jamal wants to estimate the
distance across the gorge
shown in the diagram below.
He stands at point Y and
locates a tree at point X
directly across the gorge to the
north. He then walks west
along the gorge 500ft and
marks point A. After walking
another 500ft in the same
direction, he turns 90 degrees
and walks south, perpendicular
to the gorge. He stops when
his location appears to form a
straight line with points A and
X. Jamal measures the
distance BC as 327 ft. What is the distance of XY across the gorge?

Answers

Answer 1

Jamal's estimate of the distance across the gorge is 1424.56 ft

What is Pythagorean Theorem ?

The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.

First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.

Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:

AC^2 = YA^2 + YC^2

He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:

AC^2 = 500^2 + 327^2

AC^2 = 250000 + 107649

AC^2 = 357659

AC = √357659

AC ≈ 597.56 ft

Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:

distance across gorge = XA + AY

distance across gorge = AC + YA + YC

distance across gorge = 597.56 ft + 500 ft + 327 ft

distance across gorge ≈ 1424.56 ft

This is Jamal's estimate of the distance across the gorge.

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Related Questions

At the DeBartolo Building, 3 out of every 7 employees use public transportation. There are 9,800 employees at the building. How many employees do not use public transportation? Type in the number only.

Answers

Step-by-step explanation:

3 out of every 7 employees use public transportation so 4 out of every 7 employees do NOT use public transportation.

9,800 / 7 = 1,400

1,400 * 4 = 5,600

triangle A"B"C" is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship between BC and B"C"

Answers

Answer:

the equation that explains the relationship between BC and B"C" is:

BC = 2 * B"C"

This equation states that the length of BC is equal to twice the length of B"C".

Step-by-step explanation:

If triangle A"B"C" is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin, then the coordinates of the vertices of triangle A"B"C" can be expressed as follows:

A" (x+1, y+1)

B" (3x+3, 3y+3)

C" (3x+6, 3y+6)

To find the equation that explains the relationship between BC and B"C", we can use the distance formula to find the length of both segments. The distance formula is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the distance formula, we can find the length of BC as follows:

BC = √((3x - x)^2 + (3y - y)^2)

= √((2x)^2 + (2y)^2)

= √(4x^2 + 4y^2)

= 2√(x^2 + y^2)

We can also find the length of B"C" as follows:

B"C" = √((3x+6 - 3x-3)^2 + (3y+6 - 3y-3)^2)

= √((3)^2 + (3)^2)

= √(9 + 9)

= √(18)

= 3√(2)

Graph the line that has a slope of 2 and includes the point (2,8)

Answers

Answer:

y = mx + c

8 = 2x + 2

Please help it's urgent!
part a) says write an equation and solve for x

Answers

Answer: look at explanation

Step-by-step explanation:

1. Since those are congruent you equal them to eachother: 6x-8=4x+2

2. Then you solve (steps are shown below)

a) 6x-8=4x+2

b) 2x-8=2

c) 2x=10

d) x=5

3. Answer should be x=5

hope this helps!

if the p value is less than a in a two-tailed test, a. the null hypothesis should not be rejected. b. the null hypothesis should be rejected. c. a one-tailed test should be used. d. more information is needed to reach a conclusion about the null hypothesis.

Answers

In a two-tailed test, the null hypothesis should be rejected in favor of the alternative hypothesis if the p-value is smaller than a. Therefore option (b) is the right answer.

What is null hypothesis?

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

A p-value less than 0.05 (usually 0.05) is considered statistically significant when using the P-value technique to conduct any hypothesis test. With less than a 5% chance that the null is true, it provides strong evidence against the null hypothesis (and the results are random). The alternative hypothesis is thereby accepted, whereas the null hypothesis is rejected.

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If you flip a coin 300 times,how many times would you expect it to land on tails (same question for heads) Heads Frequency:35 Tails frequency:65

Answers

I flip a coin 300 times.

So the possibility of head :

The formula for probability is

Probability=

\frac{number of total events}{number of favorable events}

From the given data in the question,

The coin is tossed total 300 times,

We got head 35 times in 300 times,

So the probability of getting a head is =

[tex] \frac{300}{35} [/tex]

Same do as Tails

Victoria depoited $15,000 into a aving account that earn an annual imple interet rate of 0. 2%. To the nearet tenth of a year, how long will it take for the account to reach $15,500?

