Q4. A. A triangle has vertices (-2, 3), (1, 1) and (-1,-2).
a. Find the length of the sides. (3mks)
b. Name this triangle. (Imks)​

The solution to the system of equations is x=2 and y=-2.

To solve the system of simultaneous equations graphically, we need to graph both equations on the same coordinate plane and find their point of intersection.

First, we'll rearrange both equations to be in the form y=mx+b, where m is the slope and b is the y-intercept.

y = 2 - 2x can be rewritten as y = -2x + 2

y = 2x - 6 can be rewritten as y = 2x - 6

Now, we'll plot both equations on the same coordinate plane. To do this, we'll create a table of values for each equation and plot the points.

For y = -2x + 2: (0,2), (1,0), (2,-2)

For y = 2x - 6:(0,-6), (1,-4), (2,-2)

Next, we'll plot these points on the same graph and draw the lines connecting them.

The point where the lines intersect is the solution to the system of equations. From the graph, we can see that the point of intersection is (2,-2).

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The correct responses are: "Triangle DBC is similar to triangle ABC" and "The length of side DE is 13."

Since triangle ABC is similar to triangle DBE, we know that the corresponding angles are congruent and the corresponding sides are proportional.

From the given information, we know that side BC of triangle ABC corresponds to side BE of triangle DBE, since they share vertex B. Therefore, we can use the proportion:

BC / BE = AC / DE

Substituting the given values, we have:

BC / 5 = 7.5 / 13

Solving for BC, we get:

BC = (5 x 7.5) / 13 = 2.88 (rounded to two decimal places)

Therefore, the length of side BC is 2.88.

Now we can check which of the given statements are true:

"The length of side AB is 3.75." We do not have enough information to determine the length of side AB, so this statement cannot be determined to be true or false based on the given information.

"Triangle DBC is similar to triangle ABC." This statement is true, since they share angle B and the sides BC and BE are proportional.

"Angle C in triangle ABC is congruent to angle D in triangle DBE." This statement cannot be determined to be true or false based on the given information, since we do not know which angle in triangle DBE corresponds to angle C in triangle ABC.

"The length of side AC is 4.29." This statement cannot be determined to be true or false based on the given information, since we only have information about side BC and side BE. We do not have enough information to determine the length of side AC.

"The length of side DE is 7.8." This statement is false, since the length of side DE is given as 13, not 7.8.

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The magnitude of vector v is:
|v| = 7

The magnitude of v is simply the length of the vector v, which can be found using the Pythagorean theorem. The vector v is given as v = 7i.

To find the magnitude of v (|v|), use the formula:
|v| = √(x² + y²)

where x and y are the components of the vector v. In this case, x = 7 (from 7i) and y = 0 (since there is no j component).

Now, plug in the values of x and y into the formula:
|v| = √(7² + 0²)
|v| = √(49 + 0)
|v| = √(49)
|v| = 7

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The final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.

The final temperature can be calculated by subtracting the total temperature change from the initial temperature of 4°C.

The total temperature change during the next six hours can be calculated by multiplying the mean rate of -0.8°C per hour by the number of hours, which is 6.

-0.8°C/hour x 6 hours = -4.8°C

Therefore, the temperature after the next six hours will be:

4°C - 4.8°C = -0.8°C

For the next two hours, the temperature changed at a mean rate of -0.8°C per hour. This means the temperature decreased by:

-0.8°C/hour x 2 hours = -1.6°C

So the final temperature will be:

-0.8°C - 1.6°C = -2.4°C.

Therefore, the final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.

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To show that the quadrilateral on the tile floor is a parallelogram, you can use the opposite sides theorem, opposite angles theorem, consecutive angles theorem, and Diagonal bisector theorem.

1. Opposite sides theorem: If both pairs of opposite sides of the quadrilateral are congruent (equal in length), then it is a parallelogram.

2. Opposite angles theorem: If both pairs of opposite angles of the quadrilateral are congruent (equal in measure), then it is a parallelogram.

3. Consecutive angles theorem: If the consecutive angles of the quadrilateral are supplementary (their sum is 180 degrees), then it is a parallelogram.

4. Diagonal bisector theorem: If the diagonals of the quadrilateral bisect each other (divide each other into two equal parts), then it is a parallelogram.

