What are the roots of the quadratic equation X² + 4X + 4. How many roots are there.

Answer: 6 m

This statement:

"Jared has run two-thirds of an 18-kilometer race" can be written as an equation:

[tex]18km.\frac{2}{3}=12km[/tex]

This means two-thirds of 18 km is equivalent to 12 km

If we substract this value to the total, we have the values of the kilometers left to run:

[tex]18km-12km=6km[/tex]

Therefore the correct option is D

The decimal equivalent of the fraction 5/33 is option A. o.15....

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given fraction is 5/33.

We have to find the decimal corresponding to the given fraction.

For that divide 5 by 33.

5 is not divisible by 33.

So add 0 and it become 50.

50 = (33 × 1) + 17

And the quotient is 0.1 with remainder 17.

Now 17 is not divisible by 33.

Add 0 and it becomes 170.

170 = (33 × 5) + 5

Quotient becomes 0.15 with remainder 5.

Again the remainder is 5 and add 0 and becomes 50.

It continues.

So the quotient is 0.1515....

Hence the decimal form is 0.(15) repeating.

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Answer:

7.31 times.

Step-by-step explanation:

We have been given that Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long.

To find the number of times Mariner Valley is longer than the Grand Canyon, we will divide 212 by 29.

[tex]\frac{212}{29}=7.3103448\approx 7.31[/tex]

Therefore, the Mariner Valley is 7.31 times longer than the Grand Canyon.

The given value h=16 ft is possible based on the quadratic equation model provided. By solving the equation h=[tex]-16t^2 + 35t[/tex] and substituting h=16, we find the possible values of t to be approximately 0.52 seconds or 1.48 seconds.

- For each given value of h, set [tex]\( h = -16t^2 + 35t \)[/tex] and solve for t.

- If you obtain real solutions, the given h is possible. If not, it isn't possible.

Checking for h=16:

1. Set h=16 and solve for t:

[tex]\[ 16 = -16t^2 + 35t \][/tex]

2. Rearrange to form a quadratic equation:

[tex]\[ -16t^2 + 35t - 16 = 0 \][/tex]

3. Solve for \( t \) using the quadratic formula:

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

  where a= -16, b=35, c=16.

  - Find the discriminant:

   [tex]\[ b^2 - 4ac = 35^2 - 4 \times (-16) \times (-16) = 1225 - 1024 = 201 \][/tex]

  Since the discriminant is positive, this quadratic has real roots, indicating that h=16 is possible.

Checking for h=20:

1. Set h=20 and solve for t:

[tex]\[ 20 = -16t^2 + 35t \][/tex]

2. Rearrange to form a quadratic equation:

 [tex]\[ -16t^2 + 35t - 20 = 0 \][/tex]

3. Solve for t using the quadratic formula:

 [tex]\[ t = \frac{-35 \pm \sqrt{35^2 - 4 \times (-16) \times (-20)}}{2 \times (-16)} \][/tex]

  - Find the discriminant:

 [tex]\[ 35^2 - 4 \times (-16) \times (-20) = 1225 - 1280 = -55 \][/tex]

  Since the discriminant is negative, this quadratic has no real roots, indicating that h=20 is not possible.

Conclusion:

- The value h=16 is possible.

- The value h=20 is not possible.

Answer:

B. More members prefer a beach vacation and a ski vacation than a cruise vacation.

Final answer:

To calculate the amount due at the end of 5 years with continuous compound interest, use the formula A = P*e^(rt), where A is the amount due, P is the principal, e is Euler's number, r is the interest rate, and t is the time. In this case, the amount due is approximately $10,021.66.

Explanation:

To calculate the amount due at the end of 5 years with continuous compound interest, we can use the formula A = P*e^(rt), where A is the amount due, P is the principal (initial amount borrowed), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, the principal is $5,500, the interest rate is 12% or 0.12, and the time is 5 years.

So, A = $5,500 * e^(0.12 * 5) = $5,500 * e^0.6 ≈ $5,500 * 1.82212 ≈ $10,021.66.

