How many solutions does the system of equations have? Pls help :(
Given the system of equations below:
[tex] \large{ \begin{cases} y = 2x + 1 \\ - 4x + 2y = 2 \end{cases}}[/tex]
The first equation is y-isolated so we can substitute in the second equation.
[tex] \large{ - 4x + 2(2x + 1) = 2}[/tex]
Use the distribution property to expand in and simplify.
[tex] \large{ - 4x + 4x + 2 = 2} \\ \large{0 + 2 = 2 \longrightarrow 2 = 2}[/tex]
The another method is to divide the second equation by 2.
[tex] \large{ \frac{ - 4x}{2} + \frac{2y}{2} = \frac{2}{2} } \\ \large{ - 2x + y = 1}[/tex]
Arrange in the form of y = mx+b.
[tex] \large{y = 1 + 2x \longrightarrow y = 2x + 1}[/tex]
When we finally arrange, compare the equation to the first equation. Both equations are the same which mean that both graphs are also same and intersect each others infinitely.
For more information, when the both sides are equal for equation - the answer would be infinitely many. If both sides aren't equal (0 = 4 for example) - the answer would be none. If the equation can be solved for a variable then it'd be one solution.
Answer
Infinitely ManyHope this helps. Let me know if you have any doubts!
Find the area of a circle with radius, r = 6.5m . Give your answer rounded to 2 DP
Answer:
A ≈ 132.73 m²
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
r = 6.5 m
Step 2: Find Area
Substitute in variables [Area of a Circle Formula]: A = (3.14)(6.5 m)²Evaluate exponents: A = (3.14)(42.25 m²)Multiply: A = 132.732 m²Round: A ≈ 132.73 m²35 points. Brainliest gets double the points.
one fourth of a number is equal to 15/16. write the expression to represnt the above sentence.
note: use x to represent a number.
Answer:
1/4x = 15/16
Step-by-step explanation:
1/4x = 15/16
a sum of money was equally distributed among some boys
had there been 10 boys more
Answer:
I think I know what question you are trying to write because it sounds like the question I did years ago.
It is Rs 200
Step-by-step explanation:
Your welcome! :)
One number is 8 times as large as another. Their difference is 21. What is the larger number?
Explanation:
x = smaller number
8x = larger number, since it's 8 times larger than the smaller
8x-x = 7x = difference of the numbers
That difference is 21, so we can say 7x = 21 which solves to x = 3
The smaller number is 3 and the larger is 8x = 8*3 = 24
As a check: 24-3 = 21, which confirms the answer.
-31,-22,-33 find the 35th term
Answer:
easy bro go and use m-a-t-h w-a-y
Step-by-step explanation:
it's going to help
2(x-7)<-12
Help!! I need this for my math
Answer:
x < 1
Step-by-step explanation:
2(x-7)<-12
Divide by 2
2(x-7)/2<-12/2
x-7 < -6
Add 7 to each side
x-7+7 < -6+7
x < 1
A rope is 9 1/2 meters long. How many pieces can be cut from the rope if
each piece is to be 1/4 meter?
what is the slope of a line perpendicular to the line whose equation is x-3y=-27
Find the area of the regular pentagon.
Answer: 172.05
Hope this helps
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
PLZ HELPP MARK BRAINLIEST 20 POINTS
Answer:
This is incorrect as 1/8 plus 3/5 is 29/40
Step-by-step explanation:
:)
Answer:
Susan is incorrect.
Step-by-step explanation:
First, what we do is add 1/8 + 3/5
Our result will be 4/13 because 1+3 = 4 would be as the numerator, and 8+5 = 13 would be as the denominator.
We can't simplify 4/13.
If we did increase the number, however, it would be 8/26, which is not close to the answer.
Therefore, Susan is incorrect.
-kiniwih426
56:05
What is the equation of the line that is parallel to the
given line and passes through the point (-4,-6 )?
O x= -6
=)
O x=-4
O y = -6
O y = -4
10 x
(-4×-6) =-24÷6=4
24÷4=6. x=4. x=6
Use an algebraic approach to solve the problem.
Aura took three biology exams and has an average score of 87. Her second exam score was 11 points better than her first, and her third exam score was 5 points better than her second exam. What were her three exam scores?
Answer:
Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.
Step-by-step explanation:
Use the formula for the mean: sum of elements / number of elements
Let x represent her first exam score.
Her second exam score can be represented by x + 11, since it was 11 points better than her first.
Her third exam score can be represented by (x + 11) + 5, since it was 5 points better than her second.
Plug in all of these expressions into the mean formula. Plug in 87 as the mean, and plug in 3 as the number of elements (since there are 3 scores):
mean = sum of elements / number of elements
87 = ( (x) + (x + 11) + (x + 11) + 5 ) / 3
Add like terms and solve for x:
87 = (3x + 27) / 3
261 = 3x + 27
234 = 3x
78 = x
So, her first score was a 78.
Find her second score by adding 11 to this:
78 + 11 = 89
Find her third score by adding 5 to the second score:
89 + 5 = 94
Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.
IF A QUADRATIC FUNCTION OPENS UPWARD, DOES IT HAVE A MAXIMUM OR MINIMUM?
Answer: It will have a minimum.
How do I do this? I’m not sure can anyone help?
value of x= 7√3
Hope it helps you...
What is the equation of the line that
contains the points (0, 5) and (3, 7)?
Answer:
y -y1=y2-y1/x2-x1(x-x1)
Jeremy is conducting a survey about his coworkers’ in-office water consumption to encourage management to install more water dispensers at their location. He found that the population mean is 112.5 ounces with a standard deviation of 37.5. Jeremy has a sample size of 96. Complete the equation that Jeremy can use to find the interval in which he can be 99.7% sure that the sample mean will lie. 37.5 112.5 75 96 150 9.8
Using the z-distribution, as we have the standard deviation for the population, it is found that the 99.7% confidence interval is given by:
[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.99.7% confidence level, hence[tex]\alpha = 0.997[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.997}{2} = 0.9985[/tex], so [tex]z = 3[/tex].
The other parameters are:
[tex]\mu = 112.5, \sigma = 37.5, n = 96[/tex]
Hence, the interval is:
[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]
To learn more about the z-distribution, you can check https://brainly.com/question/25890103
Hey im confused on how to solve this. Can Anyone help me?
Answer:
The minimum unit cost is $9374.
Step-by-step explanation:
The unit cost C for making x engines is given by the quadratic function:
[tex]C(x)=0.3x^2-162x+31244[/tex]
We want to determine the minimum unit cost.
Since this is a quadratic function with a positive leading coefficient, the minimum value will be its vertex. The vertex of a quadratic can be found using the following formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 0.3, b = -162, and c = 31244.
Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-162)}{2(0.3)}=\frac{162}{0.6}=270[/tex]
In other words, in order to achieve the minimum cost, only 270 engines must be made.
Then to find the minimum cost, substitute the value back into the function. So:
[tex]C(270)=0.3(270)^2-162(270)+31244=\$ 9374[/tex]
The minimum unit cost is $9374.
What is 5/2x + 2y = 5
Answer:
y= -x+1/2
Step-by-step explanation:
A landscaper is selecting two trees to plant. He has five to choose from. Three of the five are deciduous and two are evergreen.
What is the probability that he chooses trees of two different types? Express your answer as a percent.
30%
40%
50%
60%
Answer:
The probability that he chooses trees of two different types is 30%.
Step-by-step explanation:
Given that a landscaper is selecting two trees to plant, and he has five to choose from, of which three of the five are deciduous and two are evergreen, to determine what is the probability that he chooses trees of two different types must be performed the following calculation:
3/5 x 2/4 = 0.3
2/5 x 3/4 = 0.3
Therefore, the probability that he chooses trees of two different types is 30%.
Answer:
Actually the right answer is 60%! Not 30 %! (つД`)・゚・
Step-by-step explanation:
Becky says that when she simplifies the following expression, the value is 6 less than her age. What is Becky's age? (7+11) - 8÷2 *
20
14
26
11
Answer:
Becky's age is equal to 20.
Step-by-step explanation:
The given expression is :
(7+11)-(8÷2)
Using Bodmas rule to solve it furthur,
(18)-4 = 14
According to the given condition, let the age is A.
The value is 6 less than her age,
14 = A-6
or
14+6 = A
A = 20
Hence, Becky's age is equal to 20.
Which equation could be represented by the number line?
A. 3+ (-4) = -1
B. -3 + 4 = 1
C. 1 + (-5) = -4
D. -4 + 5 = 1
9514 1404 393
Answer:
A. 3+ (-4) = -1
Step-by-step explanation:
The arrow indicates a subtraction of 4, or an addition of -4. The only equation containing such a subtraction or addition is choice A.
Which expression is equivalent to 6^-3
Answer:
[tex] {6}^{ - 3} \\ = \frac{1}{ {6}^{3} } \\ = \frac{1}{216} [/tex]
Answer:
1/6^3
Step-by-step explanation:
6^-3
1/6^3
Note if any base has it's power negative then just do its reciprocal the exponent will be positive.
For example:
5^-y
1/5^y
Please Help!!!!!!!!!
Answer:
The answer is D. 3
Use substitution to solve the
following system of equations.
-2x + 4y = -18 AND x = y + 3
Answer:
x = -3 ; y = -6
Step-by-step explanation:
x = y + 3
-2x + 4y = -18
-2(y+3) + 4y = -18
-2y -6 + 4y = -18
2y = -12
y = -6
x = -6+3
x = -3
Answer:
x = -3 y = -6
Step-by-step explanation:
x = y + 3
x - 3 = y
-2x + 4(x - 3) = -18
-2x + 4x - 12 = -18
2x = -6
x = -3
x = y + 3
-3 = y + 3
-6 = y
Which is the graph of y-3=-2/3(x+6)
Answer:
I dont know what graph it requires to because u didnt show any graphs :)).....is there anything else I could help u with?
Step-by-step explanation:
Is 3x – 1= 7 and
3x = 8 equivalent
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Take the 1st equation & solve it :-
[tex]3x - 1 = 7 \\ 3x = 7 + 1 \\ 3x = 8[/tex]
Now, take the second equation :-
[tex]3x = 8[/tex]
[You can't further solve this equation]
So, from the 2 solved equations we can see that,
[tex]\large\bold{3x = 8 \ is \ equivalent \ (=) \ 3x = 8 }[/tex]
✐ The answer will be ⇻ Yes, 3x – 1= 7 and 3x = 8 are equivalent to each other.
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
(Please help, Very desperate and I have a limited amount of time to get this done please hurry asap)
Will give brainliest to first who answers
Answer:
Pic1 answers:
P(blue) = 4/26,
P(yellow or green) = 14/26
P(purple) = 0.0%
P(red or green) = 18/26
P(not pink) = 26/26
P(not blue) = 22/26
Pic2 answers:
P(u) = 1/12
P(Vowel) = 6/12
P(a,b,c,d,e) = 4/12
P(Not A) = 10/12
P(vowel or consonant) = 12/12
P(not an m,s,t) = 9/12