Solving for b by simplifying both sides of the equation, then isolating the variable.
b = −y + 6x
----
Choosing three values for x and substitute in to find the corresponding y values.
(0,−3) , (1,0) , (2,3)
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Answer:
Step-by-step explanation:
y = 6x -b
and -3x +y =-3
on simplifying equation 2 ,we have y = 3x -3
System of equation has infinite number of solution if one equation can be obtained by multiplying by suitable non zero number
if we multiply equation by 2 we get y =6x -6
Since coefficient of x and y is same therefore comparing the value of x b with constant in another equation which is 6 .
therefore b =6
The strength of a bar magnet's magnetic field decreases with distance according to what is known as an inverse cube law; multiplying the distance from the magnet by a factor of k divides the magnetic field strength by a factor of k^3. Suppose the magnetic field strength of the magnet is 64 Gauss at a distance of 10 cm away. What is the magnetic field strength of the magnet, 20 cm away?
Answer:
8 Gauss
Step-by-step explanation:
Since your moving the magnet from 10 to 20cm you're essentially multpliying the distance by 2.
K = 2
Therefore k ^ 3 = 2^3
64/2^3
=8
Answer:
8 Guass
Step-by-step explanation:
We multiply the distance by a factor of $2$, and thus divide the magnetic field strength by a factor of $2^3 = 2 \cdot 2 \cdot 2 = 8$. We get a magnetic field strength of 64/8 = 8
What is the y-intercept of the linear equation x-1/2y=-6?
a) –6
b) –3
c) 0
d) 12
Answer:
[tex]\large\boxed{d)\ 12}[/tex]
Step-by-step explanation:
[tex]x-\dfrac{1}{2}y=-6\\\\\text{y-intercept is for x = 0. Substitute:}\\\\0-\dfrac{1}{2}y=-6\\\\-\dfrac{1}{2}y=-6\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=(-2)(-6)\\\\y=12[/tex]
What is the value of x?
ANSWER
58°
EXPLANATION
The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is
[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]
Multiply through by 2
This implies that
[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]
We simplify to get:
[tex]102 \degree =160 - x[/tex]
Solve for x.
[tex]102 \degree - 160 \degree =- x[/tex]
[tex] - 58 \degree =- x[/tex]
[tex]58 \degree =x[/tex]
Which of these people has balanced their checkbook correctly?
OA.
Gary: The balance in his check register is $500 and the balance in his bank statement is $500.
B.
Gail: The balance in her check register is $400 and the balance in her bank statement is $500.
C.
Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.
Answer:
A! Straight up!
For the equations below which statement is true ? -2x=14 6x=-42
Figure ABCD is a parallelogram. What are the measures of angles B and D?
Answer:
c
Step-by-step explanation:
The measures of angle B and angle D of the given parallelogram will be 55°, i.e. option A.
What is parallelogram?Parallelogram is a 2D shape, having opposite sides parallel and equal. Also the opposite angles of parallelogram are congruent means equal.
We have,
A Parallelogram with,
Angle B = (2n + 15)° and,
Angle D = (3n - 5)°
So,
As mentioned above in the definition that the opposite angles of parallelogram are congruent means equal.
i.e.
Angle B = Angle D
i.e.
2n + 15 = 3n - 5
On solving we get,
20 = n
⇒ n = 20,
So,
Angle B = (2n + 15)° = (2 * 20 + 15)° = 55°
And,
Angle D = (3n - 5)° = (3 * 20 - 5)° = 55°
Hence, we can say that the measures of angle B and angle D of the given parallelogram will be 55°, i.e. option A.
To know more about Parallelogram click here
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how many terms does the polynomial x^2+xy-y^2 have
Answer:
3 TERMS
Step-by-step explanation:
There are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
What is the total number of terms of given polynomial ?The given polynomial expression is [tex]x^{2} + xy - y^{2}[/tex] .
The number of terms of any expression is the total number of independent variables present in the given polynomial expression.
We can see that there are total 3 independent variables present in the polynomial expression and therefore the number of terms present is also three.
Thus, there are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
To learn more about terms in the polynomial, refer -
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Factor k2 - 81.
(k + 9)(K + 9)
(k - 9)(k - 9)
(k - 9)(k + 9)
Answer:
(
k
+
9
)
(
k
−
9
)
(k+9)(k-9)
Step-by-step explanation:
Answer:
It's C
Step-by-step explanation:
3x + 4y=17
- 4x – 3y = - 18
Answer:
3
Step-by-step explanation:
Answer:
The correct answer is (3,2)
At the beginning of a class period, half of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are eight students remaining in class, how many students were originally in the class?
Answer:
32 students
Step-by-step explanation:
We are given that at the beginning of a class period, half of the students in a class go to the library and half of the remaining to the computer lab.
Given that there are 8 students remaining, we are to find the total number of students in the class initially.
At beginning = [tex]x[/tex] students
After half of them leave = [tex]\frac{x}{2}[/tex] students
After half of the remaining leave = [tex]\frac{x}{4}[/tex] students
So, [tex]\frac{x}{4} = 8[/tex]
[tex]x=8\times 4[/tex]
x = 32
Therefore, there were 32 students in the class originally.
there were 32 students in the class originally.
because in the computer lab before there were 16. 16 times 2 equals 32.
A taxi cab charges $1.75 for the flat fee and $0.25 for each time. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
53 miles
Step-by-step explanation:
I'm going to assume "$0.25 for each time" is "$0.25 per mile."
$1.75 is the flat fee. It costs 25 cents for each mile. We can represent this as:
1.75 + 0.25m
The sum of this equation has to be less than or equal to $15. We can display this as:
1.75 + 0.25m ≤ 15.
To solve, we must first isolate 0.25m. To do this, we subtract 1.75 from each side.
0.25m ≤ 15 - 1.75
0.25m ≤ 13.25.
Now, we must isolate the variable 'm' to determine how many miles Eddie can travel. To do this, we divide 0.25 from each side.
m ≤ 13.25 / 0.25
m ≤ 53.
Therefore, Eddie can travel 53 miles if he has $15 to spend.
Evaluate the following expression In e^e.
A) e^2
B) 1
C) 0
D) e
Answer:
D) e
Step-by-step explanation:
ln e^e
We know that ln x^a is the same as a ln x
e ln (e)
we know that ln e =1
e (1)
e
Answer:
The correct answer is: [D]: " e " .
Step-by-step explanation:
__________________________________________________
ln e^e = e * (ln e) = e * (1) = e .
__________________________________________________
Solve the following equations 4x + 3y =17 3x + 2y = 13
Answer:
(5,-1)
Step-by-step explanation:
4x+3y=17
3x+2y=13
So elimination sounds fun but we will have to do manipulation:
Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.
8x+6y=34
9x+6y=39
--------------------now subtract the equations
-x+0=-5
So x=5
Now plug it into either question (no matter which-pick and choose)
I will go with the second original 3x+2y=13
So if x=5 we have 15+2y=13
Subtract 15 on both sides: 2y=-2
Now divide both sides by 2: y=-1
Answer (5,-1)
Final answer:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, the elimination method shows that the solution is x = 5 and y = -1.
Explanation:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, one could use either the substitution method, the elimination method, or matrix methods. However, as per the guidance, we will follow the elimination method which is efficient and easily understandable.'
Let's multiply the first equation by 2 and the second equation by 3, which will give us:
8x + 6y = 34 (equation 1 multiplied by 2)
9x + 6y = 39 (equation 2 multiplied by 3)
Now, subtract the first new equation from the second new equation to eliminate y:
9x - 8x + 6y - 6y = 39 - 34
x = 5
Substitute x = 5 into one of the original equations to find y. For example, put x = 5 in 4x + 3y = 17:
4(5) + 3y = 17
20 + 3y = 17
3y = -3
y = -1
Therefore, the solution to the system of equations is x = 5 and y = -1.
Nayara wants to know the percentage of each grade level of students at her school who drive to school. She has 4 grade levels in her school.Which of the following survey methods will allow Nayara to make a valid conclusion about what percentage of each grade level of students drive to school?
Choose 1 answer:
a. Randomly select 48 students who drive to school and ask them their grade level.
b. Randomly select 12 students from each grade level and ask whether they drive to school.
Answer:
The correct answer is B
Step-by-step explanation:
You want an even number per grade level to get comparable results.
Answer: um well it’s b... sorry for being 2 years late yk I was getting a drink of water
Step-by-step explanation:
A sequence is defined recursively using the formula f(n + 1) = –0.5 f(n) . If the first term of the sequence is 120, what is f(5)?
[tex]\bf \begin{array}{rrlll} term&\stackrel{f(n+1)=-0.5f(n)}{~\hfill value~ }\\ \cline{1-2} f(1)&120\\ f(2)&-0.5(120)\\ &-60\\ f(3)&-0.5(-60)\\ &30\\ f(4)&-0.5(30)\\ &-15\\ f(5)&-0.5(-15)\\ &7.5 \end{array}[/tex]
Answer:
f(5) = 7.5
Step-by-step explanation:
The recursive formula allows a term in the sequence to be found from the previous term, thus
f(2) = - 0.5 f(1) = - 0.5 × 120 = - 60
f(3) = - 0.5f(2) = - 0.5 × - 60 = 30
f(4) = - 0.5f(3) = - 0.5 × 30 = - 15
f(5) = - 0.5f(4) = - 0.5 × - 15 = 7.5
A car rental costs $50 for the first day. Additional days cost $35 per day, unless the car is rented for 7 days or more, in which case there is a 10% discount on the daily rate.
Identify the expression which represents the cost of renting a car if the car has been rented for more than a week.
A) 45 + 35x
B) 45 + 31.5x
Eliminate
C) 50 + 35x
D) 50 + 31.5x
Answer:
D) 50+31.5x
Step-by-step explanation:
10% of 35 is 3.5
35-3.5=31.5
find next number of 32,1312,11131112,31133112
Answer:
The next number is 1321232112
Step-by-step explanation:
32 is read off as "one 3, one 2" = 1312
1312 is read off as "one 1, one 3, one 1, one 2" = 11131112
11131112 is read off as "three 1s, one 3, three 1s, one 2" = 31133112
31133112 is read off as "one 3, two 1s, two 3s, two 1s, one 2" = 1321232112
Solve 3x + 11 = k for x.
3x +11 = K
To solve for X, we need to isolate x on one side.
Subtract 11 from both sides:
3x = K -11
Divide both sides by 3:
x = (k-11)/3
Answer:
3x +11 = K
x = (k-11)/3
Step-by-step explanation:
The sum of three-fifth of w and three-fourths of g ,minus 5
Answer:
[tex]=\frac{12w+15g-100}{20}[/tex]
Step-by-step explanation:
Three-fifth of w is 3/5 of w
[tex]=\frac{3}{5} *w=\frac{3}{5} w[/tex]
Three-fourths of g is three-quarters of g
[tex]=\frac{3}{4} *g=\frac{3}{4} g[/tex]
find the sum of the fractions then subtract 5
[tex]=\frac{3}{5}w-\frac{3}{4} g-5\\\\\\=\frac{3}{5}w-\frac{3}{4}g-\frac{5}{1}[/tex]
The LCM here is 20 i.e 5*4
=[tex]\frac{3}{5} w+\frac{3}{4}g-\frac{5}{1}=\frac{12w+15g-100}{20} \\[/tex]
Which expression is a factor of 12x2 + 29x – 8?
x – 8
2x – 1
3x + 8
4x + 1
Answer:
3x + 8
Step-by-step explanation:
Please use the symbol " ^ " to indicate exponentiation: 12x^2 + 29x – 8.
To answer this question, try dividing this 12x^2 + 29x – 8 by each of the given possible factors, one by one. If the end result is a zero remainder, that indicates that the particular factor is in fact a factor of 12x^2 + 29x – 8.
Alternatively, use synthetic division; if the end result is zero, then you have identified a root of 12x^2 + 29x – 8, as well as a factor.
Let's focus on x - 8: Is this a factor? Is 8 a root? Set up synthetic division as follows:
8 ) 12 29 -8
96 1000
-----------------
12 125 992
The non-zero remainder (992) indicates that 8 is not a root of 12x^2 + 29x – 8, and that x - 8 is not a factor.
Continuing onto the next given possible factor, 2x - 1, we set this = to 0 and solve for x, obtaining x = 1/2. Use synthetic division again:
1/2 ) 12 29 -8
6 35/2
------------------------
12 35 19/2 No, 1/2 is not a root and
2x - 1 is not a factor of 12x^2 + 29x – 8.
Try possible root x = -8/3:
-8/3 ) 12 29 -8
-32 8
----------------------------
12 -3 0
This zero remainder tells us that 3x + 8 is a factor of 12x^2 + 29x – 8.
Answer:
C. on edge
Step-by-step explanation:
GEOMETRY Please help, urgent
ANSWER
66 cubic units
EXPLANATION
The volume of a triangular prism is the area of the triangular base times the height of the prism.
We calculate the volume using the formula:
[tex]volume = \frac{1}{2} bh \times H[/tex]
where b=4 is the base of the triangle and h=3 is the height of the triangle.
H=11 is the height of the prism.
We substitute these values to get;
[tex]volume = \frac{1}{2} \times 4 \times 3 \times 11[/tex]
[tex]volume = 66 \: cubic \: \: units[/tex]
simplify (4x-6)-(3x+6)
Answer:
[tex]x-12[/tex]
Step-by-step explanation:
First open the brackets
[tex]=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6[/tex]
Then collect the like terms
[tex]4x-3x-6-6[/tex]
Solve the like terms
[tex]4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12[/tex]
The simplified form is
[tex]x-12[/tex]
An equilateral triangle has an altitude of 45. Find the length of a side of the triangle.
Answer:
See attachment.
If altitude = 45 then
side = 2 * height (or altitude) / square root of 3
side = 2 * 45 / 1.7320508076
side = 90 / 1.7320508076
side = 51.9615242271
Step-by-step explanation:
Follow below steps;
When dealing with an equilateral triangle, dividing it by an altitude creates two 30-60-90 right triangles. Since we know the length of the altitude (45), which corresponds to the shorter leg in the 30-60-90 triangle, we can find the length of the side of the equilateral triangle (which is the hypotenuse of the 30-60-90 triangle) using the properties of this special right triangle.
To begin, we recognize that the ratios of the sides of a 30-60-90 triangle are 1:\\(extbackslashsqrt{3}\\):2. Thus, if the shorter leg is 45, the hypotenuse will be twice that length, because the ratio of the shorter leg to the hypotenuse is 1:2. Therefore, the length of a side of the equilateral triangle is 45 * 2, which equals 90.
What is the slope of the linear equation 30x-60y=12
Answer:
60y = 30x - 12
y = 1/2x - 1/5
The slope is 1/2
Answer:
1/2
Step-by-step explanation:
30 over 60 is half
-6.3x+14 and 1.5x-6
answer in simplified form
Answer:
The simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8
Step-by-step explanation:
We have to simplify the following
-6.3x+14 and 1.5x-6
it can be written as:
=(-6.3x+14) + (1.5x-6)
Adding the like terms
=(-6.3x+1.5x)+(14-6)
= (-4.8x)+(8)
= -4.8x+8
So, the simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8
Which of the following shows the graph of y=2e^x
The answer is:
The first option shows the graph of the given function.
Why?Since the given function is an exponential function, we are looking for an exponential function graph, with a function that intercepts the y-axis at y equal to 2, or the point (0,2).
So, since we are given just one exponential graph, let's find the y-axis intercept in order to assure that the correct option is the first graph.
The function is:
[tex]y=2e^{x}[/tex]
Finding the y-axis intercept, we need to make "x" equal to 0, so:
[tex]y=2e^{0}[/tex]
We need to remember that any number elevated or powered to 0 is equal to 1, so:
[tex]y=2*1=2[/tex]
We have that the function intercepts the y-axis at y equal to 2, or the point (0,2).
Finding the x-axis intercept, we need to make "y" equal to 0, so:
[tex]y=2e^{x}[/tex]
[tex]0=2e^{x}[/tex]
[tex]Ln(0)=Ln(2e^{x})[/tex]
Now, since the natural logarithm of "0" does not exist in the real numbers, we can see that there is not x-axis intercept for this function.
Hence, the first option shows the graph of the given function.
Have a nice day!
Note: I have attached a picture for better understanding.
Answer:
Graph A
Step-by-step explanation:
Correct on edge!
Find the missing value 4 = -8 - ?
Answer: -12
Step-by-step explanation:
Answer:
Hi there!
The answer to this question is negative 12.
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
0 8, 12, 15
O 10, 24, 26
O 12, 20, 25
15, 18, 20
Mark this and retum
Save and Exit
Next
Answer:
The set {10 , 24 , 26} formed a right triangle
Step-by-step explanation:
* Lets explain how to check the sides lengths which formed a
right triangle
- In triangle ABC
# If AC is the longest side in length
# If (AC)² = (AB)² + (BC)²
∴ AB , BC , AC formed a right angle triangle
∴ m∠B = 90° (The angle opposite to the longest side)
∴ AC is the hypotenuse
* Now lets solve the problem
- In set 8 , 12 , 15
∵ The longest side is 15 cm
∴ (15)² = 225
∵ (8)² + (12)² = 64 + 144 = 208
∵ (15)² ≠ (8)² + (12)²
∴ The set not formed a right triangle
- In set 10 , 24 , 26
∵ The longest side is 26 cm
∴ (26)² = 676
∵ (10)² + (24)² = 100 + 576 = 676
∵ (26)² = (10)² + (24)²
∴ The set formed a right triangle
- In set 12 , 20 , 25
∵ The longest side is 25 cm
∴ (25)² = 625
∵ (12)² + (20)² = 144 + 400 = 544
∵ (25)² ≠ (12)² + (20)²
∴ The set not formed a right triangle
- In set 15 , 18 , 20
∵ The longest side is 20 cm
∴ (20)² = 400
∵ (15)² + (18)² = 225 + 324 = 549
∵ (20)² ≠ (15)² + (18)²
∴ The set not formed a right triangle
* The set {10 , 24 , 26} formed a right triangle
What is the value of f(x) = 9when x = -2?
[tex]f(x)=9\Longrightarrow f(-2)=9[/tex]
The function is a constant. No matter the input the output will always be equal to 9.
Hope this helps.
r3t40
can someone help me with this plz
Answer:
the box is cheaper
Step-by-step explanation:
2L bottle=$2,8(1L=$1,4)
[tex]6 \times 12 \: l \: bottle = 3.9(1l = \frac{0.65}{12} )[/tex]
the box is cheaper