If 2^x=5, what is 2^3x-4

Answer:

Lines a and b are parallel because their corresponding angles are congruent

Step-by-step explanation:

The corresponding angle postulate states that Two lines are said to be parallel if when cut by a transversal, their corresponding angles are congruent.

Therefore given line a and line b which is cut by transversal e, both corresponding angles are equal to 110 (congruent), therefore according to the corresponding angle postulate, we can say that line a and line b are parallel to each other.

Answer: A

Step-by-step explanation:

Answer:

-1.2 Hope this helps!

Step-by-step explanation:

Answer:

8ft x 6ft

Step-by-step explanation:

For this problem, we want to create measurements of length and width that double our current area.  First we need to find the current area.

C_Length = 6 ft

C_Width = 4 ft

C_Area = C_Length * C_Width

C_Area = 6 ft * 4 ft = 24 ft^2

Now we want our new area to be double the old area.

N_Area = 2C_Area

N_Area = 2 * 24 ft^2

N_Area = 48 ft^2

Now we simply need to find the increase in width and length, distributed equally, that will create the new area.

N_Area = (C_Length + x) * (C_Width + x)

Where x is the amount that each variable is increased by to create the new area.

Now we simply solve for x.

N_Area = (C_Length + x) * (C_Width + x)

48 = (6 + x) * (4 + x)

48 = 24 + 10x + x^2

0 = -24 + 10x + x^2

Now we can either apply the quadratic formula or attempt to factor using the constant break down method.

(x + 12) (x - 2) = 0

x = -12; x = 2

Note that we will choose x = 2 since the other option would require us to have negative material, which is impossible.

Now we can check to validate our answer by plugging in the value of x.

48 ?= (6 + 2) * (4 + 2)

48 ?= (8) * (6)

48 == 48

Thus, we have found the dimensions of the new aquarium, 8ft x 6ft.

Cheers.

Answer:

0.0009

Step-by-step explanation:

9*10⁻⁴ = 0.0009

Answer:

10 steps

Step-by-step explanation:

Answer:

Fencing required = 1586 m

Step-by-step explanation:

The given statements can be thought of a triangle [tex]\triangle ABC[/tex] as shown in the diagram attached.

A be the 1st vertex, B be the 2nd vertex and C be the 3rd vertex.

Distance between 1st and 2nd vertex, AB = 435 m

Distance between 2nd and 3rd vertex, AC = 656 m

[tex]\angle A =49^\circ[/tex]

To find:

Fencing required for the triangular field.

Solution:

Here, we know two sides of a triangle and the angle between them.

To find the fencing or perimeter of the triangle, we need the third side.

Let us use Cosine Rule to find the third side.

Formula for cosine rule:

[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\Rightarrow cos 49^\circ = \dfrac{656^{2}+435^{2}-BC^{2}}{2\times 435\times 656}\\\Rightarrow BC^2 = 430336+189225-2 (435)(656)cos49^\circ\\\Rightarrow BC^2 = 430336+189225-570720\times cos49^\circ\\\Rightarrow BC^2 =619561-570720\times cos49^\circ\\\Rightarrow BC \approx 495\ m[/tex]

Perimeter of the triangle = Sum of three sides = AB + BC + AC

Perimeter of the triangle = 435 + 495 + 656 = 1586 m

Fencing required = 1586 m

Answer:

  35

Step-by-step explanation:

The law of sines tells us ...

  sin(C)/c = sin(A)/a

  a·sin(3A) = c·sin(A)

Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...

  sin(A)(4cos(A)^2 -1) = (c/a)sin(A)

  4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9

  cos(A)^2 = 25/36

  cos(A) = 5/6

__

Now, the angle B will be the difference between 180° and the sum of the other two angles:

  B = 180° -A -3A = 180° -4A

Using appropriate trig identities, we can write ...

  sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)

  = 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)

  = 4sin(A)cos(A)(2cos(A)^2 -1)

Filling in our value for cos(A), this becomes ...

  sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)

__

The law of sines tells us ...

  b/sin(B) = a/sin(A)

  b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35

The length of side b is 35 units.

Answer:

Step-by-step explanation:

combine like terms

-7x + 3x - 15y - 2y

-4x - 17y

Answer:

[tex]-4d[/tex]

Step-by-step explanation:

We can subtract a term from another if they have the same variable. Both [tex]3d[/tex] and [tex]7d[/tex] have the variable [tex]d[/tex], so we can subtract them.

When subtracting these terms, we subtract the coefficients and keep the variable.

So:

[tex]3d - 7d = 3-7(d) = -4d[/tex]

Hope this helped!

Answer:

-4d

Step-by-step explanation:

3d - 7d

=> 3 x D - 7 x D

=> (3 - 7)(D)

=> -4 x D

=> -4d

Answer:

Infinite Number of Solutions

Step-by-step explanation:

Since 4*x= 4x

and 4*4= 16

its 4x+16

which is 4x+16=4x+16

Since there are the same, and both equal each other, there are an infinite number of solutions.

