Need help on this!!!

Answer:

x = 3, x = 9

Step-by-step explanation:

When solving this problem, keep the general format of a logarithm in mind:

[tex]b^x=y\\log_b(y)=x[/tex]

Where, (b) represents the base, (x) is the exponent, and (y) is the evalutaor. Please note that others might use slightly different terminotoly than what is used in this answer.

One is given the following expression, and is asked to solve for the parameter (x);

[tex]log_5(x-4)=1-log_5(x-8)[/tex]

First, manipulate the exquestion such that all of the logarithmic expressions are on one side. Use inverse operations to do this.

[tex](log_5(x-4))+(log_5(x-8))=1[/tex]

Now use the Logarithmic Base Change rule to simplify. The Logarithmic Base Change rule states the following;

[tex]log_b(x)=\frac{log(x)}{log(b)}[/tex]

Remember, if no base is indicated in a logarithm, then the logarithm's base is (10). Apply the Logarithmic Base Change rule to this problem;

[tex]\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1[/tex]

Now remove the denominator. Multiply all terms in the equation by the least common denominator; ([tex]log(5)[/tex]) to remove it from the denominator on the left side.

[tex](\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1)*(log(5))[/tex]

[tex]log(x-4)+log(x-8)=log(5)[/tex]

All logarithms have the same base, the left side of the equation has the addition of logarithms. This means that one can apply the Logarithm product rule. The logarithm product rules the following;

[tex]log_b(x*y)=(log_b(x))+(log_b(y))[/tex]

This rule can be applied in reverse to simplify the left side of the equation. Rather than rewriting the product of logarithms as two separate logarithms being added, one can rewrite it as one logarithm getting multiplied.

[tex]log(x-4)+log(x-8)=log(5)[/tex]

[tex]log((x-4)(x-8))=log(5)[/tex]

Now used inverse operations to bring all of the terms onto one side of the equation:

[tex]log((x-4)(x-8))=log(5)[/tex]

[tex]log((x-4)(x-8))-log(5)=0[/tex]

Similar to the Logarithm product rule, the Logarithm quotient rule states the following;

[tex]log_b(x/y)=(log_b(x))-(log_b(y))[/tex]

One can apply this rule in reverse here to simplify the logarithms on the left side:

[tex]log((x-4)(x-8))-log(5)=0[/tex]

[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]

The final step in solving this equation is to use the Logarithm of (1) property. This property states the following:

[tex]log_b(1)=0[/tex]

When applying this property here, one can conclude that the evaluator must be equal to (1), therefore, the following statements can be made.

[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]

[tex]\frac{(x-4)(x-8)}{5}=1[/tex]

Inverse operations,

[tex]\frac{(x-4)(x-8)}{5}=1[/tex]

[tex](x-4)(x-8)=5[/tex]

[tex](x-4)(x-8)-5=0[/tex]

Simplify,

[tex](x-4)(x-8)-5=0[/tex]

[tex]x^2-12x+32-5=0[/tex]

[tex]x^2-12x+27=0[/tex]

Factor, rewrite the quadratic expression as the product of two linear expressions, such that when the linear expressions are multiplied, the result is the quadratic expression:

[tex]x^2-12x+27=0[/tex]

[tex](x-3)(x-9)=0[/tex]

Now use the zero product property to solve. The zero product property states that any number times (0) equals (0).

[tex]x=3,x=9[/tex]

Hello,

I suppose the question is solve for x.

