Answer:
First, let's define each case:
A conditional statement is:
If P then Q.
P = hypothesis
Q = conclussion.
Converse: If Q then P.
Biconditional: P if and only if Q.
Inverse: If not P, then not Q.
Contrapositive: If not Q, then not P.
Our statement is:
"If two angles are congruent, then they have the same measure."
P = two angles are congruent.
Q = they have the same measure.
Now let's look at the options:
1) If two angles have the same measure, then they are congruent.
or: if Q then P, this is converse.
2) If two angles are not congruent, then they do not have the same measure.
or: If not P, then not Q, this is inverse.
3) If two angles do not have the same measure, then they are not congruent.
or: If not Q, then not P, this is the contrapositive.
4) Two angles are congruent if and only if they have the same measure.
or: P if and only if Q, this is biconditional.
A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
Answer and Step-by-step explanation:
Given:
Charges includes 10 hour per month = $50
Charges for additional hour = $9
Piecewise definition of cost F(x) for a month in which a member use a car for hours.
Find limits?
Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
Lim x → 10- F(x) = 50$
Lim x → 10 [ 9x – 70] = 9( 10) – 70
= 90 – 70
= 20 > 10
Limit does not exist.
Lim x → 10+ F(x) = 50$
Lim x → 10+ F(x) = Lim x → 10+ [90x – 70]
= 90 – 70
= 20 > 10
Limit does not exist.
Lim x → 10 F(x) = 50$
An integer or an decimal.
The limit does not exist.
The piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].
Given,
Membership plan is [tex]\$50[/tex] per month.
We have to write a piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours.
Here, [tex]\$[/tex][tex]$50[/tex] per month fees includes 10 hours of driving each month, so the cost for a month is given as,
[tex]f(x)= 50+9(x-10)[/tex]
Here [tex]x[/tex] is the no. of additional hours for the month.
Further,
[tex]f(x)= 9x-40[/tex].
Now at,
[tex]lim _{x \to 10^+}f(x) = 9\times 10-40\\[/tex]
Or,
[tex]f(x)= 90-40\\f(x)=50[/tex]
Similarly, at left limit,
[tex]lim _{x \to 10^-}f(x) = 9\times (-10)-40[/tex]
Or,
[tex]f(x)=-90-40[/tex]
[tex]f(x)=-130[/tex]
Finally at [tex]x=10[/tex], [tex]f(x)=9\times10-40[/tex]
[tex]f(x)=90-40\\f(x)=50[/tex]
Since [tex]lim{x \to}10^+[/tex] [tex]\neq limx\to 10^-\neq f(x) (at x= 10)[/tex]
So the required function [tex]f(x)[/tex] is discontinuous at [tex]x=10[/tex]
Hence the piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].
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How many solutions does this system of equations have? Exactly one None Infinitely many Exactly two
Somebody please answer this question I’m begging you
Answer: The answer is A, the y value increases by 1.5 as the x value increases by 1. Therefore A does not describe the graph.
Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 20 elderly women gathered once a week to discuss different works of art. The study also included a control group of 20 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.
Required:
a. Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?
b. Explain why you think that the researchers included a control group in this study.
Step-by-step explanation:
1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.
2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.
You have $150 in a savings account and you have some cash. The tape diagram represents the ratio of the amounts of money. You want to have twice the amount of money in your savings account as you have in cash. How much of your cash should you deposit into your savings account?
Answer: $200
Step-by-step explanation:
We know that:
You have $150 in a savings account.
This is represented with two tiles.
Then each tile represents:
$150/2 = $75
And in cash you have 5 tiles, then in cash you have:
5*$75 = $375.
Then the problem is:
You have $150 in the savings account
You have $375 in cash.
You want to deposit a quantity such that you have twice the amount of money in your savings account as you have in cash.
Suppose that you move a quantity X from cash to the savings account, then now we have the situation:
Sav. Acc. = $150 + X
Cash = $375 - X
And we want that:
Sav. Acc. = 2*Cash
($150 + X) = 2*($375 - X)
Let's solve this for X.
$150 + X = $750 - 2*X
3*X = $750 - $150 = $600
X = $600/3 = $200
You should deposit $200 in the Savings acount.
Tape diagrams are used to represent numbers as a ratio
$200 from the cash should be deposited into the savings account
Represent the amount in the savings account with s, and the cash with c.
So, we have the following ratio from the tape diagram
[tex]\mathbf{s : c = 2 : 5}[/tex]
You have $150 in the savings account.
So, the ratio becomes
[tex]\mathbf{150 : c = 2 : 5}[/tex]
Express as fractions
[tex]\mathbf{\frac c{150}= \frac 52}[/tex]
Multiply both sides by 150
[tex]\mathbf{c= \frac 52 \times 150}[/tex]
[tex]\mathbf{c= 375}[/tex]
Let the deposited amount be x.
Twice the amount in the savings account as cash means that:
[tex]\mathbf{150 + x = 2 \times (375 - x)}[/tex]
Open brackets
[tex]\mathbf{150 + x = 750 - 2x}[/tex]
Collect like terms
[tex]\mathbf{2x + x = 750 - 150}[/tex]
[tex]\mathbf{3x = 600}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 200}[/tex]
Hence, $200 from the cash should be deposited into the savings account
Read more about tape diagrams at:
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Write the decimal represented by each shaded square.
A figure is made up of four congruent right triangles and a square as displayed.
What is the area, in square inches, of the figure?
Answer:
It would be 33² in.
Analyze the diagram below and answer the question that follows.
Step-by-step explanation:
option d is the correct answer
Joshua withdrew $32.50 each week for six weeks for pitching lessons. By how much did these lessons change his savings account balance?
