Answer:
The solution of the system is:
(x, y) = (-1, -6)
Step-by-step explanation:
Given the system of equations
-6x – 3y = 24
4x – 2y = 8
solving the system of equations
[tex]\begin{bmatrix}-6x-3y=24\\ 4x-2y=8\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-6x-3y=24\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12x-6y=48[/tex]
[tex]\mathrm{Multiply\:}4x-2y=8\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x-6y=24[/tex]
so
[tex]\begin{bmatrix}-12x-6y=48\\ 12x-6y=24\end{bmatrix}[/tex]
adding the equations
[tex]12x-6y=24[/tex]
[tex]+[/tex]
[tex]\underline{-12x-6y=48}[/tex]
[tex]-12y=72[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}-12x-6y=48\\ -12y=72\end{bmatrix}[/tex]
solve -5y=72 for y
[tex]-12y=72[/tex]
Divide both sides by -12
[tex]\frac{-12y}{-12}=\frac{72}{-12}[/tex]
Simplify
[tex]y=-6[/tex]
[tex]\mathrm{For\:}-12x-6y=48\mathrm{\:plug\:in\:}y=-6[/tex]
solving
[tex]-12x-6\left(-6\right)=48[/tex]
[tex]-12x+6\cdot \:6=48[/tex]
[tex]-12x+36=48[/tex]
subtract 36 from both sides
[tex]-12x+36-36=48-36[/tex]
Simplify
[tex]-12x=12[/tex]
Divide both sides by -12
[tex]\frac{-12x}{-12}=\frac{12}{-12}[/tex]
[tex]x=-1[/tex]
Therefore, the solution of the system is:
(x, y) = (-1, -6)
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The "off-peak” weekly average cost of hiring a caravan in England is £480.
In July the average cost increases to £850.
Calculate the percentage increase in cost.
Give your answer to 2 significant figures.
Answer:
77.08%
Step-by-step explanation:
850 - 480 = 370
(370 / 480 ) × 100 = 77.08333333%
Answer:
77%
Step-by-step explanation:
What’s the answer because dk
Answer:
I believe the answer to part A is 55. I just added the number of french speakers to the number of females and then subtracted 16. If that answer is correct, then the answer to part b is 68.75%
Find
(a) the value of q in radians
(b) the area of the shaded region in cm²
Answer:
(a) 1.18
(b) 99.71
Step-by-step explanation:
to know the value of q in degrees we can use cosine of q
[tex]\cos (q) = \frac{OR}{OQ}\\\\\cos (q) = \frac{5}{13}\\\\q = \cos^{-1}(\frac{5}{13})\\\\q \approx 67.38[/tex]
now to radians
the formula is
[tex]x\times\frac{2\pi}{360}\\\\[/tex]
with x the degrees
[tex]67.38\times \frac{2\pi}{360}\\\\=\frac{67.38\pi}{180}\\\\\approx 0.374\pi\\\\\approx 1.18[/tex]
so the measure of angle q is 1.18 radians
so now for part b
[tex]A = \frac{r^2 \alpha }{2}\\\\[/tex]
with [tex]\alpha[/tex] being the central angle in radians
for degrees is the following
[tex]A = \frac{\theta}{360}\times \pi r^2[/tex]
so we have
[tex]A = \frac{13^2 (1.18)}{2}\\\\A = 99.71[/tex]cm^2
Please help with this!
Tell whether x and y show direct variation. True or False?
What is the value of cos θ given that (-2, 9) is a point on the terminal side of θ?
Answer:
a) cosθ = [tex]\frac{-2\sqrt{85} }{85}[/tex]
Step-by-step explanation:
Step(i):-
Given point ( x , y ) = ( - 2 , 3 )
We know that the polar co-ordinates
x = r cos θ and y = r sinθ
where [tex]r = \sqrt{x^{2} +y^{2} }[/tex]
[tex]r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}[/tex]
Step(ii):-
x = r cos θ
cosθ [tex]= \frac{x}{r}[/tex]
cosθ = [tex]\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }[/tex]
cosθ = [tex]\frac{-2\sqrt{85} }{85}[/tex]
6+ a/4= -5
2 = n/2-10
PLEASE HELP DUE TODAY JUST 2 QUESTIONS LEFT WHICH THESE ARE THE ONE'S
Answer # 1: 6+ a/4= -5 Answer # 2: n = 24
I NEED HELP ASAP!!!!!!!
