7.4
Practice A
In Exercises 1-5, the diagonals of rhombus ABCD intersect at E. Given that
mZEAD - 67', CE - 5, and DE 12, find the indicated measure.
1. MZAED
5
2. MZADE
E
12
3. MZBAE
67
44E
5. BE
In Exercises 6 and 7, find the lengths of the diagonals of rectangle JKLM.
6. JL = 3r + 4
7. JL = 2x - 6
KM = 4x - 1
KM
*+1
In Exercises 8 and 9, decide whether quadrilateral WXYZ is a rectangle, a
rhombus, or a square. Give all names that apply. Explain your reasoning.
8. W(3, 1), X(3,-2), Y(-5, -2), 2(-5, 1) 9. W(4, 1), X (1,4), Y(-2, 1), Z(1, -2)
Р
o
R
a
10. Use the figure to write a two-column proof.
Given: PSUR is a rectangle.
PQ E TU
Prove: OS = RT
S
U
11. In the figure, all sides are congruent and all angles are right angles.
B
a. Determine whether the quadrilateral is a rectangle.
Explain your reasoning.
b. Determine whether the quadrilateral is a rhombus.
Explain your reasoning
c. Determine whether the quadrilateral is a square.
Explain your reasoning.
d. Find m2AEB.
D
e. Find mZEAD.
Answers
The properties of the quadrilaterals gives the equivalent relations used
to find the lengths and the angles.
Response:
1. m∠AED = 90°
2. m∠ADE = 23°
3. m∠BAE = 67°
4. AE = 5
5. BE = 12
6. 19
7. 22
8. WXYZ is a rectangle
9. WXYZ is a square
10. [tex]\overline{QS} \cong \overline{RT}[/tex] by Corresponding Parts of Congruent Triangles Congruent, CPCTC
11. a. The diagonals are perpendicular and the given figure is not a rectangle
b. The given figure is not a rhombus
c. The figure is a square.
d. ∠AEB = 90°
e. m∠EAD = 45°
Which properties of a quadrilateral can be used to find the required dimensions?1. The diagonals of a rhombus bisect each other at right angles
Therefore;
m∠AED = 90° (by definition of right angles)
2. m∠EAD and m∠ADE are complementary angles
Which gives;
m∠EAD + m∠ADE = 90°
m∠ADE = 90° - m∠EAD
Therefore;
m∠ADE = 90° - 67° = 23°
3. The diagonals of a rhombus bisect the angles, therefore;
m∠BAE = m∠EAD = 67°
4. The diagonals bisect each other, therefore;
AE = CE = 5
5. BE = DE = 12
6. JL = 3·x + 4
KM = 4·x - 1
Which gives;
3·x + 4 = 4·x - 1
4·x - 3·x = 4 + 1 = 5
x = 5
KM = JL = 3 × 5 + 4 = 19
The lengths of the diagonals of rectangle JKLM is 197. JL = 2·x - 6
[tex]KM = \mathbf{\dfrac{3}{2} \cdot x+ 1}[/tex]
Which gives;
[tex]\frac{3}{2} \cdot x+ 1 = 2\cdot x - 6[/tex]
[tex]2\cdot x -\frac{3}{2} \cdot x = 6 + 1 = 7[/tex]
[tex]\dfrac{1}{2} \cdot x = 7[/tex]
x = 2 × 7 = 14
JL = 2 × 14 - 6 = 22
The lengths of the diagonals of rectangle JKLM are 228. W(3, 1), X(3, -2), Y(-5, -2), Z(-5, 1)
WX = 1 - (-2) = 3
YZ = 1 - (-2) = 3
XY = 3 - (-5) = 8
WZ = 3 - 5 = 8
Slope of WX = (1 - (-2)) ÷ (3 - 3) = ∞
Slope of YZ = (1 - (-2)) ÷ (-5 - (-5)) = ∞
Slope of XY = (-2- (-2)) ÷ (3- (-5)) = 0
Slope of WZ = (1- 1) ÷ (3- (-5)) = 0
Therefore;
WX and YZ are perpendicular to XY and WZ
The properties of WXYZ are the properties of a quadrilateral having perpendicular sides.
