Which expression is equivalent to log5^(x/4)^2?

2log5(x) + log5(4)

2log5(x) + log5(16)

2log5(x) - 2log5(4)

2log5(x) - log5(4)

Answer:

–3, –9.6, –22.8

Step-by-step explanation:

Given rule is:

[tex]A(n) =-3+(n-1)(-2.2)[/tex]

So,

For first term:

[tex]A(1) =-3+(1-1)(-2.2)\\A(1) = -3 +0\\= 0[/tex]

For fourth term:

[tex]A(4) =-3+(4-1)(-2.2)\\=-3+(3)(-2.2)\\=-3+ (-6.6)\\=-3-6.6\\= -9.6[/tex]

For tenth term:

[tex]A(10) =-3+(10-1)(-2.2)\\=-3+(9)(-2.2)\\=-3+ (-19.8)\\=-3-19.8\\= -22.8[/tex]

The first, fourth and tenth terms are -3, -9.6 and -22.8 respectively.

So, third option is correct ..

Answer:

Step-by-step explanation:

6/2 evaluates to 3

Multiply x and 3

Multiply x and 1

The x just gets copied along.

The answer is x

x

6/2*x evaluates to 3x

x+6/2*x evaluates to 4x

x+6/2*x+5 evaluates to 4x+5

4x + x = 5x

The answer is 5x+5

x+6/2*x+5+x evaluates to 5x+5

To divide 1 by x

The x just gets copied along in the denominator.

The answer is

5/x evaluates to  

The answer is

x+6/2*x+5+x+5/x evaluates to  

5 + 3 = 8

The answer is

B

x+6/2*x+5+x+5/x+3 evaluates to  

The final answer is

B

Answer:

c=−35

Step-by-step explanation:

Let's solve your equation step-by-step.

−5=

c

7

Step 1: Simplify both sides of the equation.

−5=

1

7

c

Step 2: Flip the equation.

1

7

c=−5

Step 3: Multiply both sides by 7.

7*(

1

7

c)=(7)*(−5)

[tex]\frac{c}{7} = -5[/tex]

***I switched the order of c/7 and -5. It means the same thing, but I just find it easier this way

To solve for c you must isolate this by bringing 7 to the other side. To do this you must multiply 7 to both sides. This will cancel 7 from the left side (the right side in the way the equation is written in the question) and bring it over to the right side

[tex]7(\frac{c}{7} ) = -5 * 7[/tex]

c = -35

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

If you let b = x^2 the problem becomes a whole lot easier. Note that x = √b

x^2 + x - 12

Now factor this trinomial.

(x + 4)(x - 3)

Now put b back into the equation

(√b + 4)(√b - 3)

f(x) = x² - 6x - 1

To find the axis of symmetry, use the axis of symmetry formula: -b\2a, according to the Quadratic Equation y = Ax² + Bx + C. You understand?

Answer:

[tex]f(x) = x^2 - 6x -1[/tex]

Step-by-step explanation:

To find axis of symmetry we use formula

[tex]x=\frac{-b}{2a}[/tex]

[tex]f(x) = x^2 + 3x +1[/tex]

a=1, b=3

[tex]x=\frac{-3}{2}[/tex]

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

a=1, b=-3

[tex]x=\frac{3}{2}[/tex]

[tex]f(x) = x^2 + 6x + 3[/tex]

a=1, b=6

[tex]x=\frac{-6}{2}=-3[/tex]

[tex]f(x) = x^2 - 6x -1[/tex]

a=1, b=-6

[tex]x=\frac{6}{2}=3[/tex]

Answer:

Using digits it would look like 5,000,900

Answer:

Step-by-step explanation:

We have:

two triangles with base b = 6 and height h = 1

two rectangles with length l = 4 and width w = 2

one reactangel with length l = 6 and width w = 2.

The formula of an area of a triangle:

[tex]A_T=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_T=\dfrac{(6)(1)}{2}=3[/tex]

The formula of an area of a rectangle:

[tex]A_R=lw[/tex]

Substitute:

[tex]A_{R_1}=(4)(2)=8\\\\A_{R_2}=(6)(2)=12[/tex]

The surface area of the prism:

[tex]S.A.=A_T+A_T+A_{R_1}+A_{R_1}+A_{R_2}[/tex]

[tex]S.A.=3+3+8+8+12[/tex]

Answer:

QR

Step-by-step explanation:

KLMN is in the same spot as PQRS

Answer:

QR corresponds to LM

Step-by-step explanation:

Two figures are said to be similar if they have same shape but not necessarily same size.

Two polygons are said to be similar if their corresponding angles are equal and corresponding sides are proportional .

A trapezoid is a polygon in which a pair of sides is parallel .

Here, two trapezoids are given i.e KLMN, PQRS.

