Why/How do we expand brackets, i dont understand (linear equations)

Yes, that is correct. The sides of an equilateral triangle inscribed in a circle are closer to the center of the circle than the sides of a square inscribed in the same circle.

This is because an equilateral triangle has all its vertices on the circumference of the circle, whereas a square has only four of its vertices on the circumference. As a result, the sides of the equilateral triangle are closer to the center of the circle than the sides of the square. This property of inscribed shapes is important in geometry and has many practical applications in fields such as architecture and engineering.

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(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

\(d = \sqrt{10}\)

Step-by-step explanation:

Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d = \sqrt{(-2-(-5))^2+(-1-0)^2}\)

\(d = \sqrt{(-2+5)^2+(-1)^2}\)

\(d = \sqrt{(3)^2+1}\)

\(d = \sqrt{9+1}\)

\(d = \sqrt{10}\)

Therefore, the red light and the yellow light will both flash at the same time after 1.25 seconds or 5/4 seconds.

To solve the problem of finding out after how many seconds the red light and the yellow light will flash at the same time, we need to first determine their time periods. The time period of a light is the time taken for it to complete one full cycle of on-off or flashing-on-off.

To determine the time period of each light, we can take the reciprocal of their respective flashing rates or frequencies. The flashing rate is the number of flashes per unit time, usually per second.

In this problem, the red light flashes every 6 seconds while the yellow light flashes every 4 seconds. Hence, the time periods are as follows:

Time period of red light = 1 / (flashing rate of red light)

= 1 / (1 flash every 6 seconds) = 0.1667 seconds

Time period of yellow light = 1 / (flashing rate of yellow light)

= 1 / (1 flash every 4 seconds) = 0.25 seconds

We need to find out after how many seconds they both flash at the same time or they synchronize. This is equivalent to finding the least common multiple (LCM) of their time periods.

The LCM of 0.1667 seconds and 0.25 seconds is 1.25 seconds or 5/4 seconds.

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Answer: Yes it's 15

Step-by-step explanation:

20/100 x 75 = 15

Answer:

-9 is the answer

Step-by-step explanation:

So we know that the temperature was 2 degrees Fahrenheit in the morning. It dropped by 11 degrees, meaning -11 degrees.

2 + (-11) = ?

2+ (-11) = -9

When he woke up, the temperature was -9 degrees.

Hope this helped :)

Answer:

26°

Step-by-step explanation:

same side same angle

the total of angles in triangle is always 180

Answer:

To graph a system of linear inequalities, you will need to graph each inequality separately on the same set of axes. Here is the general process for graphing a linear inequality:

Begin by plotting the inequality's equation in standard form: Ax + By > C (or < C, or = C).

Determine the values of x and y that make the inequality true. To do this, set each side of the inequality equal to zero and solve for x and y. For example, if the inequality is 2x + 3y > 6, you would set 2x + 3y = 0 and solve for x and y.

Graph the line that represents the equation.

Determine the direction of the inequality by looking at the inequality symbol. If the symbol is ">," the line will be shaded above it. If the symbol is "<," the line will be shaded below it. If the symbol is "≥," the line will be shaded above it, including the line itself. If the symbol is "≤," the line will be shaded below it, including the line itself.

Repeat the process for each additional inequality in the system.

The solution to the system of inequalities is the area where all of the shaded regions overlap. This is the region where all of the inequalities are simultaneously true.

Here is an example of how to graph a system of linear inequalities:

Suppose we want to graph the following system of inequalities:

2x + 3y > 6

-x + 2y < 4

To graph the first inequality, we set 2x + 3y = 0 and solve for x and y. This gives us x = -(3/2)y. We can then plot this line on a graph.

Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is ">," so we shade the area above the line.

To graph the second inequality, we set -x + 2y = 0 and solve for x and y. This gives us x = (1/2)y. We can then plot this line on the same graph.

Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is "<," so we shade the area below the line.

