73. Given PQRS is a parallelogram.
PR bisects Angle SPQ and Angle QRS.
SQ bisects Angle PSR and Angle RQP.
Prove PQRS is a rhombus.
Answers
Answer:
See explanation
Step-by-step explanation:
PQRS is a parallelogram, then
[tex]PQ\parallel RS\\ \\QR\parallel SP[/tex]
and
[tex]PQ\cong RS\\ \\QR\cong SP[/tex]
Also
[tex]\angle P\cong \angle R\\ \\\angle Q\cong \angle S[/tex]
1. Consider triangles PQA and RQA, where A is the diagonals intersection point. In these triangles,
[tex]QA\cong QA\ [\text{Reflexive property}][/tex]
[tex]\angle PQA\cong \angle RQA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle QPA\cong \angle QRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PQA and RQA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PQ\cong RQ[/tex]
2. Consider triangles PSA and RSA. In these triangles
[tex]SA\cong SA\ [\text{Reflexive property}][/tex]
[tex]\angle PSA\cong \angle RSA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle SPA\cong \angle SRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PSA and RSA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PS\cong RS[/tex]
3. Since [tex]PQ\cong RS[/tex] and [tex]PQ\cong RQ[/tex], you have [tex]RS\cong RQ[/tex]
Therefore,
[tex]PQ\cong QR\cong RS\cong SP[/tex]
Parallelogram with all congruent sides ia a rhombus.
Related Questions
Charles rode his bike 19 miles each week while training. Here is his record of the number of miles he rode. Monday 2.2 mi Tuesday ? Wed 3.8 miles, Thursday ? and Friday 5.4 miles
Answers
Answer:
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training.
Correct statement and question:
Charles rode his bike 19 miles each week while training. Here is his record of the number of miles he rode Monday 2.2 miles Tuesday? Wednesday 3.8 miles Thursday ? Friday 5.4 miles Charles rode 1.6 miles more on Thursday than Tuesday . Find the number of miles he rode on Tuesday and Thursday
Source:
Previous question that can be found at brainly
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Miles per week Charles rode his bike = 19
Miles every Monday Charles bikes = 2.2
Miles every Tuesday Charles bikes = ?
Miles every Wednesday Charles bikes = 3.8
Miles every Thursday Charles bikes = ?
Miles every Friday Charles bikes = 5.4
Charles rode 1.6 miles more on Thursday than Tuesday
2. Find the number of miles he rode on Tuesday and Thursday.
x = Miles Charles rides every Tuesday
1.6 + x = Miles Charles rides every Thursday
Now, we can write our equation to solve for x, this way:
2.2 + x + 3.8 + x + 1.6 + 5.4 = 19
2x + 13 = 19
2x = 19 - 13
2x = 6
x = 3 ⇒ x + 1.6 = 4.6
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training
Answer:
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training.
Step-by-step explanation:
It's right I checked.
The difference of two numbers is 8 and thier quotient is 3
Answers
Answer:
x=12, y=4. (12, 4).
Step-by-step explanation:
x-y=8
x/y=3
--------
x=y+8
(y+8)/y=3
y+8=3y
8=3y-y
8=2y
y=8/2
y=4
x-4=8
x=8+4
x=12
x=12, y=4. (12, 4) is the two numbers.
What is the quotient?1: the number resulting from the division of one numeral by another.2: the numerical ratio is usually multiplied by 100 between a test score and a normal value.Here given that,
The difference between the two numbers exists at 8 and their quotient stands at 3.
Step 1
x-y=8
x/y=3
--------
x=y+8
(y+8)/y=3
y+8=3y
Simplifying,
8=3y-y
8=2y
y=8/2
Hence,
y=4
x-4=8
x=8+4
Thus,
x=12
Therefore, x=12, y=4. (12, 4) is the two numbers.
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construct a parallelogram whose sides BC=3.5cm CD=4cm BD=5.2cm
Answers
Answer:
Cd=4cm
Step-by-step explanation:
Properties. convex. In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. And Try TutorMe IS THE BEST WEBSIT AND PLZ MAKE ME THE Brainliest
If a point is chosen inside the circle, what is the probability that it will also be inside the square?
Answers
The probability that a point chosen inside a circle will also be inside a square is π/4.
Explanation:The probability that a point chosen inside a circle will also be inside a square can be determined by comparing the areas of the circle and the square. Let's assume that the circle has a radius of r and the square has sides of length 2r. The area of the circle is πr2 and the area of the square is (2r)2 = 4r2. Therefore, the probability of the point being inside the square is given by the ratio of the area of the circle to the area of the square: P = (πr2) / (4r2) = π/4.
