What are the solutions to this equation?


(x−4)^2=49



The solutions are x =
or x =
.

f(t) = 2283·(30069/2283)^(t/40) . . . . . t = years after 1960

In simplest terms, the exponential function can be written from the initial value, the ratio of given values, and the time period over which that ratio was effective. The form is ...

... f(t) = (initial value) · (ratio of values)^(t/(time period))

This works for both increasing and decreasing exponentials.

_____

Using e as a base

It can be converted to an exponential with "e" as the base by taking logarithms.

ln(f(t)) = ln(2283) + (t/40)·ln(30069/2283) = ln(2283) + 0.06445011·t

Taking antilogs, this is ...

... f(t) = 2283·e^(0.06445011·t)

_____

Comment on accuracy

The final number (30,069) when including cents (30,069.00) has 7 significant digits. In order to get the function f(t) to reproduce that number to 7 significant digits, the multiplier of t in the exponential function must be accurate to 7 significant digits. (Fairly commonly, you will see it rounded to 2 or 3 significant digits. It cannot give 30069 even to 5 digits in that case.)

Answer:

Row 2

Step-by-step explanation:

To find the mean, we add all the numbers and divide by the number of numbers

Row 1:  

(6+5+3+0+4)/5 = 18/5 = 3.6

Row 2:  

(4+5+3+5+6)/5 = 23/5 = 4.6

Row 3:  

(7+1+4+5+3)/5 = 20/5 = 4.0

Row 4:  

(4+2+5+6+3)/5 = 20/5 = 4.0

The greatest mean , or the largest mean is 4.6  or Row 2

Answer:

The answer is B) Row 2

Step-by-step explanation:

If you need any help with this question please ask me! :)

Answer:

After 15 month of membership, Brian will pay $164.5 and Seth will pay $100.

Step-by-step explanation:

Brian

y=9.50(15)+22

y=142.5+22

y=164.5

Seth

(15,100)

Answer:

a. 0.2981

Step-by-step explanation:

We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Let us find z-score for 260 days.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]x[/tex] = Sample score,

[tex]\mu[/tex] = Mean  

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{260-268}{15}[/tex]    

[tex]z=\frac{-8}{15}[/tex]  

[tex]z=-0.53[/tex]  

Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.  

From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.

Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.

Answer:

D

Step-by-step explanation:

Because it's saying what is the shape of the "Square" inside of the cylinder.

Answer:

C) rectangle, would be the best answer beacuse the shape of the dotted line clously resembles a rectangle

Step-by-step explanation:

Answer:

[tex]13\frac{1}{3}[/tex] cups

Step-by-step explanation:

We are told that a recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B.      

To find the number of cups of ingredient B we will use proportions.

[tex]1\frac{2}{3}=\frac{5}{3}[/tex]

[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{\frac{1}{2}}{\frac{5}{3}}[/tex]

[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]  

Now let us substitute our amount of Ingredient A =4 in our proportions.

[tex]\frac{4}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]

[tex]\frac{\text{Number of cups of ingredient B}}{4}=\frac{10}{3}[/tex]

Multiplying both sides of our equation by 4.

[tex]4*\frac{\text{Number of cups of ingredient B}}{4}=4*\frac{10}{3}[/tex]

[tex]\text{Number of cups of ingredient B}=\frac{40}{3}[/tex]

[tex]\text{Number of cups of ingredient B}=13\frac{1}{3}[/tex]

Therefore, we need [tex]13\frac{1}{3}[/tex] cups of ingredient B to make our recipe.

Answer:

Proportion states that the  two ratios are equal.

Given statement: A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A.

By using proportion definition to find ingredients B;

[tex]\frac{\frac{1}{2} }{1\frac{2}{3} } = \frac{4}{B}[/tex]

Simplify:

[tex]\frac{\frac{1}{2} }{\frac{5}{3}} = \frac{4}{B}[/tex]

By cross multiply we get;

[tex]B \cdot \frac{1}{2} = 4 \cdot \frac{5}{3}[/tex]

or

[tex]\frac{B}{2} = \frac{20}{3}[/tex]

Multiply both sides by 2 we get;

[tex]B = \frac{20}{3} \times 2 = \frac{40}{3} = 13\frac{1}{3}[/tex]

Therefore, [tex]13\frac{1}{3}[/tex] cups of ingredients B needs.

