Answer: y = -1 and x = 3
Step-by-step explanation:
x=-2y+6
3x-4y = 28
There are two ways to solve this: 1) solve directly with the equations, and 2) graph the line and look for the intersection.
---
Use the definition of x from the first equation and substitute it in the second:
3x-4y = 28
3(-2y+6)-4y = 28
-6y + 18 -4y = 28
-10y = 10
y = - 1
---
Graph the two lines and find the value of y at the point they intersect. See the attachment.
y = -1 at x= 8
=======================
For the second question:
y=3x-10
4x+5y=7
---
4x+5y=7
4x+5(3x-10)=7
4x+15x-50=7
19x = 57
x = 3
----
I WILL GIVE 20 POINTS! Solve for x.
Answer:
26
Step-by-step explanation:
[tex]8^{2} + 20^{2} = 21.5^{2}[/tex]
[tex]21.5^{2} + 14^{2} = 25.7^{2} \\x = 25.7[/tex]
The soccer team is conducting a fundraiser selling long-sleeved t-shirts for $14 and short-sleeved t-shirts for $10. So far the team has sold less than $200 worth of the two types of t-shirts. Which inequality best represents x, the number of long-sleeved t-shirts they have sold, and y, the number of short-sleeved t-shirts they have sold?
Answer:
Step-by-step explanation:
If x represents the number of long-sleeved shirts and each of these cost $14, then the expression for that is 14x; likewise for short-sleeved shirts that are represented by y. The expression for short-sleeved shirts that cost $10 apiece is 10y. Putting that together with the fact that they earned less than $200 when selling these at the same time, the inequality is
14x + 10y < 200
Answer:D i just got it right trust mw
Step-by-step explanation:i
Find the sum of the second multiple of 9 and the fifth multiple of 6.
Answer:
48
Step-by-step explanation:
9,18
6,12,18,24,30
18 + 30 = 48
Find the marked price if: Selling price =Rs 4999.50 and Discount percentage = 10%.
Answer:
HOPE IT HELP YOU....
if it is right plz comment me .
ILL GIVE POINTS!! PLS HELP !!!
Which set of polar coordinates describes the same location as the
rectangular coordinates (1. - 1)?
A. (sqrt2,315°)
B. (-1,135°) C. (sqrt2,225°)
D. (1,45°)
Answer:
The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.
[tex]r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2}\\[/tex]
You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.
If you would like to find it mathematically, this is the way to do it
[tex]\theta = atan(y/x) = -45[/tex]
Notice that -45 degrees is just 360 - 45 = 315
Your answer would be
[tex](\sqrt{2}, 315)[/tex]
HELP ME SOLVE THIS PLEASE
A Triangular Park ABC has sides 120 m, 80m and 50m. a gardener has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of of Rs. 20 per metre leaving a space 3m wide for a gate on one side?
The perimeter = sum of all sides
= 120 + 80 + 50
= 250
So 250 - 3
247
Left space for gate
Now cost of fencing = Rs 20/per meter
= 247 × 20
= Rs 4,940
Now the area of the triangular park can be found using heron's formula
S = (a+b+c)/2
S = (120+80+50)/2
S = 250/2
S = 125
Now
Herons formula = √s(s-a)(s-b)(s-c)
√125(125-120)(125-80)(120-50)
√125(5)(45)(70)
√5×5×5×5×5×3×3×5×14
After Making pairs
5×5×5×3√14
375√14
Therefore 375√14m is the area of the triangular park
Must click thanks and mark brainliest
$\sf\underline\bold{Answer:}$
$\sf\small\underline{\underline{Area\: planted\: by\: the\: gardener : 1452.36m^2}}$$\sf\small\underline{\underline{The\:cost\:of\:fencing\:the\:park:Rs.4940}}$$\space$
$\sf\underline\bold{Step-by-Step:}$
$\space$
$\sf\bold{Given(In \:the\:Q):}$
Sides of the triangular park are 120m,80m and 50m.$\space$
$\sf\bold{To \: find:}$
How much area of the park does she need to plant?The cost of fencing the park ?$\space$
$\sf\small{☆Area\:to\:be\:planted=Area \: of \: ∆ABC}$
$\space$
$\sf\underline\bold{Calculating\:area\:of\:∆ABC:}$
$\space$
Use heron's formula to find the area of the triangle.
$\space$
$\mapsto$ $\sf\small{Heron's\:formula=}$
[tex]\sf\sqrt{s(s-a)(s-b)(s-c)}[/tex]
$\sf{Where\:s=semi\:perimeter}$$\sf{a,b,c\: = side\:of\:the\:∆}$$\sf\small{Here\:a=120,b=80 \:and\: c=50}$$\space$
$\sf\bold{Now,find\:semi\:parameter:-}$
$\sf\small{Perimeter\:of\:the\:∆=120+80+50=250}$
$\sf\small{Semi-Perimeter:}$ $\sf\dfrac{250}{2}$ $\sf\small{=125m}$
$\space$
$\sf\small{Substitute \: the\:values\:in\:heron's\:formula:}$
$\sf{Area\:of\:the\:∆:-}$
$\mapsto$ [tex]\sf\sqrt{125(125-120)(125-80)(125-50)}[/tex]
$\space$
$\mapsto$ $\sf\sqrt{125\times(5)\times(45)\times(75)}$
$\space$
$\mapsto$ $\sf\small\sqrt{2109375}$ $\sf\small{=375}$ $\sf\small\sqrt{15}$
$\space$
$\longmapsto$ $\sf\underline\bold\purple{1452.56m^2}$
______________________________
$\sf\underline\bold{Now,find\:the\:cost\:of\:fencing:}$
$\sf{Cost\:of\:fencing-}$
$\sf{Rate = Rs.20 per \:meter}$ $\sf{Left\:space=3m}$$\space$
$\sf\underline{Hence,the\:gardener\:has\:to\:fence:}$
$\sf{= 250-3=247m.}$$\space$
So,total cost of fencing at the rate of Rs.20 per m:-
$\sf\underline\bold\purple{=247\times20=4940}$___________________________________
Which math expression means "the product of 16 and 26"?
16 +26
O 16.26
15 - 26
26-16
Answer:
The product of 16 and 26 would be 16 * 26
Step-by-step explanation:
This is because "the product of" means multiplication so *. Making it 16 * 26.
Kevin says that lines p and m will eventually intersect. Lines A and B intersect. Plane A contains lines p, m, and n. Line n is horizontal on the plane. Lines p and m are both going in the same direction and are identical. Plane B contains vertical line l which forms a right angle with line n. Is Kevin correct?
Answer:
No, because they are parallel.
Step-by-step explanation:
The lines [tex]p[/tex] and [tex]m[/tex] will not intersect, so Kevin is not correct.
It is given that planes A and B intersects. The plane A contains the line p, m and n on its plane. The lines p and m are parallel to each other. They are identical and move in the same direction.
Since the line p and m are parallel, they will not meet each other at any point because parallel lines does not intersect or meet at a point, they run parallelly along each other.
So, line p and m will not intersect.
Thus the answer is " No, because they are parallel."
Answer:
Step-by-step explanation:
no, because they are parrallel.
Find the derivative of f(x) = 6/x at x = -2. (2 points)
Using the definition of the derivative,
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{f(x) - f(-2)}{x - (-2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac6x + 3}{x + 2}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac{6+3x}x}{x + 2}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{6+3x}{x(x + 2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3(x+2)}{x(x + 2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3}{x} = \boxed{-\dfrac32}[/tex]
What is the solution to the equation?
6-ste
e
3
2+52-9
2+53 +53-9-5
a-3
2:53 -9
a+54 +5 - 9+53
a-143
2+53 -9
e
Answer:
a = 3 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
a + 5 [tex]\frac{2}{3}[/tex] = 9 ← change mixed number to improper fraction
a + [tex]\frac{17}{3}[/tex] = 9 ( multiply through by 3 to clear the fraction )
3a + 17 = 27 ( subtract 17 from both sides )
3a = 10 ( divide both sides by 3 )
a = [tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]
What is the answer please help
Answer:
i don't know sorry
Answer:
a
Step-by-step explanation:
-5 shifts the y-intercept down, and it needs to be outside of the modulus as if its in the modulus, the graph would shift 5 units to the right instead
Allowing 20 % discount on the marked price of an article and levying 15 % VAT. a buyer has to pay Rs 9.200 for the article. Find the marked price of the article.
Answer:
here I'm confused that whether the selling price is Rs.9,200 or Rs.9.200
any ways you can take the help of below procedure
Step-by-step explanation:
here,
let marked price be X
discount(d)=20%
VAT=15%
SP with VAT= 9200
now,
SP without VAT= SP - VAT of SP
= 9200-15/100 ×9200
= 9200- 1380
=Rs. 1380
again,
SP= MP - D of MP
or,7820= x- 20/100 × x
or, 7820× 100 = 100x- 20x
or,782000=80x
or, 782000/80=X
or, X= 9775.
hence MP is Rs 9775
what is the ratio for the surface areas of the rectangular prisms shown below, given that they are similar and that the ratio of
their edge lengths is 8:5
Answer:
B. 64:25
Step-by-step explanation:
the ratio of the surface areas =
(8)² : (5)² = 64 : 25
help please dilations geometry
Answer:
A' (8,16)
B' (8,-4)
C' (-16,4)
Answered by GAUTHMATH
-6>t-(-13)
slove for the inequality
Answer:
-19>t
Step-by-step explanation:
-6>t-(-13)
-6>t +(13)
Subtract 13 from each side
-6-13 > t+13-13
-19>t
SHORT ANSWER
Question 3
This expression has three restrictions. What are they?
(3x^2-3x/x-2)/(2x-10/x-4)
Answer in a complete sentence.
Answer:
The restrictions are x≠2,4,5
Step-by-step explanation:
First the denominators cannot be zero
x-2 ≠0 so x≠2
Then x-4 ≠0 so x≠4
Also, since we are dividing, when we flip the second expression, the numerator becomes the denominator, so it cannot be zero
2x-10≠0
2x≠10
x≠5
The restrictions are x≠2,4,5
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = x2 + 1 and g(x) = 3x.
Find f · g.
A.
x2 + 3x + 1
B.
3x3 + 3x
C.
3x3 + 3x + 1
D.
x2 + 3x
Answer:
I say it's a
Step-by-step explanation:
I hope this help
Please help me i don’t understand this question at all.
9514 1404 393
Answer:
D.
Step-by-step explanation:
The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)
When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.
The only reasonable choice is D.
__
Your calculator can check this for you.
√12/(√3 +3) ≈ 3.4641/(1.7321 +3)
= 3.4641/4.7321 ≈ 0.7321 = -1 +√3
__
If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.
[tex]\displaystyle\frac{\sqrt{12}}{\sqrt{3}+3}=\frac{\sqrt{12}}{(\sqrt{3}+3)}\cdot\frac{(\sqrt{3}-3)}{(\sqrt{3}-3)}=\frac{\sqrt{36}-3\sqrt{12}}{3-9}\\\\=\frac{6-3\cdot2\sqrt{3}}{-6}=\boxed{-1+\sqrt{3}}[/tex]
_____
Additional comment
We "rationalize the denominator" in this way to take advantage of the relation ...
(a -b)(a +b) = a² -b²
Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.
We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).
Find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf tan\theta=\dfrac{p}{b}}[/tex]
[tex]\\ \sf\longmapsto tan\theta=\dfrac{13}{20}[/tex]
[tex]\\ \sf\longmapsto tan\theta=0.6[/tex]
[tex]\\ \sf\longmapsto tan\theta\approx\dfrac{1}{\sqrt{3}}[/tex]
[tex]\\ \sf\longmapsto tan\theta\approx tan60[/tex]
[tex]\\ \sf\longmapsto \theta\approx 60°[/tex]
PLZ HELP!! ASAP PLZ!! NO FILES.
Answer:
Slope is (1/4)
Step-by-step explanation:
The slope is calculated by (6-5)/(5-1)=1/4
A sample of 500 nursing applications included 60 from menThe 95% confidence interval of the true proportion of men who applied to the nursing program is
Answer:
The correct solution is "(0.092, 0.148)".
