By using the rules of geometry, we can determine that if P is the midpoint of QN and MP is perpendicular to QN, then rectangles MRQ and MRN are congruent. The congruency is due to the properties of rectangles, triangles, midpoints, and the Hypotenuse-Leg Theorem.
Explanation:The proof of the congruence of rectangles MRQ and MRN involves geometry rules, particularly the properties of rectangles, triangles, and midpoints. Let's consider rectangle MRQ and MRN. We know that in a rectangle, diagonals are congruent. If P is the midpoint of QN, that means QP = PN. Additionally, if MP is perpendicular to QN, PMQR and PMNR are right triangles with the same hypotenuse.
Using the properties of triangles, we can say that if two right triangles have a congruent hypotenuse and one leg (which is MP in both cases), then these triangles are congruent. Therefore, ∆PMQR is congruent to ∆ PMNR by the Hypotenuse-Leg (HL) Theorem.
Considering that ∆ PMQR ≅ ∆ PMNR and QP = PN, we can say that quadrilaterals MRQN and MRNP are each a parallelogram. Additionally, since MP is perpendicular to QN, quadrilaterals MRQN and MRNP are actually rectangles based on the definition of a rectangle (a parallelogram with a right angle). Therefore, rectangle MRQ is congruent to rectangle MRN.
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A bird flies from the bottom of a canyon that is 59 and three fifths
feet below sea level to a nest that is 609 and one fifth
feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest?
Varia is studying abroad in Europe. She is required to pay $3500USD per year to the university, however she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.)
0.7306 euros = 1 US dollar
What's the numerator for the following rational expression? 8/y+3/y=?/y
solve x 2 −18x+81=0 for x
Explain a thought process you might use when trying to find the additive or multiplicative inverse of a number or expression. ...?
HELP! A simplified version of sin2 θ (1 + cot2 θ) = 1 is ...?
Selina claims single having one exemption. Her state tax deduction is 21% of her federal tax contribution. Calculate the amount of state tax Selina owes if her gross pay for two weeks is $840. The following federal tax table is for biweekly earnings of a single person.
Answer:
$16.80
Step-by-step explanation:
ending balance 1 59.75 outstanding deposits 175 .46 outstanding checks 231 .69 what is the balance
To calculate the balance, add the outstanding deposits to the ending balance and subtract the outstanding checks.
Explanation:To calculate the balance, we need to start with the ending balance and make adjustments for outstanding deposits and outstanding checks. First, add the outstanding deposits to the ending balance: 59.75 + 175.46 = 235.21. Next, subtract the outstanding checks from the previous result: 235.21 - 231.69 = 3.52. Therefore, the balance is $3.52.
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Isabella paid one of her bill late and owed a 4% late fee was 780. How much was Isabella's original bill in dollar
The original bill amount that Isabella owed before the late fee was $19,500.
We need to understand the relationship between the late fee and the original bill amount.
Isabella was charged a late fee of 4% of the original bill amount, and this late fee was $780.
Let's use the variable x to represent the original bill amount. Since the late fee is 4% of the original bill, we can write the equation:
[tex]0.04x = 780[/tex]
To find x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.04:
[tex]x = \frac{780}{0.04}[/tex]
Now, we can calculate this value:
[tex]x = 19500[/tex]
Which size is better in buying detergent: 32 fl oz for $1.99
50fl oz for $2.49
All real numbers that are greater than or equal to -1.5 and less than 9.2
Which expression is a cube root of 2?
A) Cube root of 2 (cos (120 degrees) + i sin (120 degrees))
B) Cube root of 2 (cos (40 degrees) + i sin (40 degrees))
C) Cube root of 2 (cos (280 degrees) + i sin (280 degrees)) ...?
