Answer:
9 is (2/9) of the way from A = 5 to B = 23.
Step-by-step explanation:
Note that there are 23-5, or 18, units separating 5 and 23.
2/9 of that distance is (2/9)(18), or 4.
Adding 4 to 5, we get 9.
9 is (2/9) of the way from A = 5 to B = 23.
If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.
Answer:
9
Step-by-step explanation:
The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9
Solve the following inequality 38<4x+3+7-3x
38<4x+3+7-3x
38<x+10
28<x
Ans: x>28
For this case we must solve the following inequality:
[tex]38 <4x + 3 + 7-3x[/tex]
We add similar terms to the right side of inequality:
[tex]38 <4x-3x + 3 + 7\\38 <x + 10[/tex]
We subtract 10 from both sides of the inequality:
[tex]38-10 <x\\28 <x[/tex]
Thus, the solution will be given by all values of "x" greater strict to 28.
Answer:
[tex]x> 28[/tex]
Given f(x) =x-7 and g(x)= x^2 find f(g(-1))
Answer:
-6
Step-by-step explanation:
f(g(-1)) means we need to find g(-1) and then plug that result into f(x).
So let's start:
g(-1) means to replace the input variable in g(x)=x^2 with -1.
So we replace x with -1.
g(-1)=(-1)^2
g(-1)=1
Now that we have g(-1) can be replaced with 1, we can further evaluate f(g(-1)).
So let's do that:
f(g(-1))
f(1)=1-7 ; I replaced the x in f(x)=x-7 with 1 to find f(1).
f(1)=-6
----
Putting altogether
f(g(-1))=f((-1)^2)=f(1)=1-7=-6.
Answer:
f(g(-1)) = -6
Step-by-step explanation:
* Lets explain how to solve the problem
- The problem is about the composite function
- A composite function is a function that depends on another function.
- A composite function is created when one function is substituted into
another function.
- Ex: f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x)
* lets solve the problem
∵ f(x) = x - 7
∵ g(x) = x²
- We want to find f(g(-1))
* At first lets find g(-1) by substitute x in the function g(x) by -1
∵ g(x) = x²
∵ x = -1
∴ g(-1) = (-1)² = 1
* Now we want to find f(g(-1)), then we will substitute x in f(x) by
the value of g(-1)
∵ g(-1) = 1
∵ f(x) = x - 7
∴ f(g(-1)) = f(1)
∵ f(1) = 1 - 7 = -6
∴ f(g(-1)) = -6
describe 4,100 tens using words
Answer:
four thousand one hundred
Step-by-step explanation:
expand the form
In Zoe's garden, the ratio of the number of green peppers to the number of red peppers is 3:4. If there number are 60 red peppers, how many green peppers are in Zoe's garden? F. 54. G. 55. H. 48. I. 45.
Answer:
I. 45.
Step-by-step explanation:
3 green peppers g green peppers
-------------------- = --------------------------
4 red peppers 60 red peppers
Using cross products
3 * 60 = 4 * g
180 = 4g
Divide each side by 4
180/4 =4g/4
45 = g
There are 45 green peppers
−2x+30>4x+12-2x+30>4x+12
Express the set using interval notation.
Answer:
[-∞, 3)
Step-by-step explanation:
We are given the following inequality which we are to express as a set using the interval notation:
[tex] - 2 x + 3 0 > 4 x + 1 2 [/tex]
Rearranging the inequality by adding the like terms together to get:
[tex] - 2 x - 4 x < 1 2 - 3 0 [/tex]
[tex] - 6 x < - 1 8 [/tex]
[tex]x<\frac{-18}{-6}[/tex]
[tex]x<3[/tex]
Since the values of [tex]x[/tex] are lesser than [tex]3[/tex] so we can express this in interval notation as:
[-∞, 3)
A teacher surveyed her class to find out how many texts the students send in a week. She created this box plot to show the data
Which of the following shows the solution set of the inequality
3x-5>_19?
