[tex]\large \bf\blue{\bigstar\boxed{\pink{\frak{Solution}}}} \blue{ \bf\longmapsto}[/tex]
Y=2x. . . . (1)Y=3x-10. . . . (2)put value of y in 1 eq in 2 eq
y= 3x - 102x = 3x - 10x = 10Put value of x in 1 eq
y = 2xy = 2 × 10y = 20Pair formed
(x , y) = (10,20)
The solution to the system of equations will be (x, y) = (10,20).
What is the equation?In a mathematical equation, two expressions—which may or may not include variables or integers—are declared to be equal. The main motivations for the development of mathematics have been attempts to methodically address the underlying issues with equations.
It is given that, the equations are y=2x and y=3x-10.
Y=2x. . . . (1)
Y=3x-10. . . . (2)
put the value of y in 1 eq in 2 eq in order to find the value of x.
y= 3x - 10
2x = 3x - 10
x = 10
Put the value of x in 1 eq in order to get the value of y,
y = 2x
y = 2 × 10
y = 20
Pair formed
(x , y) = (10,20)
Thus, the solution to the system of equations will be (x, y) = (10,20).
Learn more about the equation here,
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what is 1+1
prove me why
Answer:
1+1=2
Step-by-step explanation:
as we know that one is made up of 1/2+1/2=1
so 1/2+1/2+1/2+1/2=2
hope this helps you
have a great day :)
Hey guys can anyone help me find the missing side length pls and ty
[tex]\bold{\huge{\green{\underline{ Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
We have given a right angled triangle whose values are m, n and 2[tex]\bold{\underline{ To \: Find :- }}[/tex]
We have to find the value of m and n[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
In the given right angled triangle, we have
Perpendicular height = n units Base = 2 unitsHypotenuse = m unitsNow, By using trigonometric ratios
[tex]\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}[/tex]
[tex]\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}[/tex]
[tex]\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}[/tex]
According to the question :-
[tex]\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}[/tex]
[tex]\bold{ 1/√2= }{\bold{\frac{2}{m}}}[/tex]
[tex]\bold{\red{ m = 2√2 \: units }}[/tex]
We know that , Sum of Angles of triangle is 180° .Therefore,
Let the unknown angle be x
[tex]\sf{ 45° + x + 90° = 180° }[/tex]
[tex]\sf{ x = 180° - 135 ° }[/tex]
[tex]\sf{ x = 45° }[/tex]
Now,
[tex]\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold { n = 2√2/√2 }[/tex]
[tex]\bold{\red{ n = 2\: units }}[/tex]
Thus, The value of m = 2√2 and n = 2
[tex]\sf{\blue{ Hence, \: option \: D \: is \: Correct }}[/tex]
The area of an equilateral triangle varies directly as the square of side s. What is the equation
Answer:
A = ks^2
I hope this helps :D
Which expression is equivalent to
Answer:
10³⁰
Step-by-step explanation:
firstly working out without the power of 3
[tex]( \frac{10 {}^{15} }{10 {}^{5} } )[/tex]
this is the same as 10¹⁵ ÷ 10⁵
here the bases are the same and it's division so we subtract the powers
15 - 5 = 10
10¹⁵ ÷ 10⁵ = 10¹⁰
we are left with (10¹⁰)³, multiply the powers
10 × 3 = 30
final answer = 10³⁰
Hey there!
(10^15/10^5)^3
10^15
= 1,000,000,000,000,000
10^5
= 10 * 10 * 10 * 10 * 10
= 100 * 100 * 10
= 10,000 * 10
= 100,000
(1,000,000,000,000,000/100,000)^3
= (10,000,000,000)^3
= 10,000,000,000 * 10,000,000 * 10,000,000
= 100,000,000,000,000,000 * 10,000,000
= 10^30
Therefore, your answer is: 10^30
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
make L and h the subject of formula
[tex]V = \frac{1}{2} LBH[/tex]
Answer:
[tex]V = \frac{1}{2} LBH \\ \\ \\ LH =V \div ( \frac{1}{2} B) \\ \\ LH =V \times \frac{2}{B} \\ \\ \\LH = \frac{2V}{B} [/tex]
What is the distance between (-4, 2) and (-4, -4)
Answer:
use Pythagoras theorem and a graph to be fluent in this
Step-by-step explanation:
answer is 2sqr(7)
Write an equation of the circle with center (6,7) and radius 9.
Please help thanks.
Answer:
6,16
Step-by-step explanation:
Find the slope of the line passing through the points (8, -2) and (1, -6).
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
The equation for slope is:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can plug in the given points into the equation:
[tex]Slope=\frac{-6-(-2)}{1-8}=\frac{-6+2}{-7}=\frac{-4}{-7}=\frac{4}{7}[/tex]
Polynomials help me please
Answer:
(x³+2x²-2x)-(-3x³+4x²-x)
(x³+2x²-2x)+(3x³-4x²+x)
(x³+3x³)+(2x²-4x²)+(-2x+x)
4x³-2x²-x ----you may write till here.