Answer with explanation:
[tex]z=2^{\frac{1}{3}}\\\\z^3=2\\\\z^3=2 \times (1 + 0 i)\\\\z^3=2 \times [\cos 0^{\circ} + i \sin 0^{\circ}]\\\\z^3=2 \times [\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})],where,k=0,1,2,\\\\z=[2\times[ (\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})]]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}\times[\cos \frac{2 k\pi+ 0^{\circ}}{3} + i \sin\frac{(2 k\pi+0^{\circ})}{3}]\\\\Z_{0}=2^{\frac{1}{3}},for, k=0\\\\z_{1}=2^{\frac{1}{3}}\times[\cos \frac{(2\pi)}{3} + i \sin\frac{(2\pi)}{3}][/tex]
[tex]z_{1}=2^{\frac{1}{3}}\times[\cos(120^{\circ})+i\sin(120^{\circ})],\text{Used Demoiver's theorem}[\cos A + i\sin A]^k=\cos Ak + i\sin Ak[/tex]
Option A: →Cube root of 2 [cos (120 degrees) + i sin (120 degrees)]
Which graph represents a linear function?
A coordinate plane is shown with a curved line that starts in the bottom left area of the graph, passing through the point -1 comma -5, curving to pass through the y-axis at 2.5, then curving up again to pass through the point 1 comma 5
A coordinate plane is shown with a line passing through the x-axis at negative 2 and the y-axis at negative 6.
A coordinate plane is shown with a parabola graphed in an upward U shape. The bottom of the parabola touches the y-axis at -10 and curves upward on both sides
A coordinate plane is shown with a wavy line that sits on the x-axis and moves across the graph in even up and down waves.
Answer:
2nd Option is correct.
Step-by-step explanation:
We are given with four statements which describes a graph of a function.
We need to find the graph which represents the linear function.
Linear Function:
Linear functions are the functions whose graph are straight lines.
A linear function has the following form
y = f(x) = a + bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
So, In graphs of 1st , 3rd and 4th Options are curves not a straight line.
Only 2nd Option has graph which is straight as mentioned in it that a line passing through two points.
Therefore, 2nd Option is correct.
1/5 (7-3b) > 2
which of the following gives all values of b that satisfy the inequality above?
A) b< -1
B) b> -1
C) b< 1
D) b> 1
The value of b that satisfy the inequality are; B) b> -1 and C) b< 1
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
We have given an inequality;
1/5 (7-3b) > 2
To solve for b;
(7-3b) = 10
-3b = 10 - 7
-3b = 3
b = -3/3
b = -1
Thus, the value of b that satisfy the inequality are; B) b> -1 and C) b< 1
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The correct solution for the given inequality 1/5 (7-3b) > 2 gives us b < -1. Option A is correct.
The given inequality is 1/5 (7-3b) > 2. To find the range of values for b that satisfy this inequality, follow these steps:
Multiply both sides of the inequality by 5 to eliminate the fraction: 7 - 3b > 10.
Subtract 7 from both sides of the inequality: -3b > 3.
Since we are dividing by a negative number, remember to reverse the inequality sign: b < -1.
Therefore, the correct answer is b < -1, which is option A.
if susie is fourteen, what was her age x years ago?
Find the greatest common factor of the following monomials.
21g^3h 45g^3h^2
The table lists the values for two parameters, x and y, of an experiment. What is the estimated value of x for y = 0.049?
a) 20.4
b) 21.4
c) 23.7
d) 24.7
yep 20.4 is the correct answer for plato!!
Write a linear equation in slope intercept form to model a tree 4 feet tall the grows 3 inches per year
The linear equation that models the growth of a tree that is 4 feet tall and grows 3 inches per year is y = 3x + 48.
Explanation:The problem involves writing a linear equation in slope-intercept form to model the growth of a tree. The slope-intercept form is given by the equation y = mx + b, where 'm' represents the slope or the rate of change, and 'b' is the y-intercept or the initial value.
In the context of this problem, the tree's initial height is 4 feet and it grows at a rate of 3 inches per year. However, the units of the initial height and the yearly growth rate are different, so we need to convert 4 feet into inches. As 1 foot is equivalent to 12 inches, the initial height of the tree is 4 * 12 = 48 inches.
Therefore, the slope or rate of change 'm' is 3 inches per year and the y-intercept or initial value 'b' is 48 inches. Substituting these values into y = mx + b gives us the linear equation representing the growth of the tree: y = 3x + 48.
