The locations in a city are mapped out on a grid, where the origin represents the city center. A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

About how many fewer units would the helicopter have traveled if it went directly from one location to the other?

Answer:

slope = - 1

Step-by-step explanation:

The slope of the curve m is measured by

m = [tex]\frac{dy}{dx}[/tex] at x = a

Differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3x - x², then

[tex]\frac{dy}{dx}[/tex] = - 3 - 2x

x = - 1 → [tex]\frac{dy}{dx}[/tex] = - 3 - 2(- 1) = - 3 + 2 = - 1 ← slope at (- 1, 2 )

Answer:

79716.98

Step-by-step explanation:

Answer:

Step-by-step explanation:

let x represent the leg length

if we use the Pythagorean theorem we get:

x² + x² = 12²

then

2x² = 12²

Then

x² = 144/2 = 72

then

x = √(72)

 =8,485281374239

Step-by-step explanation:

[tex] (\frac{3}{2} ) \frac{9}{7} = \frac{3}{2} \times \frac{9}{7} = \frac{27}{14} \\ [/tex]

Answer:

it means 3/2 of 9/7

Step-by-step explanation:

those are fractions

Answer:

Therefore the new coordinate of the point is (2,-4)

Step-by-step explanation:

A point (2,4) is rotated [tex]90^\circ[/tex] clockwise .

The point (2,4) lies on the first coordinate.If the point rotated [tex]90^\circ[/tex]clockwise direction It will be go fourth coordinate.

Therefore the new coordinate of the point is (2,-4)

Answer:

3x + 6 > x

2x > -6

x > -3

answer is d

Answer:

x > -3

Step-by-step explanation:

Answer:

12 (-0.25)ⁿ

Step-by-step explanation:

recall that the general form for each term in the geometric progression is

arⁿ

such that the geometric progression looks something like.

ar⁰, ar¹, ar², ar³, ....., arⁿ, ......

also note that r⁰ = 1, hence ar⁰ is simply a

hence the G.P can be written

a, ar, ar², ar³, ....., arⁿ, ......  

also note that r can be obtained by simply dividing the 2nd term with the 1stterm. i.e

r = ar ÷ a

now we are given the first 3 terms in the GP as

12, -3, 3/4, ....

comparing with the GP in the previous paragraph, we can see that ,

a = first term = 12

also

r = 2nd term ÷ 1st term

= -3 ÷ 12

= -0.25

hence the nth term

= arⁿ

= 12 (-0.25)ⁿ

The unit rate is calculated by dividing the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, the unit rate for filling the aquarium is 10 minutes per meter.

To calculate the unit rate, you divide the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, for the unit rate in minutes per meter, you would set up the division as follows:

4 minutes / (2/5) meters

When you divide 4 by 2/5, you actually multiply 4 by the reciprocal of 2/5, which is 5/2.

So, 4 * (5/2) = 10

Therefore, the unit rate for filling the aquarium is 10 minutes per meter.

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To simplify the expression 54, divide it by 2 and 3 to get the simplified result of 9.

To simplify the expression 54, you need to consider the properties of the number 54. First, note that 54 is divisible by 2. Next, check if it is also divisible by 3. If it is, continue dividing by 3 until you can no longer do so. In this case, 54 is divisible by both 2 and 3, so you can simplify it as follows:

Therefore, the simplified expression 54 is equal to 9. So, the correct answer is A. 20.

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Answer:

study more that should help you out

Step-by-step explanation:

study more

Answer:

try to study

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3/8 is smaller than 11/12

Step-by-step explanation:

3/8 is equal to 0.375 and 11/12 is equal to 0.91, which makes 3/8 a smaller number and 11/12 a bigger number.

the answer is A

Step-by-step explanation:

Answer:

A. x + y = 216 and Two-thirds x + StartFraction 4 Over 9 EndFraction y = 118.  ☁︎✮

Step-by-step explanation:

Answer:m=-11

Step-by-step explanation:

You find the answer by dividing 187 by -17.

The value for m is -11

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: -17m=187

Thus simplifying we get m= 187/-17

                                            = -11

Hence, The value for m is -11

Learn more about BODMAS rule here:

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Answer:

5

Step-by-step explanation:

The median is 5. Cross off the dots on both sides one by one until you reach the center.

Answer:

i think its 11,700

Step-by-step explanation:

Answer:

11,700

Step-by-step explanation:

When trying to find the new area, you take you 2 numbers, 52 and 15, square the 15,  then multiply them

52 x 15^2 = 11,700

Answer:

  100°

Step-by-step explanation:

The larger one is 5/(5+4) = 5/9 of the total, so is ...

  5/9 × 180° = 100°

The measure of the larger angle is 100°.