Therefore, the amount due at the end of 5 years with continuous compound interest is approximately $10,021.66.

Answer:

The answer is D

Step-by-step explanation:

Answer:

Q1:   The correct option is:   16

Q2:   The correct options are: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]

Q3:   The correct option is:  [tex]\overline{BC}=12; \overline{EF}=16[/tex]

Step-by-step explanation:

Question 1:

As here  [tex]\triangle RST\sim \triangle MNO[/tex], so the ratio of the corresponding sides will be equal. That means.....

[tex]\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16[/tex]

So, the length of the side [tex]x[/tex] will be 16.

Question 2:

If two triangles are similar, then the ratio of their corresponding sides should be equal.  So, here the ratios of the corresponding sides are............

[tex]\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}[/tex]

So we can see that the ratio of side [tex]AC[/tex] and side [tex]DF[/tex] is not equal with the other ratios.

Thus, the proportions that show the triangles are not similar:  [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]

Question 3:

Given that,  [tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]  

The ratio of [tex]AB[/tex] and [tex]DE[/tex] is given as [tex]\frac{3}{4}[/tex]

So, the ratio of [tex]BC[/tex] and [tex]EF[/tex] will be also [tex]\frac{3}{4}[/tex]

Among the four options, if [tex]BC=12[/tex] and [tex]EF=16[/tex], only then the ratio will be [tex]\frac{3}{4}[/tex]

[tex]\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}[/tex]

So, the lengths of [tex]BC[/tex] and [tex]EF[/tex] could be 12 and 16 respectively.

Answer:

the correct answer is c

Step-by-stepth explanation:

In an hour, the minute hand, which is 1.5 units long, travels a full revolution or approximately 9.4 units, while the hour hand, 1 unit long, covers one-twelfth, or about 0.5 units. Therefore, the minute hand travels approximately 7.9 units more than the hour hand.

This question can be solved by first examining the distance each hand travels. In an hour, the minute hand completes a full revolution around the clock face, moving a distance equal to the clock's circumference. If we call the length of the minute hand 1.5 units, then its distance traveled is 2π(1.5).

In contrast, the hour hand moves onto the next hour, covering on-twelfth of the clock's face, or 2π(1/12) using a length of 1 unit for the hour hand. Substract the second measure from the first to find the difference. Thus, the minute hand travels about 7.9 units farther than the hour hand.

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Answer:

80%

Step-by-step explanation:

To convert a fraction to percent, we need to multiply the fraction with 100.

Multiply 100 and [tex]\frac{4}{5}[/tex], we get,

[tex]\frac{4}{5} (100)[/tex] = 4 × 20

= 80%

Hence, the correct option is (C) 80%.

The height of the rectangular prism is 4 feet.

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]

Given that the volume of the rectangular prism is 192 cubic feet and the base area is 48 square feet, we can set up the equation as follows:

[tex]\[ 192 = 48 \times \text{Height} \][/tex]

To solve for the height, we divide both sides of the equation by the base area:

[tex]\[ \text{Height} = \frac{192}{48} \][/tex]

[tex]\[ \text{Height} = 4 \][/tex]

Therefore, the height of the rectangular prism is 4 feet.

Answer

21.3 i think hope this can help

Roger does 600 joules of work on the box when he applies a force of 60 newtons and displaces the box 10 meters along a 30° incline.

When Roger pushes a box on a 30° incline with a force of 60 newtons and displaces the box 10 meters along the incline, the work done on the box can be calculated.

Work is given by the equation W = F  imes d imes cos(heta), where W is the work, F is the force applied, d is the displacement, and heta is the angle between the force and the direction of displacement. In this case, because the force is applied parallel to the incline and displacement is along the incline, the angle heta is 0°, making cos( heta) equal to 1.

To find the work done by Roger, we calculate it as:
W = 60 N imes 10 m imes cos(0°)
W = 60 N imes 10 m imes 1
W = 600 joules.

Hence, Roger will do 600 joules of work on the box.