Solve: log2(x-4) = 4

ANSWER

The solution is (2,1)

EXPLANATION

The given equations are:

2x+4y=8...(1)

3x-5y=1...(2)

We make x the subject in the first equation to get:

2x=8-4y

This means that,

x=4-2y...(3)

Put equation (3) into equation (2)

3(4-2y)-5y=1

Expand:

12-6y-5y=1

-6y-5y=1-12

-11y=-11

y=1

Put y=1 into equation (3).

x=4-2(1)=2

The solution is (2,1)

Answer:

There were 40 student tickets sold.

Step-by-step explanation:

First I set up equations to represent this situation.

4x+3y=380

x+y=105

x represents the adult tickets and y represents the student tickets.

I can solve this with the elimination method. I want to cancel out the x so I will multiply every term in equation 2 by -4.

4x+3y=380

-4x-4y=-420

Now I combine like terms.

-y=-40

I can divide the negative one from both sides.

y=40

40 Tickets sold.

Thank me later.

Answer:

B. Data set X is not linear, and data set Y is linear.

Step-by-step explanation:

We assume here that "form a pattern" means "roughly forms a line"... because a pattern doesn't necessarily equal a line, it would be a curve that would easily be interpreted too, but it wouldn't be linear.

Since you cannot form a pattern, and based on your choices for answer, we have have to say that data set X is NOT linear.

On the opposite, since the data set Y produces a pattern, it has to be linear.

So, X = NOT linear, Y = linear.

Answer:

(Data set x is linear, and data set y is not linear.) This is the correct answer 100%...

When i put the answer in from the other person which was (x is not linear, and y is linear) it said incorrect and gave me this answer x is linear, and y is not linear. So be careful what you put down.

Step-by-step explanation:

Answer:

[tex]-4[/tex]

Step-by-step explanation:

The given logarithmic equation is:

[tex]\log_7(x+1)+\log_7x=\log_712[/tex]

Recall and apply product rule of logarithms.

[tex]\log_aM+\log_aN=\log_aMN[/tex]

We apply this property to the left side of the equation to get;

[tex]\log_7x(x+1)=\log_712[/tex]

We take the antilogarithm of both sides to get:

[tex]x(x+1)=12[/tex]

We expand to obtain:

[tex]x^2+x=12[/tex]

We rewrite in the standard quadratic form:

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

We factor to obtain:

[tex](x-3)(x+4)=0[/tex]

Either [tex](x-3)=0[/tex] or [tex](x+4)=0[/tex]

Either [tex]x=3[/tex] or [tex]x=-4[/tex]

But the domain is[tex]x\:>\:0[/tex].

Hence [tex]x=-4[/tex] is an extraneous solution.

Answer:

True

Step-by-step explanation:

The area of a regular polygon is found by multiplying 1/2 times the apothem times the perimeter.  The area for a single triangle is 1/2 times the height (which is the same as the apothem of a regular polygon) times the base (which is one of the sides of the regular polygon which you are multiplying by  to find the perimeter of the polygon).

Answer:

The given statement is true.

Step-by-step explanation:

The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas.

This is true.

Breaking down in 7 triangles and adding separately the areas of these triangles, will give the complete area of the heptagon. We can also find the area of one triangle and multiply that by 7 to get the same result.

Answer:

  68

Step-by-step explanation:

[tex]a_2=2a_1+4=2\cdot 5+4=14\\\\a_3=2a_2+4=2\cdot 14+4=32\\\\a_4=2\cdot 32+4=68[/tex]

  a₄ = 68

_____

The explicit formula is

  an = 9·2^(n-1) -4

ANSWER

y = 3x + 6.50

EXPLANATION

The $3 for each downloaded movie is the unit rate of change.

This is represent the slope of the linear function that models this situation.

The monthly fee of monthly fee of $6.50 the constant rate.

It represents the y-intercept of the function.

The linear function is given by

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

The correct choice is y = 3x + 6.50

the answer would be C. y = 3x + 6.50, for every movie you buy (which is x), they would be 3$. therefore it would be 3x, and the monthly fee would just be added with that. :P

Answer: 8 2/3

Step-by-step explanation:

[tex]

f(4)=5\times(\frac{1}{2})^4 \\

f(4)=\frac{5\times1^4}{2^4} \\

f(4)=\boxed{\frac{5}{16}}

[/tex]

Hope this helps.

