The solution set of a linear system whose augmented matrix is [ 1 2 3 ] is the same as the solution set of =, if =[ 1 2 3 ].

Answer:

see below

Step-by-step explanation:

Monica earned twice as much as Samuel

m = 2*s

Divide each side by 2

1/2 m = 1/2 ( 2s)

1/2 m = s

If monica earned 56

1/2 (56) = s

28 =s

Answer:

it has to be 77.7

Step-by-step explanation:

Answer:

The move is that both sides were divided by 5.

Step-by-step explanation:

On the left side, dividing by five would result in x-3.

On the right side, dividing by five would result in 1.

Answer:

Absolute error = $25

Step-by-step explanation:

Given that:

Amount spent by John on shopping trip = $75

Estimated amount to spent on shopping trip = $100

Absolute error = Approximate value - Exact value

Here,

Approximate value = $100

Exact value = $75

Absolute error = 100 - 75

Absolute error = $25

Percentage = \(\frac{Absolute\ error}{Exact\ value}*100\)

Percentage = \(\frac{25}{75}*100\)

Percentage = 33.33%

Hence,

Absolute error = $25

a) The maximum height of the ball is 4 meters after 1 seconds.

b) The function f(x) is a cubic polynomial

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let h represent the height of the ball above the ground in t seconds. Hence:

h = 3 + 2t - t²

The maximum height of the ball is at h'(t) = 0, hence:

h'(t) = 2 - 2t

2 - 2t = 0

t = 1 seconds

h = 3 + 2(1) - (1)² = 4

a) The maximum height of the ball is 4 meters after 1 seconds.

b) The function f(x) is a cubic polynomial

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\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}\)

Answer:

I think it is y=1/3x -7

Step-by-step explanation:

Answer:

√85

Step-by-step explanation:

A (-3 , 4)    B (4 , -2)

AB² = (4 - -3)² + (-2 -4)² = 49 + 36 = 85

AB = √85

Answer:

45

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180

2x - 12 + 2x + 17 + 9x - 7 = 180 add like terms

13x - 2 = 180 add 2 to both sides

13x = 182 divide both side by 13

x = 14

m<X = 2x + 17 replace x with 14

2*14 + 17 = 45

The probability that the average length of a randomly selected bundle of steel rods is 155.8 then P = 0.174 cm

Given sample size 'n' = 30 steel rods

Mean of the Population = 155.1 cm

Standard deviation of the Population = 1.4 cm

Given x⁻ be the random variable of Normal distribution

Let x₁⁻ =  155.8cm

The probability that the average length of a randomly selected bundle of steel rods is  155.8-cm.

P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)

                      = P(Z <Z₂) - P(Z<Z₁)

                     = 0.5 +A(1.629) - (0.5 +A(0.7541)

                     = A(1.629) - A(0.7541)

                     = 0.4474 - 0.2734

                     = 0.1

The probability that the average length of a randomly selected bundle of steel rods is 155.8 cm = 0.174

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Answer:

13u = 26

13*2 = 26

2 is the answer

Answer:

Today: Monday, 12 October 2020

Hour: 09.17 WIB (in Indonesian)

_________________________

13u = 26

u = 26/13

u = 2

Answer: To simplify your expression using the Simplify Calculator, type in your expression like 2(5x+4)-3x.

The simplify calculator will then show you the steps to help you learn how to simplify your algebraic expression on your own.

Type ^ for exponents like x^2 for "x squared". Here is an example:

Step-by-step explanation:

don't know if this will help but I hope s

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

Step-by-step explanation:

The general solution of the given equation is y = C1e^(-5x) + C2e^(2x) + yp where C1 and C2 are constants, and yp is the particular solution we found earlier y = C1e^(-5x) + C2e^(2x) - (4/5)x - 6/25.

To find a particular solution yp of the equation y'' + 3y' - 10y = 8x, we assume that yp has the form of a polynomial of the same degree as the nonhomogeneous term (8x in this case). Since the nonhomogeneous term is a first-degree polynomial, we assume that yp is also a first-degree polynomial of the form:

yp = Ax + B

where A and B are constants to be determined.

Now, we differentiate yp twice to find its first and second derivatives:

yp' = A

yp'' = 0

Substituting these derivatives into the original equation, we have:

0 + 3(A) - 10(Ax + B) = 8x

Simplifying the equation:

3A - 10Ax - 10B = 8x

Matching the coefficients of the like terms on both sides of the equation, we have:

-10Ax = 8x (setting the coefficients of x equal)

3A - 10B = 0 (setting the constant terms equal)

From the first equation, we get:

-10A = 8

A = -8/10

A = -4/5

Substituting the value of A into the second equation, we get:

3(-4/5) - 10B = 0

-12/5 - 10B = 0

-10B = 12/5

B = -6/25

So the particular solution yp is given by:

yp = (-4/5)x - 6/25

To find the general solution of the equation, we need to consider the complementary solution (the solution of the associated homogeneous equation y'' + 3y' - 10y = 0). The characteristic equation of the homogeneous equation is:

r^2 + 3r - 10 = 0

Factoring the equation, we get:

(r + 5)(r - 2) = 0

So the roots of the characteristic equation are r = -5 and r = 2.

