Answer:
y = 8
Step-by-step explanation:
y + y + 2 = 18
2y + 2 = 18
-2 -2 (+ 2 and - 2 cancel out each other)
2y = 16
2 2
y = 8
Convert 40 miles per hour to feet per second.
A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof.
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
How to prove the angles in a Parallelogram?
From the given image of the parallelogram, we are given that;
Angle 1 and angle 3 are complementary.
Now, complementary angles sum up to 90°. Thus;
∠1 + ∠3 = 90°
Now, according to definition of parallelogram, we know that alternate interior angles of a parallelogram are congruent(equal). Thus;
∠1 = ∠2
Since ∠1 = ∠2, then by substitution property into the first equation, we have; ∠2 + ∠3 = 90°
Since the sum of ∠2 and ∠3 is equal to 90°, then we can say that they are both complementary angles.
Thus, we conclude that;
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
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A total of 491 tickets were sold for the school play. They were either adult tickets or student tickets. There
were 60 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
Adult tickets = 276
Step-by-step explanation:
a + s = 491 Eq. 1
a = s + 61 Eq. 2
a = adult tickets
s = student ticket
Replacing Eq. 2 in Eq. 1:
(s+61) + s = 491
2s + 61 = 491
2s = 491 - 61
2s = 430
s = 430/2
s = 215
from the Eq. 2
a = s + 61
a = 215 + 61
a = 276
Check:
from Eq. 1:
a + s = 491
276 + 215 = 491
00:00
Which equations show you how to find 13 - 6?
A. 7 + 3 = 10, 10+ 3 = 13
B. 6 + 4 = 10, 10+ 4 = 14
C. 6+4 = 10, 10+ 3 = 13
D. 8+2 = 10, 10+ 3 = 13
A set of three scores consists of the values 3, 7, and 2. Σ2(X – 3) =
Answer:
6
Step-by-step explanation:
[tex]\sum 2(X-3)=2(3-3)+2(7-3)+2(2-3)=0+8-2=6[/tex]
What is 13 1 3 percent as a fraction in simplest form
Answer:
2/15
Step-by-step explanation:
A percent is a number given out of 100
13 1/3% basically is 13 1/3 | 100
You divide and you get 40/3 x 1/100
Simplify by 20 = 40/300 simplify again and you get 2/15.
f(x) = x² + 2x - 3
Find f(2)
Answer:
5
Step-by-step explanation:
f(2) = (2)^2 +2(2) - 3
f(2) = 4 + 4 - 3
f(2) = 8 - 3
f(2) = 5
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A recipe calls for the following spices:1/4 teaspoon of turmeric,1/8 teaspoon of ginger, and 1/4 teaspoon of cumin. What is the total quantity of these three spices?
en que se parece el Palacio Versalles y el Palacio el escorial
Answer:
Las primeras y quizá más sobresaliente características del monasterio y palacio real San Lorenzo de el Escorial son la composición geométrica y simétrica del edificio, el uso de los espacios cuadrados, y la preferencia por lo poco ornamentado, esto resulta bastante contrastante con la arquitectura regular de Europa, en la cual, sobre todo en Italia había predilección por las líneas curvas, los espacios ovalados, circulares, asimétricos y la predominación de un estilo muy ornamanetado con la intención de mover intensamente al espectador ante la unión del poder terrenal y espiritual. Existen rasgos en común con la arquitetura barroca foránea, como el uso de lo clásico como modelo riguroso y la necesidad de representar la grandiosidad e imponencia de la nobleza en la magnitud del palacio. Juan de Herrera fue el arquitecto del rey Felipe II, y quien impuso como estilo español arquitectónico barroco lo poco ornamentado, el recuerdo de lo clásico y los edificios de líneas rectas y grandes magnitudes.
Steven has a rope that is 6ft long. He cuts it into 9 pieces. How many are in each piece
Answer:2/3
Step-by-step explanation:
never got taught this.
Answer:
|-5| is equal to 5 because absolute value is the distance from 0
Step-by-step explanation:
please help
maths geometry
Step-by-step explanation:
since both shapes are totally symmetric, a few answers are obvious :
(1) F2 = F1 = 50°
(3) B1 = D1 = 20°
last but not least, D2 = B2.
using the fact that the sum of all angles in a triangle is always 180°.
and that the sum of all angles sind a single point on one side of a line is also always 180° :
in the triangle CDF the inner angle C is
C = 180 - 20 - 50 = 110°.
therefore, C1 = 180 - 110 = 70°
E1 = 90° (a major rule for the diagonals of a kite).
D2 = 180 - 90 - 70 = 20°
and so, B2 = 20°
(2) D2 = 20°
(4) B2 = D2 = 20°
I need help answering this
Answer:
the Answer is c yo I know it bro
Answer: C
Step-by-step explanation:
x^2 + 6x + 8 = (x + 2 )(x + 4 )
Rewrite (10 + 6) + 5+ 3 using the Associative Law of Addition,
O 10+6+5+3
O 10+(6+5) + 3
O 3+5+ (10+6)
O (10+6) + 3+5
Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
How to compute the value?It should be noted that the Associative Law of Addition explains that a + (b + c) is the same as (a + b) + c.
