Marissa decides to use synthetic division to find the quotient of (x3 – 3x2 + 5x – 3) ÷ (x – 1). What value from the divisor should she write in front of the coefficients?

-3

3

-1

1

The length of the solenoid is 4 cm, the number of coils is 400, and the area of each loop is 3 cm^2. The area per unit length of the solenoid is A/l = 3/4 = 0.75 cm^2/cm.

The inductance of a solenoid of length 4 cm with 400 coils is given by the formula L = μ0n^2A/l, where n is the number of turns per unit length of the solenoid, A is the area of each loop, l is the length of the solenoid, and μ0 is the permeability of free space, which is equal to \(4π × 10^-7 T·m/A.\)

The number of turns per unit length of the solenoid is n = N/l = 400/4 = 100 turns/cm.

So, the inductance of the solenoid is
\(L = μ0n^2A/l = 4π × 10^-7 × 100^2 × 0.75 × 10^-4/4 = 2.355 × 10^-5 H.\)

The current flowing in the solenoid is given by I = (0.4 A) cos (2π60t/s). The witage across the inductor is given by the formula V = L(dI/dt). So, differentiating I with respect to t, we get

\(dI/dt = - 0.4 A × 2π60 sin (2π60t/s) = - 4.776π sin (2π60t/s)\).

\(V = L(dI/dt) = - 2.355 × 10^-5 × 4.776π sin (2π60t/s) = - 0.283 sin (2π60t/s) V.\)

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3 is 13 more than 10, and 3 is 30% of 10, so 30% im pretty sure

Answer:

130%

Step-by-step explanation:

It's 130% because 10*130% is 13.

The value of f(20) is 3 feet  , and the value of f(140) is 3.5 feet .

In the question ,

the graph represents a function which gives the distance of a dog from a post (in feet ) ,

to find, f(20) which means the distance of the dog from the post after 20sec .

As we can see from the graph that at t=20 sec the distance from post (in feet ) is 3feet .

which means f(20) = 3feet .

Also from the graph we see that at t=140 sec the distance from post (in feet ) is 3.5 feet .

which means f(140) = 3.5 feet .

Therefore , the value of f(20) is 3 feet  , and the value of f(140) is 3.5 feet .

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Answer:

m1 = 33 degrees ; m3 = 33 degrees

Step-by-step explanation:

m8 = m4 = 147 degrees

m4 + m1 = 180

147 + m1 = 180

m1 = 180 - 147

m1 = 33 degrees

m1 = m3 (vertical angles)

The equation of an exponential function is y = a(b^x)

An exponential function is a mathematical function that has a constant base raised to a variable exponent.  Exponential functions are used to model processes that exhibit exponential growth or decay, such as population growth, radioactive decay, or the spread of infectious diseases.

The general form of an exponential function is:

f(x) = ab^x

where a is the initial value, b is the base, and x is the variable exponent. If the base is greater than 1, the function will exhibit exponential growth, while if the base is between 0 and 1, the function will exhibit exponential decay.

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Answer:

15

Step-by-step explanation:

from the first then it is 0+7=7

and from the last it is 0+8=8

then the number of cars available in the station is 8+7=15

Answer:

3.14

Step-by-step explanation:

literally that

If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .

We can start by finding the area of the entire circle. The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:

A = π(5 cm)^2 = 25π cm^2

Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:

Percentage shaded = (shaded area / total area) x 100

Percentage shaded = (25 cm^2 / 25π cm^2) x 100

Percentage shaded = 100 / π ≈ 31.83%

Therefore, approximately 31.83% of the circle is shaded.

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Answer:  1,780

Step-by-step explanation:

Answer:

y= 1/4x - 2

Step-by-step explanation:

y-y1=m(x-x1)

y-3=(1/4)(x-(-4))

y-3=(1/4x)+1

y=1/4x+1-3

y=1/4x-2

Answer:

y = 5x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 9)

m = \(\frac{9-4}{2-1}\) = \(\frac{5}{1}\) = 5 , then

y = 5x + c ← is the partial equation

To find c use any ordered pair from the table and substitute into the partial equation.

Using (3, 14 ) , then

14 = 15 + c ⇒ c = 14 - 15 = - 1

y = 5x - 1 ← equation of line

Answer:

25%

Step-by-step explanation:

Amount Kedwin has for the purchase = $150

Total cost of purchase :

Item cost =. $175

Shipping cost = 0.1 * 175 = 17.5

Total cost =. $(175 + 17.5) = $192.5

Smallest sale rate in other to afford the item:

At 10%

(1 - 0.1) * 192.5 = $173.25

At 20%

(1 - 0.2) * 192.5 = $154

At 25%

(1 - 0.25) * 192.5 = $144.375

Hence, smallest sale rate needwd is 25%

Answer:

25%

Step-by-step explanation:

got it right o edge2021

a) To prove this, it needs to satisfies the Closure under addition, Closure under multiplication by elements of R and Contains the kernel of f properties. b) To prove this, it needs to satisfies the Closure under addition, Closure under multiplication by elements of S and Contains 0.

(a) Proof that \(f^{-1}\) (J) is an ideal in R containing the kernel of f:

To show that  \(f^{-1}\) (J) is an ideal in R, we need to demonstrate that it satisfies the following properties:

Closure under addition,

Let a, b be elements in  \(f^{-1}\) (J) and let r be any element in R. We have f(a), f(b) in J since J is an ideal of S. Since f is a homomorphism of rings, f(a + b) = f(a) + f(b) is in J. Therefore, a + b is in  \(f^{-1}\) (J), showing closure under addition.

