Jackie can 150 meters
every minute. She is
training for a track
meet. She ran 500
meters during a warm
up. Write a function
that represents how
many meters Jackie
can runs in total at any
given minute. Then
determine how many
meters she runs after
12 minutes
​

On the left side, you can condense the logarithms into one:

[tex]\ln(1-x)-\ln(3x+5)=\ln\dfrac{1-x}{3x+5}[/tex]

Then

[tex]\ln\dfrac{1-x}{3x+5}=\ln(1-6x)\implies e^{\ln((1-x)/(3+5))}=e^{\ln(1-6x)}\implies\dfrac{1-x}{3x+5}=1-6x[/tex]

From here it's a purely algebraic equation. Multiply both sides by [tex]3x+5[/tex] to get

[tex]1-x=(1-6x)(3x+5)[/tex]

[tex]1-x=5-27x-18x^2[/tex]

[tex]18x^2+26x-4=0[/tex]

[tex]9x^2+13x-2=0[/tex]

By the quadratic formula,

[tex]x=\dfrac{-13\pm\sqrt{241}}{18}[/tex]

or about [tex]x\approx-1.5847[/tex] and [tex]x\approx0.14023[/tex].

Before we finish, first note that in order for the original equation to make sense, we need [tex]x[/tex] to satisfy 3 conditions:

[tex]-x+1>0\implies x<1[/tex]

[tex]3x+5>0\implies x>-\dfrac53\approx-1.67[/tex]

[tex]-6x+1>0\implies x<\dfrac16\approx0.17[/tex]

or taken together,

[tex]-\dfrac53<x<\dfrac16[/tex]

so both solutions found above are valid.

To solve the logarithmic equation, combine the logarithms, set the arguments equal to each other, solve for x, and check the solution.

To solve the given equation ln(–x + 1) – ln(3x + 5) = ln(–6x + 1), we can use the properties of logarithms to simplify it.

1. Combine the logarithms using the quotient rule: ln((–x + 1)/(3x + 5)) = ln(–6x + 1).

2. Set the arguments equal to each other: (–x + 1)/(3x + 5) = –6x + 1.

3. Solve for x by cross-multiplying and simplifying the equation.

4. Check the solution in the original equation for validity.

The solution to the equation is x = -1.

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Answer:

h/g

Step-by-step explanation:

we know that

The cotangent of angle G is equal to divide the adjacent side angle G to the opposite side angle G

so

cot(G)=h/g

Answer:

The approximate population of the state of California in 2010 was [tex]37,293,600\ people[/tex]

Step-by-step explanation:

Let

x----->the estimated population of Los Angeles in 2010

y----->the estimated population of the state of California in 2010

we know that

[tex]y=9.84x[/tex] ------> equation A

we have

[tex]x=3.79*10^{6}\ people[/tex]

Substitute the value of x in the equation A and solve for y

[tex]y=9.84(3.79*10^{6})=37.2936*10^{6}\ people[/tex]

[tex]37.2936*10^{6}=37,293,600\ people[/tex]

Answer:

3.73 × 10^7 people

Step-by-step explanation:

The original equation 3.79 × 10^6 = 3790000. 3790000× 9.84=37293600. 37293600 estimated is about 37300000. That would make 3.73 × 10^7 the expression that represents the amount of people in California.

Answer:

  8.284 × 10^4 m^2

Step-by-step explanation:

The area is the product of length and width:

  (5.45·10^5 m)·(0.152 m) = 0.8284·10^5 m^2 = 8.284·10^4 m^2

Answer:

210

Step-by-step explanation:

There are calculators online that can help you with questions like this, and give you a step by step explaination to show the work

The Combination to elect four representatives out of 10 students is 210.

The correct option is (A).

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

Firstly, n=10 and r=4

Combination: C(n,r)=C(10,4)

                                 = [tex]\frac{10!}{4!(10-4)!}[/tex]

                                 = [tex]\frac{10!}{4!* 6!}[/tex]

                                 = [tex]\frac{10*9*8*7}{4*3*2*1}[/tex]

                                 = 210

and permutation: P(n,r)=P(10,4)

                                      = [tex]\frac{10!}{(10-4)!}[/tex]

                                      = 10*9*8*7

                                      = 5040

Hence, the combination of data is 210 and permutation is 5040.

