let's firstly convert the mixed fractions to improper fractions.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}[/tex]
[tex]\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x[/tex]
Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.
A. 5
B. [tex]\frac{1}{5}[/tex]
C. -[tex]\frac{1}{5}[/tex]
D. -5
Answer:
Option A k=5
Step-by-step explanation:
step 1
Find the equation of f(x)
we have the points
(-10,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+10)=1[/tex]
The function in slope intercept form is equal to
[tex]f(x)=mx+b[/tex]
we have
[tex]m=1[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]f(x)=x+4[/tex]
step 2
Find the equation of g(x)
we have the points
(-2,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+2)=5[/tex]
The function in slope intercept form is equal to
[tex]g(x)=mx+b[/tex]
we have
[tex]m=5[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]g(x)=5x+4[/tex]
step 3
Find the value of k
we have
[tex]f(x)=x+4[/tex]
[tex]g(x)=5x+4[/tex] -----> equation A
[tex]g(x)=f(kx)[/tex] -----> equation B
[tex]f(kx)=kx+4[/tex] ----> equation C
substitute equation A and equation C in equation B and solve for k
[tex]kx+4=5x+4[/tex]
[tex]kx-5x=0\\kx=5x\\k=5[/tex]
The value of k in the equation g(x) = f(k*x), where g(x) and f(x) are graphs, signifies a horizontal compression, expansion, or reflection of the f(x) graph. It depends on the given graph to determine the exact value of k.
Explanation:Without the graphical representation, it's difficult to provide a definite value for k. However, understanding the relationship between f(x) and g(x) can help us make an educated guess. If g(x) is a horizontal compression of f(x) by a factor of k, then k is positive and larger than 1. If g(x) is a horizontal expansion of f(x), then k is positive and less than 1. If g(x) is a reflection of f(x) across the y-axis and has a horizontal compression or expansion, then k is negative. For example, if g(x) completes one cycle in a space where f(x) would complete 5 cycles, then k is 5. If g(x) completes 5 cycles in a space where f(x) would complete one cycle, then k equals 1/5.
https://brainly.com/question/26896273
#SPJ3
For which of the following equations is (-4,-3) not a solution?
A.) 5x+2y=-26
B.) y=1+x
C.) 2y-3x=6
D.) -3x=4y
Answer:
D.) -3x = 4y
Step-by-step explanation:
[tex] -3(-4) ≠ 4(-3) \\ \\ 12 ≠ -12[/tex]
I am joyous to assist you anytime.
The point (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y. This is determined by substituting x with -4 and y with -3 in each equation and checking if the equation is balanced.
Explanation:To find which equation (-4,-3) is not a solution to, we substitute x with -4 and y with -3 into each equation, then see if both sides of the equation are equal.
For equation A: 5(-4) + 2(-3) equals -20 - 6, which is -26. So, (-4,-3) is a solution to this equation.For equation B: -3 equals 1 + (-4), which is -3. So, (-4,-3) is also a solution to this equation.For equation C: 2(-3) - 3(-4) equals -6 + 12, which equals 6. This equation does not equal 6. Therefore (-4,-3) is not a solution to this equation. For equation D: -3 equals 4*(-4), which is -16. This equation does not equal -16. So, (-4,-3) is also not a solution to this equation.So, (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y.
Learn more about Solving equations here:
https://brainly.com/question/18322830
#SPJ2
the number 1 is it's own multiplicative inverse. name another number with this property.
The number -1 is its own multiplicative inverse, just like the number 1, because multiplying -1 by itself results in 1.
The number 1 is indeed its own multiplicative inverse because when you multiply it by itself, you get 1. The property of a number being its own multiplicative inverse means that the number multiplied by itself equals 1. There is another number with this property, which is -1. When you multiply -1 by itself (-1 x -1), the result is 1. Therefore, -1 is also its own inverse when it comes to multiplication.
This concept is rooted in the properties of identity elements and inverses within the mathematical field of abstract algebra. When considering the set of numbers 1 and -1, they form an abelian group under the operation of multiplication. In this group, every element is its own inverse, and the identity element for multiplication is 1, as any number multiplied by 1 yields the original number.
The book display has 8 histories, 12 biographies, and 24 novels. Write the ratio of biographies to histories.
Answer:
12:8
Step-by-step explanation:
The ratio of biographies to histories is 1.5, or more simply as a whole number ratio, 3:2. This means that for every 3 biographies, there are 2 history books.
Explanation:The question wants us to calculate the ratio of the number of biographies to the number of histories in the book display. To do this, simply divide the number of biographies by the number of histories. The problem provides the number of biographies as 12 and the number of histories as 8. Thus, the ratio is: 12 (biographies) / 8 (histories) = 1.5.
In other words, for every 1.5 biographies, there is 1 history book on the display. However, since ratios are commonly expressed as whole numbers, we can multiply both sides by 2 to get the ratio as 3:2, meaning for every 3 biographies, there are 2 history books. This provides a cleaner and more interpretable ratio.
