Find the image of (-1, 3) obtained by translating
2 units down, followed by a rotation of 180°
counterclockwise about the origin.
HELP QUICK

Given that $\cos(x) = \frac{7}{11}$ in quadrant 1. We need to find the value of $\sin(2x)$.We know that $\sin(2x) = 2\sin(x)\cos(x)$Using the Pythagorean identity, we have:\[\sin^2 x + \cos^2 x = 1\]Squaring both sides, we get:\[\sin^2 x = 1 - \cos^2 x\].

Substituting the values, we get:\[\sin^2 x = 1 - \left(\frac{7}{11}\right)^2\]Simplifying, we get:\[\sin^2 x = \frac{120}{121}\]Therefore, we have:\[\sin x = \pm\frac{2\sqrt{30}}{11}\]Since $\sin x$ is positive in quadrant 1, we have:\[\sin x = \frac{2\sqrt{30}}{11}\].

Therefore,\[\sin(2x) = 2\sin(x)\cos(x) = 2\cdot\frac{2\sqrt{30}}{11}\cdot\frac{7}{11} = \frac{56\sqrt{30}}{121}\]Next, we are given that $\tan(x) = \frac{25}{2}$ in quadrant 1. We need to find the value of $\cos(2x)$.We know that $\cos(2x) = \frac{1 - \tan^2(x)}{1 + \tan^2(x)}$Substituting the values, we get:\[\cos(2x) = \frac{1 - \left(\frac{25}{2}\right)^2}{1 + \left(\frac{25}{2}\right)^2} = \frac{-375}{625} = -\frac{3}{5}\]Therefore, $\cos(2x) = -\frac{3}{5}$.

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On factorising quadratic equation 108 − 3 x − x^2 we get values of x = 9 and x = -12.

To factorise we take steps:

X² + 3X - 108 = 0

X² + 12X - 9X - 108 = 0

X(X + 12) -9(X + 12) = 0

(X - 9)(X + 12) = 0

X = 9 and X = -12

On factorising quadratic equation 108 − 3 x − x^2 we get values of x = 9 and x = -12.

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Answer:

Angle 7 or angle DHG

Step-by-step explanation:

Vertical means the opposite angle, or in dictionary definition means each of the pairs of opposite angles made by two intersecting lines. So the vertical angle to angle LHI (angle 9) will be angle DHG (angle 7)

Answer:

50

Step-by-step explanation:

The median from vertex \($a$\) is perpendicular to the median from vertex $b$. the lengths of sides \($ac$\) and \($bc$\) are 6 and 7, respectively then, \(AB^2 = \frac{85}{4}$\).

Let \($M$\) be the midpoint of side \($AC$\), and \($N$\) be the midpoint of side \($BC$\). Since the median from vertex \($A$\) is perpendicular to the median from vertex \($B$\), we have \($AM \perp BN$\).

Let \(AB = x$. Since $M\) is the midpoint of \($AC$\), we have \($CM = \frac{AC}{2} = 3$\).

Similarly, \($BN = \frac{BC}{2} = \frac{7}{2} = 3.5$\). Now we can use the Pythagorean

theorem in triangle \($ABN$\) to find \($AB$\).

Using the Pythagorean theorem, we have:

\($AB^2 = AN^2 + BN^2$\)

Substituting the known values, we get:

\($AB^2 = \left(\frac{AC}{2}\right)^2 + \left(\frac{BC}{2}\right)^2$\)

\($AB^2 = 3^2 + \left(\frac{7}{2}\right)^2$\)

\($AB^2 = 9 + \frac{49}{4}$\)

\($AB^2 = \frac{36 + 49}{4}$\)

\($AB^2 = \frac{85}{4}$\)

Therefore, \(AB^2 = \frac{85}{4}$.\)

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If the mean time is 35 minutes and standard deviation is 5 minutes , then the probability that changing the brakes on a car will take more than 44 minutes is 0.0359 .

We use the standardized normal distribution to find the probability that changing the brakes on a car will take more than 44 minutes.

First, we need to standardize the value 44 minutes using the formula:

⇒ z = (x - μ)/σ ;

where μ = mean = 35, and σ = standard deviation = 5 .

Substituting in the values, we get:

⇒ z = (44 - 35)/5

⇒ z = 1.8

Next, we need to find the area under the standard normal distribution curve to the right of z = 1.8.

⇒ P(x > 44) = P(z > 1.8)

⇒ 1 - P(z < 1.8)

⇒ 1 - 0.9641

= 0.0359.

