Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon.
Answers
The width of the canyon is 315 ft.
What is an isosceles triangle?An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Given that, Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon. (please refer to the figure attached)
m ∠ ABC = 180°-80° (Linear pair)
m ∠ ABC = 100°
In Δ ABC,
∠ A + ∠ B + ∠ C = 180° (sum of interior angles of a triangle)
∠ A = 180°-(100°+40°)
∠ A = 40°
Since, ∠ A = 40° and ∠ C = 40°
Therefore, ∠ A = ∠ C
Therefore, AB = BC (Side opposite to equal angles are equal)
That means, Δ ABC is an isosceles triangle
∵ BC = 315 ft
∴ AB = 315 ft
AB is the width of the canyon.
Hence, The width of the canyon is 315 ft.
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Related Questions
Fina wants to use substitution to solve the system of equations. explain what she needs to do before using substitution. then solve the system of equations:
2x - y = 3
-1.5x + 3y = -18
Answers
To solve the system of equations using substitution, Fina needs to isolate one variable and substitute it into the other equation. The solution to the system of equations is x = -3 and y = -9.
Explanation:To solve this system of equations using substitution, Fina needs to isolate one variable in one of the equations and then substitute that expression into the other equation.
Here are the steps:
Choose one equation and isolate one variable. Let's isolate x in the first equation: 2x - y = 3. Add y to both sides: 2x = y + 3 and divide by 2: x = (y + 3)/2.
Substitute the expression for x in the other equation. Replace x in the second equation with (y + 3)/2: -1.5((y + 3)/2) + 3y = -18.
Solve the equation for y. Simplify the equation: -1.5y - 4.5 + 3y = -18. Combine like terms: 1.5y - 4.5 = -18. Add 4.5 to both sides: 1.5y = -13.5. Divide by 1.5: y = -9.
Substitute the value of y back into the expression for x to find its value. Replace y in x = (y + 3)/2 with -9: x = (-9 + 3)/2 = -6/2 = -3.
Therefore, the solution to the system of equations is x = -3 and y = -9.
What is the solution to the following system of equations?
y = x^2+ 10x + 11
y = x^2+ x-7
O(-2,-5)
O (2,-5)
• (-2,5)
O (2,5)
Answers
Answer:
(—2,—5)
SOLUTION:Step-by-step explanation:
y = x² + 10x + 11 ..........(i)y = x² + x — 7 .................(ii)x² +10x + 11 = x² + x —7x² cancels ///
10x + 11 = x —710x —x = —7—11
9x = —18 // divide through by 9//
x = —2 .
y = x² + 10x +11y = (—2)² + 10(—2) + 11 =>y = 4 —20 + 11
y = —5Consider the following expression and determine which statements are true.
Answers
Option A: The entire expression is a sum,
Option C: The term [tex]\frac{7}{r}[/tex] is a quotient are true statements.
Solution:
Given expression:
[tex]$\frac{7}{r}+2^{3}+\frac{s}{3}+11[/tex]
To determine which statements are true:
Option A: The entire expression is a sum.
In the given expression all are addition.
So, it is true.
Option B: The coefficient of s is 3.
No, 3 is in the denominator of s.
The coefficient of s is [tex]\frac{1}{3}[/tex].
So, the given statement is false.
Option C: The term [tex]\frac{7}{r}[/tex] is a quotient.
Yes, 7 is the dividend, r is the divisor and [tex]\frac{7}{r}[/tex] is a quotient.
So, it is true.
Option D: The term [tex]2^3[/tex] has a variable.
No, there is no variable in the term [tex]2^3[/tex].
So, it is false.
Hence Option A: The entire expression is a sum,
Option C: The term [tex]\frac{7}{r}[/tex] is a quotient are true statements.
Answer: A, C,
A: The entire expression is a sum
C: The term 7/r is a quotient
Step-by-step explanation:
The entire expression is a sum
A Sun is the result of an addition problem
The espression 7/r + [tex]2^{3}[/tex] + s/3 + 11 4 terms that we add together.
The statement "The entire expression is sum" it true
The cofficience of s is 3
A coefficient is a number used to multiply a variable.
In the expresion s/3, s is being divided by 3, or more multiplied by 1/3, not multiplied by 3.
The statement " coefficient of s is 3" is nor true
The term 7/r is a quotient.
A quotient is the result of a division problem.
the expression " The term 7/r represent 7 divided by r.
The statement "the term7/r is a quotient " is a quotient" is true.
The tern [tex]2^{3}[/tex] has a varieavle.
Avariable is a letter that stands for an uknown quatity.
There are no letters in the expresion [tex]2^{3}[/tex]
The statement "The term [tex]2^{3}[/tex] has a varieble" is Not true.
The following statements are true
The entire expression is a sum.The term 7/r is a quoatient.How do you express eight less than a number squared?
