A
B
Which of the following graphs will
display the narrowest parabola?
y = -2x²+x+3
f(x) = -4x² - 30x

The area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:

Area = (1/2) * perimeter * apothem

The perimeter of the polygon can be found by multiplying the number of sides by the length of each side. Since the polygon is regular, all sides are of equal length. Let's call this length "s".

s = 2 * r * sin(π/n) where r is the radius and n is the number of sides

s = 2 * 4 * sin(π/12)

s = 1.38 (rounded to two decimal places)

The perimeter of the polygon is:

P = 12 * s

P = 16.56 (rounded to two decimal places)

To find the apothem, we can use the formula:

apothem = r * cos(π/n)

apothem = 4 * cos(π/12)

apothem = 3.77 (rounded to two decimal places)

Now we can calculate the area of the polygon:

Area = (1/2) * P * apothem

Area = (1/2) * 16.56 * 3.77

Area = 31.28 square units (rounded to two decimal places)

Therefore, the area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

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If a normal distribution has mean of 57 and standard deviation as 20, then the z-score for x=50 is -0.35 .

In order to find the z-score for x=50, we can use the formula : z = (x-μ)/σ ;

Where x is = 50, "μ" is = mean of the distribution , and "σ" is = standard deviation of the distribution ;

In this case , x = 50 , mean(μ) = 57 and standard deviation(σ) = 20;

Substituting in the values,

We get,

⇒ z = (50-57)/20,

Simplifying, We get,

⇒ z = -0.35

So, the z-score for x=50 is -0.35.

Interpretation of the z-score is that :

The z-score represents the number of standard deviations that a given value (in this case, x=50) is from the mean of the distribution (μ=57).

A negative z-score means that the value is below mean. In this case, x=50 is 0.35 standard deviations below the mean of 57.

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The given question is incomplete, the complete question is

A normal distribution has mean of 57 and standard deviation as 20. Find and interpret the z-score for x=50.

Answer:

x = 6

Step-by-step explanation:

Solve for x

[tex]11+x=7-4x[/tex]

Add 7 on both sides

[tex]18+x=4x[/tex]

Subtract x on both sides (same as 1x)

[tex]18=3x[/tex]

Divide by 3

[tex]6=x[/tex]

Answer:

Step-by-,step explanation:

s.,s

Answer:

function not defined for x = 2

Step-by-step explanation:

The open circle at x = 2 shows that the function is not defined for x = 2.

The volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm.

Volume is a measure of the quantity or amount of space an object occupies. It is measured in cubic units, such as cubic meters, cubic centimeters, and cubic feet. Volume is also used to measure the amount of liquid or gas in a container. Volume is an important concept in mathematics, science, engineering, and other subject areas. It can be used to calculate the mass, weight, density, and other physical properties of a substance or object.

The volume of water that can be enclosed in the outside layer of the glass is equal to the volume of the plastic material that encloses the glass. Since the thickness of the plastic is 0.25 cm, the volume of the plastic material is equal to its surface area multiplied by the thickness. The surface area of the glass can be calculated using the equation 4πr², where r is the radius of the glass.

Therefore, the volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm. This is equal to the volume of the plastic material that encloses the glass. It should be noted that this volume of water is only an approximation since other factors such as the porosity of the plastic material must be taken into account.

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The volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm.

Volume is a measure of the quantity or amount of space an object occupies. It is measured in cubic units, such as cubic meters, cubic centimeters, and cubic feet. Volume is also used to measure the amount of liquid or gas in a container. Volume is an important concept in mathematics, science, engineering, and other subject areas. It can be used to calculate the mass, weight, density, and other physical properties of a substance or object.

The volume of water that can be enclosed in the outside layer of the glass is equal to the volume of the plastic material that encloses the glass. Since the thickness of the plastic is 0.25 cm, the volume of the plastic material is equal to its surface area multiplied by the thickness. The surface area of the glass can be calculated using the equation 4πr², where r is the radius of the glass.

Surface area = 4πr², where r is the radius of the glass. Therefore, the approximate volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm, where r is the radius of the glass.

Therefore, the volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm. This is equal to the volume of the plastic material that encloses the glass. It should be noted that this volume of water is only an approximation since other factors such as the porosity of the plastic material must be taken into account.

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50 dozen donuts should be produced before your average cost per dozen drops to $2.45

Let x be the number of dozen donuts produced.

