Answer:
1st quadrant
Step-by-step explanation:
Both positve numbers for the points are 1rst quadrant. Both negative numbers for the points are 3th quadarant. If the x is negative then the quadrant is 2. If y is negative the quadrant is 4.
Use substitution to solve each system of equations:
x=y+6
x+y=10
In the following shape, two semicircles have been placed at the end of a rectangle whose length is twice its height. Which of the following gives the length around this figure in terms of the semicircle's radius, r?
Answer:
Perimeter of the figure is 2r([tex]\pi[/tex] + 6)
Step-by-step explanation:
Perimeter of a shape is total length of the boundaries of the shape. In the given question, we have two semicircles and a rectangle.
The circumference of a circle = 2[tex]\pi[/tex]r, thus the length of the arc of a semicircle = [tex]\pi[/tex]r.
The height of the rectangle is h, radius 'r' of the semicircle = [tex]\frac{h}{2}[/tex]
⇒ h = 2r
The perimeter of a rectangle = 2(l +b).
Given that: the length is twice its height, so that:
length = 2h
Perimeter of the rectangle = 2 (2h + h)
= 6h
But, h = 2r
Perimeter of the rectangle = 6 × 2r
= 12r
Perimeter of the figure in terms of the semicircle's radius = [tex]\pi[/tex]r + 12r + [tex]\pi[/tex]r
= 2[tex]\pi[/tex]r + 12r
= 2r([tex]\pi[/tex] + 6)
what is 8 - 3x > -25 because i have been wondering all day
Answer:
[tex]8 - 3x > -25 : \left[\begin{array}{ccc}solution: x < 11\\Interval Notation:(-\infty,11)\end{array}\right][/tex]
Step-by-step explanation:
[tex]8-3x>-25[/tex]
Subtract [tex]8[/tex] from both sides:
[tex]8-3x-8>-25-8[/tex]
Simplify:
[tex]-3x>-33[/tex]
Multiply both sides by [tex]-1[/tex] (reverse the inequality):
[tex]\left(-3x\right)\left(-1\right)<\left(-33\right)\left(-1\right)[/tex]
Simplify:
[tex]3x<33[/tex]
Divide both sides by [tex]3[/tex] :
[tex]\frac{3x}{3}<\frac{33}{3}[/tex]
Simplify:
[tex]x < 11[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you, have a good day! =)
What is the measure JKL?
O A. 186°
O B. 267°
0 C. 174°
o D. 87°
Answer:
c
Step-by-step explanation:
How is adding mixed numbers with unlike denominators the same as adding fractions with unlike denominators? How is it different?
I need help!!! And fast!!!!
On a math test ,there are 60 questions, Elena answered 50 correctly.
a)what percent did she answer correctly?
b)What is her radio to incorrect answers?
c)what is the radio of correct answers to the total number of questions fielded on her test?
Answer:
YOU MAY NEED TO CHAN
Step-by-step explanation:
solve each of the equations below and classify them based on their solution.
1.) -8x - 3x= -11x
2.) 6x = -6y - 12
3.) -3z = 8 -z
4.) -5n = 3 - 5n
No Solution, Unique Solution, Infinitely many Solution
Answer:
Answers are below
Step-by-step explanation:
1.) No solution
2.) Unique solution
3.) Unique solution
4.) No solution
I graphed the equation that had a unique solution on the graph below.
If these answers are correct, please make me Brainliest!
A row of tiny red beads is placed at the beginning and at the end of a 20‐centimeter bookmark.
A row of the same beads is also placed every 4 millimeters along the bookmark.
How many rows of the beads are used on the bookmark?
Answer:
51 rows
Step-by-step explanation:
Given
Length of bookmark = 20cm
Distance between beads = 4mm
Required
Number of rows of beads
First, the distance between the rows of beads must be converted to cm
if 1mm = 0.1cm
then
4mm = 4*0.1cm
4mm = 0.4 cm
This means that each row of beads is placed at 0.4 cm mark.