Answer:
A
Step-by-step explanation:
3x-5≥19
Add 5 to each side
3x-5+5≥19+5
3x ≥ 24
Divide each side by 3
3x/3 ≥24/3
x ≥8
Since this is greater than or equal to there is a closed circle at 8
greater than means the line goes to the right
Can you guys help me with question
first off, let's notice something, the graph seems a bit misleading, since the height of the nut is 0.5 cm, whilst the side of the base is 0.6 cm, however in the picture 0.5 appears longer. That said
1)
the volume of the nut itself is simply the volume of a hexagonal prism, which will just be the product of the area of the hexagon and the height.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=0.5\\ p=\stackrel{0.6\times 6}{3.6} \end{cases}\implies A=\cfrac{(0.5)(3.6)}{2}\implies A=0.9 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the hexagonal prism}}{\stackrel{\textit{hexagon's area}}{(0.9)}~~\stackrel{\textit{height}}{(0.5)}\implies 0.45}[/tex]
2)
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=0.4\\ h=0.5 \end{cases}\implies V=\pi (0.4)^2(0.5)\implies V\approx 0.25[/tex]
3)
well, the composite figure is just a hexagonal nut with a cylindrical hole, so if we simply get the volume of the prism and subtract the volume of the cylindrical hole, what's leftover, is the volume of the nut alone without the hole.
[tex]\bf \stackrel{\textit{from 1)}}{0.45}~~-~~\stackrel{\textit{from 2)}}{0.25}\implies 0.20[/tex]
4)
in short, dividing the mass of 3.03 by our result from 3)
3.03 ÷ 0.2 = 1.515.
Can someone please help me out ??
Answer:
Look at the picture.
Step-by-step explanation:
A height of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the side opposite the vertex).
The coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1).
Find the midpoint of FG
a- 0,4
b- 1,-2
c- 5,2
d- -4,0
Answer:
[tex]\large\boxed{d.\ (-4,\ 0)}[/tex]
Step-by-step explanation:
The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):
[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points F(-5, -3) and G(-3, 3).
Substitute:
[tex]M_{FG}(x,\ y)\\\\x=\dfrac{-5+(-3)}{2}=\dfrac{-8}{2}=-4\\\\y=\dfrac{-3+3}{2}=\dfrac{0}{2}=0[/tex]
Find Malcolm’s debt-to-income ratio if his monthly expenses are $975 and his monthly salary is $1200.
Question 8 options:
a) 1.23
b) 0.795
c) 0.75
d) 0.8125
Answer: D. 0.8125
Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.
975/1200 = 0.8125
The debt-to-income ratio is 0.8125.
Answer:
d) 0.8125
Step-by-step explanation:
Malcolm’s debt-to-income ratio is 0.8125 if his monthly expenses are $975 and his monthly salary is $1200.
All you have to do is divide monthly expenses by the monthly salary.
975 ÷ 1200 = 0.8125
The golf clubs have been sorted into woods and irons. The number of irons is four more than two times the number of woods. The equipment is 75% irons. How many woods are there?
Answer:
4
Step-by-step explanation:
16/4 = 4
if 75% of equipment is iron then do the math.
So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16
The number of woods are [tex]\fbox{\begin \\\math{4}\\\end{minispace}}[/tex].
Further explanation:
Consider the number of woods as [tex]x[/tex] and number of irons as [tex]y[/tex].
Since the number of irons is four more than two times the number of woods, the number of irons is calculated as follows:
[tex]y=2x+4[/tex] ......(1)
The number of equipment consists of the woods and irons, therefore, the number of equipment [tex]n[/tex] is written as the sum of number of woods [tex]x[/tex] and number of irons [tex]y[/tex] as follows:
[tex]n=x+y[/tex] ......(2)
From equation (1), substitute [tex]2x+4[/tex] for [tex]y[/tex] in above equation.
[tex]n=x+2x+4\\n=3x+4[/tex]
Since the total equipment contains [tex]75\%[/tex] of irons, it can be written as follows:
[tex]y=0.75n[/tex]
From equation(1) and (2) substitute [tex]2x+4[/tex] for [tex]y[/tex] and [tex]3x+4[/tex] for [tex]n[/tex] in above equation.
