Help Help Help Help Help Help Help Help Help Prove the divisibility of the following numbers: 10^9+10^8+10^7 by 555

Answer:

[tex]\displaystyle z = 4\, \log_{10} \left(\frac{32}{5}\right)[/tex].

Step-by-step explanation:

Multiply both sides by [tex](1/5)[/tex] and simplify:

[tex]\displaystyle \frac{1}{5} \times 5\, (10)^{z/4} = \frac{1}{5} \times 32[/tex].

[tex]\displaystyle (10)^{z/4} = \frac{32}{5}[/tex].

Take the base-[tex]10[/tex] logarithm of both sides:

[tex]\displaystyle \log_{10}\left(10^{z/4}\right) = \log_{10} \left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle \frac{z}{4} = \log_{10}\left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle z = \log_{10}\left(\frac{32}{5}\right)[/tex].

Answer:

Graph A

Step-by-step explanation:

Answer:

x² - x - 12 = 0

Step-by-step explanation:

Given the x- intercepts are x = - 3 and x = 4 , then the factors are

(x + 3) and (x - 4)

Expressing as a zero product

(x + 3)(x - 4) = 0 ← expand using FOIL

x² - x - 12 = 0

Answer:

Step-by-step explanation:

Mean of the data = sum of the data / number of frequencies:

Correct choice is d

Step-by-step explanation:

Right now, we would solve everything within the parenthesis first.

(8 - 16) + (8 + 6)

(-8) + (14)

14 - 8

6

But if we remove the parenthesis, it doesn't matter what order we do things in.

8 - 16 + 8 + 6

8 + 8 - 16 + 6

16 - 16 + 6

6

The reason why both of these are the same, is because the only calculations we're doing are addition and subtraction, which don't care about parenthesis.

Answer:

A

Answer:

Step-by-step explanation:

[tex]tan \ 83.1 = \frac{opposite \ side}{adjacent \ side} = \frac{BC}{100}\\\\8.2635 = \frac{BC}{100}\\\\8.2635*100=BC\\\\826.35 = BC[/tex]

Height of tower = 826.35 m

A recursive relation is a relation that defines the terms in a sequence with the previous terms.

Here, the recursive relation will be:

[tex]A_n = 2*A_{n - 1} + $50[/tex]

A₁ = $150.

We know that:

Sarah has saved $150 at the moment.

She wants to double the amount that she saves each month, so the next month she needs to save 2*$150 = $300

And if she saves the $300, then her grandma will give her another $50.

Then, if the previous month Sarah saved A, then the next month she will get the double of A plus $50, which is:

2*A + $50

Then the recursive relation is just:

[tex]A_n = 2*A_{n - 1} + $50[/tex]

Where Aₙ is the amount that she saves in the n-th month, and the first term of the sequence is the initial amount that she saved, so we have:

A₁ = $150.

If you want to learn more about recursive relations you can read:

https://brainly.com/question/13143285

Answer:

9

Step-by-step explanation:

r/3  +5 ≤ 8

Subtract 5 from each side

r/3  +5 -5≤ 8-5

r/3   ≤ 3

Multiply each side by 3

r/3  *3 ≤ 3*3

r   ≤ 9

The only value that is less than or equal to 9 is 9

Answer:

x = -124

Step-by-step explanation:

89-x=213

Subtract 89 from each side

89-x -89=213-89

-x = 124

Multiply each side by -1

x = -124

Step-by-step explanation:

89-x=213

89-213=x

x= -124

hope this helps

Answer:

sinx

Step-by-step explanation:

the shape of the graph shows a sine graph, which is usually denoted by asinbx+c

a is amplitude/2 = 2/2 = 1

b is the period, 360 = 360/b, b=1

since the graph starts at (0,0), c =0

hence, this graph is 1sin1x = sinx

The equation is y = sin(x)

Answer:

254.5

Step-by-step explanation:

Area = πr²

= π×9²

= 81π

= 254.5 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

C

Step-by-step explanation:

We know that the first integer will be "l" so the second will be l + 1, third will be l + 2, fourth will be l + 3, and the fifth will be l + 4. The question says "the greatest is g" so that means that the fifth integer is the greatest meaning that is the value of g. Now that we know the value of g, we can substitute it into the equation they gave us and simplify.

l+(l+4)/2

2l+4/2

l + 2

Best of Luck!

Answer:

C

Step-by-step explanation:

say your 5 consecutive numbers are 6-10

if 6 is l and 10 is g then

6+10 over 2 equals 8

this proves that l+2 is correct since 6+2=8

Answer:

[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]

Step-by-step explanation:

We want to find a formula for s in terms of a, b, and cos(x).

Let the point where s intersects AB be D.

