∠KPL ≅ ∠MRL as perpendicular always makes an angle of 90°.
What specifically is meant by "triangle congruency"?When two triangles' three corresponding sides and angles are the same sizes, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: ∠ K ≅ ∠M, KP⊥ PR, MR ⊥ PR
To Prove: ∠KPL ≅ ∠MRL
As MR ⊥ PR (Given), then: ∠MRL = 90°Similarly, KP⊥ PR (Given), then: ∠KPL = 90°So, ∠KPL ≅ ∠MRL.
Therefore, ∠KPL ≅ ∠MRL as perpendicular always makes an angle of 90°.
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Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually. She makes no additional deposits or withdrawals. Which amount is closest to the interest Mrs. Chavez will have earned at the end of 4 years?
If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years
Total invested amount = $8000
Interest rate = 8.62%
The interest is compounded annually
Time period = 4 years
We know
[tex]A=P(1+\frac{r}{100})^{t}[/tex]
Where,
A = Final amount
P = Principal
r = Interest rate
t = Time period
Substitute the values in the equation
A= [tex]8000(1+\frac{8.62}{100})^{4}[/tex]
A= $11136
Compounded interest = 11136-8000
=$3136
Hence, If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years
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what is the value of the expression below when A=-3, B=2, and C=-4
2
a -2ac+5c
Answer: -50
Step-by-step explanation:
2a-2a+5c
2(-3)-2(-3)(-4)+5(-4)=
-6-24-20=-50
Find the 32 nd term of each sequence. 23,30,37,44, ...........
The 32nd term of the arithmetic sequence AP is calculated to be 240.
What basically is an AP arithmetic sequence?In mathematics, an arithmetic progression (AP) is a list and possibly sequence of numbers where each term is collected by adding a sequence towards the term before it.
The fixed number, without regard to arithmetic progression, is signified by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.Finally, here is the answer to the question:
The following are the numbers with in displayed sequence:
23,30,37,44, ...........
The 32nd number in the series must be investigated because it contains 32 terms.
The common difference between two consecutive terms of an AP that are equal is denoted by the letter 'd.'
Let's consider the first term is'a₁' = 23.
Let's consider 'a₂' = 30 is the second term.
Let's consider the third term is 'a₃' = 37.
Substitute the values the above obtained equation; the 32nd term is-
d = a₂ - a₁
Estimate the common difference;
d = 30 - 23
d = 7
Substitute the values in the next formula; the 32nd term is
The formula given will estimate the nth term equation;
nth term of an AP: an = a + (n - 1) d
Total number of terms ; n = 32
Initial term is a = 23
Common difference d = 7
Substitute the given values in nth term formula;
a₃₂ = a + (n - 1) d
a₃₂ = 23 + (32 - 1)(7)
a₃₂ = 23 + 217
a₃₂ = 240
Thus, the 32nd term value of the given arithmetic sequence is estimated to be 240.
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9+4y=-5x+7y solve for x
Answer:
x=3/5y-9/5
Step-by-step explanation:
Answer:
5x=7y-4y-9
5x=9-3y
[tex]\frac{5x}{5}[/tex]=[tex]\frac{9-3y}{5}[/tex]
[tex]x=\frac{9-3y}{5}[/tex]
Joshua purchased a game card for the arcade for a total of $18. He played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each. How much did he have left on the game card?
$4.50
$6.50
$13.00
$13.50
The amount left when Joshua played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each is A. $4.50.
How to calculate the value?From the information, Joshua purchased a game card for the arcade for a total of $18 and played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each.
Therefore, the amount left will be:
= Total amount with him - Amount spent
= $18 - (2 × $3.25) - (4 × $1.75)
= $18 - $6.50 - $7
= $4.50
The amount left is $4.50
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Answer:
4.50
Step-by-step explanation:
Solve using zero-factor product property. (x + 7)(2x + 4)(3x - 6) = 0
Answer:
¯＼_(ツ)_/¯
Step-by-step explanation:
x(2x+4)+7(2x+4)[3x-6]=0
(2x^2 + 4x + 14x + 28)(3x-6)=0
(2x^2 + 18x + 28)(3x-6)=0
3x(2x^2 + 18x + 28) -6(2x^2 +18x + 28)=0
6x^2 + 54x^2 + 84x - 12x^2 - 108x - 168 =0
6x^2 + 54x^2 - 12x^2 + 84x - 108x - 168 =0
48x^2 - 24x - 168 =0 {quadratic equation}
Compare the two numbers. Use > or < .
