the length of a rectangle is 3 more than twice its width. the total area of the rectangle is 54 square units. what is the width and length of the rectangle?

Answer:

17/20

Step-by-step explanation:

The ratio 8.5 to 10 as a fraction in simplest form is 17/20. 8.5/10 = 85/100 = 17/20

(8.5:10 = 85:100 = 85/100 = 17/20)

Answer:

Impossible: Pigs can fly. It will rain in the Sahara Desert for a week.

Probability is the likelihood that an event will happen.

Unlikely: It will snow today. Dying in a shark attack.

Likely: If you are underwater for more than 2 minutes, you drown. A cat chases a mouse.

Certain: The year is 2023.

Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.

The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.

The range of x = -4 is a single point on the y-axis, y = -4.

Step-by-step explanation:

A total of 96 pots can be made in one eight-hour day.

The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group. In this instance, the multiplicand is, the multiplier is, and the product is 6.

Speed of coffee machine = 12 pots of coffee per hour.

Amount received after selling each pot of coffee = $10

For finding the total pots of coffee made by the coffee machine in 8 Hr, we will simply multiply the total number of hours which is 8 Hr to the efficiency of the machine which is 12 pots per hour.

So, the total pot made by the machine will be 12*8 = 96 pots

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The coordinates of its midpoint M are (0,6)

A line is an infinitely long object with no width, depth, or curvature.

Given that a line segment has the endpoints B(0, 2) and C(0, 10).

We need to find the  coordinates of its midpoint M.

Midpoint=(0+0/2, 2+10/2)

Midpoint=(0, 12/2)

Midpoint=(0, 6)

The coordinates of its midpoint M are (0,6)

Hence, the coordinates of its midpoint M are (0,6)

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When you divide a number by 1/2, it is the same as multiplying the number by 2. Therefore, the result of the division is two times the original number.

Let's say we have a number, X.

When you divide X by 1/2, you can rewrite the equation as:

X ÷ 1/2 = X × 2

Thus, the result of the division is two times the original number, X.

Let's say we have a number, X. When you divide X by 1/2, you are essentially multiplying X by 2. This means that the result of the division is two times the original number. In other words, if you divide X by 1/2, the answer will be 2X. To put it another way, if you take any number, X, and divide it by 1/2, the result will be two times the original number. This is because 1/2 is the same as multiplying the number by 2. For example, if you divide 10 by 1/2, the result will be 20, since 10 multiplied by 2 is 20. Similarly, if you divide 25 by 1/2, the result will be 50, since 25 multiplied by 2 is 50. In conclusion, when you divide any number, X, by 1/2, the result will always be two times the original number.

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The angle measure of triangle DEF in order of smallest to largest is m∠E = 36.03°, m∠F = 70.72° and m∠D = 73.25°.

The answer is: m∠E < m∠F < m∠D

The angle of a triangle can be found given its 3 sides using the cosine rule.

The formula is: cos(C) = (a² + b² -c²) / 2ab  

where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and cos(C) is the cosine of angle C.

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (F) = (d² + e² -f²) / 2de  

cos (F) = (70² + 43² -69²) / (2*70*43)

cos (F) = 71/215

F = cos⁻¹(71/215)

F = 70.72°

cos (E) = (d² + f² -e²) / 2df

cos (E) = (70² + 69² -43²) / (2*70*69)

cos (E) = 93/115

E = cos⁻¹(93/115)

E = 36.03°

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (D) = (e² + f² - d²) / 2ef

cos (D) = (43² + 69² - 70²) / (2*43*69)

cos (D) = 285/989

D = cos⁻¹(285/989)

D = 73.25°

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Considering the expression of a line, the slope intercept form is y= -x+2.

A linear equation o line can be expressed in the form y = mx + b

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

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Answer:

30 feet

Step-by-step explanation:

The scale factor is 1 inch = 3 feet

So 10 inches = 10 x 3 feet= 30 feet

Height of the lighthouse is 30 feet

The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex].

[tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}} = \frac{\sqrt[3]{8}}{4}$[/tex]

Minimum possible value of [tex]$ab = 32$[/tex]

[tex]= \frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{4}$[/tex]

We start with the given expression, [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex], which is in the form [tex]$\frac{p}{qr}$[/tex]. To rationalize the denominator, we need to multiply both numerator and denominator by qr (which is [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex] in this case). This gives us[tex]$\frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$[/tex]. We can simplify this expression further by dividing both numerator and denominator by [tex]$\sqrt[3]{4}$[/tex], giving us [tex]$\frac{\sqrt[3]{8}}{\sqrt[3]{2} \sqrt[3]{4}}$[/tex]. Finally, we can simplify the denominator further by multiplying both numerator and denominator by [tex]$\sqrt[3]{2}$[/tex], giving us the final result of [tex]$\frac{\sqrt[3]{8}}{4}$[/tex]. The minimum possible value of ab is 32.

