find the equation for (a) the tangent plane and (b) the normal line at the point p0(2,0,2) on the surface 2z−x2=0.

Step-by-step explanation:

perpendicular slope is negative reciprocal. -1/-1 = 1

y - 4 = x +3

y = x + 7

Answer:

x = 9

DE = 13

EF = 36

DF = 28

Step-by-step explanation:

DF = EF

7x - 35 = 4x - 8

3x = 27

x = 9

DE = x + 4 = 9 + 4 = 13

EF = 4x - 8 = 4(9) - 8 = 36

DF = 7x - 35 = 7(9) - 35 = 28

Answer:

x = 67°

Step-by-step explanation:

The 2 base angles x are congruent , then

x = \(\frac{180-46}{2}\) = \(\frac{134}{2}\) = 67°

Answer:

X= 67 degrees.

Step-by-step explanation:

All triangles must add up to 180°. This is an isosceles triangle which means once you have one degree you can find the other two.

In order to get the answer start with 180°-46°

180-46=134

The two x's equal each other. So you can divide the remaining degrees by 2 to get the answer.

134÷2=67.

So the answer is 67°.

Answer:

(5x + 2) - (-9x - 2)

O 11x2 – 5x + 8

14x + 4

–6x2 + 8x 7

-X2 + 6

Step-by-step explanation:

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{14x + 4}}}}}\)

Step-by-step explanation:

\( \sf{(5x + 2) - ( - 9x - 2)}\)

When there is a ( - ) sign in front of an parentheses in an expression , change the sign of each term in the expression. Also, remove the parentheses

\( \dashrightarrow{ \sf{5x + 2 + 9x + 2}}\)

Collect like terms

\( \dashrightarrow{ \sf{14x + 2 + 2}}\)

Add the numbers : 2 and 2

\( \dashrightarrow{ \sf{14x + 4}}\)

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Answer:

B

Step-by-step explanation:

because the square root of 3 is 1.7 and B is the closest to that.

If a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

In forensic science, the angle of impact is the angle at which a blood droplet strikes a surface. It has a range of 0 to 90 degrees and is, by definition, an acute (or right) angle.

Police can partially reconstruct a crime scene by connecting the "strings" that lead from the spatter to an origin area and knowing the angle of contact.

If a bloodstain has a tail or pattern, the angle of impact can be used to forecast how the subsequent bloodstain would look.

So, bloodstain pattern analysis examines the patterns of bloodstains found at crime scenes in an effort to piece together the sequence of events that led to the bloodshed.

Mathematically, we will have:

The angle of impact = sin⁻¹ (wide stain/length stain)

The angle of impact = sin⁻¹ (1.5/3.0)

The angle of impact = 30°

Therefore, if a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

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Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: \(a_n= a_1r^{n-1}\)

We are given: third term = 6 i,e

\(a_3=a_1r(3-1)\\6=a_1r^2----eq(1)\)

Seventh term = 96

\(a_7=a_1r(7-1)\\96=a_1r^6----eq(2)\)

Dividing eq(2) and eq(3)

\(\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}\)

So, Common Ratio r = 2

Finding First term using eq(1)

\(a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}\)

So, First term a₁ = 3/2 and common ratio r = 2

The required function for representation of the population of the frog after x years is \(f(x) = 1,200 (0.97)^x\). Option C is correct.

Given that,
Ginny is studying a population of frogs.
She determines that the population is decreasing at an average rate of 3% per year.
She began her study, the frog population was estimated at 1,200.

The function which is in format f(x) =   where, a is constant and x is variable,  the domain of this exponential function lies (-∞, ∞).  

Here,

The population is decreasing at an average rate of 3% per year, frog population was estimated at 1,200.
Let A be the population after x  years and given as
\(A = 1200 (1 - r / 100)^X\)
\(A = 1200 (1 - 0.03 / 100)^X\\A = 1200 (0.097)^X\)

Thus, the required function for representation of the population of the frog after x years is \(f(x) = 1,200 (0.97)^x\). Option C is correct.

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Answer: c

Step-by-step explanation:

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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The purchase cost of a car 24,500 with local sales tax rate 4% has following answer,

Total tax paid = $980

Total cost of a car including tax = $25.480.

Purchasing cost of a car = $24,500

Local sales tax rate on a car = 4%

Tax paid on the car purchase = (Purchase price) × (tax rate)

Substitute the value we get,

⇒ Tax amount = 4% of 24,500

⇒ Tax amount = 0.04 x 24,500

⇒ Tax amount = $980

Total cost of a car including tax = ( Tax amount ) + (Purchase price )

Substitute the value we have,

⇒ Total cost of a car  = Purchase price + Tax amount

⇒ Total cost of a car = 24,500 + 980

⇒ Total cost of a car = $25,480

Therefore, the tax paid on the car purchase and the car's total cost including tax is equal to $980 and $25,480 respectively.

