Use the substitution method to solve the system of equations.
A. (5,-7)
B. (-1,-5)
C. (-1,5)
D. (2,-1)
Answer:
correct ans is d
Step-by-step explanation:
click the photo to see process
Find the missing Angles
1. a = 68
b = 112
c = 68
2. a = 127
3. a = 35
b = 40
c = 35
d = 70
4. a = 20
b = 70
c = 20
d = 70
e = 110
5. a = 90
b = 90
c = 42
d = 48
e = 132
6. a = 70
b = 55
c = 25
Maths assignment
( x+y,x-y)=(3,1)
Step-by-step explanation:
I hope this will help you
Find the length of the segment that joins the points (-5,4) and (7,-1)
Answer:
13
Step-by-step explanation:
Calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (7, - 1)
d = [tex]\sqrt{(7-(-5))^2+(-1-4)^2}[/tex]
= [tex]\sqrt{(7+5)^2+(-5)^2}[/tex]
= [tex]\sqrt{12^2+25}[/tex]
= [tex]\sqrt{144+25}[/tex]
= [tex]\sqrt{169}[/tex]
= 13
find m to cos²x-(m²-3)sinx+2m²-3=0 have root
Answer:
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].
Step-by-step explanation:
Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:
[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].
Multiply both sides by [tex](-1)[/tex] to obtain:
[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].
[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].
If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:
[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].
[tex]a = 1[/tex].[tex]b = m^{2} - 3[/tex].[tex]c = -2\, m^{2} + 2[/tex].However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].
Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].
Determinant of this quadratic equation about [tex]y[/tex]:
[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].
Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:
[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].
[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].
Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].
The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:
[tex]-2 \le -m^{2} \le 0[/tex].
[tex]0 \le m^{2} \le 2[/tex].
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
In other words, solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].
Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
Answer this question plz
Answer:
i) 9xy
ii) 75
Step-by-step explanation:
i) add those factor
ii) get that factor
hope it helps
please mark as barinliest
Thankyou.. :)
IM AM SO CONFUSED
Find the solution set.
8x2 - 2x – 1=0
Separate the two values with a comma.
Hello,
Answer (1/2,-1/4)
[tex]8x^2-2x-1=0\\\\8x^2-4x+2x-1=0\\\\4x(2x-1)+2x-1=0\\\\(2x-1)(4x+1)=0\\\\sol=\{\dfrac{1}{2} ,-\dfrac{1}{4} \}\\[/tex]
If you were asked to equate the sides of an equation, how would you do that
Answer:
you would divide an equation from the multiple and then you would simplify the equation for an answer
A gap 2 m deep has the shape of a truncated pyramid with rectangular bases. The length and width of the top base is 3x1.5 m and of the bottom base it is 1x0.5 m. To paint one square meter of a gap surface we need 0.25 liters, of a green paint color, How many liters of the paint color, we will need, if we want to paint just the side walls and the bottom base of the gap? Show working please.
Answer:
Volume of paint required is 3.125 litres.
Step-by-step explanation:
It would be noted that each side walls would have the shape of a trapezium. So that the areas of each wall can be determined as:
wall 1 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](0.5 + 1.5)2
= 2 [tex]m^{2}[/tex]
wall 2 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](1 + 3)2
= 4 [tex]m^{2}[/tex]
wall 3 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](0.5 + 1.5)2
= 2 [tex]m^{2}[/tex]
wall 4 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](1 + 3)2
= 4 [tex]m^{2}[/tex]
Total area of the walls = 2 + 2 + 4 + 4
= 12 [tex]m^{2}[/tex]
Area of the bottom base = l x b
= 1 x 0.5
= 0.5 [tex]m^{2}[/tex]
Total area to be painted = 12 + 0.5
= 12.5 [tex]m^{2}[/tex]
But to paint one square meter of a gap surface, we need 0.25 litres of a green paint color. Thus, to paint 12.5 [tex]m^{2}[/tex] of the gap surface:
12.5 x 0.25 = 3.125
The litres of paint required is 3.125.
One number is 9 times another. Their product is 27 times their sum. Find the numbers.
the answer is not 3 btw
Answer:
270 & 30
Step-by-step explanation:
let the number is n,
the equation :
n× 1/9 n= 27(n +1/9 n)
1/9 n² = 27n + 3n
1/9 n² = 30n
1/9n²- 30n = 0
n(1/9n -30)= 0
n = 0 or
1/9n = 30 => n = 30×9 = 270
270 is a number,
the other : 270/9 = 30
Help me please and thank you :)
Answer:
A
Step-by-step explanation:
We have the equation:
[tex]\displaystyle \frac{3}{8}y=2+x[/tex]
And we want to determine whether or not this represents a direct proportion.
First, let's solve for y. Multiply both sides by 8/3:
[tex]\displaystyle y=\frac{16}{3}+\frac{8}{3}x[/tex]
Remember that direct proportions must pass through the origin point on a graph. In other words, their y-intercept or constant value is zero.
Since the constant value here is not zero (it is 16/3), the equation is not direct proportion.
Our answer is A.
How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
Someone help me asap
Answer:
A
Step-by-step explanation:
There are 270 minutes in 4.5 hrs.
divide that by 45, you get 6.
50*3^6 is 36,450
GIVING BRAINLIEST ANSWER PLZ ';CCC
Answer:
slope= difference in y ÷difference in x
=y-y1÷x-x1
=-3-(-1)÷-3-1
=-3+1÷-3-1
=-2÷-4
=1/2
Step-by-step explanation:
hope this is helpful
Y2 -Y1 ÷ X2-X1
-1 - 1 ÷ -3 - -3= 0.5 or 1/2
The pair of equations y = 0 and y = -7 has how many solutions?
Answer:
2 solutions so it can be inferred that it might be a quadratic
Step-by-step explanation:
Answer:
no solutions
Step-by-step explanation:
y = 0 and y = - 7 are horizontal parallel lines.
Since they are parallel, they never intersect and so have no solutions.
which graph shows a set of ordered pairs that represent a function. help im on a time limit!
Answer:
first one
Step-by-step explanation:
10 pointssss!!!!!:))
write the formula of the function y whose graph is shown.
a).
[tex]y = \frac{2}{x} [/tex]
b).
[tex]y = \frac{1}{ x } + 2[/tex]
c).
[tex]y = \frac{1}{x - 2} [/tex]
plss, I need helpp!!!!
9514 1404 393
Answer:
(a) y = 2/x
Step-by-step explanation:
The vertical and horizontal asymptotes are the axes, so there is neither a vertical nor a horizontal offset to the parent function y = 1/x. There is a vertical stretch by a factor of 2, so the describing function is ...
y = 2/x
Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?
Given:
Reese read twice as many pages Saturday than she read Sunday.
She read a total of 78 pages over the weekend.
To find:
The number of pages she read on Sunday.
Solution:
Let x be the number of pages she read on Sunday.
Reese read twice as many pages Saturday than she read Sunday. So, the number of pager she read on Saturday is 2x.
Total number of page she read over the weekend is:
[tex]Total=x+2x[/tex]
[tex]Total=3x[/tex]
She read a total of 78 pages over the weekend.
[tex]3x=78[/tex]
[tex]x=\dfrac{78}{3}[/tex]
[tex]x=26[/tex]
Therefore, Reese read 26 pages on Sunday.
Solve the qn in attachment .
Answer:
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Step-by-step explanation:
The given expression to us is ,
[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]
Now take the LCM as ( x - 1 ) and Simplify , we have ,
[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]
Simplifying further , we get ,
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Hence the second option is correct.
Answer:
[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1)}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2} \\ \frac{ - 4x + 7}{2(x - 1)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]
Which expression has a value of 15 when n = 7?
1: 43 minus 5 n
2: 3 n minus 5
3: 6 n minus 28
4: 19 minus StartFraction 28 Over n EndFraction
Answer:
[tex]19-\frac{28}{n}[/tex] is the expression with the value of 15 when n = 7
Step-by-step explanation:
To find the expression whose value is 15, substitute the value of n = 7 in each given expression.
Expression 1:
[tex]43-5n[/tex]
Substitute the value of n & simplify,
[tex]43-5(7)[/tex]
[tex]43-35=8[/tex]
Since the value of the expression is 8 which is not equal 15.
Hence expression [tex]43-5n[/tex] does not have value of 15 when n = 7.
Expression 2:
[tex]3n-5[/tex]
Substituting the value of n & simplify,
[tex]3(7)-5[/tex]
[tex]21-5=16[/tex]
Since the value of the expression is 16 which is not equal 15.
Hence expression [tex]3n-5[/tex] does not have value of 15 when n = 7.
Expression 3:
[tex]6n-28[/tex]
Substituting the value of n & simplify,
[tex]6(7)-28[/tex]
[tex]42-28=14[/tex]
Since the value of the expression is 14 which is not equal 15.
Hence expression [tex]6n-28[/tex] does not have value of 15 when n = 7.
Expression 4:
[tex]19-\frac{28}{n}[/tex]
Substituting the value of n & simplify,
[tex]19-\frac{28}{7}[/tex]
[tex]19-4=15[/tex]
Since the value of the expression is 15 which is equal 15.
Hence expression [tex]19-\frac{28}{n}[/tex] has the value of 15 when n = 7.