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Answer:

answer is C

Step-by-step explanation:

Answer:

15 or 16 times

Step-by-step explanation:

The ball will land on 6 or 29 about 14 times.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

There are 2 slots that have a "6" or a "29" on them. The other 36 slots have different numbers.

The probability of landing on "6" or "29"

= 2/38

= 1/19

Now, Multiply this probability by the number of trials to get

= 266 x (1/19)

= 14

Hence, we expect the ball will land on 6 or 29 about 14 times.

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Answer:

6X^2 -X -12

Step-by-step explanation:

(2X-3)(3X+4)

FOIL

first 2X*3X = 6X^2

outer 2X *4 = 8X

inner -3 *3X = -9x

last = -3 *4 =-12

Add them together = 6X^2 +8X -9X -12

                                 = 6X^2 -X -12

Answer:

6x^2 - x - 12

Step-by-step explanation:

2x(3x + 4) = 6x^2 + 8x

-3(3x + 4) = -9x - 12

6x^2 + 8x - 9x - 12

6x^2 - x - 12

Using a t-distribution calculator, it is found that the confidence level is of 95%.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

In this problem, we have that t = 2.776, df = 5 - 1 = 4 for a two-tailed interval, hence looking at the t-table it is found that the confidence level is of 95%.

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Answer:

YOU CAN HAVE 4 MORE HOURS WITH THE PHOTO BOOTH

Step-by-step explanation:

500 IS FOR 2 HOURS SHE DONT WANT TO WASTE MORE THAN 700 SO ITS 50 DOLLARS FOR ANOTHER HOUR

500 + 50 IS 550 THATS ONE HOUR ADDED 550+50 = 600 THATS 2 HOURS 600 + 50=650 THATS 3 HOURS 650+50= 700 SHE GOT IT FOR 4 HOURS IN TOTAL SHE HAD IT FOR 6 HOURS COUNTING THE 2 HOURS FOR IT AT THE PARTY . PERIODDT.....

Cindy can rent the photo booth for a maximum of 4 additional hours beyond the first two hours included in the base fee, given her budget of $700.

The student is asking how many additional hours Cindy can rent a photo booth for her party, given her budget constraints. Initially, there is a $500 fee for two hours, and each additional hour costs $50. Cindy has a budget of $700 in total, which means she can spend $200 on additional hours beyond the first two hours included in the base fee. To calculate the maximum number of additional hours, we divide the additional budget ($200) by the cost per additional hour ($50).

So, the calculation is
$200 / $50 = 4 additional hours.

Cindy can thus rent the photo booth for a maximum of 4 additional hours without exceeding her budget of $700.

Answer:

7                x

------ = -----------

20         400

Step-by-step explanation:

We want a ratio of bass over the total in the pond

Adding the samples

(8+6)           14                 7

--------    = ------------ = ---------

(20+20)        40             20

Set this equal to a ratio of 400 total fish

Bass on top, total fish on bottom

7                x

------ = -----------

20         400

Answer:

B:  down payment

Step-by-step explanation:

An increase in the down payment decreases the amount of money that has to be paid over time.

The monthly payment decrease with the increase in down payment of the loan amount. Option B is correct.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

The monthly payment is the amount which is required to pay each month to pay off the borrowed principal amount.

It can be calculated with the following formula.

[tex]M=P\left(\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]

Here, (P) is the principal amount, (r) is the interest rate and (t) is time.

The monthly payment is inversely proportional to the down payment. When the money paid as down payment is more, then the monthly payment of loan is less.

Thus, the monthly payment decrease with the increase in down payment of the loan amount. Option B is correct.

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Answer:The answer is B

Step-by-step explanation:Because the exponent is 6 for Silver Town and 8 for Lake City

Answer:

Step-by-step explanation:

10^6=1000000

1000000x8.2

silver town 8200000

lake city 164000000

Answer:

(B) The correct answer is B: m = n, so y = am / bn is the horizontal asymptote.