Answer:

y=2/15x-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-3))/(-15-0)

m=(-5+3)/-15

m=-2/-15

m=2/15

y-y1=m(x-x1)

y-(-3)=2/15(x-0)

y+3=2/15(x)

y+3=2/15x

y=2/15x-3

The value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Solution:

Given data:

[tex]$\tan^2\theta=\frac{3}{8}[/tex]

To find the value of [tex]\sec\theta:[/tex]

Using trigonometric identity,

[tex]\sec^2\theta=1+\tan^2\theta[/tex]

Substitute [tex]\tan^2\theta=\frac{3}{8}[/tex] in the identity, we get

[tex]$\Rightarrow \sec^2\theta=1+\frac{3}{8}[/tex]

1 can be written as [tex]\frac{1}{1}[/tex].

             [tex]$ =\frac{1}{1} +\frac{3}{8}[/tex]

Do cross multiplication.

            [tex]$ =\frac{8}{8} +\frac{3}{8}[/tex]

Denominators are same, so you can add the fractions.

            [tex]$ =\frac{8+3}{8}[/tex]

[tex]$\Rightarrow \sec^2\theta =\frac{11}{8}[/tex]

Taking square root on both sides, we get

[tex]$\Rightarrow \sec\theta =\pm\sqrt{\frac{11}{8}}[/tex]

Option B is the correct answer.

Hence the value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Answer:

1.29 minutes

Step-by-step explanation:

The scientist has a record of the amount of rainfall during the afternoon as around 0.43 minutes in each hours.

Now, we have to calculate the total amount of rainfall in three hours.

As the each hour rainfall is of 0.43 minutes, so the total rainfall in three hours will be (0.43 × 3) = 1.29 minutes. (Answer)

Answer:

Step-by-step explanation:

Let g = amount of general admission tickets

Let s = amount of student tickets

Since seventy people attended the concert, this includes the people who bought general admission tickets and the people who bought the student tickets. As a result, g + s = 70. A student ticket is $3.25, so it would be 3.25s and a general admission ticket is $4.75, so it would be 4.75g. Since there was $272.50 collected in all, the second equation would be 3.25s + 4.75g = 272. 50.

g + s = 70

4.75g + 3.25s = 272.50

Multiply the first equation by 3.25 (or 4.75) so that you can use elimination to get rid of one variable.

3.25g + 3.25s = 227.50

4.75g + 3.25s = 272.50

Now, you subtract so that you can eliminate s.

-1.50g = -45

g = 30

This means that there are 30 general admission tickets. Now, you substitute 30 in for g to find s.

30 + s = 75

Subtract 30 from both sides.

s = 45

This means that there are 30 general admission tickets and 45 student tickets.

The probability that in a sample of 12 customers at Noodles & Company restaurant, none of them will order a nonalcoholic beverage is 0.020211.

In this question, we are given that the probability that a customer will order a nonalcoholic beverage at Noodles & Company restaurant is 0.48. We are asked to find the probability that in a sample of 12 customers, none of them will order a nonalcoholic beverage.

To find the probability that none of the 12 customers will order a nonalcoholic beverage, we can use the concept of independent events and the multiplication rule of probability.

The probability that a customer will order a nonalcoholic beverage is 0.48, so the probability that a customer will not order a nonalcoholic beverage is 1 - 0.48 = 0.52. Since each customer's decision is independent, the probability that none of the 12 customers will order a nonalcoholic beverage is (0.52)^12 = 0.020211.

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Answer:

5x + 13 = 123

     - 13   - 13

5x = 110

5x/5 = 110/5

x = 22

Answer:

No, the expressions are NOT equivalent.

Step-by-step explanation:

Solve each:

11t - 4t

(11 × 2) - (4 × 2)

22 - 8

= 14

4t - 11t

(4 × 2) - (11 × 2)

8 - 22

= -14

14 is NOT equivalent to -14

Your equation is unclear. Do you mean the following:

(15x+21)/3=5x+7 or 3(15x+21)=5x+7

If the left equation is the correct one, the left side simplifies to 5x+7=5x+7, which must mean all real numbers are correct solutions. Thus, it has infinite real solutions.

The equation (15x + 21)³ = 5x + 7 is a cubic equation. The number of solutions can be 0, 1, 2, or 3 solutions.

The equation is (15x + 21)³ = 5x + 7. To determine the number of solutions, we need to simplify and solve the equation.
Step 1: Expand the equation using the binomial theorem. This gives us: 3375x³ + 14175x² + 19305x + 9261 = 5x + 7.
Step 2: Combine like terms on both sides of the equation. This results in: 3375x³ + 14175x² + 19305x + 9254 = 0.
Step 3: This is a cubic equation. Cubic equations can have 3 solutions at most. However, it is not guaranteed that this equation will have 3 solutions. It can have fewer solutions or even no real solutions.
Therefore, the number of solutions for this equation is either 0, 1, 2, or 3 solutions. Further analysis or calculations may be needed to determine the exact number of solutions.

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Answer: 35 F

Step-by-step explanation:

night time