Answers

At an interest rate of 0.2% per year, $15500 will be reached from $15000 in 16.67 years.

What is percent?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Here,

Principal=15000

Rate of interest=0.2%

Interest amount per year=15000*0.2%

=$30

Let n be the number of years,

15500=15000+30n

500=30n

n=50/3

n=16.67 years

It will take 16.67 years to reach the amount of $15500 from $15000 at the interest rate of 0.2% per year.

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Need help with this question

Answers

The value of the angle m∠BDC is 105°.

What is third angle theorem?If the other two sets are both congruent, then the third angles are equal.The third pair of angles must be congruent if two angles in one triangle are congruent with two angles in another triangle. The Third Angle Theorem refers to this.The Triangle Sum Theorem can be thought of as an extension of the Third Angle Theorem. The Triangle Sum Theorem states that once two angles in a triangle are known, you automatically know the third. This indicates that if you have two triangles with two pairs of congruent angles between them, you will receive the same result both times when you apply the Triangle Sum Theorem to each triangle to determine the third angle. The third pair of angles must therefore likewise be similar.

Let separate the triangles and find missing angle in triangle with given angles.

CAD = 45°

CDA = 30°

Then, CAD+CDA+ACD = 180°

45°+30°+ACD=180°

ACD=180°-75°

=105°

by applying third angle theorem,

∠CAD=∠DBC=45°

∠ADC=∠BCD=30°

Then, ∠DBC+∠BCD+∠BDC=180°

45°+30°+BCD=180°

BCD=180°-75°

=105°

Hence, The value of the angle m∠BDC is 105°.

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please help i have to make a discussion topic doesn’t have to be long just simple but still answering the question

Answers

You would add 5x + 2x = 7x

Substitute 5 for x and that = 5(5)= 35 +2(5)= 10= 45

and do it for 7(5)= 35-1 = 34 too

You can't make them equal

Following the pattern in (5)(3)+(2)(3) = (5+2)(3), we could do the same thing with 5x+2x = (5+2)x. We're basically un-distributing the common factor from each term.

And now with (5+2)x, we can add the 5 and 2 to get 7x.

If we substitute different values into 5x+2x, it works out to add up to 7 times that same substituted value. For example:

(5)(9)+(2)(9)=45+18=63

(7)(9)=63

If we substitute 9 into 7x-1, then we end up with 63-1 = 62.

In fact, any number we put into 5x+2x will always be one more than 7x-1. So, no, there doesn't seem to be any value of x that would make these equal. Since 5x+2x=7x, then 7x-1 will always be one less than 7x.

The length of a rectangle is 15 cm. What width will make the area at least 315 cm^2

Answers

Answer:

At least 16 cm

Step-by-step explanation:

315cm/15 = 16cm

HURRY!!! Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

Y=-1/4x-6 that's the answer, you're welcome

A line has a slope 1/4 and passes through the point (1,1)

By substituting into the equation, y=mx+b, find the value of b for this line

Answers

Answer: b= 3/4

Step-by-step explanation:

y=1/4x+b

1=1/4(1)+b

1/4-1/4+b=1-1/4

b=3/4

. if you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?

Answers

to measure exactly 4 quarts well first fill the 3 quart pail 2 times and pour it into the 5 quart pail and remaining answer is below.

What size is a quart?

1 US liquid quart is the same as 2 pints, 4 cups, and 32 ounces in terms of volume. It's vital to remember that a dry quart equals 4.6546 cups when converting any dry component.

Is a quart basically a liter?

A liter contains 1.057 quarts, and a quart contains 0.946 liters. This is what? Because the measurements are so similar, you can treat liters and quarts the same for many conversions.

As we an infinite supply of water and a 5 quart and 3 quart pail, and we have to measure exactly 4 quarts

so, first we'll first fill the 3 quart pail and pour it into the pail of 5 quart.

now we'll again fill the 3 quart pail and pour it into the pail of 5 quart

this time the 5 quart pail will be filled before the 3 quart pail get completely empty.

at this time; 3 quart pail is containing the 1 quart in it. now pouring into the 3 quart pail and combining with the 3 quart, it will make 4 quarts after pouring into the 5 quart pail.