Answer:
$195.00
Step-by-step explanation:
32.50 times 6 = 195.00
take 32.50 times 6 cause he took out money for 6 weeks of lessons then you do 32.50 times 6 and you should get 195
mass and weight math
Answer: There is 10,000 ug in 1 cg
Plz do fast I need it for a test The front view of a tent is.shown below if a zipper.is going to be put in along the length x how long should the.zipper be
Answer:
x=15ft
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=17^2
b^2+64=289
b^2=225
b=15
HELP, ILL GIVE BRAINLIEST BUT HELP ASAP WITH THIS!!
Answer:
proportional
Step-by-step explanation:
PLEASE HELP FAST!!!! THIS IS URGENT!!!
For the following set of triangles, fill in the blanks with the correct measure. Enter your answers as number only.
1) m∠A = _____˚
2) m∠B = _____˚
3) m∠C = _____˚
4) m∠X = _____˚
5) m∠Y = _____˚
6) m∠Z = _____˚
7) Segment AB = ___ units
8) Segment BC = ___ units
9) Segment AC = ___ units
10) Segment XY = ___ units
11) Segment YZ = ___ units
12) Segment XZ = ___ units
Answer:
a=53, b=90, c=37, x=53, y=90, z=37
segment ab=3, segment bc=4, segment ac=5
pretty sure these are the answers but sorry if not
Step-by-step explanation:
please help!! The picture has the question.
Answer:
B.
Step-by-step explanation:
They are used to the climate and they are harder the the rest.
Answer:
dry climate or
Step-by-step explanation:
they are in wet climate
Question 1
1 pts
The function f(x) = 4x + 10 models the amount of money Francis makes when babysitting
for x hours. How much money will he make for 2 hours of babysitting work?
2.
0-2
O-3
O 18
Answer:
18 would be yr answer
Step-by-step explanation:
What is y = -2/9x + 2 written in standard form?
What does round to the nearest hundredth mean?
Answer:
Step-by-step explanation:
say for example you have 105 as a answer you would round to 100 because it a closer to 100 than 200
The formula κ(x)= f′′(x) 1+f′(x)23/2 expresses the curvature of a twice-differentiable plane curve as a function of x. Use this formula to find the curvature function of the following curve. f(x)=−5x2 The curvature function is κ(x)=nothing.
Answer:
K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)
Step-by-step explanation:
considering the Given function
F(x) = [tex]-5x^2[/tex]
first Determine the value of F'(x)
F'(x) = [tex]\frac{d(-5x^2)}{dy}[/tex]
F'(x) = -10x
next we Determine the value of F"(x)
F"(x) = [tex]\frac{d(-10x)}{dy}[/tex]
F" (x) = -10
To find the curvature function we have to insert the values above into the given formula
K(x) [tex]= \frac{|f"(x)|}{[1 +( f'(x)^2)]^{\frac{3}{2} } }[/tex]
K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)
HELP ON #15 PLEASE GIVE ME ANSWER!
Answer: so it’s 85?
Step-by-step explanation:
I need help ASAP
what is the principal if the interest earned is $22 the simple annual interest rate is 2% and the time is one year
Answer:
1,100
Step-by-step explanation:Well first find the principal first Multiply the rate 0.02 by the time 1 year this gives us 0.02 then divide the interest ($22) by 0.02 then you get $1,100
Answer:
not 1,100 its 1100
Step-by-step explanation:
50 students were surveyed about their
favorite ice cream. Here are the results:
Chocolate- 13
Vanilla- 25
Cookie Dough- 12
What decimal represents the students who
prefer cookie dough?
Answer:
0.12
Step-by-step explan
Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying a scarves what do the parts of the expression 48s represents
The expression 48s represents the cost of the scarves.
Given
Emiko makes Shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves.
Let s represent the price of the scarves.
The cost of each scarves is 48.
Therefore,
The cost of scarves = Number of scarves × cost of each scarves.
The cost of scarves = s × 48
The cost of scarves = 48s
Hence, the expression 48s represents the cost of the scarves.
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Answer:In the expression 48s ,represents the number of scarves and 48 represents the price per scarf
Step-by-step explanation:
help ASAP plz and Thankyou
Answer: B
Step-by-step explanation:
A triangle has side links of 16 cm, 63 cm, and 64 cm. Classify it as acute, obtuse, or right
Answer:
acute
Step-by-step explanation:
All sides are smaller than 90 degrees
F(x)=3x+2 and g(x)=x^3 find (fog)(-5)
How do you Graph: -3x – 2y = -8
Answer:
I hope this helps!
Answer:
y = -2/3x +4 --> y = mx+b form
Step-by-step explanation:
-3x-2y = -8 --> add 3x to both side
-2y = 3x-8 --> divide by -2 on both side
y = -2/3x +4 --> y = mx+b form
the y intercept is 4 and the slope is -2/3, down 2, right 3.
therefore, the graph would contain a y intercept point of (0,4) and then from there u would start plotting down 2, going right 3 unit or up 2 and left 3 units. Then when u plotted at least 2/3/4 points, use a straightedge to draw the line.
NEED A MATH TUTOR ASAP !!!
tim has $20 in a savings account. The interest rate is 10% per year and is not compounded. How much will he have in 1 year ?
Answer:
$22
Step-by-step explanation:
20 * 1.10 = 22
Find the equation of a line that contains the points (7,3) and (−7,2). Write the equation in slope-intercept form, using fractions when required.
when is the function decreasing?
A. (15, 40)
B. (30, 55)
C. (60, -40)
D. (40, 60)
Lines l and m are parallel lines cut by the transversal line t. Which angle is congruent to ∠7?
Answer:
<3, <2 or <6
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
i had it in usatestprep