Step-by-step explanation:
Given:
Sample size,
n = 500
True proportion,
[tex]\hat {p} = \frac{60}{500}[/tex]
[tex]=0.12[/tex]
The standard error will be:
[tex]SE=\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]=\sqrt{\frac{0.12(1-0.12)}{500} }[/tex]
[tex]=\frac{0.12(0.88)}{500}[/tex]
The confidence interval is "1.96".
hence,
The required confidence interval will be:
= [tex](\hat p - 1.96 SE, \hat p + 1.96 SE)[/tex]
By substituting the values, we get
= [tex](0.12-1.96\sqrt{\frac{0.12(0.88)}{500} }, 0.12+1.96\sqrt{\frac{0.12(0.88)}{500} } )[/tex]
= [tex](0.092, 0.148)[/tex]
A bus uses 50 liters of petrolfor 1-000 km of journey' t3l Find the amount of petrol needed for 400 km journey'
Answer:
hijjijkkkmmkmjjjjjjjjjijjji
The surface area of a cylinder is given by the formula
S = 30πr + 2πr2
How many times greater is this compared to a circle with A = πr2
Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2) , Given volume and lateral area: r = 2 * V / A_l , Given base area: r = √(A_b / (2 * π)) , Given lateral area and total area: r = √((A - A_l) / (2 * π)) .
I need help with this asap pls!!
Answer:
Answer is b
Step-by-step explanation:
cuh cuh cuh cuh cuh cuh , , , , , ,,
find the missing side of the triangle.
Answer:
Step-by-step explanation:
A=2 ,B=4 ,C=?
[tex]C^{2}[/tex]=[tex]A^{2}[/tex]+[tex]B^{2}[/tex]
[tex]C^{2}[/tex]=[tex]2^{2}[/tex]+[tex]4^{2}[/tex]
[tex]C^{2}[/tex]=4+16
[tex]C^{2}[/tex]=20
C=[tex]\sqrt{20}[/tex]
7. The total cost to rent a truck is $100 and $0.20 per km.
a. Determine an algebraic model for the relationship between total cost and distance driven. Use C to
represent total cost (S) to rent the truck and d to represent distance driven (km).
Answer:
C = 100 + 0.20d
Step-by-step explanation:
Let
C = Total cost
d = distance driven(km)
$100 = fixed cost
$0.20 = additional cost
The algebraic model of the relationship:
Total cost = fixed cost + (additional cost * distance driven(km))
C = 100 + (0.20 * d)
C = 100 + 0.20d
Alex can cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces?
Answer:
Step-by-step explanation:
I think you mean 35 seconds because if it was 36 then the answer would be too long so assuming it is 35 seconds the answer is 1 minute or 60 seconds
pls help !! :// <333
Answer:
Its that squiglly one on top
Step-by-step explanation:
cuh cuh cuh cuh cuhc
The sum of the cubic powers of three rational numbers is -1009. The ratio between the first number and the second number is 2/3, and the ratio between the first number and the third number is 4/9. Find those numbers
Given:
The sum of the cubic powers of three rational numbers is -1009.
The ratio between the first number and the second number is [tex]\dfrac{2}{3}[/tex].
The ratio between the first number and the third number is [tex]\dfrac{4}{9}[/tex].
To find:
The three numbers.
Solution:
Let [tex]x,y,z[/tex] be the three numbers, then
[tex]x^3+y^3+z^3=-1009[/tex] ...(i)
[tex]\dfrac{x}{y}=\dfrac{2}{3}[/tex]
[tex]3x=2y[/tex]
[tex]\dfrac{3}{2}x=y[/tex] ...(ii)
[tex]\dfrac{x}{z}=\dfrac{4}{9}[/tex]
[tex]9x=4z[/tex]
[tex]\dfrac{9}{4}x=z[/tex] ...(iii)
Using (i), (ii) and (iii), we get
[tex]x^3+\left(\dfrac{3}{2}x\right)^3+\left(\dfrac{9}{4}x\right)^3=-1009[/tex]
[tex]x^3+\dfrac{27}{8}x^3+\dfrac{729}{64}x^3=-1009[/tex]
[tex]\dfrac{64+216+729}{64}x^3=-1009[/tex]
[tex]\dfrac{1009}{64}x^3=-1009[/tex]
[tex]x^3=\dfrac{-1009\times 64}{1009}[/tex]
On simplification, we get
[tex]x^3=-64[/tex]
[tex]x^3=-4^3[/tex]
[tex]x=-4[/tex]
Substituting [tex]x=-4[/tex] in (ii), we get
[tex]\dfrac{3}{2}(-4)=y[/tex]
[tex]-6=y[/tex]
Substituting [tex]x=-4[/tex] in (iii), we get
[tex]\dfrac{9}{4}(-4)=z[/tex]
[tex]-9=z[/tex]
Therefore, the three numbers are -4, -6 and -9 respectively.