The second part is The horizontal asymptote is y = 5

The horizontal asymptote is a horizontal line that guides the graph for values of x, but is not part of the graph

The correct option that defines the horizontal asymptote is the option;

Reason:

The possible function of the question is [tex]f(x) = \dfrac{20 + 5 \cdot x}{x}[/tex]

The general form of the rational function is presented as follows;

[tex]f(x) = \dfrac{x^m+...+ a \cdot x + c}{x^n + ...+b\cdot x + d}[/tex]

The power or degree of the numerator and denominator of a rational function  determine the nature of the horizontal asymptote

Where highest power in numerator is less than the highest power or degree of the denominator, the horizontal asymptote is at y = 0

Therefore;

m < n the horizontal asymptote is y = 0

Where the power of the numerator is larger than the power of the denominator by one, the asymptote is slant, and the graph has no asymptote

m > n, there is no horizontal asymptote

In a rational function where the power of the numerator is equal to the power of the denominator, the horizontal asymptote occurs at the ratio of the leading zeros, [tex]y = \dfrac{a_m}{b_n}[/tex]

m = n, the horizontal asymptote is [tex]y = \dfrac{a_m}{b_n}[/tex]

Therefore;

In the given function, [tex]f(x) = \dfrac{20 + 5 \cdot x}{x}[/tex], the power of the numerator is equal to the power of the denominator, therefore, we have;

The horizontal asymptote of the function is [tex]y = \dfrac{5}{1} = 5[/tex]

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Answer:

a) the temperature is y = 16° C at 9 AM.

b) The probability of selecting 2 vowels at the same time is 2.8%

Step-by-step explanation:

a)

Temperature = y=?

Time = x = 9 A.M

The given equation is:

[tex]y = 19 + 6 sin (\frac{\pi }{12}(x-11))[/tex]

Putting x = 9 and solving

[tex]y = 19 + 6 sin (\frac{\pi }{12}(9-11))\\y = 19 + 6 sin (\frac{\pi }{12}(-2))\\y = 19 + 6 sin (\frac{-\pi }{6})\\y = 19 + 6(-0.5)\\y = 19 - 3\\y = 16[/tex]

So, the temperature is y = 16° C at 9 AM.

b)

WORD CLEMSON

Total Words = 7

Vowels = e, o = 2

Probability of selecting 2 vowels at the same time = P(2 Vowels) =?

We will use the formula of combinations nCr = n! / r! (n-r)!

As we are selecting three letter out of 7, the sample space will be 7C3

And

As there are only two vowels in the given word, and we have to find the probability of selecting two vowels so our event space will be 2C2.

P(2 Vowels) = 2C2 / 7C3

                    = 1/35

                    = 0.028 = 2.8%

So, The probability of selecting 2 vowels at the same time is 2.8%

Answer:

Average = 16, standard deviation =

Step-by-step explanation:

15+12=27

27+(17+14)+22=27+31+22=80

80/5=16

Distance from 22 to 16=6, from 12 to 16=4, so deviation = 5

Answer:

Average yield per plant is 16 and standard deviation is 3.4058.

Step-by-step explanation:

Given : A homeowner has 5 zucchini plants in her garden.

Plant 1 2 3 4 5

Yield 15 12    17 14 22  

Average : [tex]\frac{\text {Sum of all yields}}{\text{Total no. of plants}}[/tex]

Average : [tex]\frac{15+12+17+14+22}{5}[/tex]

Average : [tex]16[/tex]

Standard deviation =[tex]\sqrt{\frac{\sum(x_i-\bar{x})^2}{n}[/tex]

                               =[tex]\sqrt{\frac{(15-16)^2+(12-16)^2+(17-16)^2+(14-16)^2+(22-16)^2}{5}[/tex]

                               =[tex]3.4058[/tex]

Hence average yield per plant is 16 and standard deviation is 3.4058.

Answer:

[tex]P (M\ and\ C) = \frac{1}{4}=25\%[/tex]

Step-by-step explanation:

We call M the event in which a student gets an A in math and we call C the event in which a student gets an A in chemistry. As the events are not mutually exclusive, then.