The solution to the system of inequalities is the area where the shaded regions overlap. This is the region where both inequalities are simultaneously true.

Probability of receiving at least two queens when thirteen cards are dealt from a deck of 52 cards is equal to 0.0972.

As given in the question,

Total number of cards in a deck = 52

Number of cards dealt from a pack of 52 cards = 13

Condition for dealt cards is at least 2 should be queen:

At least 2 queen mean 2 or more than 2.

Out of 4 queen

One can choose:

2 queen + 11 other cards

3 queen  + 10 other cards

4 queen. + 9 other cards

Out of 52 : 4 cards are queen and 48 are others

Probability of choosing at least 2 queens

= (Favourable outcomes) / ( total number of outcomes)

= [ ( ⁴C₂ × ⁴⁸C₁₁) +  ( ⁴C₃ × ⁴⁸C₁₀) +  ( ⁴C₄ × ⁴⁸C₉) ] / ( ⁵²C₁₃ )

= ( 61732770776) / 635013559600

= 0.0972

Therefore, probability of receiving at least two queens when thirteen cards are dealt from a deck of 52 cards is equal to 0.0972.

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Answer:

d or c

Step-by-step explanation:

On solving the provided question, we can say that Function f(x) is translated left 7 units and down 4 units (x-4) --> (x+3)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

Function f(x) is translated left 7 units and down 4 units

(x-4) --> (x+3)

+7 = translation left 7 units

-4 at end affects y (down 4 units)

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Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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3. The value of one of the numbers is 89 and the other is 40

4. The score on the first test is 83 and score on the second test is 100

From the question, we are to determine the value of the numbers

From the given information,

"One number is 9 more than twice another number"

Let one of the numbers be x and the other be y

Thus,

x = 2y + 9 --------- (1)

Also,

"the sum of the numbers is 129"

That is,

x + y = 129 ---------- (2)

Solving

Substitute equation (1) into equation(2)

x + y = 129

2y + 9 + y = 129

2y + y = 129 - 9

3y = 120

y = 120/3

y = 40

Substitute the value of y into equation (1)

x = 2y + 9

x = 2(40) + 9

x = 80 + 9

x = 89

Hence, one of the numbers is 89 and the other is 40

From the question, we are to determine the scores on each test

Let the score on the first test = m

and score on the second test = n

"Jane scored 17 points higher on her second test than on her first test"

n = m + 17 -------- (1)

Also,

"the sum of the scores on the two tests is 183 points"

n + m = 183

Substitute equation (1) into equation(2)

n + m = 183

m + 17 + m = 183

m + m = 183 - 17

2m = 166

m = 166/2

m = 83

Substitute the value of y into equation (1)

n = m + 17

n = 83 + 17

n = 100

Hence, the score on the first test is 83 and score on the second test is 100

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Answer:

D.) Yes, because it passes the vertical line test.

Step-by-step explanation:

For a function to be a function, there must be one output for every input. IN other words, there must be one "y" value for every "x" value. One can see if a graph passes this test by performing the vertical line test.

In this case, the line on the graph passes the test and represents a function. Again, this is because each "x" value has only one "y" value.

Yes, The graph is function because it passes the vertical line test.

We have to given that,

A graph of function is shown in image.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

And, The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.

Hence, By given graph,

it passes the vertical line test.

So, Graph shown is a function.

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The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.

There are four multiples: 4,8,12,16,20,24.

6, 12, 18, and 24 are multiples of 6.

12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.

LCM of 24 and 15 is equal to 222235 = 120.

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Answer

The result of 48 - 36 is 12. Then, if you divide 12 by 36, the result is 0.3333 or 1/3.

Step-by-step explanation:

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

\(\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988\)

The combined proportion is:

\(\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989\)

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

\(Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78\)

Compute the p-value as follows:

\(p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075\)

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\\)

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Answer:

F(n) =-3n+24

Step-by-step explanation:

Answer:

Volume = 12,300

Step-by-step explanation:

20 x 30 = 600

600 x 20.5 =12300

Answer:

Volume of the box is length ×breadth×height

\(20 \times 30 \times 20 \frac{1}{2} \\ = 600 \times \frac{41}{2} \\ = 12300\)

Pieces of data such as $18,000 and $350,000 represent outliers in this chart.

