let f(x, y) = 1/squareroot x^2 + y^2. Compute a) ∇f(x, y).

Answer:

4×-4y=4

-(4x+y=19)

0x -5y=-15

5y=15

y=3

4x-12=4

x=4

The point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

To find the tangent of a curve, we have to find the first derivative of the function. Hence, the tangent of the given curve is given by

⇒ [tex]f'(x) = \frac{d{f(x)}}{dx} = \frac{d{x^{2}}}{dx} + \frac{d(4x)}{dx} - \frac{d(1)}{dx}[/tex]

⇒ [tex]f'(x) = 2x + 4[/tex]

Now, as the tangent is horizontal, that means the slope of the tangent is 0, hence setting [tex]f'(x) = 0[/tex] , we get the equation

⇒ [tex]f'(x) = 2x + 4 = 0[/tex]

Solving the equation obtained for the variable x,

⇒ [tex]2x = -4\\[/tex]

⇒ [tex]x = -2[/tex]

Now, putting the obtained value for x in the original equation, we get

⇒ [tex]f(x) = (-2)^{2} + 4(-2) - 1\\[/tex]

⇒ [tex]f(x) = -5[/tex]

Hence, the point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

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The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

We have to assume that ΔABC and ΔDEF are similar.

If the triangles are similar,

Then the proportionality is:

AB/BC=DE/EF

4/3=12/x

Therefore, the proportionality used in the given diagram is 4/3=12/x.

So, option 4 is correct.

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Option B is the correct answer. corresponding sides have a proportional ratio is 1/3 of the sss theorem.

If two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. This is called the SSS Similarity Theorem.

when the three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar, it is also called SSS Similarity Theorem.

SSS Theorem png

If  ABYZ=BCZX=ACXY , then ΔABC∼ΔYZX .

Considering triangles have 3 sides, having each side has a 1/3 ratio will make it congruent to the other triangle.

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To find the total mass of all the worker bees in the hive, you need to multiply the mass of a single worker bee by the number of worker bees in the hive.

The mass of a single worker bee is 2 x 10^-4 kilograms, and there are 8 x 10^4 worker bees in the hive.

So the total mass of all the worker bees in the hive is (2 x 10^-4 kilograms) * (8 x 10^4 worker bees) = 0.16 kilograms.

In standard form, this is written as 1.6 x 10^-1 kilograms.

Step-by-step explanation:

1.

it is always the same.

the usual equation of a line is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y-value when x = 0).

we see that the y-value is +3 when x = 0. that is "b".

for the slope we pick 2 points (with integer coordinates, if possible).

I see e.g. (0, 3) and (3, 0)

x changes by +3 (from 0 to 3).

y changes by -3 (from 3 to 0).

the slope "a" is -3/+3 = -1

the equation is

y = -x + 3

2.

and again the same

we see that the y-value is -3 when x = 0. that is "b".

I see e.g. (0, -3) and (3, 0) as points.

x changes by +3 (from 0 to 3).

y changes by +3 (from -3 to 0).

the slope "a" is +3/+3 = 1.

the equation is

y = x - 3

The percent increase  from last year to this year is 7.94%

From the question, we have the following parameters that can be used in our computation:

Initial height = 63 inches

New height = 68 inches

The percent change from last year to this year is then calculated as

Percent change = (New height - Initial height)/Initial height * 100%

Substitute the known values in the above equation, so, we have the following representation

Percent change = (68 - 63)/63 * 100%

Evaluate

Percent change = 7.94%

Hence, the percentage increase is 7.94%

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Answer:

Negative

Step-by-step explanation:

Knowledge Needed

The discriminant of a quadratic function is b^2-4ac.

If the discriminant is positive, there are 2 x-intercepts.

If the discriminant is 0, there is 1 x-intercept.

If the discriminant is negative, there are 0 x-intercepts.

Question

If the parabola does not intersect with the x-intercept, the discriminant is negative.

To find the time and distance at which Liza passes Ralph, we need to solve the system of equations.