Brainliest would be great.

For this case we have a function of the form[tex]y = f (x)[/tex]

Where:

[tex]f (x) = 5 * (\frac {1} {2}) ^ x[/tex]

We must find the value of the function when x = 4, that is, f (4):

Substituting we have:

[tex]f (x) = 5 * (\frac {1} {2}) ^ 4\\f (x) = 5 * \frac {1} {2} * \frac {1} {2} * \frac {1} {2} * \frac {1} {2}\\f (x) = 5 * \frac {1} {16}\\f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]

ANswer:

[tex]f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]

Answer:

[tex]0.4n+0.1n^2\ miles[/tex]

Step-by-step explanation:

The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is [tex]a_1=0.5.[/tex]

Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, then the difference of the arithmetic sequence is [tex]d=0.2.[/tex]

The nth term of the arithmetic sequence can be found using formula

[tex]a_n=a_1+(n-1)d,[/tex]

hence

[tex]a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.[/tex]

The total distance after Miguel has trained n times can be found using formula

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n,[/tex]

thus, the total distance is

[tex]S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=\dfrac{0.8+0.2n}{2}\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.[/tex]

Answer:

First answer is C. (0.3+0.2K)

Second one is 15 Times

Step-by-step explanation:

Answer on EDG hope it helps :)

Answer:

y = -2x + 5.

Step-by-step explanation:

The general form is y = mx + b where m = the slope and b = the y-intercept.

So here m = -2 and b = 5 so our equation is:

y = -2x + 5.

ANSWER

Quadrant I

EXPLANATION

In the first quadrant all the trigonometric ratios are positive.

This implies that,both tanθ and secθ are positive in the first quadrant.

No two trigonometric ratios are positive in any other quadrant apart from the first quadrant.

Answer:

qaud I

Step-by-step explanation:

Answer:

d. a=1. b=2, c=3

multiply by the Reciprocal.

Answer:

D

Step-by-step explanation:

(5/8) / (3/8)

(5/8) * (8/3)

5/3

1 ⅔

a = 1, b = 2, c = 3

Answer D.

A flat circular plate has the shape of the region x 2 + y 2 ≤ 1. points on the plate have temperature t(x, y) = x 2 + 2y 2 − x. find the temperatures of the hottest and coldest points of the plate

a) The amount after 2 years with continuous compounding is approximately $6539.48.

b) It will take approximately 2.32 years for the amount to reach $8000 with continuous compounding.

a) To calculate the amount after 2 years with continuous compounding, you can use the formula:

[tex]A = P \times e^{rt}[/tex]

Where:

A = the amount after time 't'

P = the principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = the interest rate (as a decimal)

t = the time in years

Given that P = $5800, r = 6% (0.06 as a decimal), and t = 2 years, we can now calculate the amount (A):

[tex]A = 5800 \times e^{0.06 \times 2}[/tex]

[tex]A=5800 \times e^{0.12}[/tex]

[tex]A=5800 \times 1.1275[/tex]

A=6539.48

Hence,  the amount after 2 years is approximately $6539.48.

b) To find how long it takes for the amount to be $8000, we need to solve for 't' in the formula:

[tex]A = P \times e^{rt}[/tex]

Given that A = $8000 and P = $5800, we can rearrange the formula:

[tex]e^{rt}=\frac{A}{P}[/tex]

[tex]e^{0.06t}=\frac{8000}{5800}[/tex]

Take logarithms on both sides:

[tex]0.006t=log(\frac{8000}{5800})[/tex]

[tex]0.006t=0.139[/tex]

t=0.139/0.06

t=2.327

Hence, it takes 2.32 years for the amount to be $8000.

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After 2 years, the investment grows to approximately $6498.78. It will take around 5.37 years for the investment to grow to $8000.

We can use the formula for continuously compounded interest, which is A = Pe^(rt), where P is the principal amount ($5800), r is the interest rate (6% or 0.06), t is the time, and e is the mathematical constant approximated as 2.71828.

a) To find the amount after 2 years, sub in $5800 for P, 0.06 for r, and 2 for t to get: A = $5800 * e^(0.06*2). Evaluating this gives approximately $6498.78.

b) To find out when the amount will be $8000, we set A to $8000 and solve for t, getting: t = ln($8000 / $5800) / 0.06. Evaluating this gives approximately 5.37 years.