The total cost to produce x dozen donuts is:

Total cost = cost of raw materials + overhead costs

Total cost = 0.65x + 0.55x

Total cost = 1.20x

The average cost per dozen can be expressed as:

Average cost per dozen = Total cost / number of dozens

2.45 = 1.20x / x

To solve for x, we can cross-multiply and simplify:

2.45x = 1.20x

x = 50

Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.

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Therefore , the solution of the given problem of area comes out to be  48 sq ft + 4.5π sq ft is flower bed area.

Its total size can be determined by calculating how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. Something's total dimensions are determined by its surface area. The sum of the borders associated with each of a cuboid's six rectangular edges determines the internal water capacity of the object.

Here,

We must add the areas of the rectangular and semicircular regions to obtain the area of the flower bed visible in the picture.

The size of the rectangle, which is square and measures 8 feet by 6 feet, is:

=> A_rectangular

=> length * width

=> 8 ft × 6 ft = 48 sq ft

The radius of the semicircular area is 3 feet, and its diameter is 6 feet. Since this is only a semicircle, we must split by 2 in order to calculate the area of the semicircle using the formula A = r2.

=> A_semicircle = (πr^2)/2 = (π × 3^2)/2 = 4.5π sq ft

The area of the semicircular and rectangular parts combined gives us:

=>A_flower bed = A_rectangular + A_semicircle

= 48 sq ft + 4.5π sq ft

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The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

A reflection across the x-axis is a transformation that flips an object across the line x = 0. This means that the points in the object will be reflected across the x-axis. The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis .Let us consider the original quadrilateral, ABCD, with coordinates A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). Then, the coordinates of the reflected quadrilateral A'B'C'D are A'(-x1, y1), B'(-x2, y2), C'(-x3, y3) and D'(-x4, y4).For example, if the coordinates of quadrilateral ABCD are A(3, 5), B(7, 6), C(4, 8) and D(9, 2), then the coordinates of the reflected quadrilateral A'B'C'D will be A'(-3, 5), B'(-7, 6), C'(-4, 8) and D'(-9, 2).Therefore, the coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

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The amount of copper that is contained in 120 pounds of brass is equal to 78 pounds.

Let the amount of copper be C.

Given the following data:

Quantity of brass = 120 pounds

Percentage of copper = 65%

To calculate the amount of cooper that is contained in 120 pounds of the brass:

In this exercise, you're required to determine how many pounds of copper can be found in 120 pounds of brass. Thus, we would solve for the percentage of copper contained in this type of brass.

[tex]Copper=\frac{65}{100}*120\\\\Copper, c=78 ponds.[/tex]

This is correct because 65% of 120 pounds is equal to 78 pounds. 65% can be expressed as a decimal (0.65) and multiplied by 120 pounds to find the number of pounds of copper contained in 120 pounds of the brass.

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The growth rate given by value of dR / dc at C = 2 is 0.0021 (approx).

The given formula is, R(C) = 1.35c / (0.29 + c)

=> R(C) = 1.35c / 0.29 + 1.35c / c

Take the derivative of R with respect to c: R(C) = 1.35c / 0.29 + 1.35c / c

Differentiating with respect to c, dR / dc = 1.35(0.29 + c) - 1.35c / (0.29 + c)2dR / dc

= 1.35(0.29 + c - c) / (0.29 + c)2dR / dc

= 1.35(0.29) / (0.29 + c)2

At C = 2,dR / dc = 1.35(0.29) / (0.29 + 2)2= 0.002129

A bacterial growth rate is given by the equation R(C) = 1.35c / (0.29 + c).

We know that R(C) = 1.35c / (0.29 + c) dR / dc = 1.35(0.29 + c - c) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + 2)2dR / dc = 0.002129

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Answer:

? is equal to 8

Step-by-step explanation:

16/20= 0.8

0.8x10= 8

8/10=0.8

OR YOU COUPLE DIVIDED 16 BY TO AND 20 BY 2

Answer:8/10

Step-by-step explanation:when you divide 16 by 20, you get 0.8. So turn 0.8 into a fraction with 10, you get 8/10. (I’m not that smart, mb if I get something wrong.)

The probability of drawing the blue and even-numbered marble from the given jar is 3/10.

The given problem can be solved using the concept of Probability. Let's see how to solve it.

