What is the domain in interval notation of f(x)=(x+3)^2

Answer:

(b/2)^2  (ADD THIS TO BOTH SIDES IF YOU ARE USING IT)

B is the second term in a quadratic equation.

Step-by-step explanation:

The theorem that justifies why triangles ABC and DEF are congruent is: HL.

The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.

Given that:

angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)

AC = FD (a pair of congruent hypotenuse)

AB = DE (a pair of congruent legs)

Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.

Thus, the theorem that justifies why both triangles are congruent is: HL.

Learn more about the HL congruence theorem on:

https://brainly.com/question/2102943

#SPJ1

The mean of the population is the sum of the values divided by the total number of values: (3 + 4 + 11)/3 = 6. The standard deviation of the population can be calculated using the formula for population standard deviation.

(a) To find the mean of the sample means, we calculate the mean of all the possible sample means. In this case, there are nine different samples: (3, 3), (3, 4), (3, 11), (4, 3), (4, 4), (4, 11), (11, 3), (11, 4), and (11, 11). The mean of these sample means is (6 + 7 + 14 + 7 + 8 + 15 + 14 + 15 + 22)/9 = 12.

(b) To find the variance of the sample means, we use the formula for the variance of a sample mean, which is the population variance divided by the sample size. The population variance is calculated as the average of the squared differences between each value and the population mean. In this case, the population variance is\([(3-6)^2 + (4-6)^2 + (11-6)^2]/3\)= 22. The variance of the sample means is 22/2 = 11.

(c) To find the standard deviation of the sample means, we take the square root of the variance of the sample means. The standard deviation of the sample means is sqrt(11) ≈ 3.32.

Thus, the mean of the sample means is 12, the variance of the sample means is 11, and the standard deviation of the sample means is approximately 3.32.

Learn more about standard deviation here:

https://brainly.com/question/13498201

#SPJ11

Three randomly selected households are surveyed. The numbers of people in the households are 3​, 4​, and 11.

Assume that samples of size n=2 are randomly selected with replacement from the population of 3​, 4​, and 11.

3, 3

3, 4

3, 11

4, 3

4, 4

4, 11

11, 3

11, 4

11, 11

Compare the population variance to the mean of the sample variances. Choose the correct answer below.

Answer:

option c. 80 degree

Step-by-step explanation:

answer = 80 degree

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

Learn more about area

brainly.com/question/27683633

#SPJ11

Not always. There are some situations where 2 lines have the same y-intercept, but have infinite solutions. But, most of the time, yes.

---

sorry if this doesn't help

Answer:

always two line will intersect only once. if they have the same y intercepts then that is their point of intersection. these lines are perpendicular because their slopes are negative reciprocals of each other. as can be seen on the graph, their only point of intersection is at the y intercept.

Answer:

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

Step-by-step explanation:

Given

Shape: Cube

Dimension: (x+7y), (7x-y) and (xy-5).​

Required

Determine the volume

The volume is calculated by multiplying the dimensions:

\(Volume = (x+7y) * (7x-y) * (xy-5)\)

Evaluate the first 2 brackets

\(Volume = [x(7x-y)+7y(7x-y)] * (xy-5)\)

\(Volume = [(7x^2-xy)+(49xy-7y^2)] * (xy-5)\)

\(Volume = [7x^2-xy+49xy-7y^2] * (xy-5)\)

\(Volume = [7x^2+48xy-7y^2] * (xy-5)\)

Open brackets

\(Volume = xy[7x^2+48xy-7y^2] -5[7x^2+48xy-7y^2]\)

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

1. 2x + 3y = 1470

   3y = -2x + 1470

   y = -2/3x + 490 <== slope intercept form

==================

2. y = -2/3x + 490....slope = -2/3.....y int = (0,490)

   to graph, start at (0,490)....since the slope is -2/3, we will go down 2       spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.

