Dimension of triangle A are three times the dimensions of triangle
b. The area of triangle A is 252 cm squared. What is the area of triangle B?

Answer:

The value of a is -2 and the value of b is 4.

Step-by-step explanation:

Given expression is,

[tex](4x^a)^b = \frac{256}{x^8}[/tex]

Using [tex](ab)^m=a^m.b^n[/tex] on left side,

[tex]4^b(x)^{ab}=\frac{4^4}{x^8}[/tex]     ( [tex]4^4 = 256[/tex] )

Using [tex]a^m=\frac{1}{a^{-m}}[/tex],

[tex]4^b(x)^{ab}=4^4 (x)^{-8}[/tex]

By comparing both sides,

We get,

b = 4 and ab = -8

⇒ a = -2

Hence, the value of a is -2 and the value of b is 4.

The expression for the volume of the box is given by 6x³+11x²-3x-2

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, rectangular box with three sides visible, having width, length, and height of x plus two, two x minus one, and three x plus one

Height = x+2

Width = 2x+1

Length = 3x+1

Volume = HxLxW

Volume = (x+2)(2x+1)(3x+1)

= 2x²-x+4x-2(3x+1)

= (2x²+3x-2)(3x+1)

= 6x³+11x²-3x-2

Hence, The expression for the volume of the box is given by 6x³+11x²-3x-2

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The balance after 2 years when the interest is compounded daily is

$1,725.39.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Given:

P= $1500

R= 7%

T = 2 years

Now, using

A = P[tex](1 + r/n)^{nt[/tex]

A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]

A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]

A = $1,725.39

Hence, the balance is $1,725.39.

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The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.

To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).

Therefore, to fit a 40-cm chopstick along the diagonal:

Let d = 40 cm.

Use the equation s√2 = 40 cm to find s, the side of the square.

s = 40 cm / √2.

s ≈ 28.284 cm when rounded to three decimal places.

So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.

Answer:

The system has two solution

Step-by-step explanation:

we have

[tex]y=-2x+2[/tex] ----> equation A

[tex]y=x^{2}-3x[/tex] ----> equation B

Solve the system of equations by graphing

Remember that

The solution of the system of equations is the intersection point both graphs

There are two point of intersection between the two graphs

see the attached figure

therefore

The system has two solution

The answers are:

1. Barter

2. charge card

3. principal

4. interest accured

Hi there! :)

Answer:

x=39

*The answer must have a positive sign.*

Step-by-step explanation:

When the 2 acute angles in which means you had to used 2x from both sides of an equation.

First, only had to do is, add by 15 from both sides of an equation.

[tex]3x-15+15=2x+24+15[/tex]

Then, you add by the numbers from left to right.

[tex]24+15=39[/tex]

[tex]3x=2x+39[/tex]

Next, you subtract by 2x from both sides of an equation.

[tex]3x-2x=2x+39-2x[/tex]

Finally, you simplify.

[tex]x=39[/tex]

Final answer is x=39

Hope this helps!

Thanks!

Have a nice day! :)

:D

-Charlie

Answer:

∠A = 26°

Explanation:

If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. In case of similar triangle, corresponding angles are congruent.

Angle ∠C = 76

So, ∠T = 76     because of corresponding angle.

Given that,

m∠S=3(m∠A)

We know that,

∠S ≅ ∠B

That means ∠B = 3 (∠A)

Sum of angles in a triangle  = 180°

∠A + ∠B + ∠C = 180°

∠A + 3∠A + 76° = 180°

4∠A = 180° - 76°

4∠A = 104°

∠A = [tex] \frac{104}{4}  [/tex]

∠A = 26°

Final answer.

Answer:

Option 4th is correct.

[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

Step-by-step explanation

The explicit sequence of the geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]              ....[1]

where,

r is the common ratio

n is the number of terms

[tex]a_1[/tex] is the first term

As per the statement:

The explicit rule for a sequence is:

[tex]a_n=9(-5)^{n-1}[/tex]

On comparing [1] we have;

[tex]a_1 = 9[/tex] and r=  -5

Recursive formula for the geometric sequence is given by:

[tex]a_n = r \cdot a_{n-1}[/tex]  for [tex]n\geq 2[/tex]

Substitute the given values we have;

[tex]a_n = -5 \cdot a_{n-1}[/tex]

Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

The simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

To simplify each expression, we combine like terms:

Expression 1:

12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)

12x + 3 − 4x + 7 = 8x + 10

Expression 2:

8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5

Expression 3:

−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.

Therefore, the simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

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