Closure under multiplication by elements of R,

Let a be an element in  \(f^{-1}\)  (J) and let r be any element in R. We have f(a) in J since J is an ideal of S. Since f is a homomorphism of rings, f(ra) = rf(a) is in J. Therefore, ra is in  \(f^{-1}\) (J), showing closure under multiplication by elements of R.

Contains the kernel of f,

Let x be an element in the kernel of f, i.e., f(x) = 0 in S. Since J is an ideal of S, 0 is in J. Therefore, x is in  \(f^{-1}\) (J), showing that  \(f^{-1}\) (J) contains the kernel of f.

Therefore,  \(f^{-1}\)  (J) is an ideal in R that contains the kernel of f.

(b) Proof that if f is an epimorphism, then f(I) is an ideal in S:

To show that f(I) is an ideal in S, we need to demonstrate that it satisfies the following properties:

Closure under addition,

Let a, b be elements in f(I), and let s be any element in S. Since f is surjective, there exist elements x, y in I such that f(x) = a and f(y) = b. Therefore, f(x + y) = f(x) + f(y) = a + b is in f(I), showing closure under addition.

Closure under multiplication by elements of S,

Let a be an element in f(I), and let s be any element in S. Since f is surjective, there exists an element x in I such that f(x) = a. Therefore, f(sx) = sf(x) = sa is in f(I), showing closure under multiplication by elements of S.

Contains 0,

Since f is a homomorphism of rings, f(0) = 0 in S. Therefore, 0 is in f(I).

Therefore, if f is an epimorphism, f(I) satisfies the properties of an ideal in S.

If f is not surjective, f(I) need not be an ideal in S. This is because in this case, there may exist elements in S that are not in the image of f, and therefore f(I) may not satisfy the closure properties required for an ideal.

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Answer: x= 5/2

Step-by-step explanation::)

The rule which represents the translation from the pre-image (Δabc), to the image (Δa'b'c') is (x, y) → (y, x).

A triangle simply refers to a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

Based on this triangle, we can deduce the following points:

By critically observing the triangle, we can also deduce that points were swapped as (x, y) → (y, x) and this is a reflection across line y = x.

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Answer:

B

Step-by-step explanation:

Answer:

y = 8x +2 that's the correct answer

Answer:

33cm^2

Step-by-step explanation:

Add the areas of the individual shapes so one rectangle and a square.

4*2 + 5*5 > 8 + 25 = 33

Answer:

31 cm²

Step-by-step explanation:

The area of the large figure is the sum of the areas of the smaller rectangles, the 4 cm x 2 cm one and the 5 cm x 5 cm one.

Area of the 4 x 2: 4 x 2 = 8 cm²

Area of the 5 x 5: 5 x 5 = 25 cm²

Sum of the two: 8 cm² + 25 cm² = 31 cm²

The answer for 2 + 2 in the addition is determined as 4.

Addition is a mathematical operation that involves combining two or more quantities or values to find their total or sum.

Addition is one of the four basic arithmetic operations, along with subtraction, multiplication, and division.

In addition operation, the two or more numbers are often added to produce result called the sum.

For example, in the equation; 2 + 2 = 4.

2 and 2 are the addends, and 4 is the sum.

We can also preform addition on fractions. decimas, percentages, etc.

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Answer:

3c+ (25x)/(2) + 2

Answer:

the simplest form of 15/20 is 3/4

Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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Answer:

45

Step-by-step explanation:

divide 25 by 5 to see how they got that, which is 5. then multiply 9 by 5 bc you have to do the same thing, which is 45.

Answer:

5:9 = 25:45

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of class intervals = 7

Class width = 5

Class intervals (heights)        Frequency (Number of boys)

130 - 135                                                     3                        

136 - 140                                                     5

141 - 145                                                      3

146 - 150                                                     5

151 - 155                                                      2

156 - 160                                                     1

161 - 165                                                      1

Therefore, frequency table given above will represent the distribution of the heights and number of students.

Would the answer be 6? or 9?

Answer:

OB

because domain is all X values that satisfy graph. And on graph X has all +ve values going to infinity.

When the Function g is defined as g(x) = 2f(x – 4) + 3 so the domain of the function g is OB. {x|0 < x <♾}.

Since the Function g is defined as g(x) = 2f(x – 4) + 3

So here OB should be considered as the domain of the all x values should satisfied the graph. Also, on graph X it contains the positive values that goes to infinity.

Hence, When the Function g is defined as g(x) = 2f(x – 4) + 3 so the domain of the function g is OB. {x|0 < x <♾}.

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The balance in the account after 5 years is $10750.

The following can be deduced based on the information given:

Principal = $10000

Rate = 1.5%

Time = 5 years..

Interest = (Principal × Rate × Time) / 100

= (10000 × 1.5 × 5) / 100

= $750

The balance will be:

= Principal + Interest

= $10000 + $750

= $10750

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A savings account of $10000 pays an annual simple interest rate of 1.5%. What would be the balance in your account after 5 years?

Answer:

0

Step-by-step explanation:

Given the following equation:

\((-3)(0)(-6)(-4)\)


The indicated operation for this equation is multiplication. When they're two parentheses around two numbers with no operation symbol in-between the two then we know to multiply.

\((-3\times0)\times(-6\times-4)\)
\(-3\times0=0\)
\(-6\times-4=-24\)
\(0\times-24=0\)
\(=0\)

Hope this helps.

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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