Answers
Answer:
we can express its easy like square of 2 is 4 then it 8 less than
RSM HW HELP!!! PLEASE HELP ME ASAP!!!! I WILL GIVE BRAINLIEST IF YOU SOLVE THEM ALL CORRECTLY!!! THANKS!
Find the numerical values of the following expressions:
a) | 3 | a | +5 | b | if a=−2; b=−1
b) |2x−3y| if x=0.5; y=−0.7
c)| 4 | a | +8−a | if a=−2
d) |−3 | x | +2x−1 | if x=−5
Answers
b)
|2x−3y| if x=0.5; y=−0.7
Substitute: |2(0.5)-3(-0.7)|
Simplify: |1+2.1|
Simplify: |3.1|
Since it is an absolute value, it will always be positive: 3.1
d)
|−3 |x| +2x−1| if x=−5
Substitute: |-3(|-5|)+2(-5)-1|
Absolute value is positive: |-3(5)+5(-5)-1|
Simplify: |-15-25-1|
Simplify: |-41|
Absolute value always positive: 41
Answer for the first question:
[tex]a)3a+5b~,when~a=-2;b=-1[/tex]
[tex]=(3)(-2)+(5)(-1)[/tex]
[tex]=-11[/tex]
Answer for the second question:
[tex]b)2x-3y~,when~x=0.5;y=-0.7[/tex]
[tex]=(2)(0.5)-(3)(-0.7)[/tex]
[tex]=3.1[/tex]
Answer for the third question:
[tex]c)4a+8-a,~when~a=-2[/tex]
[tex]=(4)(-2)+8-(-2)[/tex]
[tex]=2[/tex]
Answer for the fourth question:
[tex]d)-3x+2x-1,~when~x=-5[/tex]
[tex]=(-3)(-5)+(2)(-5)-1[/tex]
[tex]=4[/tex]
y-2x=4
2x+3y=28
solve for x and y
Answers
Answer:
x=2, y=8. (2, 8).
Step-by-step explanation:
y-2x=4
2x+3y=28
----------------
y=2x+4
2x+3(2x+4)=28
2x+6x+12=28
8x+12=28
8x=28-12
8x=16
x=16/8
x=2
y-2(2)=4
y-4=4
y=4+4
y=8
Johnny has an average of an 88% on all his algebra exams
Answers
Zach has 53 flowers to plant.he wants to plant them in groups of 10s and 1 .zach can plant 10 flowers in each flower box. He can plant 1 flower in each pot. How many different ways can zach plant flowers in boxes and pots
Answers
Answer: He can also plant 26 flowers in each pot
Step-by-step explanation:
How to make improper fraction to mixed number
Answers
Number 2, write down the whole number answer
Finally, write down the remainders in the numerator spot.
81 is 18% of what number?
Answers
Answer:
n = 450
Step-by-step explanation:
18%·n = 81
18·n/100 = 81
18n = 8100
n = 8100 : 18
n = 450
Answer:
81 is 18% of 450.
Step-by-step explanation:
81 ÷ 18 = 4.5
4.5 x 100 = 450
450 - 18% = 369
450 - 369 = 81
So, 18% of 450 is 81 and 81 is 18% of 450.
there are 56 fish in a tank and each fish is yellow blue or black.
There are six more yellow fish than blue fish, and 4 fewer blackfish than blue fish.
How many blue fish are in the tank.
A) 18
B) 22
C) 20
D) 27
Answers
Answer:
c?
Step-by-step explanation:
To find the number of blue fish, we set up an equation based on the given information, solving which indicates there are 18 blue fish in the tank (option A).
Explanation:The question is a word problem asking to find out the number of blue fish in a tank given the total number of fish and the relationships between the counts of different colored fish. We can set up algebraic expressions to solve for the number of blue fish. Let the number of blue fish be represented by x. According to the problem, there are six more yellow fish than blue, which we can express as x + 6. There are four fewer black fish than blue, which we can say is x - 4. The total number of fish is given as 56.
So, the equation we can set up is:
x + (x + 6) + (x - 4) = 56
Simplifying the equation, we get:
3x + 2 = 56
Solving for x, we subtract 2 from both sides to get:
3x = 54
And then divide by 3:
x = 18
Thus, there are 18 blue fish in the tank, which corresponds to option A.
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What it’s 3 to the power of 4 equal
Answers
Answer:
81
Step-by-step explanation:
3*3*3*3= 81
Please help! I am so desperate and I need this to pass my Algebra 1 class....