[tex]\displaystyle log_5\ (a)=\dfrac{ln (a)}{ln (5)} \\\\log_5(x-4)=1-log_5(x-8)\\\\\dfrac{ln(x-4)}{ln(5)} =1- \dfrac{ln(x-8)}{ln(5)}\\\\ln(x-4)=ln(5)-ln(x-8)\\\\ln(x-4)+ln(x+8)=ln(5)\\\\ln((x-4)*(x-8))=ln(5)\\\\(x-4)*(x-8)=5\\\\x^2-12x+27=0\\\\\Delta=12^2-4*27=36=6^2\\\\x=9\ or\ x=3\\\\Sol=\{3,9\}\\[/tex]

For Moderators,

this is a mathematical resolution without any bla-bla sentences that you will easily find. (I can not do it sorry)

Answer:

565.2cm³

Step-by-step explanation:

the radius= 6/2= 3 cm

the height= 20cm

the volume= 3.14× 3²×20

= 3.14×180= 565.2 cm³

Check the picture below.

its the third choice

(-4)+12+(-20)

= 12 + (-24)

= -12

Answer:

-12

Step-by-step explanation:

The solution is in the picture ^_^ I hope it helps

Answer:

k = 5/3

x = 21

Step-by-step explanation:

Here, we have two similar shapes

The scale factor here would be the ratio of the corresponding similar sides

so we have k as 15/9 = 5/3

To find the value of x

When two shapes are similar, the ratio of the sides corresponding are equal

So we have it that;

x/35 = 9/15

= 15 * x = 9 * 35

15x = 315

x = 315/15

x = 21

Answer:

Step-by-step explanation:

We'll start with going form exponential to radical, since it may be easier to follow. For example,

[tex]x^{\frac{4}{3}[/tex] can be written, in radical form, as

[tex]\sqrt[3]{x^4}[/tex]. What happens is that the denominator of the fraction serves as the index (the number that sits in the bend of the radical) and the numerator serves as the power on the variable (or number, if that's the case). Let's look at another one:

[tex]4^{\frac{2}{3}[/tex] becomes

[tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]

And you can go the other way with it. For example,

[tex]\sqrt[5]{x^4}[/tex] becomes

[tex]x^{\frac{4}{5}[/tex], etc. Get it?

Answer:

When you're given a problem in radical form, you may have an easier time if you You can rewrite every radical as an exponent by using the following property — the top ... For example, 643/2 is easier if you write it as (641/2)3 = 83 = 512 rather than (643)1/2,  Rewrite the entire expression using rational exponents.

Answer:

m(x)

Step-by-step explanation:

Given:

The equation is:

[tex]3-2|0.5x+1.5|=2[/tex]

One solution of this equation is -2.

To find:

The another solution of the given equation.

Solution:

We have,

[tex]3-2|0.5x+1.5|=2[/tex]

It can be written as:

[tex]-2|0.5x+1.5|=2-3[/tex]

[tex]-2|0.5x+1.5|=-1[/tex]

Divide both sides by -2.

[tex]|0.5x+1.5|=0.5[/tex]

After removing the modulus, we get

[tex]0.5x+1.5=\pm 0.5[/tex]

Case I:

[tex]0.5x+1.5=0.5[/tex]

[tex]0.5x=0.5-1.5[/tex]

[tex]0.5x=-1[/tex]

Divide both sides by 0.5.

[tex]x=-2[/tex]

Case II:

[tex]0.5x+1.5=-0.5[/tex]

[tex]0.5x=-0.5-1.5[/tex]

[tex]0.5x=-2[/tex]

Divide both sides by 0.5.

[tex]x=-4[/tex]

One solution of the given equation is [tex]x=-2[/tex] and the another one is [tex]x=-4[/tex].

Therefore, the correct option is B.

Answer:

22°

Step-by-step explanation:

180° - 158° = 22°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

[tex]\$3,125[/tex]

Step-by-step explanation:

Let [tex]s[/tex] represent the amount of money he initially started with.

After he spent 20% on books, he will have [tex]100\%-20\%=80\%[/tex] of his initial money left. We can represent this as [tex]0.8s[/tex].

Following that, the boy spends 20% of the remainder of his money on food. Similarly, he will have [tex]100\%-20\%=80\%[/tex] of the remainder of money he had left after he purchased the books. Therefore, he ends up with [tex]0.8(0.8s)=0.64s[/tex] of his money left.

