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.
Answers
Answer:
Step-by-step explanation:
To estimate the distance across the gorge, Jamal can use the following steps:
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.
Related Questions
The rate of change is how a quantity is changing with respect to a change in another quantity.
True false question.
True
False
Answers
Answer: True
Step-by-step explanation:
The rate of change or the slope is the changes to another quantity with a constant.
Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.
$64.00 + x = $67.36
Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36
Answers
Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?
Answers
On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30 =4.8 and Johnny = 2x=34.8
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Take Jolly's expenditure as x.
Jimmy would have spent twice as much as Jolly.
Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.
Total amount spent: $57
Therefore,
[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]
x = 87/5
x= 17.4
Now take is that - X= 17.4.
Jolly is that - x= $17.4
Jimmy is that - =4.8
Johnny is that = =34.8
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The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 40 kilograms. What was the mass of the sixth boy?
Answers
The mass of the sixth boy is 80 kilograms.
What was the mass of the sixth boy?It's important to note that a mean simply means the average of a set of numbers that are given. In this situation, the average mass of 5 boys is 50 kilograms. The total mass will be:
= 50 × 5
= 250 kilograms
In this case, when another boy’s mass is added and the average goes to 55 kilograms. The total mass will be:
= 55 × 6
= 330 kilograms.
The average mass of the last boy will be:
= 330 - 250
= 80 kilograms
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Complete questions
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 55 kilograms. What was the mass of the sixth boy?
Are any of these numbers linear expressions? 5x+3, 8xy, 14, or 3x^2
Answers
Answer: 5x+3 is a linear expression
Step-by-step explanation:
The linear expression is y=mx+b
5x +3 has a slope and y-intercept, so it is a linear expression!
8xy is not because it is just a variable
3x^2 is not because it has ^2
three solutions of the equation y= -2x
Answers
Answer:
three solutions of the equation:
y = -2x - 1
=>
1) (0, -1)
2) (1, -3)
3) ( -1, 1)
Step-by-step explanation:
At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
40 people
Step-by-step explanation:
25% = 10
50% = 20
100% = 40
Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
Answers
The solution for the system of equations is the point (3, 5), and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the following system of equations:
5x + 3y = 30
-5x - 2y = -25
Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:
(5x + 3y) + (-5x - 2y) = 30 - 25
(5x - 5x) + (3y - 2y) = 5
0 + y = 5
y = 5
So we found the value of y, by evaluating the second linear equation in y = 5 we will get:
-5*x - 2*5 = - 25
-5x = -25 + 2*5
-5x = -25 + 10
-5x = -15
x = -15/-5 = 3
So y = 5 and x = 3, the difference x - y gives:
3 - 5 = -2
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The square root of (-2x)^2 for which values of x does the expression makes sense?
Answers
Answer: [tex]x\leq 0[/tex]
Step-by-step explanation:
The first thing we need to do is to make the argument or the number inside the square root equal or larger than zero:
-2x ≥ 0
x ≤ 0/-2
x ≤ 0
So the given expression only makes sense for x that is less than or equal to zero.
Show the work please! Thanks!!
Answers
Simplifying
2x + 5y = 2
Solving
2x + 5y = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5y' to each side of the equation.
2x + 5y + -5y = 2 + -5y
Combine like terms: 5y + -5y = 0
2x + 0 = 2 + -5y
2x = 2 + -5y
Divide each side by '2'.
x = 1 + -2.5y
Simplifying
x = 1 + -2.5y
Simplifying
5X + 10y = 17
Solving
5X + 10y = 17
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-10y' to each side of the equation.
5X + 10y + -10y = 17 + -10y
Combine like terms: 10y + -10y = 0
5X + 0 = 17 + -10y
5X = 17 + -10y
Divide each side by '5'.
X = 3.4 + -2y
Simplifying
X = 3.4 + -2y
Ahmad jogged a distance of 3200 m on Saturday and a distance of 1.8 km on Sunday.
(a) Express the distance he jogged on Saturday as a percentage of the total distance jogged on both days.
(b) Find the percentage decrease in the distance he jogged from Saturday to
Sunday.
Answers
Answer:
a) 4,000 meters
b) - 56.25% (or -56% with 2 sig figs
Step-by-step explanation:
Calculate the total distance Ahmad jogged on both days. This will require a conversion unit to make the distances the same units.
Sat.: 3200 m
Sun: 1.8 km
(1,000m/km)
(1.8km)*(1,000 m/km) = 1,800 m jogged on Sunday
Total distance jogged = 3,200 m + 1,800 m = 4,000 meters total jogged
a) Percentage jogged on Saturday:
(3,200 m)/(4,000 m) = 0.80 or 80%
b) Percentage Decrease (From Saturday to Sunday):
Sat: 3200 m
Sun: 1800 m
Difference = 1400 m (decrease)
Percentage Decrease = (1800/3200) = 56.25%
Ahmad's distance on Sunday was a 56.25% decrease from Saturday.
