The linear equation that passes through the given points is:
y + 9 = -10*(x - 1)
How to write the linear equation?A general linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:
a = (y₂ - y₁)/(x₂ - x₁)
Then using any of these points we can write the line as:
y - y₁ = a*(x - x₁)
Here the points are (1, -9) and (-10, 101), then the slope is:
a = (101 + 9)/(10 - 1) = 110/-11 = -10
And using the point (1, -9) we can write the line as:
y + 9 = -10*(x - 1)
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what is factoring: problems involving factors of polynomials
Step-by-step explanation:
Factoring a polynomial is basically simplifying it by finding greatest common factors and writing it in a distributive property form
For example:
Factor \(9a^2b^3c+18a^3b^2c^4+3a^2b^4c^2\)
3 is a greatest common factor in the numerical coefficient.
\(a^2\) is a greatest common factor
\(b^2\) is a greatest common factor
\(c\) is a greatest common factor
You would write it as \(3a^2b^2c(3b+6ac^3+b^2c)\)
If you meant like prime factorization, you just write a number as the product of prime numbers.
For example, 36 prime factorized is \(2*2*3*3\) or \(2^2*3^3\) because 4 and 9 aren't prime, so you need to factorize it further to 2*2*3*3
Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3
it took Stephanie 2 1/3 hours to travel to her Aunt's house, and then 1 2/3 hours to travel to her Grandma's house. How many total hours did Stephanie travel?
Answer:
It took Stephanie 4 hours
Step-by-step explanation:
2 1/3 + 1 2/3 = ?
To make it easier, let's add them differently
2 + 1 = 3
1/3 + 2/3 = 1
1 + 3 = 4 hours
Or turn them into mixed numbers:
7/3 + 5/3 = 12/3 = 4 hours
So our final answer is 4 hours.
Hopefully this helps :3 sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
The following expression will evaluate to 2.5:(double) (10 / 4)© True) False
The statement is False. The expression evaluates to 2.0, not 2.5.
The expression (double) (10 / 4) involves several steps of evaluation. Let's break it down to understand the process.
Integer Division: The division operation 10 / 4 is performed first. In integer division, the result is the quotient of the division without any decimal places. In this case, 10 / 4 equals 2, as the fractional part is truncated.
Type Casting: The expression (double) is a type cast that converts the result of the division to a double data type. However, the type casting occurs after the integer division has already taken place. So, the result of the type casting will not affect the value obtained in the integer division.
As a result, the expression (double) (10 / 4) evaluates to 2.0, not 2.5. The value 2.0 is a double representation of the integer 2. The type casting only affects the data type of the value, not its actual numerical value.
Therefore, the statement "The following expression will evaluate to 2.5: (double) (10 / 4)" is false. The expression evaluates to 2.0.
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True. The expression (double) (10 / 4) will evaluate to 2.5.
To evaluate the given expression, we need to follow the order of operations. First, we have the casting operation, which involves converting the result of the division to a double data type. Then, we have the division operation, which involves dividing 10 by 4.
Let's break down the steps:
Perform the division operation: 10 / 4 = 2.5Perform the casting operation: (double) 2.5 = 2.5Therefore, the expression (double) (10 / 4) will evaluate to 2.5.
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What is the solution for this system of equations?
Answer: y = x +8
Step-by-step explanation:
(a) increase the difference between 5/6 and 2/3 by 1/6
(b) decrease the product of 3/10 and 4/5 by 1/20
Answer:
(A): 1/3
(B): 4 and 4/5
Step-by-step explanation:
(A):
5/6 - 2/3 = 1/6
1/6 + 1/6 = 2/6, or 1/3
(B):
3/10 x 4/5 = 24/100
Simplify: 6/25
6/25 divided by 1/20 is 4 and 4/5
eli uses the factor theorem to determine whether x−2 is a factor of 6x5−22x2 11x−126.how does he proceed to the correct answer?
Answer:
Hello,
Step-by-step explanation:
\(P(x)=6x^5-22x^2+11x-126\\\\P(2)= 6*2^5-22*2^2+11*2-126=0\\\\x-2\ is\ well\ a \ factor\ of\ P(x).\\\\\begin{array}{c|ccccccc}&x^5&x^4&x^3&x^2&x&1\\---&---&---&---&---&---&---\\&6&0&0&-22&11&-126\\x=2&&12&24&48&52&126\\---&---&---&---&---&---&---\\&6&12&24&26&63&0\end {array}\\\\P(x)=6x^5-22x^2+11x-126=(x-2)*(6x^4+12x^3+24x^2-26x+63)\\\)
If a number is divisible by 3, then its odd
Answer:
and? obviously bc 3 isnt a even number so then the answer wont be even
A storm caused a 9m hydro pole to lean over. The top of the pole is 7.5 m above the ground.