Notice that s bisects ∠C. Then by the Angle Bisector Theorem:

[tex]\displaystyle \frac{a}{BD} = \frac{b}{AD}[/tex]

We can find BD using the Law of Cosines:

[tex]\displaystyle BD^2 = a^2 + s^2 - 2as \cos x[/tex]

Likewise:

[tex]\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x[/tex]

From the first equation, cross-multiply:

[tex]bBD = a AD[/tex]

And square both sides:

[tex]b^2 BD^2 =a^2 AD^2[/tex]

Substitute:

[tex]\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)[/tex]

Distribute:

[tex]a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x[/tex]

Simplify:

[tex]b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x[/tex]

Divide both sides by s (s ≠ 0):

[tex]b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x[/tex]

Isolate s:

[tex]b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x[/tex]

Factor:

[tex]\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x[/tex]

Therefore:

[tex]\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}[/tex]

Factor:

[tex]\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}[/tex]

Simplify. Therefore:

[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]

Answer:

Step-by-step explanation:

The volume is:

[tex]\\ \rm\Rrightarrow Volume=Area\:of\;base(Height)[/tex]

[tex]\\ \rm\Rrightarrow Volume=\dfrac{1}{2}Base\times Height \times Height\:of\;Prism[/tex]

[tex]\\ \rm\Rrightarrow Volume=\dfrac{1}{2}(8)(7)(11[/tex]

[tex]\\ \rm\Rrightarrow Volume=4(7)(11)[/tex]

[tex]\\ \rm\Rrightarrow Volume=28(11)[/tex]

[tex]\\ \rm\Rrightarrow Volume=308cm^3[/tex]

Answer:

[tex]17x-23=1/2\times81[/tex]

[tex]17x-23=40.5[/tex]

[tex]17x=40.5+23[/tex]

[tex]17x=63.5[/tex]

[tex]x=63.5/17[/tex]

[tex]x=3.73[/tex]

OAmalOHopeO

Answer:

Hello! the answer is CD is 17,0 (-2,19)

Answer:

Note that LHS means left-hand side and RHS means right-hand side.

Step-by-step explanation:

LHS = sin⁴a + sin²a cos²a

= sin²a (sin²a + cos²a)

At this point, you can use the identity sin²a + cos²a = 1,

= sin²a (1)

= sin²a

= RHS (Proved)

Answer:

Step-by-step explanation:

[tex]\Large \boldsymbol{} \sin^4a+\sin^2a \cos^2a=\sin^2a \\\\\sin^2a(\underbrace{\sin^2a+\cos^2a}_1) =\sin^2a \\\\\sin^2a\cdot 1=\sin^2a \\\\\sin^2a=\sin^2a[/tex]

Answer:  3

Step-by-step explanation:                                                                                                          

[tex]\displaystyle\ \Large \boldsymbol{} We \ have \ a \ square\ function \\\\ f(x)=ax^2+bx+c \\\\And \ we \ know \\\\ \left[\left \[ {{f(0)=a\cdot 0+b\cdot0+c=0} \atop {f(-4)=a(-4)^2+-4b+c=-24}} \right.=>[/tex]                                                [tex]\displaystyle\ \Large \boldsymbol{} \left[ \ {{c=0} \atop {16a-4b=-24}} \right. =>\boxed{4a-b=-6} \\\\\\ and \ x_0 =-\frac{b}{2a}=1 =>\boxed{ b=-2a} \\\\\\ \left \{ {{4a-b=-6} \atop {b=-2a}} \right. =>4a+2a=-6=> a=-1 \ ; \ b=2 \\\\\\then \ b-a=2-(-1)=\boxed{3}[/tex]                                                                                    

Step-by-step explanation:

3x+5+x-25=180°

4x=180°+20

x=50

Because m and n are parallel, we can use the supplementary angles theorem. This means that the two angles add up to equal 180°.

Knowing this, we can add the two angles together and they should equal 180:

(3x + 5) + (x - 25) = 180

4x - 20 = 160

4x = 160

x = 40

If needed, to find the angle measures, we can just plug in our x value to find the measures of the angles.

Answer:

x=4

Step-by-step explanation:

f(x) = x^2 - 8x+16

Set equal to zero

0 = x^2 -8x +16

Factor

what 2 numbers multiply to 16 and add to -8

-4*-4 = 16

-4+-4 = -8

0= (x-4)(x-4)

Using the zero product property

x-4 = 0  x-4 =0

x=4  x=4

Answer:

-2

Step-by-step explanation:

The output of the chart and graph drops by 2 for every input.

Answer:

X⁴–X²–2X –1=0

(X²+X+1)(X²–X–1)=0

[tex]x = - \frac{1 - i\sqrt{3} }{2} \\ x = - \frac{ 1 + i \sqrt{3} }{2} [/tex]

[tex]x = \frac{1 + \sqrt{5} }{2} \\ x = \frac{1 - \sqrt{5} }{2} [/tex]

I hope I helped you^_^

Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.

✧ Let us assume :

Seena's age be x

Her mother's age be 4x

✧ After 5 years :

Seena's age = x + 5

Her mother's age = 4x + 5

✧ Ratio of age after 5 years :

Seena's mother = 3

Seena's ratio = 1

Hence, the equation is :

[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]

By cross multiplying we get

[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]

[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]

[tex] \looparrowright \frak{x = 10}[/tex]

Hence, the ages are

Seena's age = x = 10 yrs

Her mother's age = 4x = 4 × 10 = 40 years

∴ Seena's age is 10 and her mother's is 40 respectively

Answer:

Option D, 13.2

Step-by-step explanation:

m = √{7×(18+7)}

= √(7×25)

= 5√7

= 13.2 (rounded to the nearest tenth)

Answer:

33.4

Step-by-step explanation:

tan50 = x/28

x =28tan50 = 33.3691 = 33.4 (nearest tenth)

Answer:

The parallel line is y = 1/7 x - 1  

hope this helps!

Answer:

41

Step-by-step explanation:

The absolute value means take the non-negative number

|-41| = 41