When a large municipal water tank is empty, it takes a Type JQ pump, working alone, 72 hours to fill the tank, whereas as Type JT pump, working alone, would take only 18 hours to fill the tank completely. If the tank starts at half full, how long would it take two Type JQ pumps and a Type JT pump, all three pumps working together, to fill the tank?

Answer:

D. [tex] x = 3 \pm \sqrt{10} [/tex]

Step-by-step explanation:

[tex] x^2 - 6x - 1 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

a = 1; b = -6; c = -1

[tex] x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]

[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]

[tex] x = 3 \pm \sqrt{10} [/tex]

Answer: 1.8°

Step-by-step explanation:

To calculate the angle between the vectors u and v we use the formula of the dot product.

The dot product between two vecotores is:

[tex]u\ *\ v = |u||v|*cosx[/tex]

Where x is the angle between the vectors

As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors

[tex]u=6i + 4j\\v=7i +5j[/tex]

Then:

[tex]u\ *\ v = 6*7 + 4*5[/tex]

[tex]u\ *\ v = 42 + 20[/tex]

[tex]u\ *\ v =62[/tex]

Now we calculate the magnitudes of both vectors

[tex]|u|=\sqrt{6^2 + 4^2}\\\\|u|=2\sqrt{13}[/tex]

[tex]|v|=\sqrt{7^2 +5^2}\\\\|v|=\sqrt{74}[/tex]

Then:

[tex]62 = 2\sqrt{13}*\sqrt{74}*cosx[/tex]

Now we solve the equation for x

[tex]62 = [tex]cosx=\frac{62}{2\sqrt{13}*\sqrt{74}}\\\\x=arcos(\frac{62}{2\sqrt{13}*\sqrt{74}})\\\\x=1.8\°[/tex]

Answer:

45 minutes each

Step-by-step explanation:

Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.

3x+5y=6

9x+7y=12

Now solve using substitution or elimination.  I will use elimination.

-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.

9x+7y=12, add the equations

-8y=-6 solve for y

y= 3/4 of an hour or 45 minutes

Next plug y into either equation

3x+5(3/4)=6 Solve for x.

3x+15/4=6

3x=2.25

x=0.75, also 45 minutes

To check plug in each variable value to each equation to see if they work if you need to.

Yes, the Pythagorean Theorem only works with right triangles.

You can use it to solve for the hypotenuse, or either one of the sides depending on the information you are provided with.

Answer:

yes

Step-by-step explanation:

Answer:

  a) f(x) = (x-5)/((x-3)(x-10))

  b) f(x) = (x-4)/((x+4)(x^2+1))

  c) f(x) = 2(x-1)(x+1)/((x+3)(x-4))

  d) f(x) = -2(x+5)(x-3)/((x+2)(x-5))

  e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9))

Step-by-step explanation:

Ordinarily, we think of a horizontal (or slant) asymptote as a line that the function nears, but does not reach. Some of these questions ask for the horizontal asymptote to be zero and for a function zero at a specific place. That is, the actual value of the function must be the same as the asymptotic value, at least at one location.

There are several ways this can happen:

To make the horizontal asymptote be zero, the degree of the denominator must be greater than the degree of the numerator. That is, there must be additional real or complex zeros in the denominator beyond those for the required vertical asymptotes.

__

a) f(x) = (x-5)/((x-3)(x-10)) . . . . vertical asymptote added at x=10 to make the horizontal asymptote be zero

__

b) f(x) = (x-4)/((x+4)(x^2+1)) . . . . complex zero added to the denominator to make the horizontal asymptote be zero

__

c) f(x) = 2(x-1)(x+1)/((x+3)(x-4)) . . . . factor of 2 added to the numerator to make the horizontal asymptote be 2. Numerator and denominator degrees are the same. (See the second attachment.)

__

d) f(x) = -2(x+5)(x-3)/((x+2)(x-5)) . . . . similar to problem (c)

__

e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9)) . . . . similar to the previous two problems (See the third attachment.)

_____

You remember that the difference of squares factors as ...

  a² -b² = (a-b)(a+b)

so the factor that gives zeros at x=±3 can be written (x²-9).

To write a rational function with specific characteristics, define the characteristics and use factors to create the desired asymptotes and holes.