Calculate the angle between the tilted pole and the ground. Round to the nearest degree.
Answer:
ur hyp would be 9m(cuz that's the length of the pole)
ur opp would be 7.5m
draw a right angle triangle(the 90 degrees on the left side)
the angle u need will be on the bottom left of the triangle.
now u need to use SOH cuz u got hyp and opp.
sin theta =opp/hyp
then u need to do:
sin‐1 opp/adj to find the angle
round to the nearest whole.
I'm not sure if this helped but yeah.
Vertex (-2,-5) passes through (4,4) in vertex form
The equation of parabola is \(y=1/4x^{2}+x/2-4\\\\\).
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
Given:
The equation of parabola in vertex form is
\(y=a(x-h)^{2} +k\)
Being vertex here
h=-2
k=-5
According to given question we have
∴
Equation of parabola in vertex form is
\(y=a(x+2)^{2} -5\)
. The parabola passes through point (4,4) So the point (4,4) will satisfy the equation .
\(4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4\)
Hence the equation of parabola is
\(y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\\)
Therefore, the equation of parabola is \(y=1/4x^{2}+x/2-4\\\\\).
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the equation of parabola is missing
Which of the following expressions is equal to - x2 - 4 ?
O A. (-x-21)(- 2)
O B. (x+2)(x - 21)
O C. (-x + 2)(x - 21)
O D. (-x - 2)(x+21)
A coach gives her players the option of running around feel twice or around the entire stadium once the following diagram shows the field in stadium dimensions on a corner grid which runs longer how much longer. Ill give brainliest and such this is also worth some good points
Answer:
Distance around the stadium is 75.16 monger than the field
Step-by-step explanation:
From the graph attached,
Coordinates of A → (-10, 60)
Coordinates of B → (60, -10)
Coordinates of C → (10, -60)
Coordinates of D → (-60, 10)
Perimeter of field = AB + BC + CD + DA
Since field is in the shape of a rectangle,
AB = CD and BC = DA
Therefore, perimeter of the rectangle = 2(AB + BC)
Length of AB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
= \(\sqrt{(60+10)^2+(-10-60)^2}\)
= \(\sqrt{2(70)^{2} }\)
= \(70\sqrt{2}\) m
Length of BC = \(\sqrt{(60-10)^2+(-10+60)^2}\)
= \(50\sqrt{2}\) m
Perimeter of ABCD = 2(70√2 + 50√2)
= 240√2 m
= 339.41 m
Perimeter of stadium = 2πr [Here, r = radius of the circle]
= 2π(120)
= 753.98 m
To run around the field twice, distance covered by the players = 2(339.41)
= 678.82 m
Difference in the distance covered to run around the stadium and the rectangular field = 753.98 - 678.82
= 75.16 m
Answer:
The distance around the stadium is longer than about 75
Step-by-step explanation:
On the map below, all numbered streets run parallel to each other. Both 3rd and 4th streets are intersected by King Avenue.
A delivery driver is driving around town and has noticed that every time he turns, it creates an angle. What are the measures of Angles X, Y, and Z on the map?
In your answer, give the measures of angles X, Y, and Z, and explain how you calculated each one.
Answer:
ok
Step-by-step explanation:
x:
X is adjacent to the 75 angle so x + 75 need to be 180.
180 - 75 = 105
x = 105
z:
Z is on opposite across outside corners from X so it will be the same thing.
z = 105
y:
Y is adjacent to Z so Y + Z must equal 180.
Z = 105
y + 105 = 180
y = 75
HELP ASAP PLEASE! THANKS!
Answer:
m∠x = 70°
Step-by-step explanation:
Since both 3.5 sides are congruent, then we have an isosceles triangle. That means the other unknown angle measure is also 55°. Since all angles of a triangle add up to 180°,
x + 55(2) = 180
x + 110 = 180
x = 70°
1.Let x, y be any two numbers that satisfies the conditions x ≠0, y ≠0, and x 0
C.y/x>1
D.x/y<1
2.A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A.no more than 50
B.no less than 50
C.no less than 45
D.no more than 45
3.It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
A.30 miles per hour
B.56 miles per hour
C.50 miles per hour
D.64 miles per hour
*please make sure you answer all the questions please and thank you.
Answer:
x and y can be any two numbers greater than zero such that y is also greater than x
D.no more than 45
C.50 miles per hour
Step-by-step explanation:
Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .
Suppose we take y= 9 and x= 3 then
9/3 > 1
3>1
Also
3/9 < 1
1/3 < 1
x and y can be any two numbers greater than zero such that y is also greater than x
2. Total weight that can be carried is 3000 pounds.
The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.
The smaller machines weigh 60 pounds
The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.