Answers
Answer: [tex]average\ rate\ of\ change\approx-3[/tex]
Step-by-step explanation:
For this exercise you need to use the following formula:
[tex]average\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
You need to find the average rate of change of the given function g(x) over the following interval:
[tex][-1,2][/tex]
So, you can see in the table that the point whose x-coordinate is -1, is:
[tex](-1,5)[/tex]
And the point whose x-coordinate is 2, is:
[tex](2,-3)[/tex]
Knowing this, let be:
[tex]a=-1\\f(a)=5\\\\b=2\\f(b)=-3[/tex]
Now you can substitute values into the formula:
[tex]average\ rate\ of\ change=\frac{-3-5}{2-(-1)}[/tex]
Finally, evaluating, you get that the average rate of change over the interval indicated in the exercise, is:
[tex]average\ rate\ of\ change=\frac{-8}{3}\\\\average\ rate\ of\ change=-2.66\\\\average\ rate\ of\ change\approx-3[/tex]
Simplify the expression. 7y+3x+3-2y+6
What is the coefficient of y
What is the constant
Answers
Answer:
the coefficient of y is 5 the constant is 9
Step-by-step explanation:
7y minus 2y is 5y. so the coefficient is 5
3+6 is 9 the contant is 9
How do you do 83 divided by 3 with long division
Answers
Answer:83÷3=27.6 or 27.667
Step-by-step explanation:
The number 83 divided by 3 equals 27 remainder 2.
How to solve 83 divided by 3 using long division?The long division refers to the mathematical method for dividing large numbers into multiple smaller groups or parts. The number which we divide into small groups is called the dividend, the number by which we divide is called the divisor.
27
-------------
3 | 83
- 81
-----
20
- 18
-----
20
- 18
-----
2
Therefore, the number 83 divided by 3 equals 27 remainder 2.
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. The owner of a movie theater was counting the
money from I day's ticket sales, He knew that a total
of 150 tickets were sold. Adult tickets cost $7.50
each and children's tickets cost $4.75 each. If the
total receipts for the day were $891.25, how many of
each kind of ticket were sold? PLS HELP
Answers
Answer:
35
Step-by-step explanation:
A garden table and a bench cost $1049 combined. The garden table cost $99 more than the bench. What is the cost of the bench?
Answers
Answer:
475
Step-by-step explanation:
To find the cost of the bench, subtract 99 from 1049, then divide by 2. Add 99 to the answer(475) to get the cost of the garden table(574).
Solve for m:
2/5=2m+11/8
Enter your answer as a fraction, like this: 42/53
Answers
Answer:
[tex]m=-\frac{39}{80}[/tex]
Step-by-step explanation:
we have
[tex]\frac{2}{5}=2m+\frac{11}{8}[/tex]
Solve for m
That means ----> Isolate the variable m
Multiply both sides by 40 to remove the fractions
Note: 40=(8)(5)
[tex](40)\frac{2}{5}=(40)2m+(40)\frac{11}{8}[/tex]
[tex]16=80m+55[/tex]
subtract 55 both sides
[tex]16-55=80m\\-39=80m[/tex]
Divided by 80 both sides
[tex]m=-\frac{39}{80}[/tex]
can someone please help me with this? Thank you
Answers
Answer:
h= -14
Step-by-step explanation:
pretend there is a 1 in front of the h making it -1h and divide it by 14(ignoring the h), making the 14 a negative
Answer: it is -14 instead of regular 14, because a positive and a negative make a negative. A negative negative make a positive, and so on.
Step-by-step explanation:
Hope this helps, plz mark brainliest
which value of x is the equation 3(x + 2) + x = 2x + 16 true?
Answers
Answer:
x=5
Step-by-step explanation:
we have
[tex]3(x+2)+x=2x+16[/tex]
Solve for x
Distribute left side
[tex]3x+6+x=2x+16[/tex]
Combine like terms left side
[tex]4x+6=2x+16[/tex]
Group terms that contain the same variable
[tex]4x-2x=16-6\\2x=10\\x=5[/tex]
therefore
For x=5
The equation is true
Verify
substitute the value of x=5 in the original expression and evaluate
[tex]3(5+2)+5=2(5)+16[/tex]
[tex]3(7)+5=10+16[/tex]
[tex]26=26[/tex] ----> is true
BRAINLEST! please help
Identify the formula for finding the nth term of an arithmetic sequence, where A(n) is the nth term of an arithmetic sequence, a is the first term,n is the term number and d is the common difference.
Answers
Option D: A(n) = a + (n – 1) d
Solution:
To identify the formula for finding the nth term of an arithmetic sequence.
Let a be the first term.
d be the common difference of the each term.
n be the term of the number.
A(n) be the nth term of the arithmetic sequence.
Arithmetic formula:
A(n) = a + (n – 1) d
Example: 1, 4, 7, 10, 13, 16, 19, ...
This is a arithmetic sequence.
a = 1, d = 4 – 1 = 3.
To find the 5th term:
Substitute this in the above formula, we get
A(n) = a + (n – 1) d
A(5) = 1 + (5 – 1) 3
= 1 + 4(3)
= 1 + 12
A(5) = 13
In the given sequence 5th term is 13.
