I'm confused, can someone please help?!​

Note: Consider the given figure attached with this question.

Given:

The expression is:

[tex]2^5\times 2^4[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]2^5\times 2^4[/tex]

It can be written as:

[tex]2^5\times 2^4=2^{5+4}[/tex]

[tex]2^5\times 2^4=2^{9}[/tex]

So, option A is correct and option B is incorrect.

Similarly, in options C, D, E,

[tex]2\cdot 2^9=2^{10}[/tex]

[tex]2^{10}\cdot 2^2=2^{12}[/tex]

[tex]2^{-2}\cdot 2^{11}=2^{9}[/tex]

So, options C and D are incorrect but option E is correct.

The given expression can be written as:

[tex](2\cdot 2\cdot 2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2\cdot 2)[/tex]

So, option F is correct.

Therefore, the correct options are A, E F.

Answer:

El área es 2 veces el cuadrado del ancho del rectángulo.

Step-by-step explanation:

El área de un rectángulo viene dado por:

[tex] A = a*l [/tex]

En donde:

a: es el ancho

l: es el largo

Si el largo es el doble del ancho:

[tex] l = 2a [/tex]

Entonces el área es:

[tex] A = a*l = a*(2a) = 2a^{2} [/tex]

Por lo tanto, el área es 2 veces el cuadrado del ancho del rectángulo.

Espero que te sea de utilidad!  

Answer:

She has 23 nickels and 5 dimes.

Step-by-step explanation:

Let n = the number of nickles and d = the number of dimes.

The number of each = 28. Set up the equation:

n + d = 28

Solve for n:

n = 28 - d

The total amount is $1.65 or 165 cents:

5n + 10d = 165

Substitute:

5(28 - d) + 10d = 165

140 - 5d + 10d = 165

140 + 5d = 165

5d = 165 - 140

5d = 25

d = 5, the number of dimes.

Solve for n:

n = 28 - d

n = 28 - 5 = 23, the number of nickles.

Proof:

5n + 10d = 165

5(23) + 10(5) = 165

115 + 50 = 165

165 = 165

Hope this Helps! Have an Awesome Day!!! <3

Step-by-step explanation:

Answer:

Sofia has 23 nickles & 5 dimes

Step-by-step explanation:

The number of each is 28

Form an equation:

[tex]n+d=28[/tex]

Solve for n:

[tex]n=28-d[/tex]

The total amount is $1.65 for 165 cents:

[tex]5n+10d=165[/tex]

Substitute:

[tex]5(28-d)+10d=165[/tex]

[tex]140-5d+10d=165[/tex]

[tex]140+5d=165[/tex]

[tex]5d=165-140[/tex]

[tex]5d=25[/tex]

[tex]d=25/5[/tex]

[tex]d=5[/tex]

Solve for n:

[tex]n=28-d[/tex]

[tex]n=28-5=23[/tex] ⇒ the number of nickles

CHECK:

[tex]5n+10d=165[/tex]

[tex]5(23)+10(5)=165[/tex]

[tex]115+50=165[/tex]

[tex]165=165[/tex]

hope this helps....

Answer:

yeah the answer is one of those just pick one

Answer:

[tex]m=6[/tex]

Step-by-step explanation:

Exponent properties:

We can use exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to solve this problem.

Rewrite [tex]8[/tex] as [tex]2^3[/tex], then apply exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to simplify:

[tex]2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}[/tex]

If [tex]a^b=a^c[/tex], then [tex]b=c[/tex], because of log property [tex]\log a^b=b\log a[/tex]. Using this log property, you can take the log of both sides and divide by [tex]\log a[/tex] to get [tex]b=c[/tex]

Therefore, we have:

[tex]15=2m+3[/tex]

Subtract 3 from both sides:

[tex]12=2m[/tex]

Divide both sides by 6:

[tex]m=\frac{12}{2}=\boxed{6}[/tex]

Alternative:

Given [tex]8^5=2^{2m+3}[/tex], to move the exponent down, we'll use log properties.

