The measure of the exterior angle at vertex D is: D. 54°
Recall:
The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.Thus:
In ΔDEF, (8x−2)º is an exterior angle at vertex D.
m∠E = (3x−8)° (interior angle)
m∠F = (4x+13)° (interior angle)
Therefore:
(8x−2)º = (3x−8)° + (4x+13)°
Solve for x8x - 2 = 3x - 8 + 4x + 13
Combine like terms8x - 2 = 7x + 5
8x - 7x = 2 + 5
x = 7
Exterior angle at vertex D = (8x−2)º
Plug in the value of x= 8(7) - 2
= 54º (option D)
Learn more about exterior angle theorem on:
https://brainly.com/question/24756010
£4800 is divided among three brothers
A, B and C. A receives three times as much as B and C receives twice as much as B. If B receives $x, form an equation in x.
Answer:
A: 2400
B: 600
C: 1800
Step-by-step explanation:
A= x+3x=4x
C = x+2x= 3x
4x+x+3x = 4800
8x= 4800
x= 600
share of A= 2400$
share of B= 600$
share of C= 1800$
The cubic curve y = x'3 + ax'2 + bx + c passes through the point (1,3) and has tangent line y = x - 2 at the point (0,-2). What are the values of a, b, and c?
Answer:
answer to your question is: a = 3, b = 1, c = -2
please answer the file question
Answer:
x = 15
Step-by-step explanation:
Corresponding sides have the same ratio:
UV/PR = TV/QR
(x +6)/14 = (x -3)/8
4(x +6) = 7(x -3) . . . . . . multiply by 56
4x +24 = 7x -21 . . . . . . eliminate parentheses
45 = 3x . . . . . . . . . . . add 21-4x
15 = x . . . . . . . . . . . .divide by 3
_____
Alternate solution
The long-side : short-side ratios for the two triangles are ...
14 : 8 = (x +6) : (x -3)
If we look at the differences between the ratio numbers we see ...
14 -8 = 6
(x +6) -(x -3) = 9
That is, the numbers in the second ratio must be 9/6 = 3/2 times the numbers in the first ratio. In other words, ...
x -3 = (3/2)(8) = 12
x = 15
Check: x +6 = 3/2(14) ; 15 +6 = 21
Please help. Will mark Brainliest
Which statements go in boxes 2 and 3?
What is the proof for boxes 3 and 4?
A company has two large computers. The slower computer can send all the company’s email in 50 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?
Answer:
18 minutes and 45 seconds
Step-by-step explanation:
[tex]\frac{1}{50}[/tex] + [tex]\frac{1}{30}[/tex] = [tex]\frac{3+5}{150}[/tex] = [tex]\frac{4}{75}[/tex]
1 ÷ [tex]\frac{4}{75}[/tex] = [tex]\frac{75}{4}[/tex] = 18' 45''
Answer:
18.75 minutes If A and B work together
A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long. If the gardener draws a blueprint of the garden, where each meter is equivalent to
inch, which statements are true?
Select ALL that apply.
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
The length of the blueprint is 6 meters
The perimeter of the blueprint is 28 inches.
The width of the blueprint is 8 meters
Calculator
Answer:
Catalog Name:*Shimmering Chic Earrings*
Base Metal: Alloy
Plating: Gold Plated
Stone Type: Cubic Zirconia/American Diamond
Type: Jhumkhas
Multipack: 1
Easy Returns Available In Case Of Any Issue
*Proof of Safe Delivery! Click to know on Safety Standards of Delivery Partners- https://ltl.sh/y_nZrAV3
The statements are true:
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
What is Area of rectangle?The Area of Rectangle is product of its length to its width.
So, Area of Rectangle = length x width
Given:
length= 12 inch
and width= 9 inch
Area of Blue print = l x w
= 12 x 9
= 108 square inches.