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In chemistry class, Charlie records the volume of a liquid as 13.3 milliliters. The true volume is 13.6 milliliters. What is his percent error? Round to the nearest percent

Answers

Percent error;

|Experimental value - actual value| •100/ actual value

0.3/13.6•100= 0.02•100

2%

A rectangular poter ha an area of 504 quare centimeter. The width of the poter 14 centimeter. How long i the poter? Write equation to how your work

Answers

Answer:

36 cm.

Step-by-step explanation:

In the question, we have been given ,

Area of the rectangle=504cm2

The width of the rectangle=14cm

The length of the rectangle=?

The formula for the area of the area of the rectangle is L×B. Thus A=L×B(W).

So 504cm2= L×14.

Now divide both sides by 14

504cm2/14=14L/14

Therefore L= 36cm

Two trains, Train A and Train B, weight a total of 301 tons. Train A is heavier than Train B. The difference of their weights is 217 tons. What is the weight of each train?

Answers

Answer:

Train A = 259

Train B = 42

Step-by-step explanation:

Answer:

Train A's weight is 259 tons

Train B's weight is 42 tons

Step-by-step explanation:

Let x represent train A's weight, and y represent train B's weight.

Since they both weigh 301 tons

The equation is: x+y = 301

The difference in their weight is 210, and train A is heavier

So equation is: x - y = 217

x+ y =301

x- y = 217

2x = 518

x = 259 tons

Now find train B

301 - 259 = 42 tons

Workers are loading boxes onto a truck. So far, they have loaded 48 boxes onto the truck. According to their inventory, they still need to load 96% of the boxes on the truck. What is the total number of boxes the workers are loading on the truck?

Answers

The total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.

What is percentage of a number?

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

Workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck.

According to their inventory, they still need to load 96% of boxes on the truck. There must be 100% box at the start of the loading. Thus, the percentage of boxes they have load,

p=100-96 = 4%

Thus the percentage of boxes they have load in the truck is 4%. This is equal to the 48 boxes they have loaded.

Let suppose there is x number of total boxes. Thus the 4 percent of x will be equal to the 48.

(4/100)x=48

x = 4800/4 = 1200

Thus, the total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.

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How can you show that these two circles are similar?

Answers

well, similarity on circles is a phony business

in essence, all circles are similar by definition, I mean, hell they're all circular, what's so unsimilar about that?

however, the silly proof asks to translate it about and then dilate it to be superimposed on the other.

Which of the following is equal to the square root of the cube root of 6? (4 points)

A. 6 to the power of one sixth

B. 6 to the power of one third

C. 6 to the power of two thirds

D. 6 to the power of three halves

Answers

Answer:

A. 6 to the power of one sixth

Step-by-step explanation:

To find the square root of the cube root of 6, you need to first find the cube root of 6, which is equal to 2. Then, you need to take the square root of 2, which is equal to 1.4142135623730951. Therefore, the square root of the cube root of 6 is equal to 1.4142135623730951.

To express this value using exponents, you can use the property that the square root of x is equal to x to the power of one half. Therefore, the square root of the cube root of 6 is equal to 6 to the power of one half of one third, which simplifies to 6 to the power of one sixth.

One weekend, a shop had 850 customers. 375 were men and the rest were women. What is the ratio of men to women customers in its simplest form?.

Answers

When there were 375 men and 475 women, the simple ratio of men to women clients was 15/19.

What is ratio?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Here,

Total customers=850

Total number of men=375

Total number of women,

=850-375

=475

The ratio of men to women customers,

=375/475

Divide both terms by the GCF 25,

375 ÷ 25 = 15

475 ÷ 25 = 19

=15/19

The ratio of men to women customers in its simplest form is 15/19 when there were 375 men and 475 women.

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9th grade math need help asp

Answers

Answer:

Step-by-step explanation:

look at where the 2 lines meet and then look at the minutes

Select one of the four properties—commutative, associative, identity, distributive—to explain how you remember the rule for multiplication and division. Then, explain how the rule is similar or different with addition and subtraction.

Answers

Changing the order of the factors does not change the product, according to the commutative property of multiplication.

What is cumulative property?

Changing the order of the factors does not change the product, according to the commutative property of multiplication. Here's an illustration: 4 × 3 = 3 × 4 4 x 3 = 3 x 4, or 4 x 3 = 3 x 4.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

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Help pls high points given

Answers

The answer is (- 9,3)

On Wednesday 28% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought gas. How many of these 300 customers made additional purchases?