16, √16
The value of Square root √16 is equals to 4, and the number 16 is larger than the number 4 then 16 > √16.
What is a Square root?In arithmetic, a number y whose square (the outcome of multiplying the number by itself, or y y), equals x is known as the square root of a number x.The phrase (or quantity) whose square root is under consideration is referred to as the radicand.In this situation, the expression or number under the radical sign is called the radicand and it is 9.Within the context of complex numbers, one can talk about square roots of negative numbers.Square roots can be taken into account more broadly in any situation where the concept of an object's "square" is specified.Among other mathematical structures, these include function spaces and square matrices.Let the value of √16 be 4 then 16 > √16.
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convert the following to base 10
a:325.6eight b:11101.011two
Coventry Estates sells houses.
In February they sold twice as many houses as in January.
In March they sold 10 more houses than in February.
In April they sold half as many houses as in March.
Coventry Estates sold a minimum of 123 houses from 1st January to 30th April.
Find the least number of houses sold in January.
The total number of houses sold in January by Coventry Estates are 18.
How to do the twice of number? This suggests that the amount of A is twice as large as the quantity of anything else, which in this case is B. So, if you have a dozen B items, you have twice a certain number for A, which is 24.As per the given question;
Let the total sales of the houses in January be 'x'.
In February they sold twice as many houses as in January.
February = 2x.
In March they sold 10 more houses than in February.
March = February + 10
March = 2x + 10
In April they sold half as many houses as in March.
April = March/2
April = (2x + 10)/2 = x + 5
The total sold houses = 123.
Add all the sold houses;
x + 2x + 2x + 10 + x + 5 = 123
6x + 15 = 123
On simplification;
x = 18
Thus, the total number of houses sold in January by Coventry Estates are 18.
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What are the cooridinates of the point that partitions segment HE in the ratio of 2:3?
Using proportions, the coordinates of the point C that partitions segment HE in the ratio of 2:3 are found according to the following equation:
C - H = 2/5(E - H).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have point C that partitions segment HE in the ratio of 2:3, hence it is 2/5 of the way from H to E, and the rule is given by:
C - H = 2/5(E - H).
Then:
Replacing the x-coordinates of H and E, we find the x-coordinate of C.Replacing the y-coordinates of H and E, we find the y-coordinate of C.More can be learned about proportions at https://brainly.com/question/24372153
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PLS HELP ME WITH THIS
How do you find equivalent expressions?
Image result for what is equivalent to (5x/6)
Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.
For an analysis of variance comparing four treatments, msbetween = 12. what is the value of ssbetween? group of answer choices
a. 3
b. 4
c. 36
d. 48
For an analysis of variance comparing four treatments, msbetween = 12. The value of ssbetween is 36.
What is variance ?A measure of variability is the variance. It is determined by averaging the squared deviations from the mean. Your data set's variability is shown by its variance. The variance is greater in respect to the mean when the data are more dispersed.
Finding the mean will allow you to compute the population's variance (the average). Squaring the result after deducting the mean from each data point in the sample. The outcomes are squared to make the adverse findings positive.
Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value.
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here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB
Making a perpendicular bisector on the segment that gives the half length of AB
Given that,
here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB is to explain.
A line can be defined by the shortest distance between two points is called as a line.
Here,
Two points are given on the plane,
Draw line segment joining these two points on the plane,
Now with help of a compass draw a perpendicular bisector on the line, that bisects the segment into two equal halfs.
Thus, making a perpendicular bisector on the segment that gives the half length of AB
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log6⁸+2log6³+log6¹²-log6²⁴
The solution of expression is 8log6.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
We have been given that expression as
⇒ log6⁸ + 2log6³ + log6¹² - log6²⁴
[used property : logₐ(xⁿ) = nlogₐx]
⇒ 8log6 + 6×2log6³ + 12log6 - 24log6
⇒ 8log6 + 12log6³ + 12log6 - 24log6
⇒ 8log6
Hence, the solution is 8log6.
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Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
A farmer needs to make a 1000 -square-foot rectangular enclosure for her cows. She wants to save money by purchasing the least amount of fencing possible to enclose the area. What whole-number dimensions will require the least amount of fencing?
F. 8ft by 125ft
G. 10ft by 100 ft
H. 20ft by 50 ft
J. 25ft by 40 ft
The dimensions of the 1000-square-foot rectangular enclosure with the least amount of fencing should be 25ft by 40ft.
The amount of fencing needed can be calculated by getting the perimeter of each choice of dimensions.
