eighteen more than 7 times a number is -12

[tex]3\frac{3}{4}[/tex] feet is 2.25 feet. 7.75 feet of plywood left out of 10 feet when [tex]3\frac{3}{4}[/tex] feet of plywood is cut off.

[tex]3\frac{3}{4}[/tex] feet is a mixed fraction, first we need to convert it into a fraction and then we need to find the point value of the number.

therefore [tex]3\frac{3}{4}[/tex] feet = 3 x 3 / 4

= 3 x 0.75 = 2.25 feet

now we need to find the plywood left when [tex]3\frac{3}{4}[/tex] feet is cut from 10 feet,

therefore, now that we know [tex]3\frac{3}{4}[/tex] feet is 2.25 feet we can subtract it from 10 we get:

10 - 2.25 = 7.75

therefore, we know that there is 7.75 feet of plywood left out of 10 feet when [tex]3\frac{3}{4}[/tex] feet of plywood is cut off.

To learn more about fractions, click here:

brainly.com/question/10354322

#SPJ4

Answer:

42

Step-by-step explanation:

Answer:

Step-by-step explanation:

If one-third of a number y is 14, we can express this mathematically as:

1/3 y = 14

To solve for y, we can isolate y on one side of the equation by multiplying both sides by 3:

1/3 y * 3 = 14 * 3

Simplifying, we get:

y = 42

Therefore, the number is 42.

a. The equation to represent the situation is y = -12x + 120, where x is the number of movies and y is the amount of money remaining on the gift card.

Money is a medium of exchange that is widely accepted as a way to pay for goods and services or to settle debts. Money also serves as a store of value, providing a way for people to save for the future. Money is generally created through government-backed fiat currencies, such as the U.S. dollar, which are issued and regulated by central banks. Money can also be created in the form of crypto-currencies, such as Bitcoin, which are not issued by any single government or central bank. Money is essential for economic growth and stability, as it allows for efficient exchanges of goods and services. Money can also be a source of financial security, providing people with a way to manage their finances and plan for the future.

b. The slope of -12 indicates that for every movie that Elyse sees, she will spend $12 from her gift card. The y-intercept of 120 indicates that if Elyse has not seen any movies, she will have $120 remaining on her gift card.

To learn more about money
https://brainly.com/question/30279568
#SPJ1

The situation is,

a) The line equation is [tex]y = -3x - 6[/tex]

b) The line's y-intercept is -6, which indicates that when the amount of movies x = 0 , the amount on gift y = -6

c) The slope of the line is -3, indicating that as the number of movies x increases, the rate of change of the amount on the gift is declining.

a). The equation provides the line's slope.

Slope,

[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

Changing the numbers indicated in the slope equation,

Slope,

[tex]m=\frac{(6-12)}{(4-2)}[/tex]

Slope m = -6/2

Slope m = -3

The slope is -3

The equation of the line is,

[tex]y - y_1 = m ( x - x_1 )[/tex]

Substitute the given values in the equation,

[tex]y - 12 = -3 ( x - 2 )[/tex]

Simplify the equation,

[tex]y - 12 = -3x + 6[/tex]

Adding 12 on both sides

[tex]y = -3x - 6[/tex]

The equation of line is [tex]y = -3x - 6[/tex]

b). The y-intercept of the equation of line [tex]y = -3x - 6[/tex] is [tex]-6[/tex], when [tex]x=0[/tex]

c). The slope of the line [tex]y = -3x - 6[/tex] is [tex]m = -3[/tex] and the value is decreasing

To know more about Slope, visit:

https://brainly.com/question/16949303

#SPJ1

The completr question and graph attached below,

c. What is the slope, and what does it mean in the context of the situation?

15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.

Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:

15 divided by 289 is approximately equal to 0.0519 or 519/10000.

In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.