The distance between each row follows an arithmetic progression and it can be solved as follows;
[tex]T_n = a + (n-1)d[/tex]
Where [tex]Tn = 20cm[/tex] (The last term)
[tex]a = 0 cm[/tex] (The first term)
[tex]d = 0.4cm[/tex] (The distance between each row of beads)
n = ?? (number of rows)
Solving for n; we have the following;
[tex]T_n = a + (n-1)d[/tex] becomes
[tex]20 = 0 + (n-1)0.4[/tex]
[tex]20 = (n-1)0.4[/tex]
DIvide both sides by 0.4
[tex]\frac{20}{0.4} = \frac{(n-1)0.4}{0.4}[/tex]
[tex]50 = (n-1)[/tex]
[tex]50 = n-1[/tex]
Add 1 to both sides
[tex]50 + 1= n-1 + 1[/tex]
[tex]n = 51[/tex]
Hence, the number of rows of beads is 51
think your a pro at riddles?
Mr. and Mrs. Mustard have six daughters and each daughter has one brother. How many people are in the Mustard family?
Answer:
nine
Step-by-step explanation:
Kim's business earns $10,000 per month. Kim's non-employee expenses are $3,000 per month. If Kim wants $2,000 in profit per month, how many employees can Kim have if each employee costs $1,000 per month?
Answer:
Kim's business earns $10,000 per month.
Kim's non-employee expenses are $3,000 per month.
If Kim wants $2,000 in profit per month, then the maximum amount Kim can spend for employee:
10000 - 3000 - 2000 =5000
If each employee costs $1,000 per month, Kim can recruit 5000/1000 = 5 as the maximum number of employees.
Hope this helps
:)
Answer:
5
Step-by-step explanation:
Revenue - profit = expense
10000 - 2000 = 8000
8000 = 3000 + 1000n
1000n = 5000
n = 5
How many 2-letter words can be made from the letters MATH if
Answer:
ham
tam
mat
hat
at
ha
am
ma
Step-by-step explanation:
16x^4-25 Which pattern can we use to factor the expression?
Step-by-step explanation:
Hope this helps you... Lemme know if you don't understand
Please answer quick
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor need to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning m. What is the probability that Taylor will win the game?
A. P(winning)= 4/6=66%
B.P(winning)= 3/6=50%
C. P(winning)= 5/6=83%
D. P(winning)= 2/6=33%
Answer:
It would be 2/6.
Step-by-step explanation:
2/6 simplified is 1/3 and she is going against two of her friends in which makes three.
The probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three.
To win, Taylor needs to roll a 4, a 5, or a 6.
Total number in a standard roll = 6
Favorable outcomes = 3
Probability = 3/6 or
= (3/6)×100
= 50 %
Thus, the probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ5
Which are equations? CHECK all that apply.
X+3=12
Z/7+1
25-q
6g=18
2/3m
P/3.5=2.25
9=100-f
K divided by 5.8
Answer:
X + 3 = 12
6g = 18
P/3.5 = 2.25
9 = 100 - f
Step-by-step explanation:
Equations have equal signs.
Expressions do not.
Therefore, any expression with an equal sign is an equation, making it one of the correct answers.
Answer:
X + 3 = 12
6g = 18
P/3.5 = 2.25
9 = 100 - f
Step-by-step explanation:
Just did it!
(60 POINTS) The figure is transformed as shown in the diagram. Describe the transformation.
A) dilation, then reflection
B) reflection, then rotation
C) rotation, then translation
D) translation, then reflection
Answer:
The solution is rotation, then translation. The figure has been rotated about the origin by 90° and then translated 6 units to the right.
graph y=-2/3x-3 i need help quick
Answer: just get gud at math lol
Step-by-step explanation: no
Consider a vat that at time t contains a volume V (t) of salt solution containing an amount Q(t) of salt, evenly distributed throughout the vat with a concentration c(t), where c(t) = Q(t) / V(t). Assume that water containing a concentration k of salt enters the vat at a rate rin, and that water is drained from the vat at a rate rout > rin.
(a) If V (0) = V0, find an expression for the amount of solution in the vat at time t. At what time T will the vat become empty? Find an initial value problem that describes the amount of salt in the vat at time t <= T. You may assume that Q(0) = Q0.