Given that the sides are not equal, the figure is a rectangle9. W(4, 1), X(1, 4), Y(-2, 1), Z(1, -2)
WX = √((4 - 1)² + (1 - 4)²) = 3·√2
YZ = √((1 - (-2))² + (-2 - 1)²) = 3·√2
XY = √((1 - (-2))² + (4 - 1)²) = 3·√2
WZ = √((1 - (-2))² + (4 - 1)²) = 3·√2
Slope of WX = (4 - 1) ÷ (1 - 4) = -1
Slope of YZ = (-2 - 1) ÷ (1 - (-2)) = -1
Slope of XY = (1 - 4) ÷ ((-2) - 1) = 1
Slope of WZ = (-2 - 1) ÷ (1 - 4) = 1
Therefore;
The lengths of the sides are equal and the sides are perpendicular to each other
Therefore;
WXYZ is a square10. The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
PSUR is a rectangle [tex]{}[/tex] Given
[tex]\overline{PR} = \overline{SU}[/tex] [tex]{}[/tex] Opposite sides of a rectangle
[tex]\overline{PQ} \cong \overline{TU}[/tex] [tex]{}[/tex] Given
[tex]\overline{PQ} = \overline{TU}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{PR} = \overline{RQ} + \overline{PQ}[/tex] [tex]{}[/tex] Segment addition postulate
[tex]\overline{SU} = \overline{ST} + \overline{TU}[/tex] [tex]{}[/tex] Segment addition postulate
[tex]\overline{RQ} = \overline{ST}[/tex] [tex]{}[/tex] Addition property of equality
ΔPQS ≅ ΔTUR [tex]{}[/tex] ASA rule of congruency
[tex]\overline{QS} \cong \overline{RT}[/tex] [tex]{}[/tex] CPCTC
11. The properties of a rectangle are;
The interior angles are 90°
The diagonals are not perpendicular to each other
In the given figure, the four triangles formed by the diagonals are congruent, therefore;
The angles at the vertex point of the four tringles are equal to each other and therefore, equal to 90°
Therefore;
The diagonals are perpendicular and the given figure is not a rectangleb. The lengths of the diagonals, are equal, therefore;
The given figure is not a rhombuse. The properties of the figure, which includes;
All sides are equal
The interior angles are 90°
The diagonals are equal and bisect each other at 90° indicate that the figure is a squared. The diagonals of a square are angle bisectors of the interior angles
Therefore;
m∠ABE = m∠CBE
m∠ABE + m∠CBE = 90° by definition of complementary angles
Therefore;
m∠ABE = 90° ÷ 2 = 45°
Similarly;
m∠ABE = m∠BAE = 45°
m∠AEB = 180° - (m∠ABE + m∠BAE)
m∠AEB = 180° - (45° + 45°) = 90°e. m∠EAD = m∠BAE = 45° (angles formed by the diagonal AC)
Learn more about quadrilaterals here:
https://brainly.com/question/12635945
Related Questions
20 points do all thanks
Answers
Answer:
so you don't have to give me points but I can explain how to do it
Step-by-step explanation:
so for number 1. it says y=3x-7 and the equation is 5x+4y=6
so basically your plugging in y so
5x+5(3x-7)=6 and you will get your answer
Find cot and cos
If sec = -3 and sin 0 > 0
Answers
Answer:
Second answer
Step-by-step explanation:
We are given [tex]\displaystyle \large{\sec \theta = -3}[/tex] and [tex]\displaystyle \large{\sin \theta > 0}[/tex]. What we have to find are [tex]\displaystyle \large{\cot \theta}[/tex] and [tex]\displaystyle \large{\cos \theta}[/tex].
First, convert [tex]\displaystyle \large{\sec \theta}[/tex] to [tex]\displaystyle \large{\frac{1}{\cos \theta}}[/tex] via trigonometric identity. That gives us a new equation in form of [tex]\displaystyle \large{\cos \theta}[/tex]:
[tex]\displaystyle \large{\frac{1}{\cos \theta} = -3}[/tex]
Multiply [tex]\displaystyle \large{\cos \theta}[/tex] both sides to get rid of the denominator.
[tex]\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}[/tex]
Then divide both sides by -3 to get [tex]\displaystyle \large{\cos \theta}[/tex].
