Find the equation, in standard form, of the line passing through the points
(2,-3) and (4,2).
A. 5x+2y=16
B. 5x – 2y=16
C. y=5/2x+8
D. 2x – 3y=9
Answer:
B
Step-by-step explanation:
To solve for the slope:
(2-(-3))/(4-2)=5/2
y=5/2x+b
plugin points:
2=5/2(4)+b
2=10+b
b=-8
so equation of the line is y=5/2x-8
and in standrd form its 5x-2y=16
If
3y + 1
2
= 5,
4x
3
= 8
and
z
3
+
z
4
= 2
A. y > x B. x = y C. y > z D. x > z
Step-by-step explanation:
hey, write the question properly...
If the equation are 3y + 12= 5,4x - 3= 8 and z³ + z⁴ = 2, then x = y
Let's start by solving each equation one by one to find the values of the variables.
Equation 1: 3y + 12 = 5
Subtracting 12 from both sides:
3y = 5 - 12
3y = -7
Dividing both sides by 3:
y = -7/3
Equation 2: 4x - 3 = 8
Adding 3 to both sides:
4x = 8 + 3
4x = 11
Dividing both sides by 4:
x = 11/4
Equation 3: z³ + z⁴
This equation is a bit more complex, and it seems challenging to find the exact values of z. However, we can deduce some information about the relationship between z³ and z⁴ by examining the equation. Since both terms are positive, the sum of z³ and z⁴ can never be negative. Therefore, the only possible solution is when both z³ and z⁴ are less than 2.
Now, let's compare the values of y, x, and z:
y = -7/3 ≈ -2.33
x = 11/4 ≈ 2.75
z³ + z⁴ < 2 (as explained above)
Based on these values, we can determine the relationship between the variables:
A. y > x
B. x = y
C. y > z
D. x > z
The correct answer is: B. x = y
To know more about equation here
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Explain the meaning of the following A scale on a map is 1mm:20 miles
Answer:
for every 1mm is equal to 20 miles (it is a scale)
Step-by-step explanation:
help find the value of x
Answer:
40
Step-by-step explanation:
1 inch= 2.54 cm
How many centimeters equal 8 feet?
20.32 cm
96 cm
30.48 cm
243.84 cm
HELP PLEASEE EASY QUESTION
Which statements are true about the polynomial function?
f(x)=x3−x2−4x+4
Select each correct answer.
f(x)=0 when x=−1 .
f(−1)=0
(x−1) is a factor of f(x) .
f(x) divided by (x−1) has a remainder of 0.
Answer:
D. f(x) divided by (x−1) has a remainder of 0.
C. (x−1) is a factor of f(x) .
Step-by-step explanation:
Just took a test with this question these are the answers!
The statements that are true about the polynomial function are;
(x−1) is a factor of f(x). f(x) divided by (x−1) has a remainder of 0.Given the polynomial function [tex]f(x)=x^3-x^2-4x+4[/tex]
If x = -1, hence;
[tex]f(-1)=(-1)^3-(-1)^2-4(-1)+4\\f(-1)=-1-1+4+4\\f(-1)=-2+8\\f(-1) =6[/tex]
This shows that f(x) ≠ 0 when x = −1 .
To check if x - 1 is a factor, we will substitute x = 1 into the function and check if the result is zero as shown:
[tex]f(1)=1^3-1^2-4(1)+4\\f(1)=1-1-4+4\\f(1) =0[/tex]
This shows that (x−1) is a factor of f(x).This also shows that if f(x) divided by (x−1) has a remainder of 0.
Learn more here: https://brainly.com/question/18820029
Paulo has $12 and wants to buy grapes from the fruit vendor. they cost 2.59 per pound . what is the maximum number of grapes he can buy
write the inequality and solve it
Gilberto needs to purchase baseballs and bats for his youth baseball league. He'll need at least 15 pieces of equipment, but he only has $435 to spend. Baseballs cost $20 each and bats cost $35 each. If Gilberto wants to purchase the most amount of equipment and still stay within his budget, which combination of baseballs and bats is optimal? (2 points)
a (20, 1)
b (13, 5)
c (13, 2)
d (10, 5)
Answer: A) (20, 1)
Step-by-step explanation: Largest number
Please!!! Help me :((((
Answer:
1 mile
Step-by-step explanation:
Simplify 16x^3 - 8x^2 + 4x^4 / 2x
A) 8x^2 - 4x + 2x^3
B) 8x^2 - 4 + 2x^3
C) 8x^3 - 4x + 2x^3
D) 8x^2 - 4x + 2x
Answer:
2 x ^3 + 8 x ^2− 4 x
Step-by-step explanation:
Just simplify!