To write a rational function with specific characteristics, we need to define the characteristics first. For example, let's say we want a function with a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a hole at x = -3. We can write the rational function as:

f(x) = (x + 3)(x - 2) / (x - 2)

In this function, the factor (x - 2) in both the numerator and denominator creates the vertical asymptote at x = 2. The (x + 3) factor in the numerator creates the hole at x = -3, and the horizontal asymptote at y = 0 is determined by the highest power of x in the numerator and the denominator being the same, which is x^1.

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Answer:

The approximate number of years is 10

The graph in the attached figure

Step-by-step explanation:

Let

f(x) the value of an antique plate

x is the number of yeras

we know that

The system of equations that represented the problem is equal to

[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A

[tex]f(x)=30[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (10.47,30)

see the attached figure

therefore

The approximate number of years is 10

Answer:

1st graph

Step-by-step explanation:

just did it in edge

Answer:

6144 clients

Step-by-step explanation:

Number of clients in the beginning = 3

The number of clients doubled each month. This means for every month the number of clients was 2 times the previous month. This can be modeled by a geometric sequence, with first term as 3 and common ratio of 2.

The general formula for the geometric sequence is:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Here,

[tex]a_{1}[/tex] is the first term of the sequence which is 3

r is the common ratio which is 2 and n represents the number of term.

We need to calculate the number of clients after 1 year i.e. after 12 months. So here n will be 12. Using these values, we get:

[tex]a_{12}=3(2)^{12-1}=6144[/tex]

Thus, after 1 year the company started by Nick will have 6144 clients

Answer:

12,288

Step-by-step explanation:

all i did was multiple the previous outputs by 2.

3

6

12

24

48

96

192

384

768

1536

3072

6144

12288

Answer:

C)

Step-by-step explanation:

We are given with a pair of linear equations,

y=x+12

y=3x+2

Let us solve them for x and y

In order to solve them we subtract first equation from the second ,

0=2x-10

Adding 2x on both sides we get

2x=10

Dividing both sides by 2 we get

x=5

Now replacing this value of x  in first equation

y=5+12=17

Hence the solution of the two equations is (5,12)

And by solution of a linear pair of equations, we mean that both the lines passes through that point.

Answer:

Option D

Step-by-step explanation:

The equation of a parabola in vertex form is

[tex]y = a(x - h)^{2} + k[/tex]

Where (h,k) is the vertex.

We were given the vertex as (5,-4). This implies that:

h=5, k=-4, we can see that a=2 is the leading coefficient of all the options.

We substitute the values to get:

[tex]y = 2(x - 5)^{2} + - 4[/tex]

Or

[tex]y =2( {x - 5)}^{2} - 4[/tex]

Answer:

  30

Step-by-step explanation:

You can try the answer choices to see what works.

  15·10 ≠ 750

  25·20 ≠ 750

  30·25 = 750 . . . . the larger number is 30

  50·45 ≠ 750

Answer:

The value of the greater number is 30.

Step-by-step explanation:

We need to find the values of x that satisfy the equation :

[tex]x(x-5)=750[/tex]

Working with the equation ⇒

[tex]x(x-5)=750[/tex]

[tex]x^{2}-5x=750[/tex]

[tex]x^{2}-5x-750=0[/tex]

Given an equation with the form

[tex]ax^{2}+bx+c=0[/tex]

We can use the quadratic equation to find the values of x

[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and

[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

With [tex]a=1\\b=-5\\c=-750[/tex] we replace in the equations of x1 and x2 ⇒

[tex]x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30[/tex]

[tex]x1=30[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]

Now for x2 ⇒

[tex]x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25[/tex]

[tex]x2=-25[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]

Given that both numbers are positive ⇒

[tex]x>0[/tex] and [tex](x-5)>0\\x>5[/tex]

Therefore, x2 is not a possible value for the greater number

The greater number is [tex]x1=30[/tex]

Answer:

Angles 1 and 3 are verical: Given

Angles 1 and 3 are formed by ntersecting lines:

Definition of vertical angles.

Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:

Definition of linear pair.

1 and 2 are supplementary, and 2 and 3 are supplementary:

Linear Pair Theorem

Angles 1 and 3 are congruent:

Congruent Supplement Theorem

Step-by-step explanation:

The first is given because it tells you it is given.