To know more about division problem click here:

brainly.com/question/28785787

#SPJ4

Answer:

It's D

Step-by-step explanation:

[tex]1. \: gcf = 8x \\ 2. \: 8x( \frac{16x {}^{2} }{8x} + \frac{8x}{8x} ) \\ 3. \: 8x(2x + 1)[/tex]

The average value of a necklace at Julie's shop is $4.90. For further explanation;-

Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.

The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.

Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.

To learn more about average value here:

brainly.com/question/13391650#

#SPJ11

Answer:

0

Step-by-step explanation:

-2(-3)+27÷(-3)+3

6-9+3

0

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The airplane's average rate in calm air is 600 mph.

What is an average?

In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics

Let's denote the airplane's average rate in calm air by x mph.

When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:

3000 / (x + 300) = 1000 / (x - 300)

We can cross-multiply to simplify:

3000(x - 300) = 1000(x + 300)

Expanding the brackets gives:

3000x - 900000 = 1000x + 300000

Simplifying and rearranging terms gives:

2000x = 1200000

x = 600

Therefore, the airplane's average rate in calm air is 600 mph.

To learn more about averagevisit the link:

https://brainly.com/question/130657

#SPJ9

Answer:180

Step-by-step explanation:

One possible equation Ross can make is 9 - 7 + 8 = 10

Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.

One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.

Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.

Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.

One possible equation Ross can make is:

9 - 7 + 8 = 10

Learn more about arithmetic operations here

brainly.com/question/30553381

#SPJ4

Step-by-step explanation:

Mathematics for Social Science 1011 PDF

Slope of each graph are [tex]\frac{6}{5}[/tex],[tex]\frac{-1}{3}[/tex] and 1 respectively.

Slope of a line in mathematics is defined as the ratio of the change in the y coordinate w.r.t the change in the x coordinate.

Both the change in the y-coordinate and the net change in the x-coordinate are denoted by y₂-y₁ and x₂-x₁, respectively.

Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is

m=y₂-y₁/ x₂-x₁

Taking two points as per observation

Point1: (x₁ y₁)=(0,-3)

Point2:(x₂, y₂)=(5/2,0)

Slope of line=y₂-y₁/ x₂-x₁

=[tex]\frac{0+3}{5/2-0}[/tex]

=[tex]\frac{6}{5}[/tex]

Taking two points as per observation

Point1: (x₁ y₁)=(0,3)

Point2:(x₂, y₂)=(2,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-3}{2-0}[/tex]

=-⅓

Taking two points as per observation

Point1: (x₁ y₁)=(-2,0)

Point2:(x₂, y₂)=(0,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-0}{0+2}[/tex]

=1

Hence, Slope of each graph are 6/5,-⅓ and 1 respectively.

to know more about lines, visit:

https://brainly.com/question/30003330

#SPJ1

Answer:

Step-by-step explanation:

The percentage is 42% of the population is heterozygous for the recessive genetic disorder.

To determine the percentage of the population that is heterozygous for a recessive genetic disorder occurring in 9 percent of the population,

follow these steps:

1. Identify the frequency of the recessive allele (q) by taking the square root of the 9 percent occurrence (0.09). The square root of 0.09 is 0.3.

2. Calculate the frequency of the dominant allele (p) using the equation p = 1 - q. In this case, p = 1 - 0.3 = 0.7.

3. Determine the percentage of the population that is heterozygous using the equation 2pq. In this case, 2(0.7)(0.3) = 0.42 or 42%.

So, 42% of the population is heterozygous for the recessive genetic disorder.

To know more about percentages:

https://brainly.com/question/30348137

#SPJ11

A basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.

SOLUTION:

A basis for the subspace of all vectors (x, y, z) satisfying the single equation x + y + z = 0 can be found by solving this system of linear equations.

Step 1: Choose two variables to express in terms of the remaining variable.
Let's express x and y in terms of z. From the given equation, we get:
x = -y - z
y = -x - z

Step 2: Choose two independent vectors that satisfy the equations.
We can choose two independent vectors by setting z = 1 and z = -1:

When z = 1:
x = -y - 1
y = -x - 1
Let y = 0, then x = -1, so one vector is (-1, 0, 1).

