the area of a square is 32 cm. find the length of the diagonal

The depth of water in tank A is modeled by a differentiable and increasing function h.

This means that the function h describes how the depth of water changes as time passes.

The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.

This makes sense since water is constantly being added to the tank.

Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.

learn more about function click here:

https://brainly.com/question/11624077

#SPJ11

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

To learn more on logarithms: https://brainly.com/question/30226560

#SPJ1

ansewr: the ansewr is b

explanation: did it

Answer:

A) f=8 8/9

Step-by-step explanation:

f+2/9=9 1/9

f+2/9=82/9

f=82/9-2/9

f=80/9

f=8 8/9

Answer:

No

Step-by-step explanation:

Congruent tests: Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Right angle-Hypothenuse-Side any 1 tests must be the same for both triangles

in this case, only the 3 angles are the same, which is a similarity test, not a congruence test

this is a topic on similarity and congruency. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I'll be posting the notes for this topic soon and will also be posting other topics' notes and some tips :)

Congruent triangles are similar triangles.

There is no enough information to prove that the triangles are congruent

For triangles to be congruent, then the corresponding sides and angles must be congruent.

From the attached figure, only the angles of the triangles are guaranteed to be congruent.

There is no information about the sides of the triangles.

Hence, there is no enough information to prove that the triangles are congruent

Read more about congruent triangles at

https://brainly.com/question/22062407

Answer:

13i, -13i

Step-by-step explanation:

x^2=-169

169=(13)^2

x^2=-(13)^2

the square root of -1 is i ( imaginary number )

(-13)^2=(13)^2 so x is 13i and -13i

Answer:

13i

Step-by-step explanation:

So I would solve for x

This is zero term factoring

This is a square root factor and 169's square root is 13.

However we need to factor -169

This is where imaginary numbers come in. i= Square root of -1

13i would be the answer

Answer:

\( {x}^{2} + {(y - 139)}^{2} = {125}^{2} \)

Answer:

D

Step-by-step explanation:

A. The domain of this function is infinite, since x can be any number.

B. To find the y intercept, you need to set x to 0. 7^x will become 1, and 6*1=6, so the y intercept is (0,6).

C. This function is not always decreasing. For instance, when x is positive, it exponenentially increases.

D. As I said before, the y intercept of the function is (0,6), meaning that this statement is correct.

Hope this helps!

Answer:

D.

Step-by-step explanation:

The lateral surface area measures the area of the outside of the 3D shape. *Doesn't include the bases.

Since the measure of the outside of a cylinder is essentially a RECTANGLE, the formula for area is length x width. The length here would be the height, the width would be the circumference.

Answer:

BG

Step-by-step explanation:

because the others are just diagnols through a particular side, not through the center of the cube.

Answer:

(9.52/9.65)×100 = 98.65

your 100% value decreased to 98.65

net percentage decrease: 100-98..65

=1.347 or 1.35 (rounded)

Answer: Winston should invest $75,000 in the high-risk fund and $525,000 in the low-risk fund to achieve his retirement income goal.

Step-by-step explanation:

Let x be the amount of money invested in the high-risk fund, and y be the amount of money invested in the low-risk fund. We know that x + y = $600,000, since that is the total amount Winston plans to invest.

We also know that the high-risk investments should return 12% per year, and the low-risk investments should return 4% per year. Therefore, the total return on his investment will be:

0.12x + 0.04y

Winston wants a supplemental income of $30,000 per year. We can set up an equation for this as well:

0.12x + 0.04y = $30,000

We can use the equation x + y = $600,000 to solve for one of the variables in terms of the other. For example, we can solve for y as follows:

y = $600,000 - x

Substituting this expression for y into the equation for the total return, we get:

0.12x + 0.04($600,000 - x) = $30,000

Simplifying and solving for x, we get:

0.12x + $24,000 - 0.04x = $30,000

0.08x = $6,000

x = $75,000

Winston should invest $75,000 in the high-risk fund and $525,000 in the low-risk fund to achieve his retirement income goal.

Answer:

y

2

​

=−

2

z

​

+7

Steps for Solving Linear Equation

z=18−2×2−2y2

Multiply 2 and 2 to get 4.

z=18−4−2y

2

​

Subtract 4 from 18 to get 14.

z=14−2y

2

​

Swap sides so that all variable terms are on the left hand side.

14−2y

2

​

=z

Subtract 14 from both sides.

−2y

2

​

=z−14

Divide both sides by −2.

−2

−2y

2

​

​

=

−2

z−14

​

Dividing by −2 undoes the multiplication by −2.

y

2

​

=

−2

z−14

​

Divide z−14 by −2.

y

2

​

=−

2

z

​

+7

Step-by-step explanation:

the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.

we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.

Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.

the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.

To know more about paraboloid, visit:

https://brainly.com/question/30925041

#SPJ11

Answer:

2/-5

Step-by-step explanation:

slope formula

(y2 - y1)/(x2 - x1)

(–3 - (–5))/(–7 - (–2))

(–3 + 5 )/(–7 +2 )

2/-5

Using the common factors, the expression can be rewritten as follows:

The expression can be represented as follow using common factor.

1 / 4 x³y + 3 / 4 xy²

Using the common factors,

The common factors of 1 / 4 x³y  and  3 / 4 xy² is 1 / 4 xy.

Therefore,

1 / 4 x³y + 3 / 4 xy² = 1 / 4 xy (x² + 3y)

Therefore, rewriting 1 / 4 x³y + 3 / 4 xy² using the common factors is 1 / 4 xy (x² + 3y).

learn more on common factors here: https://brainly.com/question/22179235

#SPJ1

Answer:

Step-by-step explanation:

12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12

Answer:

V÷ 2

Step-by-step explanation:

Get peevious number and divide by half.

