/tex]

Hope I helped!

Best regards!!

Answer:

y = |1/4x|

Step-by-step explanation:

The slope is 1/4

Answer:

1723

Step-by-step explanation:

10 x 70=700

Answer:

1723

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

1/4x + 1/3x + 8 = 22

1/4x + 1/3x = 7/12x

7/12x + 8 = 22

22 - 8 = 14

7/12x = 14

14/ 7/12

x = 24

Answer:

It would be B

Step-by-step explanation:

Answer

6 kg/m

Step-by-step explanation:

The linear density is said to give the way the mass is changing it's position and it's a derivatives of mass m here which is differenciated with respect to x position

Given

mass m = 3x^2.

Density ρ= dm/dx =6x

Then if we substitute x=1 into above expresion we have

ρ(1) =6 Kg/m

ρ= 6Kg/m

Hence this is how fast is the mass changing at that position.

Answer:

Below

Step-by-step explanation:

Let D be the diagonal of this square.

D forms with AB and BC a right triangle where D is the hypotenus.

We will apply then the Pythagorian theorem

●The Pythagorian theorem

● D^2 = AB^2 + BC^2

ABCD is a square, so AB=BC

● D^2 = AB^2 + AB^2

● D^2 = 2AB^2

We khow that is D= 5 cm

● 25 = 2AB^2

● 25/2 = AB^2

● 5/√2 = AB

AB is 5√2 cm

■■■■■■■■■■■■■■■■■■■■■■■■■

The perimeter is:

● P = 4AB

● P = 4×(5/√2)

● P = 20/√2

● P = 10×2/√2

● P = 10√2 cm

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area is

● A = AB^2

● A = (5/√2)^2

● A = 25/2 cm^2

Answer:

Step-by-step explanation:

the sides of a square are equal ( AB=BC=CD=DA)

diagonal of the square creates two right angle triangle

to find the side of the triangle we apply the Pythagorean theorem:

a²+b²=c² ( let AB=a, and BC=b)

2a²=25 ( since AB=BC=a)

a²=25/2

a=(5√2)/2 cm

a=3.54 ( rounded to the nearest 10)

perimeter = 4a

P=4(5√2/2)

P=10√2 cm

Area=a²=(5√2/2)²=25/2=12.5 cm^2

Answer:

[tex]x = \frac{770}{16}[/tex]

Step-by-step explanation:

Given

[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]

Required

Solve for x

[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]

Start by solving the bracket [Take LCM]

[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{7x + x}{7}) = 60[/tex]

[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{8x}{7}) = 60[/tex]

Open the bracket

[tex]x + \frac{x}{7} + \frac{8x}{77} = 60[/tex]

Take LCM

[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]

[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]

[tex]\frac{96x}{77} = 60[/tex]

Multiply both sides by 77

[tex]77 * \frac{96x}{77} = 60 * 77[/tex]

[tex]96x = 60 * 77[/tex]

Divide both sides by 96

[tex]\frac{96x}{96} = \frac{60 * 77}{96}[/tex]

[tex]x = \frac{60 * 77}{96}[/tex]

Divide the numerator and denominator by 6

[tex]x = \frac{10 * 77}{16}[/tex]

[tex]x = \frac{770}{16}[/tex]

Answer:

48.125

Step-by-step explanation:

Answer:

Buy stuff and sell them at a higher price

Step-by-step explanation:

Answer:

get a job

Step-by-step explanation:

Answer:

The pints of each of the two existing types of drinks are 22 and 88 respectively.

Step-by-step explanation:

We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.

Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.

So, according to the question;

                                   x + y = 110

                                   x = 110 - y  ---------------- [equation 1]

                             [tex]0.70x+0.95y=0.90\times 110[/tex]

                              [tex]70x+95y=9900[/tex]

                              [tex]70(110-y)+95y=9900[/tex]

                              [tex]7700-70y+95y=9900[/tex]

                              [tex]25y=9900-7700[/tex]

                                [tex]y=\frac{2200}{25}[/tex]

                                y = 88

Now, putting the value of y in equation 1 we get;

                               x = 110 - y

                               x = 110 - 88 = 22

Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.

Answer:

i think this is the answer

Answer:

the answer is [tex]\frac{3}{2}[/tex] or 1.5 or 1[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

When both the conditions hold true, F is prime.

Step-by-step explanation:

AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

  AB

+ CD

--------

  EF

1st condition, B and D are consecutive.

Adding B and D gives us F.

Possible values can be (F being the unit value after adding not considering the carry over):

B + D = F

1+2=3

2+3=5

3+4=7

4+5=9

5+6=1

6+7=3

7+8=5

8+9=7

Here F is not prime (because 9 is not prime).

Now, let us consider the 2nd condition as well.

i.e. C = 8

For the following

  AB

+ CD

--------

  EF

C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.

So, E = 8 + 1 = 9

Now, B  and D are consecutive and can not be 1, 8 or 9.

So, possible values are:

B + D = F

2 + 3 = 5

3 + 4 = 7

Here F is prime.

So, when both the conditions hold true, F is prime.

Answer:

The multiplicative inverse of -0.7 is -1/0.7

hope it helps

Answer:

x = 9

Step-by-step explanation:

Take the angle of LOJ (3x) and JOK (2x+12).

LOJ + JOK = LOK.

LOK = 57.

So, 3x + 2x + 12 = 57

3x + 2x = 5x

5x + 12 = 57

57 - 12 = 45

5x = 45

x= 9

Answer:

w = -1

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{w=-1}[/tex]

Step-by-step explanation:

[tex]w-5-4= -8-6w+8w[/tex]

Combining like terms.

[tex]w-9= -8+2w[/tex]

Adding -w and 8 to both sides.

[tex]-9+8=2w-w[/tex]

[tex]-1=w[/tex]

Answer:

5a + 5b

Step-by-step explanation:

13a - 8a + 9b - 4b =

Combine like terms. 13a and -8a are like terms and can be combined.

9b and -4b are like terms and can be combined.

= 5a + 5b

Answer:

Step-by-step explanation:

[tex]13a-8a+9b-4b\\\mathrm{Add\:similar\:elements:}\:13a-8a=5a\\=5a+9b-4b\\\mathrm{Add\:similar\:elements:}\:9b-4b=5b\\=5a+5b[/tex]

Step-by-step explanation:

1. volume = πr²h

= π×(5²)×9

= π×225

= 225π

= 707.1 cubic inches

2. volume = lwh

= 5.2 × 1.8 × 2

= 18.72 square feets

Answer:

A

Step-by-step explanation:

x - 7 = 18

Adding 7 to both sides (to get rid of the -7 on the left side) gives us:

x - 7 + 7 = 18 + 7

x = 25

Answer:

25 is the correct answer

Step-by-step explanation:

i got it right on the test