Answer:
"If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular."
Step-by-step explanation:
Let n be the least positive integer for which 149^n-2^n is divisible by 3^3.5^5.7^7.$ Find the number of positive integer divisors of n.
Calculating the LCM of all these, one gets 2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}
Step-by-step explanation:
Note that for all n, 149^n-2^n is divisible by 149-2=147 by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3 is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.
Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}
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Find the values of x and y in parallelogram PQRS.
PT =y. TR = 3x + 1, QT = 3y. TS = 5x + 11
x=
y=
PLEASE HELPPP!!!!
In the parallelogram PQRS, x = 2 and y=7
Parallelogram:
A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has opposite sides of equal length and opposite angles of equal length. Also, the interior angles on the same side of the horizontal line are supplementary angles. The sum of all interior angles is 360 degrees. A three-dimensional shape whose faces are parallelograms is called a parallelepiped. The area of a parallelogram depends on its base (one of its parallel sides) and its height (height drawn from top to bottom). The perimeter of a parallelogram depends on the length of its four sides.
Given that
PT=y, TR=3x+1, QT=3y, TS=5x+11
The diagonals of a parallelogram bisect each other
PT = TR and QT = TS
y = 3x+1 and 3y = 5x+11
Now,
We have a system of equations
Multiply the first equation by 3
3y = 9x+3 and 3y = 5x+11
Set them equal
9x + 3 = 5x + 11
⇒ 9x - 5x = 11 -3
⇒ 4x = 8
⇒ x =2
Now,
Putting the value of x =2 in equation :
y = 3x+1
=3(2)+1
=7
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Please help ASAP this is for a final test
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer: I'm sorry bro i don't know
Step-by-step explanation:
Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour before the faster and arrives at the opposite shore at the same time as the other ferry, what is the speed of the slower ferry
The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.
How to find the calculation?Let x represent the first ferry's speed.
The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)
First ferry time equals distance/speed equals
50/x
Time spent on the second ferry:
50 / x - 5
The difference in times is 1 hour because the second ferry departs an hour earlier.
50 / x - 5 - 50/x = 1
50x - 50(x - 5) = x (x - 5 )
250 = x² - 5x
x² - 5x - 250 = 0
(x - 10 )(x + 5) = 0
x = 18.5 - 13.5
Speed can never be detrimental.
Therefore, the first ferry's speed is 18.5 mph.
and the second ferry, which is slower, travels at 13.5 mph.
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Find the value of x.
2x-8
6
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
1. Cameron ran 3 miles in 24 minutes. Identify the equivalent ratio that represents Cameron's run. *
The equivalent ratio that represents Cameron's run is 1 : 8
Equivalent Ration:
In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.
For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.
Based on the question :
Cameron ran 3 miles in 24 minutes.
Now,
Therefore we can say that :
Cameron ran 1 miles in 8 minutes;
Therefore, the equivalent ration is 1 : 8.
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Find the measure of the indicated angle to the nearest degree.
Answer:
? ≈ 20°
Step-by-step explanation:
using the cosine ratio in the right triangle
cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then
? = [tex]cos^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 20° ( to the nearest degree )
x^2=Σ(o-e)^2/e
17. A candidate for mayor is discussing the crime rate in the city. She asks the police department to provide some statistics on how many people out of a group of 500
people were victims of four specific crimes. She expects that she can verify this information by doing her own survey. She then asks a group of 500 people to identify
whether they were victims of the same crimes. Her results are the observed quantities, and the police data are the expected quantities. The following is a table of the
results.
Category: observed/ expected
Robbery
24/18
Assault
15/21
Discrimination
79/56
Theft
124/138
Calculate the chi-square value for her survey. Remember, to calculate the chi-square value, use the formula shown.
A. 12.68
B. 8.56
C. 8.15
D. 14.58
On solving the provided question we cans ay that - the value of the following exponent is
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
here,
= [tex]10^2 X 10^-3[/tex] X 32
= 100 X 1/1000 X 32
=1/10 X 32
=3.2
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Is 4x² 3x 7 a polynomial?
As all the exponents of x are whole numbers, the expression 4x² – 3x + 7 is a polynomial in one variable.
What is exponents?The exponent of a number shows how many times the original value of the number has been multiplied. For example, the number 34 indicates that we have multiplied three by four. 3 × 3 × 3 × 3 × 3 is its expanded form. Exponent is another term for a number's power. It might be a decimal, a fraction, a negative number, or a whole number.
Exponents are important because without them, writing the product when a number was repeated many times on its own would be very difficult. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5.
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Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answer:
Step-by-step explanation:
Find the value of x.
2x-8
6
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
In this course, we'll begin to
explore "opposite" function types. For example, think about
a quadratic function and its key features. What key features do you think its opposite
function will have? Why?
Answer:
Some key features quadratic functions have are:
Axis of symmetryx and y-interceptsZeroesvertexPoint symmetric to y-interceptStep-by-step explanation:
Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''
Amrita divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (USE π=22/7 )
The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.
Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs
Step 1: Calculate the circumference of the original circle.
Circumference of a circle = 2πr
Circumference of the circle with a radius of
7 cm = 2πr = 2 × 22/7 × 7 = 44 cm
Step 2: Calculate the perimeter of each semicircular shape disc.