(b) Solve the initial value problem in part (a). What is the amount of salt in the vat at time t? What is the concentration of the last drop that leaves the vat at time t = T
Answer:
a.i [tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii. time at which vat will be empty
[tex]T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex] when dQ/dt = 0
b. i Amount of salt at time t
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
ii. Concentration at t = T
c(T) = [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Step-by-step explanation:
a.
i. We determine the differential equation for the solution in the vat at time,t.
Let Q be the quantity of salt in the vat at any time,t.
So, dQ/dt = rate of change of quantity of salt in the vat. = rate of change of quantity of salt into the vat - rate of change of quantity of salt out of the vat.
Now, since a concentration of salt, k enter the vat at a rate of rin, rate of change of quantity of salt into the vat = krin.
Let V(0) = V₀ be the volume of water int the vat at time t = 0. Now, the volume of water in the vat increases at a rate of (rin - rout). The increase in volume after a time t is (rin - rout)t. So the volume after a time, t is V(t) = V₀ + (rin - rout)t. The concentration of this liquid is thus Q(t)/V(t) = Q(t)/V₀ + (rin - rout)t. Now, the rate of change of quantity of salt out of the vat is thus [Q(t)/V₀ + (rin - rout)t]rin = Q(t)rout/[V₀ + (rin - rout)t].
So, dQ(t)/dt = krin - Q(t)rout/[V₀ + (rin - rout)t].
[tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii Time T at which vat will be empty
At time T, when the vat is empty, dQ(T)/dt = 0.
So
[tex]\\\frac{dQ(T)}{dt} + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\0 + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex]
b. i
i. We solve the differential equation to find the amount of salt at time,t
The integrating factor is ex
[tex]exp(\int\limits {\frac{r_{out} }{V_{0} + (r_{in} - r_{out})t} } \, dt ) = exp(\frac{r_{out}}{(r_{in} - r_{out})} \int\limits {\frac{ (r_{in} - r_{out})}{V_{0} + (r_{in} - r_{out})t} } \, dt )\\= exp(\frac{r_{out}}{(r_{in} - r_{out})} ln [V_{0} + (r_{in} - r_{out})t} ]) \\\= [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]
Multiplying both side of the equation by the integrating factor, we have
[tex][V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{dQ(t)}{dt} + [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt = krin[V(0) + (rin - rout)texp(rout/(rin - rout))]
Integrating both sides we have
∫(dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt)dt = ∫(krin[V(0) + (rin - rout)texp(rout/(rin - rout))])dt
Let exp(rout/(rin - rout) = A
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + C
At t = 0, Q(t) = Q(0),
So,
Q(0)[V(0) + A(rin - rout)×0] = AkrinV(0)t + A(rin - rout)×0²/2 + C
C = Q(0)V(0)
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + Q(0)V(0)
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
The above is the amount of salt at time ,t.
ii. The concentration of the last drop of salt at time, t = T
To find the concentration of the last drop of salt at time t = T, we insert T into Q(t) to find its quantity and insert t = T into V(t) = V₀ + (rin - rout)t.
So
Q(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]
Q(T) = [[exp(rout/(rin - rout)]krin[V(0)T + [exp(rout/(rin - rout)](rin - rout)T²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)T]
the volume at t = T is
V(T) = V₀ + (rin - rout)T.
The concentration at t = T is c(T) = Q(T)/V(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]/V₀ + (rin - rout)T.
= [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/([V(0) + A(rin - rout)T][V₀ + (rin - rout)T])
= [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Which are the center and radius of the circle with equation (x + 5)2 + (y − 4)2 = 9?
A. (−5, −4); r = 3
B. (5, −4); r = 9
C. (−5, 4); r = 3
D. (5, 4); r = 9
Answer:
C)
Step-by-step explanation:
*Look at the picture*
Juan spins two different fair spinners. One spinner has numbers 1 through 8. The other has letters A through F. What is the probaility that one spinner will land on 3 and the other will land on C?
Answer:
...
Step-by-step explanation:
3y + 6 = 18y
- What does the ( y ) variable stand for and how exactly do you find it?
Answer:
y=2/5 or 0.4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
3y + 6 = 18y -->
subtract 3y from both sides to get rid of it.
6 = 15y -->
isolate the variable by dividing it by 15.
6/15 = 15y/15 -->
simplify.
2/5 = y
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
C
Step-by-step explanation:
Since the output is just the input multiplied by 3, the output will be 15.4*3=46.2, or answer choice C. Hope this helps!
Answer:
C. 46. 2
Step-by-step explanation:
All you need to do is multiply 15.4 by 3, like so:
15.4 · 3 = 46.2
Which deduction is optional?
A. Federal income tax
B. Life insurance
C. Medicare
D. Social Security
Answer:
B. Life insurance
Step-by-step explanation:
A. Federal income tax required by law
B. Life insurance usually employer paid for a small amount and then optional
C. Medicare required by law
D. Social Security required by law
A football team scored fewer than 16 points in Saturday’s game. Than wants to write an inequality for the number of points. He uses the variable s in his inequality. What does s represent? A - the number of fans of the team
B - the number of games played by the team
C - the number of points scored by the team
D - the number of players on the team
Instructions : integrate the following
You can simplify the integrand:
[tex]\dfrac{3x^2+4x+1}{2x}=\dfrac{3x}2+2+\dfrac1{2x}[/tex]
Then integrate term-by-term:
[tex]\displaystyle\int\frac{3x^2+4x+1}{2x}\,\mathrm dx=\frac32\int x\,\mathrm dx+2\int\mathrm dx+\frac12\int\frac{\mathrm dx}x[/tex]
[tex]=\dfrac{3x^2}4+2x+\dfrac12\ln|x|+C[/tex]
PLEASE HELP ME with an explanation. Thanks in advance
Answer:
3) 0.30
The probability a randomly selected student plays a sport given they work part time = 0.30
Step-by-step explanation:
Step(i):-
Given 'A' plays a sport
B work part time
Given P(A) = 0.48
P(B) = 0.40
P(A∩B) =0.12
P(A∪B)¹ =0.24
Step(ii):-
By using conditional probability
[tex]P(B/A) = \frac{P(BnA}{P(A)}[/tex]
and similarly [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
The probability a randomly selected student plays a sport given they work part time
Now [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
[tex]P(A/B) = \frac{0.12}{0.40}= 0.30[/tex]
Final answer:-
The probability a randomly selected student plays a sport given they work part time = 0.30
Enter the solution (x, y) to the system of equations shown. y=2x+1 3y=4x+7
Answer:
Step-by-step explanation:
3(2x + 1) = 4x + 7
6x + 3 = 4x + 7
2x = 4
x = 2
y = 2(2) + 1
y = 4 + 1
y = 5
(2,5)
Answer:
2,5
Step-by-step explanation:
list down all the prime numbers which are factors of 30
Hey!!
Here's your answer:
prime numbers which are factors of 30 are:
1,2,3 and 5
Hope it helps
Answer:
1, 2, 3, 5
sorry for the confusion i didn't read it correctly
Assume {v1, . . . , vn} is a basis of a vector space V , and T : V ------> W is an isomorphism where W is another vector space. Show that the vectors w1 = T(v1), . . . ,wn = T(vn) are a basis of W.
This statement becomes false if we drop the assumption that T is invertible. Demonstrate this by finding a counterexample.
Answer:
Step-by-step explanation:
To prove that [tex]w_1,\dots w_n[/tex] form a basis for W, we must check that this set is a set of linearly independent vector and it generates the whole space W. We are given that T is an isomorphism. That is, T is injective and surjective. A linear transformation is injective if and only if it maps the zero of the domain vector space to the codomain's zero and that is the only vector that is mapped to 0. Also, a linear transformation is surjective if for every vector w in W there exists v in V such that T(v) =w
Recall that the set [tex]w_1,\dots w_n[/tex] is linearly independent if and only if the equation
[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex] implies that
[tex]\lambda_1 = \cdots = \lambda_n[/tex].