The general solution of the associated homogeneous equation is:

y = C1e^(-5x) + C2e^(2x)

where C1 and C2 are constants.

Therefore, the general solution of the given equation is:

y = C1e^(-5x) + C2e^(2x) + yp

where C1 and C2 are constants, and yp is the particular solution we found earlier:

y = C1e^(-5x) + C2e^(2x) - (4/5)x - 6/25

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Answer/Step-by-step explanation:

a. Since both cones, as shown in the figure attached below, are similar, 11/8 = l/4

Cross multiply to find l

4*11 = 8*l

44 = 8l

l = 44/8

l = 5.5cm

b. Given the slant height and diameter of cone, volume of cone can be calculated using the formula ⅓πr²*√(l² - r²)

Where, r = diameter ÷ 2 = 4/2 = 2cm

l = 5.5cm

Volume of smaller cone = ⅓*3.142*2²*√(5.5² - 2²)

= ⅓*3.142*4*√30.25 - 4)

= ⅓*12.568*√26.25

= ⅓*12.568*5.124

= 64.40/3

Volume of small cone ≈ 21.5 cm³

to divide big decimal b1 by b2 and assign the result to b1, you write the divide method.

To divide a BigDecimal b1 by b2 and update the value of b1 with the result, you can use the divide method provided by the BigDecimal class.

This method takes the divisor as its argument and returns a new BigDecimal object that represents the quotient of the division.

To update the value of b1, you can assign the result of the divide method back to b1. Here's an example:

b1 = b1.divide(b2);

This will divide b1 by b2 and assign the resulting quotient to b1.

Note that the divide method may throw an Arithmetic Exception if the divisor is zero or if the quotient cannot be represented with the current scale and rounding mode of the BigDecimal.

Therefore, you should handle this exception accordingly.

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Answer:

h = 2w + 6

Step-by-step explanation:

2 is the rate of change and 6 is the starting value.

Answer:

4 gallons of paint

Step-by-step explanation:

We solve using the formula for surface area of rectangular prism.

A=2(wl+hl+hw)

Where:

w = Width

h = Height

l = Length

The pool is 4 feet deep, 18 feet long, and 12 feet wide.

Hence,

=2 × (12 × 18 + 4 × 18 + 4 ×12)

=672 square feet

One gallon of paint covers 155 square feet.

Hence,

155 square feet = 1 gallon of paint

672 square feet = x

Cross Multiply

155 square feet × x = 672 square feet × 1 gallon of paint

x = 672 square feet × 1 gallon of paint/ 155 square feet

x = 4.335483871 gallons of paint

Therefore, based on the calculation above, approximately to the nearest whole number, Sierra uses 4 gallons of paint

Answer:

22m+42 is the answer

Step-by-step explanation:

All you have to do is simplify and add the common factors.

Answer:

Step-by-step explanation:

Answer:

A. 1,800≤250+2i .

Step-by-step explanation:

The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.

From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.

It should be noted that interest is calculated as:

= (Principal × Rate × Time) / 100

= ($13000 × 2 × 10) / 100

= $2600

The simple interest is $2600.

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The derivative of arctan√1−x1+x is -√(1-x)/[(1+x)(2-2x)].

We can use the chain rule and the formula for the derivative of arctan to find the derivative of the given expression. Let u = √(1-x)/(1+x). Then,

arctan(√(1-x)/(1+x)) = arctan(u)

By the chain rule,

(arctan(u))' = 1/(1+u²) * u'

To find u', we can use the quotient rule:

u' = [(1/2)(1-x)⁻¹/²) * (-1)/(1+x)] - [(1/2)(-1)*(1-x)⁻¹/²* (1)/(1+x)²]

Simplifying this expression gives:

u' = -1/[(1+x)√(1-x)]

Substituting this expression for u' into the previous expression for (arctan(u))', we get:

(arctan(√(1-x)/(1+x)))' = -√(1-x)/[(1+x)(1+(√(1-x)/(1+x))²)]

Simplifying the denominator and combining terms gives:

(arctan(√(1-x)/(1+x)))' = -√(1-x)/[(1+x)(2-2x)]

Therefore, the derivative of arctan(√(1-x)/(1+x)) with respect to x is -√(1-x)/[(1+x)(2-2x)].

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Answer:

the answer I belive is

Step-by-step explanation:

52400

Answer:

10/9

Step-by-step explanation:

This equation is in slope-intercept form, this is referring to the y-intercept. Slope-intercept is y=mx+b, where m is the slope and b is the y-intercept. Therefore, 10/9 is the intercept while -8 is the slope.

Answer:

2,300

Step-by-step explanation:

into hundredths.

that means each fish is cut into 100 pieces.

so, there would be

23 × 100 = 2,300

pieces of fish.

Answer:

A, 2,300.

Step-by-step explanation:

hope this helps lol

Answer:

I think the answers is 27, just add all of those squares.