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x + 3y = 5
-x + 6y = 4
Solve the system of equations.
A) x = 1, y = 2
B) x = 2, y = 1
Eliminate
C) x = 1, y = 1
D) x = 0, y = 2
Answers
Answer:
B) x =2 y = 1
Step-by-step explanation:
GIVING BRAINLIEST pls explain, Consider these proportions: 1:3 1.5:4.5 2:6 2.5:7.5 Which of the following proportions belongs to the above set? A 5:15 B 6:21 C 7:21 D 8:34 a. A and B c. B and D b. A and C d. C and D
Answers
Answer:
B. A and C
Step-by-step explanation:
1:3, 1.5:4.5, 2:6, 2.5:7.5, 3:9, 3.5:10.5, 4:12, 4.5:13.5, 5:15, 5.5:16.5, 6:18, 6.5:19.5, 7:21
+.5:+1.5
hannah says that 1/8 is not on the number line and cannot be plotted. write a note to hannah about her misunderstanding
Answers
Answer and explanation :
Hannah said that [tex]\frac{1}{8}[/tex] is not on the number line but she is wrong because [tex]\frac{1}{8}[/tex] can be represented on the number line
When we convert the fraction [tex]\frac{1}{8}[/tex] into decimal then it is equal to 0.125
And 0.125 lies between 0 and 1
If we divide one unit on number line into 10 parts then 0.125 lie between 0.1 and 0.2
And we know that any real number can be represented on number line as 0.125 is a real number so it can be represented on the number line
Answer:
This number line represents all number. Although 1
8
is not labeled, it still exists on the number line and can be plotted. 1
8
is located halfway between 0 and 1
4
Step-by-step explanation:
The height of a cylinder is 5 centimeters. The circumference of the base of the cylinder is 16π centimeters. Which measurement is closest to the volume of the cylinder in cubic centimeters?
Answers
Answer:
1,005 cubic centimeters
Step-by-step explanation:
step 1
Find the radius of the base of cylinder
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=16\pi\ cm[/tex]
so
[tex]16\pi=2\pi r[/tex]
solve for r
[tex]r=8\ cm[/tex]
step 2
Find the volume
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=8\ cm\\h=5\ cm[/tex]
substitute
[tex]V=\pi (8)^{2}(5)[/tex]
[tex]V=320\pi\ cm^3[/tex] ----> exact value
Assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=320(3.14)=1,004.8\ cm^3[/tex]
so
The approximate value is [tex]1,005\ cm^3[/tex]
The volume of the cylinder in cubic centimeters is 251.2 cm^3
The volume of a cylinder is expressed as:
V = πr²hV = base area * heightGIven the following
Base area = 16π centimeters
Height = 5cm
Substitute into the formula to have:
V = 16(3.14) * 5
V = 251.2 cm^3
Hence the volume of the cylinder in cubic centimeters is 251.2 cm^3
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Solve: (x + 1)(x – 5) = 0
Answers
Answer:
x = -1 or 5
Step-by-step explanation:
From the expression (x +1) (x - 5)
We’re to solve for x.
Therefore,
x + 1 = 0
Subtract one from both sides
x + 1 - 1 = 0 - 1
x = -1
x - 5 = 0
Add five to both sides
x - 5 + 5 = 0 + 5
x = 5
The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= __?__
Answers
Answer:
x₁ = 1
x₂ = - 3/2
Step-by-step explanation:
2x² + x - 1 = 2
2x² + x - 1 - 2 = 0
2x² + x - 3 = 0
2x² + 3x - 2x - 3 = 0
x(2x + 3) - (2x + 3) = 0
(x - 1)(2x + 3) = 0
x - 1 = 0 => x₁ = 1
2x + 3 = 0 => 2x = - 3 => x₂ = - 3/2
Answer:
Step-by-step explanation:
hello :
look this solution
A basket contains 6 peaches and 8 plums. What is the ratio of peaches to total pieces of fruit.
Answers
Answer:
3:7
Step-by-step explanation:
A basket has:
6 peaches
8 plums
The total amount of fruits is
6+8= 14
The ratio of peaches to total pieces of fruit is:
6:14
3:7
Misha and Nora want to buy season passes for a ski lift but neither of them has the $225
needed to purchase a pass. Nora decides to get a job that pays $6.25 per hour. She has
nothing saved right now but she can work four hours each week. Misha already has $80 and
plans to save $15 of her weekly allowance. Who will be able to purchase a pass first?
