Answer:
answer = -1
Step-by-step explanation:
6. m A = 8x - 2, m B = 2x - 8, and m2 C = 94 - 4x. List the sides of A ABC in order from shortest to
longest.
AC: AB: BC
AC :BC: AB
AB: AC : BC
BC: AC : AB
Given:
In triangle ABC, m∠A=(8x-2)°, m∠B=(2x-8)° and m∠C=(94-4x)°.
To find:
The sides of the triangle ABC in order from shortest to longest.
Solution:
In triangle ABC,
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex] (Angle sum property)
[tex](8x-2)^\circ+(2x-8)^\circ+(94-4x)^\circ=180^\circ[/tex]
[tex](6x+84)^\circ=180^\circ[/tex]
[tex]6x+84=180[/tex]
[tex]6x=180-84[/tex]
[tex]6x=96[/tex]
Divide both sides by 6.
[tex]x=\dfrac{96}{6}[/tex]
[tex]x=16[/tex]
Now,
[tex]m\angle A=(8(16)-2)^\circ[/tex]
[tex]m\angle A=(128-2)^\circ[/tex]
[tex]m\angle A=126^\circ[/tex]
Similarly,
[tex]m\angle B=(2(16)-8)^\circ[/tex]
[tex]m\angle B=(32-8)^\circ[/tex]
[tex]m\angle B=24^\circ[/tex]
And,
[tex]m\angle C=(94-4(16))^\circ[/tex]
[tex]m\angle C=(94-64)^\circ[/tex]
[tex]m\angle C=30^\circ[/tex]
In a triangle the smaller angle has shorter opposite side and larger angle has longer opposite side.
[tex]24^\circ<30^\circ<126^\circ[/tex]
[tex]m\angle B<m\angle C<m\angle A[/tex]
[tex]AC<AB<BC[/tex]
List the sides of triangle ABC in order from shortest to longest is AC:AB:BC.
Therefore, the correct option is A.
Alice is buying a house with 625K. She is making 20% deposit. And get a mortgage on the balance.A bank offers her two options.
1) 30 year term, fixed interest rate 4%.
2) Pay $10,000 upfront fee to buy down the rate. Still 30 year term, but at 3.75%
Explain your reason.
Answer:
By opting for the second option, Alice would save $ 15,740.00 in total mortgage cost
Step-by-step explanation:
In order to determine the better of the two options available, we need to determine the total cost under each option as follows:
Option 1:
cost of house=$625,000
loan amount=$625,000-(20%*$625,000)=$500,000
loan amount=monthly payment*(1-(1+r)^-n/r
monthly payment is the unknown
r=monthly interest rate=4%/12=0.33333333%
n=number of monthly payments in 30 years=30*12=360
500,000=monthly payment*(1-(1+0.33333333% )^-360/0.33333333%
500,000=monthly payment*(1-0.301795869 )/0.003333333
500,000=monthly payment*0.698204131 /0.003333333
monthly payment=500,000*0.003333333 /0.698204131
monthly payment=$ 2,387.08
total monthly payments=$ 2,387.08*360=$859,348.80
Option 2:
upfront fee=$10,000
loan amount=monthly payment*(1-(1+r)^-n/r
monthly payment is the unknown
r=monthly interest rate=3.75%/12=0.3125%
n=number of monthly payments in 30 years=30*12=360
500,000=monthly payment*(1-(1+0.3125% )^-360/0.3125%
500,000=monthly payment*(1-0.325222459 )/0.003125
500,000=monthly payment*0.674777541 /0.003125
monthly payment=500,000*0.003125 /0.674777541=$2,315.58
Total cost=total monthly payments+upfromt fee
total cost=($2,315.58 *360)+$10,000=$843,608.80
savings by opting for the second option=$859,348.80-$843,608.80
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. The triangles are not drawn to scale.
8
64
T
32
200
19
S
R
16
O ASRQ - AVTU: SAS.
O AQRS - AVTU; SAS.
O ARSQ - AVUT:ASA.
The triangles are not similar
Answer:
Step-by-step explanation:
ΔSRQ and ΔVTU are similar Triangle.
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, ΔRQS and ΔVUT such that,
RS = 16, QR= 64 and VT = 8, UT = 32
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
From the above condition since,
∠R = ∠T
and
[tex]\frac{QR}{SR} = \frac{UT}{VT} = \frac{4}{1}[/tex]
Thus,
ΔSRQ and ΔVTU are similar from the congruency property of SAS.
Learn more about congruent triangles here:
https://brainly.com/question/22062407
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When Ms. Wilson calls to place her order, the store informs her that the delivery fee has increased by $4, but the price of the topsoil remains the same. Write an equation to represent the new situation. Explain.
Answer:
I need a picture or something else to give answer
Step-by-step explanation:
A downtown building is 720 feet tall. Maggie makes a scale model of the building at 1:240 of its actual size. How tall is the model?
