write an equation in slope-intercept form for the line that passes through (4,1) and is perpendicular to 4x-y=3

Answer:

Step-by-step explanation:

\( \sf{x + 3x - 36}\)

Here, we have to collect like terms.

_________________________________

▪️What do you mean by like terms ?

⇒Like terms are those which have the same base. While adding or subtracting like terms, we should add or subtract the coefficients of like terms.

_________________________________

Let's add the like terms :

Answer : 4x - 36

Hope I helped!

Best regards!

the images go in order to the graph

Answer:

4a

Step-by-step explanation:

Greatest Common Factor is the largest number that the two terms can be divided by

The largest number that these could be divided by is 4a

12a/4a=3

16ab/4a=4b

4a(3+4b)

The province's population is growing at the rate of  58.34 %

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

Given:

Initial Population = 4.2 million

Population after 20 years = 6.65 million

Change in population = 6.65 - 4.2 = 2.45 million

Rate at which the province's population growing is

= \(\frac{Change in population}{Inital Population}\) x100 %

= \(\frac{2.45}{4.2}\\\) x 100%

= 58.34 %

Thus the province's population is growing at the rate of  58.34 %

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The first plan can be represented as :

• 20+ 0.19x ....... equation 1 .

The second plan can be represented as :

• 25 +0.15x ....equation 2

When we equate both equation , we ca find the minutes of call of two plans :

Solving the above equation, we get that :

The series of rigid motion transformations that map polygon A to Polygon A''' are;

A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.

The series of rigid motion transformations that map polygon A to polygon A''' are;

Transformation from A to A'

Transformation from A' to A''

Transformation from A'' to A'''

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Answer:

1.983(10⁴)

Step-by-step explanation:

Since we need to have ones and decimals as proper scientific notation, we have 1.983. Since we need the value of 19830, we need to move the decimal place 4 places to the right, so our exponent is 4.

*I double checked my work this time.

Answer:

1.983 * 10 ^4

Step-by-step explanation:

19,830

Move the decimal so there is only 1 digit before the decimal

We move it 4 places to the left

1.9830

The exponent is the number of places moved, since it was moved to the left the exponent is positive

1.983 * 10 ^4

Answer:

r =10

Step-by-step explanation:

5(r + 3) = 3r + 35.

Distribute

5r+15 = 3r+35

Subtract 3r from each side

5r+15-3r = 3r+35-3r

Combine like terms

2r +15 = 35

Subtract 15 from each side

2r+15-15 =35-15

2r = 20

Divide by 2

2r/2 =20/2

r =10

Answer:

\(a = 40600(1 + \frac{0.009}{1} ) {}^{10} = 40600 \times 1.0937 = 44405.6\)

Answer:

241/81 cm^2

Step-by-step explanation:

\(2\: lenghts = wide\\\\lenght=x\\\\2x=wide\\\\Perimeter = 2(wide+lenght)\\\\P=2(2x+x)\\\\P=2(3x)\\\\P=7\frac{1}{3}\\\\\frac{22}{3}=6x\\\\x=\frac{22}{3*6}\\\\x=\frac{11}{9}\\\\width = 2x=2(\frac{11}{9})=\frac{22}{9}\)

\(Area = lenght\times width\\\\Area = \frac{11}{9}\times\frac{22}{9}\\\\A=\frac{11*22}{9*9}\\\\A=\frac{242}{81}cm^2\)

Answer:

\(2\frac{80}{81}\) cm²

Step-by-step explanation:

A = lw

P = 2(l + w)

~~~~~~~~~~~

l = 2w

2(2w + w) = \(7\frac{1}{3}\)

2(3w) = \(\frac{22}{3}\)

3w = \(\frac{11}{3}\)

w = \(\frac{11}{9}\)

l = \(\frac{22}{9}\)

A = \(\frac{22}{9}\) × \(\frac{11}{9}\) = \(\frac{242}{81}\) = \(2\frac{80}{81}\) cm²

Step-by-step explanation:

I hope this answer is helpful ):

Step-by-step explanation:

to start, you need to understand what t(-7) is

t(-7) = 3(-7)

t(-7) = -21

that being said

s(t(-7)) = 2 - (-21)^2

s(t(-7)) = 2 - 441

s(t(-7)) = -439

Answer:

6 ≤ b.

(6).

Step-by-step explanation:

So, we are given in the question that the amount that Myra wants to say is $500 at the end of her summer vacation and she has saved up to $350. Thus, it remain ($500 - $350 = $150) for completion.

Also, "She can earn $25 cutting a lawn in her neighborhood."

Therefore, the total amount of money she wants to save = a = 500. Then,

Total amount of money, a = 350 + 25b.

500 = 350 + 25b.

=> 500 ≤ 350 + 25b.

Note that the ' =' sign has changed to '≤' sign since she wants that amount(at least). Also, the question specified that she used inequality.

Hence, the amount remaining for it to complete is $150. Therefore;

150 ≤ 25b.

6 ≤ b.

Thus, Myra will have to mow at least 6 lawns

Answer:

6

Step-by-step explanation:

Took the quiz on edge!

I think the 4th one but Im not too sure please forgive me if I'm wrong.

Answer:

(A) D.

(B) Cosh(-x)= e^-x+e^x

                            2

and the last box on the bottom would be 2

Step-by-step explanation:

Answer:

0.63

Step-by-step explanation:

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:

Offer 1. $18,600(#1) vs. $154,800(#2)

Step-by-step explanation:

Opt 1:

24000 + 9(1800)

24000 + 16200

18,600

Opt 2:

6(12000) + 6(12450) + 9(450 • 2)

72000 + 74700 + 8100

72000 + 82800

154,800

The best offer is offer 1.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Offer 1:

The payment for the first year is $24,000.

Annual increase for 9 years = $1800

= 24000 + 9(1800)

= 24000 + 16200

= 18,600

Offer 2:

For first six month = 12000

For next six month = 12450

and, for nine years there is increment  = 450

=6(12000) + 6(12450) + 9(450 • 2)

=72000 + 74700 + 8100

=72000 + 82800

=154,800

hence, the best offer is offer 1.

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The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Answer:

They are all equal at the sides so , the answer is 4.8m , I think the perimeter is given just to confuse you.....

The customer gets 5.66 hours of bike per dollar

At Hoffman's bike, it cost $17 to rent a bike for 3 hours

The number of hours gotten from the bike per dollar can be calculated as follows

17= 3
1= x

Cross multiply both sides

3x= 17

x= 17/3

x= 5.66

Hence it will cost the customer 5.66 hours to rent the bike for one dollar

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Answer:

y=8.25x-15

Step-by-step explanation:

From the information provided, the algebraic expression will need to indicate that your earnings during the first week, y, would be equal to multiplying $8.25 for the number of hours, x, minus $15. According to that, the algebraic expression is:

y=8.25x-15

Answer:

B

Step-by-step explanation:

Time can't go backwards

The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₁ + R₂ — R₂ on M, we have;

4(1) + (-5) = -1 {row 2 column 1}

4(0) + 2 = 2 {row 2 column 2}

4(3) + (-2) = 10 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

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Answer:

-8 and 8.

Product is -64.

Step-by-step explanation:

Let the numbers be x and x + 16.

We need to find the minimum of x(x + 16).

Product P = x^2 + 16x.

Convert to vertex form:

P = (x + 8)^2 - 64

The minimum value of (x + 8)^2 = 0 so:

The minimum of this is when x = -8 ,giving P  = -64.

The pair of numbers is  -8 and -8+16 = 8

and the minimum product = -46.

The pair whose product is minimum is; -8 and 8.

The two numbers whose difference is 16 can be represented as;

The product of the numbers can be represented as Product, P as follows;

By completing the square technique;

In other words;

The minimum value of (x + 8)² should be equal to 0.

(x+8)² = 0

Hence, the minimum of this is when x = -8.

The pair of numbers is then;

Ultimately, the minimum product is: -8 × 8 = -64.

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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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