As KLMN and PQRS are similar, so their angles are equal i.e

[tex]\angle K=\angle P\,,\,\angle L=\angle Q\,,\,\angle M=\angle R\,,\,\angle N=\angle S[/tex]

Also, corresponding sides are proportional i.e

[tex]\frac{KL}{PQ}=\frac{LM}{QR}=\frac{MN}{RS}=\frac{KN}{PS}[/tex]

Therefore, side QR corresponds to LM.

Answer:

The value for c is B. 49

The number of the sides of the polygon will be 15. Then the correct option is A.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Each exterior angle of a regular polygon measures 24°.

Then the number of the sides of the polygon will be

Let n be the number of the sides. Then we have

360° / n = 24°

          n = 360° / 24°

          n = 15

Then the number of the sides of the polygon will be 15.

Then the correct option is A.

More about the polygon link is given below.

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Answer:

(3 (pm) sqrt(7))/2

Step-by-step explanation:

First step: Identify a,b, and c

a=2

b=-6

c=1

Second step: Find b^2-4ac (this is called the discriminant-I will call this D)

(-6)^2-4(2)(1)=36-8=28

Third step: Find the square root of the discriminant aka sqrt(D)

sqrt(28)

Let's see if we can simplify sqrt(28)

Here is there a factor of 28 that is a perfect square? How about 4? Yep!

sqrt(28)=sqrt(4)sqrt(7)=2sqrt(7).

Fourth Step: What is -b? If b=-6 then -b=6.

Fifth step: What is 2a?  2(2)=4

So the formula is

x=(-b (pm) sqrt(D))/(2a)

or

x=(step4 (pm) step 3)/(step 5)

x=(6 (pm) 2sqrt(7))/4

Simplify

x=(3 (pm) sqrt(7))/2

*pm means plus or minus

*sqrt( ) means square root of the number that follows in the ( )

Answer:

Just took it!

Step-by-step explanation:

Answer:

HJ

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

so

The slope of the line that is parallel to a line that has a slope of 3 is equal to 3

Verify the slope of the blue and red line , because their slopes are positive

Blue line

we have

C(-3,0),D(3,2)

The slope m is equal to

m=(2-0)/(3+3)

m=2/6

m=1/3

Red line

we have

H(-1,-4),J(1,2)

The slope m is equal to

m=(2+4)/(1+1)

m=6/2

m=3

therefore

The answer is the red line HJ

Answer: x=40

Step-by-step explanation:

The solution to log (25x) = 3 is 40. This is calculated by using log rules.

A function that has log terms is said to be a logarithmic function.

Some of the rules for solving log functions are as follows:

Given that,

log (25x) =3

Using basic form [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex]

Here base b=10, m=25x and n=3

Then,

log (25x) =3

⇒ [tex]25x = 10^3[/tex]

⇒ 25x = 1000

⇒ x = 1000/25

∴ x = 40.

Hence the solution of the given function is 40.

Learn more about logarithmic functions here:

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Answer: x=4y+9

Step-by-step explanation:

All of the variables, 3x, 12y, and 27 can be divided y 3, so we will simplify by dividing the whole equation by 3.

3x/3-12y/3=27/3

Which is equal to....

x-4y=9

Now you can move -4y over to the right side by changing its sign...

x=4y+9

Let the equation be 3x - 12y = 27 then, the value of x = 9 + 4y.

Given: 3x - 12y = 27

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Solve the value of x, then

Add 12y to both sides

3x - 12y + 12y = 27 + 12 y

Simplifying the above equation, we get

3x = 27 + 12y

Divide both sides by 3, then we get

[tex]$\frac{3 x}{3}=\frac{27}{3}+\frac{12 y}{3}$$[/tex]

Therefore, the value of x = 9 + 4y.

To learn more about the value of x

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Answer:

3x - 20 = 13

Step-by-step explanation:

it says difference so it cant be the last one and three times a number is 3 x so it cant be the first one leaving the middle.

please mark brainliest

Answer:

d = 28 cm

r = 14 cm

Step-by-step explanation:

Circumference = Pi × Diameter

( Divide both sides by Pi )

Circumference ÷ Pi = Diameter

28 ÷ π = Diameter

Diameter = 28

Radius = Half the diameter

28 ÷ 2 = 14

Answer:

3 vowel in the word and theres 6 letters so 50% 3/6

Step-by-step explanation:

Answer:

the answer is 12.

Step-by-step explanation:

the explanation is in the image above

Hope this helps

Answer:

17.41

Step-by-step explanation:

497.50 x 0.035

Jodi's investment will earn $17.41 in interest in one year at an interest rate of 3.5%. Therefore, after one year, her investment will be worth $514.91.

