keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well then, that simply means that
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
Where do 2 lines intersect at
Answer:
Point of intersection is the point where two lines or two curves meet each other. The point of intersection of two lines of two curves is a point.
Step-by-step explanation:
Hope it helps! =D
2 lines intersect at:
A point
In a plane, crossed lines square measure any 2 or a lot of lines that cross each other. The purpose of intersection, which may be found on all crossed lines, is wherever the crossed lines share a standard purpose.
Perpendicular lines square measure 2 lines that cross at associate angle of right angles.
Since the purpose of intersection is that the solely location wherever the 2 graphs meet once the lines cross, the coordinates of that location offer the solution to the equations involving the 2 variables.
There are not any solutions once the lines square measure parallel.
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I need help on this question
To find the scale factor we just need to divide the final measurement by the initial measurement, then we have:
[tex]\begin{gathered} k=\frac{1120}{28} \\ k=40 \end{gathered}[/tex]Therefore, the scale factor is 40
X
If mAXC = 217°, what is m
○ 37°
71.5°
48°
A
74°
B
Answer:
Step-by-step explanation:
45 degrees -67/6
Carlo spent 2 3/8 hours studying for a test
in the morning. Then he spent 1 1/4 hours
studying in the evening. How many hours
did he spend studying for the test in all?
Answer: 3 5/8 hours
Step-by-step explanation:
2 + 1 = 3
1 / 4 = 2 / 8
3 / 8 + 2 / 8 = 5 / 8
Which is greater 16/20 or 9/20
Substitute the length of the sides (8in, 15 in, z) into the Pythagorean Theorem. Then, find the length of the missing side z.
The length of the missing side z would be 17 units which is determined by Pythagoras's theorem.
What is Pythagoras's theorem?A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
According to Pythagoras's theorem,
⇒ a² + b² = c²
Here, a = 8 b = 15 and c = z
⇒ (8)² + (15)² = z²
⇒ 64 + 225 = z²
Apply the addition operation,
⇒ 289 = z²
⇒ z² = 289
⇒ z = √289
⇒ z = 17
Therefore, the length of the missing side z would be 17 units.
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Heatheris participating in arace that is broken up into 1/5 mile sections. each section has to be run by a different person and each team member can only run once ifthe race is s5 1/5 miles long, how many please will heather need on her team?
Based on the distance of the race and the length of the sections, the number of people that Heather will need to be on her team are 26 people
How to find the number of people needed?The entire race has a length of 5 1/5 miles and this length will be divided into sections that are 1/5 miles long.
Only one member of the team can run in each of these sections so enough people are needed on Heather's team to run the 1/5 mile sections.
The number of people to be in a team can be found by the formula:
= Length of race / Length of sections
= 5 1/5 miles / (1/5)
= 26/5 ÷ 1/5
= 26/5 x 5/1
= 26 people
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I dont understand the steps to getting to the answer.
Answer:
(a) Fermat's little theorem states that for any prime p , we have
a^p-1 = 1 (mod p).
for any integer ,a. Then
999999 = 1000000 - 1 = 10^6 - 1 = 1 - 1 = 0 (mod 7)
so 7 does indeed divide 999,999.
(b) Generalizing, we have
10^12n - 1 = 999...999 (12n nines) = (10^n)^12 - 1 = 0 (mod 13)
for positive integer, n. Now, since 1 = 1001 - 1000 and -1 = (mod 1001) , it follows that 10^3 is its own inverse modulo 1001, i.e.
10^3 x = 1 (mod 1001) -----> x = 10^3
This means
10^12n = (10^3 x 10^3)^2n = 1^2n = 1 (mod 1001) ----> 10^12n - 1 = 0 (mod 1001)
Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
The required polynomial function is y=3(x+3)⁴(x-4 ) for the conditions as mentioned fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
What is Polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
What is multiplicity?The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
Here the given conditions are:
Fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
Let y be the f(x) and x be the variable.
Now, x+3 is the first term and x-4 be the second term with their multiplicity 4 and 1.
y=3(x+3)⁴(x-4)
For the above-mentioned fifth-degree conditions, the necessary polynomial function is y=3(x+3)⁴(x-4); 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
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determine whether or not the given procedure results in a binomial distribution. if not, identify which condition is not met. surveying 35 people to determine if a particular brand of candy bar is their favorite.
No, the given procedure doesn't result in a binomial distribution.
We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.
1: Each observation should be independent, it must not depend on the result of previous observation.