Therefore, Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
It should be noted that this will still give same value.
Therefore, the correct option is B.
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reflection across the y-axis
Please I need help ASP
Answer:
See the picture below.
Step-by-step explanation:
Nina can swim 4 laps in 2 1/3 minutes. At this rate, how many laps can she swim in one minute
lap(s) in one minute
nina can swim 8/7 laps in one minute
given that
nina can swim 4 laps in 7/2 minutes
we have to calculate that how many laps can nina swim in 1 minute
then 4 laps= 7/2 minutes
then 4*2 /7 =1 minute
8/7=1 minute
thus nina can swim 8/7 laps in one minute
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HELP ME! AND PLSSSS EXPLAIN!
Ariel received so many flowers for her birthday that they wouldn't all fit on her desk. By
lunch, her office was decorated with 7 flower bouquets, 5 of which were rose bouquets.
If Ariel randomly selected 4 bouquets to take home, what is the probability that all of them
are rose bouquets?
Write your answer as a decimal rounded to four decimal places.
The probability that all of them are rose bouquets is 0.143.
How to calculate the probability?It should be noted that this question is about probability without replacement.
The probability of picking a rise bouquet is 5/7. It should be noted that each value decreases since Ariel is selecting 4 bouquets.
The probability that all of them are rose bouquets will be:
= 5/7 × 4/6 × 3/5 × 2/4
= 5/7 × 2/3 × 3/5 × 1/2
= 30/210
= 1/7
= 0.143
The probability is 0.143.
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Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr
The equation that we need to solve is:
(S + 2*S)*3h = 54mi
The speed of the slower cyclist is 6 mi/h
The speed of the faster cyclist is 12 mi/h.
How to write an equation that models this situation?Let's define S as the speed of the slower cyclist, thus 2*S will be the speed of the other cyclist.
They travel in opposite directions, and after 3 hours the travel a combined distance of 54 miles, then we can write the equation:
(S + 2*S)*3h = 54mi
With that equation, we can determine the speeds of the cyclists.
Solving for S we get:
(S + 2*S)*3h = 54mi
3*S = 54mi/3h = 18 mi/h
S = (18 mi/h)/3 = 6 mi/h
Then the speed of the slower cyclist is 6 miles per hour, and the speed of the faster cyclist is twice that, so it is 2*6 mi/h = 12 miles per hour.
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The number of students at Jefferson School is even.
The number has three digits.
The digit in the tens place is 4.
Write three numbers that could be how many students
there are at Jefferson School.
school
There are a total of 36 possible answers in digit .
What is digits in math?
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.Let's assign three blanks for each digit of the unknown number. But let's fill in the tens digit because it is already specified.
_ 4 _
The last digit should be even to make it even. The possible digits for this are 2, 4, 6, and 8. The first digit could be any digit from 1 to 9. Therefore, the possible answers are
142 242 342 442 542 642 742 842 942
144 244 344 444 544 644 744 844 944
146 246 346 446 546 646 746 846 946
148 248 348 448 548 648 748 848 948
Therefore, there are a total of 36 possible answers.
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The formula for the nth pentagonal number is
[tex]P_{n}[/tex] = n(3n-1)/2
Use the formula to find the 16th pentagonal number.
The 16th pentagonal number is 376
What is a function?A function can be defined as an expression that explains the relationship between a dependent and an independent variable.
Given the function for the nth pentagonal number as;
Pn = n( 3n -1 )/ 2
To determine the 16th pentagonal number, we need to substitute the value of n as 16
We have;
P16 = 16(3(16) - 1)/ 2
P16 = 16( 48 - 1)/ 2
P16 = 16(47)/ 2
expand the bracket
P16 = 376
Thus, the 16th pentagonal number is 376
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A store has clearance items that have been marked down by 60% they are having a sale advertising an additional 30% off clearance items. What percent of the original price do you end up paying?
A motorboat can maintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 33 minutes; the return trip takes 19 minutes. What is the speed of the current?
Answer:
7 mph
Step-by-step explanation:
A boat whose speed in still water is 26 mph makes a trip upstream in 33 minutes and returns in 19 minutes. You want to know the speed of the current.
SetupThe travel time is inversely proportional to the speed, so we can write the proportion (using c for the current speed in mph) ...
time upstream / time downstream = speed downstream / speed upstream
33/19 = (26 +c)/(26 -c)
SolutionMultiplying by 19(26 -c) gives ...
33(26 -c) = 19(26 +c)
(33 -19)(26) = (33 +19)c . . . . add 33c -19(26)
14(26)/(52) = c = 7
The speed of the current is 7 miles per hour.
At a large university it is known that 30% of the students live on campus. The director of student life is going to take a random sample of 500 students. Which of the following is most likely to occur?