What do you know about distance? math
Answer: Mathematical distance is defined as the amount of space between two points. This distance can be calculated using the distance formula, which is just a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the other two sides
Step-by-step explanation:
What is solution to 3/5=z/10
A farmer wants to set up a pigpen using 40ft of fence to enclose a rectangular area of 51 square feet. Find the dimensions of the pigpen.
Answer:
The sides of the pigpen are 3 by 17
Step-by-step explanation:
Perimeter of pigpen => 2x + 2y = 40
Area of pigpen => xy = 51 (this is assuming x = length, and y = width)
Let's isolate "y" for the first equation;
2x + 2y = 40
2(x + y) = 40
x + y = 20
y = 20 - x
xy = x(20 - x) = 51 = 51
20x - x^2 = 51
x^2 - 20x + 51 = 0
According to the quadratic equation =>
x = ( - (- 20) + √(- 20)^2 - 4 * 1 * 50 ) / 2 * 1 = 17
x = ( - (- 20) - √(- 20)^2 - 4 * 1 * 50 ) / 2 * 1 = 3
The dimensions of the pigpen are actually 17 by 3
Proof: 17(3)= 51, 2(17) + 2(3) = 40
Convert 14.8 inches(1 inch= 2.54 cm)
Answer:
37.592 cm
Step-by-step explanation:
Answer:
you just did
Step-by-step explanation:
How to Solve this??! 6x-2=x+13
Answer:
x=3
Step-by-step explanation:
We are given the equation, 6x-2=x+13.
1. 6x=x+15
2. 5x=15
3. x=3
Hope this helps! Good luck on your assignment!
Answer: x=3
Step-by-step explanation:
6x-2=x+13
First get both x’s on one side
We are going to subtract x from both sides
5x-2=13
Now we want to get 5x alone
We are going to add 2 to both sides
5x=15
Now we want to get x alone
We are going to divide by 5
x=3
The door to my classroom is 84 inches tall. How many blocks would I need to stack to the height of the door, If each block is 2 inches tall?
Answer:
42 blocks
Step-by-step explanation:
If each block is 2 inches, and the height of the door is 84 inches, you need to divide the height by the block size. Once you divide 84 by 2, you should get 42 blocks as your answer.
Can someone please help me, ty!! (Will mark brainliest)
Find the perimeter of the figure below, composed of an isoceles trapezoid and one semicircle. Rounded to the nearest tenths place
I can't see the semi circle is that image. From what I see, the perimeter of the trapezoid is 41.
The run times of a marathon runner are approximately normally distributed. The z-score for his run this week is – 2 . Which one of the following statements is a correct interpretation of his z-score?
Answer:
2 standard deviation under his average time
Step-by-step explanation:
What is the answer too −2/3(12c−9)+14c=
-2/3(12c - 9) + 14c
=-8c + 6 + 14c
=6c + 6
=6(c + 1)
Find the domain and range of f(x)=x/x^2-9
Answer:
[tex]Dom(f)=(-\infty, -3 )\cup (-3, 3 )\cup (3,-\infty )[/tex]
[tex]Ran(f)=\matyhbb{R}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{x}{x^2-9}[/tex]
Once the denominator can't be zero, [tex]x\neq 3[/tex] and [tex]x\neq -3[/tex]
[tex]Dom(f)=(-\infty, -3 )\cup (-3, 3 )\cup (3,-\infty )[/tex]
The range from the graph is all Real numbers
What is The opposite of -4
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour. The speed limit on this stretch of the freeway is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (Round your answer to four decimal places.) .0074 (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? (Round your answer to two decimal places.) What is the standard deviation of the number of cars he would expect to watch? (Round your answer to two decimal places.)
Answer:
a
[tex]G = 0.007523 [/tex]
b
The number of cars the highway patrol officer would watch before a car that is seen is [tex]E(X) = 1.6027 [/tex]
The standard deviation is [tex]s = 0.9829 [/tex]
gg
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 71.5 \ miles/hour[/tex]
The standard deviation is [tex]\sigma = 4.75 \ miles/hour[/tex]
The speed limit is [tex] x = 70 \ miles /hour[/tex]
Generally the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as
[tex]p =P(X > x ) = P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > -0.31579 )[/tex]
Here
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of X )[/tex]
So
=> [tex] p= P(X > 70) = P(Z > -0.31579 )[/tex]
From the z-table
[tex]p = P(Z > -0.31579 ) = 0.62392[/tex]
So
[tex] p = P(X > 70) = 0.62392 [/tex]
Generally the probability of getting a car that is not moving with speed greater than the speed limit is mathematically represented as
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.62392 [/tex]
=> [tex]q = 0.37608 [/tex]
Generally the probability of getting 5 cars that are not speeding is mathematically represented as
[tex]G = q^5[/tex]
=> [tex]G = (0.37608)^5[/tex]
=> [tex]G = 0.007523 [/tex]
Generally the number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten is mathematically represented as
[tex]E(X) = \frac{1}{p}[/tex]
=> [tex]E(X) = \frac{1}{0.62392}[/tex]
=> [tex]E(X) = 1.6027 [/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{1 - p }{ p^2} }[/tex]
=> [tex]s = \sqrt{\frac{1 -0.62392 }{ (0.62392)^2} }[/tex]
=> [tex]s = 0.9829 [/tex]
The probability that 5 cars pass and none are speeding is 0.007523 and the number of cars the highway patrol officer would watch before a car that is seen is E(X) = 1.6027
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour.
