Answer: B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
Step-by-step explanation:
We know that a parallelogram is a quadrilateral having congruent opposite sides and its diagonals bisect each other.
A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.
Its all 4 angles are right angle.
let's check all the statements :
A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
→It can be rhombus ∵ it also has same characteristics.
B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
→ It only occurs in square.
C. A parallelogram with a right angle and diagonals that are congruent .
→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.
D. A parallelogram with diagonals that bisect each other.
→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.
The statement that must be true is (b) A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
A parallelogram has parallel and congruent opposite sides
However, the following must be true about parallelograms that can be regarded as squares:
There are congruent consecutive sidesThe diagonals are congruentHence, the true statement is (b)
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For a car rental, the rental agency charges $21.00$21.00 per day, plus $0.23$0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.
find the value of x
A market sells bananas for $0.69 per pound. Which expression represents the cost, in dollars, of p pounds of bananas? 1 p/69 2 0.69p 3 p/0.69 4 69p
Answer:
Option 2. 0.69p
Step-by-step explanation:
A market sells bananas for = $0.69 per pound
The cost, in dollars of p pounds of bananas = 0.69 × p
So the expression represents the cost, in dollars of p pounds of bananas
= 0.69p
Option 2. 0.69p is the right answer.
Help?
Simplify. 9√56x^7y^12 Assume x and y are nonnegative.
Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.
Apply the product property of square roots:
9 * √(56) * √(x^7) * √(y^12)
Evaluate the square root:
9 * 2 * √(2 * 7) * √(x^7) * √(y^12)
Multiply the numbers:
9 * 2 * √(14) * √(x^7) * √(y^12)
Simplify the square root of an exponential expression:
9 * 2 * √(14) * |x^3| * √(x) * √(y^12)
Simplify the square root of an exponential expression:
9 * 2 * √(14) * √(x) * |x^3| * y^6
Apply the product property of square roots to the product of square roots is equal to the square root of the product:
9 * 2 * y^6 * |x^3| * √(14x)
Multiply the numbers:
18 * y^6 * √(14x) * |x^3|
b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year? Show your work.
Answer:
The tax would be $ 1,263.75
Step-by-step explanation:
Given,
Total earning in one year = $ 8,425,
Income tax percentage per year on earning = 15%
Hence, the amount of tax at the end of one year
= 15% of the total earnings
= 15% of 8425
[tex]=\frac{15\times 8425}{100}[/tex]
[tex]=\frac{126375}{100}[/tex]
= $ 1,263.75
A clydesdale drinks about 120 gallons of water every 4 days.At this rate,about how many gallons of water does a clydesdale drink in 28 days
limit as x approaches 0 of csc3x/cotx
The limit of csc(3x)/cot(x) as x approaches 0 is 1, after applying trigonometric identities and the properties of limits.
Explanation:The student is asking for the limit of the function csc(3x)/cot(x) as x approaches 0. This is a limit problem in calculus, which is a part of mathematical analysis that deals with the behavior of functions near certain points. To find the limit as x approaches 0 for the function csc(3x)/cot(x), we need to apply trigonometric identities and the properties of limits. The function csc(3x) can be rewritten as 1/sin(3x) and cot(x) as cos(x)/sin(x). So the original limit becomes:
lim(x → 0) [csc(3x)/cot(x)] = lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))].
Using the trigonometric limit lim(x → 0) (sin(x)/x) = 1 and lim(x → 0) (cos(x)) = 1, we can simplify the expression by substituting 3x for x in the limit sin(x)/x. We get:
lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))] = lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x).
As x approaches 0, cos(x) approaches 1 and 3x/x approaches 3, hence:
lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x) = lim(x → 0) (sin(x)/x) × lim(x → 0) 1/cos(x) × lim(x → 0) (3x/3sin(3x)) = 1 × 1 × (3/3) = 1.
The final limit of csc(3x)/cot(x) as x approaches 0 is 1.
The perimeter of a triangle is 29 feet where one side of the triangle is twice the length of the shortest side. the largest side is 13 feet more than the shortest side. how long is the shortest side
Answer:
The shortest side is 4 feet.
Step-by-step explanation:
The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.
So the perimeter in the case of a triangle is the sum of its three sides:
L₁ + L₂ + L₃ =Perimeter
In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:
L₁= shortest sideL₂=twice the length of the shortest side → L₂=2*L₁L₃=largest side (13 feet more than the shortest side) → L₃=L₁ + 13Perimeter= 29 feetReplacing:
L₁ + 2*L₁ + L₁ + 13= 29
Solving:
(1+2+1)*L₁ + 13= 29
4*L₁ + 13=29
4*L₁ = 29-13
4*L₁ =16
L₁= 16÷4
L₁=4
The shortest side is 4 feet.