Learn more about Ratios here:https://brainly.com/question/32531170
#SPJ2
A bakery sold 16 apple pie on Saturday they sold 4 more apple pies on Sunday than they did on Saturday how many apple pies did they sell on Sunday
Answer:
20 apple pies
Step-by-step explanation:
On Saturday they sold 16, while on Sunday they sold 4 more.
16+4 = 20.
20 apple pies.
When members of the military are in a combat zone, they often eat meals-ready-to-eat (MREs). A typical MRE contains 1 comma 600 calories. If the average soldier eats 3 MREs per day and is deployed for 12 months, approximately how many calories will be consumed by a 37-member platoon of soldiers?
The number of calories by a 37-member platoon of soldiers will be 6,48,24000 calories.
What are calories?A calorie is a unit of energy. Energy is defined as the capacity to do work.
Now it is given that,
Calories contain in 1 MRE = 1,600
Number of MREs taken by a soldier per day = 3
Therefore, number of calories taken by soldier per day = 3*1600
= 4800 calories
Therefore, number of calories taken by 37 soldier per day = 37*4800
= 1,77,600 calories
Now since, 12 months = 365 days
⇒Number of calories taken by 37 soldier in 12 months = 365*1,77,600
⇒Number of calories taken by 37 soldier in 12 months =6,48,24000 calories.
Hence,The number of calories by a 37-member platoon of soldiers will be 6,48,24000 calories.
To learn more about calories :
https://brainly.com/question/17924093
#SPJ2
x+y=-9. 5x-2y=32. elimination using manipulation
Answer:
x=2, y=11.
Step-by-step explanation:
x + y = -9.
5x - 2y = 32 Multiply the first equation by 2:
2x + 2y = -18 Adding the last 2 equations to eliminate y:
7x = 14
x = 2,
Substitute x = 2 in the first equation:
2 + y = -9
y = -9 - 2
y = -11.
what is the substitution of 7+3x=1???
Answer:x= -2
Step-by-step explanation:
5. Write the phrase as an algebraic expression.
6 less than a number times 11
@ 6y - 11y © 11y - 6
6 11=Y
11+ y
I really don't know if I'm doing this right and I have a test coming up (I only need the answer for the odds)
Answer:
all work is shown and pictured
What is 204 divided by 9 in long division
Answer: the answer is 22 with a remander of 6
Step-by-step explanation:
Sally has a savings account. She
deposited $200 into her savings
account last year and has been taking
out $10 monthly to go to the movies.
Sally now was $80 in her account. How
many months has she been
withdrawing money?
HELP HELP HELP PLEASE ASAP
Answer:
Its Brand 2 :) also do you do connexus?
if so whats ur name :)
Step-by-step explanation:
Answer:
brand 4
Step-by-step explanation:
Simplify the expression. Write your answer as a complex number.
please help
Anna's running time for a race was 23.1 seconds.Another runner's time was 5.86 seconds faster.Find the other Runners time
Answer:
17.24
Step-by-step explanation:
Simple subtraction of decimals because the other runner was faster:
23.10
-5.86
=
17.24
The other Runner's time is 17.24 seconds.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that Anna's running time for a race was 23.1 seconds
And another runner's time was 5.86 seconds faster
It took Anna 23.1 seconds to complete a race.
Since the other runner was quicker,
So we did a simple decimal subtraction,
⇒ 23.10 - 5.86
⇒ 17.24
So, It took other runners 17.24 seconds to complete a race.
Hence, the other Runner's time is 17.24 seconds.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
-50-2 - 8m) = 10 + 5m
Answer:
-4 10/13
Step-by-step explanation:
-52-8m = 10 + 5m
-8m = 62 +5m
-13m = 62
-m = 62/13
m = - 62/13
m = -4 10/13
3 thousand divided 10 in unit and standard form
Answer:
300
Step-by-step explanation:
Divide 3000 by 10 by striking out each zero one-by-one [300 ÷ 1] to get 300. This is one of the fastest ways to solve with zeros.
I am joyous to assist you anytime.
The result would be 300 units and 320 units respectively.
3 thousand divided by 10 in unit and standard form:
To divide 3,000 by 10 in unit form: 3,000 ÷ 10 = 300 units.
To divide 3,000 by 10 in standard form: 3.2 × 10³ ÷ 10¹ = 3.2 × 10² = 320 units.
| n+2 | = 7 absolute value
Answer:
Step-by-step explanation:
| n+2 | = 7 : n+2 = 7 or n+2 = -7
n=5 or n = - 9
change 0.72 to a percent
Slope intercept form of y=3x+4 passing through (0,9)
Answer:
y = 3x + 9
Step-by-step explanation:
9 = 3[0] + b
0
9 = b
y = 3x + 9
This would be considered a parallel line, so 3 remains the way it is.
I am joyous to assist you anytime.
Write 454.12kg with 3 significant
Answer: 454
Step-by-step explanation:
The first three digits will be the significant digits. Round the third digit.
454.12
the digit and the 4 is 1 so 454.12 is rounded to 454
A triangle has one side that is 5 inches long and the other two sides are both of length x. Write an expression for the perimeter of the triangle in terms of x and then use the expression to find the perimeter when x=10.