When z = -1:
x = -y + 1
y = -x + 1
Let x = 0, then y = 1, so the other vector is (0, 1, -1).

Therefore, a basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.

To know more about Linear Equations:

https://brainly.com/question/11897796

#SPJ11

Answer:

x>7

Step-by-step explanation:

The circle is open so seven is not included which eliminates the second and fourth choice.

x<7 means x is less than seven which is wrong.

x> means x is greater than seven.

Answer:

x > 7

Step-by-step explanation:

We see that the arrow is going to the right, signaling greater than.

We know that it is not greater than or equal to, since the dot is not shaded.

So, the answer is x > 7.

Based on the information in the image, we can infer that the surface area is 863.5cm³.

To find the surface of the figure we must divide the figure in two, into the cone and the cylinder and find the surface of each one separately and then add it.

Cylinder surface area:

To calculate the surface area of a cylinder we must apply the following formula:

[tex]A = 2\pi r h ++ 2 \pi r^{2} \\A = 2 * \pi * 5 * 15 + 2 * \pi * 5^{2} \\A = 471 + 157\\A = 628cm^{3}[/tex]

Cone surface area:

[tex]A = \pi rh + \pi r^{2} \\A = \pi * 5 * 10 + \pi * 5^{2} \\A = 157 + 78.5 \\A = 235.5 cm^{3}[/tex]

Surface area of the entire figure:

Learn more about square centimeters in: https://brainly.com/question/27798844

#SPJ1

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.

When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.

Here we have

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.

To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.

The coordinates of A are (-4, 6), multiply each coordinate by 1/8

A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)

The coordinates of B are (-2, 2), multiplying each coordinate by 1/8

B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)

The coordinates of C are (4, -2), multiplying each coordinate by 1/8

C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)

The coordinates of D are (4, 4). Multiplying each coordinate by 1/8

D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)

Therefore,

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

Learn more about Dilation at

https://brainly.com/question/29170800

#SPJ1

Answer:

Step-by-step explanation:

312/520 equals 60%

other people 40%

The value of the sides are;

h = 2√3

c = 4√2

To determine the value, we need to note that the trigonometric identities are represented with the fraction;

sin θ = opposite /hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

Using the sine identity

sin 60 = 3/h

Now, cross multiply the values, we have;

h = 3/sin 60

find the sine value

h = 3/√3/2

divide the values

h = 6√3/3 = 2√3

For the second triangle.

sin 45 = 4/c

cross multiply

c = 4/1/√2

c = 4√2

Learn about trigonometric identities at: https://brainly.com/question/22591162

#SPJ1

Answer:

[tex]h = \boxed{2\sqrt{3}}\\\\c = \boxed{4\sqrt{2}}[/tex]

Step-by-step explanation:

We can use the law of sines to determine the sides indicated

Law Of Sines

The ratio of the sides of a triangle to the sine of the angle opposite to that side is the same for all sides

In the triangle on the leftwe have side of length 3 opposite 60° and side of length h opposite 90°

So
[tex]\dfrac{h}{\sin 90} = \dfrac{3}{\sin 60}\\[/tex]

sin 90 = 1
[tex]\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]

Therefore we get
[tex]\dfrac{h}{1} = \dfrac{3}{\dfrac{\sqrt{3}}{2}}\\\\h = 3 \times \dfrac{2}{\sqrt{3}}\\\\h = \dfrac{6}{\sqrt{3}}\\\\[/tex]

Rationalizing the denominator by multiplying by √3 we get
[tex]h = \dfrac{6\sqrt{3}}{3} = \boxed{2\sqrt{3}}[/tex]  
(Answer)

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

For the triangle on the right we have
[tex]\dfrac{c}{\sin 90} = \dfrac{4}{\sin 45}\\\\\sin 90 = 1\\\sin 45 = \dfrac{1}{\sqrt{2}}\\\\c = \dfrac{4}{\dfrac{1}{\sqrt{2}}}\\\\c = 4 \times \sqrt{2}\\\\c = \boxed{4\sqrt{2}}[/tex]

(Answer)

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

In the both above computations we are using the fact that dividing by a fraction involves flipping the denominator fraction and multiplying

There is only one equiangular octagon that Jordan can create with side lengths as the first 8 positive integers.