Therefore , the required probability is 0.0359 .

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Answer:16.1

Step-by-step explanation:

Based on the fact that Adrian will use 68 ft of fencing, the dimensions of the rectangular rabbit pen can be found to be 17 feet for the width and 51 feet for the length.

The length of the rabbit pen is to be three (3) times as long as the width so we can assume that the width is x feet.

In that case, the formula to find the value of x which is the width is:

x + 3x = 68

4x = 68

x = 68/4

x = 68/4

x = 17 feet

The length of the rectangular rabbit pen is therefore:

= 3x

= 3 x 17

= 51 feet

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Answer:

0.8 hours = 48 minutes per lawn

Step-by-step explanation:

10 lawns in 8 hours

hours per lawn 8/10 = 0.8 hours = 48 minutes

Answer:

4/5 hour per lawn

Step-by-step explanation:

We want to find Hunter's rate in hours per lawn.

Therefore, we must divide the number of hours by the number of lawns.

\(\frac{hours}{lawns}\)

He mowed 10 lawns in 8 hours.

\(\frac{8}{10}\)

This fraction can be simplified. Both the numerator and denominator can be divided by 2.

\(\frac{8/2}{10/2}\)

\(\frac{4}{5}\)

If we multiply by 60, we can find how many minutes this is. (60 minutes = 1 hour)

\(\frac{4}{5}*60=48\)

His rate is 4/5 hour per lawn or 48 minutes per lawn.

The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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A correlation coefficient based on the observational study cannot be used to support a claim of cause and effect. The correct answer is D: never.

Correlation does not imply causation, and while a strong correlation between two variables may suggest that there is a relationship between them, it does not prove that one variable causes the other. Observational studies are particularly susceptible to confounding variables, which can make it difficult or impossible to determine whether a relationship between two variables is causal or not.

To establish causality between two variables, a randomized controlled experiment is required. In a randomized controlled experiment, the experimenter can manipulate the independent variable and observe the effect on the dependent variable, while controlling for other variables that might affect the outcome. By randomly assigning subjects to different treatment groups, the experimenter can ensure that any differences in the outcome between groups are due to the treatment, rather than some other factor.

Therefore, while a correlation coefficient can be a useful tool for describing the relationship between two variables, it cannot be used to establish causality.

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Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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To prove congruence, we need to have enough information about all six corresponding parts of the triangles, or enough information to apply one of the congruence criteria (SAS, ASA, etc.).

To show that two triangles are congruent, we need to have enough information to prove that all six pairs of corresponding parts (angles and sides) are congruent.

This is known as the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) congruence criteria, depending on the order of the corresponding parts.

For example, if we know that two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then we can prove that the two triangles are congruent using the SAS criterion.

Similarly, if we know that two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then we can prove that the two triangles are congruent using the ASA criterion.

However, if we only have information about one or two pairs of corresponding parts, it may not be enough to prove congruence.

For example, knowing that two triangles have the same base and height (which are corresponding parts), does not necessarily mean that they are congruent, as there could be other non-congruent triangles with the same base and height.

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Answer:

The angle measures are

x + (x + 30) + 2x = 180

x = 37.5

Step-by-step explanation:

x + (x + 30) + 2x = 180.  (combine x and 2x)

3x + (x + 30) = 180.  (combine 3x and x, 30 cant combine)

4x + 30 = 180.  (subtract 30 from both)

4x = 150.  (divide both sides by 4)

x = 37.5

A 3D shape's net is what it looks like after it's flattened out. A net can be folded into a three-dimensional shape. The correct option is C.

A 3D shape's net is what it looks like after it's flattened out. A net can be folded into a three-dimensional shape. For the same 3D shape, there may be multiple potential networks. You can make a net out of paper and fold it into the desired shape.

The net of the square pyramid has a square and 4 triangles. For a pyramid with a base as a polygon having n sides, the number of triangles is n.

Hence, it can be concluded that a pyramid can contain any number of triangles greater than or equal to 3. Thus, the correct option is C.

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Answer:

26√2 ≈ 36.8 units

Step-by-step explanation:

Triangle is isosceles

x² = 26² + 26²

x = \(\sqrt{26^2(2)}\) = 26√2 ≈ 36.8 units

D. deposit

kaakakashshhhshssbs

Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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The marginal probability of y1 and y2 are not independent.

