(05.03 MC)
A regular heptagon with 7 sides is inscribed in a circle with radius 8 millimeters. What is the area of
the figure? (3 points)
O 25.019 mm.2
O 150.112 mm.2
O 175.130 mm.²
205.639 mm.2

The value of the variable t of the exponential equation [tex]-5\cdot e^{10\cdot t} = - 30[/tex], t = (1 / 10) · ㏑ 6 (EXACT), t = 0.179 (APPROXIMATE).

In this problem we need to clear the variable t of an exponential equation with one variable, this can done by means of relationship of exponential and logarithmic functions, logarithm properties and algebra properties.

Now we proceed to present the complete procedure for the solution to the exponential equation:

[tex]-5\cdot e^{10\cdot t} = - 30[/tex]

[tex]e^{10\cdot t} = 6[/tex]

10 · t = ㏑ 6

t = (1 / 10) · ㏑ 6

t = 0.179

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Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

Answer:

A: Function 1
B: Function 4
C: Function 2

Explanation A:

In order to solve this problem, you will have to find the slope for each function.

1st Function: For the first function, you will need to find 2 points, let's use (0, -4) and (1, 1). Remember slope is rise over run, so you would count the spaces from the first point to the second, it rises (y-axis) 5 points and runs (x-axis) 1 point. Which would give you 5/1 = 5. Function 1's slope is 5.

2nd Function: Same equation, rise over run, or y over x, so we need to find the pattern on each side. For the x-values, we can see starting from the first point that they increase by one, -2 to -1 to 0, and for the whole x-values, so 1 will be our run, since it is the x-value. For the rise, or y-values, we can see a pattern of -1 starting from the top going towards the bottom. Now, we can rise over run, -1/1 = -1

3rd Function: Slope is -4, as the equation is y = mx + b, and m stands for slope.

4th Function: Says slope is 2.

Now that we know all the slopes, we can see that Function 1's slope is the greatest.

Explanation B:
For this problem, we will have to find the y-intercept for all the functions, this means where the x-value is 0, so that the y-value will be right on the y-axis.

Function 1: We can see that the function intercepts the y-axis at (0, -4), it's y-intercept being -4.

Function 2: Where the x-value is 0, we can find the y-intercept, which is (0, 1). Making the y-intercept 1.

Function 3: Following the y = mx + b format, the b is the y-intercept, so it is -2.

Function 4: Gives you the y-intercept as 5.

In the end, the only function with a y-intercept greater than 4 is Function 4.

Explanation C:

Since we already know the y-intercepts from the previous problem, we only need to see which one is closest to 0. In this case, it would be Function 2 with a y-intercept at -1, only 1 unit off of 0, making it the closest.

If Each card corresponds to a sample point with a 1/52 probability then the  sample points in the event an ace is selected is S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

In a standard deck of 52 playing cards, there are four aces.

Each ace corresponds to a different suit: clubs, diamonds, hearts, and spades.

So, when we talk about the event of selecting an ace, we are referring to the act of choosing one of these four specific cards from the deck.

The sample points in the event "an ace is selected" are the individual cards that match this criteria.

Therefore, the sample points in this event are:

S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

These four cards are the possible outcomes when we randomly select a single card from the deck, focusing only on the event of selecting an ace.

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A) One way to write mixed fractions [tex]6\frac{2}{4} \\[/tex]  is 3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]

B) Saturday: 3 to 4 hours work = trim bushes and weed garden

Sunday: 4 to 5 hour work = paint sheet and mow lawn

A) [tex]6\frac{2}{4} \\[/tex]  can be written as a simple fraction 6 + [tex]\frac{2}{4}[/tex]

This can be further broken into and written as

3 + 3 +  [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]

B) Saturday : 3 to 4 hours of work

Trim bushes + Weed garden

[tex]1\frac{1}{6} +2\frac{2}{6}[/tex]

1 + [tex]\frac{1}{6}[/tex] + 2+ [tex]\frac{2}{6}\\[/tex]

3 + [tex]\frac{3}{6}[/tex]

3 + [tex]\frac{1}{2}[/tex]

[tex]3\frac{1}{2}[/tex]

Sunday: 4 to 5 hours of work

Paint sheet + mow lawn

[tex]1\frac{3}{6} +3 \frac{4}{6}[/tex]

1 + 3 + [tex]\frac{3}{6} +\frac{4}{6}[/tex]

4 + [tex]\frac{8}{6}[/tex]

[tex]4\frac{8}{6}[/tex]

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The Given question is incomplete the complete question is :

Mr. mason likes to work around the yard during the weekends

The numeric value of the expression 3y(9 - x) when y = 3 and x = 7 is given as follows:

18.

