All categories

3 years ago

Find the equivalent exponential expression. (4^2)4

Mathematics

1 answer:

steposvetlana [31]3 years ago

3 0

Answer:

4^8

Step-by-step explanation:

If the second 4 is an exponent, as in (4^2)^4, then multiply the exponents.

(4^2)^4 = 4^(2 * 4) = 4^8

You might be interested in

Homer wants to identify the center and radius of the circle defined by the equation x2 + y2 - 14x +

Klio2033 [76]

Homer has made mistake in step 2

When you complete the square, you need to add the values to both sides of equation

Solution:

Given equation of circle:

$x^2 + y^2 -14x + 2y -25 = 0$

Let us first calculate center and radius and find out where he did the mistake

Step 1:

Group the terms

$x^2 -14x + y^2 + 2y = 25\\\\(x^2 -14x) + (y^2 + 2y) = 25$

Step 2:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 25 + 49 + 1$

But homers step 2 is:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 25$

So homer has made mistake in this step

When you complete the square, you need to add the values to both sides of equation

But homer did not add 49 and 1 to right side of equation

Correct steps are:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 75\\\\(x-7)^2 + (y+1)^2 = 75$

Comparing general equation of circle,

$(x-h)^2 + (y-k)^2 = r^2$

Therefore, center is ( 7, -1) and radius is 8.66

8 0

3 years ago

Arrange the pairs of points in increasing order of slopes of the lines joining them

sladkih [1.3K]

Answer:

(27,2) and (243,18)

(63,9) and (84,12)

(45,15) and (60,20)

(27,12) and (72,32)

(15,30) and (20,40)

(12,32) and (18,48)

(18,63) and (24,84)

Step-by-step explanation:

Formula for slope of a line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

a) (15,30) and (20,40).

$m_a=\dfrac{40-30}{20-15}=\dfrac{10}{5}=2$

Similarly find the slope of other lines.

b) (12,32) and (18,48).

$m_b=\dfrac{48-32}{18-12}=\dfrac{16}{6}=2.67$

c) (27,12) and (72,32).

$m_c=\dfrac{32-12}{72-27}=\dfrac{20}{45}=0.44$

d) (45,15) and (60,20).

$m_d=\dfrac{20-15}{60-45}=\dfrac{5}{15}=0.33$

e) (27,2) and (243,18).

$m_e=\dfrac{18-2}{243-27}=\dfrac{16}{216}=0.074$

f) (18,63) and (24,84).

$m_f=\dfrac{84-63}{24-18}=\dfrac{21}{6}=3.5$

g) (63,9) and (84,12).

$m_g=\dfrac{12-9}{84-63}=\dfrac{3}{21}=0.143$

After arranging the slopes in increasing order, we get

$m_e$

So, required arrangement of ordered pairs is

(27,2) and (243,18)

(63,9) and (84,12)

(45,15) and (60,20)

(27,12) and (72,32)

(15,30) and (20,40)

(12,32) and (18,48)

(18,63) and (24,84)

7 0

3 years ago

A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the n

liberstina [14]

Given:
adults = x
male = 7x + 1
female = (7x + 1)/2
total number of people = 82

x + (7x + 1) + [(7x +1)/2] = 82
2x/2 + (14x + 2)/2 + (7x + 1)/2 = 82
2x + 14x + 2 + 7x + 1 = 82 * 2
23x + 3 = 164
23x = 164 - 3
23x = 161
x = 161/23
x = 7

adults = x = 7
males = 7x + 1 = 7(7) + 1 = 49 + 1 = 50
females = (7x+1)/2 = 50/2 = 25

7 + 50 + 25 = 82

6 0

3 years ago

What’s the correct graph ?

maks197457 [2]

Answer:

The correct graph is graph E.

Step-by-step explanation:

We can tell this because we know the graph must stay below 3. So any graph over 3 gets thrown out. We also know that it must not go further down than -3. This is because any number over -3 as an input, when taking an absolute value, would be greater than 3.

Graph E shows numbers that are all less than 3 and greater than -3.

8 0

3 years ago

Please help i don't understand it

Leto [7]

Answer:

for question #1) 6 times n + 12 = 60

Step-by-step explanation:

it works trust me

ps. im in high school in a GT math class

8 0

3 years ago