An outlier is a piece of information that is mathematically atypical or that differs from constant mathematical values. For example, if the number of people on a restaurant is each table is 4, 3, 2, 5, 4, 10, the outlier is 10 because his value is atypical.

In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.

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Answer:

The question is Given that we should range the graph below: 12,10,9,8,6,5,4,3,2

-12-11-10-9-8-7-6

1 2 3 4 5 6 7 8 9 10 11 12

8

-9

-10

56

-12

and the ranging of my answer is that

-12

-10

-9

-8

-6

-5

-4

-3

-2

-1.

1 2 3 4 5 6 8 8 10 12

12

10

9

8

6

5

4

The range of the given function \(y = -e^x\) can be represented in set notation as follows:

Range: {y | y ≤ 0}

As per the shown graph, the given function is  \(y = -e^x\) , which represents an exponential decay.

As x increases, the value of  \(-e^x\) decreases rapidly.

Consequently, the range of the function is all real numbers less than or equal to zero.

Here, the graph of this function forms a curve that approaches the x-axis but never intersects or goes above it.

The function has no upper bound but approaches zero as x approaches negative infinity.

However, it never reaches zero or any positive value, resulting in a range that consists of all real numbers less than or equal to zero.

The range of the given function \(y = -e^x\) can be represented in set notation as follows:

Range: {y | y ≤ 0}

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Step-by-step explanation:

(-8×2.5×2×1×6) ×(-20×2.5×1)

(-20×16) ×(-50)

-320×-50

=1600

Answer:

x> -200

Step-by-step explanation:

Answer:

Your answer would be 7,600.

Step-by-step explanation:

7,605 rounded to the nearest hundred would be 7,600 because:

The 7 is the thousands.

The 6 is the hundreds.

The 0 is the tens

The 5 is the ones.

So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600

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Answer:

A) Plumber B charges 55 dollars per hour (105=50+55(1)) because for 1 hour the total is 105, meaning that 105 is y and 1 is x. 50+55=105

B) Plumber A charges more because he charges 100 dollars vs Plumber B's 50 dollars.

C) Plumber A:  250=100+30(5)       Plumber B:  325=50+55(5)

Plumber A charges less money for working 5 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that,

Two plumbers charge an initial fee and an hourly rate.

The equation y=100+30x -----(I) models plumber A's fee, where y is the total charge, in dollars, and x is the number of hours worked.

Part A:

From the table, we have (1, 105) and (2, 160)

Now, m=(160-105)/(2-1)

= 55

Substitute m=55 and (x, y)=(1, 105) in y=mx+c, we get

105=55(1)+c

c=60

Substitute m=55 and c=60 in y=mx+c, we get

y=55x+60 -----(II)

By comparing (I) and (II), we can conclude that plumber B charges more hourly fee.

Part B: By comparing (I) and (II), we can conclude that plumber A charges more initial fee.

Part C: Substitute x=5 in y=100+30x, we get

y=$250

Substitute x=5 in y=55(5)+60, we get

y=$335

Plumber A charges less money for working 5 hours.

Therefore, plumber A charges more initial fee.

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Answer:

42

Step-by-step explanation:

The product of 6 multiplied by 7 is 42.

We have to find the value of 6×7.

To find the product of 6 multiplied by 7, you simply multiply the two numbers together.

6 multiplied by 7 can be calculated as:

6 x 7

When six is multiplied with seven we get forty two.

= 42

Therefore, the product of 6 multiplied by 7 is 42.

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Answer: x=11

Step-by-step explanation:

2(3x-1)=4(x +5)

3x-1=2(x+5)

3x-1=2x+10

3x=2x+10+1

3x=2x+11

3x-2x=11

x=11