To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The expression in the context of this problem is given as follows:

3y(9 - x).

Hence the numeric value when x = 7 and y = 3 is given as follows:

3 x 3 x (9 - 7) = 3 x 3 x 2 = 18.

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Answer:

Solution: x = 2, y = -3.

Step-by-step explanation:

Given system of equations:

Equation 1: 2x - 3y = 13

Equation 2: x + 2y = -4

Multiply Equation 2 by 2:

2(x + 2y) = 2(-4)

Simplified: 2x + 4y = -8

Add Equation 1 and Equation 3:

4x + y = 5

Solve Equation 4 for y:

y = 5 - 4x

Substitute y into Equation 2:

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

Simplify:

-7x + 10 = -4

Solve for x:

x = 2

Substitute x into Equation 5:

y = 5 - 4(2)

y = -3

Solution: x = 2, y = -3.

The value of a is given as follows:

a = 2.

The rate of change is given as follows:

2.4 inches per hour.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The line passes through the points (–1, –5) and (4, 5), hence the slope m is obtained as follows:

m = (5 - (-5))/(4 - (-1))

m = 2.

Hence:

y = 2x + b.

When x = -1, y = -5, hence the intercept b is obtained as follows:

-5 = -2 + b

b = -3.

Hence:

y = 2x - 3.

Then the value of a is obtained as the value of x when y = 1, hence:

2x - 3 = 1

2x = 4

x = 2.

The rate of change in the snowfall is given as follows:

m = (8.1 - 2.3)/2

m = 2.4 inches per hour.

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The actual length of the bus is given as follows:

45 feet.

The actual length of the bus is obtained applying the proportions in the context of the problem.

The scale drawing is of 0.5 inches to 5 feet, hence the length represented by each inch of drawing is given as follows:

5/0.5 = 10 feet.

The length of the drawing is given as follows:

4.5 inches.

Hence the actual length of the bus is given as follows:

4.5 x 10 = 45 feet.

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Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.

To calculate Salina Grant's gross pay, we need to determine the pay for each range of chairs assembled and sum them up.

Let's break down the calculation based on the given differential piece rate scale:

1-25 chairs: $10 each

Salina assembled 25 chairs in this range, so the pay for this range is

25 * $10 = $250.

26-40 chairs: $13 each

Salina assembled 15 chairs in this range, so the pay for this range is

15 * $13 = $195.

Chairs over 40: $17.50 each

Salina assembled 47 chairs in total, and since she already assembled 25 chairs in the first range and 15 chairs in the second range, the number of chairs in this range is

47 - 25 - 15 = 7 chairs.

The pay for this range is

7 * $17.50 = $122.50.

Now, let's sum up the pay for each range to find Salina Grant's gross pay:

$250 + $195 + $122.50 = $567.50

Therefore, Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.

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The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

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The probable question may be:

Which cellphone service provider was the first to be established in south africa

You would add the sales tax amount to the cost of the meal to get the total cost. In this case, the sales tax amount is $1, so the total cost would be $26.

One situation that would fit into this scenario is calculating the total cost of a meal at a restaurant that costs $25. Firstly, to calculate the sales tax, you would need to convert the percentage of sales tax into a decimal.

In this case, the sales tax rate is 5%, so you would convert it to 0.05.Next, you would multiply the cost of the meal by the sales tax rate to calculate the sales tax amount.

To do this calculation without a calculator, you can use mental math or estimation techniques.For example, you could estimate 5% of $25 by breaking the 5% into a 1% and 4% calculation.

To calculate 1%, you would simply move the decimal point two places to the left, which gives you $0.25. Then, to calculate 4%, you could multiply $0.25 by 4, which equals $1.

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It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.

Remember that when we have the quotient of two powers with the same base (like in this case, where the base is 2) the outcome will be a power of the same base, such that the exponent is equal to the difference between the other two exponents.

The rule is:

[tex]\frac{x^m}{x^n} = x^{m - n}[/tex]

Then we can use that to simplify the expression, we will get:

[tex]\frac{2^6}{2^3} = 2^{6 - 3} = 2^3 = 2*2*2 = 8[/tex]

We can see that the correct option is B.

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Answer: $71,400

Step-by-step explanation:

We will set up a proportion with income in the numerator and pounds in the denominator.

       [tex]\displaystyle \frac{\$12}{4.2\;lbs} =\frac{\$x}{24,990\;lbs}[/tex]

Then we will cross-multiply.

       4.2 * x = 12 * 24,990

       4.2x = 299,880

Lastly, we will divide both sides of the equation by 4.2.

       x = $71,400

The income from 24,990 pounds of strawberries would be approximately $71,690.14.