A. m= -2
B. m= -1/2
C. m= 2
D. m= 1/2
Answer:
A. m = -2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (0, 0)
Point (1, -2)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [SF]: [tex]\displaystyle m=\frac{-2-0}{1-0}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{-2}{1}[/tex][Fraction] Divide: [tex]\displaystyle m=-2[/tex]Simplify tan0 •sin 0+ cot0 •sin0
Answer:
0
Step-by-step explanation:
tan0 •sin 0+ cot0 •sin0 =
tan(0) • sin(0) + cot(0) • sin(0) =
(tan(0) × sin(0)) + (cot(0) × sin(0)) =
(0 × 0) + (0 × 0) = 0 + 0 = 0
HELP PLEASE I WILL GIVE BRAINLIEST IF YOU DO ALL
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Henry solved the equation 3 (m + 2) = 12 + m
and needs help checking his work. If m = 3, then
help Henry by checking if he solved the equation
correctly. Show your work on the line paper
provided.
Equation: 3(m + 2) = 12 + m
m = 3
Answer:
Henry derived the value of m correctly
Step-by-step explanation:
insert m into the equation
3(3+2)=12+3
3(5)=15
15=15
Henry derived the value of m correctly
The total cost of a ticket and the online fee for one ticket is $32.25.Let f represent the cost of ordering each ticket online.Write an equation that could be used to find the cost of ordering each ticket online.
Answer:
The equation is f = z - x
Step-by-step explanation:
The equation is
Given that
The total cost + online fee for one ticket is $32.25
Let us assume f be the cost of ordering each ticket online
Cost of each ticket be x = $24.95
And, the total cost = z = $32.25
Now the equation would be
x + f = z
So for f it would be
f = z - x
Help. Algebra rjsffjdnsifvnswkfnc
Answer:
No x-intercept/Zero
Step-by-step explanation:
f(x)=3x(3/4)x-4
To find x-intercept/zero, substitute f(x)=0
0=3x(3/4)x-4
To raise a fraction to a power, raise the numerator and denominator to that power
0=3x 3 x-4/4 x-4
Calculate the product
0=3 x-3/4 x-4
Since the right-hand side is always positive, the statement is false for any value of x
Since there is no solution for f(x)=0, there is no x-intercept/Zero
The population of New York City is approximately 8 x 106. The population
of San Francisco is approximately 8 x 105. About how many times larger
is the population of New York than the population of San Francisco?
Answer:
I think if I'm understanding it right it's 8 times larger but that may be wrong
In which quadrant does the point (10 , 25) lie?
Answer:
First quadrant
Step-by-step explanation:
Since, both x and y coordinates of the given point are positive.
Therefore, the point (10 , 25) lie in the first quadrant.
Complete the equation.
-6x2 + 15x – 6 = -3(2x - 1)(x + _)
A. 2
B. -2
C. -3
D. 6
cosa/(1+sina)+cosa/(1-sina)=2seca
prove this:)
Answer:
Please check explanations
Step-by-step explanation:
Using the difference of two squares, the lowest common multiple becomes;
1-sin^2 a
Thus, we have that;
cos a (1-sin a) + cos a (1 + sin a) /1 - sin^2 a
1 - sin^2 a = cos^2 a
That means;
{cos a - cos a sin a + cos a + cos a sin a}/ cos^2 a
= 2cos a / cos^2 a
= 2/cos a
but 1/cos a = sec a
Thus;
2/ cos a = 2 sec a
What is the dilation for the transformation below?
Answer:
The dialation is of 2
Step-by-step explanation:
QR = 3 units
QS = 2 units
RS = 2 units
Q'R' = 6 units
Q'S' = 4 units
R'S' = 4 units
So as you can see, this triangle has doubled it's size, since it has been multiplied by 2.
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Simplify the expression. -5/8(-3/8-1/4)
Answer:
25/64
Step-by-step explanation:
To get this answer, first you need to use the distributive property:
(-3/8)(-5/8) - (1/4)(-5/8)
Next, multiply:
15/64 - (-5/32)
Change the negative signs into a positive sign:
15/64 + 5/32
Multiply 5/32 by 2 on both top and bottom:
15/64 + (5)(2)/(32)(2)
You will then get:
15/64 + 10/64
Now, add the numerators. You will get:
25/64
This is your answer. I hope it helped!
Determine the equation of the line that goes through points (1.1) and (3.7).
Answer:
The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]
Step-by-step explanation:
Determine the equation of the line that goes through points (1,1) and (3,7)
We can write the equation of line in slope-intercept form [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
We need to find slope and y-intercept.
Finding Slope
Slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=1, y_1=1, x_2=3, y_2=7[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3[/tex]
We get Slope = 3
Finding y-intercept
y-intercept can be found using point (1,1) and slope m = 3
[tex]y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2[/tex]
We get y-intercept b = -2
So, equation of line having slope m=3 and y-intercept b = -2 is:
[tex]y=mx+b\\y=3x-2[/tex]
The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]
Please help ASAP!!!!!
Given:
The graph of set of ordered pairs.