To create an equiangular octagon with side lengths as the first 8 positive integers, each side must have a different length. The sum of the interior angles of an octagon is 1080 degrees, so each angle in the octagon must measure 135 degrees.

If we arrange the 8 integers in decreasing order, we can label the longest side as a and the remaining sides as b1, b2, b3, b4, b5, b6, in descending order. Then, we must have:

a + b1 + b2 = a + b2 + b3 = a + b3 + b4 = a + b4 + b5 = a + b5 + b6 = a + b6 + b1 = 135 degrees

Simplify each equation, we get:

b1 - b3 = b2 - b4 = b3 - b5 = b4 - b6 = b5 - b1 = b6 - a

Since all the side lengths are different, we can use these equations to find all possible combinations of side lengths. By inspection, we can see that there is only one set of side lengths that satisfies these conditions, namely:

a = 8

b1 = 7

b2 = 6

b3 = 5

b4 = 4

b5 = 3

b6 = 2

Learn more about integers here:

https://brainly.com/question/10930045

#SPJ4

The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length

Based on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.

The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.

Using the Pythagorean theorem, we can calculate the length of this diagonal as:

sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches

So Yeidalis needs a board that is at least 15 inches long to create her artwork.

Learn more about Pythagorean theorem at https://brainly.com/question/343682

#SPJ1

We can claim that after answering the above question, the  As a result, equation the correct answer is "Milwaukee is near a lake."

In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.  

Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

If each basket contains the same number of eggs and there are at least 4 eggs in each basket, Jenny put 3 red eggs in each of 6 baskets, and 4 orange eggs in each of 6 baskets.

Let's call the number of eggs in each basket "x." We know that Jenny placed a total of 18 red eggs, so the number of baskets with red eggs can be represented as 18/x. Similarly, the number of baskets with orange eggs can be represented as 24/x.

Since we know that each basket contains at least 4 eggs, we can set up the inequality 4 ≤ x.

Now we can use this information to set up an equation:

18/x + 24/x = total number of baskets

Simplifying this equation, we get:

42/x = total number of baskets

But we also know that the total number of baskets is an integer (you can't have a fraction of a basket), so x must be a factor of 42.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. But we also know that each basket must contain at least 4 eggs, so we can eliminate 1, 2, and 3 as possible values of x.

Therefore, the possible values of x are 6, 7, 14, 21, and 42. But we also know that there are 18 red eggs and 24 orange eggs, so x must be a factor of both 18 and 24.

The common factors of 18 and 24 are 1, 2, 3, and 6. Therefore, the only possible value of x is 6.

To learn more about count click on,

https://brainly.com/question/12699248

#SPJ4

Complete question is:

Jenny places a total of 18 red Easter eggs in several green baskets and a total of 24 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 4 eggs in each basket. How many eggs did Jenny put in each basket?

In practice, the most frequently encountered hypothesis test about a population variance is an F-test.

In statistics, hypothesis tests provide us with a tool to evaluate evidence about a population. Hypothesis testing is a crucial part of statistical inference, in which an analyst tests hypotheses using statistical methods such as t-tests, chi-squared tests, and analysis of variance (ANOVA).

In practice, the most commonly used hypothesis test for population variance is the F-test. This test can be used to test the null hypothesis that two population variances are equal. F-tests have a wide range of uses, including in quality control, financial analysis, engineering, and more. The F-test statistic is calculated by dividing the sample variance of one sample by the sample variance of another sample. The F-test requires that the data come from populations that follow normal distributions, and it is sensitive to outliers in the data.

Therefore, in practice, the most frequently encountered hypothesis test about a population variance is an F-test.