Since we're given that he had $2,000 after all these transactions, we have the following equation:

[tex]0.64s=\$2,000[/tex]

Divide both sides by 0.64 to isolate and solve for [tex]s[/tex]:

[tex]s=\frac{2,000}{0.64}=\boxed{\$3,125}[/tex]

Therefore, the boy had $3,125 to begin with.

Answer:

2800

Step-by-step explanation:

20%+20%=40%

40/100x2000=2800

Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you

Answer:

[tex]-----------[/tex]

hope it helps...

have a great day!!

Answer:

[tex] {x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)( {x}^{2} - 1)[/tex]

Answer:

Step-by-step explanation:

eq. of line with slope m and intercept 3 is

y=mx+3

∵ it passes through (10,53)

53=10m+3

10m=53-3=50

m=50/10=5

y=5x+3

so standard form of eq. is

5x-y+3=0

or

5x-y=-3

Answer:

Step-by-step explanation:

[tex]\frac{14}{4}*\frac{33}{10}=\frac{7}{2}*\frac{33}{10}\\\\ =\frac{7*33}{2*10}\\\\=\frac{231}{20}\\\\=11\frac{11}{20}[/tex]

Answer:

they exceeded their goal by 668 cans.

Step-by-step explanation:

multiplying 524 by 7 you get 3668, then subtracting 3,000 from that you get 668.

Answer:

Step 3

Step-by-step explanation:

Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?

Given :

4(x - 1/5) = 2 2/3

Open the bracket

4x - 4/5 = 2 2/3

Add 4/5 to both sides

4x - 4/5 + 4/5 = 8/3 + 4/5

Lcm of 3 and 5 = 15

4x = (40 + 12) / 15

4x = 40/15 + 12/15

4x = 52/15

Multiply by 1/4

4x * 1/4 = 52/15 * 1/4

x = 52 / 60

x = 13 / 15

Hence, the error is in step 3

15/5 * 3 = 12

Rather ; Leonardo wrote 16

Answer:

c) 25 cm^2

d) 52.5 cm^2

Step-by-step explanation:

5*2 = 1

10/2 = 5

40/2 = 20

20+5 = 25

This is just scratch work^

Answer:

(10, - 1 )

Step-by-step explanation:

Given the 2 equations

x - 3y = 13 → (1)

x + 2y = 8 → (2)

Rearrange (1) making x the subject by adding 3y to both sides

x = 3y + 13 → (3)

Substitute x = 3y + 13 into (2)

3y + 13 + 2y = 8

5y + 13 = 8 ( subtract 13 from both sides )

5y = - 5 ( divide both sides by 5 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = 3(- 1) + 13 = - 3 + 13 = 10

solution is (10, - 1 )

Answer:

[tex]{ \bf{15x + 30 = 180}}[/tex]

Answer:

D

Step-by-step explanation:

because 3x - 12y = 15 has only numbers that are divisible by 3 leaving just one single x term, and the other terms simply reduce their used numbers to still integer numbers (4 and 5).

this makes it easier to be used in the other equation.

[tex]\displaystyle\bf \left \{ {{y=-2x+4} \atop {y=-\frac{1}{3} x-1}} \right. => \\\\\\-2x+4 =-\frac{1}{3}x -1\\\\-\frac{5}{3} x=-5\\\\\boxed{x=3\quad ; \quad y=-2}[/tex]

Answer:

-2 = -2

Step-by-step explanation:

You need to substitute the values of y and x.

