2 - (7/8 - 3/4) /'s are fractions

Answer:

3✓5 or -3✓5

Step-by-step explanation:

Taking the square root of both sides, we get

x = ±3✓5

Answer:

Step-by-step explanation:

Prove that for any natural number 3^(n+4)-3n is divisible by 16.

(I'm going to assume that you mean 3^(n+4)-3^n.)

1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).

2. Solve to get 3^n * 81 - 3^n

3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)

        You may notice that 80 is divisible by 16.

4. Rewrite what we got from the last step as: 3^n*5(16).

Hope this helped you!

The proof that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16 is; it was simplified to 3ⁿ × 5

We want to show that show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is; (3ⁿ⁺⁴ - 3ⁿ)/16

From laws of indices, we know that;

aᵐ⁺ⁿ = aᵐ × aⁿ.

Thus; 3ⁿ⁺⁴ can be expressed as 3ⁿ × 3⁴.

Thus; (3ⁿ⁺⁴ - 3ⁿ)/16 is;

((3ⁿ × 3⁴) - 3ⁿ) = 3ⁿ((81 - 1)/16)

3ⁿ(80/16) = 3ⁿ × 5

The expression has been fully simplified to show that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16.

Read more about proof of numbers at; https://brainly.com/question/10657323

Answer:

2121221

Step-by-step explanation:

Answer:

6. x = 3 7. x = 120 8. x= -5

Step-by-step explanation:

the first question is x(-4) + 3 = -9

find the value of x :

-4x + 3 = -9

we can subtract 3 on both sides since we have a value of 3 on the left, which will cancel the value out.

-4x = -12

-4(3) = -12

therefore the answer to problem 6 is x=3

and for 7 :

x / 6 - 9 = 11

we can add 9 on both sides which will cancel it out;

x/6 = 20

120/6 = 20

therefore the answer to the question 7 is 120.

For problem 8 it says :

-3x -5 = 10

we can add 5 on both sides to get:

-3x = 15

-3(-5) = 15

therefore the answer to problem 8 is -5

Answer:

Look at the attachment

Answer:

a. X = (25.92 - 2.57) ÷ 5

Step-by-step explanation:

shld be a divide sign instead of a equal sign before 5

Answer:

= $5530  

Finds us 8.2%

Step-by-step explanation:

if 8.2 was recommended for utilities then we need to find 8.2% of $65,000

We take 65000 x 0.082 = 5530

Therefore the Mckinney's annual income is 65,000 less $5530 for utilities.

We write it as $5,530 in pen and type in whole amount as $ 5530.

Answer:

$5,330

Step-by-step explanation:

Read this statement:

"The McKinneys' annual income is $65,000."

Now, read this statement:

"Households with incomes from $50,000 to $70,000 spend 8.2% on utilities"

Since $65,000 is between $50,000 and $70,000, the percent you need is 8.2%.

8.2% of $65,000 = 0.082 * $65,000 = $5,330

Answer:

7x=84

divide by 7

12=x

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

We are looking for the value of x. To find this, we must isolate x on one side. To do this, we can divide by 7 on both sides, leaving us with x=12.

Answer:

Option B.

Step-by-step explanation:

The given exponential equation is

[tex]y=ab^x[/tex]  ...(1)

It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).

The graph passes through the point (-3,24), so substitute  x=-3 and y=24 in equation (1).

[tex]24=ab^{-3}[/tex]   ...(2)

The graph passes through the point (-2,12), so substitute  x=-2 and y=12 in equation (1).

[tex]12=ab^{-2}[/tex]   ...(3)

Divide equation (3) by equation (2).

[tex]\dfrac{12}{24}=\dfrac{ab^{-2}}{ab^{-3}}[/tex]

[tex]0.5=b[/tex]

Substitute b=0.5 in equation (2).

[tex]24=a(0.5)^{-3}[/tex]

[tex]24=\dfrac{a}{(0.5)^{3}}[/tex]

[tex]24=\dfrac{a}{0.125}[/tex]

[tex]24\times 0.125=a[/tex]

[tex]3=a[/tex]

Substitute a=3 and b=0.5 in equation (1).