Hence, [tex]\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}[/tex]
__________________________________________________________
Next, to find [tex]\displaystyle \large{\cot \theta}[/tex], convert it to [tex]\displaystyle \large{\frac{1}{\tan \theta}}[/tex] via trigonometric identity. Then we have to convert [tex]\displaystyle \large{\tan \theta}[/tex] to [tex]\displaystyle \large{\frac{\sin \theta}{\cos \theta}}[/tex] via another trigonometric identity. That gives us:
[tex]\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}[/tex]
It seems that we do not know what [tex]\displaystyle \large{\sin \theta}[/tex] is but we can find it by using the identity [tex]\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}[/tex] for [tex]\displaystyle \large{\sin \theta > 0}[/tex].
From [tex]\displaystyle \large{\cos \theta = -\frac{1}{3}}[/tex] then [tex]\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}[/tex].
Therefore:
[tex]\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}[/tex]
Then use the surd property to evaluate the square root.
Hence, [tex]\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}[/tex]
Now that we know what [tex]\displaystyle \large{\sin \theta}[/tex] is. We can evaluate [tex]\displaystyle \large{\frac{\cos \theta}{\sin \theta}}[/tex] which is another form or identity of [tex]\displaystyle \large{\cot \theta}[/tex].
From the boxed values of [tex]\displaystyle \large{\cos \theta}[/tex] and [tex]\displaystyle \large{\sin \theta}[/tex]:-
[tex]\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}[/tex]
Then rationalize the value by multiplying both numerator and denominator with the denominator.
[tex]\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}[/tex]
Hence, [tex]\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}[/tex]
Therefore, the second choice is the answer.
__________________________________________________________
Summary
Trigonometric Identity[tex]\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}[/tex]
Surd Property[tex]\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}[/tex]
Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.
4. Which is an algebraic expression for the word phrase "8 less than the product of 12 and a
number x?
Answers
Answer:
12x-8
Step-by-step explanation:
Answer:
12x-8
Step-by-step explanation:
Help see file...............................
Answers
Color combinations used in a presentation
2
The overall look of a presentation
4
A typeface without decorative extensions on the ends of the letters
5
The difference between objects
3
A tool used in presentation planning
1
A sports club includes 350 members.
200 members play football (F).
130 members play basketball (B).
70 members of those who play basketball DO NOT play football.
a. Fill in the Venn diagram below.
Answers
Step-by-step explanation:
You need to find the n( A n B ) and then continue the process, if you have any question revert back to me...
a town has a population of 10000 and growns at 2.5% every year what will be the population in 7 years
Answers
Answer:
The population after 7 years will be 11887
Step-by-step explanation:
Given
Population = P_0 = 10000
Growth Rate = r = 2.5%
Time = t = 7
The formula for calculating the population after given time at given rate is:
The population after 7 years will be 11887
Step-by-step explanation:
Jacinta drove her car from the mountains into the desert. She travelled from
an altitude of 4,450 feet above sea level to an altitude of 150 feet below sea level.
Jacinta drove at a constant speed and the trip took her five hours. Which
statement is true about her rate of change in elevation?
A She descended at a rate of 920 feet per hour.
B She ascended at a rate of 860 feet per hour.
C She ascended at a rate of 920 feet per hour.
D She descended at a rate of 860 feet per hour.
Answers
The statement that is true about her rate of change in elevation is She descended at a rate of 920 feet per hour.
How to calculate the rate of changeFrom the question, Jacinta traveled from an altitude of 4,450 feet above sea level to an altitude of 150 feet below sea level, then the total distance traveled will be
D = 4450 + 150
D = 4600 feet
If Jacinta drove at a constant speed and the trip took her five hours, her rate will be expressed as:
Rate = Total distance/Time
Rate = 4600/5
Rate = 920 feet perhour
Hence the statement that is true about her rate of change in elevation is She descended at a rate of 920 feet per hour.
learn more on rate of change here: https://brainly.com/question/8728504
solve and simplify 6 2/3 x 3 1 /2
Answers
[tex]6 \frac{2}{3} = \frac{2}{18} = 9[/tex]
[tex]3 \times \frac{1}{2} = \frac{1}{6} = 6[/tex]
6×9=54
Which expression represents a way to find the value 4 x 2 x 6?
Answers
Answer:
Step-by-step explanation: well the anwser is 48
given right triangle abc with altitude bd drawn to hypotenuse ac.If AB=6 and AD=3 what is the length of AC
Answers
Answer:
Step-by-step explanation:
[tex]\frac{6}{3}=\frac{AC}{6}\\AC=12[/tex]
Is the answer to -341.75 • the square root of 81 rational or irrational !!!!
