The expression 1.05x calculates what change to the value of x?

Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.

Answer:

(x + 2)² + (y - 2)² = 3²

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

So, we have (x - -2)² + (y - 2)² = 3²

subtract a minus means we add.

(x + 2)² + (y - 2)² = 3²

Answer:

unlikely

Step-by-step explanation:

60/122

60 ÷122=0.49

0.49 × 100 =49

49% chance

answer is unlikely

Answer:

64x^3 + 384x^2 + 768x + 512 and (4x + 8)^3

Step-by-step explanation:

Here, we want to check which of the polynomials is placed with its factored form.

What we only need to do here is to find the product of the factored form and see if it gives us the polynomial ;

36x^2 + 18x + 9

(6x + 3)^2

= 6x(6x + 3) + 3(6x + 3)

= 36x^2 + 18x + 18x + 9

= 36x^2 + 36x + 9

This is wrong

49x^2 + 56x -16

(7x-4)^2

= 7x(7x-4) -4(7x -4)

= 49x^2 -28x -28x + 16

49x^2 -56x + 16

This is wrong also

729x^3 -405x^2 + 225x -125

(9x -5)^3

= (9x-5)(9x-5)^2

= (9x-5)(9x(9x-5) -5(9x-5))

= (9x-5)(81x^2 -45x -45x + 25))

= (9x-5)(81x^2 -90x + 25)

= 9x(81x^2 -90x + 25) -5(81x^2 -90x + 25)

= 729x^3 -810x^2 + 225x - 405x^2 + 450x -125

= 729x^3 -1215x^2 + 675x -125

This is also wrong

That makes the last number a possible answer; let’s check

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

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

= (4x + 8)(4x(4x + 8) + 8(4x + 8))

= 4x + 8(16x^2 + 32x + 32x + 64)

= (4x + 8)(16x^2 + 64x + 64)

= 4x(16x^2 + 64x + 64) + 8(16x^2 + 64x + 64)

= 64x^3 + 256x^2 + 256x + 128x^2 + 512x + 256

= 64x^3 + 256x^2 + 128x^2 + 512x + 256x + 256

= 64x^3 + 384x^2 + 768x + 256

Answer:

D

Step-by-step explanation:

Answer:

Daughter age = x = 16 years old

Mother's age = 2x = 2 × 16 = 32 years

Step-by-step explanation:

The computation of their current age is shown below:

Let us assume that the current age of the daughter is x

And, the current age of the mother be 2x

Now nine years ago, their ages would be

daughter age is x - 9

And, the mother age would be 2x - 9

Now the equation would be

x - 9 + 2x - 9 = 30

3x - 18 = 30

3x = 30 + 18

3x = 48

x = 48 ÷ 3

x = 16.

Therefore

Daughter age = x = 16 years old

Mother's age = 2x = 2 × 16 = 32 years

Answer:

The answer is C

Step-by-step explanation:

Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

Answer:

On a coordinate plane, point S is 1 unit to the left and 2.5 units up.

Step-by-step explanation:

Answer:

Step-by-step explanation:On a coordinate plane, point S is 1 unit to the left and 2.5 units up.

Step-by-step explanation:

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

50,12

Step-by-step explanation:

any number that has 5 in the tensplace is correct

1/10 of 100 is 10

Answer:

Yes, it is a right triangle.

Step-by-step explanation:

8²+15²=17²

64+225=289

289=289 YES, it is a right triangle

Answer:

\(\displaystyle 380,13271108...\:yd.^2\)

Step-by-step explanation:

\(\displaystyle {\pi}r^2 = A \\ \\ 11^2\pi = A \hookrightarrow 121\pi = A \\ \\ \boxed{380,13271108... = A}\)

If you want to follow what the exercise wants, then multiplying \(\displaystyle 3,14\)by the square of the radius will give you \(\displaystyle 379,94\:yd.^2.\)

I am joyous to assist you at any time.