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answer:
[tex]y=-3x+14[/tex], slope intercept form
[tex]3x+y =14[/tex], standard form
Step-by-step explanation:
[tex]y + 1 = -3(x - 5)[/tex]
We need to write the given equation in slope intercept form or standard form
slope intercept form is [tex]y=mx+b[/tex]
To get slope intercept form , we need to get y alone
[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )
[tex]y+1=-3x+15[/tex] , subtract 1 on both sides
[tex]y=-3x+14[/tex]
Standard form is [tex]Ax + By = C[/tex]
To get standard form we keep x term and y term on the left hand side
[tex]y=-3x+14[/tex]
Add 3x on both sides
[tex]3x+y =14[/tex]
the slope of the line below is 2/5 and the y-intercept is (0,4) what is the slope intercept equation of the line?
Use laws of sine to answer
Liz wants to buy a shirt for $25. How much will Liz's shirt cost in Springfield(4.1%) Round up to the nearest cent? Show your work
State the vertex as an ordered pair.
y = -|3x +5|+7
14 minus the product of three and the number has 26
y=x^2+8x+6 16x-2y=-44
6 shirts 4 different pairs of pants, how many different combinations could she wear?
Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the x-axis
D) reflection across the y-axis
Answer: C is the answer
Step-by-step explanation:
Some of the cds produced by a manufacturer are defective. from the production line, 5 cds are selected and inspected. how many sample points exist in this experiment?
Final answer:
There are 32 sample points in this experiment.
Explanation:
In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times to find the total number of sample points. Therefore, there are 32 sample points in this experiment.
Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.
Describe how to graph the solution of y ≤ −x² + 2x.
Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?
multiply 17 by 6%
17 * 0.06 = 1.02 increase
17 +1.02 = 18.02 new hourly wage
Segments and angles practice with special angles find the measures of the lettered angles
Yori has 14.25 cups of cupcake batter if each cupcake used 0.75 cup of batter how many cups cakes can yori make?
Anna has 5 muffins but 8 friends coming over. How much will each friend get
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < 3/2x + 2
The origin is not included in the shaded region and the shaded area is above the line.
The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.
Answer
third option
Step-by-step explanation:
The areas of: FGHM is 12, MHIJ is 36, EFNL is 24, LNJK is 48. EGIK is a rectangle cut into the rectangles with given areas. What is the area of the shaded quadrilateral EMIN?
Line segment AB is the perpendicular bisector of line segment XZ. Which statement is true? A) XZ = AB B) XB = XZ C) ∠ABZ = ∠ABX D) ∠BAZ = ∠ABX
A perpendicular bisector is a special type of bisector because it intersects a segment at a 90 degree angle, and it passes through the segments midpoint.
Therefore based from this, we can create two true statements:
XB = BZ
and
∠ABZ = ∠ABX
Therefore the answer is:
C
Answer:
The answer is C. <ABZ = <BAX hop this hope this help
Please help me with this
for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse
so for this:
the legs would be 2sqrt(10)
A couch and coffee table cost a total of $1017. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
cost of couch:
cost of coffee:
Answer:
Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.
Step-by-step explanation:
Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,
x + y = 1017
Also, the cost of couch is two times that of coffee. So,
x = 2y
Substitute the value of x in first equation
2y + y = 1017
3y = 1017
y = 339
And, x + y = 1017
x + 339 = 1017
x = 678
Using the two equations, we find that y = $339 and x = $678.
So, the cost of couch is $678 and that of coffee is $339.
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm
Answer:
A
Step-by-step explanation:
The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are:
A. 6cm by 1.5cm because
D. 18cm by 4.5cm because
E. 80cm by 20cm because
Given that
[tex]Length = 12cm[/tex]
[tex]Width = 3cm[/tex]
Divide the length and the width of the rectangle
[tex]k = Length \div Width[/tex]
[tex]k = 12cm \div 3cm[/tex]
[tex]k = 4[/tex]
This means that a scaled copy of rectangle A must have a value of 4 when the dimensions are divided.
Possible rectangles are:
A. 6cm by 1.5cm because [tex]6cm \div 1.5cm = 4[/tex]
D. 18cm by 4.5cm because [tex]18cm \div 4.5cm = 4[/tex]
E. 80cm by 20cm because [tex]80cm \div 20cm = 4[/tex]
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You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?