Prove the following:

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

you find the slope by using this equation = y2 - y1 / x2 - x1.

For example, if you had two points, (2,4) and (3,6)

2 will be x1 because it's your first x. 3 will be x2 because it's your second x.

So with that pattern, 4 will be y1 and 6 will be your y2.

So the equation will be 6-4 / 3-2. That will equal 2/1 so the slope is 2.

Hope this helped.

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

3÷1/6

Step-by-step explanation:

here is your answer. If it helps don't forget to like and Mark me

Answer:

answer = 0

Step-by-step explanation:

99 x 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 ....etc

it will get zero eventually

Answer:

You have to put in the whole word problem

Step-by-step explanation:

Answer:

Savings accounts typically pay interest.

Step-by-step explanation:

Answer:

A , B and C

Step-by-step explanation:

evaluate the expressions following the order of operations as set out in PEMDAS

initial expression

note that • indicates multiplication

3 (2 + 6) + 4 × 5 ← evaluate parenthesis

= 3(8) + 20 = 24 + 20 = 44

A

5 × 4 + 3 × (6 + 2) ← evaluate parenthesis

= 5 × 4 + 3 × 8 ← perform multiplication

= 20 + 24 ← perform addition

= 44

B

(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis

= 8 × 3 + 4 × 5 ← perform multiplication

= 24 + 20 ← perform addition

= 44

C

3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications

= 6 + 18 + 20 ← perform addition

= 44

D

3 × 2 + (6 + 4) × 5 ← evaluate parenthesis

= 3 × 2 + 10 × 5 ← perform multiplication

= 6 + 50 ← perform addition

= 56

the expressions equivalent to the initial expression are A , B and C

A box that contains two times as many cubes as a box that is 2 by 3 by 5 can have dimensions of 2 by 3 by 10.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A box that is 2 by 3 by 5 has a total of 2 x 3 x 5 = 30 cubes. To build a box that will hold twice as many cubes, we need to find the dimensions that will give a total of 60 cubes.

Let's assume the dimensions of the new box are x, y, and z. Then, we have:

xyz = 60

We can express one of the variables in terms of the other two.

z = 60 / (xy)

Substitute this in above equation.

xy60/xy=60

60=60

This is true for any values of x and y, as long as z is calculated as z = 60 / (x y).

There are infinitely many solutions for the dimensions that will give a box with a total of 60 cubes.

set of dimensions that satisfies the condition is x = 2, y = 3, and z = 10.

Hence, a box that contains two times as many cubes as a box that is 2 by 3 by 5 can have dimensions of 2 by 3 by 10.

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Answer:

Step-by-step explanation:

$373 - $74 = $299

299 divided by 23 = 13

13 months (?)

Answer:

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Step-by-step explanation:

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Answer:

x>3

Step-by-step explanation:

|4x-5|>7

4x -5>7

4x >7+5

4x /4>12/4

x >3

solution set={4,5,6,---}

Answer:

see explanation

Step-by-step explanation:

Inequalities of the type | x | > a have solutions in the form

x < - a OR x > a thus

4x - 5 < - 7 ( add 5 to both sides )

4x < - 2 ( divide both sides by 4 )

x < - \(\frac{1}{2}\)

OR

4x - 5 > 7 ( add 5 to both sides )

4x > 12 ( divide both sides by 4 )

x > 3

Solution is x < - \(\frac{1}{2}\) or x > 3

This can be expressed in interval notation as

(- ∞, - \(\frac{1}{2}\) ) u (3, ∞ )

Answer:

124

Step-by-step explanation:

Based on the question, we are looking for a number that is equal to 31 when you divide the number by 4 (or multiply by 1/4, same thing). You can also represent this with an equation: 1/4x=31. This says: 1/4 of a number x is equal to 31.

1/4x=31

4(1/4x)=31(4)

x=124

You don't need an equation for this type of problem (you can simply multiply 31 by 4), but it can help if you are not sure what calculations to do!

The complete sentence is,

⇒ 1/4 of 124 = 31

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Let the number is,

⇒ x

Hence, We can formulate;

⇒ 1/4 of x = 31

Solve for x as;

⇒ 1/4 × x = 31

Multiply by 4;

⇒ x = 31 × 4

⇒ x = 124

Thus, The value of number is, 124

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Answer:

h=2(R-4)

h=2R-8

h+8=2R

h+8/2=R

so...R=h+8/2

Answer:

h+8/2

Step-by-step explanation:

h=2R-8

h+8=2R

h+8/2=R

R=h+8/2

Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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Answer:

because this is equal to the given matrix, the given matrix is symmetric.

Step-by-step explanation:

A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.

cot θ = 7/4 and θ in degrees = 29.744881 degrees. In this case, the adjacent side is 7 and the opposite side is 4.

Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle.

In this right angle triangle, cot θ can be calculated using the formula

cot θ = adjacent/opposite.

In this case, the adjacent side is 7 and the opposite side is 4.

Therefore, cot θ = 7/4.

Now, to find theta in degrees, we can use the inverse cotangent function, arccot.

arccot (cot θ) = θ.

Therefore, θ = arccot (7/4).

Using a calculator, arccot (7/4) = 29.744881 degrees

Therefore, cot θ = 7/4 and θ in degrees = 29.744881 degrees.

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Answer:

10520000 approximately I think

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7

The function f is guaranteed by the extreme value theorem to have an absolute maximum and an absolute minimum on the closed interval a. [-5, 5].

The extreme value theorem states that if a function f is continuous on a closed interval [a, b], then it must have both an absolute maximum and an absolute minimum on that interval. Since the function f is given as being defined on the closed interval [-5, 5], it must have both an absolute maximum and an absolute minimum on this interval.

We can check that the function f is continuous on the interval [-5, 5] as follows:

First, we need to check that the function is defined at every point in the interval. The function f is defined as f(x) = x+4/(x-1)(x+3). The only points at which this function is not defined are x = 1 and x = -3, which are not within the interval [-5, 5]. Therefore, the function is defined at every point in the interval.

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Answer:

so ez

Step-by-step explanation:

HI IM INDIAN AND STUDING IN 10TH GRADE U?

Answer:

No sollution

Step-by-step explanation:

It simple

Given data:

Wholesale price for a bookcase: $128

Furniture store marks up 19%.

1. Calculate the 19% of $128: Multiply 128 by 0.19 or (19/100)

2. Add $24.32 to the wholesale price:

Answer:

3.16227766017 is the answer

Answer: 3.16227766017

Step-by-step explanation:

Or you could round and get 3.2 or 3.16

Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

X = 13

1. Add 8 to both sides of the equation

5