Perimeter of Blue print = 2 ( l+ w)
= 2( 12+ 9)
= 42 inches
Learn more about Area of rectangle here:
https://brainly.com/question/20693059
#SPJ2
(g, 6) and (-5, -9)
Slope = 3/2
Answer:
g=5
Step-by-step explanation:
(-9)-(6) / (-5)-(g) = 3/2
3 x -(g+5) = 2 x -15
g+5=10
g=5
Answer:
g=15
Step-by-step explanation:
we first can substitute in (-5,-9) into the x and y variables in y=mx+b as well as the slope:
so we get:
-9=3/2(-5)+b
now lets solve for b:
3/2 x -5 = -15/2
-9=-15/2+b
now add the -15/2 on both sides of the eqaution:
b=-33/2
now lets substitute it back in:
y=3/2x-33/2
NOW lol substitute the 6 in to find g:
6=3/2g-33/2
solve from here to get
45/2=3/2g
multiply by 2 on each side
45=3g
divide both sides by 3:
g=15!!!!!!!!!!!!!!
I hope this helped sry it took long lol
Help.............???!!!
Answer:
Its either A or C
Step-by-step explanation:
Xavier has 29 baseball
cards he'd like to share
with his 3 best friends.
Each friend gets an equal
number of cards. How
many baseball cards will
be left over?
Math
Answer:
2
Step-by-step explanation:
29 % 3 = 9
3x9 = 27
29 - 27 = 2
7) If a point is randomly chosen on the square shown, what is the probability that it will be in the red section of the figure? A) 1/4 B) 1/3 C) 1/2 D) 3/4
Answer:
1/4
Step-by-step explanation:
1/4 because it is one piece out of the four cuts. if it were yellow, than it would be 2/4, or 1/2
cant seem to figure this out
Answer:
log14=1.146
log18=1.255
Step-by-step explanation:
Use log rules to break up the given logs, to be able to use the information give
Using the product rule, log14 = log(7 x 2) = log7 + log2
Substitute .845 + .301 = 1.146
Using the quotient rule, log18 = log(2 x 3 x 3) = log2 + log3 + log 3
Substite .301 + .477 + .477 = 1.255
12 degree C fell to -5 degree C WHAT IS THE DIFFERENCE
Answer:
7
12-5=6 this helps you''';
the length of a door is 1.8 feet longer than it's width, and it's front area is 1504.6 square feet. find the width and height of the door
Answer:
width: 37.9 ft
height: 39.7 ft
Step-by-step explanation:
Sometimes it is easier to work these problems by finding the average of the length and width. If that value is x, then the length is x+0.9, and the width is x-0.9. The area is ...
A = LW
1504.6 = (x +0.9)(x -0.9) = x^2 -0.81
1505.41 = x^2
x = √1505.41 ≈ 38.7996
width = x -0.9 = 38.8 -0.9 = 37.9
height = 38.8 +0.9 = 39.7
The width of the door is approximately 37.9 ft; the height is about 39.7 ft.
There are some red and blue balls in a bag of 21 balls and the probability of picking 2 red balls out in a row is 1/14 how many red balls are there?
Answer:
6 red balls
Step-by-step explanation:
The probability in the first pick
6/21
The probability in the second pick (without replacement)
5/20
the requested probability
(6/21)(5/20) = 30/420
simplification
30/420 = 3/42 = 1/14
Hope this helps
Answer:
6 red balls.
Step-by-step explanation:
If there are x red balls then
probability of 2 red balls
= x/21 * (x - 1)/20 = 1/14
x^2 - x / 420 = 1/14
x^2 - x = 30
x^2 - x - 30 = 0
(x - 6)(x + 5) = 0
x = 6.
Choose the number that makes the statement true: -5>?
a. 9
b. -9
C. -3
d. 3
Answer: This is B.) -9
Step-by-step explanation:
Step-by-step explanation:
All of those numbers are greater than -5 except for B.
solve the compound inequality 2(x-2)+7>-1 and 5-4x>9
Answer:
1) x > -2
2) x < -1
Step-by-step explanation:
1) 2(x - 2) + 7 > -1
2x - 4 + 7 > -1
2x + 3 > -1
2x > -4
x > -2
2) 5 - 4x > 9
-4x > 4
x < -1
Can y’all please help me with these questions
Answer:
13. STR
14. VY
Step-by-step explanation:
I hope this helps!