The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex]. The final result was[tex]$\frac{\sqrt[3]{8}}{4}$[/tex], and the minimum possible value of ab was 32.

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The vertex is (-5 , 5) , y-intercept is (0 , -20) and reflection of y-intercept across symmetry is (-10 , -20).  

What is parabola ?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

a curve made when a cone's surface collides with a plane that is perpendicular to a straight line: a curve created when a point moves in such a way that its separation from a fixed point equals its separation from a fixed line something with a bowl-like form.

Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.

In the equation you provided, the corresponding values are:

a = -1

b = -10

c = -20

Plugging in the values to find the vertex yields:

- (-10)/(2*-1)

= 10/-2

= -5

This is the x-coordinate of the vertex

-x²-10x - 20

= -(-5)² - 10×(-5) - 20

= -25 +  50 - 20

= 5

∴The vertex is located at the point (-5 , 5)

The y-intercept when x = 0

-x² - 10x - 20

= -20

The y-intercept of the vertex at the point (0 , -20)

Since you have 2 points, look at the y-intercept and imagine a point reflected across the line of symmetry.

That point will be your last point, and is located at: (-10 , -20)

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Answer: The slope is equal to "-3".

Explanation: You can obtain the slope of a linear graph if you know two points on it. In this case, these points are (-2,3) and (0, -3).

If you know these points, you can use the formula below:

Slope = (Difference between y values) / (Difference between x values)

Here => 3 - (-3) / (-2) - (0) = -3, this gives the slope.

In addition, we can conclude that the formula of the graph is (y = -3x - 3), by using a specific point with the known slope value on a linear equation (mx + n).

Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

Answer:

Untuk mencari nilai x dari persamaan 4x+7x+141+85+x+27=360, pertama-tama kita harus menyederhanakan persamaan tersebut dengan menambahkan semua x yang ada di sisi kiri persamaan.

4x+7x+x = 12x

Selanjutnya, kita harus mengurangi semua bilangan yang ada di sisi kiri persamaan dari kedua sisi persamaan:

360 = 12x + 141 + 85 + 27

Setelah itu, kita harus mengurangi semua bilangan yang ada di sisi kanan persamaan dari kedua sisi persamaan:

360 - 253 = 12x

107 = 12x

Akhirnya, kita harus membagi 107 dengan 12 untuk mencari nilai x:

x = 8.9167

Jadi, nilai x dari persamaan tersebut adalah 8.9167.

It's worth noting that some steps are not needed to be done and the equation can be simplified by doing some operations at once like : (4x+7x+x+141+85+27=360) => (12x+253=360) => (12x=107) => (x=8.9167)

Answer:

34.5 square units.

Step-by-step explanation:

We can construct a 7 x 7 square around the polygon. Then, we measure the two right triangles that together, along with the polygon, make up the 7x7 square. The total measure of the two triangles is 15/2+7=14.5. Now we subtract that from the area of the square to get the area of the polygon. 49-14.5=34.5, so 34.5 square units is the answer.

As a result, the solution is shaped like a circle ( -5 , 7 ). The second half of the text has a 6 mm diameter. Three and four are FALSE. There are ten miles between points A and B.

The construction of a circle is the outcome of following a thinking object in a plane and keeping a fixed distance from a particular location. A Greek word kirkos, which means hoop or ring, is the source of the English word circle.

Here,

Typically, a circle's equation is,

( x - h )² + ( y - k ) ( y - k )

x² = r²

( y - k ) ( y - k ) = r²

6² = r²

where the radius of the ring is and the center's coordinates are (h, k).

Part 1.

We arrive to using the formula for the common circle.

The circumference of a circle's coordinate is ( -5 , 7 )

As a result, the second choice is the best.

Part 2.

We arrive to using the formula for the common circle.

The circle's diameter is six.

The initial choice is therefore the best.

Part 3.

We arrive to using the equation again for common circle.

Circle circumference coordinate: ( 2 , 3 )

False as a result.

The axis coordinates of the circle are: ( 2 , 3 )

False, then.

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Answer:

  see attached for a graph

  a. BA≅BC (the compass told me so)

  c. AD≅CD

Step-by-step explanation:

You want a graph of ∆ABC, with A(4, 7), B(0, 0), and C(8, 1). You want to identify the congruent sides, construct an angle bisector, and comment on how it divides the opposite side.

The graph of the points, and the construction of the angle bisector are shown in the attachment.

Since you have your compass available for construction, you can use set it to the measure of one side and compare that to the other two sides. It does not take long to identify AB ≅ BC. (A compass setting shows they are the same length.)

As you know, an angle bisector is constructed by first identifying two points on the sides of the angle that are the same distance from the vertex of the angle. Then two intersecting arcs are drawn with the same radius using those points as their centers. The vertex and the intersection of the arcs defines the ray that is the angle bisector. This is shown in the attachment.