But, if not satisfied, factorize it
x(4x²-2x-1)
please mark brainliest
There are 15 female performers in a dance recital. The ratio of men to women is 2:5. How many men are in the dance recital?
Answer:
There are 6 men in the dance recital.
Step-by-step explanation:
We have a ratio of 2:5, men to women. If there are 15 female performers we can do a cross multiplication to find the males performers:
Then it will be
[tex]\tt \frac{15}{x} =\frac{5}{2}[/tex]
[tex]\tt 5x=15*2[/tex]
[tex]\tt 5x=30[/tex]
[tex]\tt x=\frac{30}{5}[/tex]
[tex]\tt x=6[/tex]
[tex]\tt Therefore,there~are~6~Men~at~the~dance[/tex]
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What’s the correct answer for this?
Answer:
-20/3
Step-by-step explanation:
m = ∆y/∆x
∆y = -8 - 12 = -20
∆x = 8 - 5 = 3
Hence m= ∆y/∆x = -20/3
Given the function f(x) = x + 1 and the linear function g(x), which function has a greater value when x = 2?
f(x) is greater.
g(x) is greater.
f(x) and g(x) are the same when x = 2.
g(x) is undefined when x = 2.
Answer:
F(x) is greater.
Step-by-step explanation:
f(2) = 2 + 1
(2,3)
Have a good day!
Answer:
F(x) is greater.
Step-by-step explanation:
Solve the following recurrence relation:
[tex]A_{n}=a_{n-1}+n; a_{1} = 0[/tex]
By iteratively substituting, we have
[tex]a_n = a_{n-1} + n[/tex]
[tex]a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)[/tex]
[tex]a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)[/tex]
and the pattern continues down to the first term [tex]a_1=0[/tex],
[tex]a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))[/tex]
[tex]\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)[/tex]
[tex]\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k[/tex]
Recall the formulas
[tex]\displaystyle \sum_{n=1}^N 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]
It follows that
[tex]a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2[/tex]
[tex]\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1[/tex]
[tex]\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}[/tex]
What is the solution to the equation below?
square root + 9 = 11
Answer:
A. x = 4
Step-by-step explanation:
[tex]\sqrt{4} +9=2+9=11[/tex]
Hope this helps
Answer:
A. [tex]x =4[/tex]
Step-by-step explanation:
[tex]\sqrt{x} + 9 = 11[/tex][tex]\sqrt{x} = 11-9[/tex][tex]\sqrt{x} = 2[/tex][tex]x = 2^2[/tex][tex]x =4[/tex]
A swimming pool is to be constructed in a 1,408-ft2 backyard. There is to be a fence that will surround a 12-by-24-foot pool. The pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. What is the width of the pool deck?
9 ft
10 ft
11 ft
12 ft
Answer:
B. 10 ftStep-by-step explanation:
Let the width of the pool deck be x.
Dimensions of the pool are 12 + 2x and 24 + 2x.Total area is 1408 ft².We have equation:
(12 + 2x)(24 + 2x) = 140812*24 + 12*2x + 24*2x + (2x)² = 1408288 + 72x + 4x² = 14084x² + 72x + 288 - 1408 = 04x² + 72x - 1120 = 0x² + 18x - 280 = 0x² - 10x + 28x - 280 = 0x(x - 10) + 28(x - 10) = 0(x - 10)(x + 28) = 01)
x - 10 = 0x = 102)
x + 28 = 0x = - 28 (discarded as negative)Correct choice is B
The width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
Here, we have to find the width of the pool deck, we need to calculate the total area occupied by the pool and the deck and then find the value of x that makes the total area equal to 1,408 square feet.
First, let's calculate the area of the pool.
The pool is 12 feet by 24 feet:
Area of the pool = Length × Width
Area of the pool = 12 ft × 24 ft
Area of the pool = 288 ft²
Now, we want to add the deck around the pool.
The length and width of the entire area (pool + deck) will be (12 + 2x) feet and (24 + 2x) feet, respectively, because we add x feet to both sides of the pool.
Area of the entire area (pool + deck) = (12 + 2x) ft × (24 + 2x) ft
We want this area to equal 1,408 square feet:
(12 + 2x) ft × (24 + 2x) ft = 1,408 ft²
Now, we can solve for x:
(12 + 2x) × (24 + 2x) = 1,408
Expand the equation:
288 + 48x + 24x + 4x² = 1,408
Combine like terms:
4x² + 72x - 1,120 = 0
Now, let's solve this quadratic equation for x.
We can either factor it or use the quadratic formula:
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
where a = 4, b = 72, and c = -1,120.
x = (-(72) ± √(72² - 4 * 4 * -1,120)) / 2 * 4
x = (-72 ± √(5,184 + 17,920)) / 8
x = (-72 ± √23,104) / 8
x = (-72 ± 152) / 8
Now, we have two possible solutions:
x = (-72 + 152) / 8
x = 80 / 8
x = 10
x = (-72 - 152) / 8
x = -224 / 8
x = -28
Since we are interested in a positive width for the deck, the width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
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A number of runners enter a race. The times that each runner finished is based on every hour. Five runners finished the race in 5 hours, 11 finished in 4 hours, 7 finished in 3 hours, 14 finished in 2 hours, and 21 finished the race in an hour.
