What is the value of w?

Answer:

2

Step-by-step explanation:

using the rules of logarithms

logx + logy = log(xy)

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

log[tex]x^{n}[/tex] ⇔ nlogx

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

3log2 + log200 - log16

= log 2³ + log200 - log16

= log8 + log200 - log16

= log(8 × 200) - log16

= log1600 - log16

= log ([tex]\frac{1600}{16}[/tex] )

= log100

let [tex]log_{10}[/tex] 100 = n , then

100 = [tex]10^{n}[/tex] = 10²

thus value of expression is n = 2 , that is 2

[tex]2 \cdot 1[/tex]Answer:

Equal to 2

Step-by-step explanation:

1. Apply log rule: [tex]alog_c(b) = log_{c}(b^a)[/tex]

[tex]3log_{10}(2) = log_{10}(2^3)[/tex]

[tex]= log_{10}(2^3) + log_{10}(200) - log_{10}(16)[/tex]

2. Apply log rule: [tex]log_c(a) + log_c(b) = log_c(ab)[/tex]

[tex]log_{10}(2^3) + log_{10}(200) = log_{10}(2^3 \cdot 200)[/tex]

[tex]= log_{10}(2^3 \cdot 200) - log_{10}(16)[/tex]

[tex]2^3 \cdot 200 = 1600[/tex]

[tex]= log_{10}(1600) - log_{10}(16)[/tex]

3. Apply log rule: [tex]log_c(a) - log_c(b) = log_c(\frac{a}{b})[/tex]

[tex]log_{10}(1600) - log_{10}(16) = log_{10}(\frac{1600}{16})[/tex]

Divide the numbers: [tex]\frac{1600}{16} = 100[/tex]

[tex]= log_{10}(100)[/tex]

Rewrite 100 in power - base form: [tex]100 = 10^2[/tex]

[tex]= log_{10}(10^2)[/tex]

4. Apply log rule: [tex]log_a(x^b) = b \cdot log_a(x)[/tex]

[tex]log_{10}(10^2) = 2log_{10}(10)[/tex]

[tex]2log_{10}(10)[/tex]

5. Apply log rule: [tex]log_a(a) = 1[/tex]

[tex]log_{10}(10) = 1[/tex]

[tex]= 2 \cdot 1 = 2[/tex]

Answer:

a) m problems, d days to complete.

m/d

b) m/15d

c)-if 15 was connected; 15d

if 15 WAS NOT connected, m problems

Answer:

THE ANSWER IS 7/4

Step-by-step explanation:

Step-by-step explanation:

[tex]5 \times \frac{7}{20} \\ = \frac{35}{20} \\ = \frac{7}{4} [/tex]

answerr......

The total balance in Raul's account after 40 years when he retires is $65,714.90.

The formula that can be used to determine the balance of the accout is: monthly amount saved x annuity factor.

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$100 x [(1.00125^480) - 1 ] / 0.00125 = $65,714.90

Here is the complete question:

Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year. What is the balance in the account after 40 years?

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Answer:

-1/3

Step-by-step explanation:

because it is a negative number and closer to zero than -3 is making it greater, becuase it is closer to a positive number.

Answer:

-1/3 is greater than -3

-3 < -1/3

Linear equations are usually organized in slope-intercept form, which looks like this:

[tex]y=mx+b[/tex]

To find the equation of a line in slope-intercept form:

We're given:

First, plug the given slope into the slope-intercept form equation:

[tex]y=mx+b\\\\y=\dfrac{1}{2}x+b[/tex]

Now, determine the y-intercept.

[tex]y=\dfrac{1}{2}x+b[/tex]

⇒ Plug in the given point (4,1) and solve for b:

[tex]1=\dfrac{1}{2}(4)+b\\1=2+b\\b=-1[/tex]

⇒ Therefore, the y-intercept is -1. Plug this back into our original equation:

[tex]y=\dfrac{1}{2}x-1[/tex]

[tex]y=\dfrac{1}{2}x-1[/tex]

Answer:

1 / 216, or 0.00462...

Step-by-step explanation:

Answer:

input:   1    2   6   18

output:   5   10   30  90

Step-by-step explanation:

The age of Nina and sam are 15years and 10 years respectively now

They consists of equations and unknown variables

Let their current age be x and y

If five years ago, Nina was twice as old as Sam then;

x - 5 = 2(y-5)

If in five years she will be 1.5 times as old as Sam, then;

x = 1.5y

Substitute

1.5y - 5 = 2y -10

-0.5y  = -5

y =5/0.5

y = 10

Since x = 1.5y

x = 15years

Hence the age of Nina and sam are 15years and 10 years respectively now

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[tex]x^2+y^2=r^2~\hfill x=rcos(\theta )~\hfill y=rsin(\theta ) \\\\[-0.35em] ~\dotfill\\\\ r=3sin(A)\implies \stackrel{\textit{multiplying both sides by "r"}}{r^2~~ = ~~3~rsin(A)}\implies x^2+y^2=3y[/tex]

r = 3sinA is written in rectangular form as[tex]x^2+y^2 = 3y.[/tex]

Any complex number z = a + ib can be written in polar form as:

[tex]z = r(\cos(\theta) + i\sin(\theta))[/tex]

Complex numbers are those numbers that contain the imaginary and the real part.

Raising this to nth power (n being an integer), we get:

[tex]z ^n = r^n (\cos(n\theta) + i\sin(n\theta))[/tex]

We need to find r = 3sinA is written in rectangular form as[tex]x^2+y^2[/tex].