The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.

The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.

The fourth statement comes from the theorem of linear pairs.  Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.

The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.

Answer:y = 18(1.15)^x

Step-by-step explanation:

g o o g ; e

Answer:

The required equation is [tex]y = 18(1.15)^x[/tex].

Step-by-step explanation:

Consider the provided information.

The Initial value of poster = $ 18

After 1 year amount of increase = $ 20.70

With the rate of 15% = 0.15

Let future value is y and the number of years be x.

[tex]y = 18(1.15)^x[/tex]

Now verify this by substituting x=1 in above equation.

[tex]y = 18(1.15)^1=20.7[/tex]

Which is true.

Hence, the required equation is [tex]y = 18(1.15)^x[/tex].

Answer:

C. -5.3

Step-by-step explanation:

Simply add the negatives straight across to arrive at your answer.

I am joyous to assist you anytime.

Answer: C.-5.3

Step-by-step explanation: I could be wrong

Answer: C. 13,839 (the answer is not among the given options, however the result is near this value)

Step-by-step explanation:

The exponential decay model for Carbon- 14 is given by the followig formula:

[tex]A=A_{o}e^{-0.0001211.t}[/tex]  (1)

Where:

[tex]A[/tex] is the final amount of Carbon- 14  

[tex]A_{o}=[/tex] is the initial amount of Carbon- 14

[tex]t[/tex] is the time elapsed (the value we want to find)

On the other hand, we are told the current amount of Carbon-14 [tex]A[/tex]  is [tex]19\%=0.19[/tex], assuming the initial amount of Carbon-14 [tex]A_{o}=[/tex] is  [tex]100\%[/tex]:

[tex]A=0.19A_{o}[/tex] (2)

This means: [tex]\frac{A}{A_{o}}=0.19[/tex] (2)

Now,finding [tex]t[/tex] from (1):

[tex]\frac{A}{A_{o}}=e^{-0.0001211.t}[/tex]  (3)

Applying natural logarithm on both sides:

[tex]ln(\frac{A}{A_{o}})=ln(e^{-0.0001211.t})[/tex]  (4)

[tex]ln(0.19)=-0.0001211.t[/tex]  (5)

[tex]t=\frac{ln(0.19)}{-0.0001211}[/tex]  (6)

Finally:

[tex]t=13713.717years[/tex]  This is the age of the paintings and the option that is nearest to this value is C. 13839 years

Answer:

Step-by-step explanation:

1, 2. Central Angle, Interior Angle

See the 3rd attachment for the values. (Angles in degrees.)

The central angle is 360°/n, where n is the number of vertices. For example, the central angle in a pentagon is 360°/5 = 72°.

The interior angle is the supplement of the central angle. For a pentagon, that is 180° -72° = 108°.

These formulas were implemented in the spreadsheet shown in the third attachment.

3. Angles vs. Number of Sides

The size of the central angle is inversely proportional to the number of sides. In degrees, the constant of proportionality is 360°.

_____

Comment on the drawings

The drawings are made by a computer algebra program that is capable of computing the vertex locations around a unit circle based on the number of vertices. The only "work" required was to specify the number of vertices the polygon was to have. The rest was automatic.

The above calculations describe how the angles are computed. Converting those to Cartesian coordinates for the graphics plotter involves additional computation and trigonometry that are beyond the required scope of this answer.

These figures can be "constructed" using a compass and straightedge. No knowledge of angle measures is required for following the recipes to do that.

Answer:

The other guy is right but I wrote this

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

(f o g)(x) =  2(√(x-5)) - 8

So (f o g)(30) = 2 √(30-5) - 8

= 2 * √25 - 8

=  2* 5 - 8

= 2.

To find (f ° g)(30) for the functions f(x) = 2x - 8 and g(x) = √x-5, you first calculate g(30), which is 5, and then apply f to this result to get f(5) = 2. Therefore, (f ° g)(30) equals 2.

If f(x) = 2x - 8 and g(x) = √x-5, we want to find (f ° g)(30). The notation (f ° g)(x) means we apply g(x) first and then apply f(x) to the result of g(x). Thus, we first find g(30).