You can count grid squares (or use the compass) to determine that AD and CD are the same length: D is the midpoint of AC.

This reinforces your knowledge that the angle bisector of the a.pex angle of an isosceles triangle is also an altitude and a median.

The given condition can be modeled by the compound inequality:

x < -3 or x > 3.

We want to find an inequality that describes the next condition:

"All real numbers X with an absolute value of greater than three"

So our variable will be X, and the absolute value of X is written as:

|X|

We want to have an absolute value larger than 3, so we can write the inequality:

|X| > 3.

The absolute value part can be separated into two, such that we will get two inequalities:

x > 3

x < -3

So the inequality that illustrates the given condition is the compound inequality:

x < -3 or x > 3.

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The measure of the largest angle in wxyz is 4 times the measure of angle w, plus double that measure, plus 3 degrees.

Angle w: x = 4w

Angle y: y = 2x = 8w

Angle z: z = y + 3 = 8w + 3

The largest angle in wxyz is z = 8w + 3.

In a convex quadrilateral wxyz, the degree measure of angle x is four times that of angle w. This means that the measure of angle x is four times the measure of angle w. The measure of angle y is double that of angle x. This means that the measure of angle y is twice the measure of angle x, or eight times the measure of angle w. Lastly, the measure of angle z is 3 degrees larger than that of angle y. This means that the measure of angle z is eight times the measure of angle w plus three degrees. Therefore, the measure of the largest angle in wxyz is 8w + 3.

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The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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Now your friend would also like to determine the most likely continent of origin for each coin. Logistic regression model best suited to predict the continent of origin. So the option b is correct.

A variable's value can be estimated using linear regression analysis depending on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Based on a given dataset of independent variables, logistic regression calculates the likelihood that an event will occur, such as voting or not voting. Given that the result is a probability, the dependent variable's range is 0 to 1.

The log chances of the outcomes are modelled as a linear combination of the predictor variables in multinomial logistic regression, which is used to model nominal outcome variables.

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The complete question is:

Now your friend would also like to determine the most likely continent of origin for each coin. Which model best suited to predict the continent of origin?

(1) Linear regression

(2) Logistic regression

(3) Multinomial logistic regression

The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.

Percentage is used to denote a fraction of a hundred.

Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:

w1 = 60% q = 0.6 q

Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:

w1 = 80% x 70 = 56 lb

The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:

weight of rye grass = w1 + w2

                                = 0.6 q + 56

Total weight of the final mixture = (q + 70) lb

74% = 0.74 = (0.6 q + 56) / (q + 70)

0.6 q + 56 = 0.74 (q + 70)

0.74 q - 0.6 q = 56 - 0.74 x 70

0.14 q = 4.2

q = 4.2/0.14 = 30

Hence, the weight of 60% mixture is 30 lb.

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462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

given that

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has n elements, the number of k-combinations, denoted as nck

there are 5 hats

there are 11 people

now , we need to distribute all five hats among all eleven people so that no one gets more than one hat = 11 [tex]C_{5}[/tex]

= [tex]\frac{11!}{5!(11-5)!}[/tex]

=462 combinations

462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

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The kind of triangle in the image above is a scalene triangle.

A scalene triangle is a type of triangle that has three sides with different lengths. It is one of the three main types of triangles, the other two being isosceles and equilateral triangles. They also have three different angles.

Scalene triangles do not have any congruent sides or angles, making them the most diverse and versatile type of triangle. They can be used to construct many different shapes and figures, and have many unique properties and characteristics that make them useful in a variety of fields, including mathematics, physics, and engineering.

In the image given, the three sides of the triangle appears to be of different sizes.

Therefore, we can conclude that the triangle is a scalene triangle.

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The data set would list each day in February with a temperature measurement, measured on an interval scale.

The data set in question would list the temperatures in Albany, NY each day in the month of February. This data set would be classified as interval data, as it would measure temperatures on a numerical scale. Interval data is composed of numerical values that are measured on an interval scale, meaning that the difference between any two values is the same, regardless of their position on the scale. Temperature is an example of an interval data type, as it is measured numerically and the difference between two temperatures is the same regardless of where they are on the scale (e.g. the difference between 50°F and 55°F is the same as the difference between 90°F and 95°F). This data set would be useful for tracking temperature trends over a period of time, and for making predictions about future temperatures in a certain area.

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The study method used to evaluate mother-child attachment is best described as option A: experimental.

Children who refuse food by acting negatively or in opposition seem to be a common theme in feeding interactions between depressed mothers and their kids. The purpose of this study was to examine parenting behaviours in the setting of feeding in moms who were suffering from serious depression from an attachment theory perspective. The easiest way to sum up the research design used to assess mother-child attachment is option A: experimental.

The idea of sensitive responsiveness was developed by attachment theory to measure a mother's capacity to empathetically recognise and respond to her child's signals. Their attitudes and behaviours when providing care may be badly impacted by this distress, which may be pervasive.

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