Answer:

Similar rectangles states that the corresponding sides are in proportion.

As per the statement:

Rectangle ABCD is similar to rectangle WXYZ.

WX = 8 feet, AD = 12 feet and WZ = 16 feet.

Since. Rectangle ABCD and rectangle WXYZ are similar

then;

their corresponding sides are in proportion:

[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]

To find the value of AB:

[tex]\frac{AB}{WX}=\frac{AD}{WZ}[/tex]

Substitute the given values we have;

[tex]\frac{AB}{8}=\frac{12}{16}[/tex]

Multiply both sides by 8 we have;

[tex]AB = \frac{12}{16} \times 8 = \frac{96}{16}=6[/tex]

Therefore, the value of AB is 6 units.

The value of AB in the similar rectangles ABCD and WXYZ, given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, is calculated as 6 feet by using the property of similar rectangles that the ratios of their corresponding sides are equal.

The subject in question deals with similar rectangles. Since rectangle ABCD is similar to rectangle WXYZ, the ratio of their corresponding sides will be equal. This means that the ratio of side AB to side WX should be the same as the ratio of side AD to side WZ.

Given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, we can set up the proportion as AB/WX = AD/WZ. Substituting the known values into this proportion we get AB/8 = 12/16.

To find the value of AB, we can cross multiply and solve for AB to get AB = (8 * 12) / 16 = 6 feet.

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Answer:

Correct choice is A

Step-by-step explanation:

If a function has an inverse, then there is at most one x-value for each y-value.

The tangent function is periodic with period [tex]\pi.[/tex] Hence, at each value for which [tex]f(x)=\tan x[/tex] is defined, [tex]f(x+n\pi )=\tan x[/tex] for each integer n. Therefore, the function [tex]f(x)=\tan x[/tex] does not have an inverse. Since tangent is not a one-to-one function, the domain must be limited. From examining the graph of the tangent function, we see that in each interval of the form

[tex]\left((2k−1)\dfrac{\pi}{2},(2k+1)\dfrac{\pi}{2}\right)[/tex]

where k is an integer, the tangent function assumes every value in its range. Moreover, in each such interval, each y-value is achieved exactly once. Hence, we can create an invertible function by restricting the domain tangent function to one such interval. Such interval is an interval between two consecutive vertical asymptotes [tex]x=(2k−1)\dfrac{\pi}{2}[/tex] and [tex]x=(2k+1)\dfrac{\pi}{2}.[/tex]

Answer:

The rate of change is 1 mile per hour per month

Step-by-step explanation:

We are given

initial speed = 3 mph

final speed =6 mph

total number of months =3

now, we can use rate of change formula

we know that

rate of change = ( final speed - initial speed)/(total number of months)

now, we can plug values

and we get

Rate of change is

[tex]=\frac{6-3}{3}[/tex] mph per month

=1 mph per month

Jason's rate of change in biking speed is 1 mile per hour per month.

Jason is training for a marathon bike ride. His average speed increases from 3 miles per hour to 6 miles per hour in 3 months. To find the rate of change in the miles per hour that Jason bikes, we use the formula:

Rate of Change = (Final Speed - Initial Speed) / Time Period

The final speed is 6 miles per hour, the initial speed is 3 miles per hour, and the time period is 3 months. Therefore:

Rate of Change = (6 - 3) mph / 3 months

Rate of Change = 3 mph / 3 months

Rate of Change = 1 mph per month

Therefore, Jason's rate of change in biking speed is 1 mile per hour per month.

Answer:

62 kg: A

Step-by-step explanation:

The black line is called line of best fit. This line shows the points plotted and how they compare to the predicted amounts. The reason why A is the correct answer is because all of the other blue points line up with the line of best fit. Since the point 62kg is NOT on the line of best fit, that is the point where experimental error may have occurred.

1) [tex]x+2=\sqrt{3x+10}[/tex]

Square both sides to get

[tex](x+2)^2=(\sqrt{3x+10})^2\implies x^2+4x+4=3x+10\implies x^2+x-6=0[/tex]

Factorize and solve:

[tex]x^2+x-6=(x+3)(x-2)=0\implies x=-3,x=2[/tex]

2) I assume we take [tex]\sqrt x[/tex] to be defined only for [tex]x\ge0[/tex]. Under this condition, a solution would be extraneous if [tex]\sqrt{3x+10}[/tex] is undefined, which happens if [tex]3x+10<0[/tex].