35.6 355⅝5555555555555555555545455555555

Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

Answer:

c=-9

Step-by-step explanation:

Hello,

\((ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9\)

We can identify the like terms so:

a = 4

b-3a = c

3b = 9 <=> b = 3

So c = 3 - 3*4 = 3-12 = -9

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The probability of exactly 5 occurrences is (Rounding to three Decimal places), we get P(X ≤ 3) ≈ 0.251.

a) The probability of exactly 5 occurrences is given by the Poisson probability mass function:

P(X = 5) = (e^(-λ) * λ^5) / 5! = (e^(-5.1) * 5.1^5) / 120 ≈ 0.1755

Rounding to four decimal places, we get P(X = 5) ≈ 0.1755.

b) The probability of more than 6 occurrences can be calculated as the complement of the probability of 6 or fewer occurrences:

P(X > 6) = 1 - P(X ≤ 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

P(X = 4) ≈ 0.174

P(X = 5) ≈ 0.1755

P(X = 6) ≈ 0.1493

Substituting these values into the formula, we get:

P(X > 6) ≈ 1 - (0.006 + 0.031 + 0.079 + 0.135 + 0.174 + 0.1755 + 0.1493) ≈ 0.249

Rounding to three decimal places, we get P(X > 6) ≈ 0.249.

c) The probability of 3 or fewer occurrences is given by the cumulative distribution function:

P(X ≤ 3) = ∑ P(X = k), for k = 0, 1, 2, 3.

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

Adding these probabilities, we get: P(X ≤ 3) ≈ 0.251

Rounding to three decimal places, we get P(X ≤ 3) ≈ 0.251.

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Answer:

f(6) = 12

f(x) = 20, x= 10

Step-by-step explanation:

to solve these questions you have to fill in the x value

f(x)= 2x   you have to multiply the 6 and 2 to get 12

d. divide 20 by 2 to get x which would be 10 (20=2x) divide by 2 and get 10

The time taken by the runner is equal to 9.064 hours.

In this problem we find the case of runner taking a time (t), in hours, to run a certain distance (d), in miles, at constant speed (v), in miles per hour. The kinematic equation is now introduced:

v = d / t

Now we proceed to determine the missing time:

(26.2 mi) / (4.75 hours) = (50 mi) / t

t = 9.064 h

The runner takes a time of 9.064 hours to run a distance of 50 miles.

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Answer:

2

Step-by-step explanation:

Answer:

18pi or 56.55 to the nearest hundredth.

Step-by-step explanation:

Circumference = pi * diameter.

Answer:

  (b) 5π/2

  (c) 7π/2

  (e) 13π/2

Step-by-step explanation:

You want the angles in the list where sin(θ) is -√2/2.

The sine function is negative for angles in the 3rd and 4th quadrants. The magnitude is √2/2 for angles whose reference angle is π/4. These angles are ...

  5π/4, 7π/4, 13π/4, 15π/4

__

Additional comment

Adding √2/2 to the given equation makes it ...

  sin(θ) + √2/2 = 0

The solutions will be found at the x-intercepts of sin(θ) + √2/2 as shown in the attached graph.

The sine is the y-coordinate of points on the unit circle. In the second attachment, you will notice that the coordinates are (•, -√2/2) for angles 5π/4 and 7π/4. Adding 2π = 8π/4 to these values gets the next pair of angles with the right sine value.

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Answer:

The jumping dolphin is approx. 6 meters under sea level

The flying seagull is approx. 8 meters under sea level

The mobula ray is approx. 2 meters under sea level

The clownfish is approx.t 4 meters under sea level

The octopus is approx.  8 meters under sea level

The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.

The flying seagull: The mobula ray is 11 meters lower than the flying seagull.

The octopus: The mobula ray is 11 meters higher than the octopus.

The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.

The flying seagull: The albatross is 3 meters lower than the flying seagull.

The octopus: The albatross is 13 meters higher than the octopus.

The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.

The flying seagull: The clownfish is 10 meters lower than the flying seagull.

The octopus: The clownfish is 6 meters higher than the octopus.

If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.

If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.

✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