3. Total distance = Speed * time
= 48 * (40/60) = 32 miles
New distance = 32+ 8= 40 miles
New time = 48 minutes
Speed = distance / time = 40/ 48/60= 50 miles per hour
PLSSSSSS HELP!!!!!!!
Jamie has two similar rectangular boxes. If the sides of one box are three times the lengths of the corresponding sides of the other box, which one of the following is true?
a. The volume of one box is 3 times the volume of the other.
b. The volume of one box is 6 times the volume of the other.
c. The volume of one box is 9 times the volume of the other.
d. The volume of one box is 27 times the volume of the other.
Answer:
B
Step-by-step explanation:
(There is 2 sides.)
Convert the following equation
into standard form.
y = -x - 3
Answer:
x+y=−3
Step-by-step explanation:
hope this heps:)
Answer:
x+y=-3 (put -3 into the box)
Step-by-step explanation:
add x to both sides, and you get x+y= -3.
Answer this qn sm1
Also, can others check on my latest 2 qns?
Answer:
Check the attachment.
Which of the following is equivalent to x4 - y4? Select all that apply.
(-y)(x + y)3
(x2 - y2)2
(x - y)2(x + y)2
O 62 - y2)(x2 + y2)
o 6-y)6+y)(x2+x2)
Answer: (x^2-y^2) (x^2+y^2) and (x-y)(x+y)(x^2+y^2)
Step-by-step explanation:
(x2 − y2) (x2 + y2)Expand (x2 − y2) (x2 + y2) using the FOIL Method.
Apply the distributive property.
x^2 (x^2 + y^2 ) − y^2 (x^2 + y )
Apply the distributive property.
x^2 x^2 +x^2 y^2 - y^2 (x^2 y^2 )
Apply the distributive property.
x^2 x^2 + x^2 y^2 - y^2 x^2- y^2 y^2
Combine the opposite terms in x^2 x^2 + x^2 y^2 - y^2 x^2 - y^2 y^2.
Reorder the factors in the terms x^2 y^2 and − x^2 y^2.
x^2 x^2+ x^2 y^2 - x^2 y^2 - y^2 y^2
Subtract 2 2 from 2 2.
x^2 x^2+ 0 - y^2 y^2
Add 2 2 and 0.
x2 x2- y2 y2
Simplify each term.
Multiply x2 by x2 by adding the exponents.
x^4 − y^2y^2
x^4 − y^4
(x-y)(x+y)(x^2+y^2)(x − y) (x + y) (x^2 + y^2)
Expand (x − y) (x + y) using the FOIL Method.
(x ⋅ x + xy − yx − y ⋅ y) (x^2 + y^2)
Combine the opposite terms in x ⋅ x + xy − yx − y ⋅ y.
(x ⋅ x − y ⋅ y) (x^2 + y^2)
(x^2 − y^2) (x^2 + y^2)
Expand (x^2 − y^2) (x^2 + y^2) using the FOIL Method.
Apply the distributive property.
x^2 (x^2 + y^2) − y^2 (x^2 + y^2)
Apply the distributive property.
x^2 x^2 + x^2y^2 - y^2 (x^2 + y^2)
Apply the distributive property.
x^2 x^2 + x^2 y^2 - y^2 x^2 - y^2 y ^2
Combine the opposite terms in x^2x^2 + x^2y^2 − y^2x^2 − y^2y^2.
x^2x^2 − y^2y^2
x^4 − y^4
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the largest of the following integers which divides each of the numbers of the sequence $1^5 - 1,\, 2^5 - 2,\, 3^5 - 3,\, \cdots, n^5 - n, \cdots$ is:
The sequence's numbers are all multiples of 30. Every number can be divided by 30.
If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)
At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable
Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.
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I NEED HELP ASAP!!! 100 POINTS
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
f=3
f=4
f=5
f=6
Answer:
A
Step-by-step explanation:
We are given:
\(\cos(22f-1)=\sin(7f+4)\)
Recall the co-function identity:
\(\sin(\theta)=\cos(90-\theta)\)
Let θ = 7f + 4. So:
\(\sin(7f+4)=\cos(90-(7f+4))\)
Substitute:
\(\cos(22f-1)=\cos(90-(7f+4))\)
Remove the cosine:
\(\displaystyle 22f-1=90-(7f+4)\)
Distribute:
\(22f-1=90-7f-4\)
Subtract:
\(22f-1=-7f+86\)
Add 7f and 1 to both sides:
\(29f=87\)
Therefore:
\(f=3\)
Use x for number of
meters and y for number of kilometers.
meters
1,000
3,500
500
75
1
kilometers
1
The number of kilometers are 1,3.5,0.5,0.075,0.001.
Meters are 1000,3500,500,75,1.
The number of meters is x.