The given marginal probability function of y1 was derived to be binomial with n=2 and p=1/3.  To check the independence, let's compute the joint probability of y1 and y2 using the marginal probability functions of both random variables.

Let's denote the joint probability as P(y1,y2).From the given information, the probability function of y1 is P(y1=k) = (2Ck) * (1/3)^k * (2/3)^(2-k), for k=0,1,2.  (2Ck) is the binomial coefficient or combination.The probability function of y2 can also be derived in the same way as P(y2=k) = (2Ck) * (1/3)^k * (2/3)^(2-k), for k=0,1,2.The joint probability of y1 and y2 can be computed asP(y1,y2) = P(y1=k1 and y2=k2) = P(y1=k1) * P(y2=k2)For k1=0,1,2 and k2=0,1,2, P(y1,y2) can be computed using the above equation.

For instance, when k1=1 and k2=2,P(1,2) = P(y1=1) * P(y2=2) = (2C1) * (1/3) * (2/3) * (2C2) * (1/3)^2 * (2/3)^0 = 0.In general, if y1 and y2 are independent, P(y1,y2) = P(y1) * P(y2) should hold for any pair (y1,y2). However, the joint probability computed above may not always be equal to the product of marginal probabilities, which implies y1 and y2 are not independent.

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To determine the probability of an event where both dice are odd, let's first list all the possible odd numbers on a die: {1, 3, 5}.

Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

Now, let's find all the combinations of two dice showing odd numbers:

1. (1, 1) 2. (1, 3) 3. (1, 5) 4. (3, 1) 5. (3, 3) 6. (3, 5) 7. (5, 1) 8. (5, 3) 9. (5, 5)

There are a total of 9 combinations where both dice show odd numbers.

So, the size of the set that corresponds to the event that both dice are odd is 9.

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Answer:

a:make a table ,chart or list

Answer:

x = 1/10

Step-by-step explanation:

3x - 4/5 = -1/2

-1/2 + 4/5 =

-5/10 + 8/10 =

3/10

3x = 3/10

x = 1/10

Answer: 36

Step-by-step explanation: 56 is the width 2/3 of 56 is 36

Answer:

36

Step-by-step explanation:

Answer:

Substitution property

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

if 5 20s is 100 then do it times three if that makes sence lol

Answer:

2, 1

Step-by-step explanation:

half of 64 is 32

half of 32 is 16

half of 16 is 8

half of 8 is 4

half of 4 is 2

half of 2 is 1

Answer:

2, 1

Step-by-step explanation:

you are dividing it in half or by two

The running rate is 5 miles per hour.Let's denote the running rate as "r" and the driving rate as "9r" (since the driving rate is nine times the running rate).

To find the running rate, we need to determine the time spent driving and running separately and then add them together to equal 3 hours.

The time spent running can be calculated as the distance divided by the running rate:

Time running = Distance / Running rate = 5 / r

The time spent driving can be calculated similarly:

Time driving = Distance / Driving rate = 90 / (9r) = 10 / r

The total time spent driving and running is given as 3 hours:

Time running + Time driving = 3

5 / r + 10 / r = 3

To solve this equation, we can combine the fractions on the left side:

(5 + 10) / r = 3

15 / r = 3

Next, we can cross-multiply to isolate the variable:

15 = 3r

Dividing both sides by 3, we find:

r = 5

Therefore, the running rate is 5 miles per hour.

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When the pile is 22 feet high, the height of the pile changes to 20/1089π.

Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?

The volume of cone is V = 1/3 * pi * r ^ 2 * h

d=3h

2r = 3h

r = (3h)/2

V = 1/3 * pi * r ^ 2 * h

= 1/3 * pi * ((3h)/2) ^ 2 * h

= 1/3 * pi((9 * H ^ 2 )/4) * h

= (9pi)/12 * h ^ 3

Differentiate w.r.to t

(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)

(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)

(dV)/(dt)=20, h=22 feet

20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)

(dh)/(dt) = 80/ (9pi * (22^ 2))

h^ t = 20/ 1089 *pi   ft / min

Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π

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The distance between starting and the ending point is 19.92 miles.

The diagram for the question is shown:

First 6 miles in north direction shown by AB.

Then 19 miles in east direction shown by BC.

Now distance between starting and the ending point is: AC.

AC² = AB² + BC²

AC² = 6² + 19²

AC² = 36 + 361

AC = √397

AC = 19.92

Thus, distance between starting and the ending point is 19.92 miles.

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