If [tex]x=-3[/tex], then [tex]3x+10=-9+10=1[/tex], so it is not extraneous.

If [tex]x=2[/tex], then [tex]3x+10=6+10=16[/tex], so it is not extraneous.

So there are not extraneous solutions to this equation.

3) Lots of information on this on the web...

The solution for the given equation is x=2. -3 is an extraneous solution caused by the squaring operation and it doesn't satisfy the original equation. An extraneous solution is a solution that does not satisfy the original equation.

To find the solution of the equation x+2=√(3x+10), we first square both sides to eliminate the square root: (x+2)2=3x+10.

This simplifies down to x2 + 4x + 4=3x+10. Rearranging terms then gives us x2 + x - 6=0. The solutions of this quadratic equation are x=2 and x=-3.

However, if we substitute x=-3 back into the original equation, it does not hold true. Thus, -3 is an extraneous solution. This extraneous solution arises in this case because we applied the squaring operation, which is not a reversible process. An extraneous solution, generally, is a solution to a transformed equation that does not satisfy the original equation.

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Final answer:

Mark solved 90% of the problems correctly on his math quiz, calculated by dividing 18 (correct answers) by 20 (total questions) and then multiplying by 100%.

Explanation:

To calculate the percent of problems Mark solved correctly on his math quiz, we use the formula for percentages, which is: (Number of items of interest ÷ Total number of items) × 100%

In this case, Mark solved 18 out of 20 problems correctly. So, we set up the calculation as follows:

(18 ÷ 20) × 100% = 0.9 × 100% = 90%

Therefore, Mark got 90% of the problems correct on his quiz.

Answer:

The total number of people at the movie theatre is 700.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

At the movie theatre 30% of the audience members were children.

If the number of children at the movie theatre was 210.

Percentage = 30%

Part value =  210

Put in the formula

[tex]30 = \frac{210\times 100}{Total\ value}[/tex]

[tex]Total\ value = \frac{21000}{30}[/tex]

Total value = 700

Therefore the total number of people at the movie theatre is 700.

Answer:

-60 3/4m

Step-by-step explanation:

The diver first dives down 50 1/4m, which is represented by the -50 1/4m. He then descends another 10 1/2m down. So -50 1/4m - 10 1/2m.

-50-10=-60

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

(1/4+1/2)=(2/8+4/8) you can only add with the same denominators.

=6/8 (simplifies down to 3/4)

Start with a line segment connecting two points, A and B. [tex]\dfrac{DA}{BA}=3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\dfrac{DB}{BA}=2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\dfrac{AB}{CB}=\dfrac12[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let [tex]d[/tex] be the length of AB. Then the length of CD in terms of [tex]d[/tex] is [tex]4d[/tex]. We have the coordinates of C and D, and the distance between them is [tex]\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2[/tex]. So

[tex]4d=4\sqrt2\implies d=\sqrt2[/tex]

The slope of the line through C and D is

[tex]\dfrac{0-4}{4-0}=-1[/tex]

and so the equation of the line through these points is

[tex]y-4=-(x-0)\implies x+y=4[/tex]

So the coordinates of A are [tex](x,y)=(x,4-x)[/tex]. The distance between C and A is [tex]d=\sqrt2[/tex], so we have

[tex]\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1[/tex]

Since A falls to the right of C (in the [tex]x,y[/tex] plane, not just in the sketch), we know to take the positive value [tex]x=1[/tex]. Then the [tex]y[/tex] coordinate is [tex]y=4-1=3[/tex].

All this to say that A is the point (1, 3), so

[tex]2x+y=2+3=5[/tex]

The value 2x + y of  is 5.