[tex]2x+4=0.75(3x+4)\\\Leftrightarrow2x+4=2.25x+\\\Leftrightarrow4-3=2.25x-2x\\\Leftrightarrow1=0.25x\\\Leftrightarrow x=1/0.25\\\Leftrightarrow x=4[/tex]
Substitute 4 for [tex]x[/tex] in equation (1) to obtain the number of irons.
[tex]y=2(4)+4\\y=8+4\\y=12[/tex]
Thus, the number of woods are 4 and number of irons are 12.
Learn more:
1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)
https://brainly.com/question/1332667
2. which is the graph of f(x) = (x – 1)(x + 4)?
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Answer details:
Grade: Middle school.
Subjects: Mathematics.
Chapter: Linear equation.
Keywords: Linear equation, Function, Golf club, woods, y=2x+4, Variable, Middle term split method, Binomial, straight lines, Quadratic, Polynomial, Zeros, Zeros of a function, Expression, Equation, x, -x.
f:[1/2,infinity)—>[3/4,infinity)
f(x)=x^2-x+1
find the inverse of f(x);please explain
Answer:
[tex]f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}[/tex]
Step-by-step explanation:
y=x^2-x+1
We want to solve for x.
I'm going to use completing the square.
Subtract 1 on both sides:
y-1=x^2-x
Add (-1/2)^2 on both sides:
y-1+(-1/2)^2=x^2-x+(-1/2)^2
This allows me to write the right hand side as a square.
y-1+1/4=(x-1/2)^2
y-3/4=(x-1/2)^2
Now remember we are solving for x so now we square root both sides:
[tex]\pm \sqrt{y-3/4}=x-1/2[/tex]
The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.
This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.
That is we want:
[tex]\sqrt{y-3/4}=x-1/2[/tex]
Add 1/2 on both sides:
[tex]1/2+\sqrt{y-3/4}=x[/tex]
The last step is to switch x and y:
[tex]1/2+\sqrt{x-3/4}=y[/tex]
[tex]y=1/2+\sqrt{x-3/4}[/tex]
[tex]f^{-1}(x)=1/2+\sqrt{x-3/4}[/tex]
Below is an excerpt from a home loan contract.
“The sum of the principal of the loan and all applicable interest will be divided into 360 monthly payments according to the amortization schedule.
The Buyer shall make each monthly payment by the first day of the month it is due. A payment not received by the first day of the month it is due will be considered delinquent. A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00. If a payment is not received by the last day of the month it is due, the Buyer and transaction shall be reported to the appropriate credit agencies.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
According to the contract, which of the following is not a responsibility of the buyer?
a.
Pay the monthly payment on time.
b.
Notify the bank if a payment is going to be late.
c.
Pay an additional $75.00 with a payment made after the 15th day of the month it was due.
d.
Notify the bank of his or her intent to split a late payment into three partial payments.
Answer:
Option B
Step-by-step explanation:
As per the contract
"The Buyer shall make each monthly payment by the first day of the month it is due."
this makes option a :"Pay the monthly payment on time." responsibility of the buyer.
"A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00."
this makes option c :"Pay an additional $75.00 with a payment made after the 15th day of the month it was due." responsibility of the buyer.
"Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
this makes option d :"Notify the bank of his or her intent to split a late payment into three partial payments." responsibility of the buyer.
So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.
Hence Option B is correct
Notify the bank if a payment is going to be late!
The option that is not a responsibility of the buyer is notify the bank if a payment is going to be late.
What is a contract?A contract is an agreement that is enforceable legally between two or more parties to give something or render a services.
What are the responsibilities of the buyer?Pay the monthly payment on the first day of each month. When there is delinquency, the buyer should notify the bank of his or her intent to split a late payment into three partial payments.Pay a late charge of $75 when the payment is not received by the 15th day.To learn more about contracts, please check: brainly.com/question/12991600
What is the value of y?
Answer:
C. 54°Step-by-step explanation:
We know: measures of angles in a triangle add up to 180°.