Let P = perimeter
P = 3x + 5
Let x = 10
P = 3(10) + 5
P = 30 + 5
P = 35
A taxi cab charges $1.75 for the flat fee and $0.25 for each mile. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
.25x+1.75=15 and x=53
Step-by-step explanation:
first subtract 1.75 from both sides
then divide by .25 on both sides
and you will get x=53
there are 52 legs and they all belong to hamsters.how many hamsters are there
There are 52 legs and they all belong to hamsters. so 13 Hamsters are there.
Are hamsters a good pet?Hamsters are rodents from the subfamily Cricetinae, which includes 19 species divided into seven genera. They have established themselves as popular tiny pets. The golden or Syrian hamster is the most well-known species of hamster and is the variety most usually kept as a pet.Hamsters are terrific pets for many people. They don't take much attention, receive adequate exercise when running on their wheel, and are attractive, cuddly, and enjoyable to hold. Some children may find them to be a good first pet. Hamsters, however, do not come with care instructions.Total No. of legs = 52
Each hamsters have 4 legs.
No. of Hamster = 52/4 =13 Hamsters
To learn more about Hamster refer,
https://brainly.com/question/28474669
#SPJ2
Henry can write 5 pages of his novel in 3 hours. At this rate, how many pages can Henry write in 8 hours?
Given that Henry can write 5 pages in 3 hours, his rate is 5/3 pages per hour. Multiplying this rate by 8 hours, we get approximately 13.33 pages. Therefore, Henry can write approximately 13 to 14 pages in 8 hours at the given rate.
Explanation:The subject of this question is mathematics, specifically, it is dealing with the concept of rates. Given that Henry can write 5 pages in 3 hours, we can set up a rate, which is simply a ratio that compares quantities in different units. So, Henry's rate of writing is 5/3 pages per hour.
To find out how many pages Henry can write in 8 hours at this rate, we multiply his rate (5/3) by the number of hours (8 hours). So, (5/3) x 8 = 40/3 = 13.33. However, since we cannot have a fraction of a page, we can round this to 13 pages for a conservative estimate or to 14 pages for a liberal estimate.
So, at the rate given, Henry can write approximately 13 to 14 pages in 8 hours.
Learn more about Rate Problem here:https://brainly.com/question/29624094
#SPJ12
Henry can write approximately 13.33 pages in 8 hours.
Explanation:To find out how many pages Henry can write in 8 hours, we can set up a proportion using the given information.
Since Henry can write 5 pages in 3 hours, we can write the proportion as 5/3 = x/8.
To solve for x, we can cross multiply and then divide to find that x = 40/3.
So, Henry can write approximately 13.33 pages in 8 hours.
Learn more about Proportions here:https://brainly.com/question/34018947
#SPJ12
find the area of of the rectangle with the given base and height.
2ft 4in
ANSWER IN INCHES
Answer:8in
Step-by-step explanation:
You will multiply 2in•4in=8in
The length of a rectangular frame is represented by the expression 2x+4 and the width of the rectangular frame is represented by the expression 2x+10. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches
2x^2+20x-80=0
4x^2+28x+40=0
4x^2+28x-80=0
x^2+8x+20=0
Answer:
4x^2 + 28x - 80=0
Step-by-step explanation:
(2x+4)(2x+10) = 120
1. Use FOIL (Distribute):
4x^2 + 20x +8x + 40 = 120
2. Group like terms:
4x^2 + 28x+ 40 = 120
3. Subtract 120 from both sides:
4x^2 + 28x - 80 = 0
Answer:
Option 3 - [tex]4x^2+28x-80=0[/tex]
Step-by-step explanation:
We have given,
The length of a rectangular frame is represented by the expression L=2x+4.
The width of the rectangular frame is represented by the expression B=2x+10.
The total area of a rectangular frame is A=120 square inches.
To find : Write an equation to solve for the width of a rectangular frame ?
Solution :
The area of the rectangle is given by,
[tex]\text{Area}=\text{Length}\times \text{Breadth}[/tex]
Substitute the values,
[tex]120=(2x+4)\times(2x+10)[/tex]
[tex]120=4x^2+20x+8x+40[/tex]
[tex]4x^2+28x+40-120=0[/tex]
[tex]4x^2+28x-80=0[/tex]
The required equation is [tex]4x^2+28x-80=0[/tex]
Therefore, option 3 is correct.
b) Mr. Wonderful has called on these students in class:
boy, boy, girl, boy, girl, boy, girl, girl, boy, boy
Based on this data, what is the probability that the next student called on
The elevation of your plot of land is 2 feet below sea level. You add 7 feet of dirt to your land. What is the new elevation of your land?
Answer: 5
Step-by-step explanation: -2+7=5
when the signs are different you subtract and when the signs are the same you add. Then you keep the sign of the bigger number.
What is the probability of rolling a 6-sided die and getting a 4 or a number
divisible by 3?
Event A = rolling a 4 on a single die
Event B = rolling a number divisible by 3 (3 or 6) on a single die
There are three outcomes possible in total if either event A happens or event B happens. This is out of six outcomes total.
Divide the values and reduce: 3/6 = 1/2
Final Answer: 1/2