3(y+8)=2y-6 what is y=
Answer:
y = -30
Step-by-step explanation:
3 (y + 8) = 2y - 6
3y + 24 = 2y -6 Distribute the 3
y + 24 = -6 Subtract 2y on both sides
y = -30 Subtract 24 on both sides
During the first year with a company, Finley was paid an annual salary of $57,000, with a 4% raise for each following year. Which equation represents Finley's annual salary, f (n), during the nth year?
f (n) = 57,000(0.04n – 1)
f (n) = 57,000(1.04n)
f (n) = 57,000(1.04n – 1)
f (n) = 57,000(0.96n)
Answer:
Step-by-step explanation:
C I took the test
The equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.
What is the percentage?The percentage is defined as ratio expressed as a fraction of 100.
Finley was paid an annual salary of $57,000
with a 4% raise for each following year
Finley's annual salary, during the 2th year
⇒ 4% of 57,000 + 57,000
⇒ (0.04)57,000 + 57,000
⇒ 2280 + 57,000
⇒ 59280
Finley's annual salary, during the 2th year
Determine the difference between year 2 and year 1 salary.
Rate of change = 4% of 57,000 - 57,000
Rate of change = (0.04)57,000 - 57,000
Rate of change = 57,000(0.04 - 1)
Finley's annual salary, during the 5th year
Determine the difference between year 5 and year 4 salary
⇒ 57,000(0.04(5) - 1)
That's the constant.
Finley's annual salary, during the nth year
So, f (n) = 57,000(1.04n – 1)
Hence, the equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.
Learn more about percentage here:
brainly.com/question/24159063
#SPJ2
I need Help please ASAP!!!!
Please
Please
Answer:
1.8?
Step-by-step explanation:
Answer:
its 1 4/5 your welcome
Step-by-step explanation:
What are the coordinates of B
Answer: (-7,-5)
Step-by-step explanation:
Because when you mark point M and A if you mirror point M and A on the x Axis then you will get (-7,-5)
Fill in the missing numbers below.
5 feet + 12 inches = blank
yard(s)
Blank inches = 1 foot + 1 yard
Blank feet = 3 feet + 24 inches
Answer:
5 feet + 12 inches = 2 yards
48 inches = 1 foot + 1 yard
5 feet = 3 feet + 24 inches
Step-by-step explanation:
To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:
1 feet = 12 inches
3 feet = 1 yard
To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.
12 inches = 1 feet
Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.
Blank inches = 1 foot + 1 yard
To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.
Blank feet = 3 feet + 24 inches
Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.
A choir teacher is dividing 48 sopranos and 32 altos into singing groups. He wants each
group to have the same combination of sopranos and altos, with no singers left over. What is
the area
Answer:
32
Step-by-step explanation:
x(48 - 2x) = 32
Hope it helps.
Kangaroo hops 2 kilometers in 3 minutes how long does it take the kangaroo to travel 5 kilometers
Answer:
7.5minutes
Step-by-step explanation:
If it travels 2kilometers every 3 min, that means it travels 2/3 kilometer per minute. Then divide 5 kilometers by 2/3kilometers/min, which gets you 7.5minutes
Please help me in this!!!!
Step-by-step explanation:
you really don't see this ?
this is rotated by 180 degrees around the origin.
do you see how the different points change positive from one shape to the other ?
think what happens when you rotate a disk (like a plate) with something on it. how does that something on it change is position and orientation ?
this here is the same thing. look at H and how it turns into O.
-6x+6y=9 (1/2,2) please helppppp
Answer:
A. Solution
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Step-by-step explanation:
*Note:
A coordinate is a solution if both the left side and right side of the equation is equal.
Step 1: Define
Identify.
-6x + 6y = 9
(1/2, 2)
Step 2: Verify
Substitute in variables [Equation]: -6(1/2) + 6(2) = 9[Order of Operations] Evaluate: 9 = 9Since 9 does indeed equal 9, the coordinate (1/2, 2) is a solution.
purchase good from naresh rs 9000 and isued a cheque of rs 4000 only as payment
Answer:
that means you have a 5000 dollar debt
Hope This Helps!!!
