Use point-slope form to write the equation of a line that passes through the point (18,16) with slope -\frac{11}{8}− 8 11 ​ .

The value of x is 7, therefore AC = 23 and BD = 23, which means diagonals AC = BD.

What is linear equations in two variables?

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation in two variables is a straight line in the Cartesian coordinate system.

In a trapezium, the diagonals divide the trapezium into four triangles. The diagonals of a trapezium are also equal to the sum of the two parallel sides.

Let the two parallel sides of the trapezium be a and b. Then, we have:

8x - 33 = a + b ...(1)

37 - 2x = a + b ...(2)

We can solve for x by setting (1) and (2) equal to each other:

8x - 33 = 37 - 2x

10x = 70

x = 7

8(7) - 33 = 23

37 - 2(7)  = 23

Therefore, the value of x is 7.

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Answer:

[tex]\sqrt{106}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]

Answer:

arc FA = 150°

Step-by-step explanation:

the central angle of a circle is equal to the measure of the arc that subtends it.

given BF is the diameter of the circle , then

∠ FCA + ∠ ACB = 180°

∠ FCA + 30° = 180° ( subtract 30° from both sides )

∠ FCA = 150°

then

arc FA = ∠ FCA = 150°

The probability of selecting a student who is wearing a yellow shirt is 36 %

The total number of students is 45 students and out of these, 3 / 7 are wearing blue shirts while 2 / 9 are wearing red shirts.

This means that the number of students wearing yellow is:

= 45 - ( 45 x 3 / 7 ) - ( 45 x 2 / 9 )

= 45 - 19 - 10

= 16 students

The probability of selecting a student who is wearing yellow is :

= 16 / 45

= 36 %

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The full question is:

A class has 45 students of the students are wearing 3/7 blue shirts, of

them are 2/9  wearing red shirts, and the rest are wearing yellow shirts.

What is the probability of selecting a student who is wearing a yellow

shirt?

The value of x is approximately 0.8 cm when rounded to the nearest tenth.

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.

The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:

sin(IHJ) = IJ/IH

Taking the sine of both sides and substituting the given values, we get:

sin(23°) = x/2

Multiplying both sides by 2, we have:

x = 2*sin(23°)

Using a calculator, we get:

x ≈ 0.83

Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.

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Step-by-step explanation:

ABC and ADE are similar triangles.

that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.

so, we see that AB = 2, AD = 2+1 = 3

the scaling factor f from AB to AD is then

AB × f = AD

2 × f = 3

f = 3/2

the same scaling factor now applies between BC and DE (= x).

BC × f = x

1 × 3/2 = x

x = 3/2 = 1.5

A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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Answer:

18.84

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]

Step-by-step explanation:

g(x) = 4x + 5

f(x) = -3x² - 3x

= 4x + 5 + (-3x² - 3x)

= 4x + 5 - 3x² - 3x

= 4x - 3x + 5 - 3x²

= x + 5 - 3x²

[tex]\rule[225]{225}{2}[/tex]

Answer:

7

Step-by-step explanation:

35-8-4-2=21

21/3=7

Answer:

7 pounds

Step-by-step explanation:

8+4+2=14

35-14=21

21/3=7

Answer:

Step-by-step explanation:

.....-_-.....-__-....-___-_--____--_--_____--_--______________--_________________-u streched ma face dude.

Answer:

To find the number of courts with doubles matches, we need to determine the total number of players playing doubles. If each court with a doubles match has 4 players, then the total number of players playing doubles would be 4 times the number of courts playing doubles.

Since there are 28 players in total, and each court with a singles match has 2 players, the number of players playing singles would be 28 - 4x, where x is the number of courts playing doubles.

Since each court with a singles match has 2 players, the number of courts playing singles would be 28/2 = 14.

So, 28 - 4x = 14, and solving for x, we get x = 7.

Therefore, there are 7 courts with doubles matches and 14 courts with singles matches.

The number of crickets Great fed last week to Lizzy is 56.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Last week, Greta fed Draco 77 crickets.

Let the number of crickets Great fed last week be x.

Now, 11:8::77:x

11x=77×8

x=7×8

x=56

Therefore, the number of crickets Great fed last week to Lizzy is 56.

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"Your question is incomplete, probably the complete question/missing part is:"

Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets. How many crickets did Greta feed Lizzy?

The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.

A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.

In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.

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Answer:

B

Step-by-step explanation:

We start by trying out option A

2(1) + 3(3) = 9

1 + 5(3) = 15

9 and 15 are not equal to one another.

This means it has to be the other option, B.

We can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

What is confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is an interval estimate computed from a sample of data and is used to describe the uncertainty or variability associated with a sample estimate of a population parameter.

To calculate the confidence interval, we need to first find the point estimate of the proportion of applicants accepted by Bridgeton University:

Point estimate = number of applicants accepted / total number of applicants = 392 / 1000 = 0.392

The standard error of the proportion can be calculated as:

SE = sqrt(p*(1-p)/n), where p is the point estimate and n is the sample size.

SE = sqrt(0.392*(1-0.392)/1000) = 0.0194

To find the 95% confidence interval, we can use the formula:

CI = point estimate +/- z*SE, where z is the z-score for a 95% confidence level (1.96).