Therefore we have the equation:
[tex]\gamma+\gamma+72^o=180^o[/tex] subtract 72° from both sides
[tex]2\gamma=108^o[/tex] divide both sides by 2
[tex]\gamma=54^o[/tex]
(xy + 9y + 2) and (xy – 3)
Answer:
x^2y^2 +9xy^2-xy-27y-6
Step-by-step explanation:
(xy+9y+2) (xy-3)
Each term of second bracket will be multiplied with the terms of first bracket
= xy(xy+9y+2) -3(xy+9y+2)
= x^2y^2+9xy^2+2xy-3xy-27y-6
=x^2y^2+9xy^2-xy-27y-6
What is the equation of the line that passes through (-3, -1) and has a slope of 2,5 ? Put your answer in slope-intercept form.
Answer:
y+1 = 2/5(x+3)
Step-by-step explanation:
We have a point and a slope so we can use point slope form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y--1 = 2/5 (x--3)
y+1 = 2/5(x+3)
the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).
Answer:
[tex]\large\boxed{for\ (-3,\ 2):\ y-2=-\dfrac{1}{5}(x+3)}\\\boxed{for\ (2,\ 1):\ y-1=-\dfrac{1}{5}(x-2)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
========================================
We have the points (-3, 2) and (2, 1).
Substitute:
[tex]m=\dfrac{1-2}{2-(-3)}=\dfrac{-1}{5}=-\dfrac{1}{5}[/tex]
for (-3, 2)
[tex]y-2=-\dfrac{1}{5}(x-(-3))\\\\y-2=-\dfrac{1}{5}(x+3)[/tex]
for (2, 1)
[tex]y-1=-\dfrac{1}{5}(x-2)[/tex]
The coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .
What is the perimeter of the polygon?
Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
units
Step-by-step explanation:
i have answered ur question
The Perimeter of the given polygon can be calculated using the distance formula for each of its sides. The calculated distances are added to give a total perimeter of approximately 18.5 units.
Explanation:The Perimeter of a polygon is calculated by adding the lengths of all its sides. Here, we need to calculate the distance between each pair of points, which gives the length of the sides of the polygon.
The distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2-x1)² + (y2-y1)²) .
To find the Perimeter of the polygon, we calculate the distances between each pair of vertices and then add them up:
Adding these distances, we get a perimeter of approximately 5 + 4.1 + 3.2 + 4.2 + 2 = 18.5 units, rounded to the nearest tenth of a unit.
Learn more about the Perimeter of a polygon here:https://brainly.com/question/15387363
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What is the midpoint of the segment shown below?
The answer to the question is A
Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.
Number of cranes Total time (minutes)
555 17.517.517, point, 5
888 282828
121212 424242
Write an equation to describe the relationship between ccc, the number of cranes, and ttt, the total time in minutes.
Answer:
t = 3.5c
Step-by-step explanation:
The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.
We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)
First we need to find the slope of the line which gives the relation between the two variables.
[tex]Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]
y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:
[tex]Slope=\frac{28-17.5}{8-5}=3.5[/tex]
Thus, the equation of the line will be of the form:
t = mc + b
m is the slope here. Using its values, we get:
t = 3.5c + b
b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.
Using the point (5, 17.5), we get:
17.5 = 3.5(5) + b
b = 0
This means, the equation of the line would be:
t = 3.5c
Answer:
t=3.5c
Step-by-step explanation:
choose the correct ordered pair.
X+ y = 3
y=8
A. (5,8)
B. (11,8)
C. (-5,8)
D. (-11,8)
Answer: C
Step-by-step explanation:
plug in y=8 to
x+y=3
x+8=3
x=-5
There is no need to look at the other answer choices since they do not have x equaling to -5.
So,
[tex]x+y=3\Rightarrow y=3-x[/tex]
Then,
[tex]8=3-x\Rightarrow x=-5[/tex]
The ordered pair is therefore,
[tex]C(-5,8)[/tex]
Hope this helps.
r3t40
Can someone please help me ??
Answer:
$1.80
Step-by-step explanation:
Based on the ratio shown in the double number line, the cost for 1 pound of avocados is $1.80.
5 pounds = 9$
9 divided by 5 = 1.8$/pound
Answer:
$1.80
Step-by-step explanation:
Note this:
5 lbs of avocado/$9
So, how much for 1 lb?
Remember units!!! They REALLY are important!!