===================

3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry

===================

4. graph the function....it will be the same line as the graph I explained before...y = -2/3x + 490

y int = (0,490)

x int = (735,0)

===================

5. original :                            new :

   2x + 3y = 1470                 2x + 3y = 1593

   3y = -2x + 1470                3y = -2x + 1593

    y = -2/3x + 490                y = -2/3x + 531

similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.

differences : These lines will have different x and y intercepts

y = -2/3x + 490 : y int = (0,490), x int = (735,0)

y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)

======================

6. pick 2 points on the line.....(0,300) and (450,0)

find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)

(0,300)....x1 = 0 and y1 = 300

(450,0)...x2 = 450 and y2 = 0

now we sub and find the slope

slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3

now we use y = mx + b

slope(m) = -2/3

use either of ur points...(450,0)...x = 450 and y = 0

now sub and find b, the y int

0 = -2/3(450) + b

0 = - 300 + b

300 = b

so ur equation is : y = -2/3x + 300....or  2x + 3y = 900

GCF(110,220) = 110

LCM(110,220) = ( 110 × 220) / 110

LCM(110,220) = 24200 / 110

LCM(110,220) = 220

hopefuly it help!!!

The simple exponential smoothing forecast for the 3rd week, given α = 0.3, cannot be calculated as the time series values for the preceding weeks are not provided.

 To calculate the error for the 3rd week using the Naïve forecast, the forecasted value for the 3rd week needs to be determined. However, since the previous time series values are not given, the Naïve forecast and subsequent error calculation cannot be performed.

  To calculate the simple exponential smoothing forecast for the 3rd week, we would need the time series values for the preceding weeks. The simple exponential smoothing method requires historical data to compute the forecast. As the values for the previous weeks (Weeks 1 and 2) are not provided, it is not possible to calculate the forecast for the 3rd week using α = 0.3.

   The Naïve forecast is a simple forecasting technique where the forecasted value for a given period is equal to the observed value of the previous period. However, in this case, only the time series value for Week 1 is provided, and the values for Weeks 2 and 3 are missing. Therefore, it is not possible to determine the forecasted value for the 3rd week using the Naïve method.

Since we cannot determine the forecasted value, we cannot calculate the error for the 3rd week using the Naïve forecast. The error calculation requires a comparison between the forecasted and actual values, which cannot be done without the necessary data.

LEARN MORE ABOUT  time series HERE:

https://brainly.com/question/29743783

#SPJ11

To find the probability of selecting a card that is either a 4 or a spade, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

Number of favorable outcomes:

There are four 4s in a deck of 52 cards, and there are 13 spades in a deck of 52 cards. However, we need to be careful not to count the 4 of spades twice. So, we subtract one from the total number of spades to avoid duplication. Therefore, there are 4 + 13 - 1 = 16 favorable outcomes.

Total number of possible outcomes:

There are 52 cards in a deck.

Now we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 16 / 52

Probability ≈ 0.3077

Therefore, the probability of selecting a card that is either a 4 or a spade is approximately 0.3077, or you can express it as a fraction 16/52.

Learn more about probability here:

brainly.com/question/32560116

#SPJ11

The answers for real objects are OA: Side a = 3.5 inches, OB: Side a = 126 inches, OC: Side a = 3 inches, and OD: Side a = 108 inches.

To determine the side lengths of the real object using the given scale factor and the side lengths of the scale drawing, we need to multiply the corresponding lengths of the scale drawing by the scale factor.