[tex]y=3(0.5)^x[/tex]

Therefore, the correct option is B.

Answer:

7 inches

Step-by-step explanation:

250.4/36= 6.955555 rounded to nearest inch is 7

Answer:

r = 3m

Step-by-step explanation:

Formula for the volume of a sphere: V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

We want to find the radius so we use algebra to rearrange the equation to make the radius (r) the subject of the equation

Divide both sides by [tex]\frac{4}{3}[/tex]

[tex]\frac{3V}{4}[/tex] = [tex]\pi[/tex][tex]r^{3}[/tex]

Divide both sides by [tex]\pi[/tex]

[tex]\frac{3V}{4\pi }[/tex] = [tex]r^{3}[/tex]

Take the cube root of both sides

[tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex]= r

Substitute V = 36[tex]\pi[/tex] into the equation

r = [tex]\sqrt[3]{\frac{3(36\pi) }{4\pi } }[/tex]

Expand the bracket

r = [tex]\sqrt[3]{\frac{108\pi }{4\pi } }[/tex]

Divide 108[tex]\pi[/tex] by 4[tex]\pi[/tex] (For this, the two [tex]\pi[/tex] in the numerator and denominator cancel each other out, and you only need to divide 108/4)

r = [tex]\sqrt[3]{27}[/tex]

The cube root of 27 is 3, because [tex]3^{3}[/tex] = 3 x 3 x 3 = 27

r = 3

Answer:

-1, -1/2

Step-by-step explanation:

The solution is the intersecting point. The two lines intersect at (-1, -1/2)

Answer:

1= 105, 2= 75

Step-by-step explanation:

Based on the 75 degree angle, since alternate interior angles have the same measurements, angle 2 will also measure 75 degrees. Furthermore, since angle 1 and angle 2 are supplementary angles, angle 1 will be 105 degrees because 105 + 75 is 180.

Answer:

Step-by-step explanation:

This is a linear pair, whose sum always equals 180 degrees,

hence, we can set up the equation:

2z+140=180

2z=180-140

2z=40

z=40/2

z=20

Thus, the answer is 20 degrees

Answer:

z = 20°

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

2z+ 140 = 180

Subtract 140 from each side

2z+140-140 = 180-140

2z = 40

Divide by 2

2z/2 = 40/2

z = 20

Answer:

Step-by-step explanation:

Two angles are supplementary when their sum is 180

∠AXB + ∠BXC = 180°   {Supplementary angles}

8x + 10 + 2x - 20 = 180    

Add the like terms

10x - 10 = 180

10x = 180 + 10

10x = 190

x = 190/10

x = 19°

∠AXB  = 8x + 10

          = 8 * 19 +10

          = 152 + 10

∠AXB  = 162

Answer:

180 degrees

Step-by-step explanation: the measure of angle AXB is ( a + a )  and the sum of the measured angles AXB and BXC  = 180 , so a + ( a + a) = 180.

both these angles add up to be 180 degrees because they are both supplementary angles  they both share the sides  of x  and b.  

if it confuses you, just use  a bit of repeated addition and multiplication

for example  : 30 + 30 + 30 + 30 + 30 = 5 x 30 which equals to 150

because you add 30 , 5 times .

Answer:

Step-by-step explanation:

2.25t + 5 = 13.5t + 14

5 = 13.5t + 14 - 2.25t

5 = 11.25t +14

2.25t + 5 = 13.5t + 14

2.25t + 5 -13.5t= 14

-11.25t +5 =14

2x + 6 = 3x -8

2x+6-3x=8

-x+6 =8

2x + 6 = 3x -8

6 =3x-8-2x

6= x-8

Feel free to ask for more if needed or if you did not understand something.

