Answer:
For the first equation we have:
A*x = b
solving for x, we get:
x = b/A
If it always has a solution, then we can not have A = 0, because that causes an undefined operation.
so for example, if we have A = 1 and b = 2
x = b/A = 2/1
For the other case,
A*y = 0
dividing both sides by A
y = 0/A = 0
y = 0
Here we have only one possible solution, the trivial one, y = 0.
And the dependence on A disappears (because the quotient between zero and a number different than zero is always zero)
?
Which graph contains the points of intersection
satisfying this linear-quadratic system of equations?
x2 + y2 = 20
x-y + 2 = 0
Answer:
Step-by-step explanation:
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?
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.)
Find the distance between A (2,0,-1) and B (3,1,4) and find the mid-point of line segment AB."
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 )
Which polynomial function has a root of 1 with
multiplicity 2 and a root of 6 with multiplicity 1?
Of(x) = (x - 1)(x – 6)
O f(x) = 2(x - 1)(x – 6)
O f(x) = (x - 1)(x - 1)(x – 6)
O f(x) = (x - 1)(x - 6)(x-6)
Answer:
The 3rd:
f(x) = (x - 1)(x - 1)(x – 6)
Step-by-step explanation:
Its roots are the x-values for which f(x)=0, that are:
x1=1
x2=1
x3=6
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)
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
What would this be helpppp
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.
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.
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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(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.
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
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.
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:
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find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20
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
3/4 - 5/8
can someone plz tell answer
Answer: 1/8
Step-by-step explanation:
Convert 3/4 so it has 8 as the denominator. 3/4 = 6/8. Now you can subtract. 6/8 - 5/8 = 1/8.
pa help po pls pls pls
Answer:
acute angle and number 3 is obtuse
Step-by-step explanation:
The function g(x) is a transformation of the cube root parent function,
Answer:
I believe that the answer is B as well
Step-by-step explanation:
This might be for Ap3x but not 100% sure
Z Is An Even Integar Greater Than 30 And Less Than Or Equal To 34.
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. :)
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.
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 !!!!
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]
The sum of the digits in a 2 digit number is 5. If the number is subtracted by 9 then the digits will be reversed. Find the number. If the tens digit is x then what is the equation?
Answer:
Let ten's place digit =x and unit place digit =y
Number=10x+y
x+y=5 ...(i)
10x+y−9=10y+x
9x−9y=9x−y=1 ...(ii)
from (i) and (ii) we get,
x=3,y=2
∴Number=10×3+2=32.
Step-by-step explanation:
Hope it helps!
Given PQR, R=90º....
Answer:
RQ = 9 units
Step-by-step explanation:
estimate the answer 210,000 divied by 0.12
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
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).
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).
Use the elimination method to solve the system of equations.
A. Infinitely many solutions
B. (10, 10)
C. (16, 18)
D. No solution
Answer:
they are the dame line...
A. Infinitely many solutions
Step-by-step explanation:
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
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
solve the following simultaneous linear equations by the substitution method.
3x + 4y = 1
2x + 3y = 1
[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]
Difference between DIRECT and INDIRECT ratio?
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:
, .
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
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.
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?
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.
Change 18° into sexagesimal seconds.
Answer:
She's, "HOT"!
Step-by-step explanation:
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?
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]
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
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!
The measures of the exterior angles of a pentagon are x', 38°, 45°,
5x", and 72. Solve for x.
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
