Which of the following best describes a geometric rotation?
A
A transformation that enlarges or reduces the size of a figure by certain scale factor
B
A transformation that slides a figure to a new location
С
A transforation that flips a figure across a line
D
A transformation that turns a figure around a point

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope / gradient

c is the y intercept

y = 3x + 7

Comparing this equation with the general form above

Gradient of the line = 3

2y - 6x = 8

Divide both sides by 2

We have

y - 3x = 8

To make y the subject move 3x to the right side of the equation

That's

y = 3x + 8

Comparing with the general form above that's y = mx + c

The gradient = 3

y = 3x + 7

A(2 , y ) , B( x , 4)

Since they lie on the line we can substitute their values into the equation to find the missing points

For A(2 ,y)

We have

y = 3(2) + 7

y = 6 + 7

For B( x , 4)

4 = 3x + 7

3x = 4 - 7

3x = - 3

Divide both sides by 3

Hope this helps you

Answer: 13

Step-by-step explanation:

3/2(4x – 1) – 3x = 54 – (x + 2)

x=13.375

Hope this helps

Answer:

6a

Step-by-step explanation:

Answer:

6a

Step-by-step explanation:

3a+2a+a= 6a

6-4-2=0

6a+0=6a

Answer: C: y=6×6^x

Step-by-step explanation:

Hope this helps! Good luck!

Answer:

I can't understand the typing

Answer:

cant see the image

Step-by-step explanation:

By answering the above question, we may state that Shade the region to line the left of the open circle, since x is less than 4.

A line is a geometric object that is infinitely long and has no width, depth, or curvature. A line, which can also exist in two-, three-, and more-dimensional spaces, is therefore a one-dimensional object. A line is often used to refer to a line segment with two points as its endpoints. A line is a flat, one-dimensional object that may extend indefinitely in both directions and has no thickness. The terms "straight line" or "old correct line" are sometimes used to describe a line that has no "wobble" anywhere along its length.

plot the inequality 4x-22<-6 on a number line,

4x - 22 + 22 < -6 + 22

4x < 16

4x/4 < 16/4

x < 4

Plot an open circle at 4 on the number line to indicate that x is not included in the solution set.

Shade the region to the left of the open circle, since x is less than 4.

The resulting graph should look like this:

     ○----------------->

     |  |  |  |  |  |  |

   -∞  -5  -4  -3  -2  -1  0  1  2  3  4  5  6

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Answer:

GCF is 8

32x - 24 = 8(4x - 3)

Step-by-step explanation:

1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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Answer:

No solutions

Step-by-step explanation:

3(x-6)= 3x-18

3x=15≠3x-18

Answer:

Step-by-step explanation:

Find the distance between A(-7, 1) and C(1, 1), since the y-coordinates are same, the distance is the difference of x- coordinates:

AC and BD are diagonals both are same

\(\\ \sf\longmapsto AC=\sqrt{1+8)^2+(1-1)^2}\)

\(\\ \sf\longmapsto AC=\sqrt{8^2+0^2}\)

\(\\ \sf\longmapsto AC=\sqrt{64}\)

\(\\ \sf\longmapsto AC={8}units\)

The revised MeanMedian2 class allows the user to input up to 20 values, with the option to stop entering numbers by inputting 9999. It calculates both the mean and median of the provided values.

To implement this functionality, the MeanMedian2 class can prompt the user to enter values in a loop until either 20 values are entered or the user inputs 9999. The entered values can be stored in a list. Once the user is done entering values, the class can compute the mean and median. For the mean, it can sum all the values in the list and divide by the number of values. For the median, it needs to handle two scenarios: an odd number of values and an even number of values. If the list has an odd number of values, the median can be obtained by simply finding the middle value. However, if there is an even number of values, the two middle values can be averaged to get the median.

With this revised class, users can easily input any number of values, up to 20, and get accurate mean and median calculations. Additionally, the option to quit by entering 9999 provides a convenient way for users to stop entering values whenever they want. This updated implementation improves the flexibility and usability of the MeanMedian2 class.

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A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time-efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.

Answer:

90 + 10 = 100 ;-;

Step-by-step explanation:

Choir B has a higher percentage of students who like musicals.

what is percentage ?