To find out how much Jodi's investment is worth in one year, we can use the formula for simple interest, which is Interest = Principal x Rate x Time. In this case, the principal is $497.50, the rate is 3.5% (or 0.035 in decimal form), and the time is 1 year.

So, the interest earned in one year would be $497.50 x 0.035 x 1 = $17.41.

To find the total worth of her investment after one year, we add the interest earned to the initial principal. So, $497.50 (the principal) + $17.41 (the interest) = $514.91. Therefore, her investment is worth $514.91 after one year.

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The histogram would change due to the different distribution of ages when all 20 students join the same event.

A histogram is a graphical representation of the distribution of numerical data. It consists of bars, where the length or height of each bar corresponds to the frequency or relative frequency of data within a specific interval or range. Histograms provide insights into data patterns and distributions.

The histogram would change when all 20 students join the same event compared to the original because the distribution of ages would be different. The original histogram would show the number of students participating in each event, while the new histogram would show the number of students in each age group. The new histogram would have different bars representing each age group, and the heights of these bars would be determined by the number of students in each age group.

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Answer:

[tex]\frac{1}{2} z[/tex]

Step-by-step explanation:

Answer:

X=12

Step-by-step explanation:

3(80-9x)=X-96 Distribute 3 through the parenthesis

240-27x=x-96

Move the variable to the left side and change its sign

Move constant to the right side and change its sign

-27x-x+240=-96

collect the like terms

calculate the difference

-28x=-336

Divide both sides of the equation by -28

x=12

Answer:

(2,4)

Step-by-step explanation:

The range is the y values

y = x+5

Let y=7

7 =x+5

Subtract 5

7-5 x+5-5

2=x

Let y= 9

Subtract 5

9-5 x+5-5

4=x

The domain is (2,4)

Answer:

A. Multiplicative Inverse Property

X=1

Step-by-step explanation:

First, you do is multiply fractions from left to right.

[tex]\frac{2*3}{3*2}x=1[/tex]

Then, you can cancel the fraction out.

Common factor term of 2.

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

Divide the numbers.

[tex]\frac{3\div3=1}{3\div3=1}=1[/tex]

[tex]x*1=1[/tex]

X=1 is the correct answer.

Multiplicative Inverse Property is the correct answer.

Answer:

A

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 14 and h = 4, hence

A = [tex]\frac{1}{2}[/tex] (14 × 4) = 28

Answer:

360 and 60.

Step-by-step explanation:

Let Christopher earns x amount of money and y be money earned by Michael.

Firstly, Christopher has six times as much money as Michael so,

x=6y........ (i)

If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael so,

x+60=3(y+80)

From (i),

6y +60= 3(y+80)

3(2y+20)=3(y+80)

2y+20=y+80

2y-y=80-20

y=60

Substituting value of y in equation (i),

x=6×60=360.

Therefore, Christopher earned 360 and Michael earned 60.

Final answer:

Initially, Michael has $60, and Christopher has $360. After Michael earns $80 and Christopher earns $60, Michael will have $140, and Christopher will have $420.

Explanation:

Let's denote Christopher's initial amount of money as C and Michael's initial amount of money as M.

According to the given information, Christopher has six times as much money as Michael: C = 6M.

When Michael earns $80, and Christopher earns $60, Christopher will then have three times as much money as Michael: C + $60 = 3(M + $80).

Now we can solve these two equations together:

C = 6M

C + $60 = 3(M + $80)

Substitute the expression from the first equation into the second equation:

6M + $60 = 3(M + $80)

6M + $60 = 3M + $240

Combine like terms:

6M - 3M = $240 - $60

3M = $180

Divide both sides by 3:

M = $60

Use the value of M to find C:

C = 6M = 6 × $60

C = $360

Now, adding their respective earnings:

Michael's new total: $60 + $80 = $140

Christopher's new total: $360 + $60 = $420

Answer:

The radius of the base is [tex]r=6.3\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=288\ in^{3}[/tex]

[tex]h=7\ in[/tex]

[tex]\pi=3.14[/tex]

substitute and solve for r

[tex]288=\frac{1}{3}(3.14)r^{2} (7)[/tex]

[tex]864=(3.14)r^{2} (7)[/tex]

[tex]r^{2}=864/[(3.14)(7)][/tex]

[tex]r=6.3\ in[/tex]

Answer:

the domain is from -5 to infinity

Step-by-step explanation:

f(x+5)+3=√x+5  +3

x+5>0

x>-5

the domain is from -5 to infinity

Answer:

A. {x | x > –5}

the greater than sign should be greater than or equal to

Answer:

w=32

Step-by-step explanation:

w/4 = 8

4/1 * w/4 = 8*4

w=32

Answer:

2

Step-by-step explanation:

The median is the middle. The middle of 5 numbers is the third number. the list goes through 12235 so the median is 2