204
You get 204 because first you divided 85 and 5 which equals 17.
Then you multiply 12 and 17 which equals 204.
I hope that this helps! :)
Answer:
204 miles
Step-by-step explanation:
So first we have to divide 85 by 5 which we get 17 then we multiply 17 by 12 which is 204. I hope this help but sorry I'm not that good at explaining thing
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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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 whichplease 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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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.
A2.1.2: More Function Types
Which statements are true about the graph?
Select all that apply.
A)The range is {yly ≤ 6}
B)The domain is {z-5≤x≤ 10}
C)The graph is increasing when x 24
D)The graph is decreasing when a ≤ -3
E)The graph has a relative maximum at (4,6)
F)The graph has a relative G)minimum at (-5,0)
H)Duration: 00:01:01
Answer:
Step-by-step explanation:
On a recent trip, the Baxter family drove 143 miles and used 4 2/3
gallons of gas. How many miles per gallon of gas did they travel?
They travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.
This is solved by unitary method.
Distance travelled by (4 and 2/3) or 14/3 gallons of gas = 143 miles.
So, we get that for 1 gallon of gas it will be given as:
Distance travelled by 1 gallon of gas = 143 miles × 3/14
= 30.64 miles
So, they travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.
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A is 40% of B. What percentage is B of A?
Answer:
250%
Step-by-step explanation:
divide both sides by 0. 4 so A/0.4=B then rearrange so then its (1/0.4)xA=B then divide so its 2.5A=B and obviously 2.5= 250/100 so that makes the answer 250%
is that better?
Solve for the missing value:
One-half of what number is 30?
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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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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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:
Plot the image of point Q under the translation (x,y) (x+1,y+2)
The image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)
To plot the image of point Q under the translation we need given information.
The translation is given as:
(x,y) -> (x+1,y+2)
The point Q is located at
(-4,4)
So, the image would be:
(x,y) -> (-4+1,4+2)
Evaluate
(x,y) -> (-3,6)
Hence, the image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)
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Part A: State the vertical angles theorem.
Part B: Identify the pairs of vertical angles in the figure.
Part C: Determine the measures of triangle a triangle b and triangle c in this figure. Show your work.
Answer:
A) Vertical angles are congruent
B) 40 and b are vertical angles and c and a are vertical angles.
C) <a = 40
<b = 140
<c = 140
Step-by-step explanation:
A straight angle is a straight line. It is 180°
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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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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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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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
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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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.
12
3
|
3 2 7 6 9
− 2 7 ↓ ↓
0 6
− 0
6
0
The greatest common factor of 48 and 18
2. What is the value of the expression when a = 6 and b = -4? Show your work to support your answer.
The value of the expression when a = 6 and b = -4 is -1
How to determine what is the value of the expression when a = 6 and b = -4?The expression is given as
2a/3b
The values are given as
a = 6 and b = -4
Substitute a = 6 and b = -4 in the expression 2a/3b
2a/3b = 2 * 6/3 * --4
Evaluate the products
2a/3b = 12/-12
Evaluate the quotient
2a/3b = -1
Hence, the value of the expression when a = 6 and b = -4 is -1
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Complete question
What is the value of the expression when a = 6 and b = -4? 2a/3b
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.
The integers that will make the inequality false are integers greater than 3
How to determine which integer will make the inequality false?The inequality expression is given as
5x + 6 ≤ 2x + 15
Collect the like terms.
So, we have
5x - 2x ≤ -6 + 15
Evaluate the like terms.
So, we have
3x ≤ 9
Divide both sides of the expression by 3
So, we have
x ≤ 3
Hence, the integers that will make the inequality false are integers greater than 3
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Write the fraction shown by this point…
Answer: -5/8
Step-by-step explanation:
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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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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$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!
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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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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sqrt (25+9)!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
[tex]\sqrt{25+9}[/tex] =
[tex]\sqrt{34}[/tex] =
≈5,83095 (5,8309518948453)