-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]
Find: [tex]\textsf{The equation in point-slope form}[/tex]
Solution: We need to take the values that were given to us and plug them into the point-slope form. It doesn't seem like the problem is asking for anything more than that so we will leave it at that.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).
Answer:
[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
Step-by-step explanation:
[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]
We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).
Then, we substitute these values into the Point-Slope Form to find the equation.
Here are both forms for future reference:
⇒ Slope-Intercept Form: y = mx + b
[ Where: m is the slope, and b is the y-intercept (when x = 0). ]
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
[ Where: m is the slope, and (x₁, y₁) is a given point. ]
Substitute the values into the Point-Slope Form:
[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
Learn more here:
https://brainly.com/question/27971495
Work out, giving your answer in its simplest form:
2/3 x 3 3/5
Answer: 12/5
Step-by-step explanation:
[tex]3 \frac{3}{5}=\frac{18}{5}\\\\\implies \frac{2}{3} \times 3 \frac{3}{5}=\frac{2}{3} \times \frac{18}{5}\\\\=\frac{36}{15}\\\\=\boxed{\frac{12}{5}}[/tex]
Gene has a gasoline budget of $300 per month. He uses an average of $6 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
Answer:
300-6x
Step-by-step explanation:
Trust me
[tex]\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }[/tex]solve this equation
Answer:
Step-by-step explanation:
Exponent law:
[tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]
[tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]
First convert radical form to exponent form and then apply exponent law.
[tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]
[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]
[tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]
Select the statement below that correctly describes the relationship between the number of workers and the hours that they work.
Less workers = more hours
OR the answer might be worded as
More workers = less hours
The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds. Using the empirical rule, what is the probability that a cat will weigh less than 11 pounds?
If the value of the z-score is 1. Then the probability that a cat will weigh less than 11 pounds will be 0.84134.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds.
Then the probability that a cat will weigh less than 11 pounds will be
The value of z-score will be
z = (11 – 9) / 2
z = 1
Then the probability will be
P(x < 11) = P(z < 1)
P(x < 11) = 0.84134
Thus, the probability that a cat will weigh less than 11 pounds will be 0.84134.
More about the z-score link is given below.
https://brainly.com/question/15016913
#SPJ1
sum of numbers 975,983,923,913 and 985 rounded upto hundredth place is
Answer:
4800
Step-by-step explanation:
If a question is asking for the "sum" of numbers, this just means we have to add them altogether.
975+983+923+913+985 = 4779
To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).
7 > 5 so we round up. 7 becomes 8.
4800.
what does 5r-r-9=15 look like after combining like terms ?
and whats the answer for r?
The value of r from the expression is 6
Simplifying expressionGiven the expression below;
5r-r-9=15
Add 9 to both sides
5r - r - 9 + 9 = 15 + 9
4r = 15 + 9
4r = 24
After combining the like terms the expression will be 4r = 24
4r/4 = 24/4
r = 6
Hence the value of r from the expression is 6
Learn more on expression here: https://brainly.com/question/723406
#SPJ1
Which expression is equivalent to startfraction (4 p superscript negative 4 baseline q) superscript negative 2 baseline over 10 p q superscript negative 3 baseline endfraction? assume p not-equals 0, q not-equals 0.
The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]
What are indices?
An index is a small number that tells us how many times a term has been multiplied by itself.
The plural of index is indices.
Below is an example of a term written in index form :[tex]4^{3}[/tex]
4 is the base and 3 is the index.
We can read this as ‘4 to the power 3’
Another way of expressing [tex]4^{3}[/tex] is
4 x 4 x 4 = 64
Indices can be positive or negative numbers.
Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
= [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex] By using the property of exponents is given by:
[tex](a^{m})^{n}=a^{m n}[/tex]
=[tex]\frac{p^{7}q}{10 .16}[/tex] By using the property of exponents given by
[tex]a^{m}a^{n}=a^{m + n}[/tex] and [tex]a^{-m}= \frac{1}{a^{m}}[/tex]
= [tex]\frac{p^{7}q}{160}[/tex]
Learn about indices here :
https://brainly.com/question/27327380
#SPJ4
Mr. Lopez fruit salad recipe requires 3/4 of a cup of fresh peaches for 1 serving. He uses 9 cups of fresh peaches to prepare the salad. How many servings of the fruit salad did he prepare?
Answer:
6.75 servings
Step-by-step explanation:
[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]
Answer:
9 servings
Step-by-step explanation:
feel free to ask where you don't understand.
Inventory was taken on Day 1, Day 2, Day 5, Day 6, and Day 7. Norris wants to know roughly what the inventory was on Day 3.
What should he do to estimate the inventory on Day 3?
He should use the value for Day 2 because it is closest in value to Day 3.
He should randomly pick a point near the fitted line where x=3.
He should evaluate the function f(x)=−1/3 x+4 for y=3.
He should evaluate the function f(x)=−1/3 x+4 for x=3.
Answer:
A
Step-by-step explanation:
guessing
He should evaluate the function f(x)=−1/3 x+4 for x=3 , Option D is the correct answer.
What in Interpolation ?Interpolation is when the line of best fit is used to determine the value of a point that is within the range of plotted points.
It is given to find the value at Day 3 which lies in the range of the points used for plotting
The line for best fit is
f(x) = (-1/3)x +4
At x = 3
f(3) = (-1/3) * 3 +4
f(3) = -1+4 = 3
Therefore He should evaluate the function f(x)=−1/3 x+4 for x=3
Option D is the correct answer.
To know more about Interpolation
https://brainly.com/question/18768845
#SPJ1
Find all solutions of the equation in the interval .
Write your answer in radians in terms of .
If there is more than one solution, separate them with commas.
The solutions to the trigonometric equation in the desired interval are given as follows:
[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]
What is the solution to the trigonometric equation?The trigonometric equation is given by:
[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]
Solving it similarly to an equation, we have that:
[tex]\sqrt{3}\cot{\theta} = 1[/tex]
[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]
Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:
[tex]\tan{\theta} = \sqrt{3}[/tex]
The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:
[tex]\theta = \frac{\pi}{3}[/tex]
In the fourth quadrant, the equivalent angle is:
[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]
More can be learned about trigonometric equations at https://brainly.com/question/24680641
#SPJ1
Factor x² - 4x + 5.
A Prime
B (x + 5)(x - 1)
C (x - 5)(x - 1)
D (x + 5)(x + 1)
Answer:
[tex]\huge\boxed{\sf Option \ A}[/tex]
Step-by-step explanation:
Given expression:= x² - 4x + 5
We can not factor out this expression, because of we apply mid-term break to it, the factors -4x will break into are -5x + x the coefficients of which when multiplied give -5 and not +5 (side term). This is a known rule in the mid-term break formula.
So, the given expression is a prime expression.[tex]\rule[225]{225}{2}[/tex]
(02.07)
The equation below shows the relationship between the
temperature in degrees Celsius, C, and degrees Fahrenheit, F:
H
C
(F-32)
Which of the following formulas correctly solves for F? (1 point)
Answer:
[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]
Step-by-step explanation:
The correct relation between degrees Celsius, °C, and degrees Fahrenheit, °F is :
[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]
PLEASE HELP 15 POINTS
Answer:
B
Step-by-step explanation:
Used elimination method.
first plugged in (0,0)which remove A,D
than saw the line is not solid so chose B
$Need help with this pls (quickest answer gets brainliest)
Answer:
-1/2
Step-by-step explanation:
IK
8 1/2 - 3/8=?
pls answer fast
Answer:
65/8
Step-by-step explanation:
1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?
2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8
3) Can not simplify since there are no common factors between 65 and 8.
Find the slope of every line that is parallel to line on the graph (0,-3) (5,-4)
The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5
How to find the slope of a parallel lines?Parallel lines have the same slope.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
Therefore,
x₁ = 0
x₂ = 5
y₁ = -3
y₂ = -4
Therefore,
slope = -4 - (-3) / 5 - 0
slope = -4 + 3 / 5
slope = - 1 / 5
learn more on slope here: https://brainly.com/question/8978282
#SPJ1
Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let represent the number of students who bought a cup of orange juice and represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
+ 3 = 76
+ = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables.
In order to eliminate one of the variables, subtract one of the equation from the other equation.
How to eliminate one of the variables?Given these equations:
o + 3s = 76 equation 1
o + s = 36 equation 2
Where:
o = number of orange juice bought
s = number of sandwiches bought
In order to eliminate one of the variables, subtract equation 2 from equation 1. The result is :
2s = 40
s = 20
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ1
The temperature fell at a rate of 0.65 °C/h. The temperature was recorded at 37 °C
at 6 p.m. Which function can be used to represent this situation?
Of(x) = 37 -0.65x
Of(x) = 0.65x - 37
Of(x) = 37x + 0.65
Of(x) = 0.65x+37
The linear function that can be used to represent the temperature in x hours after 6 pm is given by:
f(x) = 37 - 0.65x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem:
The y-intercept is the initial temperature of 37ºC.The slope is the rate of change of -0.65ºC/h.Hence the function is:
f(x) = 37 - 0.65x.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Need Help Fast!!!!!! The graph of the piecewise function f(x) is shown. f(x) What is the range of f(x)?
Answer:
The second option
Step-by-step explanation:
If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4
Andrea has 3 tiles. One is a regular octagon, one is a regular pentagon and one is a regular hexagon. Andrea thinks the 3 tiles will fit together perfectly, as shown in the diagram. Show calculations to prove that she is wrong.
From calculations, we can say that the given tiles will not fit together perfectly.
How to find the sum of interior angles of a Polygon?If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
Read more about Interior angles of a Polygon at; https://brainly.com/question/224658
#SPJ1
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
Using proportion, the equivalent units of the following units rounded to the nearest hundredth are as follows:
6km = 3.73 miles2.5 Litres = 0.66 gallons90 pounds = 40.82 kgHow to use proportion to find equivalent units?Using proportion,
1.60934 km = 1 miles
6 km = ?
cross multiply
distance(m) = 6 / 1.60934 = 3.7282364199 = 3.73 miles
1 litre = 0.264172 gallons
2.5 litres = ?
volume(gallons) = 2.5 × 0.264172 = 0.66 gallons
1 pounds = 0.453592 kg
90 pounds = ?
cross multiply
weight(kg) = 40.82328 = 40.82 kg
learn more on proportion here; brainly.com/question/14063625
#SPJ1
its math help me out?
Its the first one
--------------------
Answer:
$24 = $0.40(60)
Step-by-step explanation:
Match the input value and its location in the equation.
__
$24 = $0.40(60)
_____
Additional comment
When input is liters and output is dollars, the constant of proportionality must have units of "dollars per liter." The dollar sign of these units is not shown in the left panel, but is shown on the answer choices. If you understand units conversion, this should not be a mystery. (The mystery is why the curriculum materials are inconsistent.)
answer?.............
Answer:
-21
Step-by-step explanation:
A passenger jet plane cruises at 550 knots. It enters a jet stream with
a tailwind speed of 120 knots. If the speed of sound is 661 knots,
will the jet travel faster or slower than sound during its journey?
Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.
What is the ground speed?The jet's speed, considering that there is a tailwind, is given by:
J = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 550 knots.Wind: 120 knots.Hence the jet's speed is given by:
J = 550 + 120 = 670 knots.
670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.
A similar problem, involving plane and wind's speed, is given at brainly.com/question/25547425
#SPJ1
John is 1/8 meter shorter than Paul, and Paul is 0.25 meter taller than Andrew. John's height is 13/4 meters, what is Andrews height?
Answer:
About 2.13
Step-by-step explanation:
13/4 multiply by 7/8 to get 91/32, then multiply by 0.75(3/4), which is 273/128
CAN SOMEONE HELP ME PLS?????
You are correct, P(red) = P(green) = 0.25.
Ahman has a lawn care business. he charges $25 per lawn to mow the grass. if his monthly expenses are $100, how many lawns must he mow in order to make a profit of at least $250 per month?
Answer:
14
Step-by-step explanation:
you can write an equation to represent the situation:
let x represent the number of lawns he has to mow
then, the monthly profit would be 25x - 100.
in order to make $250, this equation has to be equal to 250:
[tex]25x-100=250[/tex]
now, solve this:
add 100 to both sides
[tex]25x = 350[/tex]
divide both sides by 25
[tex]x = 14[/tex]
he must mow 14 lawns
Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To solve the problem substitute the value of n as 5 in each expression and then simplify to check if it equals to 16 or not.
A.) (25/n) + 7
= (25/5) + 7
= 12
This is not the required expression.
B.) 30 - 3n
= 30 - 3(5)
= 15
This is not the required expression.
C.) 7+ (45/n)
= 7 + (45/5)
= 7 + 9
= 16
This is the required expression.
D.) n² - 114
= (5)³ - 114
= 125 - 114
= 11
This is not the required expression.
Hence, the correct option is C.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
Which expression is the simplest form of 2x^3 - x^2 + 3 (x^3 - 4x^2)
The simplest form of the given expression is 5x^3-5x^2.
We have given that
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)[/tex]
We have to determine the simplest form of the given expression.
What is the distributive property?
The distributive property of binary operations generalizes the distributive law, which asserts that equality is always true in algebra. elementary.
Use the distributive property we get,
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)\\=2x^3 - x^2 +3x^3-12x^2\\[/tex]
Add like terms we get,
Therefore we get,
[tex]=5x^3-5x^2[/tex]
Therefore the simplest form of the given expression is 5x^3-5x^2.
To learn more about the expression visit:
https://brainly.com/question/723406
#SPJ1