To learn more about “hypothesis test” refer to the https://brainly.com/question/4232174

#SPJ11

.

In the figure of circle provided. the value of x is

In a circle, equal chords subtends equal arc length.

In the problem it was given that:

chord SU is equal to chord ST hence we have that

x + x + 38 = 360 (angle in a circle)

collecting like terms

2x + 38 = 360

2x = 360 - 38

2x = 322

Isolating x by dividing both sides by 2

2x / 2 = 322 / 2

x = 161

Learn more about arc measures at:

https://brainly.com/question/30543683

#SPJ1

Answer:

12π feet

Step-by-step explanation:

The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area is 36π ft², so we can set up an equation:

36π = πr²

To solve for the radius, we can divide both sides by π:

36 = r²

Taking the square root of both sides, we get:

r = 6

Now that we know the radius is 6 feet, we can use the formula for the circumference of a circle, C = 2πr:

C = 2π(6)

Simplifying, we get:

C = 12π

Therefore, the circumference of the circle is 12π feet.

The probability that the second chip drawn is red is 1/3.

The probability of drawing a red chip on the first draw is 6/10, or 3/5. After one chip is discarded, there are 9 chips remaining, 3 of which are red. So the probability of drawing a red chip on the second draw, given that a chip has already been discarded, is 3/9, or 1/3.

Therefore, the probability that the second chip drawn is red is 1/3. This is because the first chip drawn could be either white or red, so there are two possible scenarios. If the first chip drawn is white, there will be 6 red chips and 3 white chips left, so the probability of drawing a red chip on the second draw will be 6/9 or 2/3. If the first chip drawn is red, there will be 5 red chips and 4 white chips left, so the probability of drawing a red chip on the second draw will be 5/9. To get the overall probability of drawing a red chip on the second draw, we need to take the average of these two probabilities, weighted by the probability of the first chip being white or red, respectively.

The probability of the first chip being white is 4/10, or 2/5, and the probability of the first chip being red is 6/10, or 3/5. So the overall probability of drawing a red chip on the second draw is

(2/5) x (2/3) + (3/5) x (5/9) = 4/15 + 1/3 = 3/9 = 1/3.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.

Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.

Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.

We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:

a/sin A = b/sin B = c/sin C

Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.

First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:

angle ACB = 180 - angle ABC - angle BCA

angle ACB = 180 - 68 - 73

angle ACB = 39 degrees

Next, we can use the Law of Sines to find a and b:

a/sin 68 = c/sin 39

b/sin 73 = c/sin 39

Solving for c in both equations gives:

c = a sin 39 / sin 68

c = b sin 39 / sin 73

We can set these two equations equal to each other and solve for b:

a sin 39 / sin 68 = b sin 39 / sin 73

b = a (sin 39 / sin 73) * (sin 68 / sin 39)

b = a (sin 68 / sin 73)

We know that a + b = 50, so we can substitute the expression for b into this equation:

a + a (sin 68 / sin 73) = 50

Solving for a gives:

a = 50 / (1 + sin 68 / sin 73)

a ≈ 23.3 meters

Substituting this value of a into the expression for b gives:

b ≈ 26.7 meters

So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.

To know more about expression visit:

https://brainly.com/question/17248750

#SPJ1

The complete question is

Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.

The answer to this question is 289 miles. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

Sum is the total of two or more numbers added together. It is a mathematical operation used to find the aggregate of two or more numbers or amounts. Sum is calculated by adding the numbers together to get the total.

This is because Julie will be driving a total of 89 miles from York to Derby, then 73 miles from Derby to Corby, for a total of 162 miles. She will then have to drive 127 miles from Derby back to York, giving a total of 289 miles.

Once these distances are determined, the total number of miles is simply the sum of the three distances. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

To further illustrate this answer, it can be thought of as a triangle, where each location is a vertex and the lines connecting them are the distances between the locations.

For more questions related to distances

https://brainly.com/question/17273444

#SPJ1