[tex]P (M\ or\ C) = P (M) + P (C) - P (M\ and\ C)[/tex]

In this case we know that:

[tex]P (M\ or\ C) = \frac{7}{10}[/tex]

[tex]P (M) =\frac{17}{20}[/tex]

[tex]P (C) =\frac{1}{10}[/tex]

So

[tex]P (M\ and\ C) = P (M) + P (C) - P (M\ or\ C)[/tex]

[tex]P (M\ and\ C) = \frac{17}{20} + \frac{1}{10} -\frac{7}{10}[/tex]

[tex]P (M\ and\ C) = \frac{1}{4}[/tex]

ANSWER

x=24 , y=8√3

EXPLANATION

The given triangle is a right triangle

To find x, we use the cosine ratio, given by:

[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(30 \degree) = \frac{x}{16 \sqrt{3} } [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{x}{16 \sqrt{3} } [/tex]

Solve for x,

[tex]x = \frac{ \sqrt{3} }{2} \times 16 \sqrt{3} [/tex]

[tex]x = 8 \times 3 = 24[/tex]

To find the value of x, we use the sine ratio:

[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin(30 \degree) = \frac{y}{16 \sqrt{3} } [/tex]

[tex] \frac{1}{2} = \frac{y}{16 \sqrt{3} } [/tex]

Solve for y to get,

[tex]y = \frac{1}{2} \times 16 \sqrt{3} [/tex]

[tex]y = 8 \sqrt{3} [/tex]

Answer:

[tex]\sqrt{8^{2} + 3^{2} }[/tex]

Step-by-step explanation:

We see that this is a rectangle triangle, and that the ZY side is the hypotenuse.

It's length is then square root of the sum of the squares of the other sides:

[tex]hyp = \sqrt{a^{2} + b^{2} }[/tex]

So, in this case:

[tex]ZY = \sqrt{8^{2} + 3^{2} }[/tex]

The 8 and 3 numbers are easy to get from the graphic... and the order doesn't matter (8² + 3² = 3² + 8²).

That's an easy rule to remember.

I hope it helps.

Answer:

[tex]|ZY|=\sqrt{8^2+3^2}[/tex]

Step-by-step explanation:

ZY is the hypotenuse of triangle XZY.

The two shorter legs are;

YX=3 units

and

XZ=8 units.

According to the Pythagoras Theorem;

[tex]|ZY|^2=|XZ|^2+|YX|^2[/tex]

This implies that;

[tex]|ZY|^2=8^2+3^2[/tex]

We take the positive square root to obtain;

[tex]|ZY|=\sqrt{8^2+3^2}[/tex]

The second choice is correct

Answer:

[tex]l=\frac{A-2wh}{2w+2h}[/tex]

Step-by-step explanation:

We were given that; the formula for the surface area, A, of a prism is given by

[tex]A=2lw +2lh +2wh[/tex]

where is the length of the prism, w is the width, and h is the height.

We want to solve this formula for l,

Group the l terms;

[tex]A-2wh=2lw +2lh [/tex]

Factor l on the right;

[tex]A-2wh=(2w +2h)l [/tex]

Divide both sides by 2w +2h

[tex]\frac{A-2wh}{2w+2h}=l[/tex]

Therefore:

[tex]l=\frac{A-2wh}{2w+2h}[/tex]

Answer:

What he said.

Step-by-step explanation:

Answer:

k = 3

Step-by-step explanation:

The graph P(x) is a square root function. It has a vertex of (0,0) and has the following points:

x      f(x)

0       0

1         1

2       √2

3       √3

4       2

P(x) appears to be the function √x.

The image of l(x) changes the points of the function to

x      f(x)

0       0

1        3

2      3√2

3       3√3

4       6

You can divide the function values of l(x) by P(x).

3/1 = 3

6/2 = 3

The scale factor for the dilation is 3. k= 3.

Answer:

Counting aces: 30%.

Not counting aces: 23%

Step-by-step explanation:

If you're counting aces, it's 30%. But if you're only counting Queens, Kings and Jokers then it's about 23%.