1_lb_ x $9____ = (1 x 9)/5 = 1.8
5 lbs
**where are the numbers in our conversion coming from? Our notes!
We must now convert our answer to $'s, so $1.80 is our answer!
| 4.75 - 2.3
as a fraction simply
Answer:
2.45 or 2 9/20
Step-by-step explanation
Zane is washing cars to help pay for a school trip. He gets paid $8 for every car he washes and made a total of $64 on Saturday. Write an equation to show how many cars Zane washed on Saturday.
A)8 − x = 64
B)64x = 8
C)8 + x = 64
D)8x = 64
Answer:
The correct option is D.
Step-by-step explanation:
Let the number of cars Zane washed on Saturday be x.
It is given that he gets paid $8 for every car he washes and made a total of $64 on Saturday.
We need to write an equation to show how many cars Zane washed on Saturday.
If he get $8 for one car, then the total amount he get for x cars is
Total amount = 8x
He made a total of $64 on Saturday, so
[tex]8x=64[/tex]
The required equation is 8x=64.Therefore the correct option is D.
what is the solution to 3x + 5 > or equal to 7
Answer:
[tex]x \geq\frac{2}{3}[/tex]
Step-by-step explanation:
The question is [tex]3x+5 \geq 7[/tex]
We simply take the numbers to one side and variables to one side and solve via algebra (shown below):
[tex]3x+5 \geq 7\\3x \geq 7-5\\3x \geq 2\\x \geq\frac{2}{3}[/tex]
This range of values is the solutions of the inequality.
The polynomial f(x) is written in factored form:
f(x) = (x − 6)(x + 5)(x − 9)
What are the zeros of the polynomial function?
x = 6, x = −5, x = 9
x = 6, x = 5, x = 9
x = −6, x = 5, x = −9
x = −6, x = 6, x = −5, x= 5, x = −9, x = 9
Answer:
x = 6, x = -5, x = 9
if f(x)=(x-6)(x+5)(x-9)
Step-by-step explanation:
The zeros of a polynomial in factored form can be found by setting the polynomial equal to zero and then realizing if a product is zero, then at least one of it's factors is zero.
So we have the zero's are the x's that satisfy
(x-6)(x+5)(x-9)=0.
We just need to solve three equations:
x-6=0
This can be solved by adding 6 on both sides: x=6
x+5=0
This can be solved by subtracting 5 on both sides: x=-5
x-9=0
This can be solved by adding 9 on both sides: x=9
The solutions are in { 6,-5,9 }.
Answer:
x = 6, x = -5, x = 9
Step-by-step explanation:
If the polynomial f(x) is written in factored form, f(x) = (x − 6)(x + 5)(x − 9), the zeros of the polynomial function are x = 6, x = -5, x = 9.
x-6=0 x = 6
x+5=0 x = -5
x-9=0 x = 9
Therefore, x = 6, x = -5, x = 9 would be the correct answer.
54/6 findind fraction of whole number
Answer:
The answer is 9
Step-by-step explanation:
When you divide 54 by 6 you get 9 because 10 times 6 equals 60 so if you minus 6 you get 54 which equals 6 times 9. :)
Answer:
9 or 9/1
Step-by-step explanation:
To convert improper fractions to whole numbers, you have to divide the numerator by the denominator.
So, 54 divided by 6 is 9
So 54/6 as a whole number 9
If you want to keep as a fraction it would be 9/1
What is the equation of a line that is perpendicular to the line represented by y=7/6x+4
Answer: y=-6/7x
Step-by-step explanation: A perpendicular slope is opposite reciprocal. The opposite reciprocal of 7/6 is -6/7. The equation of the perpendicular line is y=-6/7x.
PLZ HELP!! Select the correct answer.
Which rational equation fits the graph?
Answer:
C
Step-by-step explanation:
When we set the numerator equal to 0 and solve for x, that value is the horizontal asymptote (a line the graph come towards, but never crosses).
Looking at the graph, the horizontal asymptote is x = 2, so which one of the 4 functions has a horizontal asymptote of 2? Let's check.
A) 2x - 1 = 0
x = 1/2
B) same, x = 1/2
C) 2x -4 = 0
x = 2
D) same as A,B, x = 1/2
As we can see, option C has the right horizontal asymptote and A,B,D are eliminated. So answer is C.