Answers

Answer:70 i think srry if its wrong

Step-by-step explanation:

In this triangle, what is the value of x?

Answers

Answer: 4.46cm

Step-by-step explanation:

Use [SOH CAH TOA]

We have two sides that are labeled. Use 85cm and x.

Using the angle 63 degrees would mean you are using SOH.

SOH = Opposite/Hypotenuse.

If the above is true, then: Sin63 = x/85

Since we don't know what x is, you want to move 85 to the other side.

85(Sin63) = x

Now, you can find x. Multiply 85 and Sin63. Your answer should be 4.46 (if rounded to 2 decimals).

Suzanne has 12 jars of beads. some of her jars have 15 beads, and the others have 9 beads. she has 126 beads in all. How many of her jars have 9 beads?

A 3 jars
B 6 jars
C 9 jars

Answers

The number of Suzanne jars that have 9 beads is 9.

How to find the number of jars that have 9 beads?

Suzanne has 12 jars of beads. some of her jars have 15 beads, and the others have 9 beads. she has 126 beads in all.

The number of jars that have 9 beads can be calculated as follows:

let

the number of jars that have 15 beads = x

the number of jars that have 9 beads = y

Hence,

x + y = 12

15x + 9y = 126

multiply equation(i) by 15

15x + 15y = 180

15x + 9y = 126

subtract equation(i) from equation(ii)

6y = 54

divide both sides by 6

y = 54 / 6

y = 9

Therefore,

jars with 9 beads = 9

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What is the result of subtracting the second equation from the first? \begin{aligned} 8x-4y &= -4 \\\\ -3x+4y &= 5 \end{aligned} 8x−4y −3x+4y =−4 =5

Answers

The resulting equation after the equations are subtracted is 11x - 8y = -9

How to determine the resulting equation after the subtraction?

From the question, we have the following parameters that can be used in our computation:

8x-4y &= -4 \\\\ -3x+4y &= 5

Rewrite these equations properly

So, we have the following representations

8x-4y = -4

-3x+4y = 5

When the second equation is subtracted from the first, we have the following representation

8x + 3x - 4y - 4y = -4 - 5

Evaluate the like terms

So, we have

11x - 8y = -9

Hence. the solution is 11x - 8y = -9

Answers

The point is NOT to fix the system. There was just one equation that produced an identity. The right answer option 3

Equation: What is it?

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

X = 6 and Y = -8 are the points in BEN'S WORK SHOWN's 2x + y = 4 equation, and after solving it, we have the verification.

However, for x + 3y = -20, the points x = 6 and y = -8 are not solved, and since points here only fulfill one equation,

The point is NOT a solution to the system. Only one of the equations resulted in an identity.

if both the solution would have been then we can say that point is a solution to the system. but this is not true as one equation is not satisfy

The point is NOT a solution to the system. Both equations resulted in identities. this is also not true as one is identities not both.

The point IS a solution to the system. Both equations resulted in identities. this is also not true as both are not identities as only one is identities.

Thus option 3 is correct

The point is NOT a solution to the system. Only one of the equations resulted in an identity.

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Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3 : 7

Imran then gives 3/5 of his share of the money to Bhavin.

What percentage of the 6000 rupees does Bhavin now have?
Give your answer correct to the nearest whole number.

Answers

The total amount of money owned by Bhavin will be $3100. The percentage of the money will be 51%.

What are ratios and proportions?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3: 7 Imran then gives 3/5 of his share of the money to Bhavin.

Bhavin's share of the money will be calculated as,

2x + 3x +7x = 6000\x = 500

Bhavin's share = 2x = 2 x 500 = $1000

Imran's share = 7x = 7 x 500 = $3500

Bhavin's total after = 1000 + (3500 x 3 / 5)

Bhavin's total after = 1000 + 2100 = $3100

The percentage of the money,

Percentage = 3100 / 6000 = 51%

Therefore, the total amount of money owned by Bhavin will be $3100. The percentage of the money will be 51%.

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Find the length of AB.
8 m
80°
AB =[? ]m
Round your answer to the nearest hundredth.

Answers

Answer:11.17

Step-by-step explanation:

pi x D x angle /360

pi x 8x2x80/360

=11.170

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