Answers
=-341.75 x ±9
= -341.75 x 9 or -341.75 x -9
= -3075.75 or 3075.75
Hence is a rational number since it can be expressed as a quotient or fraction of two integers i.e -3075.75=-12303/4 or 12303/4
HELP ASAP PWESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answers
Khan Academyyyyyyyyyyyyyyyy
Answers
Answer:
(© 105 + 90 = (52 - 70)
Step-by-step explanation:
hey! im still confused on how 3(x+4)=36 can be solved with the distributive property... can you help me?
Answers
The distributive property is basically expanding brackets.
So if you take 3(x + 4) = 36 and remove the brackets (so multiplying out the 3), you get:
3x + 12 = 36
And from there you simplify :)
3x + 12 = 36
3x = 24
x = 8
The distributive property was used to multiply the 3 through the brackets, thus making the equation easier to solve I guess
Step-by-step explanation:
Which is the logarithmic form of 25 = 52? log25 = 25 log252 = 5 log525 = 2 log52 = 25.
Answers
The value of the logarithm function log₅25 is 2. Then the correct option is C.
What is a logarithm?Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic form of 25 will be
We know that if the base of the logarithm is the same as the number then the value of the logarithm will be 1 one that is given as
[tex]\rm log_a a = 1[/tex]
Then take the log with the base value of 5.
log₅25 = log₅5²
log₅25 = 2 × log₅5
log₅25 = 2
The value of the logarithm function log₅25 is 2. Then the correct option is C.
More about the logarithm link is given below.
https://brainly.com/question/7302008
Answer:
c
Step-by-step explanation:
Identify the area of OK in terms of pi
radius is 7 cm
Answers
Answer:
K=49π cm^2
Step-by-step explanation:
Area of a circle: πr^2
r=7
7^2=49
Therefore, the answer is 49πcm^2
Multiply 34.92 and 0.56 *
1 point
A. 19.5
B. 19.5552
C. 19.55
D. 19.52
Answers
Answer:
19.5552
Step-by-step explanation:
34.92 x 0.56
Use calculator or use long multiplication.
3492
×56
20952
+17460
195552
How many numbers are after the point on both of the numbers?
2 each. 2 + 2 = 4
We will take our result 4 points back or divide it by 10^4
195552 / 10000 = 19.5552
What is the value of P ? 45/20= 40.5/P?
Answers
Answer:
P=18
Step-by-step explanation:
45/20= 40.5/P
45p=810
p=18
1. If the measure of angle D=162º and
angle C=122° Angle A= B=
2. If the measure of angle D=171° and
angle C =128° Angle A= B=
3. If the measure of angle A=22° and
angle B =35° Angle C= D=
4. If the measure of angle A= 20° and
angle B =29° Angle C= D=
Answers
Answer:
1.= 178 2.= 165 3.= 93 4.= 46
Step-by-step explanation: If you read the letter coordations and minus the orbs and graphs then you would get your first answer then you would multiply it by the same number. hope this helps :)
It is well-documented that watching TV, working on a computer, or any other activity involving artificial light can be harmful to sleep patterns. Researchers wanted to determine if the artificial light from e-Readers also disrupted sleep. In the study, 12 young adults were given either an iPad or printed book for four hours before bedtime. Then, they switched reading devices. Whether the individual received the iPad or book first was determined randomly. Bedtime was 10 P.M. and the time to fall asleep was measured each evening. It was found that participant took an average of 10 minute s longer to fall asleep after reading on an iPad. The P-value for the test was 0.009.
(a) What is the research objective?
(b) What is the response variable? It is quantitative or qualitative?
(c) What is the treatment?
(d) Is this a designed experiment or observational study? What type?
(e) The null hypothesis for this test would be that there is no difference in time to fa ll asleep with an e-Reader and print ed book. The alternative is that there is a difference. Interpret the P-value.
Answers
Answer:
(a) the objective is to determine if the artificial light from e-Readers also disrupted sleep.
sorry thats all i know
You are taking a class in which your grade is determined from: Quizzes: 15%
Exam (3): 15% for each
Homework: 10%
Final: 30%
Your scores are: Average quiz mean = 85 Exam = 78,81, 92 Homeworks mean = 85 Your final = 89
If the minimum average for B + is 87, did you get B + at the end of the semester. (Show your working.)