Perimeter is defined as the distance that surround any two-dimensional shape. For a rectangle, the perimeter is given by the formula
P = 2l + 2w
Solving for the perimeter of each of the following choices:
F. 8ft by 125ft
P = 2l + 2w
P = 2(8) + 2(125)
P = 16 + 250
P = 266ft
G. 10ft by 100ft
P = 2l + 2w
P = 2(10) + 2(100)
P = 20 + 200
P = 220ft
H. 20ft by 50ft
P = 2l + 2w
P = 2(20) + 2(50)
P = 40 + 100
P = 140ft
J. 25ft by 40ft
P = 2l + 2w
P = 2(25) + 2(40)
P = 50 + 80
P = 130ft
The dimensions with the least perimeter will require the least amount of fencing.
Hence, a 1000 -square-foot rectangular enclosure, with dimensions 25ft by 40ft, will require the least amount of fencing.
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Write an equation of a parabola with its vertex at the origin and the given characteristics. directrix x=7
Answer:
ggr44tt55ttffghhtft hyy
nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}[/tex] =[tex]= 11\sqrt{2} - 5\sqrt{7}\\[/tex]
Given an Simplification :
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}Now, \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2}\sqrt{28} = \sqrt{2 \times 2 \times 7} = 2\sqrt{7}∴ 9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}= 9\sqrt{2} - 3\sqrt{7} + 2\sqrt{2} - 2\sqrt{7}= 9\sqrt{2} + 2\sqrt{2} - 3\sqrt{7} - 2\sqrt{7}= 11\sqrt{2} - 5\sqrt{7}[/tex]
Simplifying rational expressions entails lowering the value of a rational expression to its simplest form. A rational expression is simplified in the same way that fractions are simplified. When the numerator and denominator of a rational number have no common factor other than 1, we consider it to be its simplified version in fractions. The same method may be used to simplify rational expressions; the only difference is that polynomials are included in the fraction.
The procedure for conducting operations on rational expressions is same to that for fractions.
Simplifying rational expressions means reducing their value to their most basic form. Rational expressions are simplified in the same manner that fractions are.
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When striping the practice football field, Mr. Hawkins first painted the sidelines. Next he marked off 10-yard increments on one sideline. He then constructed lines perpendicular to the sidelines at each 10-yard mark. Why does this guarantee that the 10 -yard lines will be parallel?
This ensures that the lines will be parallel since two lines that are perpendicular to one another must also be parallel.
What is a perpendicular line?Two lines that meet or cross at right angles (90°) are known as perpendicular lines in geometry. The word "perpendicular" comes from the Latin "perpendicularis," which denotes a plumb line.
We can write two lines, AB and CD, as AB ⟂ CD if they are perpendicular to one another. The lines are denoted as being perpendicular by the ⟂ symbol.
The following list includes the two main characteristics of perpendicular lines.
These lines will always cross at right angles.Two lines will always be parallel to one another if they are perpendicular to the same line.Learn more about perpendicular
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simplify with the steps
By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.
How to simplify an algebraic expression
In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:
[(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] Given[(3 · a · b²) / (5 · b²)] ÷ [√(9 · a²) / √(100 · b²)] Square root of a division[(3 · a · b²) / (5 · b²)] ÷ [(√9 · √a²) / (√100 · √b²)] Square root of a product[(3 · a · b²) / (5 · b²)] ÷ [(3 · a) / (10 · b)] Definition of square root[(3 · a · b²) · (10 · b)] / [(5 · b²) · (3 · a)] Division of fractions(30 · a · b³) / (15 · a · b²) Associative and commutative properties / Definition of multiplication / Multiplication of powers of equal base2 · b Associative and commutative properties / Definition of division / ResultThe expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.
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Which is the graph of the solution set of −2x + 5y > 15?
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (5, 1). Everything below and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 5) and (10, 9). Everything above and to the left of the line is shaded.
Answer:
it is the first option
Step-by-step explanation:
First step. Switch the greater than sign and turn the linear inequality to slope formula. after that graph the line. it is a dashed line due to not being greater than EQUAL to. if not equaled to then it is dotted. then you need a point as your testing point to see if it is shaded in that area. I chose to(0,0) but you could have chose any point. Once you plug in the zeros you will notice you get the false statement of 0 greater than 15. so obviously that is a no so you shade the opposite side of your testing point. phew
Answer:
A. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
Step-by-step explanation:
80 students visited the library
over three days. The two-way
table shows some information
about these students.
Monday
Year 7
Year 8
Total
14
Tuesday Wednesday Total
13.