Answer:

3+3+3+3+3+3+3+3+3=27

Step-by-step explanation:

just add it together.

Answer:

2

Step-by-step explanation:

Isolate the variable:

6x - 5 = 7

     +5   +5

6x = 12

/6     /6

x = 2

Check our work:

6(2) - 5 =7

12 - 5 = 7

7 = 7

Correct!

If row-reducing the augmented matrix does not produce any non-zero entries in the right-hand side, then the columns of A are linearly independent.

To determine if the columns of matrix A form a linearly independent set, we need to check if the equation Ax = 0 has only the trivial solution x = 0.

Let's assume the given matrix A is:

A = [a1, a2, a3, ..., an]

If the columns of A are linearly independent, then the equation Ax = 0 has only the trivial solution.

To solve the equation Ax = 0, we set up the augmented matrix [A | 0] and row-reduce it:

[A | 0] =

[a1, a2, a3, ..., an | 0]

Row-reducing the augmented matrix will help us determine if there are any non-trivial solutions to the equation Ax = 0.

If row-reducing the augmented matrix leads to a row of zeros with a non-zero entry in the corresponding row of the right-hand side (0), then the columns of A are linearly dependent, and there exists a non-trivial solution.

If row-reducing the augmented matrix does not produce any non-zero entries in the right-hand side, then the columns of A are linearly independent.

By performing row operations on the augmented matrix [A | 0] and examining the resulting row echelon form, we can determine if the columns of A are linearly dependent or independent and find the dependence relation if they are dependent.

To learn more about equation visit;

https://brainly.com/question/29657983

#SPJ11

Answer:

1.5 pounds

Step-by-step explanation:

Answer:

Step-by-step explanation:

Candice = 25mph for 4 hours.

Candice has driven= 25 * 4= 100miles.

Liz =50mph

Liz time to catch up to candice= 50 * 2= 100miles.

Therefore, It would have taken Liz two hours to catch up with Candice

x = -32/11 This answer doesn't make sense because we can't have a negative number of students in a van.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

Let's assume that each van has 'x' number of students and each bus has 'y' number of students.

From the given information, we know that:

High School A rented 14 vans and 3 buses, with a total of 307 students.

High School B rented 2 vans and 4 buses, with a total of 226 students.

We can express this information in the form of equations:

14x + 3y = 307 --- equation 1

2x + 4y = 226 --- equation 2

We can simplify equation 2 by dividing both sides by 2, which gives:

x + 2y = 113 --- equation 3

Now we have two equations with two variables, which we can solve simultaneously. We can start by multiplying equation 3 by 3, which gives:

3x + 6y = 339 --- equation 4

We can now subtract equation 4 from equation 1, which eliminates the variable 'y':

14x + 3y - (3x + 6y) = 307 - 339

Simplifying this equation gives:

11x = -32

Dividing both sides by 11 gives:

x = -32/11

However, this answer doesn't make sense because we can't have a negative number of students in a van. This suggests that there may be an error in the problem statement.

Alternatively, if we assume that the problem statement is correct and there are no errors, we can solve the equations as follows:

Multiplying equation 3 by 3 gives:

3x + 6y = 339

Subtracting equation 2 from this gives:

3x + 6y - (2x + 4y) = 339 - 226

Simplifying this gives:

x + 2y = 113

Now we have two equations with two variables:

14x + 3y = 307

x + 2y = 113

We can solve this system of equations using substitution or elimination. Here, we will use elimination. Multiplying equation 2 by 3 gives:

3x + 6y = 339

Subtracting this from equation 1 gives:

14x + 3y - (3x + 6y) = 307 - 339

Simplifying this gives:

11x = -32

Dividing both sides by 11 gives:

x = -32/11

This answer doesn't make sense because we can't have a negative number of students in a van. Therefore, we conclude that there may be an error in the problem statement.

To learn more about quadratic equation from the given link:

brainly.com/question/30098550

#SPJ9

Answer:

18.84

Step-by-step explanation:

The diameter is 2 times the radius, so just multiply 6 by 3.14

please mark brainliest ( :

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's calculate the circumference ~

\(\qquad \sf  \dashrightarrow \: c = \pi d\)

\(\qquad \sf  \dashrightarrow \: c = 3.14 \times 6\)

\(\qquad \sf  \dashrightarrow \: c =18.84 \: ft\)

Answer:

x = 13.2

Step-by-step explanation:

cos ∅ = base / hypotenuse

cos 25° = 12 / x

cos 25° * x = 12

.91 * x = 12

x = 12 / .91

= 13.18

by rounding off to the nearest tenth,

x = 13.2

Answer:

\(a_4=19\)

Step-by-step explanation:

Given:

\(\implies a_2=a_{1}+4=7+4=11\)

\(\implies a_3=a_{2}+4=11+4=15\)

\(\implies a_4=a_{3}+4=15+4=19\)

Put values get answer

The value of the given expression is \(\frac{1}{5}\). The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," can be used to describe all the real numbers. The operations like division, multiplication, addition, and subtraction gives the results as quotient, product, sum, and difference respectively in mathematics.

We are given an expression as \(\frac{3}{5}\) - \(\frac{2}{5}\).

Since, both the terms have the same denominator which is 5 so, using the subtraction operation, we get the following value:

⇒  \(\frac{3}{5}\) - \(\frac{2}{5}\) =  \(\frac{1}{5}\)

Hence, the second option is the correct answer.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ1