A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram, MN ∥ PO and MP ∥ NO. Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary. Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary. Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary. Therefore, __________ and _________ because they are supplements of the same angle. Which statements should fill in the blanks in the last line of the proof?

∠M is supplementary to ∠N; ∠M is supplementary to ∠O
∠M is supplementary to ∠O; ∠N is supplementary to ∠P
∠M ≅ ∠P; ∠N ≅ ∠O
∠M ≅ ∠O; ∠N ≅ ∠P

Answer:

3.13

Step-by-step explanation:

Given :

y = 2x + 4 -------- eq1

y = 2x - 3 -------- eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-3 -------rearrange---> 2x - y -3 = 0

Comparing with the general form, we get A = 2, B = -1, C = -3

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-3) |  / √(2² + (-1)²)

d = | -4 + 0 - 3 |  / √(4 + 1)

d = | -7 |  / √5

d = 7  / √5

d = 3.13

The distance between the pair of given parallel lines is;

A: 3.13

We are given equation of the two lines as;

y = 2x + 4 - - - (eq 1)

y = 2x - 3 - - - (eq 2)

Let us put 1 for x in eq 1 to get;

y = 2(1) + 4

y = 6

Ax + By + C = 0

We have;

2x - y - 3 = 0

Thus;

A = 2

B = -1

C = -3

D = |Ax1 + By1 + c|/√(A² + B²)

Where;

x1 is the value of x imputed into the first equation

y1 is Tha value of y gotten from the input of x1

Thus;

D = |(2 × 1) + (-1 × 6) + (-3)|/(√(2² + (-1²))

D = |-7|/√5

We will take the absolute value of the numerator to get;

D = 7/√5

D = 3.13

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Answer:

1.5 feet

Step-by-step explanation:

Bob wants to plant a 7 foot by 10 foot garden.

Area = [tex]7\times10=70[/tex] square feet

He wants to make a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle.

Means we have to factor 28 in a way that the length and width is less than 10 and 7.

28 = 2 x 2 x 7

Means 4 feet can be width and 7 feet the length of the area where tomatoes need to be planted.

So, we have [tex]10-7=3[/tex] feet less than outer garden means at each side [tex]3/2=1.5[/tex] feet decreases.

Similarly, we have [tex]7-4=3[/tex] feet less width and at each side it is 1.5 feet.

Therefore, the border of petunias will be 1.5 feet wide on all sides.

Answer:

Width of the border is 1.5 feet.

Step-by-step explanation:

Let x be the width ( in feet ) of the border,

Given,

The dimension of the garden =  7 foot by 10 foot,

So, the dimension of the middle ( garden area excluded border )= (7 - 2x) foot by (10 - 2x) foot

Hence, the area of the middle = (7 - 2x)(10 - 2x)

According to the question,

[tex](7 - 2x)(10 - 2x)=28[/tex]

[tex]70 -14x-20x + 4x^2=28[/tex]  

[tex]4x^2 -34x+70-28=0[/tex]

[tex]4x^2 -34x+42=0[/tex]        ( Combine like terms )

[tex]4x^2-(28+6)x+42=0[/tex]  ( Middle term splitting )

[tex]4x^2-28x-6x+42=0[/tex]

[tex]4x(x-7)-6(x-7)=0[/tex]

[tex](4x-6)(x-7)=0[/tex]

By zero product property,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since, width of the border can not be equal to the dimension of the garden,

Therefore, the width would be 1.5 foot.

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:

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:

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:

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:

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:

  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:

see explanation

Step-by-step explanation:

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

Answer:

F and E

Step-by-step explanation:

[tex](3x+4)^2=14[/tex]

We could get rid of the square on the (3x+4) by square rooting both sides:

[tex]3x+4=\pm \sqrt{14}[/tex]

Now you are left with a linear equation to solve.

Subtract 4 on both sides:

[tex]3x=-4 \pm \sqrt{14}[/tex]

Divide both sides by 3:

[tex]x=\frac{-4 \pm \sqrt{14}}{3}[/tex]

You could rearrange the numerator using commutative property:

[tex]x=\frac{\pm \sqrt{14}-4}{3}[/tex]

If you wanted two write the two answers out, you would write:

[tex]x=\frac{\sqrt{14}-4}{3} \text{ or } \frac{-\sqrt{14}-4}{3}[/tex].