Answers
State the first step in solving the equation. - 1/5y + 2 = -3
a. subtract two from both sides
b. multiply both sides by -1/5
c. divide both sides by -1/5
d. add two to each side
Answers
Find decimal notation 1.29%
Answers
1.29 % is converted to decimal as 0.0129
Solution:
"Percent" means "per 100" or "over 100"
To convert 1.29% to a decimal rewrite 1.29 percent in terms of per 100 or over 100
Given percentage is 1.29 %
1.29 % = 1.29 over 100
[tex]1.29 \% = \frac{1.29}{100}[/tex]
1.29 over 100 is the same as 1.29 divided by 100
Completing the division we get:
[tex]1.29 \% = \frac{1.29}{100} = 0.0129[/tex]
Thus the given 1.29 % is converted to decimal as 0.0129
What is the solution to this equation? x/-5=15
Answers
Answer:
x = -75
Step-by-step explanation:
x/-5=15
x = 15 x -5
x = -75
Answer:
-75
Step-by-step explanation:
Step by step solution :
Step 1 :
x
Simplify ——
-5
Equation at the end of step 1 :
x
—— - 15 = 0
-5
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using -5 as the denominator :
15 15 • -5
15 = —— = ———————
1 -5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • -1 - (15 • 5) -x - 75
————————————————— = ———————
5 5
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-x - 75 = -1 • (x + 75)
Equation at the end of step 3 :
-x - 75
——————— = 0
5
Step 4 :
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-x-75
————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-x-75 = 0
Solving a Single Variable Equation :
4.2 Solve : -x-75 = 0
Add 75 to both sides of the equation :
-x = 75
Multiply both sides of the equation by (-1) : x = -75
One solution was found :
x = -75
brainlest please
Marcus ran to the park and then walked to the store. He
ran 3 times as long as he walked. The total time spent
walking and running was 24 minutes. What equation is
used to solve for how long it took Marcus to walk from the
park to the store?
Answers
Answer:
Step-by-step explanation:
The answer is 24 x 3 or 3 x 24. It says that he ran 3 times and it took 24 minutes. 3 x 24 is 72
Answer:
Step-by-step explanation:
The answer is 24 x 3 or 3 x 24. It says that he ran 3 times and it took 24 minutes. 3 x 24 is 72
hope this helps
Which of these expressions is equivalent to log (9.4)?
O A. log (9) + log (4)
O B. log (9) - log (4)
O c. 9. log (4)
O D. log (9) • log (4)
Answers
The solution to the given expression is log (9) + log (4).
What is Logarithm?The logarithm function is defined as the inverse of exponential function. If b = e^(a) then a is defined as a = log(b).
The logarithm of the product of two numbers is equal to the sum of their individual logarithms. The logarithmic properties can be written as log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b) and log(aⁿ) = nlog(a).
The given expression is log(9 × 4).
It can be rewritten as,
log(9 × 4)
Use the property of the logarithm log(ab) = log(a) + log(b) to obtain,
log(9 × 4) = log(9) + log(4)
Hence, the given logarithmic expression can be solved as log (9) + log (4).
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A line represents a proportional relationship. Which set of points could be on the line? A) (−4, −2), (2, 1), (6, 3), (14,7) B) (6, 8), (4, 0), (18, 24), (20, 26) C) (3, 6), (4, 8), (9, 4), (11, 2) D) (1, 1), (2, 1), (3, 3), (4, 2)
Answers
Answer:
The answer for this question is a because it shows the proportional relationship of half of each number
Answer: B
Step-by-step explanation:
How do you find a volume of a cone?
Answers
Answer:
V = (1/3)πr²h
Step-by-step explanation:
The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.
Cylinder Volume = πr²h
Cone Volume = (1/3)πr²h
where r is the radius (of the base), and h is the height perpendicular to the circular base.
_____
Comment on area and volume in general
You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...
V = Bh . . . . . for an object with congruent parallel "bases"
V = (1/3)Bh . . . . . for a pointed object with base area B.
This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)
Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)
__
* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.
What fraction is equivalent to 4/12
Answers
fractions include 1/3,8/24,12/36 and so on
1/3 because 4÷4=1 and 12÷4=3 so it is a total of 1/3
Jimmy and his brother bought chocolate at the store. Jimmy bought a certain number of pieces, and his brother bought ten fewr than half the number Jimmy bought. Write an expression to represent how many pieces of cany Jimmy's brother bought.
Answers
Answer:
Lets say Jimmy is represented by J. And his brother is represented by B. The total of their candy is T.
J + B = T
B = 1/2J - 10
You would plug in any numbers that you know and then get your answer.
Hope this helps.
Which expression is equivalent to 7 − x?
Answers
Answer:
Step-by-step explanation:
I need pic
The equivalent expression is y = [tex]e^{x log 7}[/tex].