Choose the most appropriate theorem based on the given information and apply it to prove that the quadrilateral is a parallelogram.

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For the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, the simplified-value is 9m¹⁰n⁻¹p⁻⁷.

To simplify the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, we first use the exponent-rule that states (qᵃ)ᵇ = qᵃᵇ to simplify the first part of the expression:

⇒ (3m⁴n)³ = 3³(m⁴)³n³ = 27m¹²n³;

Next, we can simplify the denominator by using the rules of exponents to combine the like terms:

⇒ 6m⁴n⁹p⁸ = 2×3m⁴n⁹p⁸;

Substituting the values,

We get;

⇒ (27m¹²n³)×(2m²n⁵p)/(2*3m⁴n⁹p⁸);

Simplifying the expression by cancelling out the common factors, we get:

⇒ 9m¹⁰n⁻¹p⁻⁷;

Therefore, the simplified-value is : 9m¹⁰n⁻¹p⁻⁷.

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The given question is incomplete, the complete question is

What is the simplified form of the expression below (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸;

Answer:

If point R is reflected across the x-axis, its y-coordinate will change sign. Therefore, the y-coordinate of R' will be 3 (the opposite of -3). Thus, the answer is A. (-8, 3)

Step-by-step explanation:

The shape formed by a solid intersecting with a plane, so the At level X = 3, the area of the vertical cross-section A is 108 square units.

To find the area of the vertical cross section A at the level X = 3, we need to find the equation of the circle when it is intersected by the plane X = 3.
First, let's find the value of y when X = 3 using the equation of the circle x^2 + y^2 = 36:

(3)^2 + y^2 = 36
9 + y^2 = 36
y^2 = 27
y = ±√27

Since we are dealing with a circle, there are two points on the circle at X = 3, which are (3, √27) and (3, -√27).

The distance between these two points will be the base of the triangle, which is also equal to its height (as given in the problem).

Base and height of the triangle: 2 * √27

Now we can find the area A of the vertical cross-section, which is a triangle with equal base and height:

A = 1/2 * base * height
A = 1/2 * (2 * √27) * (2 * √27)
A = 4 * 27
A = 108

So, the area of the vertical cross-section A at the level X = 3 is 108 square units.

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Point B is the image of point A under a rotation about the origin.

Rotation is a transformation in which an object or a point is turned around a fixed point or a fixed axis. The fixed point or axis is called the center of rotation, and the angle of rotation specifies the amount and direction of the turn. When an object is rotated, its orientation changes but its shape and size remain the same.

For example, if you rotate a square by 90 degrees around its center, it will look the same as before, but it will be oriented differently. Similarly, if you rotate a point in a coordinate system around the origin, its position will change, but its distance from the origin will remain the same.

Rotations are commonly used in geometry, physics, and engineering to describe the motion of objects, such as the rotation of the Earth around its axis or the rotation of a wheel on an axle. They are also used in computer graphics to create animations and in robotics to control the movement of robotic arms and other devices.

When point A is rotated about the origin to form point B, the distance between the origin and each point remains the same. The direction from the origin to point A and the direction from the origin to point B are related by the angle of rotation. Specifically, point B is the image of point A under a rotation about the origin.

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The average rate of change of the function g(x)=6x from x=-1 to x=3 is found to be 6.

The function g(x) = 6x describes a relationship between x and the value of 6 times x. We want to find the average rate of change of this function from x = -1 to x = 3. The average rate of change tells us the average amount by which the function changes per unit of change in x over this interval.

In this case, by using the function g(x) = 6x and evaluating it for x = 3 and x = -1, a difference of 18 - (-6) = 24 is found. The difference in x's values is equal to 3 - (-1) = 4. We divide these to get an average rate of change of 6.

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So the estimated value of √6.02 using differentials is approximately 2.4556.

The change in g(x,y,z) can be estimated using partial derivatives and differentials.