2: The probability of success should stay same from trial to trial.
3: n is fixed (the number of observations)
4: There are only two outcomes success or failure.
Surveying 2828 people to determine which statistics courses they have taken.
3 is satisfied since n is fixed
1 is satisfied since each observation is independent
4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).
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choose the equation that matches each line
The equation y = - 2x + 4 matches the line
How to find the equation?
The line passes through two points .
[tex](x_1, y_1) = (2, 0)\\\\(x_2, y_2) = (0, 4)[/tex]
We know that slope (m) is given by,
[tex]m =\frac{y_2 -y_1}{x_2 -x_1} \\\\m =\frac{4-0}{0-2} \\\\m= -\frac{4}{2} \\\\m= -2[/tex]
We know the slope- intercept form of an equation is:
y = mx+ c ----(1)
Let us substitute the point [tex](x_1, y_1)[/tex] and m in (1)
y = mx+ c
0 = -2(2) +c
c = 4
Let us substitute c and m in (1)
The slope- intercept form of the equation is:
y = -2x + 4
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solve the following system of equations algebraically
x+y-z=6
2x-3y+2z=-19
-x+4y-x=17
Answer: {x,y,z}={-11/14,27/7,-41/14}
Step-by-step explanation:
System of Linear Equations entered :
[1] x+y-z=6
[2] 2x-3y+2z=-19
[3] -x+4y-x=17
Equations Simplified or Rearranged :
[1] x + y - z = 6
[2] 2x - 3y + 2z = -19
[3] -2x + 4y = 17
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = -x + z + 6
// Plug this in for variable y in equation [2]
[2] 2x - 3•(-x +z +6) + 2z = -19
[2] 5x - z = -1
// Plug this in for variable y in equation [3]
[3] -2x + 4•(-x +? +6) = 17
[3] -6x = -7
// Solve equation [2] for the variable z
[2] z = 5x + 1
// Plug this in for variable z in equation [3]
[3] -6x = -7
[3] 14x = -11
// Solve equation [3] for the variable x
[3] 14x = - 11
[3] x = - 11/14
// By now we know this much :
x = -11/14
y = -x+z+6
z = 5x+1
// Use the x value to solve for z
z = 5(-11/14)+1 = -41/14
// Use the x and z values to solve for y
y = -(-11/14)+(-41/14)+6 = 27/7
Solution :
{x,y,z} = {-11/14,27/7,-41/14}
draw two lines in the following trapezoid to create three equilateral triangles
A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary.
What is a trapezoid?In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. As opposed to the particular examples below, a scalene trapezoid is a trapezoid without equal sides.
The Greek mathematician Euclid identified five different quadrilateral shapes, of which four had two sets of parallel sides (the square, rectangle, rhombus, and rhomboid in English) and one did not (a trapezia, meaning "a table," which comes from "four" and means "a foot; end, boundary, edge").
In his commentary on the first book of Euclid's Elements, Proclus (412–485) developed two varieties of trapezia: one pair of parallel sides, or a trapezium (v), divided into isosceles (equal legs), and scalene (unequal) Similar to how cuboid and rhomboid both mean "resembles," trapezia with no parallel sides is a trapezoid, trapezoeidé, or literally "trapezium-like."
English followed Proclus's arrangement until the late 18th century, when a prominent mathematical lexicon produced by Charles Hutton in 1795 endorsed a transposition of the terms without providing an explanation. Although this error was fixed in British English around 1875, it remained in American English till the present..
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Carson works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 15% of his total sales for the week. How much would Carson make in a week in which he made $1575 in sales? How much would Carson make in a week if he made x dollars in sales?
The amount of money that Carson make in a week in which he made $1575 in sales is $686.25.
How to calculate the amount?From the information, Carson makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 15% of his total sales for the week.
Therefore, the amount that he will be paid when he sees $1575 will be:
Base salary + Commission
= $450 + (15% × $1575)
= $450 + $236.25
= $686.25
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Pregunta, si hay 3% de probabilidades de encontrara algo especial en una caja cuantas cajas debería abrir para encontrarlo?
The number of boxes that should be opened to find it is 98 boxes.
What is probability?Probability simply means the likelihood of the occurence of an event.
When there is a 3 percent chance or finding something special in a box,the number of boxes that will be opened will be illustrated thus:
Let the number of boxes be 100.
Therefore, the number of boxes will be:
= Total boxes - Percentage given
= 100 - 3
= 97
In this case, the 98th box will give the person the chance of getting it.
