Answer:
See explanation
Step-by-step explanation:
The two linear equations can be solved simultaneously;
4x+3y=8 -----(1)
−2x−3y=−4---(2)
If we multiply equation (1) by 1 and equation (2) by (2)
We have;
4x+3y=8 -----(3)
-4y - 6x = 4 ---(4)
Adding equation (3) and (4)
-3x = 12
x= -4
Substitute x = -4 into equation (1)
4(-4) + 3y = 8
-16 + 3y = 8
3y = 8 + 16
y= 24/3
y= 8
Hence;
x= -4 and y =8
PLZ HELPPP!!!!!!!!!! ASAP
Answer:
They are consecutive terms in the Fibonacci Sequence.
Step-by-step explanation:
The sequence goes 1,1,2,3,5,8,13,21,...
Since 13 and 21 are consecutive here, that is the answer.
Can some help with this problem
Find the lateral surface area of this
cylinder. Round to the nearest tenth.
r = 5 cm
5 cm
LSA = [ ? ] cm2
Enter
Answer:
[tex]A=157.07\ cm^2[/tex]
Step-by-step explanation:
Given that,
The radius of a cylinder, r = 5 cm
Height of the cylinder, h = 5 cm
We need to find the lateral surface area of the cylinder. The formula for the lateral surface area of the cylinder is given by :
[tex]A=2\pi r h[/tex]
Put all the values,
[tex]A=2\pi\times 5\times 5\\\\=157.07\ cm^2[/tex]
So, the lateral surface area of the cylinder is [tex]157.07\ cm^2[/tex].
How many digits from 10 to 1000 have each digit greater than its following digit?
Answer:
10 has 2 digits
1000 has 4 digits
Difference of 2 digits
7. State the type of system of equations.
y + 5x = 6
5y + 25x = 80
Step-by-step explanation:
the systems of equations shown are parallel because they have the same slope
ax + by = c and mx + ny = d and an # bm then these simultaneous equations have a) Only one common solution. b) No solution. c) Infinite number of solutions. d) Only two solutions.
Answer:
a) Only one common solutionStep-by-step explanation:
The first line has slope of a/b and the second one has slope of m/n.
As an ≠ bm ⇒ a.b ≠ m/n, the slopes are different.
Since the slopes are different the lines are not parallel, hence they intersect at one point.
This means there is one solution only.
ax + by = c and mx + ny = d and an # bm then these simultaneous equations have Only one common solution.
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Describe fully the single transformation that maps a onto shape b
Answer:
Reflected over y-axis
Help please? thank you
Answer:
Answer is A
Step-by-step explanation:
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
10 + 2.5 x less-than-or-equal-to 40
Which best describes the number of bags of balloons she can buy?
Answer:
She can buy from 0 to 20 bags, but no more.
Answer:
b <3
Step-by-step explanation:
4x⁴+3x²y²+9y⁴
solve by step by step
Answer:
4x^4+3x^2y^2+9y^2
(2x^2)^2 + 2×2x^2×3y^2 + (3y^2)^2 - 9
(2x^2 + 3y^2)^2 - (3)^2
(2x^2 +3y^2+3)(2x^2+3y^3-3)
If the ratio of a to b is 2.3 and the ratio
of to bis 3:4, which of the following is
equal to the ratio of a to c.?
Answer:5.7 D
Step-by-step explanation:
f(x)=2x+3/4x+5
find f(-9)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]f(x) = \frac{2x + 3}{4x + 5} \\[/tex]
For [tex]f(-9)[/tex], put "[tex]-9[/tex]" for every value of "[tex]x[/tex]".