Answer:

[tex]\mathrm{B}[/tex]

Step-by-step explanation:

[tex]126+3x=180[/tex]

[tex]3x=180-126[/tex]

[tex]3x=54[/tex]

[tex]\frac{3x}{3}=\frac{54}{3}[/tex]

[tex]x=18[/tex]

Answer:

[tex]x = 18[/tex]

Step-by-step explanation:

Co - interior angles = 180°

[tex]3x + 126 = 180 \\ 3x = 180 - 126 \\ 3x = 54 \\ \frac{3x}{3} = \frac{54}{3} \\ x = 18[/tex]

Step-by-step explanation:

Problem 5:

Since parallelogram ABCD has to be a parallelogram, than that means that all opposite sides have to be congruent on it. One side has to be equivalent to the opposite side, so the equation on that line is equivalent to the equation on the opposite side, as well. EXAMPLE: 5x = 3x+10, which turns to 2x = 10, which turns to x = 5.

Problem 6:

Just like Problem 5, the opposite lines in the middle of the rhombus have to be congruent to one another since the given shape must be a parallelogram. So 4x = 8, and that turns to x = 2. I solved all of these problems using multi-step equations.

Hope this helped!

Answer:

Option A

Step-by-step explanation:

An equilateral triangle's sides are equal to each other, and all their angles are equal.

The best option is A.

All angles in a equilateral triangle are 60° each. They are not obtuse.

All three angles of a equilateral triangle are congruent. Again, they all measure 60° each.

All sides of a equilateral triangle are congruent.

Answer:

45 combinations

Step-by-step explanation:

15*3= 45

Answer:

a and c

Step-by-step explanation:

∠ 1 = 60° ( vertical angle )

The sum of the 3 angles in a triangle = 180°, thus

∠ 2 = 180° - (60 + 70)° = 180° - 130° = 50° → a

(7)

∠ 3 = 180° - (60 + 40)° = 180° - 100° = 80°

∠ 3 and ∠ 4 are adjacent angles and supplementary , thus

∠ 4 = 180° - ∠ 3 = 180° - 80° = 100° → c

Answer:

(0,4)

Step-by-step explanation:

4x+5y=20

5y=20-4x

y=4-4/5x

y-intercept means a point on the y-axis(x=0)

y=4-4/5x

y=4-4/5(0)

y=4

Therefore, y-intercept is at (0,4)

Answer:

the length is 50 gallons

Step-by-step explanation:

Answer:

p = 50°.

Step-by-step explanation:

To find the value of 'p', we will need to solve for the measure of the other angles of the triangle using the Supplementary Angles theorem.

Notice 140° at the top of the figure. This angle is supplementary to the top angle of the triangle. We can find this angle by:

180 - 140 = 40°.

Repeat this same step for the other angle.

180 - 90 = 90°.

Since the sum of all 3 sides = 180, we must subtract these from 180 to get the measure of 'p'.

180 - 90 - 40 = 50°.

Therefore, p = 50°.

Answer:

This expression contains a one root  (x= -10) of multiplicity 9

Step-by-step explanation:

Notice that this polynomial is given in factor form, since it is equivalent to 9 products of the same factor (x+10):

[tex](x+10)^9=(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)[/tex]

Therefore, there is a single root x = -10, since when x=-10 each of these binomial factors result in a zero.

In mathematical terms, such type of root is said to have multiplicity. And in this case, the multiplicity is "9" (the number of equal binomial factors of the polynomial form).

Answer:

9

Step-by-step explanation:

(x+10)^9 is the 9-degree polynomial so it has 9 roots

if it is equal to zero then it has 9 equal roots of x= -10

Answer:

2l + 2w is the formula for perimeter. l = 2w + 6 can be written as "the length is 6 feet more than two times its width."

The answer is B.

Answer:

B

Step-by-step explanation:

Answer: A hope it helps

i think its a

Answer:

2

Step-by-step explanation:

7 1/2 - 5 1/2

7.5 - 5.5

2

Answer:

A

Step-by-step explanation:

The angles in a quadrilateral add up to 360 degrees.

100 + 87 + 106= 293

360 - 293 = 67

The missing angle is 67°.  (A)

EVERY quadrilateral has four inside angles that add up to 360°.  It doesn't matter whether the quadrilateral is the size of a strep bacterium or the size of a galaxy. The inside angles always add up to 360°. It's a quadrilateral thing.

In this question, the first three angles add up to (100°+87°+106°) = 293°.

From there, it takes 67° more to get to 360°, so that's what the fourth angle has to be.