x + y = 3, 4y = -4x - 4
System of Equations
Answers
Answer:
no solutions
Step-by-step explanation:
Hi there!
We're given this system of equations:
x+y=3
4y=-4x-4
and we need to solve it (find the point where the lines intersect, as these are linear equations)
let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable
we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4
y=-x-1
now we have y set as an expression containing x
substitute -x-1 as y in x+y=3 to solve for x
x+-x-1=3
combine like terms
-1=3
This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.
Therefore the answer is no solutions
Hope this helps! :)
The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution
Related Questions
Explain why |−3| + |9| represents the distance between the points (−3Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5)., −5) and (9, −5).
Answers
Answer:
Here we need to use:
[tex]\sqrt{x^2} = |x|[/tex]
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Then the distance between:
(-3, -5) and (9, -5) is just:
[tex]D = \sqrt{(-3 - 9)^2 - (-5 - (-5))^2} \\\\D = \sqrt{(-3 - 9)^2} = |-3 - 9|[/tex]
because both numbers inside the absolute value, we can rewrite it as:
|-3 - 9| = |-3| + |-9| = |-3| + |9| = 12
So, by finding the distance between (−3, −5) and (9, −5), we got the given expression, in this way we prove that the given expression represents the distance between these points.
Answer:
under
Step-by-step explanation:
The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).
Given PQR, R=90º....
Answers
Answer:
RQ = 9 units
Step-by-step explanation:
pa help po pls pls pls
Answers
Answer:
acute angle and number 3 is obtuse
Step-by-step explanation:
Choose the function that has:
Domain: x*-1
Range: y# 2
O
Ax)= x+2
x-1
O
2x+1
Ax)=
x+1
2x+ 1
(x) =
x-1
Answers
Given:
[tex]Domain\neq -1[/tex]
[tex]Range\neq 2[/tex]
To find:
The function for the given domain and range.
Solution:
A function is not defined for some values that makes the denominator equals to 0.
The denominator of functions in option A and C is [tex](x-1)[/tex].
[tex]x-1=0[/tex]
[tex]x=1[/tex]
So, the functions in option A and C are not defined for [tex]x=1[/tex] but defined for [tex]x=-1[/tex]. Therefore, the options A and C are incorrect.
In option B, the denominator is equal to [tex]x+1[/tex].
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
So, the function is not defined for [tex]x=-1[/tex]. Thus, [tex]Domain\neq -1[/tex].
If degree of numerator and denominator are equal then the horizontal asymptote is [tex]y=\dfrac{a}{b}[/tex], where a is the leading coefficient of numerator and b is the leading coefficient of denominator.
In option B, the leading coefficient of numerator is 2 and the leading coefficient of denominator is 1. So, the horizontal asymptote is:
[tex]y=\dfrac{2}{1}[/tex]
[tex]y=2[/tex]
It means, the value of the function cannot be 2 at any point. So, [tex]Range\neq 2[/tex].
Hence, option B is correct.
find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20
Answers
Answer:
The sum of the first 20 terms is -1440.
Step-by-step explanation:
We want to find the sum of the first 20 terms of the arithmetic sequence:
4, -4, -12, -20...
The sum of an arithmetic sequence is given by:
[tex]\displaystyle S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term.
Since we want to find the sum of the first 20 terms, k = 20.
Our initial term a is 4.
Our last term is also the 20th term as we want the sum of the first 20 terms.
To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:
[tex]x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n is the nth term.
Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:
[tex]x_n=4-8(n-1)[/tex]
Then the last or 20th term is:
[tex]x_{20}=4-8(20-1)=4-8(19)=-148[/tex]
Therefore, the sum of the first 20 terms are:
[tex]\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}[/tex]
Answer:
- 1440
Step-by-step explanation:
First-term is 4 and we subtract 8 to get the next term so the general term is
a(n) = 4 - 8(n -1)
The sum of the sequence is the average of the first and last terms multiplied by the number of terms: (a1 + an)/2 * n
We need the 20th term: a20 = 4 - 8(20–1) = 12 - 160 = - 148
The sum is (4 - 148)/2 * 20 = 10*(-144) = - 1440
Which product is positive?
O (2/5) (-8/9) (-1/3) (-2/7)
O (-2/5) (8/9) (-1/3) (-2/7)
O (2/5) (8/9) (1/3) (-2/7)
O (-2/5) (-8/9) (1/3) (2/7)
Answers
Answer:
D
Step-by-step explanation:
because there is an even number of negatives\
Hope this help have a good day
Answer:
4 th option
Step-by-step explanation:
The product of an even / odd amount of positive numbers is positive
The product of an even amount of negative numbers is positive.