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Answer:

32 units.

Step-by-step explanation:

look up a picture of a 306090 triangle, it will make sense :)

Answer:

32

Step-by-step explanation:

cos 30 = \(\frac{\sqrt{3} }{2}\)

\(\frac{\sqrt{3} }{2}\) = 16\(\sqrt{3}\) / n

n = 16\(\sqrt{3}\) * \(\frac{2}\sqrt{3} }\)

n = 32 units

The amount of money would be $1115.45 the zoo makes selling the waste that day.

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

They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.

To determine the amount of money would the zoo make selling the waste that day.

P(z ≤ z₀) = 0.1

z₀ = -1.28

⇒z₀ =(x₀ -μ ) / σ

Substitute the values and solve for x₀,

⇒ -1.28 =(x₀ -250 ) / 21

⇒x₀ = (-1.28)×21 - 250

⇒x₀ = 223.09

So the amount of money would be as :

⇒ 223.09 × 5

⇒ 1115.45

Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.

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The equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

To translate the function (j(x) = |x| right 8 units and up 6 units, we need to modify the expression inside the absolute value function.

The translation right 8 units means we need to replace x with (x - 8).

The translation up 6 units means we need to add 6 to the entire expression.

So the equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

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Reflecting the triangle ABC over the line y = x - 5 maps it to the triangle A"B"C"

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

Triangles ABC and A"B"C"

Also, we have the figure

From the figure we can see that

Translation would not map the triangles

Of all the other transformations, a reflection over the line y = x - 5 may map the triangles

This means that reflecting the triangle ABC over the line y = x - 5 maps it to the triangle A"B"C"

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Answer:

C

Step-by-step explanation:

To make it easy, if there are 3 yellow, 2 green, and 8 total, just find the equation that has the fraction result of 5/8.

Answer: The correlation between variables must be significant

Step-by-step explanation: In order to make reliable predictions using the equation of a regression model, the correlation Coefficient between the dependent and independent variables must be significant (that is a correlation Coefficient value close to either 1 or - 1). This is because the range of value of the correlation Coefficient is between - 1 to +1 and the closer the correlation Coefficient value is to either of these numbers, depicts the strength of the relationship which exists between them hence, enabling us to make good and accurate predictions which are close to the actual value.

Regression Analysis is a statistical and reliable process for making predictions using the regression model.

The correct option is:

Option B. The correlation between variables must be significant

The regression line can be explained as:

1. The correlation coefficient between the dependent and independent variables must be significant.

2. The correlation coefficient value should be near 1 or -1.

3. Thus, the values closer to - 1 and +1 will depict the strength of the relationship between the coefficient values.

Thus, regression lines help to predict accurate and reliable results that are close to the actual value.

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Based on the given information, the graph represents the relationship between the number of adults present and the maximum number of children allowed on a field trip. Since the trip is allowing for a maximum of 12 children, we will analyze the graph to determine how many adults will be present.

Without the graph, we cannot provide the exact number of adults needed for 12 children. However, once you have the graph in front of you, simply locate the point on the graph where the number of children allowed (y-axis) is equal to 12. Then, trace the point horizontally to the corresponding number of adults on the x-axis. This will give you the number of adults required to supervise the 12 children during the field trip.

Remember to follow any guidelines or ratios that may be established by your school or organization regarding adult-to-child ratios on field trips, as this can impact the number of adults needed for the trip.

this graph represents the maximum number of children that are allowed on a field trip depending on the number of adults present to supervise. a trip is allowing for a maximum of 12 children. how many adults will be present? enter your answer in the box.

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Answer:

-15

Step-by-step explanation:

Multiplying 3 * -5 gives you -15

Answer:

-15

Step-by-step explanation:

divide by 3

you'll should get -15

Answer:

She can walk 5 miles in 2 1/2 hours.

Step-by-step explanation:

1/4 of an hour means that 4/4 is 1 hour. If she can walk 1/2 of a mile in 1/4 of an hour, then 1/2 + 1/2 + 1/2 + 1/2 = 1 hour. 1/2 + 1/2 + 1/2 + 1/2 = 2 hours. To get 1/2 of an hour from 1/4 you need to add 1/4 by itself to get 1/2, so you have to add  1/2 + 1/2 to get 5 miles in 2 1/2 hours.

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I hope this helped you!

Answer:

She can walk 5 miles in 2 1/2 hours.1/4 of an hour means that 4/4 is 1 hour. If she can walk 1/2 of a mile in 1/4 of an hour, then 1/2 + 1/2 + 1/2 + 1/2 = 1 hour. 1/2 + 1/2 + 1/2 + 1/2 = 2 hours. To get 1/2 of an hour from 1/4 you need to add 1/4 by itself to get 1/2, so you have to add  1/2 + 1/2 to get 5 miles in 2 1/2 hours.