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]7^x[/tex]
Let y = [tex]7^x[/tex]
Now,
Taking logs on both sides.
log y = log [tex]7^x[/tex]
log y = x log 7
Taking exponent on both sides.
[tex]e^{logy}[/tex] = [tex]e^{x log 7}[/tex]
y = [tex]e^{x log 7}[/tex]
Thus,
The equivalent expression is y = [tex]e^{x log 7}[/tex].
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The complete question is given below:
Which numbers are rational? Select all that apply
A. 3.14
B. Square root of 50
C. 2.33333
D. Square root of 144
Answers
Answer:
A. 3.14
C. 2.33333
D. Square root of 144
Step-by-step explanation:
A. 3.14 true
B. Square root of 50 false because 50 is not a perfect square
C. 2.33333 true
D. Square root of 144 true because √144 = 12
a cell phone plan charges $39.90 a month, plus $0.05 per text message Which expression can be solved to find how many text messages ,x, can be sent while still keeping the monthly bill under $50
Answers
X=20
Step-by-step explanation:
39.90-50= 10.1
10.1÷0.05=202
X=202 texts
Check work 0.05×202=10.1 + 39.90=50
What is the interquartile range of this data set -5,-4,-3,-2,-1,0,1,2,3,4,5,7,7,7
Answers
Answer:
IQR=5+2=7 because you have to find the median and the median below the median and above the median to get 5 and a negative two and 5 subtract a negative is the same as adding a positive so then you get 7.
Step-by-step explanation:
Please help! AREA OF COMPOSITE FIGURES, what is the area of this figure in photo!???
A.) 49.5in²
B.) 66.5in²
C.) 84 in²
D.) 91 in²
Answers
Answer:
D. 91 in.^2
Step-by-step explanation:
We have two shapes, a square and a triangle.
Area of a square = lw
Area of a triangle = (lw)1/2
Starting off with the square...
A = lw
A = 7 x 7
A = 49
Next with the triangle...
A = (lw)1/2
A = (12 x 7)1/2
A = (84)1/2
A = 42
Add together the areas...
42 + 49
91 in^2
area= D 91in^2
4. The dot plot shows the number of miles Amanda skated each day over two months:
Which statement is best supported by the dot plot? Choose ONE and explain your answer.
I. The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III. The mode of the number of miles Amanda skated in July is equal to the mode of the number of miles skated in August.
Answer explanation:
i only need number 4 the others ive done already PLS HURRY IM IN A RUSH ILL GIVE BRAINLYIST
Answers
Answer:
The statements i) and iii) are best supported by the dot plot.
i) The range of the number of miles Amanda skated in
August is less than the range of the number of miles she
skated in July.
iii) The mode of the number of miles Amanda skated in July
is equal to the mode of the number of miles skated in
August.
Step-by-step explanation:
i) The range of the number of miles Amanda skated in August is 1 to 3
The range of the number of miles Amanda skated in July is 1 to 4
The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
This is a true statement and this is the correct answer
ii)The distribution of data for the month of July is almost symmetrical but the
data in August is not.
The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
This statement is not true.
iii)The mode of the number of miles Amanda skated in July is 1.
The mode of the number of miles Amanda skated in August is 1.
The mode of the number of miles Amanda skated in July is equal to the mode of the number of miles skated in August.
This is also a true statement.
43 POINTS I'M BEING TIMED
In the problems below, f(x) = log₂x and
g(x) = log₁₀x
Which point do the graphs of f and g have in common?
Answers
Answer:
(1,0)
Step-by-step explanation:
The point that f(x) = log₂x and g(x) = log₁₀x have in common is where both graph intersect.
Recall that the logarithm of 1 is 0.
This implies that, when we plug in x=1 into both function we get 0.
g(1) = log₁₀1=0
f(1) = log₂1=0
This means the two graphs intersect at (1,0)
Therefore the graphs of f and g have (1,0) in common
Which algebraic expression represents the phrase "two times the quantity of a number minus 12"?
2y - 12
2(y -12)
2ly +12)
2y + 12
Answers
Answer:
the correct answer is B
This is because the two is being multiplied by the expression inside the parentheses (y-12)
All employees at three stores of a large retail chain were asked to fill out a survey.
Is it random, systematic, stratified, or cluster?
Answers
Answer:
Cluster
Step-by-step explanation:
Random: Each element in the population has an equal probability of selection, and each combination of elements has an equal probability of selection. For instance picking a picking name from a hat.
Stratified: Divide population into groups called strata that differ in important ways. For instance, for a population of a state, male and female strata. for people working in a city, resident and non-resident strata
Systematic: Each element has an equal probability of selection, but combinations of elements have different probabilities
Cluster: this is a form of random sampling. Population is divided into groups, usually geographic or organizational