The product of an odd amount of negative numbers is negative.
Option 1
The product of 1 positive and 3 negative numbers will be negative
Option 2
Similar to option 1
Option 3
The product of 3 positive and 1 negative will be negative
Option 4
The product of 2 negative and 2 positive numbers will be positive
A 90 % confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. the interval was ($133, 306, $150, 733). To make useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?
A) Increase the sample size and increase the confidence level.
B) Decrease the sample size and increase the confidence level.
C) Decrease the sample size and decrease the confidence level.
D) Increase the sample size and decrease the confidence level.
Answers
Answer: D) Increase the sample size and decrease the confidence level.
Step-by-step explanation:
A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.
A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.
Evaluate (3n+2) -10 when n=3 !!!!
Answers
Hello!
(3n + 2) - 10 =
= (3 × 3 + 2) - 10 =
= (9 + 2) - 10 =
= 11 - 10 =
= 1
Good luck! :)
[tex]\displaystyle\bf (3n+2) -10 \ if \ n=3\Longrightarrow 3\cdot3+2-10=11-10=\boxed{1}[/tex]
Find the distance between A (2,0,-1) and B (3,1,4) and find the mid-point of line segment AB."
Answers
Step-by-step explanation:
To Find :-
Distance between the two points .Solution :-
Using Distance Formula ,
> d = √{ ( 2-3)² + (0-1)² + (-1-4)² }
> d = √{ (-1)² + (-1)² + (-5)² }
> d = √{ 1 + 1 + 25 }
> d = √26 .
Using midpoint formula ,
> m = ( 2+3/2 , 0+1/2 , -1+4/3 )
> m = ( 5/2 , 1/2 , -3/3 )
> m = ( 2.5 , 0.5 , -1 )
Use the elimination method to solve the system of equations.
A. Infinitely many solutions
B. (10, 10)
C. (16, 18)
D. No solution
Answers
Answer:
they are the dame line...
A. Infinitely many solutions
Step-by-step explanation:
Z Is An Even Integar Greater Than 30 And Less Than Or Equal To 34.
Answers
Answer:
32, 34
Step-by-step explanation:
The answer must be grater than 30 so 30 is not an option the integers in the range are 31, 32, 33, and 34 the only even integers in this set are 32, and 34. Hope this helps. :)
Difference between DIRECT and INDIRECT ratio?
Answers
Step-by-step explanation:
In a direct proportion, the ratio between matching quantities stays the same if they are divided. (They form equivalent fractions). In an indirect (or inverse) proportion, as one quantity increases, the other decreases. In an inverse proportion, the product of the matching quantities stays the same.
Answer:
Both direct and indirect proportion are a comparison between two quantities (usually with different units).
In a direct proportion, as one quantity increases, the other also increases.
Examples would include:
If you buy more packets, it will cost more money.
If you have further to travel it will take more time.
If more people are to be fed, more food will be need.
If more people are to be transported, more cars/buses are needed.
More petrol is needed for longer distances.
Bigger area of floor will require more tiles/paint/wood.
A longer distance will need more paces to cover.
More dresses to be made will require more material.
In a direct proportion, the ratio between matching quantities stays the same if they are divided. (They form equivalent fractions).
k
=
x
y
In an indirect (or inverse) proportion, as one quantity increases, the other decreases.
If more people share a task, it will be done in less time.
Travelling at a faster speed means a trip will take less time.
If sugar is packed in smaller packets, more packets will be needed for the same mass.
For the same amount of money, a small parcel can be sent further than a bigger parcel.
If more people are being fed, food will be used up quicker.
For a fixed amount of money, as the price of presents increases, fewer can be bought.
Walking with longer strides means fewer paces are needed.
In an inverse proportion, the product of the matching quantities stays the same.
k
=
x
×
y
A hyperbola is the graph of inverse proportion.
Step-by-step explanation:
, .
Three years ago, Daniel bought a baseball card for $20. The baseball card gains a value of $10 each year for the next three years. A friend offers to buy the baseball card foe twice the value, how much would the friend pay?
Answers
Answer:
The friend would pay $100
Step-by-step explanation:
The price of the card was $20 when Daniel bought it, it gained a value of $10 every year,
since Daniel bought it 3 years ago we will add $30 to $20 as the value increased by $10/year
so the price becomes $50, but his friend says he'll pay twice the value so,
$50×2= $100
Dr black is standing 13 feet from a streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50° to the nearest foot the streetlamp is about
Answers
Dr black is standing 13 feet from a streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50° to the nearest foot the streetlamp is about 26 feet tall.
I hope this helps!
(Will put as Brainliest) Please help! :")
A speciality candy shop makes chocolate covered cherry and graham cookie bites. The cherry is spherical with a diameter of 3cm and the graham cookie is a rectangular prism with a base measuring 5cm by 5cm and a thickness of 0.5cm. What is the total surface area of the bite if each piece is drenched in chocolate from top to bottom before being put together, to the nearest tenth of a square centimetre.
Answers
Answer:
88.27 cm^2
Step-by-step explanation:
Cherry=4(3.14)(1.5)^2
=28.27
Cookie=2·(5·5+0.5·5+0.5·5)
=60
60+28.27=88.27
What would this be helpppp
Answers
Answer:
The last answer choice, or [-15 14 4a]
[-4 5b -23]
[ ? ? ? ]
Step-by-step explanation:
In order to subtract matrices, they have to have the same dimensions, which this problem provides(both 3x3) Then, just subtract the numbers on the right from the corresponding numbers on the left. Example: -3-12=-15, which is the top left answer. Repeat with all positions.
A field is 360 feet long and 160 feet wide. Sod can be purchased in squares in increments from 1 foot wide up to 7 feet wide. What is the largest size squares Steve can purchase with which he can cover the field completely without any gaps or overhangs?
Answers
Answer:
We need 1600 squares with a width of 6 feet to cover the entire field without any gaps nor overhangs.
Step-by-step explanation:
The number of squares required to cover the field is equal to the area of the field divided by the area of a square:
[tex]n = \frac{A}{l^{2}}[/tex] (1)
Where:
[tex]n[/tex] - Quantity of squares, in feet.
[tex]A[/tex] - Area of the field, in square feet.
[tex]l[/tex] - Length of each square, in feet.
If we know that [tex]A = 57600\,ft^{2}[/tex], then we have the following hyperbolic function:
[tex]n = \frac{57600}{l^{2}}[/tex]
Now we plot the function with the help of graphing tools, whose result is presented below. Please notice that quantity of squares must be an integer and we need 1600 squares with a width of 6 feet to cover the entire field without any gaps nor overhangs.
The measures of the exterior angles of a pentagon are x', 38°, 45°,
5x", and 72. Solve for x.
Answers
Answer:
Step-by-step explanation:
sum of exterior angles of a polygon=360°
x+38+45+5x+72=360
6x=360-155=205
x=205/6=34 1/6
second question
x+3x+4x+5x+7x=360
20x=360
x=360/20=18
x=18
A strawberry and banana juice blend is made with a ratio of strawberry to banana of 2:3. Fill in the table to show different proportional amounts. Amount of strawberry Amount of banana 1 b. Explain why these amounts are proportional.
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
Let
[tex]S \to[/tex] Strawberry
[tex]B \to[/tex] Banana
[tex]S : B = 2 : 3[/tex]
Solving (a):
Complete the table
The table, to be complete, is not given; so, I will generate one myself.
[tex]\begin{array}{cccccc}S & {2} & {3} & {4} & {5} & {6} \ \\ {B} & {3} & {4.5} & {6} & {7.5} & {9} \ \end{array}[/tex]
The table is generated as follows:
[tex]S : B = 2 : 3[/tex]
Multiply by 1.5
[tex]S : B = 2 * 1.5 : 3 * 1.5[/tex]
[tex]S : B = 3 : 4.5[/tex]
Multiply by 2
[tex]S : B = 2*2 : 3*2[/tex]
[tex]S : B = 4 : 6[/tex]
And so on....
In summary, whatever factor is multiplied to S must be multiplied to B; in order to keep the ratio constant
Solving (b): Why the amount are proportion
Because the ratio is constant and it remains unchanged all through.
The function g(x) is a transformation of the cube root parent function,
Answers
Answer:
I believe that the answer is B as well
Step-by-step explanation:
This might be for Ap3x but not 100% sure
estimate the answer 210,000 divied by 0.12
Answers
ANSWER:-
[tex] 210,000 \: divied \: by \: 0.12 \\ - - > \frac{210000}{0.12} \\ - - > \frac{210000 \times 100}{12} \\ - - > 1,750,000[/tex]
Answer:
1750000
Step-by-step explanation:
when dividing a non decimal number by a decimal number you have to first multiply both the numbers by the number of decimal places of the numbers that has has a decimal,In this case will multiply both numbers by 100 because there are decimal places on 0.12, giving us
21000000/12
=1750000
A farmer with 4000 meters of fencing wants to enclose a rectangular plotthat borders a straight river. If the farmer does not fence the side along theriver, what is the largest rectangular area that can be enclosed
Answers
Answer:
I know that the Perimeter is 4000. So, 4000=L+2w because we are not using on of the lengths.
What I did is inputed 4000-2x in for L, but I got 0. What do I do?
Step-by-step explanation:
it just is I think it should be
Change 18° into sexagesimal seconds.
Answers
Answer:
She's, "HOT"!
Step-by-step explanation:
?
Which graph contains the points of intersection
satisfying this linear-quadratic system of equations?
x2 + y2 = 20
x-y + 2 = 0
Answers
Answer:
Step-by-step explanation:
This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A
B
C
DF
Frequency 5
10
15
3
2.
Find the probability that a student earns a
grade of D or F.
p = [?]
Enter a decimal rounded to the nearest hundredth.
Answers
Answer:
Answer is 0.14.
Step-by-step explanation:
The probability that a student earns a grade of D or F is 0.14.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To find the probability that a student earns a grade of D or F, we need to add the frequencies of these two grades and divide by the total number of students:
P(D or F) = (3 + 2) / 35
P(D or F) = 5 / 35
P(D or F) = 0.14 (rounded to the nearest hundredth)
Therefore,
The probability that a student earns a grade of D or F is 0.14.
Learn more about probability here:
https://brainly.com/question/14099682
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solve the following simultaneous linear equations by the substitution method.
3x + 4y = 1
2x + 3y = 1
Answers
[tex]\displaystyle\bf \left \{ {{3x+4y=1} \atop {2x+3y=1}} \right. => \left \{ {{x=\frac{1-4y}{3} } \atop {2x+3y=1}} \right. => \\\\\\2\cdot\frac{1-4y}{3} +3y=1\: |\times3\\\\2-8y+9y=3\\\\y+2=3\\\\y=1 \;;\:x=(1-4y):3=-1\\\\\\Answer: (-1;1)[/tex]
Compare the rates for different numbers of texts. If Roger's father wants to get a 600-text message plan, what is the difference in price for the Dial It Up and Ring Ring plans?
Answers
Answer:
[tex]\$6[/tex]
Step-by-step explanation:
Given
See comment for complete question
Required
The difference in the cost of 600 text messages plan
Representing the given data as; Cost to Number of text messages, we have:
[tex]Dial\ Up = \$5 : 100[/tex]
and
[tex]Ring\ Ring= \$8 : 200[/tex]
Multiply the dial-up by 6 to get the cost of 600
[tex]Dial\ Up = \$5 *6 : 100 * 6[/tex]
[tex]Dial\ Up = \$30 : 600[/tex]
So, the cost of 600 text messages is $30 --- for dial-up
Multiply the Ring Ring by 3 to get the cost of 600
[tex]Ring\ Ring= \$8 *3: 200*3[/tex]
[tex]Ring\ Ring= \$24: 600[/tex]
So, the cost of 600 text messages is $24 --- for Ring Ring
The difference (d) is:
[tex]d = \$30 - \$24[/tex]
[tex]d = \$6[/tex]
Abc similar to def the area of abc is 45cm and the area of triangle def is 20cm one side of triangle abc is 3.6cm the the length of corresponding side of triangle def is
Answers
Answer:
2.4cm
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
that means two lengths of the triangle have to be multiplied.
and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.
multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).
so, if the area of triangle 1 is
"baseline 1" × "height 1" / 2 = 45 cm²
then the area of triangle 2 is
"baseline 2" × "height 2" / 2 =
= "baseline 1"×f × "height 1"×f /2 =
= "baseline 1" × "height 1" × f² / 2 =
= ("baseline 1" × "height 1" / 2) × f² =
= 45 × f² = 20 cm²
f² = 20/45 = 4/9
f = 2/3
so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is
3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm
For this graph, mark the statements that are true.
A. The domain is the set of all real
numbers.
B. The range is the set of all real
numbers greater than or equal to
zero.
C. The domain is the set of all real
numbers greater than or equal to
zero.
D. The range is the set of all real numbers.
Answers
Based on the graph, the following statements are true:
A. The domain is the set of all real numbers.
D. The range is the set of all real numbers greater than or equal to zero.
The graph demonstrates that the function will always produce a real number larger than or equal to zero regardless of the real number used as an input. The set of all real numbers constitutes the domain, whereas the set of all real numbers larger than or equal to zero constitutes the range. The other two claims are false. The range is neither the set of all real numbers, nor is the domain restricted to real numbers larger than or equal to zero.
As a result, the right responses are A and D.
To know more about graph:
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Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3.4%/year. At the end of the year, he earned simpler interest of $413. How much did he invest at 5%/year?
Answers
Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making y the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of y in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
(y = 10,000 - x
∴ y = 10,000 - 4,562.5 = 5,437.5
The amount Arvin invested in Canada savings bonds, y = $5,437.5.)
