In the next four questions, complete the proof of the converse of Theorem 37 (The diagonals of a rectangle are congruent.) by selecting the best reason or statement.
Answers
Answer:
Step-by-step explanation:
1) WXYZ is a rectangle 1. Given
2) ∠Z ≅ ∠Y 2. Definition of rectangle
3) WZ ≅ XY 3. Definition of rectangle
4) ZY ≅ ZY 4. Reflexive property
5) ΔWZY ≅ ΔXYZ 5. SAS
6) WY ≅ XZ 6. CPCT -Corresponding parts of congruent triangles
The diagonals of rectangle are congruent
Related Questions
You’ve just moved into a new home and are decorating it with furniture. You head to Target and see a dining room table for $425, but everything is on sale for 20% off. What is the amount of the discount? What is the cost of the table after the discount?
Answers
Answer:
Amount of Discount: 85, Discounted cost of item: 340
Step-by-step explanation:
You Start by dividing the main price of the item by 100
You then multiply your answer from that by however much the discount is.
We divide by 100 because there is 100 percent when you are paying full price, dividing by 100 gives you the amount that is equal to 1 percent of that price
You then multiply the answer from that by 20, this will give you 20% of the full price, this will give you a discount of 85 Dollars.
To find the Discounted price you then subtract 85 from 425 and you will have an answer of 340 dollars. Hope this helps!
Please answer this question now
Answers
Answer:
e =7.1
Step-by-step explanation:
[tex]Hypotenuse = 10\\Opposite =e\\Adjacent =7\\\\Using\:Pythagoras\:Theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\10^2 =e^2 + 7^2\\100 =e^2+49\\100-49=e^2\\\\51 =e^2\\\sqrt{51} =\sqrt{e^2}\\ e = 7.141\\\\e = 7.1[/tex]
A bus traveled 40 miles during the second hour of a trip. This was 1/3 more than the distance traveled during the first hour. In the third hour the bus traveled a distance that was 1/4 more than in the second hour. What was the total distance that the bus traveled in 3 hours
Answers
Answer:
120 miles
Step-by-step explanation:
Distance in 2nd hour: 40 miles
Distance in 1st hour:
40/(4/3) = 30 miles
Distance in 3rd hour:
(5/4) * 40 = 50 miles
Total distance:
40 + 30 + 50 = 120 miles
Help me with 5c-4c+c
Answers
5c-4c+c=2c
Step-by-step explanation:
Since there is only addition and subtraction and no other operations, just work from left to right.
5c-4c = c
c+c=2c
Done!
Answer:
2c
Step-by-step explanation:
Because this whole equation consists of numbers with c's and addition and subtraction, you can just add and subtract as if they were regular numbers!
5c-4c+c
c+c
2c
Hope this helped!! :)
Calcule o valor dos produtos a) (-4). (-7/8) b) (-4). (-7/8) n sei pq tá repetido tá aqui na folha ;-; c) (-4).(+ 3,5) d) (-2).(-3/4). (-1/7) PRA HOJEE
Answers
Answer:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Step-by-step explanation:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
É repetido talvez com sinal alterado para mostrar a diferença na resposta. Se o sinal for alterado, a resposta também se tornará negativa. Seria - 28/8.
Quando um número negativo é multiplicado por um número negativo, obtém um número positivo. Mas quando um número positivo é multiplicado por um número negativo, dá uma resposta negativa.
Sempre se lembre
negativo * negativo = positivo
positivo * negativo = negativo
negativo * positivo = negativo
positivo * positivo = positivo
Em palavras simples, dois sinais diferentes dão um sinal negativo e dois sinais semelhantes dão um sinal positivo na multiplicação.
English
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Its repeated maybe with a changed sign to show the difference in the answer. If the sign is changed the answer would also become negative . It would become - 28/8.
When a negative number is multiplied with a negative number it gives a positive number. But when a positive number is multiplied with a negative number it gives a negative answer.
Always remember
negative * negative= positive
positive *negative=negative
negative *positive =negative
positive * positive = positive
In simple words two unlike signs give a negative sign and two similar signs give a positive sign in multiplication.
According to a commercial, 4 out of 5 dentist recommend a certain brand of toothpaste. Suppose There are 120 dentist in your area. What is the expected number of dentist who recommend the brand? What is the standard deviation?
Answers
4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.
If f'(x) = 12x^3 - 2x^2 - 17 and f(1) = 8 , find f(x).