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Step-by-step explanation:

Answer:

D this is because -2 times 3 is -6 and 1 times 4 is 4 so -6+4=-2 and 2 times -2 is -4 and 1 times -4 is -4 so -4-4 is -8 D

Step-by-step explanation:

To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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Answer: smallest area- 56.25cm2      largest area- 70.56cm2

Answer:

3/7 divided by 2 1/2 = 6/35

Explanation:

3/7 ÷ 2 1/2

= 3/7 ÷ 5/2

= 3/7 × 2/5

= (3 × 2)/(7 × 5)

= 6/35

Answer:

et's solve your equation step-by-step.

(x+3)2−1=35

Step 1: Simplify both sides of the equation.

x2+6x+8=35

Step 2: Subtract 35 from both sides.

x2+6x+8−35=35−35

x2+6x−27=0

Step 3: Factor left side of equation.

(x−3)(x+9)=0

Step 4: Set factors equal to 0.

x−3=0 or x+9=0

x=3 or x=−9

Answer:

x=3 or x=−9

Answer:

Add 1 to each side

Take the square root of each side

Subtract 3 from each side

Step-by-step explanation:

(x+3)^2  -1 = 35

Add 1 to each side

(x+3)^2  -1+1 = 35+1

(x+3)^2   = 36

Take the square root of each side

sqrt ((x+3)^2)   =±sqrt (36)

x+3 = ±6

Subtract 3 from each side

x+3-3 = -3±6

x = -3±6

x = -3+6          x = -3-6

x = 3                x = -9

Answer:

(3,-1)

Step-by-step explanation:

(y,-x) is the "formula" to use on this ordered pair to find the counterclockwise rotation of 270 degrees (you should probably memorize these for your test). This means that (1,3) would become (3,-1) after flipping the x- and y-coordinates and making the x-coordinate negative.

The image of the point (1,3) after a counterclockwise rotation of 270° is (3, -1).

The given coordinate point is (1, 3).

We need to find the image of the point (1,3) after a counterclockwise rotation of 270°.

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

When we rotate a figure of 270° counterclockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

So, points (1,3) changed to (3, -1).

Therefore, the image of the point (1,3) after a counterclockwise rotation of 270° is (3, -1).

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To determine the number of students who took the test, we need to count the stems in the stem-and-leaf diagram. From the given diagram, we can see that there are 4 stems: 6, 7, 0, and 9. Each stem represents a ten's place value, so there are 10 students for each stem. Therefore, the total number of students who took the test is:

4 stems × 10 students per stem = 40 students

To find the lowest score on the test, we look at the smallest leaf value in the diagram, which is 1. However, since the smallest leaf value corresponds to the stem 0, we need to combine them to determine the lowest score. Therefore, the lowest score on the test is 01.

To find the highest score on the test, we look at the largest leaf value in the diagram, which is 9. Since the largest leaf value corresponds to the stem 9, the highest score on the test is 99.

The mean score on the test is calculated by adding up all the scores and dividing by the total number of students. Let's calculate it:

Mean score = (6 + 7 + 7 + 0 + 0 + 0 + 0 + 0 + 9 + 9 + 9 + 3 + 4) / 40

Mean score = 63 / 40

Mean score ≈ 1.575

The midrange of test scores is calculated by adding the lowest and highest scores and dividing by 2. Let's calculate it:

Midrange = (01 + 99) / 2

Midrange = 100 / 2

Midrange = 50

Therefore, the mean score on the test is approximately 1.575, and the midrange of test scores is 50.

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Answer:

emma: 6 toys, sally: 13 toys, james: 23 toys

Step-by-step explanation:

if emma had x toys, sally would have (x-3) toys. and we know that if james had 6 more toys, he would have the same amount as both girls combined. so in this case in terms of x, james would have (x+x-3-6) toys, after simplification we get 2x-9 toys..

since we know that the three of them have 52  nerf toys as total, we can set up the equation:

x= number of toys emma has

2x-9+x+x-3=52  

         4x-12=52

               x=16

emma has 16 toys, and sally has (16-3)=13 toys. finally, james has (2*16-9)=23 toys. 16+13+23=52

The mean and the standard deviation of the sampling distribution of the sample means are 49 and 1.62. The correct answer is: a. 49 and 1.62

The mean and the standard deviation of the sampling distribution of the sample means can be calculated using the formulas:

Mean of sampling distribution = Mean of population = 49

Standard deviation of sampling distribution = Standard deviation of population / Square root of sample size

= 7 / √17 ≈ 1.62

Therefore, the correct answer is: a. 49 and 1.62

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