Consider the equation 5(10)^(z/4)=32 Solve the equation for z, express the solution as a logarithm in base-10

Answer:

B only

Step-by-step explanation:

well to solve this question we can consider factor theorem which states that if a Polynomial f(x) is divided by a monomial x-a then x-a is a factor of f(x) if and only if f(a)=0

and to figure "a " we can consider the following equation:

[tex] \displaystyle x - a = 0[/tex]

substitute the given value of a:

[tex] \displaystyle x - 2= 0[/tex]

therefore,

[tex] \displaystyle x = 2[/tex]

plugin the value of x to the function A(x):

[tex] \displaystyle A(2) = {2}^{3} + {2}^{2} + 4[/tex]

simplify which yields:

[tex] \displaystyle A(2) = 16[/tex]

since A(2)≠0 x-2 is not a factor of A(x)

similarly substitute the value of x to the function B(x) which yields:

[tex] \displaystyle B(2) = {2}^{3} - {2}^{} - 6[/tex]

simplify:

[tex] \displaystyle B(2) =0[/tex]

so, B(2)=0 Hence x-2 is a factor of x³-x-6

substitute the value of x to the function C(x)

[tex] \displaystyle C(2) = {2}^{4} + 3.{2}^{} - 10[/tex]

simplify:

[tex] \displaystyle C(2) =12[/tex]

as C(2)≠0 x-2 is not a factor of C(x)

likewise plugin the value of x to the function D(x):

[tex] \displaystyle D(2) = {2}^{4} - 2.{2}^{3} - 2[/tex]

simplify and that yields:

[tex] \displaystyle D(2) = - 2[/tex]

therefore,D(2)≠0 hence,x-2 isn't a factor of D(-2)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

The factor

we have find the value of x .

Now,

we have to select all the polynomial which has x-2 As a factor.

According to the question,

[tex]A(x)=x^3+x^2+4\\\\A(2)=(2)^3+(2)^2+4\\\\=8+4+4\\\\16≠0[/tex]

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

[tex]C(x)=x^4+3x-10\\\\=C(2)=(2)^4+3(2)-10\\\\=16+6-10\\\\12≠0[/tex]

[tex]D(x)=x^4-2x^3-2\\\\D(2)=(2)^4-2(2)^3-2\\\\=16-16-2\\\\-2≠0[/tex]

The option B is correct.

Answer:

both substitutions

Step-by-step explanation:

in 5. based on 3 BC is substituted by its equal counterpart AB.

and in 6. we use 1. to substitute AC by its associated absolute value.

Answer:

3 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 1/2 * 3/2 * 4

V = 3 cm^3

Answer:

3 cm³

Step-by-step explanation:

V = L * W * H

V = (4 cm)(3/2 cm)(1/2 cm)

V = 12/2 * 1/2 cm³

V = 12/4 cm³

V = 3 cm³

Answer:

10 degrees = C

Step-by-step explanation:

Total internal angles add to 180 degrees.

Add all values of c and set equal to 180.

18c = 180.

c=10

Answer:

c = 10

Step-by-step explanation:

3c + 6c + 9c = 180 degrees. Every triangle has 180 degrees.

18c = 180                Combine the like terms. Divide by 18

18c/18 = 180/18

c = 10

Answer:

the 3rd won for sure

Step-by-step explanation:

hope I helped

Answer:

C

Step-by-step explanation:

The coordinates are all in (x, y) form.

X is how left or right

y is how tall.

If you just look for the individual coordinates given, you will see that all of the Coordinates in C are on the graph.

I hope this helps!

Answer:

I think SAS is the correct Ans

Answer:

[tex]x=opposite\: side\: of \:22[/tex]

[tex]16=hypotenese[/tex]

[tex]sin22=opp/hyp[/tex]

[tex]sin22=\frac{x}{16}[/tex]

[tex]\Longrightarrow x=16\times sin22[/tex]

[tex]x=5.99[/tex]

[tex]x=6.0[/tex]

[tex]OAmalOHopeO[/tex]

Answer:

100998 is the answer.

I hope this help u.

Answer:

100998

Step-by-step explanation:

₁ ₁ ₁ ₁ ₁

99999

+   999

100998

you can also think of it as

99999(+1) + 999(-1)

100000+998

100998

Answer:

I think its B.

Step-by-step explanation:

sorry if i am wrong.

Answer:

(A). x² + y² - 4x + 6y - 3 = 0

Step-by-step explanation:

(x - 2)² + (y + 3)² = 4²

x² - 4x + 4 + y² + 6y + 9 - 16 = 0

x² + y² - 4x + 6y - 3 = 0

AB: 20

BC: 12

AC: 16

AD: 10

DE: 6

AE: 8

Answer:

if the village is of 120 people and  120 people are over the age of 60 then 0 people are under the age of 25.