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ANSWER

B.

[tex]112\pi \: {units}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated using the formula:

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

where r=4 units is the base radius of the cone.

and h=21 units is the vertical height of the cone.

We plug in the values to get;

[tex]Volume = \frac{1}{3} \times \pi \times {4}^{2} \times 21[/tex]

[tex]Volume = 112\pi \: {units}^{3} [/tex]

Answer:

The correct answer is option B.  112π units ³

Step-by-step explanation:

Formula

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here radius r = 4 units

Height h = 21 units

Volume = (πr²h)/3

= (π * 4² * 21)/3

= 112π units ²

Therefore the correct answer is option B.  112π units ³

Answer: 3421.19

Step-by-step explanation:

look up cylinder formula and r= radius which is just the diameter cut in half

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 3421.1944 cm³.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Given the diameter of the cylinder is 22 cm, therefore, the radius of the cylinder is 11cm, Also, given the height of the cylinder is 9 cm.

The volume of the cylinder = πR² × H

                                             = π × (11cm)² × 9cm

                                             = 1089π cm³

                                             = 3421.1944 cm³

Hence, the volume of the cylinder is 3421.1944 cm³.

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Answer:

Your salary will be $62,500.

Step-by-step explanation:

This is an arithmetic sequence with first term $45,000 and common difference $2,500.

The appropriate formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is a counter and d is the common difference.

In this particular case, a(8) = $45,000 + (8-1)($2,500) = $62,500

Your salary will be $62,500.

A function assigns the values. Your salary after completing the 8th year within the company will be $62,500.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the starting salary will be $45,000 while the salary will increase every year by $2,500. Therefore, the function that can represent the salary after (n-1) years can be written as,

y = $45,000 + $2,500(n-1)

Now, the salary after 8th year will be,

y = $45,000 + $2,500(n-1)

y = $45,000 + $2,500(8-1)

y = $62,500

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Answer:

Second Option

[tex]a=1.46[/tex]

Step-by-step explanation:

The triangle of the figure is a straight triangle.

We know the length of the hypotenuse, h = 2, and we know the angle A = 43°. We need to find the length a. Side a is the side adjacent to the 43° angle

By definition we know that

[tex]cosx = \frac{adjacent}{hypotenuse}[/tex]

Then

adjacent = a

hypotenuse  =2

x =43°

[tex]cos(43\°) = \frac{a}{2}[/tex]

[tex]a= 2cos(43\°)[/tex]

[tex]a= 1.46[/tex]

Answer:

it is the third one (from left to right)

Step-by-step explanation:

no explation

Answer:

11.6 cm²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of sector - area of triangle

area of sector = area of circle × fraction of circle

                       = π × 9.28² ×[tex]\frac{68.9}{360}[/tex] ≈ 51.78 cm²

area of triangle = [tex]\frac{1}{2}[/tex] × 9.28 × 9.28 × sin68.9°

                         = 0.5 × 9.28² × sin68.9 ≈ 40.17 cm²

Area of shaded region = 51.78 - 40.17 ≈ 11.6 cm²

he would hove to work 20 hours to meet the second job I think

To make the same total earnings at the first job as the second job (including benefits), Phillip would have to work an additional 4 hours (to account for the $100 benefits). If the workdays are 8 hours each, then for every two days (which is 16 hours) worked at job 2, Phillip would need to work an additional 4 hours at job 1, summing up to 20 hours.

This problem is about comparing the earnings from the two jobs. For the second job, Phillip earns $20 per hour and also gets benefits equivalent to $100 per pay period.

If Phillip wants to earn the same amount in the first job (which does not offer any benefits), we calculate how many hours he would need to work to earn an additional $100 (the value of the benefits).

To do this, we divide $100 (benefits of the second job) by the first job's hourly pay rate ($25) which results in 4 hours.

So, Phillip must work an additional 4 hours to make up for the benefits. Meaning, for any given number of hours he would work at the second job, he would need to work an extra 4 hours at the first job to get the same total earnings.

Therefore, the right answer is not among the choices given because we have an extra step to add to each option. If we consider a standard 8-hour workday, working at the second job for two days gives 16 hours with an additional $100 for benefits. To make the same in the first job, Phillip would need to work, 16 hours (from the second job) + 4 hours (to compensate for the $100 benefits) = 20 hours.