Percentage is a way of expressing a proportion or a fraction out of 100. It is a widely used concept in mathematics, finance, statistics, and other fields. For example, if 20 out of 100 students in a class like pizza, we can say that the percentage of students who like pizza is 20%. To calculate the percentage, we usually multiply the given fraction by 100. For instance, if 3 out of 5 students like math, we can calculate the percentage of students who like math as follows:

(3/5) x 100 = 60%

Thus, 60% of the students in the class like math.

To determine which choir has a higher percentage of students who like musicals, we need to calculate the percentage of students in each choir who like musicals.

For choir A, 39 out of 52 students like musicals:

39/52 = 0.75 or 75%

For choir B, 35 out of 44 students like musicals:

35/44 = 0.795 or 79.5%

Therefore, choir B has a higher percentage of students who like musicals.

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Since both sides simplify to 1, we have shown that (2 - 1) (2 - 1) = 2 - 1 when x and y are positive integers.

The positive integers are the numbers 1, 2, 3, ... sometimes called the counting numbers or natural numbers. A positive number is any number greater than 0.

To show that (2 - 1) (2 - 1) = 2 - 1 when x and y are positive integers, we can expand both sides of the equation and simplify:

Left side: (2 - 1) (2 - 1)

= 1 * 1

= 1

Right side: 2 - 1

= 1

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If a coccus (a spherical bacteria) divides along two perpendicular planes and four cells remain attached together, it is called a tetrad. Therefore, the correct answer is A. tetrad.

A. Tetrad: A tetrad refers to a group of four cells resulting from the division of a single bacterium along two perpendicular planes. This arrangement forms a square or cube-like structure where the four cells remain attached together. Tetrads are commonly observed in certain bacteria, such as the genus Micrococcus.

B. Sarcina: Sarcina is a term used to describe a specific arrangement of cocci bacteria. In this arrangement, cocci divide along three perpendicular planes, resulting in packets of eight cells. Each packet resembles a cube-like structure composed of eight cells tightly attached together. Sarcinae are commonly observed in the genus Sarcina.

C. Staphylococcus: Staphylococcus refers to a genus of bacteria that are spherical (cocci) in shape. However, staphylococci typically divide randomly in multiple planes and form irregular clusters or grape-like arrangements rather than specific patterns like tetrads or sarcinae.

D. Streptococcus: Streptococcus is another genus of bacteria that are spherical (cocci) in shape. However, streptococci typically divide along a single axis and form chains or pairs rather than specific patterns like tetrads or sarcinae.

Considering the given scenario where a coccus divides along two perpendicular planes and four cells remain attached together, the correct term to describe this arrangement is A. tetrad.

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The term for a coccus bacterium dividing along two distinct perpendicular planes, resulting in four attached cells, is a 'tetrad'. This is different than 'sarcina', which is a genus of bacteria known for this behavior, and 'staphylococcus' and 'streptococcus', which are other forms of bacterial groupings.

When a coccus bacterium divides in two distinct perpendicular planes resulting in four cells that remain adhered together, it forms a particular structure called a tetrad. This pattern of cell division and grouping is characteristic of some gram-positive bacteria. However, it's important to differentiate here that 'tetrad' just refers to this particular grouping of four cocci bacteria, whereas Sarcina is a genus of bacteria that are known for grouping in this fashion. On the contrary, Staphylococcus and Streptococcus represent other forms of groupings - spherical bacteria arranged in irregular clusters or chains, respectively.

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Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

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Step-by-step explanation:

112+68+112+x = 360⁰

292⁰+x = 360⁰

x = 360⁰- 292⁰

x= 68⁰

Answer:

-2

Step-by-step explanation:

from one point to another, you go down 2 and over 1

Answer:

the answer is -2

Step-by-step explanation:

this is because for every unit it goes to the right it goes down 2 which makes it negitive if it is facing down and positive if facing up.

Answer:

Step-by-step explanation:

An angle is defined as a figure formed by two rays with a common endpoint, called the vertex, that determines the measure of extent of the figure from one ray to the other.

Answer: An angle is a combination of two rays (half-lines) with a common endpoint.

Step-by-step explanation:

The length of the segment QR, obtained using the angle bisector theorem is; SR ≈ 11.4 units

The angle bisector theorem states an angle bisector in a triangle, intersects opposite side, such that the ratio of the two segments formed by the point of intersection is the same as the ratio of the other two sides of the triangle.