Answer:

infinite number of solutions

Step-by-step explanation:

4(x + 4) = 4x + 16

Distribute on the left side.

4x + 16 = 4x + 16

Subtract 16 from both sides.

4x = 4x

Divide both sides by 4.

x = x

x = x is a true equation for every value of x.

Answer: infinite number of solutions

Answer:

If the total scored was 123 and your team scored 67 in the first half then in the second half they will score 56 points.

Step-by-step explanation:

Answer:

a = √10

Step-by-step explanation:

a² + b² = c²

a² + 9² = (√91)²

a² + 81 = 91

a² = 10

a = √10

hope this helps :)

Answer:

square root of 10

Step-by-step explanation:

a^2 + b^2 = c^2

=> a^2 + 9^2 = square root of 91^2

=> a^2 + 81 = 91

=> a^2 = 91 - 81

=> a^2 = 10

=> a = square root of 10

Answer:

1.47 is the answer

Answer:

1.4666667 rounded off to 1.47

Step-by-step explanation:

Answer:

Hey there!

Three basic rules determine this:

Positive Numbers are always greater than Negative Numbers.

If both are positive, the number with the greater magnitude is larger.

If both are  negative, the number with the smaller absolute value is larger.

Let me know if this helps :)

Answer:

23x15=23x(10+5)                     Method 1 and 5

=23x10+23x5

=230+115

23x15=(20+3)x15                      Method 2

=20x15+3x15

=300+45

23x15=(20+3)x(10+5)

   =20x10+20x5+3x10+3x5      Method 3 and 6

=200+100+30+15

Step-by-step explanation:

Answer:

[tex]\bold{x = \dfrac{8}{9}}[/tex]

Step-by-step explanation:

We have to rewrite the below as simplified fraction.

[tex]\large{0.\overline{8} = {?}}[/tex]

Solution:

Let [tex]x =0.\overline 8[/tex] which means [tex]x =0.888888.......[/tex]

Here a bar over 8 means that there the given decimal value is non terminating and there are a large numbers of 8 present after the decimal.

To solve the given non terminating decimal as fractions, we will have to eliminate the bar term from the given value.

So, we can rewrite [tex]x[/tex] as:

[tex]x =0.8\overline8[/tex] ......(1)

Now, let us multiply the above with 10.

[tex]10x = 0.8\overline 8 \times 10\\\Rightarrow 10 x= 8.\overline8[/tex] ....... (2)

Now, let us subtract (1) from (2):

[tex]10x-x=8.\overline8 - 0.\overline8\\\Rightarrow 9x = 8\\\Rightarrow \bold{x = \dfrac{8}{9}}[/tex]

So, in simplified fractions:

[tex]\large{0.\overline{8} = \bold{\dfrac{8}{9}}}[/tex]

Answer:

There is no statements/info.

Step-by-step explanation:

Answer: x = 21

Step-by-step explanation: First, isolate the x term by

subtracting 5 from both sides of the equation.

We get 1/3x = 7.

Next, multiply both sides of the equation by

the reciprocal of 1/3 which is 3/1 to get x by itself.

On the left, 3/1(1/3) cancels and on the

right when we multiply 7(3/1), we get 21.

So we have x = 21.

Answer:

7.6525 hours

Step-by-step explanation:

11 / 4 = 2.75 so he spent 2.75 h doing his HW.

and he spent (11/4) x 2.75 practicing piano

(11/4) x 2.75 = 7.6525

The number of hours Carlos spends practicing piano will be 7.6525 hours.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that 11 / 4 = 2.75  he spent 2.75 h doing his HW. and he spent (11/4) x 2.75 practicing piano.

The number of hours Carlos spends practicing piano will be calculated as below:-

(11/4) x 2.75 = 7.6525 hours

Therefore,  the number of hours Carlos spends practicing piano will be   7.6525 hours.

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Answer:

one solution

Step-by-step explanation:

3x − 7 = 4 + 6 + 4x

Combine like terms

3x-7=4x+10

Subtract 3x from each side

-7=x+10

Subtract 10 from each side

-17 =x

There is one solution

Answer:

  f(x) = |x -1|

Step-by-step explanation:

The parent absolute value function f(x) = |x| is shifted one unit to the right. We know that replacing x with (x-h) will shift a function h units to the right. Here, we want h=1. The shifted function is ...

  f(x) = |x -1|

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]3x^2+ 7x - 11 =0\\\\\Delta=b^2-4ac=7^2-4*3*(-11)=49+132=181\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-\sqrt{181}}{6}=-3.40894...\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+\sqrt{181}}{6}=1.075604...[/tex]

So, it gives -3.41 and 1.08

Thank you.