Start by simplifying:

[tex]\log 32,768=2^{2m+3}[/tex]

Take the log of both sides, then use log property [tex]\log a^b=b\log a[/tex] to move the exponent down:

[tex]\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2[/tex]

Divide both sides by [tex]\log2[/tex]:

[tex]2m+3=\frac{\log (32,768)}{\log(2)}[/tex]

Subtract 3 from both sides:

[tex]2m=\frac{\log (32,768)}{\log(2)}-3[/tex]

Divide both sides by 2:

[tex]m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}[/tex]

Answer:

Find the area of the triangle from the coordinate plane.

Y

A

10-

5-1

с

B.

0

-20

-15

-10

-5Step-by-step explanation:

Answer:

The cost of an adult ticket is $12.50

Step-by-step explanation:

The given information are;

The cost of two adult tickets and three children tickets = $43.00

The cost of one adult ticket and one child ticket = $18.50

Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;

2·x + 3·y = 43.00...(1)

x + y = 18.5...(2)

(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;

2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6

2·x - 2·x + 3·y - 2·y = 0 + y = 6

∴ y = 6

The cost of each the children ticket = $6.00

From equation (2), where y = 6, we get;

x + y = 18.5

∴ x + 6 = 18.5

x = 18.5 - 6 = 12.5

The cost of an adult ticket, x = $12.50.

Answer:

95%-70%=15%

$876.08×15% =$131.412

Answer:

512.51

Step-by-step explanation:

Hope this helps! :)

Answer:

(x + 6)² + (y - 4)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 6, 4 ) and r = 3 , then

(x - (- 6) )² + (y - 4)² = 3² , that is

(x + 6)² + (y - 4)² = 9

Answer:

x = 27

Step-by-step explanation:

I'm going to use letters to label the parts of the triangle while explaining how to solve for x:

Angle A = x (bottom left angle of the triangle)

Angle B = 4x (top angle of the triangle)

Angle C = empty angle (bottom right angle of the triangle)

Angle D = 3x + 54 (angle outside of the triangle)

A line has a angle measurement of 180 degrees.

Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.

To find Angle C, we would subtract Angle D's equation from 180 like this:

180 - (3x + 54)

Now Angle C equals 180 - (3x + 54)

Now we have all the angles inside the triangle. To find x, we are going to sum up  Angle A, B, & C and set it equal to 180.

We set the equation to 180 because a the sum of the interior angles for a triangle is 180.

The equation looks like this:

(180 - (3x + 54)) + 4x + x = 180

Now we use basic algebra to solve it:

(180 - (3x + 54)) + 4x + x = 180

(distribute the - to (3x + 54))

180 - 3x - 54 + 4x + x = 180

(add like terms on the left side of the equation)

126 + 2x = 180

(subtract 126 from both sides)

2x = 54

(divide both sides by 2)

x = 27

To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.

Hope it helps (●'◡'●)

Answer:

one solution

Step-by-step explanation:

Answer:

9= 512m/1000m

SIMPLIFY IT

Step-by-step explanation:

Answer:

yeah it is

y is directly proportional to x

proportionality constant is 9

Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

Answer:

[tex]\frac{15}{ \sqrt{31} - 4}} = \sqrt{31} + 4[/tex]

Step-by-step explanation:

[tex]\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4[/tex]

Answer:

I guess that we want to find the equation for each case.

First, let's define the translations:

Horizontal translation.

For a function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, the translation is to the left

if N < 0, the translation is to the right.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

if N > 0, the translation is upwards

if N < 0, the translation is downwards.