Let's apply this approach to each case:

OA:

Scale factor: 6:1

Scale drawing:

  b

  a

  21 in

Real object:

  3.5 in

To find the length of side a in the real object, we multiply the length of side a in the scale drawing (21 in) by the scale factor:

Side a = 21 in * (1/6) = 3.5 in

OB:

Scale factor: 6:1

Scale drawing:

  b

  a

  21 in

Real object:

  126 in

Using the same approach, we can find the length of side a in the real object:

Side a = 21 in * (6/1) = 126 in

OC:

Scale factor: 6:1

Scale drawing:

  b

  a

  18 in

Real object:

  12 in

Applying the formula, we calculate the length of side a:

Side a = 18 in * (1/6) = 3 in

OD:

Scale factor: 6:1

Scale drawing:

  b

  a

  18 in

Real object:

  24 in

Similarly, we multiply the length of side a in the scale drawing by the scale factor to find the length in the real object:

Side a = 18 in * (6/1) = 108 in

For more questions on scale factor, click on:

https://brainly.com/question/25722260

#SPJ8

The square roots of the given fractions are:

√(121/625) = 11/25
√(225/729) = 15/27
√(64/441) = 8/21

What is fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

To find the square root of a fraction, we can take the square root of the numerator and the square root of the denominator separately.

Square root of 121/625:

The square root of 121 is 11, and the square root of 625 is 25. Therefore,

√(121/625) = 11/25.

Square root of 225/729:

The square root of 225 is 15, and the square root of 729 is 27. Therefore,

√(225/729) = 15/27.

Square root of 64/441:

The square root of 64 is 8, and the square root of 441 is 21. Therefore, √(64/441) = 8/21.

So, the square roots of the given fractions are:

√(121/625) = 11/25
√(225/729) = 15/27
√(64/441) = 8/21

To learn more about fraction visit:

https://brainly.com/question/17220365

#SPJ4

This statement is true

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring. Probability is the measure of the likelihood of a random event happening, and it is expressed as a number between 0 and 1, with 0 implying that the event would never occur and 1 implying that it is certain to happen.

The probability of an event happening is referred to as its likelihood. Probability can be expressed as a fraction, percentage, or decimal, and it is a vital tool in statistics. It is frequently utilized in mathematics to estimate real-world situations that involve random variables such as coin flips, weather patterns, stock market trends, and even sporting events.

Learn more about probability

https://brainly.com/question/31828911

#SPJ11

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

Learn more about: Parabola

brainly.com/question/11911877

#SPJ11

The lower bound for the 99% confidence interval for the difference between clones and their original plants is -10.58 cm.

To calculate the confidence interval, we can use the formula:

\(CI = X - t * (s / \sqrt{n})\)

Where X is the sample mean difference (-5.2 cm), t is the critical t-value for a 99% confidence level with 14 degrees of freedom (since there are 15 pairs of plants and we are estimating the difference between the means), s is the sample standard deviation (6.7 cm), and n is the sample size (15 pairs).

Using a t-table or calculator, we find that the critical t-value is 2.977. Plugging in the values, we get:

\(CI = -5.2 - 2.977 * (6.7 / \sqrt{15}) = -10.58\)

Therefore, we can be 99% confident that the true mean difference between the clones and the original plants is at least -10.58 cm.

For more questions like Confidence Interval visit the link below:

https://brainly.com/question/1558096

#SPJ11

The speed of the boat increases steadily for 10 minutes and travels at a constant speed after 10 minutes.

Option D is the correct answer.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The x-axis can be assumed as 10 minutes for each unit.

Now,

From the graph, we see that the speed is steadily increasing as the time increases from x= 0 to x = 10.

From x = 10, the line on the graph is horizontal this means, the speed is constant.

Thus,

The speed of the boat increases steadily for 10 minutes and travels at a constant speed.

Learn more about speed here:

https://brainly.com/question/7359669

#SPJ2

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

160 miles because half of 300is 150 and 150-10=140 then 300-140=X or 160

The estimated population of the city in 2054, based on the exponential model, is approximately 169,725. This estimation assumes a growth rate of 0.67659% per year.

The exponential model for population growth is represented by the equation y = y0 * e^(kt), where y is the population at time t, y0 is the initial population, k is the growth rate, and t is the time elapsed. In this case, the initial population in 1990 is 103,000.