The angle congruence marks at angle ∠Q, indicates that the angle ∠PQS and the angle ∠SRQ are congruent.

Therefore, the segment QS is an angle bisector of the angle ∠PQR.

The angle bisector theorem, indicates that we get;

30/12 = PS/SR

PS = PR - SR, therefore;

30/12 = 5/2 = (PR - SR)/SR

Plugging in the values, we get;

5/2 = (40 - SR)/SR

5 × SR = 2 × (40 - SR) = 80 - 2 × SR

5 × SR + 2 × SR = 80

7 × SR = 80

SR = 80/7 ≈ 11.4

The length of the segment SR is about 11.4 units

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Answer:

m<TSU = 65

Step-by-step explanation:

As one can see, the measure of angle (RST) is (90) degrees. This is indicated by the box around the angle. As a general rule, when there is a box around an angle, the angle measure if (90) degrees. It is also given that the measure of angle (RSU) is (25) degrees. As per the given diagram, the sum of the measures of angles (RSU) and (UST) is (RST). Therefore, one can form an equation and solve for the measure of angle (UST).

(RSU) + (UST) + (RST)

Substitute,

25 + (UST) = 90

Inverse operations,

25 + (UST) = 90

UST = 65

(<UST) is another way of naming angle (TSU).

Answer:

∠ TSU = 65°

Step-by-step explanation:

∠ RST = 90°

∠ RSU + ∠TSU = ∠ RST , that is

25° + ∠ TSU = 90° ( subtract 25° from both sides )

∠ TSU = 65°

Answer:

x-intercept : (-1.2,0) 

y-intercept : (0,-0.7)

Step-by-step explanation:

Hello!

An x-intercept is when the y-value is 0, and a y-intercept is when the x value is 0.

Another way to think about it, x-intercepts intersect with the x-axis, while the y-intercept intersects with the y-axis.

A coordinate, a point on a graph, is written as (x,y) or x-position and y-position.

x-intercept : (-1.2,0)  

y-intercept : (0,-0.7)

Answer:

Step-by-step explanation:

Examples: 4.121121112... For each square below, is the side length rational or irrational? A Blom A = 89 cm 1. What is the formula for the area of a...

Answer

First Question

Options A and B are correct.

The correct answers that satisfy the inequality given include 1600 and 2000.

Second Question

d = 948.6 m

Explanation

We are given that

√x ≥ 40

We are then asked to pick the options that satisfy the given expressio,

To do this, we need to first square both sides

√x ≥ 40

x ≥ 1600

So, for the options, we will pick the answers that are greater than or equal to 1600

The correct answers include 1600 and 2000.

All the other options are not equal to or greater than 1600.

Second Question

We are given that the expression that gives the relationship between the distance the object falls (d) and the time taken (t) is

√d = (t) . (2.8)

√d = 2.8t

We are then asked to solve the distance a screw that falls for 11 seconds falls

√d = 2.8t

t = 11 seconds

√d = 2.8t

√d = 2.8 (11)

√d = 30.8

Square both sides

d = 948.6 m

Hope this Helps!!!

When Alonzo splits 3/4 pounds of candy among 4 people the unit rate in pounds per person is 3/16 pounds per person

The ratio of two measures, with one as the second of the item, is known as unit rate.

For the problem where Alonzo have to split 3/4 pounds of candy, the  unit rate is solved by division.

In this case, Alonzo will divide each the 3/4 pounds by 4 to get a value of which is the unit rate

The unit rate of candy in pounds per person

= 3/4 pounds / 4 persons

= 3/16 pounds per person

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Answer:

42 square inches

Step-by-step explanation:

Area of a triangle = (1/2)(base)(height)

A = 1/2(12)(7)

A = 1/2(84)

A = 42

Answer:

7/2

Step-by-step explanation:

Answer:

a= 5    and   b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2​

We should note that since it has infinitely many solutions then,

\(\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }\)

Hence

2/a-b  =  3/a+b   =     7/3a +b-2

2/a-b  =  3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b  -------------------------------------------(1)

Similarly

3/a+b   =     7/3a +b-2

cross-multiply

7(a+b)  = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b =   -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2)   and solve for b

-2(5) + 4b = -6

-10  +  4b  = -6

add 10 to both-side of the equation

-10  + 10+ 4b  = -6+10

4b = 4

divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore,   a= 5    and   b=1