Step 1: Total Number of Marbles in the Jar

Number of red marbles in the jar = 3

Number of blue marbles in the jar = 7

Total number of marbles in the jar = 3 + 7 = 10

Step 2: Find the Probability of Marble is Blue and Even Numbered

Number of blue marbles which are even-numbered = 3 (Blue marbles numbered 2, 4, and 6 are even-numbered marbles)

Total number of marbles in the jar = 10

Probability of marble is blue and even-numbered = Number of blue marbles which are even-numbered / Total number of marbles in the jar = 3/10

So, the required probability of drawing the blue and even-numbered marble is 3/10.

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The area of the garden is given as follows:

A = 20.6925 ft².

The garden has a rectangular format, hence it's area is given by the multiplication of it's length l by it's width w, as follows:

A = lw.

From the image, converting the mixed numbers to decimal, the dimensions of the garden are given as follows:

Hence the area in feet squared is given by the multiplication of these two dimensions, as follows:

A = 7.75 x 2.67

A = 20.6925 ft².

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The religious make-up of the United States Congress is reflective of that in the general population.

Answer:Yes, the religious make-up of the United States Congress is reflective of that in the general population.The steps to test whether the distribution of religion among U.S. adults differs significantly from that among the 114th U.S. Congress with an α = 0.01 level of significance are given below:First, calculate the expected frequencies for Mormon and Unaffiliated using the formula:Expected frequency = (total sample size) x (proportion)Expected frequency of Mormons = (1500) x (0.030) = 45Expected frequency of Unaffiliated = (1500) x (0.019) = 28.5Next, calculate the chi-square statistic using the formula:Chi-square = ∑ [(observed frequency - expected frequency)² / expected frequency]To find the observed frequency - check the frequency table below.Religion Frequency Expected Contribution Protestant 772 858.0 8.620 Catholic 368 460.5 18.580 Mormon 34 45.0 8.690 Orthodox 12 13.5 0.167 Jewish 46 78.0 13.128 Other 61 16.5 120.015 Unaffiliated 207 28.5 149.969The degrees of freedom for the chi-square test = (number of categories - 1) = 7 - 1 = 6Finally, compare the calculated chi-square statistic with the critical value from the chi-square distribution table with 6 degrees of freedom at α = 0.01 level of significance. If the calculated chi-square statistic is greater than the critical value, then the null hypothesis is rejected and we conclude that the distribution of religion among U.S. adults is significantly different from that among the 114th U.S. Congress. If the calculated chi-square statistic is less than or equal to the critical value, then the null hypothesis is accepted, and we conclude that the distribution of religion among U.S. adults does not differ significantly from that among the 114th U.S. Congress.

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(13/4)z^(5)x^(2) - 6/x

The given expression is: (13z^(5)x^(5)-24zx^(5))-:(-4x^(3)x^(4)) To simplify the given expression, we will use the rules of division of two algebraic expressions. The division of two algebraic expressions is equal to the multiplication of the first expression with the reciprocal of the second expression. The reciprocal of an expression is the inverted expression of that expression. So, (13z^(5)x^(5)-24zx^(5))-:(-4x^(3)x^(4))=(13z^(5)x^(5)-24zx^(5)) x ( -1/4x^(3)x^(4))Simplify the above expression by combining the like terms as follows:(13z^(5)x^(5)-24zx^(5)) x ( -1/4x^(3)x^(4))=(13z^(5)x^(5) x (-1/4x^(3)x^(4))) + (-24zx^(5) x (-1/4x^(3)x^(4)))=-(13/4)z^(5)x^(2) - 6/x Therefore, the simplified form of the given expression is -(13/4)z^(5)x^(2) - 6/x.

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Answer: y=28

Step-by-step explanation:

The coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

To find the coordinates of the foci of the ellipse given by the equation 4x² + y² = 64, we can compare it to the standard form of an ellipse:

(x²/a²) + (y²/b²) = 1

In this case, the equation 4x² + y² = 64 can be rewritten as:

x²/(8²) + y²/(8²) = 1

Comparing the equation to the standard form, we find that a = 8 and b = 8. The foci of the ellipse can be calculated using the formula:

c = sqrt(a² - b²)

For our ellipse, c = sqrt(8² - 8²) = sqrt(64 - 64) = 0.

Since c = 0, the foci coincide with the center of the ellipse. Thus, the coordinates of the foci are the same as the center of the ellipse.

Therefore, the coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

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a. The perimeter in the scale is 36 centimeters

The area in the scale drawing is 80 square centimeters.

b.  The actual perimeter is 40 millimeters.