We can start by finding the partial derivatives of g(x,y,z) with respect to x, y, and z:∂g/∂x = 3 + cos(z)∂g/∂y = -sin(z) + 1∂g/∂z = -x sin(z) - y cos(z)Next, we can use the point P0(1,-3,0) and the distance ds = 0.1 to find the differentials dx, dy, and dz:dx = -2/√6 dsdy = 2/√6 dsdz = 1/√6 dsUsing these values, we can estimate the change in g:Δg ≈ (∂g/∂x) dx + (∂g/∂y) dy + (∂g/∂z) dzΔg ≈ (3 + cos(0)) (-2/√6 ds) + (-sin(0) + 1) (2/√6 ds) + (-1 sin(0) - (-3) cos(0)) (1/√6 ds)Δg ≈ (3 - 2/√6) dsPlugging in ds = 0.1, we get:Δg ≈ (3 - 2/√6) (0.1)Δg ≈ 0.389

Therefore, the change in g(x,y,z) is estimated to be approximately 0.389 units if the point P(x,y,z) moves from P0(1,-3,0) a distance of ds = 0.1 unit toward the point P1(-1,-1,2).

Suppose we want to estimate the value of √6.02 using differentials. We can start by choosing x = 6 and Δx = 0.02. Then, we need to find the derivative of f(x) = √x with respect to x:

f(x) = √x

f'(x) = 1/(2√x)

Using these values, we can estimate Δy:

Δy ≈ dy = f'(x) Δx

dy ≈ (1/(2√6)) (0.02)

dy ≈ 0.005

This means that a small change of 0.02 in x produces a small change of approximately 0.005 in y. To estimate the value of √6.02, we can add this change to the known value of √6:

√6.02 ≈ √(6 + 0.02) ≈ √6.04 ≈ 2.4556

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Answer:

Domain is all x values

Range is all y values

Step-by-step explanation:

Your image is not clear enough for me to see the x or y coordinates so hope that helps you to figure it out on your own

To construct a confidence interval for the population proportion of Americans over 40 who smoke, we can use the formula:

Confidence Interval = Sample Proportion ± (Critical Value) x Standard Error

where the sample proportion is the number of individuals who don't smoke divided by the total sample size (806/1089), the critical value can be found using a normal distribution table or calculator with the given confidence level (85%), and the standard error can be calculated using the formula:

Standard Error = √[ (Sample Proportion x (1 - Sample Proportion)) / Sample Size ]

Plugging in the given values, we get:

Sample Proportion = 806/1089 = 0.740
Sample Size = 1089
Standard Error = √[(0.740 x 0.260) / 1089] = 0.016
Critical Value (using a normal distribution table or calculator) = 1.440

Therefore, the 85% confidence interval for the population proportion of Americans over 40 who smoke is:

0.740 ± (1.440 x 0.016) = 0.740 ± 0.023

Rounding to three decimal places, the confidence interval is (0.717, 0.763). This means that we can be 85% confident that the true proportion of Americans over 40 who smoke falls between 71.7% and 76.3%.

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The composite function fg(x) is a linear function​ by the proof shown below

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

f(x) = 2x - 1

g(x) = -x + 3

The above functions are linear functions

This means that the function fg(x) will also be a linear function​

To prove this, we have

f(g(x)) = 2(g(x)) - 1

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

f(g(x)) = 2(-x + 3) - 1

So, we have

f(g(x)) = -2x - 7

Hence, the function is a linear function

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Answer:

64

Step-by-step explanation:

Answer:

64...i think

Step-by-step explanation:

125 - 88=37

88-64=24

PLS MARK BRAINLIEST

The number of different committees that are possible is: 126

When you have a number of elements and then want to form subsets of elements of particular smaller size, you can utilize combinations or permutations. If the order of placement of the elements does not matter, we use combinations to quantify the number of groups formed.

Now, the order of the members in the committee does not matter and as such we will use combinations which has the formula:

nCr = n!/(r!(n - r)!)

We are given:

n = 9

r = 5

Thus:

9C5 = 9!/(5!(9 - 5)!)

= 126 different committees

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Only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

Total number of correct cuts = 42 + 55 + 13 + 24 + 17 = 151

Total number of cuts = 100 + 100 + 100 + 100 + 100 = 500

Percentage of correct cuts = (151/500) * 100 = 30.2%

This statement is not valid, as only 30.2% of the cuts are the correct length.

One machine is considerably more unreliable than the rest."

By examining the number of correct cuts for each machine, we can see that Machine 3 has only 13 correct cuts, while the other machines have more than 17. This statement is valid.