(X,Y) =

(3, -2)

y= - 2x + 4

-2= -2(3) +4

-2= - 6 + 4

-2=-2

y= - 1/3x - 1

-2= - 1/3 (3) - 1

-2 = -1 -1

-2 = -2

The answer is  -2 = -2, so this means that both equations are true

Answer:

X would be 63.9

Hope it helps

Step-by-step explanation:

The value of the variable 'x' using the cosine formula will be 63.9 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of 'x' is given by the cosine of the angle ∠QSR. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have

cos 35° = x / 78

x = 63.9

The value of the variable 'x' using the cosine formula will be 63.9 units.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

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Answer:

the side XY

Step-by-step explanation:

we know 2 angles in a triangle. but are 45 degrees.

that means the third angle Z is 180-45-45 = 90 degrees.

the side opposite of the largest angle is the longest side.

opposite of Z is the side XY.

Answer:

I believe this would be the answer?

Step-by-step explanation:

{2, 3, 4, 6, 8, 9, 10, 12}

Answer:

B: g(x) = -4(x + 3)^2

Step-by-step explanation:

When we shift to the left by a units

we have the new equation become

( x + 3)^2

Stretching by a factor of 4, we have it that;

4(x + 3)^2

reflecting over the x-axis means the y-axis value becomes negative

So we have

g(x) = -4(x + 3)^2

Step-by-step explanation:

there is something wrong with what your write here as problem description.

either there is something missing in the main expression, or in the answer options.

given your nth-term expression 7n-2, none of the 4 answer options can fit.

so, I thought, maybe there was a typo.

the possible interpretations of the expression could be

7n - 2

7(n-2)

[tex] {7}^{n} - 2[/tex]

[tex] {7}^{n - 2} [/tex]

we know that

a1 = 1

a2 = either

a1 + 2 = 3

a1 - 2 = -1

a1 + 7 = 8

a1 - 7 = -6

so, we can eliminate both negative answer options, because they would cause only negative sequence elements, but the main expression (neither of the 4 possibilities) does not allow that.

but also none of the 4 possibilities of the expression delivers any of the 4 values for a2 as described above.

7×2 - 2 = 14 - 2 = 12

7(2-2) = 7×0 = 0

7² - 2 = 49 - 2 = 47

[tex] {7}^{2 - 2} = {7}^{0} = 1[/tex]

similar not for a3.

so, if I consider your answer options right, we have 4 possible arithmetic sequences:

1. 1, 3, 5, 7, 9, 11, 13, 15, ...

2. 1, -1, -3, -5, -7, -9, -11, -13, ...

3. 1, 8, 15, 22, 29, 36, 43, 50, ...

4. 1, -6, -13, -20, -27, -34, -41, ...

the nth term expression is for

a. an = 2n - 1

b. an = 2×(-n) + 3 = 2×(-n + 1) + 1

c. an = 7n - 6

d. an = 7×(-n) + 8 = 7×(-n + 1) + 1

so, please pick the right expression from this list, and then use the answer option with the same letter.

Answer:

x=24 y=131

Step-by-step explanation:

it is right answer

Answer:

x = 24, y = 131

Step-by-step explanation:

The sum of the 3 angles in Δ ABC = 180°

Sum the 3 angles and equate to 180

72 + 35 + 25 + 2x = 180 , that is

2x + 132 = 180 ( subtract 132 from both sides )

2x = 48 ( divide both sides by 2 )

x = 48

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

Similarly in the lower triangle

25 + x + y = 180

25 + 24 + y = 180

49 + y = 180 ( subtract 49 from both sides )

y = 131

Answer:

a=1

Step-by-step explanation:

Hopefully this helps :)

The equation of the parabola is: y = (x - 2)² - 2. Finding the value of A

The vertex of the parabola is at (2,-2). Since the parabola opens upward, the equation of the parabola will be of the form:

y = A(x - 2)² - 2

We can plug the point (3,-1) into this equation to find the value of A.

-1 = A(3 - 2)² - 2

Simplifying the right side of the equation, we get:

-1 = A - 2

Adding 2 to both sides of the equation, we get:

1 = A

Therefore, the value of A is 1.

Writing the equation of the parabola

The equation of the parabola is:

y = (x - 2)² - 2

To know more about parabola:

https://brainly.com/question/11911877

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