The actual area is 937.5 square millimeters. ​

To find the perimeter of the icon in the scale drawing, you need to add up the length of all its sides. Using the ruler provided, measure the length and width of the icon and round them to the nearest half centimeter. Then, add up the length and width and multiply by 2 to get the perimeter.

a. Assuming the scale of the drawing is 1 cm : 2 units, the length of the icon in the drawing would be 2 x 5 = 10 units and the width would be 2 x 4 = 8 centimeters.

The perimeter in the scale drawing would be 2 x (length + width) = 2 x (10 + 8) = 36 cm (rounded to the nearest half-centimeter).

The area in the scale drawing would be length x width = 10 x 8 = 80 square cm.

b. Assuming the scale of the drawing is 1 cm : 2 units, the actual length of the icon would be 2.5 cm / 2 = 1.25 units and the actual width would be 1.5 cm / 2 = 0.75 units.

The actual perimeter would be 2 x (length + width) = 2 x (1.25 + 0.75) = 4 cm = 40 mm.

The actual area would be length x width = 1.25 x 0.75 = 0.9375 square cm = 937.5 square mm.

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Answer:

52 miles

Step-by-step explanation:

Matthew runs 20 miles in the first week. We want to increase this number by 4 each week. For this question we will use m for a variable for miles.

This will look like

20 + 4m = total miles ran

if he ran 8 miles, we will enter this number into the variable m.

20 + 4 × 8 = 52

The total miles Matthew ran was 52 miles after 8 weeks.

Graphs allow us to show that the following is true: D. Both plans will be costing the same when 50 texts are sent is accurate.

The graph is just a organised representation of the data. It helps in our understanding of the data. The numerical information gathered through observation is referred to as data.

The answer is that both plans are same in price when 50 texts are sent because both lines intersect at a cost of $22.5 for 50 texts, indicating that they are equal in price.

The other options are not right:

A-plan Hiroto's costs more than Emilia's plan when more than 50 messages are sent. This is untrue, as you can see from the graph that Emilia's line is higher after 50 texts, indicating that her plan is more expensive.

B-When 22 messages are sent, the cost of both plans is the same. This is false because when 22 texts are sent, the lines do not cross at the same spot.

C-When more than 22 SMS are sent, Emilia's is more expensive than Hiroto's plan. This is untrue because Hiroto's plan is more expensive until they send 50 messages, which is the only time they cost the same. At that moment, Emilia's plan costs about $15.5 and Hiroto's plan costs about $21.

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The complete question is:

Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs  $10 per month and $0.25 per text. Using the graph below,  which statement is true?

A. Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.

B. Both plans cost the same when 22 texts are sent.

C. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.

D. Both plans cost the same when 50 texts are sent.

Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).

Answer: u = 2.83, -2.83.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two sides separated by an equals sign (=). The expressions on both sides of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The goal in solving an equation is to find the value or values of the variable(s) that make the equation true.

The real numbers are a set of numbers that includes all rational and irrational numbers. Real numbers can be represented on the number line, where every point corresponds to a unique real number. The real number system is denoted by the symbol R.

In the given question,

To solve the equation 7u² - 56 = 0, we can start by isolating the variable u by adding 56 to both sides of the equation:

7u² - 56 + 56 = 0 + 56

Simplifying the left side, we get: 7u² = 56

Dividing both sides by 7, we get: u² = 8

Taking the square root of both sides, we get: u = ±√8

Simplifying the square root, we get: u = ±2.83

Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).

Answer: u = 2.83, -2.83.

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Landon would need to invest approximately $1,150 to reach a future value of $3,250 in 18 years with an interest rate of 6.6% compounded daily.

To determine how much Landon needs to invest, we can use the compound interest formula, which is:

A = P(1 + r/n)^(nt)

where A is the future value of the account, P is the principal amount (the amount Landon needs to invest), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the interest rate is 6.6% or 0.066, the account is compounded daily, so n = 365, and t = 18. We want to find the principal amount, P, that will result in a future value of $3,250.

Substituting these values into the formula, we get:

3,250 = P(1 + 0.066/365)^(365*18)

Simplifying the right-hand side of the equation, we get:

3,250 = P(1.000181)^6,570

Dividing both sides by (1.000181)^6,570, we get:

P = 3,250 / (1.000181)^6,570

Using a calculator, we can evaluate this expression to find that:

P ≈ $1,150.52

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The length of each side of the hexagon is 13 units long, which is equal to length of the park.

In order to determine the length of every side of the hexagon, it is necessary to compute the distance between each pair of neighboring vertices.

This can be accomplished by employing the distance formula, which is represented as follows:

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² ).

To facilitate the process, we will designate the vertices as A, B, C, D, E, and F in sequence, with A being the vertex at the top.

