Answer:
Option A
Step-by-step explanation:
Central angle of the pentagon = [tex]\frac{360}{\text{Number of sides of the regular polygon}}[/tex]
= [tex]\frac{360}{5}[/tex]
= 72°
Measure of ∠BAC = 72°
Therefore, measure of ∠BAD = [tex]\frac{72}{2}[/tex]
= 36°
By sine rule in ΔABD,
sin(36°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{BD}{AB}[/tex]
= [tex]\frac{BD}{14}[/tex]
BD = 14(sin36°)
= 8.23 mm
Similarly, by cosine rule,
cos(36°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AD}{AB}[/tex]
= [tex]\frac{AD}{14}[/tex]
AD = 14(cos36°)
= 11.33 mm
Area of ΔABC = 2(Area of ΔABD)
= [tex]2(\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= AD × BD
= 11.33 × 8.23
= 93.21 mm²
Since, area of regular pentagon given in the picture = 5(area of ΔABC)
= 5(93.21)
= 466 mm²
Therefore, Option A will be the answer.
Writing an equation to represent the following situation? Maria wants to buy apples and pears at the store. Let x = number of apples and y = the number of pears. Apples are $4 a pound and pears are $2 a pound. She has a total of $20 to spend.
Answer:
4x+2y=20
Step-by-step explanation:
x=apples ($4/lb)
y=pears ($2/lb)
0.42, 0.84, 1.26, 1.68, ............
Find the 63rd term
a
26.28
b
27.3
c
26.46
d
24.64
Answer:
Step-by-step explanation:
Find the nth term so the sequence is going up by 0.42
0.42*63=26.46
63rd term=26.46
Jane has 1 quarter, 3 dimes, and 4 nickels. What percent of dollar does Jane have?
i know the answer is 44% but can someone please explain how i got 44%??
Answer:
ok so I'm English not a hundred percent sure on your break down of money......so if I'm right in thinking that a nickel = 5 cents, dime = 10cents and a quarter =25cents
you add the amounts together
so 25 + 30 +20 = 75 cents.
there are 100 cents in a dollar so 100/100 X 75=75%
I have no idea how you got to 44%
Help its urgent!!!!!!!!!!
Answer:A>
Step-by-step explanation:
Elena made $1,350 in 18 days. Let c represent the amount of money she made each day. If Elena made the amount of money each day, how much did she make in 1 day? Write an division equation.
The rate of money earned per day will be $75 per day.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Elena made $1,350 in 18 days.
Earning per day = ($1350/18) = $75 per day.
Hence "The rate of money earned per day will be $75 per day".
To learn more about the rate of change here,
brainly.com/question/12786410
#SPJ2
What is the approximate area of
the figure? Use 3.14 for T.
-12 m-
A. 57 square meters
B. 113 square meters
C. 226 square meters
D. 452 square meters
1. Johnny typically drives his truck between 250 and 300 miles a day for work. Last week he worked 5 days and drove a total of 1300 miles. Is this reasonable?
Answer:
1350
Step-by-step explanation:
I've been given this for maths and I have no clue what to do can someone help me out?
what equation of a line passes through the points (0,8) and (6,4)
Answer:
y=-3/2x+6
Step-by-step explanation:
You will need to find the equation of the line in slope-intercept form y=mx+b.
First, find the slope m using slope formula m = (y_2-y_1)/(x_2-x_1) which is m=(6-(-6))/(0-8)=-12/8=-3/2
Now that you found the slope, your equation intercept form looks like y=-3/2 x+b.
Both points (8, -6) and (0.6) belong to this line, therefore both points coordinates satisfy line above which means: 6=-3/2(0)+b (i used second point here)
Solving for b we will get y intercept which is b=6
Finally, the line that passes through points (8,-6) and (0,6) has equation: y=-3/2 x + 6
Employees at a large office building took a survey. The results show that those who began work earlier tended to drink less tea. Which statement is most likely true?
Answer:
B) There is a correlation between start time and amount of tea consumed. There may or may not be causation. Further studies would have to be done to determine this.
Step-by-step explanation:
Correlation in terms of statistics refers to the relationship that exists between two components. The extent to which the two components or data are related to each other is highlighted with correlation. The change in one component brings the same amount of change in the other component. Correlation discloses the way the variables are related.