1) Construct a histogram from the data below:
The histogram for the data is given at the end of this answer.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
In this problem:
The elements of x are given by the time in hours.The histogram shows the number of runners that finished the race in x hours.Hence, the graph given at the end of this answer is the histogram.
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Brainliest if correct
10
Answer:
[tex] - 1(2)( - 5) \\ - 2 \times ( - 5) \\ = 2 \times 5 \\ 10[/tex]
Answer:
10
Step-by-step explanation:
-1(2)(-5)
-1(-10) = 10
[RevyBreeze]
Help please due today.
Answer:
I think its 2nd one
HOPE IT HELPS, BE SAFE! Brainiest if possible pls! :)
A square has a perimeter of 36 cm.
What is the length of each side?
Answer:
9cm
Step-by-step explanation:
a square has 4 equal sides therefore if you divide 36 by 4 you will get the length of 1 side
What is the width and height of this triangle?
Answer:
The base is 6.69 and the height is 6.02 (these are rounded to the nearest hundredth)
Step-by-step explanation:
soh-cah-toa
cos 42 = adjacent/9
adjacent = cos 42 x 9
adjacent = 6.69
sin 42 = opposite/9
opposite = sin 42 x 9
opposite = 6.02
What is the value of x ? (Make sure you give the value of x !!!!)
A 20 degrees
B 50 degrees
C 30 degrees
D. 40 degrees
Answer:
The value of x is 20 degrees.
Step-by-step explanation:
The three angles of a triangle must equal 180 degrees.
100 + 40 + 2x = 140 + 2x
180 - 140 = 40 (goal)
2(x) = 40
2(20) = 40
A) 20 degrees
How do we find the equivalent ratio of 8/20 PLS HELP ITS RLLY IMPORTANT!!!!
Answer:
2/5, 4/10, 6/15, 8/20, 10/25, 12/30, 14/35, 16/40, 18/45, 20/50, 22/55, 24/60, 26/65, 28/70, 30/75, 32/80, 34/85, 36/90, 38/95, 40/100 ...
Your cell phone costs $50 a month plus $0.25 for each text message, (t). How much would your monthly bill be if you sent 40 text messages?
Your total monthly bill would be $____
if you sent 40 text messages.
Answer:
$60
Step-by-step explanation:
40 text messages × .25 each = $10. Plus the $50 per month is $60.
Answer:
it should be $60 a month
The area of a parallelogram is 48 ft. If the base of the parallelogram is 8 feet, what is its height?
8 feet
6 feet.
5 feet
7 feet
[tex]\textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ A=48\\ b=8 \end{cases}\implies 48=8h\implies \cfrac{48}{8}=h\implies 6=h[/tex]
Help need because i´m stuck
Answer:
594 in²
Step-by-step explanation:
There are several ways to do this.
divide the shaded region into rectangles, and add their areasdivide the shaded region into trapezoids and add their areassubtract the white space from a bounding rectangle.Given the way the figure is dimensioned, the last strategy is the easiest.
A rectangle that surrounds the entire figure will be 36 inches wide and 22 inches high. The white space rectangle in the lower right corner is shown to be 18 inches wide and 11 inches high.
The area of a rectangle is the product of its length and width:
A = LW
So the difference in area between the "bounding" rectangle and the whitespace rectangle is ...
shaded area = (36 in)(22 in) -(18 in)(11 in) = 792 in² -198 in²
shaded area = 594 in²
_____
Additional comment
You can also recognize that the dimensions of the cut out corner are each half the overall dimensions. That means the shaded area is 3/4 of the overall "bounding" rectangle. There are several ways you can make use of that fact.
In a chess club, 75% of the members are boys. Of these boys, 8% have hazel eyes. If 6 boys have hazel eyes, how many people are in the chess club.
Define a variable for the unknown quantity.
Percentage
8% x 75%.x = 6
0.06x = 6
x = 100
If f(x) = 2x + 1 and g(x) = x^2, the function (gοf)(x) is:
Answer:
4x² + 4x + 1
Step-by-step explanation:
to evaluate (g ○ f)(x) , substitute x = f(x) into g(x)
g(f(x))
= g(2x + 1)
= (2x + 1)² ← expand using FOIL
= 4x² + 4x + 1
I need the answer and quick, please!
0.65 T = _ lb
Answer:
Step-by-step explanation:
1 ton = 2000 pounds
thus:
0.65T * (2000lb / 1 T) = 1300 lbs
Hope that helps!
Find the perimeter of the figure to the right
Answer:
241/20 or 24.05 0r 481/20
Step-by-step explanation:
First simply your fractions
then add 6+4 to your fractions !!
Answer:
24 1/20 meters
Step-by-step explanation:
To find perimeter, you add all the side lengths.
6 4/5 + 4 + 6 + 7 1/4 = 24 1/20
Find the value of b.
A 57
B 50
C 123
D 61.5
Answer: The answer is 50
Step-by-step explanation:
I did the test