What is an equation of the line that passes through the point (4,−3) and is perpendicular to the line 4x+y=3
Answer:
[tex]y = \dfrac{1}{4} x - 4[/tex]
Step-by-step explanation:
Slope intercept form of line equation is y = mx + b, m = slope, b = y-intercept
Slope of line perpendicular to y =m x + b will have slope - (1/m)
4x+y=3 can be re-written as
y = -4x + 3
Slope = -4
Slope of line perpendicular to this line is - (1/-4) = 1/4
Line equation: y = (1/4) x + b
Plug in x, y values from given point into this line equation to find b
-3 = 1/4 x 4 + b
-3 = 1 + b
-3 -1 = b
b = -4
So equation of perpendicular line is y = (1/4)x - 4
8 4/5 - 5 1/10 math.
Answer:
3 7/10
Step-by-step explanation:
8 4/5 - 5 1/10
8 8/10 - 5 1/10
8 - 5 = 3 8/10 - 1/10 = 7/ 10
3 7/10
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 6.9 in Kobe, Japan, in 1995
The intensity level of the earthquake was compared to the intensity level of each earthquake below
1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.
2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.
3) The earthquake at New Madrid was of greater intensity than earthquake at Charlottesville.
4) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values.
The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle.
A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other.
The greater than sign is an approximation of a closing square bracket.
Hence, The magnitude of the earthquake was compared to each earthquake's magnitude above.
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The question is incomplete. The complete question is
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
1. magnitude 7.7 in San Francisco, California, in 1906
2. magnitude 9.5 in Valdivia, Chile, in 1960
3. magnitude 3.2 in Charlottesville, in 2001
4. magnitude 6.9 in Kobe, Japan, in 1995
Solve the equation 6y² + 5y -4 = 0 Give each answer as an integer or as a fraction in its simplest form.
Answer:
y1=-4/3, y2=1/2
Step-by-step explanation:
1/7 + (-3/4)
1/6 + (-4/9)
need help with these two questions, I’m very tired atm
Step-by-step explanation:
first question:
1/7 - 3/4 LCM : 28
4/28 - 21/28
= -17/28
second equation:
1/6 - 4/9 LCM : 36
6/36 - 16/36
= -10/36
= -5/14
( I believe these are the answers )
c. What happens to the y -values as x increases? As x decreases?
If the variation is direct, then the value of y decreases with a decrease in x and increases when x increases.
On the other hand side, if we are following inverse variation then the value of y will decrease if x increases and increase if x decreases.
How does direct variation work?If there is a constant k that is nonzero and such that y = kx, then the variable y fluctuates directly as x. The expression y = kx is referred to as a direct variation equation, and the variable constant is denoted by the number k.
Inverse variation: what is it?A function with the following equation as its definition is known as an inverse variation: xy = k , where k is a constant real integer that is not zero. There are several instances when one quantity changes as another does so indirectly.
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A company had $50,000 to invest in three funds. after one year it had $54,500. the growth
fund returned 12%, the income fund returned 8%, and the money market fund returned 5%.
the company invested twice as much in the income fund as in the money market fund. how
much did it invest in each fund?
The amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively
Let the amount invested in the growth fund, income fund and money market fund be x, y and z respectively
As per the question, the company invested twice as much in the income market as in the money market
Therefore,
y = 2z
Equations will be:
x + 2z + z = 50000
12/100x + (8/100)*2z + 5/100z = 4500
Solving the equations
x + 3z = 50000
12x + 21z = 450000
Multiplying the first equation by 7 for equating
7x + 21z = 350000
12x + 21z = 450000
Equating these two we get
5x = 100000
x = 20000
Putting x = 20000 in 7x + 21z = 350000
z = 10000
2z = 20000
So, the amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively
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please do A 1-4 and B 1-2
it’s due when i get to skoo
For item a, the linear functions are given as follows:
1. y = 1.5x.
2. y = 0.5x - 1.
3. y = -0.5x + 1.
4. y = -1.5x - 1.
For item B, we have that:
1. The functions are:
a. y = 2x + 3.
b. y = 0.5x - 1.
2. The unit rates(slopes) are:
a. 2
b. 0.5.
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.Item AIn graph 1, the function goes through (0,0), hence b = 0, and through point (2,3), hence the slope is:
m = (3 - 0)/(2 - 0) = 3/2 = 1.5.
Hence the function is:
y = 1.5x.
In graph 2, the function goes through (0,-1), hence b = -1, and through point (2,0), hence the slope is:
m = (0 - (-1))/(2 - 0) = 1/2 = 0.5.
Hence the function is:
y = 0.5x - 1.
In graph 3, the function goes through (0,1), hence b = 1, and through point (2,0), hence the slope is:
m = (0 - 1)/(2 - 0) = -1/2 = -0.5.
Hence the function is:
y = -0.5x + 1.
In graph 4, the function goes through (0,-1), hence b = -1, and through point (2,-4), hence the slope is:
m = (-1 - (-4))/(0 - 2) = -3/2 = -1.5.
Hence the function is:
y = -1.5x - 1.
Item BIn table a, the function goes through (0,3), hence b = 3, and through point (1,5), hence the slope is:
m = (5 - 3)/(1 - 0) = 2.
Hence:
y = 2x + 3.
The unit rate, which is the slope, is of 2.
For table b, the function goes through (2,0) and (6,2), hence the slope is:
m = (2 - 0)/(6 - 2) = 1/2 = 0.5.
Hence:
y = 0.5x + b.
When x = 2, y = 0, hence we can find b as follows.
0 = 0.5(2) + b
b = -1.
Thus:
y = 0.5x - 1.
The unit rate is of 0.5.
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The number of hamburger sales per week at a fast food restaurant is 350. The number of weekly sales goes down by 30. 0 hamburgers per week when the price of a hamburger is increased by 12%. Find the relative change in weekly sales
The relative change in weekly sales is mathematically given as
relative change= -12.857%
This is further explained below.
What is the relative change in weekly sales?This Sale per week after the price decreases
=350-45
=305
Generally, the equation for relative change is mathematically given as
[tex]\left(\frac{\text { final Value - Intial value }}{\text { Intial value }}\right) \times 100 \%$[/tex]
Hore final value =305 week
Initial Value =350 week
Relative Change[tex]=\left(\frac{305-350}{350}\right) \times 100[/tex]
[tex]&=\frac{-45}{350} \times 100[/tex] \\
=-12.857%
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A court reporter can type 215 words per minute.
How many minutes will it take the reporter to type a document that is 1,505 words long?
Enter the correct answer in the box.
It will take the reporter 7 minutes to type the document
The reporter can type 215 words in one minute
The reporter wants to type a document that is 1505 words long
The amount of time it will take the reporter to type a document that is 1505 long can be calculated as follows
215 = 1
1505 = x
cross multiply both sides to get the value of x
215x= 1505
divide both sides by the coefficient of x which is 215
215x/215 = 1505/215
x= 7
Hence the reporter will use 7 minutes to type out the 1505 word document
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Can anyone answer this please?
Using the above exponent rule, the value of t in the given equality [tex]5^3/ 5^9 = 5^t[/tex] will be t = -6.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
WE need to find the value of t in the given equality 5^3/ 5^9 = 5^t
Using the above exponent rule, we get
[tex]5^{3 -9 }= 5^t\\\\5^{-6}= 5^t[/tex]
Therefore, compairing both the side we get;
t = -6.
Hence the value of t in the given equality[tex]5^3/ 5^9 = 5^t[/tex]will be t = -6.
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3+10(9x+4)=763 what is my answer
Answer:
x = 8
Step-by-step explanation:
3 + 10(9X + 4) = 763 Distribute the 10
3 + 10(9x) + 10(4) = 763
3 + 90x + 40 = 763 Combine like terms
90x + 43 = 763 Subtract 43 from both sides
90x = 720 Divide both sides by 90
x = 8
Answer:
x=8
Step-by-step explanation:
What is the mode of the following set of numbers? {16, -10, 13, -8, -1, 5, 7, 10}
Answer:
there is no mode
Step-by-step explanation:
a mode is a number that appears more than once in a set of numbers whichWrite the fraction shown by this point…
Answer: -5/8
Step-by-step explanation:
Find the inverse of each function. Determine whether each inverse is a function. f(x)=15-3 x
The inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.
We are given the function:
f (x) = 15 - 3 x
Now, we need to find the inverse of the function.
For this, first we write the function as:
y = 15 - 3 x
Now, we will find the function in terms of x
3 x + y = 15
3 x = 15 - y
x = 5 - y/3
So, the inverse will become:
f ⁻¹ (x) = 5 - x/3
g (x) = 5 - x/3
Now, for one one function:
g (x₁) = g (x₂)
5 - x₁/3 = 5 - x₂/3
- x₁ / 3 = - x₂ / 3
x₁ = x₂
So, it is one - one.
So, the inverse is also a function as every element of x only has one image in y.
Therefore, the inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.
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$14 dollar meal 20% tip
Answer: A $14 dollar meal with a 20% tip would be $16.80. The tip would be $2.80.
Step-by-step explanation:
People generally tip 15-20% of the bill. To calculate the tip multiply the total check by 1 plus the decimal percentage tip you'd like to leave. If you wanted to leave a 20% tip, you would add 1 to 0.20 to get 1.20. Multiply 14 by 1.20 to get the total amount you'd leave including the tip which would be $16.80.
Hope this helps!
Ellen purchased a dishwasher, which cost $315 before the 9.22% sales tax. She used the machine an average of 10 times per week for the next six years, at which point she replaced it. Each time she ran the dishwasher it cost her $0.09 for water and $0.13 for electricity. What was the lifetime cost of Ellen's dishwasher? a. $1,030.44 b. $686.40 c. $1,093.73 d. $749.69 Please select the best answer from the choices provided. A B C D
The lifetime cost of Ellen's dishwater is $1,030.44
What is Number system?
A system of writing to express the number is called number system.
Given that;
Cost of dishwasher before sales tax 9.22% is = $315
And, Sales tax = 9.22%
Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043
And, Average of 10 times per week for the next 6 years before replacing it.
Since, There are 52 weeks in a year.
So, Average uses is calculated as,
10 * 52 * 6 = 3120
Since, cost for water = $0.09
Cost for electricity = $0.13
Total cost per uses = $0.22
Hence, Cost of uses = 0.22 * 3120 = $686.40
Now, Purchase cost = $344.043
And, Cost of uses = $686.40
Hence, Lifetime cost = $344.043 + $686.40 = $1,030.443
So, The lifetime cost of Ellen's dishwater is $1,030.44.
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Write 0.4444 as a fraction in lowest terms:
Answer:
1111/2500
Step-by-step explanation:
A banquet room is being set up for a party
using round tables. How many chairs are used
for the round tables?
The number of chair being set up for a round table in a party is 6.
What is probability?The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is called as probability.
Given that,
Banquet table rentals are often suited for less formal gatherings as opposed to round tables for formal ones.
Banquet tables are typically 4 feet, 6 feet, or 8 feet long and 30 inches wide. 8-foot tables
The most widely utilized dimension for guest seats. 4 chairs are present.
Eight people can sit comfortably at an 8-foot table.
Although seating can be provided at 4 and 6 foot tables
These sizes are often employed for different objectives.
4 guests may fit comfortably at a 4 foot banquet table, and 6 guests can
Banquet table can comfortably sit 6.
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the three medians of a triangle meet at a point called the ____
Answer: The three medians of the triangle are concurrent. The point of concurrency is called the centroid. Point A is the centroid of the triangle.
Step-by-step explanation:
Answer:
Centroid.
Step-by-step explanation:
This point is where the three medians of a triangle meet. The median in a triangle is the line between a vertex and the opposite side.
The table shows the relationship between the number of club a person belongs to and the amount of free time the person has per week. Number of Clubs Free Time (hours) 12 7 22 4 32 1 41 818. (1 point) Is the above relationship a linear function? What is the rule to describe the function f(x) that gives free time hours in terms of x, number of clubs a person belongs to? (ASAP I NEED IT TO BE ANSWERED I HAVE TESTING TMR )
The relationship a linear function and the equation is y = -3x + 24
Is the above relationship a linear function?The table of values is given as
Number of Clubs Free Time (hours)
1 27
2 24
3 21
4 18
A linear relationship is any relationship with a constant rate
From the above table, we can see that as x increases by 1, y decreases by 3
This means that
Slope = Rate = -3
Hence, the relationship a linear function
What is the rule to describe the function f(x)?In (a), we have
Slope = -3
Also, we have
Number of Clubs Free Time (hours)
1 27
Reduce the above parameters by the constant rate
So, we have
Number of Clubs Free Time (hours)
0 24
1 27
The above means that
y-intercept = 24
A linear equation is represented as
y = Slope * x + y-intercept
So, we have
y = -3x + 24
Hence, the equation is y = -3x + 24
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sum of 4(3x + 2) – 9 this is for algebra 2
Answer:
[tex] \sf \: 12x−1[/tex]
Step-by-step explanation:
Let's simplify step-by-step.
4(3x+2)−9
Distribute:
=(4)(3x)+(4)(2)+−9
=12x+8+−9
Combine Like Terms:
=12x+8+−9
=(12x)+(8+−9)
=12x+−1
=12x−1
Construct quadrilateral of wxyz wx is 4 cm xy3.5cm yz5cm wz5.5cm and angle x75degree
we have constructed the given quadrilateral.
The dimensions of the quadrilateral are:
WX = 4 cm
XY = 3.5 cm
YZ = 5 cm
WZ = 5.5 cm
∠ x = 75°
First draw a line segment WX = 4 cm.
Now from the point X, construct an angle of 75°.
Now, on the ray of that angle, mark an arc that is 3.5 came long and mark the intersection point as Y
Now, from point Y, draw an arc of 5 cm and from point W draw an arc of 5.5 cm.
Mark their intersecting point as Z
Join WZ and YZ
The quadrilateral is formed.
Therefore, we have constructed the given quadrilateral.
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Solve. Check for extraneous solutions. √3 x+13 -5=x
No The extraneous solution of this equation
The given equation is
[tex]\sqrt{3x + 13}[/tex] - 5 = x
[tex]\sqrt{3x + 13 }[/tex] = x + 5
We have to find the value of x, so we need to square both sides of the equation
[tex](\sqrt{3x + 13} )^{2}[/tex] = [tex](x + 5)^{2}[/tex]
3x + 13 = [tex]x^{2}[/tex] + 10x + 25
[tex]x^{2}[/tex] + 7x + 12 = 0
[tex]x^{2}[/tex] + 4x + 3x + 12= 0
x( x + 4) + 3( x + 4) =0
(x + 4) ( x + 3 ) = 0
x = - 3, -4
To find the value of the extraneous solution we need to put both the value of x in the equation
x = -3
[tex]\sqrt{(3 * -3) + 13}[/tex] - 5 = -3
[tex]\sqrt{-9 + 13}[/tex] - 5 = -3
[tex]\sqrt{4}[/tex] - 5 = -3
2 - 5 = -3
-3 = -3
Now
x = -4
[tex]\sqrt{(3 * -4 ) + 13}[/tex] - 5= -4
[tex]\sqrt{-12 +13}[/tex] - 5 = -4
[tex]\sqrt{1}[/tex] - 5 = -4
-4 = -4
Hence we get that the value of x is the solution to the equation.
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Ratios equivalent to 1:7
Answer:
2:14
Step-by-step explanation:
[tex]\frac{1 \times 2}{7 \times 2} = \frac{2}{14}/2:14[/tex]
For each function, find f(-x) and -f(x) and then determine whether it is odd, even, or neither. Justify your answer. f(x)=x^5-3x^3
The given function → f(x) = x⁵ - 3x³ is odd in nature.
What are even and odd functions?A function f(x) is even if f(−x) = f(x) and is odd if f(−x) = − f(x).
Given is the function -
f(x) = x⁵ - 3x³
In order to find f(-x), replace 'x' by '-x' in f(x) -
f(x) = x⁵ - 3x³
f(-x) = (-x)⁵ - 3(-x)³
f(-x) = - x⁵ + 3x³
f(-x) = 3x³ - x⁵
Now -
f(-x) ≠ f(x)
So, it is not a even function.
In order to find '-f(x)', multiply f(x) by '-1' -
f(x) = x⁵ - 3x³
- f(x) = - (x⁵ - 3x³) = - x⁵ + 3x³ = 3x³ - x⁵
Now -
f(-x) = -f(x)
So, it is a odd function.
Therefore, the given function → f(x) = x⁵ - 3x³ is odd in nature.
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Luis says figure Y is a rotation of figure X. Explain Luis’s error.
Answer:
Figure Y is not a rotation of figure X because the length of individual side is different.
Step-by-step explanation:
Figure Y is not a rotation of figure X because the length of individual side is different.
12
3
|
3 2 7 6 9
− 2 7 ↓ ↓
0 6
− 0
6
0
The greatest common factor of 48 and 18
Ashley is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 100, find Ashley's age.
Answer:
28 yearsStep-by-step explanation:
Given conditions:Ashley is the oldest sibling There are four siblings Sum of their ages are consecutive even integers Sum of their ages is 100To Find :Ashley's age.Solution :Let,
One of the siblings age be = x
So, the other siblings ages are = x+2, x+4 and x+6
Since,
Ashley is the oldest sibling so his age is x + 6
∴ By the problem,
=> x + (x+2) + (x+4) + (x+6) = 100
(Now adding up the like terms we get)=> 4x + 12 = 100
(Transposing the like terms to same sides)=> 4x = 100 - 12
(Subtracting the like terms)=> 4x = 88
(Dividing both sides by 4)=> x = 22
Now,
We got the age of the youngest one that is 22 years
As,
Ashley is the oldest sibling so his age is
= 22 + 6 = 28 years
Hence,
The age of Ashley is 28 years (Ans)
Answer:
28 years old
Step-by-step explanation:
100/4 = 25
The ages are consecutive even numbers,
so add 1 to and subtract 1 from 25.
Add 3 to and subtract 3 from 25.
Ages: 22, 24, 26, 28
Ashley is the oldest: 28 years old
Write the expression in exponential notation.
27 27 27 27
O 274
O 427
.
O 331, 776
O 27.4
Answer:
27^4
2.74*10^2
4.27*10^2
Step-by-step explanation:
in exponential notation the number is expressed like this.