Hence Option D is the correct answer.
A(n) = a + (n – 1) d
Answer:
A(n) = a + (n - 1)d
Step-by-step explanation:
got it right on quiz
A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day. Another day she sold 16 ribeye steak dinners and 6 grilled salmon dinners, totaling $584.46. How much did each type of dinner cost?
Answers
The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20
Solution:
Let "a" be the cost of each ribeye steak dinners
Let "b" be the cost of each grilled salmon dinners
A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day
Thus we frame a equation as:
11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63
[tex]11 \times a + 12 \times b = 560.63[/tex]
11a + 12b = 560.63 -------- eqn 1
Another day she sold 16 ribeye steak dinners and 6 grilled salmon dinners, totaling $584.46
Thus we frame a equation as:
16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46
[tex]16 \times a + 6 \times b = 584.46[/tex]
16a + 6b = 584.46 ------------ eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 2 by 2
32a + 12b = 1168.92 ------- eqn 3
Subtract eqn 1 from eqn 3
32a + 12b = 1168.92
11a + 12b = 560.63
( - ) ----------------
21a = 1168.92 - 560.63
21a = 608.29
Divide both sides by 21
[tex]a = 28.96 \approx 29[/tex]
Substitute a = 29 in eqn 1
11(29) + 12b = 560.63
319 + 12b = 560.63
12b = 560.63 - 319
12b = 214.63
Divide both sides by 12
[tex]b = 20.13 \approx 20[/tex]
Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20
Function S
x y
–2 –9
0 1
4 21
6 31
The graph models function R. The table of values models function S. Which statement is true about these functions?
A) The two functions have the same rate of change.
B) Both functions do not have a constant rate of change.
C) Function R has a greater rate of change than Function S.
D) Function S has a greater rate of change than Function R.
Answers
The answer is D, I know this because I just did the USATESTPREP
Step-by-step explanation:
The redwood national park is home to some of the largest trees in the world. Hyperion is the tallest tree in the park, with a height of approximately 379 feet. Tom wants to find the height of the tree in yards
Answers
Final answer:
To find the height of the tree in yards, divide the height in feet by 3, the conversion factor from feet to yards.
Explanation:
The Redwood National Park is home to some of the largest trees in the world, including Hyperion, the tallest tree in the park at approximately 379 feet. To find the height of the tree in yards, we can convert the height from feet to yards by using the conversion factor of 1 yard = 3 feet.
Height in yards = Height in feet / Conversion factor
Height in yards = 379 feet / 3 feet/yard
Height in yards = 126.33 yards
Therefore, the height of Hyperion is approximately 126.33 yards.
Last week katlin drove 254 miles. This week she drove c miles. Using c,write an expression for the total number of miles she drove in two weeks
Answers
The expression for the total number of miles she drove in two weeks is 254 + c miles
Solution:
Given that,
Last week katlin drove 254 miles
This week she drove c miles
To find: Expression for the total number of miles she drove in two weeks
From given,
Last week = 254 miles
This week = c miles
Therefore,
Total miles in two weeks = last week + this week
Total miles in two weeks = 254 + c
Thus the expression for the total number of miles she drove in two weeks is 254 + c miles
Solve for x. -x = -5 5/7
Answers
Answer:
40/7
Step-by-step explanation:
-5 5/7=-40/7
-x=-40/7
x=40/7
I need help with this I don't understand this
Answers
Answer:
45.8
Step-by-step explanation:
We need to find the surface area for this entire figure!
We can see that this is a pyramid here - we must find the area of the 3 triangles and the base triangle at the bottom.
The 3 triangles building up the pyramid are all equal to each other.
To find the area of a triangle, use [tex]Area = base*height/2[/tex]
[tex]Area=3(\frac{5*7}{3} )+(\frac{5*4.3}{2})\\Area=35+10.75=45.75[/tex]
Round to the nearest tenth: 45.75 -> 45.8
please answer this answer correctly if u answer this question correctly then i will mark u as brain list.
Answers
Answer:
12 is your answer.I did that and i got it right.
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
since there are 3 different colour hats
4 different colour scarves and
5 different colour jacket
1 hat can be selected in 3 ways
1 scarf can be selected in 4 ways
1 jacket can be selected in 5 ways
Therefore , Tina will have 3 x 4 x 5 different combinations.
This means she will have 60 different combinations
Please help me!
Simplify the expression (x+3)2−4(x+3).
Answers
Answer:
-6-2x
Step-by-step explanation:
Expand:
(x+3)2 = 2x+6
-4(x+3) = -4x-12
2x+6-4x-12 = -6-2x
5. In Jaden's town, the middle school has 443 more students than
the high school. If the middle school has 817 students, how
many students are at the high school?