3. When a machine misses the correct length, it tends to cut too long."

We need to compare the number of cuts that are too long (1.26-1.27 feet) with those that are too short (1.23-1.24 feet) across all machines:

Total number of cuts too long = 4 + 2 + 3 + 6 + 4 = 19

Total number of cuts too short = 980 + 72 + 67 = 1119

This statement is not valid, as the machines tend to cut too short rather than too long.

4. "Machine 5 will cut every batch the correct length at least 92% of the time."

To check this statement, we need to find the percentage of correct cuts for Machine 5:

Percentage of correct cuts for Machine 5 = (17/100) * 100 = 17%

This statement is not valid, as Machine 5 only cuts the correct length 17% of the time, which is less than 92%.

only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

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Answer:

2(2(3) + 2(5) + 3(5)) = 2(6 + 10 + 15) = 2(31)

= 62

D is the correct answer.

Check the picture below.

The value of the expression is 2

Index forms are described as those forms that are used to represent numbers that are too large or small in more convenient forms.

They are also described as numbers that are raised to a variable or an exponents.

Other names for index forms are scientific notations and standard forms.

One of the rules of index forms is that the exponents are added when the have the same and are being multiplied.

From the information given, we have that;

(2^-1/2) / (2^1/2)

subtract the exponents

2^-1/2-1/2

subtract the values

2^ -1

Then, we have;

2

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Answer:

There is an outlier at 28.

After drawing our frequency table, we also find out that our mean is 6.73.

To make a frequency table, we have to count the number of times each value appears in the data set.

Frequency table:

Value       Frequency

5              4

6              8

7              4

8              6

9              3

To find the mean, we will add all values and divide by total number of values. The mean is:

= EF / N

= (6 + 7 + 6 + 6 + 7 + 6 + 5 + 8 + 6 + 5 + 9 + 8 + 5 + 6 + 8 + 9 + 5 + 8 + 8 + 6 + 8 + 7 + 5 + 6 + 9 + 7 + 7 + 9 + 6 + 7) / 30

= 6.83333333333

= 6.83.

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The plumber worked for 4.5 hours and charged $138.70 for their services

To find out how many hours the plumber worked, we first need to subtract the initial charge of $14.95 from the total bill of $138.70.

$138.70 - $14.95 = $123.75

This gives us the amount that the plumber charged for the hours worked. Now, we can divide this amount by the hourly rate to find the number of hours:

$123.75 ÷ $27.50 per hour = 4.5 hours

However, we need to convert the decimal part (0.5) into minutes. We can do this by multiplying it by 60:

0.5 x 60 = 30 minutes

But we need to add the initial charge of $14.95 to get the final answer.

4 hours and 30 minutes is equivalent to 4.5 hours.

4.5 hours x $27.50 per hour = $123.75

$123.75 + $14.95 = $138.70

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Answer:

  (c)  y < -x +1

Step-by-step explanation:

You want the inequality that matches the graph.

The boundary line of the shaded area has a negative slope: it falls one unit for each unit to the right, so the slope is ...

  m = rise/run = -1/1 = -1

The line crosses the y-axis at y = 1, so the y-intercept is b = 1.

The equation of the boundary line is ...

  y = mx + b

  y = -x +1

The boundary line is dashed, so its values are not part of the solution set. The shading is below the line, so only y-values less than those on the line are included.

The inequality is ...

  y < -x +1 . . . . . choice C

<95141404393>

The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:

Range of V: [0, ∞)

To find the domain and range of the function V(x, y) = 9√(9y – 45x^2), we need to consider the values of x and y that make the expression under the square root non-negative, since we cannot take the square root of a negative number.

So, we have:

9y – 45x^2 >= 0

Dividing both sides by 9 and rearranging, we get:

y >= 5x^2/3

This means that the domain of V is all points (x, y) such that y is greater than or equal to 5x^2/3:

Domain of V: {(x, y) | y >= 5x^2/3}

To find the range of V, we note that the square root is always non-negative, so V(x, y) will be non-negative whenever 9y – 45x^2 is non-negative. The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:

Range of V: [0, ∞)

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Answer:

12

325

Step-by-step explanation:

When it mentions the word "fit", you use TSA.