Using point estimation, the sample proportion falls between 0.2 and 0.4.
What is point estimation?The sample distribution offers details on the point estimator to choose. If the distribution's mean matches the actual value of the population parameter, the estimator is considered to be impartial. As a result, the population percentage p and the sample proportion p ought to be quite similar.
The correct option is C, because the average of 0.2 and 0.4 is 0.3
Complete Question is -At a large university it is known that 30% of the students live on campus. The director of student life is going to take a random sample of 500 students. Which of the following is most likely to occur?
a.) The sample proportion falls between 0.3 and 0.5.
b.) The sample proportion falls between 0.1 and 0.3.
c.) The sample proportion falls between 0.2 and 0.4.
d.) The sample proportion falls between 0.25 and 0.35.
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F (x) =2x+3^2 (x-1)3 state of degree
Translate into an expression T times B times 4
hi
"times " = multiply by
B*T*4 = 4BT (as it is the custom to put numbers before letters, and letters in alphabetic order)
kofi use 15min to type 500papers. How many minutes will he take 900papers
Answer:
27 minutes
Step-by-step explanation:
Hello!
500 and 900 are both multiples of 100, so let's first find the rate at which it takes Kofi to type 100 pages.
15m = 50015m / 5 = 500/53m = 100It takes 3 minutes to type 100 papers.
Since 900 is 9 times 100, we can also multiply the time by 9.
3m = 1003m*9 = 100*927m = 900It takes 27 minutes to type 900 papers.
=
Find the exact value of the expression. Do not use a calculator.
sin 26° - cos 64°
sin 26° - cos 64° =
=
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The value of the expression is 0 without calculation.
We have to find the exact value of
sin 26° - cos 26°
From the trigonometric function we know that:
cos (90°-Ф) = sinФ and,
sin(90° -Ф) = cosФ
By this, we have an expression that,
=sin 26° - cos 64°
=sin 26° - cos (90° - 26)
=sin 26° - sin 26°
=0
Therefore the value of sin 26° - cos 64° =0.
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A bedroom (14 ft by 12ft) and hallway (8ft by 3ft) are getting new wood flooring. Wood flooring is priced at $6.20 per square foot. How much will it cost to add the wood flooring?
If a bedroom (14 ft by 12ft) and hallway (8ft by 3ft) are getting new wood flooring. Wood flooring is priced at $6.20 per square foot. The amount it will cost to add the wood flooring is: $1,190.40.
Cost priceFirst step is to calculate the bedroom square feet
Bedroom square feet=14ft ×12ft
Bedroom square feet= 168 sq feet
Second step is to calculate hallway square feet
Hallway square feet=8ft × 3ft
Hallway square feet=24 sq feet
Third step is to calculate the total square feet
Total square feet=168+24
Total square feet=192
Fourth step is to calculate the cost
Cost=$6.20× 192
Cost= $1,190.40
Therefore the amount it will cost to add the wood flooring is: $1,190.40.
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maths geometry
i just need 4)
i’ve worked everything else out
Step-by-step explanation:
good job then !
the first thing I see in the graphic is that
BG is half of BD (as a major definition of diagonals in a parallelogram).
BD on the other hand is the Hypotenuse (the side opposite of the 90° angle at A) of the triangle ABD.
to be able to use Pythagoras to get BD, I need to find the length of AB.
this I get from the triangle ABE. this is also a right-angled triangle. AE = 4cm. the angle B1 = 50°. the angle A = 90°.
so, the angle E1 = 180 - 90 - 50 = 40° (remember, the sum of all angles in a triangle is always 180°).
now we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles.
so, we have here
AE / sin(50) = AB / sin(40)
4 / sin(50) = AB / sin(40)
AB = 4×sin(40) / sin(50) = 3.356398525... cm
so (Pythagoras),
BD² = AB² + AD² = 3.356398525...² + 9² =
= 11.26541106... + 81 = 92.26541106...
BD = 9.60548859... cm
BG = BD/2 = 4.802744295... cm
and now look at that.
because of the fact that I did not have to go through the other points, I chose the first approach that went through my mind.
and it showed that your teacher created an impossible (contradicting) scenario :
the angle of B1 does not fit to the ratios of the various line segments.
as you correctly calculated CD as 3 cm, that must mean that AB is also 3 cm.
that makes
BD² = 9² + 3² = 81 + 9 = 90
BD = 9.486832981... cm
BG = BD/2 = 4.74341649... cm
PLEASE, USE THIS VALUE.
there is a difference to my previous calculation. and the reason for this is : the 50° for B1 are not correct.
with AE = 4, AB = 3 and then BE = 5, we get
AE / sin(B1) = BE / sin(A)
4 / sin(B1) = 5 / sin(90) = 5
sin(B1) = 4/5 = 0.8
B1 = 53.13010235...°
and not 50° !!!!
Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 253.63 miles on a business trip, what
is his mileage reimbursement?
Answer:
17.75
Step-by-step explanation:
253.63 ×0.07=17.7541