Calculate g(30):
g(30) = √(30 - 5)g(30) = √25g(30) = 5

Now that we have g(30), we apply f to this value:
f(g(30)) = f(5)f(5) = 2(5) - 8f(5) = 10 - 8f(5) = 2

Therefore, (f ° g)(30) = 2.

Answer:

Step-by-step explanation:

3π/2 is equivalent to 270°.  The "opposite side" for this angle is -2; the adjacent side is 0, and the hypotenuse is 2.

Thus, sin 3π/2 = opp/hyp = -2/2 = -1, and

         cos 3π/2 = adj/hyp = 0/2 = 0.

Answer:

[tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]

Step-by-step explanation:

We are given that a unit circle

We have to find the value of [tex]sin\frac{3\pi}{2}[/tex] and [tex]cos\frac{3\pi}{2}[/tex] by using the unit circle

Radius of  circle=r=1 unit

We know that

[tex]x=r cos\theta[/tex] and [tex]y=r sin\theta[/tex]

We [tex]\theta=\frac{3\pi}{2}[/tex]

Then x=[tex]1\cdot cos\frac{3\pi}{2}[/tex]

[tex]x=cos (2\pi-\frac{\pi}{2})[/tex]

[tex]x=cos \frac{\pi}{2}[/tex]  ([tex]cos(2\pi-\theta)=cos\theta[/tex])

[tex]x=0 (cos\frac{\pi}{2}=0)[/tex]

[tex]y=1\cdot sin\frac{3\pi}{2}[/tex]

[tex]y=sin(2\pi-\frac{\pi}{2})[/tex]

[tex]y=-sin\frac{\pi}{2}[/tex]  ([tex]sin(2\pi-\theta)=-sin\theta[/tex])

[tex]y=-1[/tex]   ([tex]sin\frac{\pi}{2}=1[/tex])

Hence, [tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]

The sequence "emdangl" rearranges to "mangled" (an appropriately fitting word scramble solution).

There are 7 letters in the sequence "emdangl", so there are 7! = 7*6*5*4*3*2*1 = 5040 different permutations of the seven letters. The exclamation mark is shorthand to represent factorial notation. Factorials are the idea of multiplying from that integer counting down until you get to 1. The reason why this works is because we have 7 letters to pick from for the first slot, then 6 for the next, and so on until all seven slots are filled out.

Since there is one solution ("mangled") out of 5040 total permutations, this means the probability of getting the solution just by random chance/guessing is 1/5040

Use a calculator shows that 1/5040 = 0.0001984 approximately.

The word 'emdangl' can be arranged in 5040 ways. The probability of randomly selecting one arrangement is 1/5040.

The word 'emdangl' has 7 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of distinct objects, which is n-factorial (n!). For this word, there are 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways to arrange the letters.

Now, let's determine the probability of randomly selecting one arrangement of the given letters. Since there is only one correct unscrambling, the probability is 1 out of the total number of arrangements, which is 1/5040.

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Answer:

see explanation

Step-by-step explanation:

Translate 4 units to the left and then reflect over the x- axis

Answer:

0.390 to the nearest thousandth or 39%.

Step-by-step explanation:

That would be 0.79^4

= 0.3895.

The probabilities are multiplied  because each selection is independent.

The probability that 4 adults randomly selected from a town with 79% health insurance coverage will all have health insurance is approximately 0.389.

The probability that 4 adults selected at random from a town where 79% of adults have health insurance, will all have health insurance. To solve this, we use the concept of independent events in probability. Since each selection is independent, and the probability that one adult has health insurance is 0.79, the probability that all four adults have health insurance is the product of their individual probabilities.

So the calculation would be:
0.79 times 0.79 times 0.79 times 0.79

This equals approximately 0.389 or rounded to the nearest thousandth, 0.389.

Answer:

The measure of angle x is 74°

Step-by-step explanation:

we know that

The inscribed angle measures half of the arc that comprises

so

∠ABC=(1/2)[arc ADC]

substitute the given values

150°=(1/2)[4x+4]

300°=[4x+4]

4x=300-4

4x=296

x=74°

Answer:

The measure of arc EF = 146°

Step-by-step explanation:

From the figure we can see two circles  with same center.