38
33
26
80
The missing values of the table are a=7, b=18, c=15, d=13, e=42 and f= 21
We can easily complete the give table using simple addition and subtraction
Monday Tuesday Wednesday Total
Year 7 7 18 13. 38
Year 8 14 15 13 42
Total 21 33 26 80
The correct question is 80 students visited the library
over three days. The two-way
table shows some information
about these students.
Monday Tuesday Wednesday Total
Year 7 a b 13. 38
Year 8 14 c d e
Total f 33 26 80
Complete the table.
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Tell whether the difference of two positive integers is always, sometimes, or never positive.
The difference of two positive integers is sometimes positive.
How to illustrate the information?For example the difference of 3 and 5 will give a value of -2. This is negative.
On the other hand, the difference of 10 and 6 is 4. Therefore, this is positive.
Therefore, the difference of two positive integers is sometimes positive. It can also be negative.
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Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = -12x/5 for x=-1
f (-1) = 12/5 the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x) = -12x/5
Put x = -1 ⇒ - 12 * -1 /5
⇒ 12/5
Therefore f (-1) = 12/5
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My little sister, Savannah, is three years old and has a piggy bank that she wants to fill. She
started with five pennies and each day when I come home from school, she is excited when I give her three pennies that are left over from my lunch money. How much money will Savannah have after 10 days? How many days will it take for her to have at least $1.50? Justify your answer with a mathematical model of the problem situation.
Answer:
after 10days savannah will have 31 pennies
Step-by-step explanation:
arithmetic progression (AP)
(a1) started with, 5 pennies
common difference (d), 3 pennies
formula: Tn = a + (n-1)d
after 10 days, T10 = 5 + (10- 1)(3)
T10 =5 + 27
T10= 31
therefore after ten days savannah has 31 pennies
The flywheel on a steam engine rotates 60 revolutions every 15 seconds.
What is the flywheel’s rate of revolutions per second?
Identify the unit rate.
Answer:
Step-by-step explanation:
4 revolutions per second
3x+4y=10 , 2x +3y = 7
Answer: x=2, y=1
Step-by-step explanation:
Find the exact circumference of circle by using the given polygon.
b. circumscribed square with side 10 feet long
The hypotenuse of the right triangle is the diameter of the circle then the circumference of the circle is 17[tex]\pi[/tex] centimeters.
What is circumference of a circle?The midpoint is the point in the middle of a line segment in geometry. It serves as the segment and endpoint centroid because it is equidistant from both endpoints. The segment is cut in half.
The diameter of the circle is the hypotenuse of the right triangle.
Use the Pythagorean Theorem to find the diameter.
By using Pythagorean theorem we get
[tex]$$c^2 = a^2 +b^2[/tex]
substituting the values in the above equation, we get
[tex]$$c^2 = 8^2 +15^2[/tex]
simplifying the equation
[tex]$$c^2[/tex] = 289
c = 17
The diameter of the circle is 17 cm.
The circumference C of a circle is given by C = [tex]\pi[/tex] d.
Circumference of a circle = [tex]\pi[/tex]d
= [tex]\pi[/tex] (17) = (17) [tex]\pi[/tex]
Therefore, the circumference of the circle is 17[tex]\pi[/tex] centimeters.
The correct question is:
Find the exact circumference of each circle by using the given inscribed or circumscribed polygon.
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Can you guys help me please
The shortest length of fabric, in inches, that Kirk could use to make the tablecloth without putting any separate pieces of fabric together is 30 inches
How to solve for the shortest length of fabric required to make the table clothGiven data
diameter of the table = 3 feet
hang down dimension = 5 inches
sew down dimension = 1 inch
width of rectangular fabric = 60 inches
The question seeks for area of the table cloth, for a circular table area of a circle = pi * r^2
required radius of cloth
= radius of the table + hang down dimension + sew down dimension
= 3 feet / 2 + 5 inches + 1 inch
= 1.5 * 12 inches + 5 inches + 1 inch
= 18 + 5 + 1
= 24 inches
Area of required cloth
= pi * 24^2
= 1809.557 square inches
Area of fabric = Area of required cloth
length * wide = 1809.557 square inches
length * 60 = 1809.557 square inches
length = 1809.557 / 60 square inches
length = 30.159 inches ≈ 30 inches
Therefore option H which is 30 inches is the answer
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what's a factor in math
Answer:
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
If w = 22, what is the value of 4w − 12?
Answer:76
Step-by-step explanation:
you replace W with 22
4(22)-12
=88-12
=72
hope this helps! :)
Answer:
76
Step-by-step explanation:
4w-12
4(22)= 88-12
88-12
76
Hope It Helps
Sorry If I'm Wrong