Answer:
3 feet
Step-by-step explanation:
720ft
1ft:240ft
720/240=3
3ft:720ft
Four tomatoes and eight avocados cost $10. Six tomatoes and fourteen avocados cost $17.
Part A: Determine the price for a single tomato and a single avocado.
Part B: Analyze your results to determine if they are feasible.
Answer:
(a)
A single avocado costs $1
A single tomato costs $0.5
(b)
An avocado costs twice as much as a tomato
Step-by-step explanation:
Represent the tomatoes with T and the avocados with A.
So, we have:
[tex]4T + 8A = 10[/tex] --- (1)
[tex]6T + 14A = 17[/tex] --- (2)
Solving (a): The price of each
Multiply (1) by 1.5
[tex]1.5(4T + 8A = 10)[/tex]
[tex]6T + 12A = 15[/tex] --- (3)
Subtract (3) from (2)
[tex](6T + 14A = 17) - (6T + 12A = 15)[/tex]
[tex]6T - 6T + 14A - 12A = 17 - 15[/tex]
[tex]14A - 12A = 17 - 15[/tex]
[tex]2A = 2[/tex]
Divide both sides by 2
[tex]A = 1[/tex]
Substitute 1 for A in (1)
[tex]4T + 8A = 10[/tex]
[tex]4T + 8(1) = 10[/tex]
[tex]4T + 8 = 10[/tex]
Make 4T the subject
[tex]4T = 10 - 8[/tex]
[tex]4T = 2[/tex]
Divide both sides by 4
[tex]T = \frac{2}{4}[/tex]
[tex]T = 0.5[/tex]
Solving (b): Analysis
In (a), we have:
[tex]T = 0.5[/tex]
[tex]A = 1[/tex]
We can say that an avocado costs twice as much as a tomato
I need help with this
Answer:
Step-by-step explanation:
((((((.5 mile = .25 hour<<<<<<<<<<<<<<<<<<<<<<<<<<
Multiply both sides by 4, because there are 4 quarters in 1 hour
(4)(.5) = (.25)(4)
2 miles =1 hr
Multiply both sides of the original equation by 3 to figure out how far in 3/4 of an hour
(3)(.5) = (3)(.25)
1.5 miles = 3/4 of an hour
now add the two answers together to figure out that the person walked 3.5 miles in 1 3/4 hours
***You also could have multiplied both sides of the original equation by 7, recognizing that that there are 7 quarters in 1.75 hours.
PLEASE HELP!!!!!!!!!!!!
Answer: Numbers of servings: 10 and 13, Liters of punch: 14
Step-by-step explanation:
Number of servings - 6 = Liters of punch.
how far is the dog to the bird?
Answer:
96 feet squared
Step-by-step explanation:
to find the triangles area you would have to multiply 16 times 12 which would get you 192 then you would have to divide it by 2. Therefore the answer is 96.
Emilio spent half of his savings to buy a video game. The video game cost $63.75. How much was Emilio’s savings? Define a variable and write an equation for this real-world problem. 6. In Austin, Texas, the State Capitol Building has a height of 308 feet. This is 274.4 feet higher than the Alamo located in San Antonio, Texas. What is the height of the Alamo? Define a variable and write an equation for this real-world problem.
Answer:
1) Emilio's total saving - $127.5
2) 33.6ft
Step-by-step explanation:
1) $63.75 x 2 = $127.5
2) 308ft - 274.4ft = 33.6ft
The sum of all the interior angles in a triangle is blank degrees. Please HELP
Answer:
180º
Step-by-step explanation:
All the interior angles add up to 180º degrees.
Answer:
180 degrees
Step-by-step explanation:
In a Euclidean space, the sum of angles of a triangle equals the straight angle
I need help please. I do not understand this.
Answer:
B
Step-by-step explanation:
Okay, so we know they can run 1/4 a mile in 25 seconds. Now we want to know how far they can run in a minute ( 60 sec.). Because there is 25 seconds in 60 seconds 2.4 times, we multiply 1/4 by 2.4. We get 0.6. We know that there is 60 minutes in an hour, so we multiply 0.6 by 60. Now we know they can run 36 miles in an hour/ 36 miles per hour. So that eliminates C and D.
Anyways, B is correct because if you divide 1/4 by 25 you get 0.01. Multiply that by 60 to get a minute. (Because there is 60 seconds in a minute) Which is 0.6. Then multiply it again by 60 for an hour( because there is 60 minutes in an hour), and you get 36 hours.
33 folders cost \$2.91$2.91dollar sign, 2, point, 91.
Which equation would help determine the cost of 222 folders?
Choose 1 answer:
Answer:
The answer is 646.02 tell me if you need an explaination
does anyone think they can explain how to do this?
PLEASE HELP ME WILL GIVE BRAINLIEST TO THE RIGHT ANSWER HELP ASAP!!!!!