In the given excerpt, the correlation between start time and amount of tea consumed has been highlighted. This data is required for further research about the cause.
y = 5x - 6
slope
y-intercept
Answer:
slope:5
y intercept: -6
Step-by-step explanation:
Será buys 1.20 pounds of skittles 3½ pounds of m&m's and 5.2 pounds of pretzels if the candy cost $1.20 a pound and the pretzels cost $1.10 a pound how much did será spend?
Answer:
3:00
Step-by-step explanation:
The product of 6g2 and -2g3 is equals to
Answer:
We conclude that:
[tex]\left(6g^2\:\right)\times \left(-2g^3\right)=-12g^5[/tex]
Step-by-step explanation:
Given
6g²-2g³The product of 6g² and -2g³ can be determined by multiplying each other such as:
[tex](6g^2\:)\times \:(-2g^3)[/tex]
Apply the rule: a(-b) = -ab
[tex]\left(6g^2\:\right)\times \left(-2g^3\right)=-6g^2\times \:\:2g^3[/tex]
Apply exponent rule: [tex]a^b\times \:a^c=a^{b+c}[/tex]
[tex]=-6g^{2+3}\times \:2[/tex]
[tex]=-6g^5\times \:2[/tex]
[tex]=-12g^5[/tex]
Therefore, we conclude that:
[tex]\left(6g^2\:\right)\times \left(-2g^3\right)=-12g^5[/tex]
William got scores of q sub 1, , and q sub 3 on three quizzes.
a. Write a formula for the average x of all three quizzes.
b. William got an 85 and an 88 on the first two quizzes. What formula can William use to determine the score he needs on the third quiz to get an average of 90? What score does he need?
Answer:
a. The average is =(++) .
b. He can use the formula =−− q sub 3 , equals 3 x minus , q sub 1 , minus , q sub 2. He will need a score of =()−−= q sub 3 , equals 3 open 90 close minus 85 minus 88 equals 97 on his third quiz.
Step-by-step explanation:
Simplify this expression 5x-3(x-2)-x
Answer:
x+6
Step-by-step explanation:
5x-3(x-2)-x
5x-3x+6-x
combine like terms
x+6
Given quadrilateral EFGH at e(-4,7) f(8,4) G(t,-5) and h(-7,-1) using coordinate geometry prove EFGH is a rectangle
The above question was not properly written.
Complete Question
Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5,-5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle.
Answer:
Quadrilateral EFGH is a rectangle.l because:
EF = GH and FG = EH
Step-by-step explanation:
The formula for coordinate geometry is given as :
√(x2 - x1)² + (y2 - y1)² when we have coordinates: (x1, y1) and (x2 , y2)
For the quadrilateral EFGH with given coordinates above to be a rectangle,
EF = GH
FG = EH
Hence:
For side EF
E(-4,8), F(8,4)
= √(8 - (-4))² + (4 - 8)²
= √12² + -4²
= √144 + 16
= √160 units
For side FG
F(8,4), G(5,-5)
=√(5 - 8)² + (-5 - 4)²
= √-3² + -9²
= √9 + 81
= √90 units
For Side GH
G(5,-5) , H(-7,-1)
= √(-7 - 5)² + (-1 - (-5))²
= √-12² + 4²
= √144 + 16
= √160 units
For side EH
E(-4,8), H(-7,-1)
= √(-7 -(-4))² +(-1 - 8)²
= √-3² + -9²
= √9 + 81
= √90 units
From the above calculation, we can see that truly,
EF = GH
FG = EH
Therefore, quadrilateral EFGH is a rectangle.
9.How much interest do you earn when you deposit $100 at 25% for 2 years?
10.In question #9, how much does the bank owe you at the end of those two years?
Answer:
For simple interest: $50, for compound interest: $56.25
Step-by-step explanation:
Year 1) 100+100(.25) = 125
Year 2) 125+125(.25) = 125+31.25 = $156.25
156.25 - 100 = $56.25
25 x 2
=50
write the equation of a line passing through the points (-3,4) and (3,4)
Answer:
m=0 y=4
Step-by-step explanation:
At 5:30 p.m., the temperature was recorded as 4 °F. At 10:00 p.m., the temperature had dropped 2 °. Which number line below best shows the
temperature at
10:00 p.m.?