Answers
Answer:
f(x) = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + [tex]\frac{68}{3}[/tex]
Step-by-step explanation:
To find f'(x), we will follow the steps below:
We will start by integrating both-side of the equation
∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx
f(x) = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + C
Then we go ahead and find C
f(1) = 8
so we will replace x by 1 in the above equation and solve for c
f(1) = 3(1)⁴ - [tex]\frac{2(1)^{3} }{3}[/tex] - 17(1) + C
8 = 3 - [tex]\frac{2}{3}[/tex] - 17 + C
C =8 - 3 + 17 + [tex]\frac{2}{3}[/tex]
C = 22 + [tex]\frac{2}{3}[/tex]
C =[tex]\frac{66 + 2}{3}[/tex]
C = [tex]\frac{68}{3}[/tex]
f(x) = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + [tex]\frac{68}{3}[/tex]
Small roads with lower speed limits are known as:
O A. interstate highways.
O B. secondary roads.
C. streets
O D. county roads.
Answers
Answer:
B. secondary roads
Step-by-step explanation:
While all of streets, county roads, and secondary roads are generally designed to carry less traffic and/or have lower speed limits than interstate highways, the generic name for such roads is ...
secondary roads.
What is the coefficient of the second term in the expression 12x+xy-7y?
Answers
Answer:
1
Step-by-step explanation:
GRADE
Perimeter: Change in Dimensions
A rectangle ABCD has a width of 3 inches and a length of 7 inches.
a) What is the Perimeter of the rectangle?
BINDEX
b) What is the Perimeter of the new rectangle if you double the width of rectangle ABCD? How did you find
it? How many times bigger or smaller did the new Perimeter get? (You can divide the new Perimeter over the
old one to find the times of increase/decrease)
c) What is the Perimeter of the new rectangle if you double the width and length of rectangle ABCD? How did
you find it? How many times bigger or smaller did the new Perimeter get compared to the perimeter of
rectangle ABCD?
d) Now choose a different shape of your liking and give it your own dimensions. Answer questions a), b), c)
and d) for the shape you chose.
e) Can you generalize what happens to the Perimeter if you change one of the dimensions of a shape and
what happens when you change both dimensions of the shape?
lick "Create lournal Fntn" tn antar un
Answers
Answer:
A) 20 in
B) 26 in and it got bigger by 1.3 times
C) 40 in and it got bigger by 2 times
Step-by-step explanation:
A) so the formula for finding perimeter is P= 2(L+W) so its (3+7)*2 = 20
B) if you double 3, 3*2=6 then it is 2*(6+7) = 26. 26/20= 13/20= 1.3 times more
C) if you double 3, 3*2=6 and 7, 7*2= 14 then it is (14+6)*2 = 40. 40/20=2/1 = 2 times more.
Also i couldnt solve D for you but try to solve it using what I wrote below.
Hope it helps :)
Nine less than five times a number is three more than twice the number?
Answers
Answer:
x = 4
Step-by-step explanation:
5x-9 = 2x+3
3x = 12
x = 4
Answer:
4
Step-by-step explanation:
A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people.
If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
a. Different sample proportions would result each time, but for sample size 100 they would be centered (have their mean) at the true population proportion, whereas for sample size 900 they would not.
b. For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be 0.
c. Different sample proportions would result each time, but for sample size 900 they would be centered (have their mean) at the true population proportion, whereas for sample size 100 they would not.
d. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
Answers
answer:
choice letter b
please heLp :’) thank you
Answers
Answer:
A
Step-by-step explanation:
Just like in the last problem, we have a right triangle but in this case, x is a leg, 10 / 2 = 5 is the other leg, and 13 is the hypotenuse. Using the 5 - 12 - 13 Pythagorean Triple, we know that x = 12.
Mr. Johnson has $15,000 to invest. Part of it is put in the bank at 4 percent, and part he puts in a savings and loan at 7 percent. If his yearly (simple) is $951, how much did he invest at each rate?
Answers
Answer:
$3300 at 4%
$11700 at 7%
Step-by-step explanation:
Total investment = $15000
Total simple interest on investment = $951
Investment A:
Rate = 4% =0.04
Investment B:
Rate = 7% =0.07
Simple interest (S. I) = principal * rate * time
(S. I on investment A + S. I on investment B)
Let principal amount in investment A = A
principal amount in investment B = B
(A * 0.04 * 1) + (B * 0.07 * 1) = $951
0.04A + 0.07B = $951 - - - - (1)
A + B = $15000 - - - - (2)
from (2)
A = 15000 - B
Substitute A = 15000 - B into (1)
0.04(15000 - B) + 0.07B = 951
600 - 0.04B + 0.07B = 951
600 + 0.03B = 951
0.03B = 951 - 600
0.03B = 351
B = 351 / 0.03
B = $11700
From (2)
A + B = $15000
A + $11700 = $15000
A = $(15000 - 11700)
A = $3300
12 miles below sea level
Answers
Answer:
In terms of figures, up to 12 nautical miles (22 km) from the coast, the sea belongs to the coastal state. In these territorial waters, anyone who fishes, finds an object or even an offense must submit to its laws. The coastal state can even suspend the right of a foreign country to navigate there
Step-by-step explanation:
The integer 12 can be written as -12 for 12 miles below sea level the answer is -12.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
An integer can be defined as a whole number it can be a negative whole number or a positive whole number for example: 2, 4, 1, -8, 0, etc.