TSA cuboid = 2[LH+BH+LH] = 2 [ (2×3/2)+(3/2×7/2)+(2×7/2)] = 2 [ 3 + 21/4 + 7] = 2 [5¼+10] = 2 [15¼] = 2 × 61/4 = 61/2 = 30½ ft²

TSA ½ foot cube = 6L² = 6(½)² = 6×¼ = 2½

Number of cubes = 30.5÷2.5 = 12.2 = 12

TSA ⅛ foot cube = 6(⅛)² = 6×1/64 = 3/32

Number of cubes = 30.5÷3/32 = 325⅓ = 325

Answer: TJ has 17 quarters and Demi has 26 quarters.

Step-by-step explanation:

Let t be the number of quarters TJ has and d be the number of quarters Demi has.

First, we will write an equation based on the first detail given:

       d = t + 9

Next, we will write an equation based on the second detail given:

       2t + 3d = 112

Now, we will substitute the first equation into the second and solve for t.

       2t + 3d = 112

       2t + 3(t + 9) = 112

       2t + 3t + 27 = 112

       5t + 27 = 112

       5t = 85

       t = 17 quarters

Lastly, we know that Demi has 9 more quarters than TJ. We will add 9.

       17 quarters + 9 quarters = 26 quarters

Answer:

TJ has 17 quarters.

Step-by-step explanation:

Let d and t equal the numbers of quarters Demi and TJ have, respectively.

"Demi has nine more quarters than TJ."

d = t + 9

"if you double the number of quarters TJ has and triple the number of quarters then he has you would get 112 quarters in total"

I think that "then he" above really should read "Demi."

2t + 3d = 112

d = t + 9

2t + 3d = 112

2t + 3(t + 9) = 112

2t + 3t + 27 = 112

5t = 85

t = 17

Answer: TJ has 17 quarters.

The graphs are identified as follows

1. the domain is option G

2. the range is option E

3. the domain is option D

4. the range is option C

In coordinate geometry, the domain and range are concepts used to describe the set of possible inputs (x-values) and outputs (y-values) of a function, respectively.

The domain of a function is the set of all possible x-values for which the function is defined. In other words, it is the set of all values that can be plugged into the function and produce a meaningful output.

The range of a function is the set of all possible y-values that the function can take on as x varies over its domain. In other words, it is the set of all values that the function can output.

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The sample space for choosing one marble from the given marbles which are red, green, blue, yellow, and orange is s = {red, green, blue, yellow, orange}

Given color of the marbles which are present in the paper bag are,

The five color marbles are present in the paper bag so, the sample space also contains all five marbles without repeating any color again.

Sample space: sample space is nothing but listing all the outcomes of the event. In the above event, we have to list the all outcomes when choosing one marble from the paper bag which containing five different marbles.

So, the sample space S = {red, green, blue, yellow, orange}

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For a random sample of 155 observations results in 62 successes.

a) A 90% confidence interval for the population proportion of successes is equals to the (0.335 , 0.465).

b) A 90% confidence interval for the population proportion of failure is equals to the (0.535 , 0.665).

We have a random sample of 155 observations results in 62 successes. So,

Observed value, x = 62

Sample size,n = 155

Population Proportion, p = x/n

= 62/155

= 0.4

a) We have to determine 90% confidence interval for the population proportion of successes. Using the distribution table, for 90% confidence interval, z-score value is equals to 1.6. Consider Confidence interval formula with proportion, CI [tex]= p ± z×\sqrt\frac{p(1-p)}{n}[/tex]

substitute all known values in above formula, [tex]= 0.4 ± 1.64\sqrt\frac{0.4(1- 0.4)}{155}[/tex]

= 0.4 ± 0.0645

= (0.4 - 0.0645 , 0.4 + 0.0645)

= (0.335 , 0.465)

b) Now, we have to determine a 90% confidence interval for the population proportion of failures.

Now consider, here failure observed values, x = 155 - 62

= 93

proportion, p = x/n

= 93/155 = 0.6

Consider the confidence interval formula, CI [tex]= p ± z×\sqrt\frac{p(1-p)}{n}[/tex]

substitute values, [tex]= 0.6 ±1.64×\sqrt\frac{0.6(1-0.6)}{155}[/tex]

= 0.6 ± 0.0645

= (0.6 - 0.0645 , 0.6 + 0.0645)

= (0.535 , 0.665)

Hence, required value is (0.535 , 0.665).

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