Answers
- Supplementary angles (two angles that form a straight angle when added) add to 180°
- The interior angles of a triangle add to 180°
- Sides opposite congruent angles in a triangle are also congruent
- Alternate interior angles are congruent when formed by a transversal through two parallel lines
With that in mind, let's get to the problem. First, what data have we been given?
Let's drop another point on the ground to the left of point T called S, so we can get all of this data together. We know that:
[tex]AB = 2.4\ mi\\\overrightarrow{ST}||\overrightarrow{AC}\\\angle{ATS}=40\textdegree\\\angle{BTS}=80\textdegree[/tex]
We don't know the measure of ∠ATB, but we do know that it shares the larger angle ∠BTS (which is 80°) with ∠ATS (which is 40°). Since ∠ATB + ∠ATS = ∠BTS, we can clearly see that ∠ATB must also be 40°, so now we have the new data that ∠ATB = 40° to work with.
Next, notice that ∠BTS and ∠CBT are alternate interior angles, and the lines they rest on, [tex]\overrightarrow{ST}[/tex] and [tex]\overrightarrow{AC}[/tex], are parallel. This implies that ∠BTS and ∠CBT are congruent, which makes ∠CBT = 80°.
∠CBT and its neighboring angle ∠ABT, when combined, form a straight angle, making them supplementary to one another. This means that ∠CBT + ∠ABT = 180°, or 80° + ∠ABT = 180°. Subtracting 80° from both sides, we see that ∠ABT = 100°.
We're almost done; we now bring our attention now to the triangle formed by the points ABT. What do we know about this triangle? We're given that one of its sides, AB, is equal to 2.4 mi; most recently, we determined that one of its angles, ∠ABT, was equal to 100°; and even earlier, we found that the second one of its angles, ∠ATB, was equal to 40°. We have two angles and a side, which, as I'm about to demonstrate, is more than enough for our purposes. If we've found the measures of two angles of triangle ABT, we can use the fact that a triangle's interior angles add to 180° to find the third angle, ∠BAT. We have:
∠ABT + ∠BTA + ∠BAT = 180°
Substituting ∠ABT and ∠BTA for the values we found for them:
100° + 40° + ∠BAT = 180°
140° + ∠BAT = 180°
∠BAT = 40°
We now know that ∠BAT and ∠BTA are congruent, which means that the triangle BTA is isoceles. This means that the sides opposite those angles will also be congruent. The side opposite ∠BTA is the line segment AB, which we know to be 2.4 mi, which means the side opposite ∠BAT, BT - the side we've been looking for - must also be 2.4 mi.
Related Questions
I have little tolerance for risk, so I must be willing to accept lower returns on my investment
Answers
The odds against Chip beating his friend in a round of golf are 1 : 5. Find the probability that Chip will beat his friend
Answers
5 (number of times he beats his friend) / 6 (total of the odds: 5+1)
The formula y-y1 = m(x-x1) is the point-slope form of the equation of a lie where m is the slope of the line and (x,y) and (x1,y1)are points of the line. Solve the equation for m, and find slope of a line that includes the points (4,-2) and (5,0)
Answers
m = Y - y1/X - x1
m = -2 - 0/4 - 5
m = -2/-1
m = 2.
The slope of the line is a positive one, where m = 2.
Answer:
m=2
Step-by-step explanation:
Over the last week the daily low temperatures in degrees Fahrenheit have been -4 , 6.2 , 18 1/2 , -5.9 , 21 , -1/4 , And 1.75.list all these numbers in order from greatest to least
Answers
NEED HELP ASAP THANKS
Evan is making a table that will be created in the shape of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint, he needs to know the area of the table top. He can only spend $10 on paint, which is enough to cover 150 ft2 of surface area. What is the maximum length of the base of the rectangle he can build? An image of a compound shape made up of a rectangle and a triangle is shown. The length of the rectangle is labeled x and the width is labeled 6 feet. The base of the triangle is labeled 4 feet and the height is labeled 6 feet.
x = __________________ ft
Numerical Answers Expected! Answer for Blank 1:
Answers
Area of rectangle is : length × width
Area of triangle : 1/2 × base × height
So...
6x + (1/2 × 4 × 6) = 150
6x + 12 = 150
6x = 138
x = 23
The maximum length of the base of the rectangle he can build is 23 feet.