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In rectangle ABCD, BC=30 and AB=40. If diagonals AC and BD intersect at E, find the measure of BE.
To find the measure of BE in rectangle ABCD, we can use the properties of a rectangle and similar triangles. By using the Pythagorean theorem, we find the length of the diagonal AC. Then, we use the properties of similar triangles to calculate the length of BE.
Explanation:To find the measure of BE, we can use the properties of a rectangle. In rectangle ABCD, the diagonals are equal in length and bisect each other. Therefore, we can use the Pythagorean theorem to find the length of the diagonal AC: AC^2 = AB^2 + BC^2. Plugging in the values given, AC^2 = 40^2 + 30^2 = 2500, so AC = sqrt(2500) = 50. Since the diagonals bisect each other, we can conclude that AE = 50/2 = 25. Now, we can use the properties of similar triangles to find the length of BE. Triangle ABE is similar to triangle ACE, so we can set up the following proportion: AB/AC = BE/AE. Plugging in the values, 40/50 = BE/25. Solving for BE, we get BE = (40/50) * 25 = 20.
To find the measure of BE in rectangle ABCD, we use the Pythagorean Theorem. As the diagonals bisect each other, BE is half the length of diagonal AC, resulting in BE = 25.
Explanation:In rectangle ABCD with BC=30 and AB=40, the diagonals bisect each other. That means E, the point of intersection, is the midpoint of both diagonals AC and BD. Since ABCD is a rectangle, its diagonals are equal, and AC = BD. To find BD, we use the Pythagorean Theorem in ΔABC:
AC² = AB² + BC²AC² = 40² + 30²AC² = 1600 + 900AC² = 2500AC = √2500AC = 50Since E is the midpoint of BD, BE is half the length of BD:
BE = BD/2BE = AC/2 (because AC = BD)BE = 50/2BE = 25
On a hike jason found a california king snake that was 42 inches long how many feet is that
The area of a square is found by squaring one of its sides, (A = s 2). A certain square has an area of z 2 + 18z + 81. Factor the trinomial to find a side of the square.
A.) side = z + 27
B.) side = z + 18
C.) side = z + 9
Answer:
C.) side = z + 9
An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the x-axis.
Choices are in the attachment
Answer:
So basically it’s D
Step-by-step explanation:
:)
What is the r value of the following geometric sequence? 4, 7, 12.25, 21.4375.
Answer:
r ( common ratio) = 1.75
Step-by-step explanation:
Given : geometric sequence 4, 7, 12.25, 21.4375.
To find : What is the r value .
Solution : We have given
Geometric sequence 4, 7, 12.25, 21.4375.
r ( common ratio) = [tex]\frac{second\ term}{first\ term}[/tex].
r ( common ratio) = [tex]\frac{7}{4}[/tex] = 1.75
r ( common ratio) = [tex]\frac{12.25}{7}[/tex] = 1.75
Therefore, r ( common ratio) = 1.75
Write a justification for each step.
The area of one face of a cube is 7 cm2. what is its surface area?
A real estate agent sells a house for $92,000. She receives a 6% commission on the sale of the house. How much did she earn on the sale? Round your answer to the nearest cent. Enter your answer in the box. $
A. 3x^2+2x-7
B. 3x^2+2x-3
C. 3x^2+8x+3
D. 5x^2+8x-7
state the degree x^3y^2+7x^2y^5-3xy^8
Answer:9
Step-by-step explanation:
CD is perpendicular to AB and passes through point C (5,12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x- intercept of CD is:
(12, 0)
(15, 0)
(17, 0)
or (19,0).
The point:
(-5, 24)
(-2, 19)
(7, -10)
or (8, 11)
lies on CD.
Answer
CD is 17,0
The point -2,19
Step-by-step explanation:
What is the factorization of the trinomial below?
x2 - 10x + 25
A. (x - 25)(x + 1)
B. (x - 25)(x - 1)
C. (x - 5)(x - 5)
D. (x - 5)(x + 5)