So I see this in F and E.

You could separate the fraction:

[tex]x=\frac{\sqrt{14}}{3}-\frac{4}{3} \text{ or } -\frac{\sqrt{14}}{3}-\frac{4}{3}[/tex].

The solutions to the given equation (3x + 4)^2 = 14 are x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

To find the solutions to the equation (3x + 4)2 = 14, first we need to take the square root of both sides of the equation to remove the square from (3x + 4):

√{(3x + 4)2} = √14, which simplifies to 3x + 4 =  √14 and 3x + 4 = -√14.

Then, we solve for x in each equation by subtracting 4 from both sides, which gives us 3x = √14 - 4 and 3x = -√14 - 4.

Lastly, we divide each side by 3 in both equations to isolate 'x', thus our solutions are: x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

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Step-by-step explanation:

10 is the value of A ......

Answer:

Value of A = 10

Step-by-step explanation:

Here Isoke is solving the quadratic equation by completing the square

        10x² + 40x – 13 = 0

         10x² + 40x – 13 + 13 = 0 + 13

         10x² + 40x + 0 = 13

         10x² + 40x = 13

          10 ( x² + 4x) = 13

   Here it is given as

           A(x² + 4x) = 13  

Comparing both

           We will get A = 10

Value of A = 10

Answer:

area of circle = 9/64 π square inches

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

It is given that diameter of circle = (3/4) in

Therefore radius  r = diameter/2 = (3/4)/2 = 3/8 in

To find the area of circle

Area =  πr²

 =  π(3/8)²

 =  π * 9/64

 = 9/64 π square inches

The correct answer is 9/64 π square inches

Using the law of sin.

Sin(angle) = Opposite leg / hypotenuse

Sin(33) = x / 23

Solve for x:

Multiply both sides by 23:

x = sin(33) * 23

x = 12.5267

Rounded to the nearest hundredth = 12.53 cm.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

3192 persons! ✔️

Step-by-step explanation:

From the statement, we know that μ = 40 [minutes] and σ = 6 [minutes]

There are 3900 people. And we need to find how many of the lie within one standard deviation below the mean and two standard deviations above the mean.

We need to find the probability between: 34 minutes and 52 minutes. With the help of a calculator we get that the probability is: P(34<z<52) = 0.8186

Therefore, 0.8186×3900 = 3192 persons! ✔️

Answer:

Option B is correct.

Step-by-step explanation:

[tex]10^{(3/4)x}[/tex]

We need to write the above equation in square root form.

We know that 1/4 = [tex]\sqrt[4]{x}[/tex]

So, [tex]10^{(3/4)x}[/tex] can be written as:

[tex](\sqrt[4]{10})^{3x}[/tex]

Option B is correct.

For this case we have that by definition of properties of powers and roots it is fulfilled:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, we have the following expression:

[tex](10) ^ {\frac{3} {4} x}[/tex]

So, in an equivalent way we have:

[tex](\sqrt [4] {10}) ^ {3x}[/tex]

Answer:

Option b

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:

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:

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:

V = $3.50t + $90.5....

Step-by-step explanation:

V(t) is a function of t that expresses the value in year 2000+t.  

We know that the increase is $3.50 times t.

So,

V(t) = $3.50t + c  

where c is the constant.

V(15) =  $3.50 (15) + c = $143     [t=15 as mentioned in the question]

and therefore  

c = $143 - $3.50 (15)

c= $143 - $52.50

c= $90.5  

Now we got the value of c. We can write the equation as  

V = $3.50t + $90.5....

The subject of this question is linear equation. The dollar value of a product expected to change over several years can be calculated using the future value formula V = P(1 + r)^(t-15), where P is the present value, r is the rate of change per year, and t represents the year.

To develop a linear equation that represents the dollar value V of a product in a certain year t, you can use the formula for future value received years in the future: V = P(1 + r)^(t-15), where P is the present value in 2015, r is the rate of change per year, and t represents the year.