To find the income from 24,990 pounds of strawberries, we need to use a proportion:

4.2 pounds of strawberries sells for $12, so 1 pound of strawberries sells for $12/4.2 = $2.86 (rounded to two decimal places).

Therefore, 24,990 pounds of strawberries would sell for:

$2.86 x 24,990 = $71,690.14 (rounded to two decimal places).

The lines intersect at only one specific point (-5, 9)

The correct answer is: There is one unique solution (-5, 9).

When two straight-line equations intersect at a point, it means that there is one unique solution to the system of equations. In this case, the point of intersection is (-5, 9), which indicates that the system has a single solution. This means that there is a unique set of values for the variables that satisfy both equations simultaneously.

If the system had no solution, it would mean that the two lines are parallel and will never intersect. However, since the lines in the given system intersect at (-5, 9), it implies that there is a solution.

Alternatively, if the system had infinitely many solutions, it would mean that the two equations represent the same line. In this case, the lines intersect at every point along their entire length, resulting in an infinite number of solutions. However, the fact that the lines intersect at only one specific point (-5, 9) indicates that there is one unique solution to the system of equations.

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The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

The probability is determined using the normal approximation to the binomial distribution.

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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The expression 2ab + [tex]c^2[/tex]  represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.

The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.

[tex]2ab +c^2=a^2+b^2+2ab[/tex]

Subtracting 2ab from both sides

[tex]c^2=a^2+b^2[/tex]

Figure of a square with some shaded triangles.

Area of the triangle formula is 1/2 times base times height

base =a and height =a

Area of one triangle = 1/2ab

There are 4 shaded triangles

Area of 4 shaded triangles = 4 x 1/2ab

Area of the square = side times side

Now we find the area of outer square. side length is a+b

Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]

Using the length of the figure to represent the area.

Thus, now set both the areas equal to each other.

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Your question seems incomplete, the probable complete question is

Answer: 216

Step-by-step explanation:

592-376

592-300= 292

292-70= 222

222-6= 216

Answer:

CaCL2 + KL → KCL + CaL2

Step-by-step explanation:

To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.

Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.

Ionic charges are not yet supported and will be ignored.

Replace immutable groups in compounds to avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.

Compound states [like (s) (aq) or (g)] are not required.

You can use parenthesis () or brackets [].Li + Ag = Li + Ag

KOH + KMnO4 + H2SO4 = KOH + KMnO4 + H2SO4

C6H6O + KOH = C6H7KO2

CUO + HNO3 = CU(NO3)2 + H2O

C4H6O4 + KOH = C2K2O4 + C2H6O2

Zn + Sr(OH)2 = Sr + Zn(OH)2

Al + Pb(No3)2 = Al(No3)3 + Pb

HNO3 + Zn = Zn(NO3)2 + H2

ZnO + CH3COOH + H2O + Al2O3 = Zn(CH3COO)2*2H2O + Al2O3

BeO + Zn(OH)2 = Be(OH)2 + ZnO

CH3COOK + CH3Br = CH3COOCH3 + KBr

Pb(NO3)2 + HBr = PbBr2 + NHO3

The integers that satisfy the inequality are -1, 0, 1, and 2.

To find the integer values that satisfy the inequality x < 6/(x - 1), we can start by analyzing the domain of the expression.

First, note that the denominator (x - 1) cannot be equal to zero since division by zero is undefined. Therefore, we must exclude x = 1 from the domain.

Next, consider the sign of the expression 6/(x - 1). When the denominator (x - 1) is positive, the expression will be positive. Similarly, when the denominator is negative, the expression will be negative.

Considering the inequality x < 6/(x - 1), we can divide the problem into two cases based on the sign of (x - 1):

Case 1: (x - 1) > 0

In this case, the expression 6/(x - 1) is positive. To satisfy the inequality x < 6/(x - 1), x must be less than the positive value of 6/(x - 1). Since the denominator is positive, we can drop the absolute value sign. Therefore, the inequality becomes:

x < 6/(x - 1)

Case 2: (x - 1) < 0

In this case, the expression 6/(x - 1) is negative. To satisfy the inequality x < 6/(x - 1), x must be greater than the negative value of 6/(x - 1). Since the denominator is negative, we need to flip the inequality sign and change the direction. Therefore, the inequality becomes:

x > 6/(x - 1)

Now, let's solve each case separately:

Case 1: (x - 1) > 0

Since the denominator (x - 1) is positive, we can multiply both sides of the inequality by (x - 1) without changing the direction of the inequality. This gives:

x(x - 1) < 6

Expanding the left side:

x² - x < 6

Rearranging the inequality:

x² - x - 6 < 0

Now we can factorize the quadratic:

(x - 3)(x + 2) < 0

To determine the solution, we need to consider the sign of the expression for different intervals:

When x < -2, both factors are negative, so the expression is positive.