Then, the length of side AB is calculated as follows:

|AB| = √((38.5-26.5)² + (7-12)²)

|AB| = √((12)² + (-5)²)

|AB| = √(144 + 25)

|AB| = √169

|AB| = 13

Similarly, we can calculate the length of each side:

|BC| = √( (26.5-38.5)² + (2-7)² ) = 13

|CD| = √( (13.5-26.5)² + (2-2)² ) = 13

|DE| = √( (1.5-13.5)² + (7-2)² ) = 13

|EF| = √( (13.5-1.5)² + (12-7)² ) = 13

|FA| = √( (26.5-13.5)² + (12-12)² ) = 13

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Answer:

13 units

Step-by-step explanation:

d^2 = (x2 – x1)^2 + (y^2 – y^1)^2

Now we calculate the distance between 2 points:

d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2

d^2 = 169

d = 13

Therefore the length of each side of the park is 13 units.

The first five terms of the sequence given the definition are -1, 0, 1, 2 and 3

To find the first five terms of the sequence {an}, we can use the recursive definition of the sequence and compute each term one by one:

a1 = -1

For n = 2, we have:

a2 = a1 + (-1)² = -1 + 1 = 0

For n = 3, we have:

a3 = a2 + (-1)³ = 0 - (-1) = 1

For n = 4, we have:

a4 = a3 + (-1)⁴ = 1 + 1 = 2

For n = 5, we have:

a5 = a4 + (-1)⁵ = 2 - (-1) = 3

Therefore, the first five terms of the sequence {an} are:

a1 = -1

a2 = 0

a3 = 1

a4 = 2

a5 = 3

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Therefore , the solution of the given problem of amount comes out to be Sylvia's homes insurance covers personal property up to a maximum of $123,250.

aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess

Here,

Sylvia's house is covered for $225,000. Accordingly, the coverage for personal belongings is as follows:

The policy offers coverage for personal belongings equal to 55% of the insured value of the home.

=> Personal property coverage = 0.55 x $225,000, or $123,750.

Sylvia, however, has a $500 personal property exemption. This implies that she is responsible for covering the first $500 of the insured loss.

So the amount covered for personal belongings under Sylvia's homeowners insurance is:

=> $123,750 -  $500 is the amount insured for personal property, or

=> $123,250.

Sylvia's homes insurance covers personal property up to a maximum of $123,250.

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Answer:

52.08 Euros

Step-by-step explanation:

21.70 euros / 20 uk pounds = 1.085 per pound

so 48 euro x 1.085 pounds = 52.08 euros

Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). The coordinates of the intersection point are (1,3).

What is rhombus?

A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.

Since ABCD is a rhombus, its diagonals AC and BD are perpendicular bisectors of each other, and they intersect at their mutual midpoint M.

The midpoint M of AC is the average of the coordinates of A and C, namely:

M = ((-1+3)/2, (2+4)/2) = (1, 3)

Similarly, the midpoint of BD is the average of the coordinates of B and D. Since we don't know the coordinates of B and D, we need to find them first.

The other two vertices of the rhombus are obtained by reflecting A and C about the midpoint M, since opposite sides of a rhombus are parallel and equal in length. To do this, we subtract the coordinates of M from those of A and C, and then add them to M:

B = 2M - A = 2(1,3) - (-1,2) = (3,4)

D = 2M - C = 2(1,3) - (3,4) = (-1,2)

Now we can find the midpoint of BD:

N = ((3-1)/2, (4+2)/2) = (1, 3)

Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). Therefore, the coordinates of the intersection point are (1,3).

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the high-temperature range which is most likely represented by the shaded area labeled 1 is 90°F to 99°F.\

Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).

In Science, the temperature is measured by using a thermometer and its units include the following:

Celsius (°C)

Kelvin (K)

Fahrenheit (°F)

Based on the weather map shown in the image attached below, we can deduce that the high-temperature range which is most likely represented by the shaded area labeled 1 is 90°F to 99°F.

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Answer: x = 24

Step-by-step explanation:

To solve for x, we need to simplify the left side of the equation first by combining like terms:

4x - 2 + 3x + 14 = 180

7x + 12 = 180

Next, we will isolate the variable by subtracting 12 from both sides:

7x + 12 - 12 = 180 - 12

7x = 168

Finally, we will solve for x by dividing both sides by 7:

7x/7 = 168/7

x = 24

Therefore, the solution to the equation 4x-2+3x+14=180 is x = 24.