After sitting in a refrigerator for a while, a turkey at a temperature of 34^\circ34
∘
F is placed on the counter and slowly warms closer to room temperature (67^\circ67
∘
F). Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the room, as given by the formula below:
T=T_a+(T_0-T_a)e^{-kt}
T=T
a
+(T
0
−T
a
)e
−kt
T_a=T
a
= the temperature surrounding the object
T_0=T
0
= the initial temperature of the object
t=t= the time in minutes
T=T= the temperature of the object after tt minutes
k=k= decay constant
The turkey reaches the temperature of 45^\circ45
∘
F after 15 minutes. Using this information, find the value of kk, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 60 minutes.
Enter only the final temperature into the input box.
The temperature of the body after 60 minutes is 60.5° F.
Using the Newton's law of cooling;
T(t) =[tex]Ts + (To - Ts)e^-kt[/tex]
T(t) = temperature at time t
Ts = temperature of the surrounding
To = Temperature of object
t = time taken
k = cooling constant
Now;
[tex]T(t) -Ts=(To - Ts)e^-kt\\45 - 67 = (34 - 67)e^-15k\\-22 = -33e^-15k\\-22/-33 = e^-15k\\0.667 = e^-15k\\ln(0.667) = ln( e^-15k)\\-0.405 = -15k\\k = -0.405/ -15\\k = 0.027[/tex]
At t = 60 min
[tex]T(t) = Ts + (To - Ts)e^-ktT(60) = 67 + (34 - 67)e^-( 0.027*60)\\T(60) = \\67 + (-33)e^-( 0.027 * 60)\\T(60) = \\60.5 F[/tex]
T(60) = 60.5° F
Learn more about Newton's law of cooling: https://brainly.com/question/13748261
Answer:
T≈169
Step-by-step explanation:
Enter only the final temperature into the input box.
T_a = 67\hspace{50px}T_0=210
T
a
=67T
0
=210
\text{Write Formula:}
Write Formula:
T=67+(210-67)e^{-kt}
T=67+(210−67)e
−kt
Plug in givens
\color{blue}{T}=67+143e^{-k\color{green}{t}}
T=67+143e
−kt
Simplify
\text{Plug in given time and temperature:}
Plug in given time and temperature:
\color{blue}{193}=67+143e^{-k(\color{green}{1.5})}
193=67+143e
−k(1.5)
Simplify
\text{Solve for }k\text{:}
Solve for k:
193=
193=
\,\,67+143e^{-1.5k}
67+143e
−1.5k
-67\phantom{=}
−67=
\,\,-67
−67
126=
126=
\,\,143e^{-1.5k}
143e
−1.5k
\frac{126}{143}=
143
126
=
\,\,\frac{143e^{-1.5k}}{143}
143
143e
−1.5k
Divide by 143
0.8811189=
0.8811189=
\,\,e^{-1.5k}
e
−1.5k
\ln\left(0.8811189\right)=
ln(0.8811189)=
\,\,\ln\left(e^{-1.5k}\right)
ln(e
−1.5k
)
Take ln of both sides
\ln\left(0.8811189\right)=
ln(0.8811189)=
\,\,-1.5k
−1.5k
\frac{\ln\left(0.8811189\right)}{-1.5}=
−1.5
ln(0.8811189)
=
\,\,\frac{-1.5k}{-1.5}
−1.5
−1.5k
Divide by -1.5
0.0843751=
0.0843751=
\,\,k
k
k\approx
k≈
\,\,\color{blue}{0.084}
0.084
Round k to nearest thousandth
\text{Complete Formula:}
Complete Formula:
T=67+143e^{-\color{blue}{0.084}t}
T=67+143e
−0.084t
Plug in k
\text{Find temperature after }\color{green}{4}\text{ minutes:}
Find temperature after 4 minutes:
T=67+143e^{-0.084(\color{green}{4})}
T=67+143e
−0.084(4)
Plug in time
T=67+143e^{-0.336}
T=67+143e
−0.336
Multiply
T=169.1911041
T=169.1911041
Plug into the calculator
T\approx 169
T≈169
3. My divisor is 8.
I am less than 30.
I am greater than 3 X 8.
My remainder is 5.
What dividend am I?
Answer: 29
Step-by-step explanation:
29 ÷ 8 = 3 remainder: 5
I solved using long division.
Answer:
29
Step-by-step explanation:
30
24
5
8x3=24
24+5= 29
Beacuase it had to be smaller than 30
(5x + 3) + (9x + 5)
Help!!!!!!!