Step-by-step explanation:

Answer:

3(a +3)

Step-by-step explanation:

(a+3)^2 -a(a+3)

FOIL

a^2 +3a+3a+9 -a(a+3)

Distribute

a^2 +3a +3a +9 -a^2 -3a

Combine like terms

3a +9

FACTOR out a+3

(a+3)( a+3 -a)

(a+3) (3)

3(a+3)

Answer:

3(a+3)

Step-by-step explanation:

Expand the first set of brackets first

(a+3)^2

A^2 + 3a + 3a +9

=A^2 + 6a + 9

Expand the second set of brackets

-a(a+3)

=-a^2 - 3a

Add both sets together

3a + 9

Factorise:

3(a+3)

Answer:

T = 55 + 6w and $103

Step-by-step explanation:

We have already saved $55, so that is our constant. We gain $6 per week, so that will be our w value

T = 55 + 6w

Solving for T when w = 8 weeks

T = 55 + 6(8)

T= 55 + 48

T = $103

Answer:

I think its 1.4

Step-by-step explanation:

if you divide 42 by 1.4 it makes 30 and if u multiply 30 by 1.4 it makes 42

Answer:

the scale factor is 7/5

Step-by-step explanation:

42/30=

42/30=

then you find a common factor between the two is 6, so you divide both sides of the fraction by 6 to get 7/5. and because they both are the same you know that they both have the same scale factor. Which is 7/5. I am not quite sure if you need to find the missing side length but in case you do multiply 40 by 7/5 so it looks like 40/1 x 7/5. 40 x 7 = 280. 280/5 = 56. so your side length is 56.

Answer:

-611.031 < μd < 4260.031

Step-by-step explanation:

This is a matched pair design :

______Day1 Day 2 Day 3 Day 4

x1 Kill room 3175 2526 1763 1090

x2 Processing 529 141 362 224

First we obtain the difference, d ;

d = (x1 - x2)

d = 2646, 2385, 1401, 866

The mean difference, dbar = Σd/ n = 7298 / 4 = 1824.5

The standard deviation of difference,

Sd = √(Σx-dbar)²

Using calculator, Sd = 834.086

The 99% confidence interval :

Mean ± margin of error

dbar ± margin of error

Margin of Error = Tcritical * Sd/√n

Tcritical at 99%, df = n-1 ; df = 4-1 = 3

Tcritical = 5.84

Margin of Error = 5.84 * 834.086/√4 = 2435.53112

Confidence interval = 1824.5 ± 2435.53112

(-611.031 ; 4260.031)

Answer:

Yes.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Any line that follows slope-intercept form will be a function.

If we graph this line, we can see that each x-value has its own y-value and it passes the vertical line test.

∴ y = 0.860x + 3.302 is indeed a function.

Answer:

x= plus or minus 1 plus imaginary root times square root of 5.

Step-by-step explanation:

[tex] {x}^{2} - 2x + 6 = 0[/tex]

Complete the Square.

[tex] {x}^{2} - 2x = - 6[/tex]

[tex] {x}^{2} - 2x + 1 = - 5[/tex]

[tex](x - 1) {}^{2} = - 5[/tex]

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

Answer:

[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]

Answer: 7.25

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{x = -4}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3x - 5 = 5x + 3\\-----------\\\rightarrow 3x - 5 + 5 = 5x + 3 + 5\\\\\rightarrow 3x = 5x + 8\\\\\rightarrow 3x - 5x = 5x - 5x +8\\\\\rightarrow -2x = 8\\\\\rightarrow \frac{-2x=8}{-2}\\\\\rightarrow \boxed{x = -4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x=10

Step-by-step explanation:

16/24=(x-2)/12

or, 16/2=x-2

or, 8=x-2

or, x-2=8

or, x=10

Answered by GAUTHMATH

Answer:

[tex]\frac{(x+2)}{(x-1)}[/tex]

Step-by-step explanation:

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

[tex]\frac{(x+2)(x-1)}{(x-2)(x-1)}[/tex] =

[tex]\frac{(x+2)}{(x-1)}[/tex]

Answer:

(A)

x= 5y-3

(x+3)/5

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

i took the test lol

Answer:

Step-by-step explanation:

7

Answer:

it would be

D.

(7,-4)

Mark me as brainliest pleases

Answer:

it would be A (-7,-4)

Step-by-step explanation:

Answer:

75°

Step-by-step explanation:

First, we need to know that the interior angle sum of a triangle is always 180°.

Now, to find the missing angle aside from x, we need to complete the sum 180-155=25, seeing 155° lies on a straight line. Remembering the interior angle sum of a triangle is always 180°, it is thus clear that 25+80+x=180. If we complete this equation, x=75.

Hope this helps!

Answer:

32

Step-by-step explanation:

Green : black

3             4

We have 24 green

3+8=24

so  multiply each side by 8

Green : black

3*8         4*8

24            32

There are 32 black grapes

Answer:

32

Step-by-step explanation:

By Question :-

Let :-

Therefore,

Answer:

∠ 6 = 55°

Step-by-step explanation:

∠ 6 and 125° are same- side interior angles and sum to 180° , then

∠ 6 = 180° - 125° = 55°