CI = 0.392 +/- 1.96*0.0194

CI = (0.354, 0.430)

Therefore, we can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

To evaluate whether Bridgeton's claim seems accurate, we can compare the confidence interval with the claimed acceptance rate of 42%. We can see that the claimed acceptance rate of 42% does not fall within the confidence interval, which suggests that the claim may not be accurate. However, it is important to note that this sample may not be representative of the entire population of applicants to Bridgeton University, and further investigation may be needed to confirm the accuracy of the claim.

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Histogram 1 is positively skewed, and Histogram 2 is symmetric, which is a true statement about the distributions represented by the histograms.

An illustrated display of data points arranged into user-specified ranges is called a histogram. By taking several data points and organising them into logical ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an easily understood graphic.

Among graphing tools, the histogram is widely used. It is utilised to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

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Answer:

C) Histogram 1 is negatively skewed, and Histogram 2 is positively skewed.

Step-by-step explanation:

When most of the data on a histogram is gathered to the right, then the distribution is negatively skewed. If most of the data is gathered to the left, then the distribution is positively skewed.

Assuming you are going off of these Histograms:

C is the correct answer.

The profit that they will make if they have 24 dogs for adoption is given as follows:

$160.

The profit is obtained with the subtraction of the revenue by the costs.

The revenue and the costs for this problem are obtained as follows:

Hence the profit made is obtained as follows:

Profit = 45 x 24 - 920

Profit = $160.

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Answer:

SSS

Step-by-step explanation:

Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.

With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.

In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".

Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.

The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.

To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:

2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6

Expanding the right side of the equation:

2x = 9 + 16 + 25 + 36

= 86

Dividing both sides of the equation by 2:

x = 43

So there are 43 points where exactly 2 lines intersect.

This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.

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Type I error would be weather remains dry, but school is needlessly canceled. Type II error would be don't cancel school, but the snow storm hits. The correct option is B.

In hypothesis testing, the null hypothesis is the default assumption that is being tested. In this case, the null hypothesis is that the weather will remain dry. The school superintendent must decide whether to reject or accept this null hypothesis based on the evidence available.

There are two types of errors that can occur in hypothesis testing: Type I and Type II errors.

Type I error occurs when the null hypothesis is rejected, even though it is actually true. In other words, the school superintendent decides to cancel school due to a snowstorm, but the weather remains dry. This can result in unnecessary school closures, which can disrupt students, teachers, and parents' schedules.

Type II error occurs when the null hypothesis is accepted, even though it is actually false. In other words, the school superintendent decides not to cancel school because of the assumption that the weather will remain dry, but a snowstorm hits. This can put students, teachers, and parents in danger as they try to commute to school in hazardous conditions.

The consequences of a Type I error and a Type II error can be significant in this scenario. The school superintendent must weigh the potential risks of making each type of error to make the best decision for the safety and well-being of the school community.

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Complete question is:

A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?

A. Type I error: don't cancel school, but the snow storm hits.

Type II error: weather remains dry, but school is needlessly canceled.

B. Type I error: weather remains dry, but school is needlessly canceled.

Type II error: don't cancel school, but the snow storm hits.

C. Type I error: cancel school, and the storm hits.

Type II error: don't cancel school, and weather remains dry.

D. Type I error: don't cancel school, and snow storm hits.

Type II error: don't cancel school, and weather remains dry.

E. Type I error: don't cancel school, but the snow storm hits.

Type II error: cancel school, and the storm hits.

Answer:

4) 7 SqrRt( 5 )

5) 2 SqrRt( 10 )

6) 8 SqrRt( 6 )

The total length of the two welded together is 26ft.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

Given that the length of the two pieces of the pipe is 23ft and 3ft.

The total length of the two welded together is:

23 + 3 = 26ft

Hence, the total length of the two welded together is 26ft.

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the answer is 40780

I would show you my calculations  but I don't know how to add pictures to your answer .sorry

I hope that helped

As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.

If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.

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Answer: None

Step-by-step explanation: I Just did it

Answer:

280

Step-by-step explanation:

Give me a moment, I am still gathering my explanation

Answer:

Step-by-step explanation:

if the sum of two consecutive even numbers is 42 find the number

42 - 2 = 40                       remove the difference (2)

40 : 2 = 20                       find the smallest number

20 + 2 = 22                      find the largest number

------------------------------------

(20 + 22 = 42)                

The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.

A fraction is a mathematical expression that represents a part or a proportion of a whole.

Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.

Now, let's consider the area of the circle. The formula for the area of a circle is

=>  A=πr².

Therefore, the area of the circle is πr².

The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is

=> (2r)²=4r²,

and the area of the inner square is

=> (r√2)²=2r².

Hence, the area between the two squares is

=> 4r²−2r²=2r².

The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is

=> πr²−2r²=(π−2)r².

Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,

ratio = (π - 2)r² / 2r

We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,

ratio = (π - 2) / 2

This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 51% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 51%. The alternative hypothesis would be that the true proportion is less than 51%. After gathering information from 380 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis.

If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 51% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.

m(BD) = 120°

If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.

Therefore, we have:

6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)

Solve for x:

6x - 12 = 1/2[(-12 + 21x - 12x + 24)

2(6x - 12) = -12 + 21x - 12x + 24

12x - 24 = 9x + 12

12x - 9x = 24 + 12

3x = 36

x = 36/3

x = 12

m(BD) = 12x - 24 = 12(12) - 24

m(BD) = 120°

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