Subtracting the first equation from the second, we get:

65x - 60x = y - 25

5x = y - 25

y = 5x + 25

Substituting this value of y into the first equation, we get:

60x + 25 = 5x + 25

55x = 0

x = 0

This means that Liza will pass Ralph 0 hours after she leaves, or at the same time as Ralph. At this time, they will have both traveled 0 miles.

Therefore, the answer is A: Liza will not pass Ralph, because she will never catch up with him.

Answer:

slope = 6

Step-by-step explanation:

(0,6)
(1,12)

12-6

-------- = 6

1-0

The equations that are true if x = 8 are:

B. x + 11.5 = 20.5

C. 23.42 - x = 15.42

D. 11x = 88

In equation B, x is equal to 8, so 8 + 11.5 = 20.5, which is a true statement. In equation C, x is also equal to 8, so 23.42 - 8 = 15.42, which is a true statement. In equation D, x is equal to 8, so 11*8 = 88, which is a true statement.

Equation A is not true because the expression 0^2/x is undefined, since division by zero is not allowed. Equation E is not true because 40 ÷ 8 is equal to 5, not 6.

Answer:

whats f

Step-by-step explanation:

Answer:y=7.5x

Step-by-step explanation:

In the 9th grade HMH Math book for teachers, it explains that you must divide 150 by 20 and put it in the equation.

In terms of b, the perimeter expression is 6 + 4b and the value of b is 9

From the question, we have the following parameters that can be used in our computation:

Dimensions = 8cm and 2b - 5 cm

The above parameters mean that

Length = 8

Width = 2b - 5

The perimeter is calculated as

Perimeter = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (8 + 2b - 5)

Evaluate the like terms

Perimeter = 2 * (3 + 2b)

Open the brackets

Perimeter = 6 + 4b

Here, we have

Perimeter = 42

This means that

6 + 4b = 42

So, we have

4b = 36

Divide by 4

b = 9

Hence, the value is 9

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Answer:

graph D

Step-by-step explanation:

if x ≥ 0

5x + 3 < 18

5x < 18 - 3

5x < 15

x < 15/5

x < 3

0≤ x < 3

if x < 0

5(-x) < 18 - 3

- 5x < 15

x > 15/-5

x> -3

-3 < x < 0

final solution

-3 < x < 3

Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.

What is called multiplication?

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.

Given that :

One segment measures 161 cm

To find the multiple according to the number 3, divide 161 by 3.

161 ÷ 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 × 3

                                                                   = 162

To find the submultiple according to the number 7, divide 161 by 7.

161 ÷7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 ÷ 23

                                                                          = 7

Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.

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Answer: Sofia needs to order an additional 100 - 24 = 76 pieces of sushi.

Since each roll contains 12 pieces, Sofia needs to order 76 / 12 = 6 additional rolls of sushi.

At a cost of $8 per roll, Sofia will need to pay an additional 6 * $8 = $48 for the additional sushi.

Step-by-step explanation:

Answer:

She answered 9 wrong and 33 right.

Step-by-step explanation:

Choices:

She answered 9 wrong and 33 right.

She answered 33 wrong and 9 right.

She answers 14 wrong and 22 right.

She answered 22 wrong and 14 right.

11:3 = 22:6 = 33:9 = 44:12 = 55:15 = 66:18 = 77:21 = 88:24 = ...

33 right 9 wrong works.

Answer: She answered 9 wrong and 33 right.

The linear equation that represents the plant height is the one in the first option:

y = 14 + (3/2)x

We know that the initial height of the plant (this will be the y-intercept of the line) is 14cm, and we also know that the plant grows at a rate of 3/2 cm each day.

So, after x days, the plant is x times 3/2cm plus 14 cm of height, so the linear equation is:

y = 14 + (3/2)x

So the correct option is the first one.

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Answer:

  500

Step-by-step explanation:

You want to know the rate in 4 years if it is 380 units per day, and increasing by 30 units per day per year.