The conservation club has 32 members. There are 18 girls in the club.
What is the ratio of girls to boys in simplest form?
716
916
97
79
Answers
Answer:
9:7
Step-by-step explanation:
i took the test
Steve was offered $5,025 per year for a weekend lifeguard ing job at a local pool. he wants to know how much his monthly income will be at this salary level. what is his rate of pay in dollars per month ?
Answers
The rate of his salary per month is $418.75
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Steve was offered $5,025 per year
We know, 1 year= 12 month
So, Steve's Salary per month would be
= 5025/ 12
= $418.75
Hence, the rate of his salary per month is $418.75
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what is this answer because I don't know how to do it
Answers
13 + 5 = n - 5 + 5
18 = n
Hope this helps!
13 = x - 5
You add 5 to both sides to get x by itself.
18 = x
So now lets check our work by plugging in the variable! :)
13 = 18 - 5
13 = 13
It is a solution so 18 is your answer.
I hope this helps love! :)
A 6-foot-wide hallway is painted as shown, using equal amounts of white and black paint.
a. How long is the hallway?
b. Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint? Explain.
Answers
we know that
The hallway is painted using equal amounts of white and black paint
so
To know the amount of white paint------> calculate the area of white paint
[tex]A=5x*6=30x\ ft^{2}[/tex]
To know the amount of black paint------> calculate the area of black paint
[tex]A=(x+1)*4*6=(24+24x)\ ft^{2}[/tex]
equate the areas
[tex]30x=(24+24x)\\30x-24x=24\\6x=24\\x=4\ ft[/tex]
Find the length of the hallway
[tex]5x+(4x+4)=9x+4=9*4+4=40\ ft[/tex]
therefore
the answer part a) is
The hallway is [tex]40\ ft[/tex] long
Part b) Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint?
we know that
the amount of white paint is [tex]30x\ ft^{2}[/tex]
if the black paint is twice that the white paint
then
amount of black paint is [tex]2*30x=60x\ ft^{2}[/tex]
amount of black paint with the same pattern is [tex](24+24x)\ ft^{2}[/tex]
equate
(24+24x)\ ft^{2}=(60x)\ ft^{2}
solve for the new value of x
[tex]24x+24=60x\\ 60x-24x=24\\ x=24/36\\x= 2/3\ ft[/tex]
Find the new length of the hallway
[tex]5x+(4x+4)=9x+4=9*(2/3)+4=10\ ft[/tex]
therefore
the answer is
Yes, the same hallway can be painted with the same pattern, using twice as much black paint as white paint, but the hallway decreases in length
Answer:
Thank you so much callculista
Step-by-step explanation:
(5 x 8) x (5 x 8) = ___ squared
Answers
40×40
1,600
ron wants to buy a videoo game with a selling price of $48 on sale for 50% off. the sales tax in his state is 4.5% A)how much will ron have to pay in all? B) if he has $25 can he afford to purchase the game?
Answers
Rachel types 162 words in 3 minutes Rachel types at a constant rate how many words does Rachel type per minute
Answers
Answer:
54 words does Rachel type per minute
Step-by-step explanation:
Unit rate defined as the rates are expressed as a quantity as 1 such as 4 meter per seconds or 5 km per hour
As per the statement:
Rachel types 162 words in 3 minutes Rachel types at a constant rate.
We have to find how many words does Rachel type per minute.
By definition of unit rate:
[tex]\text{Unit rate per minute} = \frac{162}{3}[/tex]
Simplify:
[tex]\text{Unit rate per minute} =54[/tex] words
Therefore, 54 words does Rachel type per minute
The number of words typed by Rachael in one minute at a constant rate is 54 words
The parameters given :
Step-by-step explanation:
Number of words typed = 162 words Time taken = 3 minutesSince, the typing rate is constant ; the typing rate per minute can be calculated thus :
(Number of words typed ÷ number of minutes) (162 / 3) = 54 words per minute.Therefore, Rachael types at a constant rate of 54 words per minute.
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If a litre of water is provided for 20 people, how much for 50 people?
Answers
Write two expressions that represent 3/12
Answers
Find 3 consecutive odd integers such that the sum of 7 times the smallest and twice the largest is -91?