We know that

x = r cosA

y = r sin A

We have been given ;

r = 3sinA

Multiply by r on both sides;

[tex]r^2 = 3r sin A\\\\r^2 = 3 y[/tex]

therefore,

[tex]x^2+y^2 = 3y[/tex]

Hence, r = 3sinA is written in rectangular form as [tex]x^2+y^2 = 3y[/tex].

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Answer:

11

Step-by-step explanation:

The formula for the area of a triangle is bh(1/2).

We can model an equation with:

22=4x(1/2)

multiply both sides by 2

44=4x

x=11

Answer:

my best estimate would be 15,116,600

Step-by-step explanation:

,

Answer:

The discount given on the cost of the meal is $15

Step-by-step explanation:

How to calculate tax on a given price

According to the question, we are given the following information

The original cost of the meal = $75

Off coupon = 20%

Required

The number of coupons given

coupon amount = 0.2 * 75

coupon amount = $15

Hence the discount given on the cost of the meal is $15

Answer:

About 0.1

Step-by-step explanation:

If you divide 7.35 by 63, you get about 0.1.

Answer:

[tex]m=\frac{6}{7}[/tex]

Step-by-step explanation:

[tex]m=\frac{10-4}{9-2}=\frac{6}{7}[/tex]

Answer:  [tex]\frac{6}{7}[/tex]

Explanation:

In the numerator we have [tex]y_2 - y_1 = 10-4 = 6[/tex] to represent the change in y, aka the rise. This is the vertical change. It's how much we go up.

The denominator has [tex]x_2 - x_1 = 9-2 = 7[/tex] to represent the run. It is the horizontal change, or how much we go to the right.

We go up 6 and to the right 7 to have a slope of [tex]m = \frac{\text{rise}}{\tex{run}} = \frac{6}{7}[/tex]

Here's how you can show the steps

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{10-4}{9-2}\\\\m = \frac{6}{7}\\\\[/tex]

Note: To write [tex]\frac{6}{7}[/tex] on the keyboard, you can type 6/7

Answer:

42 in

Step-by-step explanation:

The lengths of the tangent segments drawn from an external point to a circle are equal.

AT and RT meet at point T

⇒ AT = RT = 9 in

RE and GE meet at point E

⇒ RE = GE = 5 in

AN and NG meet at point N

⇒ AN = GN = 7 in

Total perimeter = AT + RT + RE + GE + GN + AN

                          = 9 + 9 + 5 + 5 + 7 + 7

                          = 42 in

Answer:

I'm not 100% sure but it might be b

Step-by-step explanation:

Answer:

some number increased by two: (E) b+2

A variable decreased by two: (D) x-2

Product of an unknown value and two (C) 2z

Quotient: (A) a / 2

An unknown value squared: (B) y2

Answer:

F= -4t+61

T= -1/4f + 61/4

Answer:

angle1=70

angle2=65

angle4=115

angle7=45

angel6=45

angle5=45

Step-by-step explanation:

110+angle1 = 180

angle1 =180-70

angle1 = 70

115+angle2=180

angle2=180-115

angle2=65

angle4=115 because lines are parallel

angle1+angle2+angle7=180 because triangle

70+65+angle7=180

135+angle7=180

angle7=180-135

angle7=45

angel6=45

angle5=45

Answer:

  30°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in any triangle is 180°. A right triangle has one angle that is 90°, so the sum of the remaining two acute angles is 180° -90° = 90°. That is, the acute angles in a right triangle are complementary.

__

The other acute angle is ...

  90° -60° = 30°

Applying the combination formula, the number of ways there are is: 66.

Combination is a technique in maths used in selecting objects from a group of objects in a way that the order in which they are selected does not matter.

Combination formula is given as:

[tex]nC_r = \frac{n!}{r(n - r)!}[/tex]

Given the following:

Plug in the values:

[tex]12C_2 = \frac{12!}{2(12 - 2)!}\\\\12C_2 = \frac{12!}{2(10)!}\\\\12C_2 = \frac{12 \times 11}{2(1)}[/tex]

[tex]\mathbf{12C_2 = 66}[/tex]

Therefore, applying the combination formula, the number of ways there are is: 66.

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Answer:

No solution

Step-by-step explanation:

(I am going to use substitution)

2x−10y=−2

y=x/5−1

(Substitute the y into the other problem)

2x - 10 (x/5 -1) = -2

2x - 2x + 10 = -2

10 = -2

No solution

Hope this helps :)

Answer:

the area of the rhombus is 56 square inches

Answers:

Area = 254.34 square feet

Circumference = 56.52 feet

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

Work Shown:

Area = pi*(radius)^2

A = pi*r^2

A = 3.14*9^2

A = 254.34 square feet

----------------

Circumference = 2*pi*(radius)

C = 2*pi*r

C = 2*3.14*9

C = 56.52 feet

The two results are approximate since pi = 3.14 is approximate.

1st area of circle:

[tex]\bold{\ area \ of \ circle \ : \pi r^2}[/tex]

[tex]\hookrightarrow \sf (3.14)(9)^2[/tex]

[tex]\hookrightarrow \sf 254.34 \ ft^2[/tex]

2nd circumference of circle:

[tex]\bold{circumference \ of \ circle \ : \ 2\pi r}[/tex]

[tex]\hookrightarrow \sf 2(3.14)(9)[/tex]

[tex]\hookrightarrow \sf 56.52 \ ft[/tex]

Answer:

hopefully this helps :] 16th line down I think

Answer:

Θ = 84°

Step-by-step explanation:

using the identity

cosx = sin(90 - x) , then

cos6° = sin(90 - 6)° = sin84°

that is Θ = 84°

Answer:

A. evaluate progress

Step-by-step explanation:

common sense