To estimate the population in 2054, we substitute the values into the equation:

y = 103,000 * e^(0.0067659 * 64)

After evaluating the exponential expression, the estimated population in 2054 is approximately 169,725.

To learn more about exponential click here: brainly.com/question/29160729

#SPJ11

Answer:

Step-by-step explanation:

HOPE IT HELPS

Answer:

The expression that could help calculate the price of the TV is;

$P - 20% of $P

Step-by-step explanation:

Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.

From the question, we can see that the regular price is $P

So now we are having 20% off;

This corresponds to;

20/100 * p = p/5 = 0.2p

So in the expression form, we can have;

$P - 20% of $P

By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:

Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:

m∠B + m∠C + m∠D = 180°

Then:

13x - 35 + 5x - 19 + 2x + 14 =180

20x -40 = 180

20x = 180 + 40

20x = 220

x = 220/20

x = 11

Now that we know the value of x, we can find the measures of the angles.

m∠B = (13x- 35)° = (13*11 - 35)° = 108°

m∠B = (5x - 19)° = (5*11 - 19)° = 36°

m∠D = (2x + 14)° = (2*11 + 14)° = 36°

Learn more about internal angles:

https://brainly.com/question/25215131

#SPJ1

The coordinates of B' are given as follows:

B'(12, -9).

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The coordinates of B are given as follows:

B(4, -3).

The scale factor is given as follows:

k = 3.

Hence the coordinates of B' are given as follows:

B'(12, -9).

A similar problem, also about dilation, is given at brainly.com/question/3457976

#SPJ1

The coordinates of B' include the following: D. (12, -9).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the dimensions (size) or side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimensions (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario and exercise, we would have to dilate the coordinates of the pre-image (triangle ABC) by using a scale factor of 3 centered at the origin in order to determine B' as follows:

Coordinate B (4, -3)        →       (4 × 3, -3 × 3) = X' (12, -9).

Read more on dilation here: brainly.com/question/11812796

#SPJ1

Answer:

14

Step-by-step explanation:

this is a 30-60-90° Δ and the sides, respectively, have the ratio of 1 : \(\sqrt{3}\) : 2

we can set up a proportion and cross-multiply based on that ratio:

w / 7\(\sqrt{3}\) = 2 / \(\sqrt{3}\)

\(\sqrt{3}\)w = 14\(\sqrt{3}\)

w = 14

Answer:

2

Step-by-step explanation:

If 1+1=2

2x1=2

Because if you add 1 two times, it is the same as multiplying 1x2

So, your answer is 2.

Four of them have in all 504 cards.

Multiplication: In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

It is given that Stephanie has 126 basketball cards

and also said that her three friends have the same number of cards as she does

which gives 126 each of three friends so, three of them are having

friend 1 =126

friend 2=126

friend 3=126

=3×126 by combining three friends cards which gives,

=378

four of them will have 4×126=504 cards.

To learn more about Multiplication visit:

brainly.com/question/5992872

#SPJ4

Of them, four have all 504 cards.

What does "multiplication" mean?

Multiplication in mathematics is the addition of equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Given her collection of 126 basketball trading cards

and added that she shares the same number of cards with her three friends.

which amounts to 126 for each of the three friends, meaning that three of them

buddy 1 = 126

friend 2=126

friend 3=126

=3×126 by combining three friends cards which gives,

=378

four of them will have 4×126=504 cards.

If a contractor is constructing a pool with the labels ABCD and if AC = 5y + 6 and BD = 8y-3, then the  value of y which is 03 that ensures the pool is a rectangle.

The statement  states that  he is building a pool labeled ABCD on the plans. If AC = 5y + 6 and BD = 8y-3

We know that rectangle has 2 diagonals of equal length.

Diagonal 1 = Ac

Diagonal 2 = BD

AC = BD

5y+ 6 = 8y -3

9 = 3y

3 = y

3 value of y ensures the pool is a rectangle .

To learn more about rectangle here-

brainly.com/question/15019502

#SPJ4