Answers
7n+2(n+4)=-91
7n+2n+8=-91
9n=-99
n=-11
so the three odd integers are -11,-9,-7
Answer: -11, -9, -7
the smallest: 2x+1 = -11
Step-by-step explanation:
{z - some integer}
2z+1 - the smallest number
7(2z+1) - seven times the smallest number
2z+1+2=2z+3 - the middle number
2z+3+2 = 2z+5 - the largest number
2(2z+5) - twice the largest number
7(2z+1) + 2(2z+5) - the sum of 7 times the smallest and twice the largest
7(2z+1) + 2(2z+5) = -91
14z + 7 + 4z + 10 = -91
-17 -17
18z = -108
÷18 ÷18
z = -6
2z+1 = 2(-6)+1 = -12 + 1 = -11
2z+3 = 2(-6)+3 = -12 + 3 = -9
2z+5 = 2(-6)+5 = -12 + 5 = -7
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Mt. Everest rises 54768 feet in the air while Mt. Rushmore stretches a mere 8976 feet . What is the difference in the height of these two mountains expressed in scientific Notation?
Answers
In scientific notation, that would be 4.5792 x 10^4
The difference in height between Mt. Everest and Mt. Rushmore is 45,792 feet expressed in standard notation and 4.5792x10^4 feet in scientific notation.
Explanation:
The student is asked to calculate the difference in height between Mt. Everest and Mt. Rushmore and express that difference in scientific notation. The height of Mt. Everest is 54,768 feet and the height of Mt. Rushmore is 8,976 feet. To calculate the difference in height, subtract the height of Mt. Rushmore from the height of Mt. Everest: 54,768 feet - 8,976 feet = 45,792 feet.
To express this difference in scientific notation, move the decimal point to just after the first digit (4), resulting in 4.5792. Then count how many places you moved the decimal. In this case, it moved 4 places, so the exponent is 4. Therefore, the difference in height between Mt. Everest and Mt. Rushmore is approximately 4.5792x10^4 feet in scientific notation.
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An office supply store sells 128 pens in each bag. A business bought 9 bags of pens one month and 7 bags of pens the next month. How many pens total did the business buy?
A. 2,304 pens
B. 2,048 pens
C. 6,712 pens
D. 7,764 pens
Answers
Easiest way to solve this is to add the amount of bags the business bought.
7 + 9 = 16
After you find to total amount of bags bought you multiply the amount of pens in each bag by the total amount of bags the business bought.
16 * 128 = 2048
The business bought a total of 2,048 pens over two months. In the first month, they purchased 1,152 pens, and in the second month, they purchased 896 pens.
Explanation:The problem involves simple multiplication and addition operations. First, we need to find out how many pens the business bought in total for each month. In the first month, the business bought 9 bags of pens, and each bag contains 128 pens. So, we multiply 9 (number of bags) by 128 (number of pens per bag) to get 1,152 pens for the first month.
For the second month, the business bought 7 bags of pens. Again, we multiply 7 (number of bags) by 128 (number of pens per bag) to get 896 pens.
Finally, we add together the totals for the two months: 1,152 pens (for the first month) plus 896 pens (for the second month) gives us a total of 2,048 pens bought by the business over the two months. So, the correct answer is B. 2,048 pens.
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The height of a window is 0.6 feet less than 2.5 times its width. If the height of the window is 4.9 feet, which equation can be used to determine x, the width of the window?
Answers
2.5x - 0.6 = 4.9
Solve -
2.5x -0.6 + 0.6 = 4.9 + 0.6
2.5x = 5.5
2.5x ÷ 2.5 = 5.5 ÷ 2.5
x = 2.2
Answer:
The CORRECT answer is 2.5x - 0.6 = 4.9
how do you find the markuo and markup rate if the price is $49.95 and the cost is 26.97
Answers
49.95 / 26.97
= This equals (1.85205784205) or 185.205784205%
Then subtract by 100
You get = 85.2057%
markup rate = 85 percent
A bakery sells packages of 6 cupcakes for $10. If the bakery starts selling the cupcakes in packages of 12, how much would you expect a package of 12 to cost?
Explain your reasoning.
Answers
the value of 9 in 901,532 is how many times the value of the 9 in 157,900?