From the figure itself we get measure of arc AB is same as measure of arc EF, measure of arc Ac is same as measure of arc ED and measure of arc BC is same as arc FD.

The measure of arc AB = 146°

Therefore the measure of arc EF = 146°

Answer:

Multiplication with division

Subtraction with addition

Division with multiplication

addition with subtraction

Step-by-step explanation:

they are the opposite of each other... just that simple :))

hope this helps.

Answer:

Multiplication matches with division.

Subtraction matches with addition.

Division matches with multiplication.

Addition matches with subtraction.

Step-by-step explanation: Addition adds to something while subtraction takes away something. Dividing a number gets it much smaller, and multiplying gets a number much bigger.

Answer:

.43

Step-by-step explanation:

If I see % in a number I like to think of it as times 1/100 or divided by 100 (those are the same thing).

So we are doing 43 divided by 100 (or 43/100) which gives you .43 .

Anytime you divide by 100 you have to move the decimal left twice. (43 is 43. so 43. divided by 100 is .43)

Example

23.5%=.235

Why?

23.5 divided by 100 is .235

Another example

4%=.04

Why?

4. divided by 100 is .04

Answer:

Answer in the picture.

Answer:

[tex](-7)(-1.2)\leftrightarrow 8.4[/tex]

[tex](-2\frac{1}{2})(-2)\leftrightarrow 5[/tex]

[tex](2.5)(-2)\leftrightarrow -5[/tex]

[tex](7)(-1.2)\leftrightarrow -8.4[/tex]

Step-by-step explanation:

Product rule of signs:

(+)(+) = (+)

(+)(-) = (-)

(-)(+) = (-)

(-)(-) = (+)

Using these signs simplify the given expression.

[tex](-7)(-1.2)=8.4[/tex]

It means (-7)(-1.2) is equivalent to 8.4.

[tex](-2\frac{1}{2})(-2)=(-\frac{5}{2})(-2)=5[/tex]

It means [tex](-2\frac{1}{2})(-2)[/tex] is equivalent to 5.

[tex](2.5)(-2)=-5[/tex]

It means (2.5)(-2)- is equivalent to -5.

[tex](7)(-1.2)=-8.4[/tex]

It means (7)(-1.2) is equivalent to -8.4.

Answer:

Yes, because the total will be $31.75

Step-by-step explanation:

Let

x -----> number of hours weeding grandmother's garden

z ----> number of hours selling seashells at the flea market

we know that

The inequality that represent this situation is

[tex]2.25x+5.50z+5.25\geq30[/tex]

so

For x=2 hours, z=4 hours

substitute in the inequality

[tex]2.25(2)+5.50(4)+5.25\geq30[/tex]

[tex]4.50+22+5.25\geq30[/tex]

[tex]31.75\geq30[/tex] -----> is true

therefore

Janice will have enough to buy the necklace

Answer:

yes

Step-by-step explanation:

because the total will be $31.75.

Answer:

A'(7,-3)

Step-by-step explanation:

We were given the coordinates, A(-7,3) of quadrilateral ABCD and we want to find the image of A after a reflection across the x-axis followed by a reflection in the y-axis.

When we reflect A(-7,3) across the x-axis we negate the y-coordinate to obtain: (-7,-3).

When the image is again reflected in the across the y-axis, we negate the x-coordinate to get (--7,-3).

Therefore the coordinates of A' after the composed transformation is (7,-3).

Answer:

it is c

Step-by-step explanation:

Answer:

x+(-2), y+(-3)

Step-by-step explanation:

Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).

The reflection across the y-axis has the rule

(x,y)→(-x,y),

so

The translation that maps points A', B', C' and D' to E, H, G, F is

and has a rule

(x,y)→(x-2,y-3)

Answer:

$3.45

Step-by-step explanation:

$20.30 / 10  = $2.30 = 10%

$2.30 / 2  = $1.15 = 5%

$2.30 + $1.15 = $3.45 = 15%

I will assume that you meant to type (g o f)(8).

First we find f(8).

f(8) = 8 - 1 or 7.

We now find g(f(8)), which means g(7).

g(7) = 7^3 or 343

Answer:

(g o f)(8) = 343

Answer:7^3

Step-by-step explanation:

f(8)=8-1=7

g(f(8))= 7^3