To find:
The domain of the set of number.
Solution:
Domain is the set of input values or x-values.
From the given graph it is clear that the set of ordered pair is:
{(1,2), (2,4), (3,1), (4,6), (5,4), (6,5)}
Here, the x-values are 1, 2, 3, 4, 5, 6. So, the domain is the set of these values.
Domain = {1, 2, 3, 4, 5, 6}
Therefore, the correct option is A.
i need to do this for extra credit because my low grade...someone please help me!! i’ll make you a brainliest:)
Answer:
A. 4+4
B. 2x4
C. a=2
D. a=5 b=7
What would be the new set of numbers if the Scale Factor was 2? 3:4:5:6
Answer:
6:8:10:12
Step-by-step explanation:
Scale factor of 2-
3:4:5:6
multiply each number by 2
6:8:10:12
Please help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
cero que la pregunta es el numero cuatorce
Step-by-step explanation:
as it may not be much, It's the best i can do, with such little wealth, take my earning, consider thy points as your spoils.
1^2 +68=69 skippa bap
Answer:
Thank you!
Step-by-step explanation:
Have a nice day/night lol
Answer:
1^2 +68=69
Step-by-step explanation:
by sqrt rooting 2 by 1 is 1
Guys please help..
I have 2 questions, please help with both
1. Find the Time in years if Principal, p= 6500, Rate (p. a)= 7% and Simple Interest, SI = Rs . 1365
2. If 80% of the students of a class of 40 students like Mathematics, then the number of students who do not like it is _______
Please answer soon
Answer:
1. I=P*i*t
1365=6500*7%*t
1365=455*t
t=3
2.-Students 40
Like mathematics
= 40*80
=32
Don´t like it is
=40-32
=8
Step-by-step explanation:
1. I=P*i*t
1365=6500*7%*t
1365=455*t
t=3
2.-Students 40
Like mathematics
= 40*80
=32
Don´t like it is
=40-32
=8
Identify the scale factor used to graph the image below
Answer:
[tex]Scale = \frac{2}{3}[/tex]
Step-by-step explanation:
To solve this question, I'll use the coordinates of SV and S'V' as points of reference.
From the attachment:
[tex]S = (3,6)[/tex]
[tex]V = (15,3)[/tex]
[tex]S' = (2,4)[/tex]
[tex]V' = (10,2)[/tex]
First, calculate distance SV
Distance formula is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
For SV:
[tex]d_1 = \sqrt{(15 - 3)^2 + (3 - 6)^2}[/tex]
[tex]d_1 = \sqrt{(12)^2 + (-3)^2}[/tex]
[tex]d_1 = \sqrt{144 + 9}[/tex]
[tex]d_1 = \sqrt{153}[/tex]
For S'V'
[tex]d_2 = \sqrt{(10 - 2)^2 + (2 - 4)^2}[/tex]
[tex]d_2 = \sqrt{64 + 4}[/tex]
[tex]d_2 = \sqrt{68}[/tex]
The scale factor is then calculated using:
[tex]Scale = \frac{S'V'}{SV}[/tex]
[tex]Scale = \frac{d_2}{d_1}[/tex]
Substitute values of d1 and d2
[tex]Scale = \frac{\sqrt{68}}{\sqrt{153}}[/tex]
[tex]Scale = \sqrt{\frac{68}{153}}[/tex]
[tex]Scale = \sqrt{\frac{1}{2.25}}[/tex]
[tex]Scale = \frac{1}{1.5}[/tex]
Express as a proper fraction
[tex]Scale = \frac{1*2}{1.5*2}[/tex]
[tex]Scale = \frac{2}{3}[/tex]
Lynns mom is baking treats for lynns birthday party. She has 12 eggs to use for this purpose. A batch requires two eggs and a batch of brownies requires 3 eggs. Write an inequality to match this solution.
Answer: 2x +3y ≤ 12
Step-by-step explanation:
Given: Lynn's mom has 12 eggs to use for this purpose..
i.e. she can use maximum 12 eggs.
A batch of cookies requires two eggs and a batch of brownies requires 3 eggs.
Let x= Number of batches of cookies , y= Number of batches of brownies
Then, 2x +3y ≤ 12 (maximum eggs = 12)
hence, the required inequality : 2x +3y ≤ 12
put (six times the daily amount of fiber f in your diet) in an algebraic expression
Answer:
6f
Step-by-step explanation:
As part of a grand opening, an arcade gave out free tokens to the first 100 customers. If you spent $5, you got 61 tokens. If you spent $6, you got 72 dollars, if you spent $7 you got 83. Construct an equation in y = mx + b
Answer:
your teacher is they are giving out FREEE tokens so why do you have to pay
Step-by-step explanation