Using the new scale and starting from the origin, where will point A be?
Answer:
A will be at 6,6
Step-by-step explanation:
I think this because the graph is the same so it most likely will be the at the same position. Hope this is right !
A pair of shorts cost $32. If the shorts were on sale for 25% off, how much will they cost
Answer:
Step-by-step explanation:
$8.75
hope it helps
Answer:
24
Step-by-step explanation:
half 32 and half it again u get 8 then u do 32-8
Evaluate each expression.
24 : (-15 + 13-8-07- -6 x -5 - -10)
options
-2
22
10
8
Tyler’s game piece landed on space 30 while playing a board game. On his next turn, he moved his piece 17 spaces backward. Which expression can be used to find which space Tyler’s piece was on after his turn?
Answer:
30+(−17) is the answer
Step-by-step explanation:
if m<6=×,m<7=×-20,and m<11=80,thenx=
Arrange the following set of decimal numbers.
1.Least to Greatest-
6.134 , 8.015 , 3.98
2.Greatest to Least-
0.541 , 0.314 , 0521
3.Greatest to Least-
19.6 , 19.006 , 19.06
4.Least to Greatest-
714.4 , 0.7134 , 7.134
5.Greatest to Least-
509.107 , 590.817 , 5,190.18
Answer:
1. 3.98 , 6.134 , 8.0152. 0.541 , 0.521 , 0.3143. 19.006 , 19.06 , 19.64. 0.7134 , 7.134 , 714.45. 590.817 , 5,190.18 , 509.107Step-by-step explanation:
I HOPE IT HELPS :)
What is the value of x?
Answer:
x in all equations just normally means 1
Step-by-step explanation:
x is always 1
Can someone Help pls!!!
Answer:
{0, infinity)
Step-by-step explanation:
range is always the y coords
Terry’s investment of
$2,200 in the stock market earned
$528 in two years. Find the simple
interest rate for this investment.
The expression 5(2x - 1) - 3x(2x - 1) when factorized fully is equal to
my name is jeff Step-by-step explanation:
Please hurry What is the measure of LABD? a:51° b:39° c:49° d: 141°
Answer: Angle ABD is 39°
Step-by-step explanation:
Angle CBA is 90° (given by "box" on the corner of the right triangle)
Angle CBD is given as 51°
Subtract:
90° - 51° = 39°
The square of the sum of
8 and 7 is
Answer:
225
Step-by-step explanation:
8+7=15
15*15=225
Answer:
225
Step-by-step explanation:
8 + 7 = 15
15² = 225
hope this helps...
g a club of 12 people would like to choose a person for each office of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office
Answer:
220 possible ways
Step-by-step explanation:
Given
[tex]n = 12[/tex] --- people
[tex]r = 3[/tex] -- posts [tex](President, Vice\ President\ and\ Secretary)[/tex]
Required
Determine the number of selection
Since there is no condition attached, the number of selection is:
[tex]Selection = ^nC_r[/tex]
Substitute values for n and r
[tex]Selection = ^{12}C_3[/tex]
Apply combination formula
[tex]Selection = \frac{12!}{(12-3)!3!}[/tex]
[tex]Selection = \frac{12!}{9!3!}[/tex]
[tex]Selection = \frac{12*11*10*9!}{9!*3*2*1}[/tex]
[tex]Selection = \frac{12*11*10}{6}[/tex]
[tex]Selection = \frac{1320}{6}[/tex]
[tex]Selection = 220[/tex]
Hence, there are 220 possible ways
(x²+x+1)+(-2x² 3x+5)
Step one: (((x2)+x)+1)+((0-(2x23•x))+5)
Step two: Check for a perfect cube. 2.1 -2x24+x2+x+6 is not a perfect cube.
2.2 Factoring: -2x24+x2+x+6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x+6
Group 2: -2x24+x2
Pull out from each group separately :
Group 1: (x+6) • (1)
Group 2: (2x22-1) • (-x2)
The groups have no common factor and can not be added up to form a multiplication.
So the answer would be, -2 (x24) + (x2) ++ 6.
I WILL GIVE BRAINLIEST The toll on a bridge is $1.00 for cars and $2.50 for trucks. In one hour, a tollbooth operator collects a total of $105 in tolls.
Write an equation that represents the relationship between the number of cars, c, and the number of trucks, t, which could have passed by this tollbooth.
Answer:
The toll on a bridge is $1.00 \:for\: cars\: and\: $2.50 for trucks. In one hour, a tollbooth operator collects a total of $105 in tolls.
Equation :---
[tex]\boxed{c + 2.5t = 105}[/tex]
Above equation represents the relationship between the number of cars, c, and the number of trucks, t, which could have passed by this tollbooth.
Michael has7 dimes in his pocket how much money does Michael have ( make sure your answer has a unit)
Answer:
70 units
Step-by-step explanation:
