The given equation 3y = -12x + 6 has infinitely many solutions.
The given equation 3y = -12x + 6 can be solved using the substitution method to determine whether this equation has no solution, 1 solution or infinitely many solutions.
Given equation,
3y = -12x + 6
Rearranging the terms of the equation, we get the value of y in terms of the variable x.
=> 3y = -12x + 6
=> y = -12x/3 + 6/3
=> y = -4x + 2
Next, we substitute this value of y in terms of the variable x in the original equation,
=> 3 ( -4x + 2 ) = -12x + 6
=> -12x + 6 = -12x + 6
=> -12x + 12x = 6 - 6
=> 0 = 0
From the obtained result, we can conclude that this system has infinitely many solutions. This implies, the lines are coincident and the system is consistent and dependent.
Therefore, it can be concluded that the given equation 3y = -12x + 6 has infinitely many solutions.
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(2) six spheres of radius 1 are positioned so that their centers are at the vertices of a regular hexagon of side length 2. the six spheres are internally tangent to a larger sphere whose center is the center of the hexagon. an eighth sphere is externally tangent to the six smaller spheres and internally tangent to the larger sphere. what is the radius of this eighth sphere? (2013 amc 10a
The radius of 8th sphere is 3/2.
The 8th sphere's center and the hexagon's two opposing ends should form an isosceles triangle. Then put up another triangles between the point of tangency of the 7th and 8th spheres, and the point of tangency between the 7th sphere and 2 of the original spheres on different sides of the hexagon. Each triangle's side length should be expressed in terms of r (the sphere's 8 radius) and h. (the height of the first triangle). The values of h and r may then be determined by setting up two equations for the two triangles using the Pythagorean Theorem.
(1+r)² = [tex]2^{2}[/tex] + [tex]h^{2}[/tex]
(3√2)² =3² + (h+r)²
r= 3/2
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I don’t understand this question
X/2 - 2 =x/4 + 2
Verruca counted protrusions. she found that 3 times the number of protrusions was 15 less then -4 times the opposite of the number of protrusions. how many protrusions did she count?
15 protrusions were counted by her.
Clearly, there are multiple ways to treat verruca. For this type of patient, we would try a prescription for Drysol to apply topically once daily. In many of these patients, the skin is too moist. In our practice, we write a prescription for physical therapy for ultrasound application to the verruca. There is no guarantee with any treatment for verruca. Vitamin A adjunct treatment is often instituted: approx 7500 IU /day for 3 weeks.
Let no. of protrusions be x
3 * x = -4 * (-x) - 15
3x-4x = -15
x = 15
Therefore 15 protrusions were counted by her.
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What is the result of the subtraction problem that is represented on the number line?
Enter your answer as a decimal, like this: 42.5
The required subtraction problem that is represented on the number line is 3 -(-5). Option B is correct.
Given that,
To determine the subtraction problem that is represented on the number line.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
The line marked above the number line from -5 to 3
The subtraction problem would be given as 3 - (-5)
Thus, the required subtraction problem that is represented on the number line is 3 -(-5). Option B is correct.
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Since questions seem to be incomplete,
The given solution is based on the question given below,
Which subtraction problem is represented by the number line?
A: 3-5
B: 3 - (-5)
C: 3-8
D: 3-(-8)
Point M is on line segment
L
N
‾
LN
. Given
L
N
=
9
,
LN=9,
M
N
=
4
x
,
MN=4x, and
L
M
=
5
x
,
LM=5x, determine the numerical length of
M
N
‾
.
MN
The value of x from the given expression is 1
Addition postulateIf the point M is on the line LN, then the equivalent addition postulate is expressed as;
LM+MN = LN
Given the following
LN=9,
MN =4x
LM=5x
Substitute
5x + 4x = 9
9x = 9
x =9/9
x = 1
Hence the value of x from the given expression is 1
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suppose the random variables x1, x2,..., xn are independent an identically distributed , each with variance
The random variable is 3×sigma²/4.
Since, X1, X2 & X3 are independent & identically distributed.
so we have,
var(X1) = var(X2) = var(X3) = \sigma².
And,[tex]cov(X1 , X2) = cov(X2 , X3) = cov(X1 , X3) = 0.[/tex]
Now, [tex]var(Y1) = var(X2 + X3) = var(X2) + var(X3) + 2.cov(X2 , X3) = \sigma² + \sigma² + 0 = 2.\sigma²[/tex]
[tex]var[(Y1 + Y2 + Y3)/2] = (1/4). [var(Y1) + var(Y2) + var(Y3) + 2.cov(Y1 , Y2) + 2.cov(Y1 , Y3) + 2.cov(Y2 , Y3)] = (1/4). (\sigma² + \sigma² + \sigma² + 0 + 0 + 0) = 3.\sigma²/4[/tex]
What is random variable and example?The collection of potential outcomes for a random event is referred to as the sample space, which is the domain of a random variable. When a coin is tossed, for instance, there are only two possible outcomes: heads or tails. Read Related Links as well. Probability.
Different from an algebraic variable is a random variable. An algebraic equation's variable is an unknowable but calculable value. The formula [tex]10 + x = 13[/tex] demonstrates that we can determine the precise value of x, which is [tex]3.[/tex] As seen in the example of the dice above, a random variable has a set of values, and any of those values could be the outcome.
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The diameter of a strand of rope is 1.2 × inch. The diameter of a strand of floss is 2.0 × inch.
How much longer is the diameter of the strand of rope than the diameter of the strand of floss?
A. 2.0 × inch
B. 1.0 × inch
C. 2.0 × inch
D. 1.0 × inch
The rope's diameter is 10⁻³ inches greater than that of the floss, for example.
The diameter of a stand of rope is 1.2 × 10⁻³ inch.
The diameter of a strand of floss is 2 × 10⁻⁴ inches.
Subtract the diameter of the floss strand from the diameter of the rope to determine how much longer the diameter of the rope is than the diameter of the floss.
Therefore, the length by which the diameter of the strand of rope is longer than the diameter of the strand of floss will be:
= 1.2 × 10⁻³ inch - 2 × 10⁻⁴ inches
Now,
= 12 × 10⁻⁴ inch - 2 × 10⁻⁴ inch
= 10 × 10⁻⁴ inch
= 10⁻³ inch
The diameter of the strand of rope is 10⁻³ inches longer than the diameter of the strand of floss.
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When writing the range for the quadratic
parent function we use a bracket next to
infinity. Why do we use parenthesis next to
zero for the range of the exponential parent
function?
the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.
Why do we use parenthesis next to zero for the range of the exponential parent function?When we write in interval notation, the parenthesis are used to denote that the "ends" of the interval don't belong to the interval.
This means that in (a, b).
a and b don't belong to that interval.
While if instead we wrote [a, b]
In that case, a and b belong.
For the case of the exponential function:
y = a^x
As x tends to really large negative values, the value of y will tend to zero asymptotically. This means that y is really close to zero, but it is never equal to zero.
Then the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.
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simplify. 2(x-2y)-5x+6y-1=
If f(x) = -2x - 3 and g(x) = x^2 5x what is f(-1)
Answer:
it's -2/67x12w<3(xyz)
Arthur is 7 years older than his brother. In 8 years, Arthur will be twice his brother's current age. How old is Arthur now?
Answer:
15 years old
Step-by-step explanation:
Answer: 22
Step-by-step explanation:
this problem is solved by a system of equations
Let Arthur’s current age be represented by:a
His brother’s current age will be represented by: b
The first equation will be:
a = 7 + b
The second equation will be:
a + 8 = 2b
now we solve for the equations. Plug in a = 7+b into a in the second equation.
So now we have
b+7+8=2b
Simplify:
B+15=2b
15=b
We aren’t done yet though
Arthur’s brother is 15 years old but since he is 7 years older we need to add 7 to 15
Hence, Arthur is 22 years old.
how many critical numbers does f(x) have? note: critical numbers must be within the domain of the function.
The critical number of the given function {g(t) = 3t ㏑t} is t = e⁻¹
What is critical number?Assume f(x) is a function with an open interval (a,b). If c is in the interval (a,b) and either f'(c) =0 or f'(c) does not exist, we say c is a critical number of f(x).
Each local minimum as well as maximum of f(x) must correspond to a critical number of f(x). The opposite is not truly the case: not all critical number of f(x) must correspond to a local maximum as well as minimum of f(x).
Now, as per the question;
It should be noted that the broadest possible domain of {g(t) = 3t ㏑t} is given in the set {t : t > 0} as ㏑t can not be defined for negative numbers of zero.
Now, differentiate the given function with respect to t.
[tex]g^{\prime}(t)=\frac{d}{d t}(3 t \ln t)[/tex]
Apply the product rule of differentiation;
[tex]\begin{aligned}&=\left[\frac{d}{d t}(3 t)\right] \ln t+3 t \frac{d}{d t}(\ln t) \\&=3 \ln t+3 t \frac{1}{t} \\&=3 \ln t+3 \\&=3(\ln t+1)\end{aligned}[/tex]
Now, put this value of g'(t) = 0 for finding the critical points.
0 = g'(t)
= 3(㏑t + 1)
Divide equation by 3.
0 = ㏑t + 1
㏑t = -1
Taking anti log;
t = e⁻¹ (critical value)
Therefore, the critical value obtained for the given function is t = e⁻¹.
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The complete question is-
how many critical numbers does {g(t) = 3t ㏑t} have? note: critical numbers must be within the domain of the function.
Sophia buys 13 bottles of cranberry juice at the corner store for a total cost of $7.02. If each bottle costs the same amount, how much is 14 bottles of juice?
The cost for 14 cranberry juice bottles would be $7.56
In this question, Sophia buys 13 bottles of cranberry juice at the corner store for a total cost of $7.02
If each bottle costs the same amount, we need to find the amount for 14 bottles of juice.
Let x be the cost of one bottle of cranberry juice.
13 bottles of cranberry juice costs $7.02
So, we get an equation,
13x = $7.02
We solve above equation to find the cost of 1 bottle of cranberry juice.
x = $0.54
By unitary method the cost for 14 cranberry juice bottles would be,
14 × 0.54 = $7.56
Therefore, the cost for 14 cranberry juice bottles would be $7.56
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A triangle’s base is 5 cm more than its height of x cm. Find its height if the triangle’s area is 10 cm2. Quadratic equation
Answer:
A=2.5×x
10cm=2.5×x
10÷2.5=2.5÷2.5×x
x=4
The nth term of a sequence is 4−7. The last term of the sequence is 393.How many terms are there in the sequence?
Answer:
There are 98 terms in this sequence.
Alberto invests $1,130 in a savings
account with a fixed annual interest rate
compounded 6 times per year. After 8
years, the balance reaches $1,325.71.
What is the interest rate of the account?
The interest rate of the account is 2%
Compound interestFrom the question, we are to determine the interest rate of the account
From the compound interest formula, we have that
A = P(1 + r/n)^{nt}
Where A is the amount
P is the principal
r is the rate
n is the number of times compounded
t is the time in years
From the given information,
A = $1,325.71
P = $1,130
n = 6
t = 8 years
Thus,
1325.71 = 1130(1 + r/6)⁶⁽⁸⁾
1325.71 = 1130( 1 + r/6)⁴⁸
1325.71/1130 = ( 1 + r/6)⁴⁸
Take the 48th root of both sides
1.003333 = 1 + r/6
1.003333 - 1 = r/6
0.003333 = r/6
r = 6 × 0.003333
r = 0.019998
r ≈ 0.02
r ≈ 2%
Hence, the interest rate of the account is 2%.
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how do I figure this out
Answer:
[tex]27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}[/tex]
Step-by-step explanation:
Rewrite 9 as 3²:
[tex]\implies 9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{(2 \cdot \frac{3}{2})}=3^3[/tex]
Therefore:
[tex]\implies 3^3= 3 \cdot 3 \cdot 3=27[/tex]
---------------------------------------------------------
Rewrite 27 as 3³:
[tex]\implies 27^{\frac{1}{3}}=\left(3^3\right)^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{(3 \cdot \frac{1}{3})}=3^1[/tex]
Therefore:
[tex]\implies 3^1=3[/tex]
---------------------------------------------------------
Rewrite 125 as 5³:
[tex]\implies 125^{\frac{2}{3}}=\left(5^3\right)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 5^{(3 \cdot \frac{2}{3})}=5^2[/tex]
Therefore:
[tex]\implies 5^2=5 \cdot 5=25[/tex]
---------------------------------------------------------
Solution
In order, from smallest to largest:
[tex]27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}[/tex]
Can someone halp real quick.
Brainliest award
The equation of the line passing through (14, 25) and (9, -10) is given by y = 7x - 73
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a line is:
y = mx + b
Where m is the rate of change and b is the y intercept
The equation of the line passing through the point (14, 25) and (9, -10) is:
y - 25 = [(-10 - 25)/(9 - 14)](x - 14)
y = 7x - 73
The equation of the line passing through (14, 25) and (9, -10) is given by y = 7x - 73
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How many times larger is (1.092 × 101) than (7 × 10−1)?
0.156
15.6
6.41
6.908
The number 1.092×[tex]10^{1}[/tex] is 15.6 times larger than 7×[tex]10^{-1}[/tex]
Given,
The first number = 1.092×[tex]10^{1}[/tex]
The second number =7×[tex]10^{-1}[/tex]
Here,
Convert the given numbers to the simplest form
The first number 1.092×[tex]10^{1}[/tex] =1.092×10
=10.92
The second numbers 7×[tex]10^{-1}[/tex]= 7×0.1
=0.7
We know the division is one the basic arithmetic operations in the mathematics. It is the process of the splitting a particular amount or number into equal parts.
To find how many time larger 1.092×[tex]10^{1}[/tex] than 7×[tex]10^{-1}[/tex], we have to divide the first number by second number.
10.92 ÷ 0.7 =15.6
Hence, the number 1.092×[tex]10^{1}[/tex] is 15.6 times larger than 7×[tex]10^{-1}[/tex]
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Find the future value of an account compounded quarterly at 5.67% for 4 years, if $7,000 was deposited into the account.
Step 1) : We know that,
[tex]\begin{cases}P = 7000& \\r = 5.6 \% & \\ n = 4 & \\ t = 4 & \end{cases}[/tex]
Step 2) : Formulate and Substitute:
[tex]Substitute\begin{cases}P = 7000& \\ r = 5.6 \% & into \: formula \\ n = 4 & \\ t = 4 & \end{cases}[/tex]
[tex]\bf\longrightarrow{F = P * (1 + \frac{r}{n} )^{(n*t)}} [/tex]
Put the values according to the formula:
[tex]\bf\longrightarrow{F = 7000 * (1 + \frac{ \frac{5.67}{100} }{4} )^{(4*4)}}[/tex]
Step 3) : Evaluate the equation/expression:
[tex]\bf\longrightarrow{8768.1}[/tex]
If Naomi were to paint her living room alone, it would take 7 hours. Her sister Colleen could do the job in 8 hours. How many hours would it take them working
together? Express your answer as a fraction reduced to lowest terms, if needed.
Answer: 3.23
Step-by-step explanation:
Add 1/6 + 1/7 = 13/42 Take the reciprocal = 42/13 hrs ≈ 3.23 hrs
Solve the inequality and express your answer in interval notation.
X^2+8x+5<0
Answer: (-4-[tex]\sqrt{11}[/tex], -4+[tex]\sqrt{11}[/tex]) ==> B
Step-by-step explanation:
x^2+8x+5<0
x^2+8x+16-11<0
(x+4)^2-11<0
(x+4)^2<11
x+4<[tex]\sqrt{11}[/tex]
x<-4+[tex]\sqrt{11}[/tex]
x+4>-[tex]\sqrt{11}[/tex]
x>-4-[tex]\sqrt{11}[/tex]
(-4-[tex]\sqrt{11}[/tex], -4+[tex]\sqrt{11}[/tex]) ==> B
Remember, the solution doesn't include the x values -4-[tex]\sqrt{11}[/tex] and -4+[tex]\sqrt{11}[/tex] since if they were plugged in x^2+8x+5, the expression would equal 0. The expression is supposed to be LESS than 0, not equal to 0.
Answer:
Answer: (-4-\sqrt{11}11 , -4+\sqrt{11}11 )
x^2+8x+5<0
x^2+8x+16-11<0
(x+4)^2-11<0
(x+4)^2<11
x+4<\sqrt{11}11
x<-4+\sqrt{11}11
x+4>-\sqrt{11}11
x>-4-\sqrt{11}11
(-4-\sqrt{11}11 , -4+\sqrt{11}11 )
14a + 2 =?
16a
16a +2
14a + 2
Answer:
16a
Step-by-step explanation:
14a+2=14+2+a=16a.
how is dimension related to the number of coordinates need to locate a point?
For a party, Carlos buys 8 bags of popcorns and 4 bags of pretzels on sale for $10.36. During the party, he goes back to the store after the sale is over to buy 4 more bags of popcorns and 2 bags of pretzels for $20.72. Let x represent the price of each bag of popcorn and let y represent the price of each bag of pretzels. Which system of linear equations can you solve to find the price of each bag ofpopcorn and each bag of pretzels?
Answer:
addingadddddddddddddddddd
Which is different? Find “both” answers.
Find AC+CB .
Find BC-AC .
Find AB .
Find CA+BC
The "different" answer is [Blank}
. The "same" answer is [Blank]
Answer:
The "different" answer is BC-AC and AB
The "same" answer is AC+CB and CA+BC
Step-by-step explanation:
AC+CB and CA+BC if are rearranged wold be the same CA becomes AC and CB becomes BC
A clothing pattern calls for 4.81 yd2 of fabric. how many square inches of fabric does the pattern use? (note: 1 yd = 3 ft., 1 ft = 12 in.)
Pattern uses 6233.76 inches² fabric.
Firstly we will convert units in required form. Therefore, converting equivalent of yard² in inches². As per the given information, 1 yard = 3 feet and 1 foot = 12 inches.
As 1 foot = 12 inches, so, 3 feet = 36 inches, which is further equal to 1 yard.
Now, 1 yard² = (36 inches)²
1 yard² = 1296 inches²
Coming back to the problem, we will now calculate inches² from fabric measurement in yard². So, relating the units for conversion.
1 yard² = 1296 inches²
4.81 yard² = 1296 × 4.81
Performing multiplication
Measurement of 4.81 yard² in inches² = 6233.76
Hence, the pattern uses 6233.76 inches² fabric.
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(2x² + 4x³) + (-4x² + 6x³ - 2)
Mr. Thompson has a class of 14 students. He can spend $25 on each student to buy math supplies for the year. He first buys all of his students calculators,
which costs a total of $84. 14. After buying the calculators, how much does he have left to spend on each student?
Answer:
he has $6 left.
Step-by-step explanation:
Answer:
$18.99 for each student
Step-by-step explanation:
First we need to find out how much he spent on each student for the calculators.
We can do that by dividing 84.14, the total, by the number of students, 14:
84.14/14 = 6.01
He spent 6.01 on each student and has 25 for each student, so we can subtract that:
25 - 6.01 = 18.99
Miriam is 5 cm taller than her sister,who is ? cm tall.write an expression of mia's height in cm.
The expression of Mia's height in cm is 5 + x
How to write an expression of Mia's height in cm?The given parameters are
Mia's height = 5 cm taller than her sister
Her sister's height = x
The parameter "Mia's height = 5 cm taller than her sister" means that
Mia's height = 5 cm + her sister's height
Substitute Her sister's height = x in Mia's height = 5 cm + her sister's height
Mia's height = 5 cm + x
This means that the expression of Mia's height in cm is 5 + x
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