Recall that [tex]w_i = T(v_i)[/tex] for i=1,...,n. Consider [tex]T^{-1}[/tex] to be the inverse transformation of T. Consider the equation
[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex]
If we apply [tex]T^{-1}[/tex] to this equation, then, we get
[tex] T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) =T^{-1}(0) = 0[/tex]
Since T is linear, its inverse is also linear, hence
[tex]T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) = \lambda_1T^{-1}(w_1)+\dots + \lambda_nT^{-1}(w_n)=0[/tex]
which is equivalent to the equation
[tex]\lambda_1v_1+\dots + \lambda_nv_n =0[/tex]
Since [tex]v_1,\dots,v_n[/tex] are linearly independt, this implies that [tex]\lambda_1=\dots \lambda_n =0[/tex], so the set [tex]\{w_1, \dots, w_n\}[/tex] is linearly independent.
Now, we will prove that this set generates W. To do so, let w be a vector in W. We must prove that there exist [tex]a_1, \dots a_n[/tex] such that
[tex] w = a_1w_1+\dots+a_nw_n[/tex]
Since T is surjective, there exists a vector v in V such that T(v) = w. Since [tex]v_1,\dots, v_n[/tex] is a basis of v, there exist [tex]a_1,\dots a_n[/tex], such that
[tex]a_1v_1+\dots a_nv_n=v[/tex]
Then, applying T on both sides, we have that
[tex]T(a_1v_1+\dots a_nv_n)=a_1T(v_1)+\dots a_n T(v_n) = a_1w_1+\dots a_n w_n= T(v) =w[/tex]
which proves that [tex]w_1,\dots w_n[/tex] generate the whole space W. Hence, the set [tex]\{w_1, \dots, w_n\}[/tex] is a basis of W.
Consider the linear transformation [tex]T:\mathbb{R}^2\to \mathbb{R}^2[/tex], given by T(x,y) = T(x,0). This transformations fails to be injective, since T(1,2) = T(1,3) = (1,0). Consider the base of [tex]\mathbb{R}^2[/tex] given by (1,0), (0,1). We have that T(1,0) = (1,0), T(0,1) = (0,0). This set is not linearly independent, and hence cannot be a base of [tex]\mathbb{R}^2[/tex]
Calculate CDEFtrapezium
｡☆✼★ ━━━━━━━━━━━━━━ ☾
You need to find the length of A F and BC first
Lets call BC --> 'x'
Lets form an equation
9 + 9 + x + x = 28
18 + 2x = 28
- 18
2x = 10
/ 2
x = 5
So now we have the length BC
We can subtract this length from the 11cm to find the vertical height of the trapezium
11 - 5 = 6
Now we have all we need to work it out.
area = (a + b) / 2 x h
area = (5 + 9) / 2 x 6
area = 42 cm^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
42 cm²
Step-by-step explanation:
We can see this shape is made of 2 shapes that we are familiar with which are a rectangle and a trapezium.
⇒ The first step in working out the area of the trapezium is working out the length of CB and then working out the height of trapezium. We are given that the perimeter of the rectangle is 28 cm and we know that opposite sides of a rectangle are equal so we will call the length we want to work out x
→ x + x + 9 + 9 = 28
⇒ Simplify
→ 2x + 18 = 28
⇒ Minus 18 from both sides to isolate 2x
→ 2x = 10
⇒ Divide both sides by 5 to isolate x
→ x = 5
5 cm is the length of CB, we will need to minus that from 11 to find the height of the trapezium so,
11 - 5 = 6. The height of the trapezium is 6
Now we have the height of the trapezium (6), we have the base (9) and we have the top length (5). All we do now is substitute these numbers into the trapezium formula which is
→ 0.5 × ( a + b ) × h
Where 'a' and 'b' are the parallel sides and 'h' is the height
Now we begin to substitute in the values,
→ 0.5 × ( a + b ) × h
⇒ Substitute in the values
→ 0.5 × ( 5 + 9 ) × 6
⇒ Simplify
→ 0.5 × ( 14 ) × 6
⇒ Simplify further
→ 42
The area of the trapezium is 42 cm²