[tex]↬f( - 9) = \frac{2( - 9) + 3}{4( - 9) + 5}\\ [/tex]
[tex]↬ f(-9) = \frac{ - 18 + 3}{ - 36 + 5} \\[/tex]
[tex]↬ f(-9) = \frac{ - 15}{ - 31}\\ [/tex]
[tex]↬ f(-9)= \frac{15}{31}\\ [/tex]
[tex] ↬f(-9)= 0.48\\ [/tex]
[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{f(x) = \dfrac{2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{ 2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{2(-9) + 3}{4(-9) + 5}}[/tex]
[tex]\mathsf{2(-9)}[/tex]
[tex]\mathsf{\bf = -18}[/tex]
[tex]\mathsf{y = \dfrac{-18 + 3} {4(-9) + 5}}[/tex]
[tex]\mathsf{-18 + 3}\\\mathsf{= \bf -15}[/tex]
[tex]\mathsf{y = \dfrac{ -15} {4(-9) + 5}}[/tex]
[tex]\mathsf{4(-9)}\\\mathsf{\bf = -36}[/tex]
[tex]\mathsf{y = \dfrac{-15}{-36 + 5}}[/tex]
[tex]\mathsf{-36 + 5}\\\mathsf{= \bf-31}[/tex]
[tex]\mathsf{y = \dfrac{-15}{ -31}\rightarrow\boxed{\bf \dfrac{15}{31}}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = \dfrac{15}{31}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The temperature of a cup of coffee varies according to Newton's Law of Cooling: -"dT/dt=k(T-A), where is the temperature of the coffee, A is the room temperature, and k is a positive
constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25*C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes,
74
67
60
42
Answer:
B) 67°C.
Step-by-step explanation:
Newton's Law of Cooling is given by:
[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]
Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.
And we want to find the temperature of the coffee after four minutes.
First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:
[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]
Integrate:
[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]
Raise both sides to e:
[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]
The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:
[tex]\displaystyle T=Ce^{kt}+A[/tex]
We are given that A = 25. Hence:
[tex]\displaystyle T=Ce^{kt}+25[/tex]
Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:
[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]
Hence:
[tex]T=75e^{kt}+25[/tex]
We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.
So, T = 90 given that t = 1. Substitute:
[tex]90=75e^{k(1)}+25[/tex]
Solve for k:
[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]
Therefore:
[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]
Then after four minutes, the temperature of the coffee will be:
[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]
Hence, our answer is B.
Calculate cos (theta) to two decimal places. PLS HELP ASAP
Answer:
B. -0.07
Step-by-step explanation:
Apply the Law of signs find θ.
Cos θ = (a² + b² - c²)/2ab
Where,
a = 7
b = 8
c = 11
Plug in the values
Cos θ = (7² + 8² - 11²)/2*7*8
Cos θ = (49 + 64 - 121)/112
Cos θ = -8/112
Cos θ = -0.0714285714
Cos θ = -0.07 (to 2 decimal places)
A farmer in China discovers a mammal
hide that contains 37% of its original
amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t=0)
N = amount of C-14 at time t
k= 0.0001
t = time, in years
Answer:
Step-by-step explanation:
I'm going to take a giant leap here and guess that you are looking for how old this mammal hide is. At least that's what I'm going to work out for you. Filling in the formula is relatively easy as long as we remember that the initial amount of hide was 100%:
[tex]37=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get
[tex].37=e^{-.0001t}[/tex] In order to get that t down from its current position, we have to take the natural log of both sides. The reason we do natural log as opposed to common log is because the natural log will cancel out the e:
[tex]ln(.37)=ln(e^{-.0001t})[/tex] and again, because the log cancels out the e we have:
ln(.37) = -.0001t and divide both sides by -.0001 to get
t = 9942.5 years
Answer:
answer is 9943
Step-by-step explanation:
Write a phrase in words to match each expression.
5+3
——
n
Answer:
sum of five and 3 is divided by n
A rectangular piece of paper has an area of ⅓ square meter. If the length of the paper is ⅗ meter, what is the breadth of the paper?
Answer: [tex]\frac{5}{9}\ m[/tex]
Step-by-step explanation:
Given
Area of the rectangular piece of paper is [tex]A=\frac{1}{3}\ m^2[/tex]
Length of the paper is [tex]l=\frac{3}{5}\ m[/tex]
Suppose width of the paper is [tex]w[/tex]
Area is the multiplication of length and width
[tex]\therefore A=lw\\\\\Rightarrow \dfrac{1}{3}=\dfrac{3}{5}\times w\\\\\Rightarrow w=\dfrac{5}{9}\ m[/tex]
Thus, the width of the paper is [tex]\frac{5}{9}\ m[/tex]
a. 65
b. 67
c. 43
d. 23
(14) (55, 42, 32, 48, 55, x), mean = 49
Answer:
78
Step-by-step explanation:
Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done
click the image below to find out the question.