I hope this helps

Answer:

  (5x − 4)(x + 2)

Step-by-step explanation:

For the purpose, it is sufficient to make sure the middle terms match.

The middle term in the product of each of the answer choices is ...

  -1+40 ≠ 6

  -8+5 ≠ 6

  -4+10 = 6 . . . . . the third selection is the one you want

  -2+20 ≠ 6

Answer:  The correct option is (C) (5x − 4)(x + 2).

Step-by-step explanation:  We are given to determine the factors of the following quadratic expression :

[tex]E=5x^2+6x-8.[/tex]

To factorize the given expression, we need to find two integers whose sum is 6 and whose product is -40.

The factorization is as follows :

[tex]E\\\\=5x^2+6x-8\\\\=5x^2+10x-4x-8\\\\=5x(x+2)-4(x+2)\\\\=(5x-4)(x+2).[/tex]

Thus, the factors of the given expression are (5x - 4) and (x + 2). That is,

[tex]5x^2+6x-8=(5x-4)(x+2).[/tex]

Option (C) is CORRECT.

-Hello There-

A square is always a rhombus because it satisfies all the properties of rhombus but every rhombus cannot a square.

Therefore, If KLMN is a square, then it must be a rhombus.

Have A Fantastic Day

Be Safe,

TheBlueFox

Answer:

It must be a rhombus

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Did the Quiz on Edge

Answer:

Then, a=-1 and b=-1

Step-by-step explanation:

We need to solve the following system of equations using the adition method:

2a+3b=-1       (i)

3a+5b=-2      (ii)

First, we multiply the equation (i) by -3 and the equation (ii) by 2, so we get:

-6a-9b=3

6a+10b=-4

Adding the two equations we have:

-6a-9b=3

6a+10b=-4

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

 0  + b = -1

Then b=-1. Now, let's substitute the value of b into equation (i):

2a+3b=-1

2a + 3(-1) = -1

2a -3 = -1

2a = 2

a = 1

Then, a=-1 and b=-1

Answer:

a = 1 and b= -1

Step-by-step explanation:

It is given two equations,

2a + 3b = -1  and

3a + 5b = -2  

To find the solution of given equations

Let, 2a + 3b = -1   ----(1)

3a + 5b = -2   ------(2)

(1) * -3 ⇒

-6a - 9b = 3    ----(3)

(2) * 2 ⇒

6a + 10b = -4   -----(4)

(3) + (4 )⇒

-6a - 9b = 3    ----(3)

6a + 10b = -4   -----(4)

  0 + b  = -1

(1) ⇒ 2a + 3b = -1  

2a + (3 * -1) = -1

2a = -1 + 3 = 2

a = 2/2 =1

Therefore, a = 1 and b = -1

Answer:

True

Step-by-step explanation:

True.

The solution to a system of equations is the point where two equations intercept. In both cases, we can see that the interception of the two systems shown occurs at (0, 1). So the statement is correct.

Answer:

It's True

Step-by-step explanation:

Answer:

t= $ 6.75 cost for table

c= $ 1.50 chair cost

Step-by-step explanation:

Answer:

chair 2.50

table 8.50

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

The line segment divides the sides in proportion, that is

[tex]\frac{14}{10}[/tex] = [tex]\frac{2x-3}{x}[/tex] ( cross- multiply )

10(2x - 3) = 14x ← distribute left side

20x - 30 = 14x ( subtract 14x from both sides )

6x - 30 = 0 ( add 30 to both sides )

6x = 30 ( divide both sides by 6 )

x = 5

Answer:

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  f(x) = x^2 + 4x - 21.

This function has a graph which is a parabola that opens up.

Its vertex is found by completing the square:

x² + 4x + 4 - 4 - 21, or

 (x + 2)² - 25

Comparing this to the standard equation

 (x - h)² + k, we see that h = -2 and k = -25.

Thus, the vertex (and the minimum of this function) is (-2, -25).

Thus, the range is [-25, ∞ ).  This being a polynomial function, it has no restrictions on the domain:  the domain is (-∞, ∞ )