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I believe the answer is d. 156,029

I think the answer is D

Answer:

y = 2 x - 1

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

When x = 1 , y= 1

x = 2 , y=3

Answer:

The three integers are 13,14,15

Step-by-step explanation:

Let x be the first integer

x+1 be the second integer

x+2 be the third integer

The sum of the three integers is 42

x+ (x+1) + (x+2) = 42

Combine like terms

3x+3 = 42

Subtract 3 from each side

3x+3-3 = 42-3

3x= 39

Divide by 3

3x/3 = 39/3

x = 13

x+1 = 14

x+2 = 15

The three integers are 13,14,15

Answer:

96in^2

Step-by-step explanation:

because first find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Example: The surface area of a rectangular prism 5 cm long, 3 cm.

Answer:

96

Step-by-step explanation:

Did quiz

Answer:

sandals costed $32.55

Step-by-step explanation:

Final answer:

To find the cost of the sandals, subtract the cost of the T-shirt from the total cost. The equation 8.95 + c = 41.50 leads to c = 32.55, meaning the sandals cost $32.55.

Explanation:

The question asks us to find the cost of sandals that Tina bought, given the total cost of a T-shirt and the sandals combined, and the cost of the T-shirt alone. To solve for the cost c of the sandals, we start with the equation 8.95 + c = 41.50. We then isolate c by subtracting 8.95 from both sides of the equation:

c = 41.50 - 8.95

c = 32.55

Therefore, the cost of the sandals was $32.55.

The answer is:

The missing step is the step shown in the last option:

D. [tex]324=0.042x+16[/tex]

To find which is the missing step, we need to remember that to cancel a square root, we need to elevate it, so:

Starting from the last step before the missing step, we have:

[tex]-18=-\sqrt{0.042x+16}[/tex]

In order to calculate the value of the variable (x) we need to square both sides of the equation, since squaring a root will cancel the root.

We must remember the following properties:

[tex]\sqrt{a^{m} }=a^{\frac{m}{2}}\\\\(a^{b})^{c}=a^{b*c}[/tex]

Now, finding the missing step, we need to find what to do in order to get the expression of the following step.

So, squaring both sides of the equation in order to cancel the square root and isolate the variable, we have:

[tex]-18=-\sqrt{0.042x+16}\\\\(-18)^{2} =(-\sqrt{0.042x+16})^{2} \\324=0.042x+16\\324-16=0.042x\\\\x=\frac{304}{0.042}=7333[/tex]

Hence, we found the the missing step is:

D. [tex]324=0.042x+16[/tex]

Have a nice day!

Answer:

The fourth graph (last graph)

Step-by-step explanation:

Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:

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

[tex](x-1)(x+4)=0[/tex]

[tex]x-1=0,x+4=0[/tex]

[tex]x=1,x=-4[/tex]

Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.

Since both x values inside the parenthesis are positive, our parabola is opening upwards.

The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.

We can conclude that the graph of [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.

ANSWER

See attachment.

EXPLANATION

The given function is

f(x) = (x – 1)(x + 4).

This parabola will open upwards because the leading coefficient is positive.

The x-intercepts can be found by equating the function to zero.

[tex](x - 1)(x + 4) = 0[/tex]

By the zero product property;

[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]

This implies that,

[tex]x = 1 \: or \: x = - 4[/tex]

The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.

The correct choice is D.

Answer: Permutation; number of ways = 120

Step-by-step explanation:

Answer with explanation:

Number of runner= 5

Number of Distinct Medal = 5

First Medal can be Awarded in 5 ways, second Medal can be awarded in 4 ways and third Medal can be awarded in 3 ways , fourth medal can be awarded in 2 ways and fifth Medal can be awarded in one way.

So, total number of ways =5 × 4×3×2×1=120 way

⇒We will use the concept of Permutation as there are five distinct medal and five different runners

So, Five distinct places can be filled in 5! or [tex]_{5}^{5}\textrm{P}[/tex] ways as order of arrangement is Important because any of the five candidates can win first second, third , fourth or fifth Prize.  

= 5!=5×4×3×2×1=120 ways

Because, n!=n×(n-1)×(n-2)×........1.