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about 9% of the population has a particular genetic mutation. 800 people are randomly selected. find the mean for the number of people with the genetic mutation in such groups of 800.
Using the binomial distribution, it is found that the mean for the number of people with the genetic mutation in such groups of 800 is of 72
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, we have that:
About 9% of the population has a particular genetic mutation, hence p = 0.09
800 people are randomly selected, hence n = 800.
Then, the mean is given by:
E(X) = np = 800 x 0.09= 72
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Need this done asap need to be turned in the next 20min please help
A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields then the function exists described as: y = 9000 + 1500 h.
What is meant by linear function?The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields.
The given parameters exists:
Initial = 9000
Rate = 1500
The function exists estimated as: y = Initial + Rate × h
Where h represents the number of hours.
Let the equation be y = Initial + Rate × h
Substituting the values in the above equation, we get
y = 9000 + 1500 × h
y = 9000 + 1500 h
Therefore, the function is represented as: y = 9000 + 1500 h
The complete question is:
A 21,000-gallon swimming pool contains 9000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1500 gallons per hour. Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.
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When a man observed a sobriety checkpoint conducted by a police department, he saw drivers were screened and were arrested for driving while intoxicated. Based on those results, we can estimate that , where w denotes the event of screening a driver and getting someone who is intoxicated. What does denote, and what is its value?.
The thing that P(W) represents is A. It denotes the probability of screening a driver and finding that he or she is not intoxicated.
The value is 0.99257
What is probability?It should be noted that probability simply means the likelihood that something will happen or occur based on the information given.
From the information, the man observed a sobriety checkpoint conducted by a police department, he saw drivers were screened and were arrested for driving while intoxicated.
P(W) = 0.000743
Therefore, those that are not intoxicated will be:
= 1 - P(W)
= 1 - 0.000743
= 0.99257
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3. Maria gave David x cards, gave Tina two
more cards than she gave David, and
gave Samuel five fewer cards than she
ovalno
gave Tina. In terms x, how many cards
did Maria give Tina, David, and Samuel
all together?
Answer:
4x-5
Step-by-step explanation:
Help please need urgent help
In the picture we can see there is a line with an intersection line.
∠3=(13x+7)° and ∠6 =(9x+59)°. The angles ∠5=4°, Option A is correct.
Given that,
In the picture we can see there is a line with an intersection line.
A transversal is a line that creates angles when it crosses two parallel lines (or lines on a plane) at various points.
∠3 =(13x+7)° and
∠6 =(9x+59)°
In the parallel lines alternatives angles are always equal.
So,
∠3=∠6
13x+7=9x+59
13x-9x=59-7
4x=52
x=52/4
x=13
Now,
∠3 =(13x+7)°=(13×13+7)°=(169+7)°=176°
∠6 =(9x+59)°=(9×13+59)°=(117+59)°=176°
Now,
From the supplementary angles.
∠5+∠6=180°
∠5=180°-∠6
∠5=180°-176°
∠5=4°
Therefore, We got the angles ∠5=4°, Option A is correct.
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What is the value of y
The answer is 7^6. But just put a 6 in the box.
The reason is because 7 x 7 x 7 x 7 x 7 x 7 = 117,649.
Also, 7^6 is equivalent to 117,649.
So, the answer is 7^6 or just 6.
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Elwyn is packing food for a family picnic.He has prepared 15 sandwiches and 30 corn dogs.He wants everyone to have an identical number of sandwiches and corn dogs and with nothing leftover.How many members at the maximum can be served
In order for everyone to have an identical number of sandwiches and corn dogs, with nothing left over, a maximum of 15 people, each person gets 2 corn dogs and 1 sandwich. Note that this is an HCF problem.
What is the calculation justifying the above?The HCF (Highest Common Factor) of two numbers is the highest number among all of the provided numbers' common factors. The HCF of 10 and 30, for example, is 10 since 10 is the highest common factor of 10 and 30.
In this case, the HCF is 15.
Proof:
We can divide 30/15 and still get an integer
= 2
hence we can distribute the sandwiches in 15 ways making 15 people. Hence, each person will get 2 Corn Dogs leaving no remainder.
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PLEASE SOLVE ASAP!!!!
Answer:
(0, 6)
(-1 , 5)
Step-by-step explanation:
A ball is thrown in the air. The function H = 30t - 5t^2 can be used to find the height (H) of the ball in meters after t seconds.