It is given that:
The integer number is 12
Thus, the integer 12 can be written as -12 for 12 miles below sea level the answer is -12.
Write an integer for the situation: 12 miles below sea level
Learn more about the number here:
brainly.com/question/17429689
#SPJ2
Brock wants to compete for the featherweight boxing title, but the upper limit for that weight class is 126 pounds. He currently weighs 134 pounds. Brock can lose 3 pounds per day if he does vigorous workouts. The number of days, d, that Brock will need to work out to compete at the featherweight level is represented by the inequality 134 – 3d < 126. Select the fewest number of days he would have to work out to compete at the featherweight level. A. 1 B. 2 C. 3 D. 4 E. 5
Answers
Answer:
C. 3
Step-by-step explanation:
Brock weighs 134 pounds, he will lose 3 pounds a day until he is 126 pounds
D will represent the number of days he will work out.
134 - 3d < 126
134 - 3(3) < 126
134 - 9 = 125
125 < 126
3 days
We can say that Brock needs to workout for minimum 3 days to compete at feather weight level.
Which of the following options have the same value as 15 percent of 20?
Answers
Answer: A, C, D
(3/20)*20 = 0.15*20 = 3
0.15*20 = 3
(15/100)*20 = 0.15*20 = 3
all expressions lead to the same result of 3
another thing to notice
3/20 = 15/100 = 0.15 = 15%
which are multiple ways to say the same thing just in a different form
how would you solve for x here
Answers
Answer:
x=-1.30068.......
Step-by-step explanation:
x( 3x^2 - 2) = -4
Distribute
3x^3 - 2x = -4
Add 4 to each side
3x^3 - 2x +4 = 0
Plot using a graphing calculator
x=-1.30068.......
What the answer now fast
Answers
Answer:
45°
Step-by-step explanation:
This is right triangle with equal legs of √31
Since two sides are equal and the angle between them is 90°, other angles are equal and their value is:
(180°- 90°)/2= 45°Answer is m∠V= 45°
answer pls in the pic
Answers
Answer:
Hey there!
6 increased by a scale factor of 1.5 is 9.
9 increased by a scale factor of 1.5 is 13.5.
Thus, the area would be 9 times 13.5, or 121.5
Hope this helps :)
Answer:
121.5 [tex] {in}^{2} [/tex]Step-by-step explanation:
Let's find the enlarged area:
[tex] = {(scale \: factor)}^{2} \times original \: area[/tex]
Plug the values
[tex] = {(1.5)}^{2} \times 6 \times 9[/tex]
Evaluate the power
[tex] = 2.25 \times 6 \times 9[/tex]
Calculate the product
[tex] = 121.5 \: {in}^{2} [/tex]
Hope this helps...
Best regards!!
What type of right triangle would you use this formula for and why?
c=2a
Answers
Answer:
30 60 90 triangle
the hypotenuse is twice the length of the shorter leg length.
Find the missing angle measures in the given rhombus.
Answers
Answer:
1 = 4 = 38°, 2 = 3 = 90°
Step-by-step explanation:
Because the diagonals of rhombi are perpendicular, ∠2 = ∠3 = 90°. Since the sum of angles in a triangle is 180°, ∠1 = 180° - 52° - 90° = 38°. If we look at the triangle with 1 and 4 as its base angles, we notice that it's an isosceles triangle, therefore ∠1 = ∠4 = 38°.
Answer:
Step-by-step explanation:
In rhombus, diagonals are perpendicular to each other.
∠2 = ∠3 = 90°
52° + ∠1 + ∠ 2 = 180° { Angle sum property of triangle}
52 + ∠1 + 90 = 180
∠1 + 142 = 180
∠1 = 180 - 142
∠1 = 38°
∠4 = ∠1 = 38° { Isosceles triangle}
Pleas answer it now in two minutes
Answers
Answer:
30
Step-by-step explanation:
cos^-1(square root of 3 divided by 2)
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds out he is off course and 160 miles from island B. What bearing should he turn to, so he is heading to island B?
Answers
CHECK THE COMPLETE QUESTION BELOW
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?
A. 111.65
B. 119.84
C. 21.65
D. 135.53
Answer:
OPTION A IS CORRECT
A. 111.65
Step-by-step explanation:
This question can be explained using a triangle, let us say triangle ABD
and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .
We will be making use of cosines rule to calculate our angles, and we know that from cosine rule
D² = a² + b² -2abCosD
Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles
250²= 60² + 260² - 2(160*260)Cos(D)
62500= 625600+ 67600- 83200CosD
83200CosD= 25600+ 67600 - 625600
83200CosD= 30700
CosD= 30700/83200
CosD= 0.369
D= cos⁻¹ (0.369)
D=68.35
Therefore, the angle inside the triangle is 68.35°
Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )
Then the angle he would turn will be external angle of the triangle - 68.35°
= (180 - 68.35)
= 111.65°
Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.
If 300men can do a piece of work in 16days,how many men would do 1/5 of the work in 15days?
Answers
Answer:
60men
Step-by-step explanation:
300 men - 15 days - 1 work
men? - 15 days - 1/5 of work
When 1 man does 1/5 of work,
how many days needed = (15 × 1/5) × 300 = 900days
Men needed to complete 1/5 work in 15 days = 900 ÷ 15 = 60men
What is the approximate angle between two position vectors if their terminal points are (5, -2) and (7, 3)?
Answers
Hi,
Answer:
[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°
Have a good day.
Please help me with this question regarding TRIGONOMETRY!
Answers
Answer:
The answer is option 2.
Step-by-step explanation:
First, you have to find the length of CD using Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: θ = 48[/tex]
[tex]let \: oppo. = cd[/tex]
[tex]let \: adj. = ad = 110[/tex]
[tex] \tan(48) = \frac{cd}{110} [/tex]
[tex]cd = 110 \tan(48)[/tex]
[tex]cd = 122.17 \: feet[/tex]
Next, you have to find the length of BC using Sine Rule:
[tex] \sin(θ) = \frac{oppo.}{hypo.} [/tex]
[tex]let \: θ = 65[/tex]
[tex]let \: oppo. = cd = 122.17[/tex]
[tex]let \: hypo. = bc[/tex]
[tex] \sin(65) = \frac{122.17}{bc} [/tex]
[tex]bc = \frac{122.17}{ \sin(65) } [/tex]
[tex]bc = 134.8 \: feet \: (near.tenth)[/tex]
Answer:
[tex]\boxed{134.8 \: \mathrm{ft}}[/tex]
Step-by-step explanation:
Let’s take triangle ACD.
Find length CD.
tan θ = [tex]\frac{opposite}{adjacent}[/tex]
tan (48) = [tex]\frac{CD}{110}[/tex]
110 tan (48) = CD
CD ≈ 122.167
Let’s take triangle BCD.
Find length BC.
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (65) = [tex]\frac{122.167}{BC}[/tex]
BC = [tex]\frac{122.167}{sin(65)}[/tex]
BC ≈ 134.796
The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions of the rectangle. length and width.
Answers
Answer:
Length = 12 ftWidth = [tex] \frac{7}{2} ft[/tex]
Step-by-step explanation:
Given,
Area of rectangle = [tex]42 \: {ft}^{2} [/tex]
Width = X
Length = 2x + 5
Now,
[tex]x(2x + 5) = 42[/tex]
[tex]2 {x}^{2} + 5x = 42[/tex]
[tex]2 {x}^{2} + 5x - 42 = 0[/tex]
[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]
[tex]2x(x + 6) - 7(x + 6) = 0[/tex]
[tex](2x - 7)(x + 6) = 0[/tex]
Either
[tex]2x - 7 = 0[/tex]
[tex]2x = 0 + 7[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} [/tex]
Or,
[tex]x + 6 = 0[/tex]
[tex]x = 0 - 6[/tex]
[tex]x = - 6[/tex]
Negative value can't be taken.
So, width = [tex] \frac{7}{2} ft[/tex]
Again,
Finding the value of length,
Length = [tex]2x + 5[/tex]
[tex]2 \times \frac{7}{2} + 5[/tex]
[tex]7 + 5[/tex]
[tex]12[/tex]
Length = 12 ft
Answer:
length = 12 ft, width = 3.5 ft
Step-by-step explanation:
w = width
l = length = 2w + 5
A = wl = w(2w + 5) = 42
2w² + 5w - 42 = 0
(w + 6)(2w - 7) = 0
w + 6 = 0, w = -6 (dimension cannot be negative)
2w - 7 = 0, w = 3.5
l = 2(3.5) + 5 = 12
what is the 8th term of the geometric sequence with this explicit formula ?
Answers
Answer: C.) - 896
Step-by-step explanation:
Given the explicit formula :
An = 7 × (-2)^(n-1)
The 8th term of the geometric sequence using the formula will be :
n = 8
A8 = 7 × (-2)^(8-1)
A8 = 7 × (-2)^7
A8 = 7 × (-128)
A8 = - 896
HELP! 8TH GRADE MATH. I WILL NAME BRAINLIEST!!!
Answers
Answer:
Step-by-step explanation:
y = -|x| + 1
Start with the absolute value function: y = |x|. Reflect it over the x-axis by making it y = -|x|. Finally, shift up 1 unit by adding one, getting a final answer of y = -|x| + 1.