Answer:
the answer is A
Step-by-step explanation:
(HURRY I’LL GIVE YOU THE BRAINIEST IF YOU GET IT RIGHT) What is 3 3/4 x 2 1/2 in fractions?
Answer:
9 3/8
Step-by-step explanation:
or 75/8
Answer:
I think its 15/4
Step-by-step explanation:
:)
The equation of the line that goes through (-3,5) and (2,-4)
Answer:
y=-9/5x-2/5
Step-by-step explanation:
Answer:
y=-9/5x-2/5
Step-by-step explanation:
Slope=m=Rise/Run=(y2-y1)/(x2-x1)=(-4-5)/(2-(-3))=(-9)/(5)=-9/5
So the equation becomes y=-9/5x+b
Plug in one of the given points:
y=-9/5x+b
-4=-9/5(2)+b
-4=-18/5+b
-0.4=b
b=-0.4
Therefore the equation of the line is y=-9/5x-2/5
Can someone tell me some good puns on cheese ?
(Don’t mind the purpose) Thank you !
Answer:
What Did the Blind Man Say after Being Handed a Cheese Grater?
"That's the most violent book I've ever read."
Step-by-step explanation:
Answer: I could but it will be a little cheesy
Step-by-step explanation:
find the perimeter of the new shape
A DVD has a diameter of 18 centimeters. What is the area of the DVD? Round your answer to the nearest hundredth. Use 3.14 for π.
Answer:
. SAME THING YOU PUT FOR MY ANSWER IM GONNA DO THE SAME FOR YOU
Step-by-step explanation:
Find the equation of the line.
To find the equation of the line, we need to figure out the slope and y-intercept.
To find the y-intercept, look at the number where the line intersects the y-axis. The number is 5. The equation so far is y = ?x + 5.
We still didn't figure out the slope yet. To figure out the slope, pick two points. Use the rise over run method. It is in the image below. The line is going up to the left, so the slope will be negative. Now we know the slope is -1/3. The equation now that we figured out the slope is y = -1/3x + 5.
I hope this helps you! Let me know if I got something wrong.
Find the missing number so that the equation has infinitely many solutions
-3x + _= -5x + 20 + 2x
Answer:
20
Step-by-step explanation:
-3x+20=-5x+20+2x
reduced:
-3x+20=-3x+20
subtract 20 from each side
Then
-3x=-3x
Write the word sentence as an equation. Then solve.
The difference between a number p
and 6
is −14
.
Answer:
Equation- p-6= -14
Answer- p=-8
Step-by-step explanation:
I REALLY need help with this question please.
================================================
Work Shown:
Plug in t = 2 and we get the following
[tex]a = 500*\left(\frac{3}{4}\right)^{t}\\\\a = 500*\left(\frac{3}{4}\right)^{2}\\\\a = 500*\left(0.75\right)^{2}\\\\a = 500*0.5625\\\\a = 281.25\\\\[/tex]
The answer is choice D. There are 281.25 mg of aspirin in the bloodstream after 2 hours.
-----------------
Side notes:
The 500 represents the initial amount of aspirin (in mg) in the bloodstream. This is the amount when t = 0.The 3/4 converts to 0.75; when solving 1+r = 0.75, we get r = -0.25, and this shows a 25% reduction in aspirin each time t goes up by 1. Every hour, the amount of aspirin in the bloodstream reduces by 25%Answer:
375
Step-by-step explanation:
because if you look at the question 3\4 is 1 hour with the aspren 500 after 2 hours you 2 the ammount i think
A ______ always has a numerator of 1
A. fraction
B.Simplest form
C. unit fraction
(answer asap) please and ty!
Answer:
C. Unit Fractions
Step-b
Write the formula for the following sequence.
5.8, 3.6, 1.4,...
PLEASE SHOW YOUR WORK.
[tex]tn = t(n - 1)- 2.2[/tex]
common difference is
3.6 - 5.8 = -2.2
let T1 = 5.8
T2 = 3.6
assuming we are to find T2
T2 = T(2-1) -2.2
= T1 -22
= 5.8 -2.2
= 3.6