A large pizza at palanzio pizzeria cot $6. 80 plu $. 90 for each topping. The cot of a large pizza at guido' pizza i $7. 30 plu $. 65 for eachtopping. How many topping need ti be added ti a large pizza from palanziod pizzeria and guido' pizza in order for the pizza to cot the ane not including tax
Answers
2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Let x be the number of toppings to be added to each pizza and y be the total cost of pizza.
A large pizza at Palanxio's Pizzeria cot $6. 80 plu $. 90 for each topping.
So, we get an equation,
y = 6.80 + 0.90x
The cot of a large pizza at Guido's Pizza i $7. 30 plu $. 65 for eachtopping.
So, we get an equation,
y = 7.30 + 0.65x
We need to find the number of toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Now let's equate the costs of both pizzas and solve for x.
6.80 + 0.90x = 7.30 + 0.65x
0.25x = 0.50
x = 2
Therefore, 2 toppings to be added to each pizza
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when $n$ is divided by $8$, the result is greater than $5$. what is the least possible integer value of $n$?
Answers
when N is divided by 8, the result is greater than 5 the least possible integer value of N is 48.
Zero, a positive natural number, or a negative integer with a minus sign are all examples of integers. The additive inverses of the positive numbers are the negative numbers. The boldface Z is frequently used in mathematics to denote the set of integers.
Positive integers: If a number is greater than zero, it is positive. Example: 1, 2, 3 . . .Negative integers: If a number is less than zero, it is negative. Example: -1, -2, -3 . . .Zero cannot be thought of as either a negative or a positive integer. It's an entire number.the least possible integer greater than 5 is 6,
and when 6 × 8 = 48 thus,
the least possible integer value of N is 48.
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choose the best graph to match the given expression.
F(x)= [x+1]
Answers
Answer:
Step-by-step explanation:
I don't see a graph from which to choose. Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?
The graph of functions
(F(x) = (x+1), and
(F(x) = |x+1| are both attached.
Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1).
1. 1/3
2. 1
3. 2
4. 4/3
Answers
Answer:
4. 4/3
Step-by-step explanation:
(-2, -3) (1,1)
1+3/1+2=
4/3
1/2 - 1/7 =
3/5 - 1/2
Answers
Answer:
1/2 - 1/7 = 5/14
3/5 - 1/2 = 1/10
Step-by-step explanation:
Jaylen bought 5 pounds of apples for 12.99 and 4 cupcakes for 2.99 each. He went to the store with $48. How much did Jaylen have left after his shopping trip?
23.05
37.94
10.06
24.95
Answers
Answer:
$24.95
Step-by-step explanation:
2.99 times 4 is 11.96, and you would add that with 12.99 to get 24.95.
Answer:
Jaylen have left 23.05 $
Step-by-step explanation:
5 pounds of apples = 12.99 $
4 cupcakes = 2.99 $/apple
Total money = 48 $
All the cupcakes costs = 4*2.99 = 11.96 $
Then she bought in total:
48 -(12.99 + 11.96)
48 - 24.95 = 23.05
Which equation represents how to determine the speed of an object?
Answers
The equation that the speed of an object is speed = distance/time
How to determine the equation of an objectFrom the question, we have the following parameters that can be used in our computation:
Parameter = Object
Argument = Speed
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
Hence, the equation is Speed = Distance/Time
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Algebraic fractions which option is correct
Answers
Answer:
A
Step-by-step explanation:
because to solve this question the division would change into multiplication and the second fraction would be converted upside down
Write a rule for the n th term of the sequence. Then find a_{20}
$51,48,45,42,...$
Answers
The rule for the nth term of arithmetic sequence is a + (n - 1)d.
What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.Here also,
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
Here first term (a1) = 51
common difference (d) = a2 - a1
= 48 - 51
= -3
We have to find 20th term,
a[20] = a1 + (20 - 1) d
= 51 + 19 x -3
= 51 - 57
= - 6
Therefore 20th term of the sequence 51,48,45,42,... is -6.
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Danny opened a savings account and deposited $100.00. The account earns 2% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how
much will he be able to spend on the bike?
nt
P(1 + 1)^²₁. where A is the balance (final amount), P is the principal
Use the formula A = P 1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answers
Answer: f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
time periods are months.
rate is the percent divided by 100.
p = 100
r = 6% per year / 12 = .5% per month / 100 = .005 per month.
n = 2 years * 12 = 24 months.
formula becomes f = 100 * (1 + .005) ^ 24
solve for f to get:
f = 112.7159776 = 112.72
that's how much Danny will be able to spend on the bike in 2 years.