Answer:

[tex]\bold{x = 34^\circ}[/tex]

Step-by-step explanation:

Given:

[tex]cos x = sin (x + 22^\circ)[/tex]

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

[tex]sin(90^\circ-\theta )=cos\theta[/tex]

OR

[tex]cos(90^\circ-\theta )=sin\theta[/tex]

We can apply above property to solve for [tex]x[/tex] as per given equation.

[tex]cos x = sin (x + 22^\circ)[/tex]

Changing [tex]cosx[/tex] to sine form:

[tex]cosx=sin(90^\circ-x)[/tex]

[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]

[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]

So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:

[tex]\bold{x = 34^\circ}[/tex]

Answer:

Christianity and Islamic religion

Step-by-step explanation:

Based on the picture you provided It would be Christianity and Islamic religion.

Based on the Events of the Common Era (year 0) was the birth of Jesus of Nazareth. From Year 0 to year 29 Jesus of Nazareth expanded his faith. During the 29th year Jesus of Nazareth was crusified in Jeruselem.

Estimated around Year 570 Muhammad  (the Prophet of Islam) was born and rose his religion to great heights. In 632 Muhammad died.

Hope this helps

Answer:

Christianity and Islam

Step-by-step explanation:

Answer:

Here is my answer I hope this helps <(^w^)>

The correct expression is [tex]6^{x} = 256[/tex]

An exponential equation is an equation with exponents where the exponent a part of the exponent is a variable.

Given an exponential equation, [tex]log_{6} 256 = x[/tex]

Using formula :-

[tex]y = log_{a} x \\x = a^{y}[/tex]

[tex]log_{6} 256 = x[/tex]

[tex]6^{x} = 256[/tex]

Hence, the correct answer is [tex]6^{x} = 256[/tex]

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Answer:

7.5

Step-by-step explanation:

How long does it take a car to travel 1 mile if its average speed is 40 mph? The answer is 1/40 of an hour or 1.5 minutes. multiply this by 5

Answer:

0.1 hours to the nearest tenth (0.125 hours exact)

Step-by-step explanation:

For this problem, we simply need to do a conversion to find the length of time.

We are given the rate 40 miles per hour, and the distance of 5 miles.  We simply need to know the amount of time.

5 miles * (1 hour per 40 miles) =  1 hour / 8

Note, the distance unit cancels out.

So, to travel 5 miles it will take 1/8 of an hour.

1/8 as a decimal is equal to 0.125.  The answer rounded to the nearest tenth would be 0.1 hours, since the 2 rounds down.

Cheers.

Answer:

In step 1

Step-by-step explanation:

She has [tex]27(36)=27(3+12)[/tex]

this mean that 36=3+12

that's her mistake

Answer:

step 1

Step-by-step explanation:

Answer:

6 kg/m

Step-by-step explanation:

mass m = 3x^2.

rho ρ= dm/dx =6x

ρ(1) =6 Kg/m

linear density is the derivative of mass (m)  with respect to position(x)

that is how fast is the mass changing at that position.

Answer:

A) 4 Hours (of running)

B) 5 Hours (of biking)

Step-by-step explanation:

So Suzette ran and biked for a total of 80 miles,

and she did all of that in 9 hours.

Let x equal the total hours of Suzette ran and let y equal the total hours of Suzette biked.

Therefore:

[tex]x+y=9[/tex]

This represents the total hours. We know that the hours she had ran and biked totals 9. Thus, x plus y must equal 9.

And also:

[tex]5x+12y=80[/tex]

The 5x represents the miles she had ran in x hours, while the 12x represents the miles she had biked in y hours. All together, they must equal 80 miles total.

Therefore, our system is:

[tex]x+y=9\\5x+12y=9[/tex]

We can solve this using substitution. First, subtract x from the top equation:

[tex]x+y=9\\y=9-x[/tex]

Now, substitute the y into the second equation:

[tex]5x+12y=80\\5x+12(9-x)=80[/tex]

Distribute:

[tex]5x+108-12x=80[/tex]

Combine like terms:

[tex]-7x+108=80[/tex]

Subtract 108 from both sides:

[tex](-7x+108)-108=(80)-108\\-7x=-28[/tex]

Divide both sides by -4:

[tex]x=4[/tex]

Therefore, Suzette ran for a total of 4 hours.

Since she biked and ran for a total of 9 hours, she must have biked for 9-4 or 5 hours.

Checking:

4 hours of running plus 5 hours of biking does indeed equal 9 hours total:

[tex]4(5)+5(12)=20+60=80[/tex]

So by running 5mph for 4 hours and by biking 12mph for 5 hours, she did indeed reach a total of 80 miles.

Step-by-step explanation:

Michelle orders soup, or she orders salad goes with disjunction.

The fireworks were loud and colorful goes with conjunction.

If the watch is broken, then it it showing the wrong time goes with conditional.