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3 years ago

Please help me

Mathematics

2 answers:

aleksley [76]3 years ago

8 0

Step-by-step explanation:

A. Exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r.

dexar [7]3 years ago

5 0

Answer:

a) f(x) = a(1 + r)x

Step-by-step explanation:

exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r.

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How to find the factor of a trinomial?

BaLLatris [955]

I can tell you about the 'ac' method of factoring trinomials by way of an example:-

Factor 3x^2 - 4x - 15

first multiply the first number by the last That is 3 * -15 = -45

Now we need to find 2 factors of -45 which will when added give - 4 ( the coefficient of x)

-9 and = 5 look like the ones so we write

3x^2 - 9x + 5x - 15

Now factor this by grouping:-

= 3x(x - 3) + 5(x - 3)

x - 3 is common to the 2 parts so we have:-

(3x + 5)(x - 3) <-------- These are your factors

Any trinomial can be factored in this way.

6 0

4 years ago

Determine the mechanical energy of this object a 1kg pendulum at a height of 1-meter

Lemur [1.5K]

Answer:

Step-by-step explanation:

Mechanical energy (ME) is Kinetic energy + potential energy

Where

Kinetic Energy (KE) = 1/2 * m * v^2

where m is the mass (in kg) and v is the speed of the object (in m/s)

and

Potential Energy (PE) = m*g*h

Where m is the mass (in kg) and g is the gravitational constant (9.81 m/s) and h is the height (in meters)

Hence

ME = KE + PE (note the pendulum DOES NOT have any speed, so v = 0, and thus KE = 0)

So,

$ME=KE+PE\\ME=\frac{1}{2}mv^2+mgh\\ME=\frac{1}{2}(1)(0)^{2}+(1)(9.81)(1)\\ME=0+9.81\\ME=9.81$

Hence, Mechanical Energy is 9.8 Joules (rounded to 1 decimal place). Correct answer is A.

7 0

3 years ago

Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th

Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is $\frac{1}{t}$

∵ The rate of Mary is $\frac{1}{t+3}$

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by $\frac{1}{2}$ (their rate together)

∴ $\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}$

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ $\frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}$

- Add the two fractions in the left hand side

∴ $\frac{t+3+t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{2t+3}{t^{2}+3t}=\frac{1}{2}$

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0

3 years ago

Angle Submit Answer 98 85 View One Minute Version Angles - Check My Underst

yulyashka [42]

Answer:

x = 13°

Step-by-step explanation:

Check the diagram attached below to see how the angles labelled A and B, which are interior angles of the triangle where x is found.

Let's find the measure of angle A and angle B.

m<A = 85° (vertical angles are congruent)

m<B = 180° - 98° = 82° (corresponding angles/supplementary angles)

Thus:

x + A + B = 180° (sum of interior angles of a ∆)

x + 85° + 82° = 180° (substitution)

x + 167 = 180

x = 180 - 167 (Subtraction property of equality)

x = 13°

4 0

3 years ago

Which solid has congruent horizontal and vertical cross sections?

Zinaida [17]

Answer:

triangular prism (pyramid) and cylinder.

Step-by-step explanation:

A pyramid is a polyhedron with one base that is a polygon and faces that are triangles.

A cylinder is a three-dimensional figure with congruent, parallel bases that are circles connected with a curved side.

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3 years ago