The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.
Perimeter of each semicircular shape disc
= 44 cm/2
= 22 cm
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Dave can clean pools at a constant rate of 3/5 pools/hour. How long does it take Dave to clean 15 pools?
9 hours will it take to clean the 15 pools.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Dave can clean pools at a constant rate of 3/5 pools per hour.
This also means that he cleans 3 pools in 5 hours
So, the time taken to clean 15 pools is
= 15×3/5
= 9 hours.
Hence, the time taken is 9 hours.
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3) Camile offers you a challenge. Are the triangles below similar? Examine them and tell how
you know.
a) Use a flowchart to organize your explanation.
b) Camile says, "These triangles aren't just similar-they're congruent!" Is Camile
correct? What special value in your flowchart indicates that the triangles are
congruent?
a) The flowchart for the congruency of triangles is given below.
b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.
What is congruency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
In the given diagram, it can be seen that -
Line segment DQ = Line segment XZ.
Similarly, Line segment PQ = Line segment XY.
Since, the two sides of the triangle are equal, hence the third side must also be equal.
Line segment PD = Line segment ZY.
Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.
Therefore, the triangles PDQ and ZXY are equal and congruent.
The flowchart for the same is given below.
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Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Constructing a line segment of length 2 and then finding the
midpoint
B. Drawing a perpendicular line segment through a given point on a
given segment
C. Drawing a line through a given point parallel to a given line
D. Drawing a perpendicular line segment from a given point to a
given segment
Answer: Constructions A, B, and D can be accomplished with paper folding.
Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.
Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.
Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.
Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.
Step-by-step explanation:
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment. What is construction in mathematics?Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -
Constructing bisectors of lines and angles.Constructing regular polygons inscribed in circles.Constructing circumcircles and incircles.Constructing a line tangent to a circle.Given is to find which of the following constructions can be accomplished with paper folding.
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.Therefore, the following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.To solve more questions on constructions, visit the link-
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The manufacturer's price for a Jinko car is $x
Ben was given a 7% discount on the manufacturer's price when he bought a Jinko.
Ben paid $23 622 when he bought his Jinko.
(a) Calculate the value of x.
Answer:
x = $25,400 [the original price of the Junko car]
Step-by-step explanation:
The price Ben paid, $23,622, is after the 7% discount. Let x be the original price of the Jinko car. Ben's prices reflect a 7% discount:
x*(1-0.07) = $23,622 [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]
(0.93)x = $23,622
x = $25,400
need help on both these , preciate it .
Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units
Triangle - what is it?A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
The total of the circle, triangle, and square's surface areas.
The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.
=>A = 210 – 123 = 87 square units
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Why is triangle always 180 degrees?
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places
The sprinkler should be set to rotate through the angle 6.42 degrees.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
r = 50 yards
Area, A = 140 square yards
Θ = angle
A= (Θ /360) πr²
140 = (Θ /360) * 3.14 * 50*50
Θ = (140*360)/(3.14*25*100) = 6.42 degrees
The sprinkler should be set to rotate through the angle 6.42 degrees.
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3. Find the values of a and b. 36° 113° O
The measure of angles a and b is 144° and 67° respectively.
What is quadrilateral?There are four sides, four vertices, and four angles in a closed quadrilateral. It has a polygonal shape. It is produced by joining four non-collinear points. The total internal angle of a quadrilateral is always 360 degrees.
The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides. Each of a quadrilateral's four sides does not always have to be the same length.
Given a quadrilateral,
in which opposite sides are parallel,
so, When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional to 180°.
36° + a° = 180°
and 113° + b° = 180°
a° = 180° - 36° = 144°
and b° = 180° - 113°
b° = 67°
Hence the values of a° is 144° and b° is 67°.
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Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12
Consider rigid-body physics in a higher or lower dimension than three. How many coordinates are required to specify the location and orientation of a rigid body:If the space is two-dimensional?a. 2b. 3c. 4d. 5
In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.
In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.
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Select the correct answer.
Which phrase best describes the relationship indicated by the scatter plot?
A. constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Answer: B
Step-by-step explanation:
Correlation tells us the relationship of 2 variables. Looking at the graph, the data appears to going down, as we read graphs from left to right. We can automatically eliminate C and D, since we have determined going down. We know it's also not A because if the correlation is constant, then all the dots would be lined up, and not scattered around. Since the dots are going down, this tells us that it is a negative correlation. Hence, B is the answer.
Answer:
B. negative correlation
Step-by-step explanation:
expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
How do you tell if something is a difference of squares?
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.
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At summer camp this year, Clare is leading the beadwork class. Each of the 9 craft tables has a bucket of beads. The graph shows the weight of the beads in each bucket.
If Clare distributes all of the beads equally among the 9 buckets, how much will the beads in each bucket weigh?
The beads in each bucket will weigh 1 pound
How to determine the weight of the beads in each bucket?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.
In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.
weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound
Thus, each bucket weighs 1 pound
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Which of the following chocies is not a function?
A {(0, 0), (1, 4), (2,8)}
B {(0, 0), (3, 16), (16, 49)}
C {(1, 1), (2, 2), (3, 3), (4,4)}
D {(7, 1), (6, 2), (5, 3), (5,4)}
E All of these choices are functions.
One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
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