Ask question

Ask question

All categories

3 years ago

11

Consider this expression and the steps to evaluate it. 45(−2)9 48(−2)3 1. Apply the quotient of powers: (−2)a 4b 2. Evaluate pow

ers: c d

1 answer:

olga nikolaevna [1]3 years ago

4 0

Answer:

a = 6

b = 3

c = 64

d= 64

Step-by-step explanation:

1. Apply the quotient of powers:

$(-2)^a / 4^b$

In the given expression:

$4^5(-2)^9/4^8(-2)^3$

base same then the powers are subtracting if the bases are in numerator and denominator

i.e $a^m/a^n = a^{m-n}$

Solving:

$=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3$

therefore, the values of a and b are: a = 6

b = 3

2. Evaluate Powers

c/d

We have

$(-2)^6/4^3$

When power is even negative sign changes into plus sign

64/64

Therefore, we get the values of c and d

c = 64

d= 64

You might be interested in

A plan that costs $29.99 another company $19.99 and $0.35 during nights and weekends for what numbers of night and weekend does

Masja [62]

Answer:

<em>29 minutes more</em>

Step-by-step explanation:

Let m represent minutes

changing the statement to algebra, since the second company charges a different rate at night and weekend we have the equation below;

$19.99 + $0.35m > $29.99

Subtract 19.99 from both sides to isolate m and we have;

$19.99 -$19.99 + $0.35 > $29.99 - $19.99

= $0,35m > $10.00

Divide both side by 0.35 to obtain the value of m;

$\frac{0.35m}{0.35}$ > $\frac{10}{0.35}$

= m > 28.57

<em>m ⩾ 29 minutes</em>

<em>The second company's will be twenty nine minutes or more costlier than the first company</em>

5 0

3 years ago

Read 2 more answers

1. Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the sec

Alex

Answer:

Step-by-step explanation:

b) 1- scale factor from the first map to the second map:

$\frac{8}{6}$ = 1.33

2- landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

Side lengths of the landmark on the second map

Divide the length by scale factor:

side lengths of 3 mm: $\frac{3}{1.33}$ = 2.25 mm

side lengths of 4 mm: $\frac{4}{1.33}$ = 3.007 mm

side lengths of 5 mm: $\frac{5}{1.33}$ = 3.75 mm

5 0

3 years ago

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

scZoUnD [109]

Answer:

Option B m<ZA+m<ZB = 155° is correct option.

Step-by-step explanation:

We know that sum of angles of triangle is equal to 180°

And Isosceles triangle, 2 angles are same

So, let Angle 1 = x

Angle 2 = x

Angle 3 = 130°

Finding values of angle x

x+x+130=180

2x=180-130

2x=50

x=25

So, Angle 1 = 25 °

Angle 2 = 25°

As, angle B is greater than 90°, the sum of angles added must be greater than 90°

So, Option A, C and D can't be correct, as their sum is less than 90°

Option B m<ZA+m<ZB = 155° is correct option.

Verify:

m<ZA = 25° (as found earlier)

m<ZB = 130° (given)

So, m<ZA+m<ZB = 155°

25°+130° = 155°

8 0

2 years ago

A team of scientist surveying a forest found that there were four oak trees for every 10 pine trees. If they counted 24 more pin

Ipatiy [6.2K]

Answer:

There are 16 Oak tree in the forest.

Step-by-step explanation:

Given: There are 4 Oak tree on every 10 pine trees.

There are total 24 more pine tree than Oak tree.

Using the ratio of trees to find the number of trees.

Lets assume there are total number of Oak tree be "x".

∴ Total number of Pine trees will be $"x+24"$

We know the ratio of Oak to Pine tree is 4:10 or $\frac{4}{10}$

⇒ $\frac{x}{x+24} = \frac{4}{10}$

Multiplying both side by $x+24$

⇒ $x= \frac{4(x+24)}{10}$

Using distributive property of multiplication, distributing 4 with x and 24.

⇒ $x= \frac{4x+96}{10}$

Multiplying both side by 10

⇒ $10x= 4x+96$

subtracting both side by 4x

⇒ $6x= 96$

dividing both side by 6

⇒ $x= \frac{96}{6}$

∴ $x= 16$

Hence, There are 16 Oak trees in the forest.

5 0

3 years ago

Please help me thank you so much. Just not sure of my answers

Sedaia [141]

Answer:

An interesting experiment is given. We need to address various questions based on our knowledge of calculus.

Step 2

Part (a)

Time taken for the radius to grow to 2 cm = t1 = r/0.5 = 2/0.5 = 4 hours

Time taken for the radius to become 0 = t2 and the same can be obtained by solving:

r = 2 - √t2 = 0

Hence, t2 = 22 = 4 hours

Hence, the time duration of the entire experiment (from the introduction of the bacteria until its disappearance) = t1 + t2 = 4 + 4 = 8 hours

Step 3

Part (b)

r(t) = 0.5t for 0 ≤ t ≤ 4

and

r(t) = 2 - √(t - 4) for t > 2

Step-by-step explanation:

7 0

3 years ago