A sum of money earns the interest ar the rate of Rs. 5 per Rs.25 in a year. how many years would it trible itself?
a. 5
b. 10
c.15
d. 20
f) 1 5/2 +8x4 =
alluda :(
Answer:
35.5
Step-by-step explanation:
1 5/2 + (8*4)= 35.5
(8*4)= 32
32+1 5/2
1 5/2=3 1/2
32+3 1/3
35.5 or 35 1/2
A tower is 543m from your house. The angle of elevation to the top of the tower is 33.4°. How high is the tower?
Answer:
358
Step-by-step explanation:
the step by step is in the photo so look at it
Help!!!! hurry quick pls
Answer:
A.
by-step explanation:
m to k
1 to 1.609
using the formula of Sin 2A ,cos2a and tan 2a establish that; tab A is = +- root under 1 - cos 2A by 1 + cos 2a
Answer:
Step-by-step explanation:
Given identity is,
[tex]\text{tanA}=\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}[/tex]
To prove this identity, we will take left side of the identity,
[tex]\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}=\pm\sqrt{\frac{1-(1-2\text{sin}^2A)}{1+(2\text{cos}^2A-1)} }[/tex]
[tex]=\pm\sqrt{\frac{1-1+2\text{sin}^2A}{1+2\text{cos}^2A-1} }[/tex]
[tex]=\pm\sqrt{\frac{2\text{sin}^2A}{2\text{cos}^2A} }[/tex]
[tex]=\pm(\sqrt{\text{tan}^2A})[/tex]
[tex]=\text{tanA}[/tex] [Right side of the identity]
Hence, proved.
Choose the answer that is equivalent to the quotient.
(-4x3 + 16x2 21x + 22) divided by (2x – 3)
0-222 +51 - 3+
13
21-3
o 22 – 3+3
O-212 + 52 - 3+
16
21-3
0-222 + 52 - 3
Intercept Form
Point (-3,4)
Slope 5
m= b=
Answer:
y = 5x + 19
Step-by-step explanation:
y = 5x + b
4 = 5(-3) + b
4 = -15 + b
19 = b
A(-4,-2), B(-1,-1), C(-1,-4)
what are the coordinate of triangle ABC when reflected over the line y=-x?
A). A'(-2,4), B'(1,1), C(-4,1)
B). A'(2,4), B'(1,1), C(4,1)
C). A'(4,2), B'(1,2), C'(2,1)
D). A'(2,4), B'(1,-1),C' (4,-1)
Answer:
B
Step-by-step explanation:
Fip numbers and change both signs when reflecting over y=-x
Answer:
C
Step-by-step explanation:
What’s the equation of the line that passes through the point (-4,4) and has a slope of 3/4
Answer:
y-y1=m(x-x1)
y-4=3/4(x+4)
y=3/4x+7
Please answer fast!!!!!!
The sum of the reciprocals of two consecutive even integers is
9/40. This can be represented by the equation shown.
1/x+1/x+2=9/40
Use the rational equation to determine the integers. Show all work.
Answer:
8 and 10
Step-by-step explanation:
Given
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{x+2}[/tex] = [tex]\frac{9}{40}[/tex] ← combine the fractions on the left side
[tex]\frac{x+2+x}{x(x+2)}[/tex] = [tex]\frac{9}{40}[/tex]
[tex]\frac{2x+2}{x^2+2x}[/tex] = [tex]\frac{9}{40}[/tex] ( cross- multiply )
9(x² + 2x) = 40(2x + 2) ← distribute both sides
9x² + 18x = 80x + 80 ( subtract 80x + 80 from both sides )
9x² - 62x - 80 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 9 × - 80 = - 720 and sum = - 62
The factors are - 72 and + 10
Use these factors to split the x- term
9x² - 72x + 10x - 80 = 0 ( factor the first/second and third/fourth terms )
9x(x - 8) + 10(x - 8) = 0 ← factor out (x - 8) from each term
(x - 8)(9x + 10) = 0
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
9x + 10 = 0 ⇒ 9x = - 10 ⇒ x = - [tex]\frac{10}{9}[/tex]
x is an integer , then x = 8 and x + 2 = 8 + 2 = 10
The integers are 8 and 10
Answers: Integers are x=8, x=10.