Start with a line segment connecting two points, A and B. [tex]\frac{DA}{BA} =3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\frac{DB}{BA} =2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\frac{AB}{CB} =\frac{1}{2}[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let  be the length of AB. Then the length of CD in terms of  is . We have the coordinates of C and D, and the distance between them is

[tex]\sqrt{(4-0)^2+ (4-0)^2} =4\sqrt{2}[/tex]

So

4d= 4√2 = d= √2

The slope of the line through C and D is

[tex]\frac{0- 4}{4-0} = -1[/tex]

and so the equation of the line through these points is

y- 4 = -(x- 0) =x + y =0

So the coordinates of A are (x, y) = (x,4 -x). The distance between C and A is d= √2, so we have

[tex]\sqrt{(x-0)^2+(4- x - 4)^2} = \sqrt{2x^3} = |x| \sqrt{2} = \sqrt{2} = |x| = 1[/tex]

Since A falls to the right of C (in the x, y plane, not just in the sketch), we know to take the positive value . Then the  coordinate is .

All this to say that A is the point (1, 3), so 2x + y= 2+3=5

for such more question on coordinates

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Question

Let us have four distinct collinear points a, b, c, and d on the cartesian plane. the point c is such that [tex]\dfrac{ab}{cb} = \dfrac{1}{2}[/tex] and the point d is such that [tex]\dfrac{da}{ba} = 3[/tex] and [tex]\dfrac{db}{ba} = 2[/tex] c = (0, 4), d = (4, 0), and a = (x, y), what is the value of 2x + y?

Answer:

The vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].

Step-by-step explanation:

The given function is

[tex]f(x)=4+x^2-2x[/tex]

The vertex form is

[tex]f(x)=(x-h)^2+k[/tex]

Rewrite the given function

[tex]f(x)=(x^2-2x)+4[/tex]

[tex]-\frac{b}{2a}=-\frac{-2}{2(1)}=1[/tex]

Add and Subtract [tex](-\frac{b}{2a})^2[/tex].

[tex]f(x)=(x^2-2x+1)+4-1[/tex]

Use [tex](a-b)^2=a^2-2ab+b^2[/tex]

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

Therefore the vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].

Answer: A on Edge 2020

Step-by-step explanation:

Answer:

About 4

Step-by-step explanation:

Answer: B: 3 Days

Step-by-step explanation:

Let x be the number of days when Jack and Emily have the same amount of money.

Then, the total amount saved by Jack =4x+55

The total amount saved by Emily  = 13x+28

According to the question,

13x + 28 = 4x + 55

13x - 4x = 55 - 28

9x = 27

x = 3

Brainiest PLZ

Answer:

3

Step-by-step explanation:

To have full outfits he can only make three

Answer:

she can make 12: A

Step-by-step explanation

add up the numbers of pants, shoes , shirts you will get 12

i think that its is w,k,j. i could be wrong though

There was no increase. There was actually a decrease of people in the population. If you are asking for the percent of decrease, the answer is 3200/25000=0.128 0.128*100=12.8%.

Answer:

(x-7)(x+6)

Step-by-step explanation:

The solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].

Given equation :-   [tex]x^{2} - x - 42[/tex]

For finding factors of the equation, we have equate the given polynomial with zero.

∴    [tex]x^{2} - x - 42 = 0[/tex]

Factorizing the above equation,

⇒   [tex]x^{2} - 7x + 6x - 42 = 0[/tex]

⇒   [tex]x (x -7) + 6(x - 7) = 0[/tex]

⇒   [tex](x + 6)(x - 7) = 0[/tex]  

∴ Either x + 6 = 0  or  x - 7 = 0  

∴ x1 = -6  and  x2 = 7

Where x1 and x2 are the respective factors of the given polynomial in the question.

Thus, the solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].

To learn more about factorization of polynomials, refer -

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Answer:

The answer is B, I just took the test.

Step-by-step explanation:

Answer:

hello there the answer is b hope this helps

Step-by-step explanation:

Answer: p(x) = steeper

               q(x) = less steep and reflection

               r(x) = reflection

Step-by-step explanation:

The parent graph is: f(x) = 1.5x³

p(x):  2 > 1.5 , so it is stretched (steeper).

p(x): coefficient has a positive sign, so it is NOT a reflection

q(x):  1  < 1.5 , so it is shrunk/compressed (less steep).

q(x): coefficient has a negative sign, so it is a reflection over x-axis

r(x): 1.5 = 1.5 so it is neither a stretch or a shrink

r(x): coefficient has a negative sign, so it is a reflection over x-axis

The graph of the function f(x) = 1.5x^3 has a steep increase or decrease, exhibits symmetry, and passes through the origin.