Maths Aryabhatta
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Solve the following pair of linear equations using substitution method :-
2x+3y + 5 = 0 ; 5x-3y+9=0
Answer:
(- 2, - [tex]\frac{1}{3}[/tex] )
Step-by-step explanation:
Given the 2 equations
2x + 3y + 5 = 0 → (1)
5x - 3y + 9 = 0 → (2)
Rearrange (1) expressing 3y in terms of x by subtracting 2x + 5 from both sides
3y = - 2x - 5
Substitute 3y = - 2x - 5 into (2)
5x - (- 2x - 5) + 9 = 0 ← distribute parenthesis on left side and simplify
5x + 2x + 5 + 9 = 0
7x + 14 = 0 ( subtract 14 from both sides )
7x = - 14 ( divide both sides by 7 )
x = - 2
Substitute x = - 2 into either of the 2 equations and solve for y
Substituting into (1)
2(- 2) + 3y + 5 = 0
- 4 + 3y + 5 = 0
1 + 3y = 0 ( subtract 1 from both sides )
3y = - 1 ( divide both sides by 3 )
y = - [tex]\frac{1}{3}[/tex]
solution is (- 2, - [tex]\frac{1}{3}[/tex] )
A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that there is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are 0.7, 0.2, and 0.1, respectively. a. How certain is sh
Answer:
65 percent certain to get the job
Step-by-step explanation:
The given parameters are;
The chance that she gets the job if she receives a strong recommendation, P(J|S) = 80 percent = 0.8
The chance that she gets the job if she receives a moderately good recommendation, P(J|M) = 40 percent = 0.4
The chance that she gets the job if she receives a weak recommendation = 10 percent, P(J|W) = 0.1
The probability that the recommendation will be strong, P(S) = 0.7
The probability that the recommendation will be moderate, P(M) = 0.2
The probability that the recommendation will be weak, P(W) = 0.1
Therefore, the probability that she gets the job given any condition, is given as follows;
P(J) = P(J|S)×P(S) + P(J|M)×P(M) + P(J|W)×P(W)
∴ P(J) = 0.8 × 0.7 + 0.4×0.2 + 0.1×0.1 = 0.65
Therefore, she is 65 percent certain to get the job
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:
Area of this figure
When do you need to state a domain in your final answer?
Answer:
Not sure what you are asking.
Domain is all x values .
It can be stated in coordinates (x,y). X is the input. Y is output
It can be stated in Domain Notations such as {x | x ≥ 0}
WILL GRANT BRAILIEST PLZ REAL ANSWERS ONLY OR REPORTING!
Hello,
If the question is simplify then
we suppose x not equal to 5 and x not equal to -5
[tex]\dfrac{x^2-10x+25}{(x-5)(x+5)} \\\\=\dfrac{(x-5)^2}{(x-5)(x+5)} \\\\=\dfrac{x-5}{x+5} \\\\[/tex]
else
if the question is to find the euclidian 's quotient then
[tex]\dfrac{x^2-10x+25}{(x-5)(x+5)} \\\\= 1 + \dfrac{-10x+30}{x^2-25} \\\\=1-\frac{10}{x+5} \\[/tex]
euclian's quotient is 1
remainder is -10/(x+5)
Which of the following equations have no solutions?
Choose all answers that apply:
Α.
5x + 5 = -42 – 5
B
-4x + 5= -42 - 4
–4x + 5 = -4x – 5
D
4x + 5 = -4x + 5
Answer: b and c
a) 5x + 5 = -4x - 5
9x = - 10
x = -10/9
-
b) - 4x + 5 = -4x - 4
0x = -9 (no solution)
-
c) -4x + 5 = -4x - 5
0x = -10 (no solution)
-
d) 4x + 5 = -4x + 5
8x = 0
x = 0
-
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Question 19 (5 points)
Determine the measure of
82.49
43.1°
55.0° °
46.3°
Answer: 43.1 degrees (choice B)
==================================================
Work Shown:
Use the law of sines
sin(A)/a = sin(C)/c
sin(A)/20 = sin(82)/29
sin(A) = 20*sin(82)/29
sin(A) = 0.68294349
A = arcsin(0.68294349)
A = 43.074088
A = 43.1 degrees
Answer:
43.1°
Step-by-step explanation:
Hello, just finished the quiz and the correct answer is 43.1 degrees.
Question 22 (5 points)
If the legs of a right triangle are 20 units and 21 units, what's the length of the
hypotenuse?
29 units
4.4 units
6.4 units
22 units
through my working i got to 41² is the hypotenuse.
21²+20²=c²
factor out the square
(21+20)²=c²
41²=c²
and 41² is 1681
Answer:
29 units
Step-by-step explanation:
i just took the quiz
What is the value of the expression shown below?
(3/6) 2 + 7 x 4 -5
A 6 1/4
B 6 1/2
C 23 1/4
D 23 1/2
Answer:
24
Step-by-step explanation:
(3/6) 2 + 7 × 4 - 5
0.5 × 2 + 7 × 4 - 5
1 + 7 × 4 - 5
1 + 28 - 5
29 - 5
24