Now that we know these, we can find the equations for each case:

1. the graph of y = x² is moved five units upward

the graph is given by a vertical translation of 5 units upward.

y = x^2 + 5

2 the graph of y = 5x² is moved six units to the left

this is:

y = 5*(x + 6)^2

3: the graph of y = -2x² is moved seven units downward

this is:

y = -2x^2 - 7

4: the graph of y = -x² is moved two units to the left and four units downward

now we have two translations, first 4 units to the left and then 4 units downwards, this gives:

y = -(x + 4)^2 - 4

5: the graph of y = -3x² is moved two units to the right

Remember that to move the graph to the right, we need to have N negative, then:

y = -3(x - 2)^2

Answer:

the equation would be (x+5)2+(y−4)2=r2

Step-by-step explanation:

The equation would be

(x+5)2+(y-4)2=r2

Answer:

I believe the answer should be 0 to -1

Step-by-step explanation:

the range of a function is the lowest y value to the highest y value of that function. so in that example, the lowest y value you have on that curved line is at 0, and the highest y value you have on that curved line is 1, so the range should be from 0 to 1, or {0, 1}.

Answer:

20,160

Step-by-step explanation:

The arrangement of the 9 differently colored bead can be presented as follows;

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

Where 1 is the purple bead and 2 is the green bead, the number of ways of arrangement where the green bead cannot be adjacent to the green either horizontally, vertically, or diagonally

Placing the purple bead at 1, the location of the green bead = 3, 6, 7, 8, or 9

The number of ways = 5 ways × 7! ways of arranging the other beads

With the purple bead at 2, the location of the green bead = 7, 8, or 9

The number of ways = 3 × 7!

With the purple at 3, we also have 5 × 7! ways

At 4, similar to 2, we have, 3 × 7! ways

At 5, we have, 0 × 7!

At 6, we have 3 × 7!

For 7, 8, and 9, we have, (5 + 3 + 5) × 7!

The total number of ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7! ways

However, placing the purple bead at 1, 2, 3, 4, 6, 7, 8, and 9, (8 positions) can be taken as reflection and rotation of each other and can be considered the same

Therefore, the total number of acceptable ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7!/8 = 20,160 ways

===========================================================

Explanation:

Let's label the friends as A,B,C,D.

Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.

Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.

Person C's probability is 5/14 and person D has a probability of 4/13

-------------------------

So we have these fractions: 7/16, 6/15, 5/14, 4/13

Once again, we have the numerators and denominators counting down by 1 each time.

Multiplying those fractions gets us...

(7/16)*(6/15)*(5/14)*(4/13)

(7*6*5*4)/(16*15*14*13)

840/43680

(1*840)/(52*840)

1/52

So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.

1/52 = 0.0192 = 1.92% approximately

So this happens about 1.92% of the time.

Answer:

358

Step-by-step explanation:

the step by step is in the photo so look at it

Answer:

Maximum at (-5, 3)

Step-by-step explanation:

The quadratic equation is in vertex form, which specifically shows the vertex.

Since the a is negative, you get a maximum y value of 3.

Vertex form: y=a(x-h)^2+k

Answer:

27 cm²

Step-by-step explanation:

The surface area is the area of the square plus the area of the 4 congruent triangles.

area of square = 3² = 9 cm²

area of 1 triangle = [tex]\frac{1}{2}[/tex] × 3 × 3 = 4.5 cm²

area of 4 triangles = 4 × 4.5 = 18 cm²

Total surface area = 9 + 18 = 27 cm²

Step-by-step explanation:

SA of a pyramid

=L(2h+L)

=3(2(3)+3)

=3(9)

=27cm^2

Answer:

[tex]-1\leq x<\infty[/tex]

Step-by-step explanation:

We want to convert the interval [-1, ∞) to inequality notation using x as the variable.

The interval [-1, ∞) reads: "All real numbers between -1 and positive infinity."

In other words, it is all numbers greater than or equal to -1 and less than positive infinity.

Therefore:

[tex]-1\leq x<\infty[/tex]

Note that we do not use "or equal to" for the infinity as we can never really "equal" infinity.

Answer:

1042-96i

Step-by-step explanation:

(3 + 16i)(6 - 64i)

6(3 + 16i)(3 - 32i)

(6) 9 - 96i + 48i +1024