For example, if a firm's payment was $20 million in 2015 and was expected to increase by 10% per year, then the value in 2020 (t = 20) would be calculated as: V = $20 million * (1 + 0.10)^(20-15).

From this equation, you can predict the future value of the product in terms of the year and rate of inflation.

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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:

56 degrees

Step-by-step explanation:

So those angles are called alternate exterior angles because they happened at the difference intersections along the transversal on opposite sides of that transveral while on the outside of the lines that the transversal goes through.

If these lines that the transversal goes through are parallel then the alternating angles are congruent.

So they are because of the little >> things on those lines.

So x=56 degrees

Answer:

  22 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the necessary relationship. If the sledding slope is modeled as the hypotenuse of a right triangle with 25° as one of the acute angles, the side opposite the angle (the hill height) satisfies ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin

  height = (52 ft)sin(25°) ≈ 22.0 ft

The height of the hill is about 22 feet.

The height of the hill can be calculated using the formula Height = sin (angle) x length of ride. By substituting the given values, it comes out to be approximately 22.05 ft.

In this question we are given an angle of elevation and the length of the ride. The problem is essentially about using trigonometry to estimate the height of the hill. The hill forms a right triangle, with the length of the ride as the hypotenuse and the height we want to find as the opposite side. In trigonometry, the sine of an angle is equal to the opposite side divided by the hypotenuse. So to find the height of the hill, we take the sin of the angle, multiplied by the length of the ride.

Therefore, Height = sin (angle) x Length of ride = sin (25°) x 52 ft = approximately 22.05 ft. The estimated height of the hill is around 22.05 ft.

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Answer:

73920

Step-by-step explanation:

Number of ways to choose 9 appetizers from 12: ₁₂C₉

Number of ways to choose 3 main courses from 8: ₈C₃

Number of ways to choose 2 desserts from 4: ₄C₂

The total number of ways is:

₁₂C₉ × ₈C₃ × ₄C₂

= 220 × 56 × 6

= 73920

Answer:

Product B

Step-by-step explanation:

Divide the number of ounces i the bottle by the price of the bottle. Product A has a unit price of $0.17 and Product B has a unit price of $0.20. Therefore Product B has a lower unit price :))

Answer:

  2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

  (8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

Check

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

Rational numbers are numbers that can be represented as a fraction of two integers. The greatest rational number (r) such that [tex]\frac 8{15} \div r : \frac {18}{35} \div r[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Let the numbers be represented as:

[tex]n_1 = \frac 8{15} \div r[/tex]

[tex]n_2 = \frac {18}{35} \div r[/tex]

To calculate the value of r such that [tex]n_1 : n_2[/tex] is a whole number, we make use of Euclid's algorithm.

Using Euclid's algorithm, the value of r is the common divisor between both fractions

[tex]r = n_1 - n_1[/tex]

[tex]r =\frac 8{15} \div r - \frac {18}{35} \div r[/tex]

Ignore the "r"

[tex]r =\frac 8{15} - \frac {18}{35}[/tex]

Take LCM

[tex]r=\frac {8 \times 7 - 18 \times 3}{105}[/tex]

[tex]r =\frac {2}{105}[/tex]

Hence, the greatest rational number is such that [tex]n_1 : n_2[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

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Note that,

[tex]9x^2+24x+20=4\Longrightarrow9x^2+24x+16[/tex]

Which factors to,

[tex](3x+4)^2=0\Longrightarrow3x+4=0[/tex]

And simplifies to solution C,

[tex]\boxed{x=-\dfrac{4}{3}}[/tex]

Hope this helps.

Any additional questions please feel free to ask.

r3t40

Answer:

[tex]\large\boxed{C.\ x=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}[/tex]

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:

26/35

Step-by-step explanation:

If the events are mutually exclusive, all you have to do for P(S or T) is do P(S)+P(T).

So we are doing 1/7 + 0.6.

I prefer the answer as a fraction so I'm going to rewrite 0.6 as 6/10=3/5.

So we are going to add 1/7 and 3/5.

We need a common denominator which is 35.

Multiply first fraction by 5/5 and second fraction by 7/7.

We have 5/35+21/35.

This gives us 26/35.

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:

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