The number of kilometers is y.
kilometer = 1/1000×meter
y = 1/1000×x
The units of length and distance are meters and kilometers, respectively. The kilometer, or 1,000 meters, serves as the unit of distance measurement in the metric system. Therefore, one meter is equivalent to a thousandth of a kilometer.
A meter is denoted by the letter m, whereas a kilometer is denoted by the letter km. The default unit of length measurement in the metric system. Between the length of a ruler and the spacing between objects in a room, meters are used to measure everything.
Therefore the number of kilometers are 1,3.5,0.5,0.075,0.001.
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there are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue. you pick a box at random and randomly select a marble from it. the marble is blue. what is the strength factor of the evidence you just got that you picked the special box?
The strength factor of the evidence you just got that you picked the special box is 4.
Given:
There are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue.
Hypothesis = The box the blue marble was picked from is the special box.
Prior confidence = 1:3 (ratio of special boxes to non special boxes )
Now P(B | S) = 1/2 (given that a box is selected from the special box, there is 1/2 chance that it is blue)
And P(B | NS) = 1/8 (given that a box is selected from a non-special box, there is 1/8 chance that it is blue)
According to bayes factor ,we get:
P(B | S)/P(B | NS) = (1/2)/(1/8) = 4
Thus, 4.
Therefore the strength factor of the evidence you just got that you picked the special box is 4.
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You know the length and the width of a scale model. What additional information do you need to know to find the scale of the model? The options are... A. The width or height of the actual item B. The length or width of the actual item C. The height or width of the actual item D. The depth or height of the actual item and how would I explain my reasoning depending on the answer?
Answer:
B; The length or width of the actual item
Step-by-step explanation:
In cases like this, to find the scale factor, we will need to make a comparison between the length or width of the scale model and the length or width of the actual item
By having a further information about the length or width of the actual item, then we can actually make a comparison by dividing the length or width of both cases by each other
This means that we compare the length of the scale model and the length of the actual item
Then the width of the scale model and the width of the actual item
zeros are also called roots, x-intercepts, and solutions. question 1 options: true false
The given statement "Zeros are also called roots, x-intercepts, and solutions" is true.
Zeros, roots, x-intercepts and solutions are all the same and interchangeable terms. These terms are used to describe the value of x for which a function's value is 0. Zeros of a function are called roots because they are solutions to the equation f(x) = 0.
They are called x-intercepts because the x-axis is the line where the value of y is 0, and so the zeros occur at the points where the graph intersects the x-axis. Finally, they are called solutions because finding the zeros of a function is equivalent to solving the equation f(x) = 0. In conclusion, all these terms are synonymous with each other, meaning that they refer to the same thing, the value(s) of x for which the function's value is zero.
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A standing wave can be mathematically expressed as y(x,t) = Asin(kx)sin(wt)
A = max transverse displacement (amplitude), k = wave number, w = angular frequency, t = time.
At time t=0, what is the displacement of the string y(x,0)?
Express your answer in terms of A, k, and other introduced quantities.
The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.
At time t=0,
the standing wave can be mathematically expressed as
y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.
This means that the displacement of the string is zero at time t=0.
However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.
As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).
The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.
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Given a standard normal distribution, determine the following probability. Round the solution to four decimal places, if necessary.
P(-0.15 < z < 2.67)
To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.
Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:
P(z < 2.67) ≈ 0.9960
P(z < -0.15) ≈ 0.4404
To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:
P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)
≈ 0.9960 - 0.4404
≈ 0.5556
Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.
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john has a bag that contains one tile for each letter of the alphabet. why is the probability that he will pull out a vowel
Answer:
19% chance he pulled out aeio and u
You pick a card at random. Without putting the first card back, you pick a second card at random. Card numbers are 2, 3, 4, and 5 What is the probability of picking a 2 and then picking a number greater than 3? (Write your answer as a fraction or whole number.)
Answer:
1/6
Step-by-step explanation:
When trying to calculate the probability of a sequence of events you need to multiply the probability of the first event happening by the probability of the second event happening. There are a total of 4 numbers (2,3,4,5) and only one is a 2. Therefore the probability of the first pick being a 2 is 1/4. Now there are only 3 cards left (3,4,5) and only 2 numbers are greater than 3 so the probability of picking one of these cards is 2/3. Now that we have both of these probabilities we simply multiply them together.
1/4 * 2/3 = 2/12 or 1/6
Therefore, the probability of picking a 2 and then picking a number greater than 3 is 1/6
PLEASE HELP I'm literally failing math and this is hard
Answer:
b = 12.5
YZ= 100
Step-by-step explanation:
X__Y__Z
XZ = XY + YZ
175 = 6b + 8b
175 = 14 b
b = 175/14
b = 12.5
YZ = 8 b = 8 × 12.5 = 100
I hope I helped you^_^