The rate in 4 years will be the sum of the current rate and the amount of increase. The amount of increase is the rate of increase, multiplied by time:

  amount of increase = (30 units/day)/year × (4 years) = 120 units/day

Then the rate in 4 years will be ...

  new rate = current rate + increase

  new rate = 380 units/day + 120 units/day = 500 units/day

The company will be producing 500 units per day in 4 years.

The expression to which the distance Kane run in a training session after w week is {3+(1÷4)w}...

Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week.

Let w be the number of week.

So the expression is formed  as that in 1st week if he sart running 3 miles and after every week 1/4 miles added ,it's mean 1 by forth part of one mile is added after every week so if;

we suppose that we have to calculate it for "w" weeks then these weeks will be multiply with 1/4 and then added to the starting miles which are 3 miles

So the expression will be:

{3+(1÷4)w}

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Your question is may be misspelled it will be...(Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week. Write an expression to how the distance Kane run in a training session after 'w' weeks?

The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

It is represented mathematically as;

Probability = Number of Expected outcomes / Total number of outcomes

From the question, we can have the following outcomes;

Clothing = 4

Colors = 3

Pr (pick a clothing) = 1/4

Pr (pick a color) = 1/3

Pr (picking an orange hat) = 1/4 x 1/3

Pr (picking an orange hat) = 1/12.

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The team of Rosie's Riveters beat the Susan Bees by 3 runs.

Given are the scores for two softball teams for seven innings.

The total score of Rosie's Riveters will be -

T{R} = 1 + 3 + 4 + 2 + 1 + 0 + 2 = 13

The total score of Susan Bees will be -

T{S} = 0 + 0 + 5 + 3 + 0 + 1 + 1 = 10

Now -

T{R} - T{S} = 13 - 10 = 3

T{R} - T{S} = 3

Therefore, the team of Rosie's Riveters beat the Susan Bees by 3 runs.

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Answer:

Step-by-step explanation:

Answer is B.

Function 1: slope is 2

Function 2: (-5 + 4)/(2-1)= -1/1= -1

Answer:

7020

Step-by-step explanation:

2÷390,702,468

2÷195,351,234

3÷

Answer:4c=h

Step-by-step explanation:

The first linear equation, 4c=h

As per the unitary method, the number would you expect to be confirmed for MDD at the follow-up visit is approximately 166.

The term unitary method in statistics refers a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have to find how many of your 500 clients would you expect to have major depressive disorder and  if you used the phq-2 to screen for MDD, what number of those who are depressed would screen positive.

In order to find the number of patients with MDD, we must know the process of PHQ - 2.

The process of PHQ - 2 involves the following steps:

Here the score ranges from 0-6.

And if the score is 3 or greater, then major depressive disorder is likely.

Based on these we have to test the 500 with PHQ test, let us consider that there is 2 person in every two person has MDD.

So, the number of MDD patient is approximately 166.

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Answer:48

Step-by-step explanation:

Given the prime factorization of 90. The number that complete thi prime factorization is 2 × 3² × 5.

Factor tree

  90

   /\

2  45

     /\

  3  15

       /\

    3   5

The prime factorization

90 = 2 × 3 × 3 × 5

     = 2 × 3² × 5

So, the number that complete thi prime factorization is 2 × 3² × 5.

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The required values of the z-score as per the corresponding blood pressure readings are: z-score = 1.267 when reading is 142, z-score = 0.6 when reading is 130, and z-score = -1.2- when reading is 103.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

Normally distributed with a mean of 121 and a standard deviation of 15.

As per the given question, we have

mean ц = 121

standard deviation σ = 15

For X₁ = 140

z-score = (X₁ - ц )/σ

z-score = (140 - 121)/15

z-score = (19)/15 = 1.267

For X₂ = 130

z-score = (X₂ - ц )/σ

z-score = (130 - 121)/15

z-score = (9)/15 = 0.6

For X₃ = 103

z-score = (X₃ - ц )/σ

z-score = (103- 121)/15

z-score = (19)/15 = - 1.2

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