How long does it take the ball to reach a height of 45 meters?
The ball to rise 45 meters in 3 seconds.
How do you find the solutions of a quadratic equation?
Put the equal sign with all terms on one side and zero on the other.Factor.Each factor should be set to zero.Fix each of these problems.Put your solution into the original equation to make sure.Since these are the values of x for which f(x) = 0, the roots of the function f(x) = ax2 + bx + c correspond to the solutions of the quadratic equation ax2 + bx + c = 0.Depending on the sign of the discriminant, there are always either 0, 1, or 2 real solutions to a quadratic equation. However, if you include both real and complex numbers, there is always at least one answer.here
Function : [tex]H= 30t-5t^{2}[/tex]
height = 45m
then [tex]30t-5t^{2} = 45[/tex]
simplify the quadratic equation ⇒ [tex]6t-t^{2} -9=0[/tex]
⇒ [tex]t^{2} -6t+9=0[/tex]
⇒ [tex](t-3) (t-3)=0\\t=3.[/tex]
time required to reach 45m = 3 sec.
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PLS SOMEONE HELP ME PLS!•A figure is dilated by a scale factor of 4. Which of the following is true about the figure and its dilation? A. The perimeter of the image is 4 times as large as the perimeter of the pre-image.B The perimeter of the image is 8 times as large as the perimeter of the pre-image.C The perimeter of the image is 16 times as large as the perimeter of the pre-image.D The perimeter of the image is the same as the perimeter of the pre-image.
Answer:
A. The perimeter of the image is 4 times as large as the perimeter of the pre-image.
Explanation:
To answer this question, we use an example.
Given the pre-image:
• A square with side length 1 cm
,• Perimeter = 4 x 1 = 4cm
If the square is dilated by a scale factor of 4:
• Side length = 4cm
,• Perimeter = 4 x 4 =16cm
We see therefore that 'The perimeter of the image is 4 times as large as the perimeter of the pre-image.'
The correct choice is A.
HELP PLEASE IF YOU CAN SOLVE YOUR A GENIUS FR FR
Answer:
[2005]=25.29
Step-by-step explanation:
[tex]y = 7.41 + 2.98x[/tex]
Aera of paraellgrams
i don’t know how to solve this problem
Answer:
x = 5, y = 25
Step-by-step explanation:
I use the substitution method to solve. (I hope I got the equations correct)
6x + y = 55 ---1
10x + 3y = 125 ---2
From 1: y = 55 - 6x ---3
Substitute 3 into 2:
10x + 3(55 - 6x) = 125
10x + 165 - 18x = 125
- 8x = - 40
x = 5
Substitute x into 3
y = 55 - 6(5) = 25
The ratio of boys to girls in the 9th grade is 7 to 9. There are 218 girls. Set up a proportion to model this information.
The ratio of boys to girls in the 9th grade is 7 : 9. Girls are 218
proportion of girls in total students are [tex]\frac{218}{9}[/tex] = 24.2
According to the question, given that
In class ratio of boys and girls is 7 : 9
and girls in the class are 218
Proportion of girls in total class = [tex]\frac{218}{9}[/tex]
= 24.2
Therefore, we get proportion of girls in the class is 24.2
When determining if two ratios or fractions are equivalent, the proportion formula is utilized. The proportional formula is as follows:
a : b :: c : d = a/b = c/d
Proportion Formula
a:b::c:d = a/b = c/d
where,
a, d = Extreme terms
b, c = Mean terms
The product of means equals the product of extremes is one of the various proportional formulas. You can write this as ad = bc.
Two additional proportional formulas that depend on direct or indirect variation are available. When two quantities x and y are in direct proportion, y = k x, and when x and y are in indirect proportion, y = k/x, with k serving as the proportionality constant in both cases.
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109. How many positive, even integers satisfy the
inequality 4n+ 13 ≤ 69 ?
A.
1
B.
2
C. 5
D. 7
All real numbers n that is less than 14 when plugged in for x will be less than 14 in inequality .
What is inequality in math?
A relationship between two expressions or values that is not equal to each other is referred to as inequality in mathematics.The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Some people in the medical field receive better and more skilled care than others. Additionally, they must pay more for these services.inequality = 4n+ 13 ≤ 69
= 4n ≤ 69 - 13
= 4n ≤ 56
= n ≤ 56/4
= n ≤ 14
Thus, all real numbers n that is less than 14 when plugged in for x will be less than 14.
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