Answers
Answer:
No, you did not get a B+, you got an 85.6% for the class
Step-by-step explanation:
So, let's split the grades into different parts:
Quiz: 15%
Exam1: 15%
Exam2: 15%
Exam3: 15%
Homework: 10%
Final: 30%
Each part of the grade adds up together to be 100%, so here, we are going to multiply each weighting of the grade with the average amount of points you got for each assignment then add it all up.
(Notice how I convert the percentages to decimals to make it easier to multiply)
Quiz: 0.15(85) = 12.75
Exam1: 0.15(78) = 11.70
Exam2: 0.15(81) = 12.15
Exam3: 0.15(92) = 13.80
Homework: 0.10(85) = 8.50
Final: 0.3(89) = 26.70
Adding these all up:
12.75 + 11.70 + 12.15 + 13.80 + 8.50 + 26.70 = 85.6
You got an 85.6% for the class, which is not a B+
Feel free to ask any questions you may have in the comments! :D
I need help with Rational Functions
Answers
Answer: 105 minutes
Step-by-step explanation:
The volume of a cylinder is given by v, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this can?
Answers
Answer:
V= π r2h
is this right
The axis of symmetry for the graph of the function f(x)=3x2 bx 4 is x equals three-halves. What is the value of b?.
Answers
The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 , the value of b is -9.
What is an axis of symmetry?
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.
Given
The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 .
The axis of the symmetry is given by;
[tex]\rm x=\dfrac{-b}{2a}[/tex]
The value of x is 3/2 and a is 3.
Substitute all the values in the formula
[tex]\rm x=\dfrac{-b}{2a}\\\\\dfrac{3}{2}=\dfrac{-b}{2 \times 3}\\\\\dfrac{3}{2}=\dfrac{-b}{6}\\\\ -b = \dfrac{6 \times 3}{2}\\\\ b = \dfrac{=18}{2}\\\\b =-9[/tex]
Hence, the value of b is -9.
To know more about the axis of symmetry click the link given below.
https://brainly.com/question/12896816
5 – 4 + 7x +1 = __x + __
Fill in the blanks to get no solutions
Answers
Answer: 7, 2 in order.
Step-by-step explanation:
We can combine like terms.
5 - 4 + 1 = 2.
Therefore, 5 - 4 + 7x +1 = 7x + 2.
Thus, the blanks are 7, 2 in order.
Answer:
7x + 2
Step-by-step explanation:
5-4 +7x +1
= 7x+1+5-4
= 7x + 2
HELLPPPP PLEASE!
What is the probability of drawing a face card (jack, queen, king) from a standard deck of 52 playing cards?
Enter your answer as a fraction, like this: 42/53
Answers
Answer:
12/52 or 3/13
Step-by-step explanation:
So lets go over what we know:
There are 12 face cards in a deck of cards
There are 52 cards in a deck
So there are 12 face cards out of 52 cards.
The ratio of this is:
12 : 52
This looks like this in fraction form:
[tex]ratio1 : ratio2[/tex] = [tex]\frac{ratio1}{ratio2}[/tex]
So the ratio 12 : 52 = [tex]\frac{12}{52}[/tex]
So the answer is 12/52(this can be simplified to 3/13)
Hope this helps!
What is the exact circumference of a circle with a radius of 15 cm?
o 10 pi cm
o 15 pi cm
o 30 pi cm
o 60 pi cm
Answers
Answer:
(C) 30πcm
Step-by-step explanation:
In order to find circumference you use the formula C (circumference)=2(pi)(r) in which r is the radius. In this case, two and 15 are thirty so to find the circumference all you have is the equation 30 times pi centimeters is equal to the Circumference.
WORTH 50 POINTS FIND THE VALUE OF X
Answers
Answer:
D) 10
Step-by-step explanation:
Singe a right triangle has to be 90 degrees, 60+(3*10)=90:)
therefore x=10
Answer:
D
Step-by-step explanation:
the angles 60 and 3x form a right angle , then
60 + 3x = 90 ( subtract 60 from both sides )
3x = 30 ( divide both sides by 3 )
x = 10 → D
express $12.00 as a fraction of $20.00
Answers
Answer:
12/20 = 6/10 = 3/5Step-by-step explanation:
laptop screens are determined by the length of the diagonal portion of the screen rounded to the nearest whole number the laptop screen is 16.5 inches wide and 10.5 in tall calculate the screen size?