When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.

When x > 3, both factors are positive, so the expression is positive.

Therefore, the solution to Case 1 is:

-2 < x < 3

Case 2: (x - 1) < 0

Since the denominator (x - 1) is negative, we need to flip the inequality sign. Multiplying both sides of the inequality by (x - 1) changes the direction of the inequality. This gives:

x(x - 1) > 6

Expanding the left side:

x² - x > 6

Rearranging the inequality:

x² - x - 6 > 0

Factoring the quadratic:

(x - 3)(x + 2) > 0

Considering the sign of the expression for different intervals:

When x < -2, both factors are negative, so the expression is positive.

When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.

When x > 3, both factors are positive, so the expression is positive.

Therefore, there are no solutions in Case 2.

Combining the solutions from both cases, we find that the integer values satisfying the inequality x < 6/(x - 1) are:

-2 < x < 3

In other words, the integers that satisfy the inequality are -1, 0, 1, and 2.

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Answer:

[tex]\frac{4685}{288}[/tex]

Step-by-step explanation:

The explanation is attached below.

The total interest charges to the Roth Family, after 15 years, given the monthly payment would be $ 118, 000

First, find the total amount paid over the 15 years by the Roth Family to be :

= Number of years x Monthly payment x Number of months per year

= 15 x 1, 850 x 12

= $ 333, 000

The total interest charges that the Roth Family paid would be :

= Total amount paid after 15 years - Total amount borrowed as mortgage

= 333, 000 - 215, 000

= $ 118, 000

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The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given that:

Principal P = $340

Interest Rate r = 6.6%

Time t = 9 years

First convert the interest rate from percent to decimal:

Rate = r/100

Rate = 6.6/100

Rate = 0.066

Now, plug the values into the above formula and solve for interest.

I = P × r × t

I = $340 × 0.066 × 9

I = $201.96

Therefore, the simple interest is $201.96.

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The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².

We have,

To verify the equation

E_θ = E_0 cos^4θ = E_0 (1/2 + cos2θ/2)², we can expand the right-hand side and simplify it.

Starting with the right-hand side of the equation:

E_0 (1/2 + cos2θ/2)²

Expanding the square using the binomial expansion:

E_0 [(1/2)² + 2(1/2)(cos2θ/2) + (cos2θ/2)²]

Simplifying:

E_0 [1/4 + cos2θ + (cos2θ)²/4]

Combining the terms:

E_0 [1/4 + 4cos²θ/4 + (cos²θ)²/4]

Simplifying further:

E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]

Combining the terms again:

E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4] = E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]

Simplifying the expression yields:

E_0 cos⁴θ = E_0 cos⁴θ

Therefore,

The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².

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Answer:

Step-by-step explanation:

Total cost function, C = 15+9x-6x²+x

By differentiation,

dc/dx= 9-12x²+1

but

dc/dx= 0

9-12x²+1 = 0

-12x = -10

x=10/12

x=5/6

Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.

Given:

Simple interest = Principal × Rate × Time

Simple interest = $900 × 0.015 × 3

Simple interest = $40.50

Present Value = Future Value / (1 + Rate x Time)

Present Value = $580 / (1 + 0.015 × 3)

Present Value = $580 / 1.045

Present Value = $558.95

Total amount $580 loan is $558.95.

Total amount owed = $940.50 + $558.95

Total amount owed = $1499.45

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The distance between each pair of points include the following:

44. 2.8 units.

45. 5.8 units.

46. 12.0 units.

47. 16.6 units.

48. 7.1 units.

49. 4.5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Question 44.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(3 - 1)² + (2 - 4)²]

Distance = √[(2)² + (-2)²]

Distance = √8

Distance = 2.8 units.

Question 45.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-2 + 7)² + (0 - 3)²]

Distance = √[(5)² + (-3)²]

Distance = √34

Distance = 5.8 units.

Question 46.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-6 - 2)² + (-2 - 7)²]

Distance = √[(-8)² + (-9)²]

Distance = √145

Distance = 12.0 units.

Question 47.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(1 - 8)² + (-8 - 7)²]

Distance = √[(-7)² + (-15)²]

Distance = √274

Distance = 16.6 units.

Question 48.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-5 - 2)² + (-4 + 5)²]

Distance = √[(-7)² + (1)²]

Distance = √50

Distance = 7.1 units.

Question 49.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(5 - 3)² + (5 - 1)²]

Distance = √[(2)² + (4)²]

Distance = √20

Distance = 4.5 units.

Read more on distance here: brainly.com/question/12470464

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