Step-by-step explanation:
. if you start with 1/4, you can create an entire class of fractions equivalent to 1/4 like the one above, by multiplying 1/4 by different forms of what number?
Answers
If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.
What are fractions?The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.
Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.
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Simplify the expression below
7/2h - 3(5h - 1/2)
step by step please
Answers
Answer: [tex]-\frac{23}{2}h+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{7}{2}h-15h+\frac{3}{2}\\\\\frac{7}{2}h-\frac{30}{2}h+\frac{3}{2}\\\\-\frac{23}{2}h+\frac{3}{2}[/tex]
4. The chart below represents the kinematics of a freely falling body.
Time
(seconds t)
Total Distance
meters d (t)
1
5
2
20
45
80
125
3
4
5
a. Is the relationship between time and distance an arithmetic sequence?
Explain.
b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s². Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
Answers
a. The given sequence is not an arithmetic sequence.
b. The distance a falling body covered in t = n seconds of movement is 5n²meters.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
a. A sequence can be said arithmetic sequence if the difference between any two consecutive terms remains the same.
In this case, the difference between 20 and 5 is 15, and the difference between 45 and 20 is 25, this shows that the difference between two consecutive terms is not the same.
Hence, it can be said that the given sequence is not an arithmetic sequence.
b. To evaluate the distance covered by the body in “n” seconds, Substitute t=n in d(t) then d(n) will represent the distance covered by the body in “n” seconds
d(n)=1/2 g(n)²
d(n) = 1/2(10)(n)²
d(n) = 5n²meters
Hence, the distance a falling body covered in t = n seconds of movement is 5n²meters.
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Graph the solution to this inequality on the number line. 1/2x−3<−1 3/8
Answers
The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.
How to Graph the Solution of an Inequality on a Number Line?Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.
1/2x - 3 < -1 3/8 [given]
1/2x - 3 < -11/8
Add 3 to both sides of the equation:
1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]
1/2x < 13/8
Multiply both sides by 2:
1/2x * 2 < 13/8 * 2 [multiplication property of equality]
x < 13/4
The solution to this inequality, x < 13/4 is given in the graph below.
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There are 75 fifth graders and 125 fourth graders. They are going to be grouped in teams for Field Day with the same number of students on each team. If there must be the same number of fifth graders on each team, how many teams can there be at most?
Answers
3 fifth graders each
5 fourth graders each
Answer:25
Step-by-step explanation:
3
5
The angles of a triangle are 44 degrees, 110 degrees, and 26 degrees. Classify the triangle
Answers
The measure of angles form an scalene triangle.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.
We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.
Since we know that angle sum property of a triangle;
44 + 110 + 26
180
Therefore, the measure of angles form an scalene triangle.
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Using the unit circle, on what interval is the cosine function increasing? (0, startfraction pi over 2 endfraction) (0, pi) (startfraction pi over 2 endfraction, startfraction 3 pi over 2 endfraction) (pi, 2 pi)
Answers
The interval where the cosine function is increasing is (π, 2π).
Finding the value of the cosine function in different intervals:The cosine function for the interval (0, π/2) gives
cos(x) = cos(0) = 1
cos(x) = cos(π/2) = 0
So, the value of the function is decreasing in this interval.
Then, for the interval (0, π), it gives
cos(0) = 1; cos(π) = -1
So, the value of the cosine function is decreasing in this interval.
Then, for the interval (π/2, 3π/2), it gives
cos(π/2) = 0
cos(π) = -1
cos(3π/2) = 0
So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).
Then, for the interval (π, 2π), the cosine function gives
cos(π) = -1
cos(2π) = 1
Thus, the cosine function in this interval increase from -1 to 1.
Therefore, in the interval (π, 2π), the cosine function is increasing.
This is explained by using a unit circle below:
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Answer:
D
Step-by-step explanation:
got it right
for every 8chin ups Melanie can do Theresa can do 5. If Melanie did 48 chin ups, how many fewer did Theresa do
Answers
Answer: Theresa did 18 fewer chin-ups.
Step-by-step explanation:
Melanie 8,16,24,32,40,48
Theresa 5,10,15,20,25,30
48-30=18
PLEASE HELP ASAP!!!!!! I WILL GIVE BRAINIEST!!!!! I only need 2 and 3. Please explain your answer so I can understand this!!
Answers
The least expensive per pound is Customer A.
How to illustrate the expression?It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The rate for the first customer will be:
= $14.50 / 1.75
= $8.29 per pound.
The second Customer rate will be:
= $26.25 / 2.5
= $10.5 per pound
The third Customer will be:
= $5.50 / 0.375
= $14.47 per pound.
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