Answers
the value of 9 in 157,900 = 900
to find out how many times greater, we must divide
900,000 / 900 = 1000
so it is 1000 times greater <==
Gina works at a diner.She earns 6$ each hour plus tips.In one week,She worksed 37 hours a week and earned 434$ in tips.How much dud she nake altogether? Write an equation.Use a variable for the unknown.Solve
If answer is 86 please say true if not put answer thanks
this is just my sister's homework not mines I'm a sixth grader not a fourth grader.
.3.
Answers
6(x)+434=?
x= number of hours so problem can be rewritten as
6(37)+434
———
222+434=
656
Erica Sutherland earns a yearly salary go 45,650, how much would Erica earn in a monthly paycheck
Answers
divide the yearly pay by 12 ( 12 months in a year)
45650 / 12 = 3804.17 per month
Ryan made 3/4 of a gallon of lemonade. Each glass holds 1/8 of a gallon of lemonade. How many glasses can Ryan fill?
Answers
3/4=6/8
1/8= one glass
So since there is 6/8 of a gallon, there would be 6 glasses.
6 Glasses Ryan can made.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Ryan made 3/4 of a gallon of lemonade.
Each glass holds 1/8 of a gallon of lemonade.
so, the number of glasses of Ryan made
= (3/4)/ (1/8)
= 3/4 x 8
= 3 x 2
= 6
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0.5,1/5,0.35,12/35,4/5 least to greatest
Answers
1/5, 12/25, 0.35, 0.5, 4/5.
0.5, 0.2, 0.35, 0.336, 0.8 and in order it is:
1/5, 12/35, 0.35, 0.5, 4/5
Using the distributive property, an expression equivalent to 48 + 30 is
Answers
Answer: 6(8+5)
By using a distributive property the expression 48 + 30 will be written as 6(8+5).
What is distributive property?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
Given expression of addition is 48 + 30. The expression by using distributive property will be written as:-
E = 48 + 30
Take 6 commons from the above equation.
E = 48 + 30 = 6 ( 8 + 5 )
48 + 30 = 6( 8 + 5 ) ( Distributive property )
Therefore, by using a distributive property the expression 48 + 30 will be written as 6(8+5).
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math help Brainliest will be given I solved RS wrong how do I do it I got 112
Answers
SR+RT = ST
plug in the given expressions to get
(-2x+24)+(4x+10) = 4x+12
Now solve for x
(-2x+24)+(4x+10) = 4x+12
-2x+24+4x+10 = 4x+12
2x+34 = 4x+12
2x+34-2x = 4x+12-2x
34 = 2x+12
34-12 = 2x+12-12
22 = 2x
2x = 22
2x/2 = 22/2
x = 11
If x = 11, then RS is,
RS = -2*x+24
RS = -2*11+24
RS = -22+24
RS = 2
-------------------------------------
-------------------------------------
Answers:
x = 11 and RS = 2
RS and RT are both segments on the same line. Therefore their equation can be added together and set equal to the equation that is given representing the entire length of segment ST.:
4x+10+ -2x+24=4x+12
Now that you have created one larger equation to solve for x you can now go ahead and combine like terms, (all the x's with the x's and the regular numbers with the regular numbers)
2x+34=4x+12
Now you must move the variables and constants to the opposite sides of the equation. This is called isolating the variable:
2x= 22
Now you can solve for x by dividing by 2 and your answer is x = 11
Now that you have solved for the value of x you can take that value and plug it into the equation that is given for the length of segment RS.
-2X+24 NOW BECOMESSS......
-2(11)+24= -22+24= 2
The length of segment RS is 2
The length of segment RT is 54The total length of segment ST is 56
5x - (x-2) > 2x - 4 (x -8)
Answers
5x-x+2>2x-4+36
4x+2>2x+32
2x+2>32
2x>30
x>15
determine whether the ordered pair (8,-5) is a solution to the equation 3x-2y=6
Answers
3(8) -2(-5)= 6
24- (-10) =6
34=6
34=/=6
Since these two are not equal, the ordered pair is not a solution.
Jill says that 6 is a common factor of 56 and 36 is she correct explain
Answers
Wrong : 56
Because : there is no number that 6 can multiply into to get 56.