When comparing the graphs of different functions, it's important to analyze their key characteristics. In the case of the function f(x) = 1.5x^3, the graph will be a cubic function. Here are three significant differences between the graph of f(x) = 1.5x^3 and other functions:

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An3x=2x+1

subtract 2x from both sides

x=1 answer

Step-by-step explanation:

it will only take one day

Answer:

a * b^(n-1)

Step-by-step explanation:

I guessed and got it right :/

She saves $100.She saves 10% more.They want to know how much they will save after 6 months. Multiply 10% by 6months and you get 60%.Then you multiply the answer of .60 (60%) by 100 and you get 60. Lastly, since you wanna know how much you saved,subtract $100-60 and your final answer you get is that she saves $40.Hope that helped!

Answers: 1h, 2e, 3d, 4a, 5f, 6b, 7c, 8g

 Statement                                             Reason

1. JKLM is a rectangle                         1. Given

2. ∠K and ∠L are right angles            2. Definition of rectangle

3. ΔJKM and ΔMLJ are right angles   3. Definition of right triangles

4. [tex]\overline{JM}[/tex] ≅ [tex]\overline{JM}[/tex]                                         4. Reflexive Property

5. [tex]\overline{JK}[/tex]  ≅ [tex]\overline{LM}[/tex]                                        5. Definition of rectangle

6. ΔJKM ≅ Δ MLJ                                 6. HL congruency theorem

Answer:

1/2

Step-by-step explanation:

(4-2)

----------

2^2

The numerator is 4-2 = 2

The denominator is 2^2 = 4

2

------

4

1/2

Answer:

Colby makes more money by teaming with Danielle

Step-by-step explanation:

Colby's income =f(x) = 3x+12

and Danielle's income = g(x) = 5x+10

If they combine their efforts the combined income would be

h(x) = 3x+12+5x+10 = 8x +22

If shared equally between them

Colby would get 1/2(8x+22) = 4x+11  and

Danielle would get  1/2(8x+22) = 4x+11

Since given they worked each for 4 hours

Colby income = Danielle income= 4(4) +11 = 27

If not combined, then

Colby income 3(4) + 12=24 and

Danielle income= 5(4) +10 = 30

Because of combining Colby makes more money by teaming with Danielle.

The difference is 3 for 4 hours work.

Answer:

B

Step-by-step explanation:

team with Danielle , h(x)=8x+22

Answer:

The correct answer option is 42.6.

Step-by-step explanation:

We know that in a arithmetic sequence, [tex]a_{13}=1.9[/tex] and the common difference is [tex](d)=3.7[/tex].

The standard form of an arithmetic sequence is given by:

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

So we will substitute the given values in this formula to find the value of [tex]a_1[/tex].

[tex]a_{13}=a_1+(13-1)3.7[/tex]

[tex]1.9=a_1+(12)3.7[/tex]

[tex]1.9=a_1+44.4[/tex]

[tex]a_1=-42.5[/tex]

Now finding the 24th term"

[tex]S_{24}=a_1+(n-1)d\\\\S_{24}=-42.5+(24-1)3.7\\\\\\S_{24}=42.6[/tex].

Therefore, the 24th term of the given arithmetic sequence is 42.6.

Answer:

Just took this test the correct answer is 1.2

Answer:

1 : 140

Step-by-step explanation:

Ratio is 30 : 4200

Divide both numbers by 30:-

= 1 : 140   (answer)

To calculate the ratio of time to words, divide the minutes by the number of words, resulting in a 30:4200 ratio. This ratio highlights the efficiency of typing, useful for productivity analysis.

The question involves calculating the ratio of time in minutes to the number of words typed. Elvie can type 4,200 words in 30 minutes. To find the ratio of time in minutes to the number of words, we divide the number of minutes by the number of words.

First, express both quantities in their simplest forms: 30 minutes and 4,200 words. Then, create the ratio as follows:

Time in minutes : Number of words = 30 : 4,200

For easier comparison or further calculations, the ratio can be simplified by dividing both terms by the greatest common divisor. However, in this case, presenting the ratio in its initial form already communicates the relationship clearly, showing how many words are typed in a given amount of time. The ratio can be crucial for understanding productivity and efficiency in typing or other time-bound tasks.