The speed limit on this stretch of the freeway is 70 miles/hour.
Generally, the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as;
[tex]p = P(X > x) = P(X > 70) = P(z = \dfrac{X - \mu}{\sigma } > \dfrac{70 - 71.5}{4.75})\\\\p = P(X > 70 ) = P(\dfrac{X -\mu}{\sigma} > -0.31579)[/tex]
From the z-table
[tex]p = P(X > 70)= P(z > -0.31579) \\\\p = 0.62392[/tex]
Generally, the probability of getting a car that is not moving with speed greater than the speed limit will be
q = 1 - p
q = 1 - 0.62392
q = 0.37608
Generally, the probability of getting cars that are not speeding will be
G = q⁵
G = 0.37608⁵
G = 0.007523
The number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten will be
[tex]\rm E(X) = \dfrac{1}{p}\\\\E(X) = \dfrac{1}{0.62392}\\\\E(X) = 1.6027[/tex]
The standard deviation will be
[tex]\sigma = \sqrt{\dfrac{1-p}{p}}\\\\\\\sigma = \sqrt{\dfrac{1-0.63292}{0.62392}}\\\\\\\sigma = 0.9829[/tex]
More about the normal distribution link is given below.
https://brainly.com/question/12421652
[ it's a fraction but i can't write it as such. ]
Solve for M.
m/5 = 4
9
20
-9
-20
Answer:
the value of m will be 20
An x-box cost $230 but is discounted 28%. What is the new cost of the x-box?
The new cost of the Xbox is $165.60
1.00 - 0.28 = 0.72
0.72 * 230 = 165.60
Write 3 < x < 9 in interval notation.
Answer:
(3, 9)
Step-by-step explanation:
If we have ≤ or ≥, we use brackets to signify it includes the values.
If we have < or >, we use parenthesis to signify it doesn't include the values.
Simplify 3-8 divided by 3-2
Answer:
-5
Step-by-step explanation:
[tex] \frac{3 - 8}{3 - 2} [/tex]
[tex] \frac{ - 5}{1} [/tex]
[tex] - 5[/tex]
15 less than a number is equal to 12
Answer:
Step-by-step explanation:
x - 15 = 12
x = 27
Sunshine City was designed to attract retired people. Its current population of 75,000 residents has a mean age of 63 years and a standard deviation of 17 years. The distribution of ages is skewed to the left. A random sample of 250 residents of the city had a mean of 61.4 and a standard deviation of 19. Show work for any necessary calculations. (6 pts) a) Identify the variable of interest. b) Describe the center and spread of the population of Sunshine City. c) Describe the center and spread of the random sample of Sunshine City residents taken. What shape does it probably have
Answer:
a) Identify the variable of interest.
Ages of the residents
b) Describe the center and spread of the population of Sunshine City.
Center of the population of Sunshine city = 63 years
Spread of the Population of Sunshine city = 17 years
c) Describe the center and spread of the random sample of Sunshine City
residents taken.
Center of the random sample of Sunshine city = 61.4 years
Spread of the random sample of Sunshine city = 19 years
What shape does it probably have:
It has a skewed(left) shape
Step-by-step explanation:
a) Identify the variable of interest.
Ages of the residents
The center of a distribution tells us about the Mean or Median of the distribution
The spread of a distribution tells us about the standard deviation of the population
b) Describe the center and spread of the population of Sunshine City.
Center of the population of Sunshine city = Mean of the population of Sunshine city = 63 years
Spread of the Population of Sunshine city = Standard Deviation of the population = 17 years
c) Describe the center and spread of the random sample of Sunshine City
residents taken.
Center of the random sample of Sunshine city = 61.4 years
Spread of the random sample of Sunshine city = 19 years
What shape does it probably have:
It has a skewed(left) shape
This is because the mean is farther out to the left side of the tail of the distribution.
Answer please I need it ASAP
Answer:
answer what???
Step-by-step explanation:
