How many solutions are there to this equation?
5x + 2 -2(x-1) = 3x + 4
A. No solution
B. Exactly one solution
C. At least two solutions
D. Infinitely many solutions
(I solved it and i got 4 = 4 but i don't know what that means)
PLEASE ANSWER, WILL GIVE BRAINLIST

Answer:

See solutions below

Step-by-step explanation:

a) Given the expressions

x³y and x⁴y³

Find their factors

x³y = (x * x * x * y)

x⁴y³ = (x * x * x * y) * x * y * y

GCF = x*x*x*y

GCF = x³y

The expressions in parenthesis is the GCF. Hence the GCF of x³y and x⁴y³ is x³y

b) For 48m⁶n⁵p⁴ and 20m⁴n⁵p⁶

48m⁶n⁵p⁴ =12 * (4 * m⁴ * n⁵ * p⁴) * m²  

20m⁴n⁵p⁶ = 5 * (4 * m⁴ * n⁵ * p⁴) * p²  

GCF is the expression common to both terms

GCF = 4 * m⁴ * n⁵ * p⁴

GCF = 4m⁴n⁵p⁴

An expression is defined as a set of numbers, variables, and mathematical operations. The correct expression is B.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to (f·g)(2) is,

f(x) = 7x²-3

g(x) = 5x

(g·f)(x) = g(f(x)) = 5(7x²-3)

                       = 5(7·2² - 3)

Hence, the correct expression is B.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ1

Answer:  C

Step-by-step explanation:

400 multiply by 2 equals 800

and then 800 subtracted by 400 will be 400

and 400 subtracted by 1 will be 399.

Therefore, answer is C

Answer:

Fifth degree polynomial

Step-by-step explanation:

Given data:

e^0.3

error = 0.0001

let the function ; f(x) = e^x

note : x = 0.3

The Maclaurin polynomial f(x) = e^x = 1 + x + x^2 / 2!  + x^3/3!  ---  + ∑ x^n/n!

= 1 + 0.3 + (0.3)^2/2! + (0.3)^3 / 3! --- +  ∑ (0.3)^n/n!

Attached below is the remaining part of the solution

Answer:

m=102

Step-by-step explanation:

You forgot to attach an image of the lines, but I have it here, so no worries

We know that two parallel lines are crossed by a transversal. m are consecutive interior angles. We know that they add up to 180 degrees.

So, our equation is

78 + m = 180

m = 102

T: P₂ → P4, is the transformation that maps a polynomial p(t) into the polynomial p(t)- t²p(t). Let’s find out the image of p(t) = 6 + t - t² and show that T is a linear transformation and find the matrix for T relative to the bases (1, t, t²) and (1, t, 12, 1³, 14).

Step by step answer:

a) The image of p(t) = 6 + t - t² is;

T(p(t)) = p(t) - t² p(t)T(p(t))

= (6 + t - t²) - t²(6 + t - t²)T(p(t))

= 6 - t + 5t² - 13t + 14T(p(t))

= 20 - t + 5t²

Therefore, the image of p(t) = 6 + t - t² is 20 - t + 5t².

b)To show T as a linear transformation, we need to prove that;

(i)T(u + v) = T(u) + T(v)

(ii)T(cu) = cT(u)

Let u(t) and v(t) be two polynomials and c be any scalar.

(i)T(u(t) + v(t))

= T(u(t)) + T(v(t))

= [u(t) + v(t)] - t²[u(t) + v(t)]

= [u(t) - t²u(t)] + [v(t) - t²v(t)]

= T(u(t)) + T(v(t))

(ii)T(cu(t)) = cT (u(t))= c[u(t) - t²u(t)] = cT(u(t))

Therefore, T is a linear transformation.

c)The standard matrix for T, [T], is determined by its action on the basis vectors;

(i)T(1) = 1 - t²(1) = 1 - t²

(ii)T(t) = t - t²t = t - t³

(iii)T(t²) = t² - t²t² = t² - t⁴

(iv)T(1) = 1 - t²(1) = 1 - t²

(v)T(14) = 14 - t²14 = 14 - 14t²

Therefore, the standard matrix for T is;\($$[T] = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & -13 & 0 \\ 0 & 0 & -14 \end{bmatrix}$$\)Hence, the solution of the given problem is as follows;(a) The image of p(t) = 6 + t - t² is 20 - t + 5t².(b) T is a linear transformation because it satisfies both the conditions of linearity.(c) The standard matrix for T relative to the bases (1, t, t²) and (1, t, 12, 1³, 14) is;\($$[T] = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & -13 & 0 \\ 0 & 0 & -14 \end{bmatrix}$$\)

To know more about polynomial visit :

https://brainly.com/question/11536910

#SPJ11

The probabilities using Binomial Expansion is

A) P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:

P(X = k) = C(n, k) \(p^k(1-p)^{n-k}\)

Where:

C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).

p is the probability of success

(1 - p) is the probability of failure.

Let's calculate the probabilities for each combination:

A) 4 males, 0 females:

P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) 3 males, 1 female:

P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) 2 males, 2 females:

P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) 1 male, 3 females:

P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) 0 males, 4 females:

P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

Lear more about Binomial distribution here:

https://brainly.com/question/29163389

#SPJ1

Answer:

Im not sure that really makes sense but I think your grade would be 90% if you did 8/9 or somewhere around that

Step-by-step explanation:

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

for such more question on scale factor

https://brainly.com/question/3381225

#SPJ8

Answer:

answer is A

Step-by-step explanation:

Answer:

To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.

For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.

Substituting these values into the first equation, we get:

5 = 2(1) + 1

5 = 2 + 1

5 = 3

This statement is not true, so (1, 5) is not a solution of this system.

On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.

I hope this helps! Let me know if you have any more questions.

Step-by-step explanation:

According to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

The natural logarithm, often denoted as ln(x), is a mathematical function that represents the logarithm to the base e, where e is the mathematical constant approximately equal to 2.71828.

To find out how long it will take for 300 grams of Mercury 203 to decay, we can use the exponential decay model.

The general formula for exponential decay is given by:

A(t) = A₀ * e^(-rt),

where A(t) represents the amount of the substance at time t, A₀ is the initial amount, r is the decay rate, and e is the base of the natural logarithm.

In this case, we have the initial amount A₀ = 300 grams and the decay rate r = 0.01481 (1.481% written as a decimal).

We want to find the time t when the amount A(t) is equal to zero. Substituting these values into the formula, we have:

0 = 300 * e^(-0.01481t).

To solve for t, we can divide both sides of the equation by 300 and take the natural logarithm of both sides:

ln(0) = ln(e^(-0.01481t)),

0 = -0.01481t.

To isolate t, we divide both sides by -0.01481:

0 / -0.01481 = t,

t = 0.

Therefore, according to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

To know more about exponential decay, visit:

https://brainly.com/question/2311769

#SPJ11

Answer:

As the number of pegs added increases, the number of moves required decreases.

The extra pegs allow for more places to move disks, reducing the number of intermediate stacking steps.

An example would be three disks with four pegs. This requires 5 moves to solve, instead of 7.

Step-by-step explanation:

Answer:

As the number of pegs added increases, the number of moves required decreases.

The extra pegs allow for more places to move disks, reducing the number of intermediate stacking steps.

An example would be three disks with four pegs. This requires 5 moves to solve, instead of 7.

Step-by-step explanation:

To conclusively test the hypothesis "among these four people, those above age 30 definitely have feature a", you need to gather age and feature A information for Anne, Bob, Charlie, and Daniel.

You have the ages of Anne (35) and Bob (24) and feature A status of Charlie (has feature A) and Daniel (doesn't have feature A). You need to ask Anne and Bob about their feature A status and Charlie and Daniel about their ages.


1. Ask Anne if she has feature A.
2. Ask Bob if he has feature A.
3. Ask Charlie his age.
4. Ask Daniel his age.

After obtaining the missing information, compare it with the hypothesis to check if it holds true. The hypothesis will be true if both people above 30 years of age have feature A, and the others do not.

To know more about hypothesis  visit:

brainly.com/question/29519577

#SPJ11

Answer:

Step-by-step explanation:

4(x-3)^2 = 80

4x-12^2= 80              --- (distribute)

4x+144= 80          --- ( why a positive 144 because a (-) * a (-) = a (+)

4x =  (80-144)      --- ( subtract -144 from +144(do it on both sides)

4x = -64    --- (divide both sides by 4)

x= -16

Answer:

2√5 +3

Step-by-step explanation:

Isolate x:

4(x-3)^2 = 80

Divide both sides by 4.

(x-3)^2 = 20

Then take the square root of each side.

(x-3) = √20

Add 3 to each side.

x = √20 + 3

√20 can be rewritten as 2√5.

x = 2√5 + 3

If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

To know more about differentiable refer to-

https://brainly.com/question/13958985

#SPJ11

Answer:

x+y=0 and

3x-2y=10

Step-by-step explanation:

x+y=0——equation 1

3x-2y=10——equation 2

Above are the equations

When the values of x and y are replaced into a linear inequality in two variables, such as Ax + By > C, the solution is an ordered pair (x, y) .

In mathematics, an inequality is a connection between two expressions or values that is not equal. As a result, inequality results from imbalance. In mathematics, an inequality establishes a connection between two non-equal numbers. Egality is different from inequality. Use the not equal sign, which is most frequently used, when two values are not equal (). Values of any size can be contrasted using various inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be resolved. But a lot of factors support inequality: On either side, negative values are split or added. 

given

Rule 1: An inequality sign remains unaltered when the same amount is added to or subtracted from both sides.

Rule 2: The inequality sign remains constant when both sides are multiplied or divided by a positive number.

When the values of x and y are replaced into a linear inequality in two variables, such as Ax + By > C, the solution is an ordered pair (x, y) .

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

Answer:

600 square feet

Step-by-step explanation:

I notice it says "Estimate" in bold. Therefore, you would round all of the measurements. They're all pretty simple to round (to the nearest tens place). From here, you subtract the length of the large room from the length of both rooms. So, 50 - 30 = 20. This is the length of the small room. We now multiply this by the width of the small room (since area of a rectangle is length * width) and we get:

20 * 30 = 600, our final answer

Hope it made sense. I would appreciate Brainliest, but no worries.

The total number of ways to distribute all the fruits to the 30 children, ensuring each child who prefers apples gets at least 2 apples and each child who prefers oranges gets at least 2 oranges, is given by the product of C(29, 9) and C(59, 19).

To find the total number of ways, we can consider the distribution of apples and oranges separately. For the children who prefer apples, we need to distribute 20 apples among 10 children, with each child receiving at least 2 apples. This can be calculated using the stars and bars combinatorial technique. Similarly, for the children who prefer oranges, we need to distribute 40 oranges among 20 children, with each child receiving at least 2 oranges.

The number of ways to distribute the apples can be calculated as C(20+10-1, 10-1) = C(29, 9). Likewise, the number of ways to distribute the oranges can be calculated as C(40+20-1, 20-1) = C(59, 19). To find the total number of ways to distribute both fruits, we multiply these two values together.

Therefore, the total number of ways to distribute all the fruits to the 30 children while satisfying the given conditions is C(29, 9) x C(59, 19).

learn more about combinatorial technique here:

https://brainly.com/question/30589727

#SPJ11

Answer: 21.5

Step-by-step explanation:

add 18 and 25 equals 43

then divide that by 2 and the answer is 21.5

Hope this helps :)

Answer:

1200

Step-by-step explanation:

i=prt is the interest equation however we must find the total because it says After 2 years

first lets do 1000*.1*2=200

1000+200=

1200

9514 1404 393

Answer:

Step-by-step explanation:

To find fees per hour, divide fees by hours.

  $1728/(144 h) = $12/h

Toby's cost is $12 per credit hour.

Answer: 628 cubic feet

Step-by-step explanation: First, find the area of the circle. Using the formula "TTr^2", you can find the area of the circle. Since the diameter is given, and not the radius, divide 10 by 2, and it gives you 5. Now, use the formula. 5 x 5 = 25, and then multiply it by 3.14 which gives you 78.5. Now that we have found the area of the circle, multiply the area by 8 to find the volume of the cylinder. 78.5 x 8 is 628 cubic feet, and that is the volume of the cylinder.

The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

To know more about Z score here

brainly.com/question/2473932

#SPJ4

The sequence is arithmetic. The common difference is 6. Answer: b

If a sequence is arithmetic, there exists a common difference d that is added to each term to get the next term. For instance, given the sequence 2, 5, 8, 11, 14, ...  to get each of the subsequent terms, we add 3. 2 + 3 = 5; 5 + 3 = 8, and so on.

The given sequence is 2,7,13,20, ...To determine whether it is an arithmetic sequence, we need to find the common difference d.

Subtract each subsequent term from its preceding term;7 - 2 = 513 - 7 = 620 - 13 = 7

Therefore, the common difference d is 6.

learn more about arithmetic here

https://brainly.com/question/6561461

#SPJ11

Answer:

$400

Step-by-step explanation:

If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment

Answer:

As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} , 3 & 10 and 5 & 12 are the only two pair of numbers whose difference is 7 . But Least common multiple of 3 and 10 is 30

Answer:

1/2

Step-by-step explanation:

1/4+1/4=1+1/4(because the have same denominator we can take one denominator as common)

=2/4=1/2 (when simplified)

1-1/2=1/2 to know how much is left