7x=7.7 How would i figure this out ?

The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

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Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

Answer:

120 bicycles

Step-by-step explanation:

The overall length of the difference between the two boards is 48 inches.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

When we subtract the length of one from another, the result is a positive number representing the difference between the boards' combined lengths.

The red cedar board is 80 inches long overall:

(8 x 10) = 80

The tiger maple board measures 128:

(16 x 8) = 128

Therefore, (128 - 80) = 48 inches is the difference.

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Answer:

\(g(x)=(x-4)^2+1\)

Step-by-step explanation:

The graph is shifted 4 to the right and 1 up. When a graph is moving left or right, the sign switches. Right means -, left means +.

The equation of the blue graph is g(x)  = (x+4)² - 2

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

parabola, open curve, a conic segment produced via the intersection of a proper circular cone and a plane parallel to an element of the cone.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

x+4 because adding 4 to the x coordinate would shift it over 4

y+2 because adding 2 to the y coordinate would shift it up 2

⇒ g(f(x)) = ( x+4, y +2 )

⇒ g(x) + 2 = (x+4)²

Hence, the equation of the blue graph is g(x)  = (x+4)² - 2

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Answer:

Step-by-step explanation:

x=55

Step-by-step explanation:

out of the first equation we get

x = 2y - 3z - 1

this we use in the second equation

-3(2y - 3z - 1) + 6y - 9z = 3

-6y + 9z + 3 + 6y - 9z = 3

0 = 0

this is the same equation as the first one, just multiplied by -3.

and we see the third equation is again the same one as the first just multiplied by 2.

so, there are infinite solutions.

this has not a single solution, as in the end this is just one equation with 3 variables.

Answer:

f(x)

Step-by-step explanation:

Because f(x) = 4x + 5

Answer:

f(x)

Step-by-step explanation:

g(x) intercept Is shown to be 2

f(x) if u sub 0 into x to find the y intercept gives you 5

h(x) I you sub 0 into the equation in place of x to find the y intercept it gives you -1.84

and if you look at all ghe y intersect values f(x) is the greatest

Answer:

Step-by-step explanation:

The area of the flooring:

Cost of flooring:

Answer:

m=25/28

Step-by-step explanation:

You are not dumb. No one is dumb. Einstein failed math in high school.

Anna is x years old.

Jane is y years younger.

This means the Jane is x - y years old.

In three years, Anna will be x + 3 years old.

In three years, Jane will be (x - y) + 3 years old.

Let S = the sum of their ages in 3 years.

S = x + 3 + (x - y) + 3

S = 2x + 6 - y

Got it?

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

Answer: To find the sales tax rate as a percentage, we can use the following formula:

Sales Tax Rate = (Sales Tax / Cost Before Tax) * 100%

In this case, the sales tax is given as $20, and the cost before tax is $500. Plugging these values into the formula, we have:

Sales Tax Rate = ($20 / $500) * 100%

Simplifying the expression:

Sales Tax Rate = (0.04) * 100%

Sales Tax Rate = 4%

Therefore, the sales tax rate for the item is 4%.

Step-by-step explanation:

Answer:

6x⁴ + 26x³ + 8x²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

(6x² + 2x)(x² + 4x)

Step 2: Expand

The next number in the sequence 1, 2, 6, 22 is 86.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 1, 2, 6, 22

Consider the provided sequence 1, 2, 6, 22, ____ ?

Observe the pattern of the sequence.

To obtain the sequence you need to add the next even square of 2 in the previous number.

1+2⁰=2

Now the next even number is 2.

2+2²=6

Now 6+2⁴=6+16=22

Therefore, the next number should be:

22+2⁶=86

Hence, the next number in the sequence 1, 2, 6, 22 is 86.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

220

Step-by-step explanation:

First find out what 10% is

To get to 10 from 100, we divide by 10

Now do the same with 200

200/10 = 20

100% + 10% = 110%

200 + 20 = 220

That's my answer!

Hope this helps!

Answer:220

Step-by-step explanation:you only have to multiply by 2. If 100 is 100% 110 is 110% so if 200 is 100% 220 is 110%

Answer:

26 and 27

Step-by-step explanation:

Let the numbers be x and y

x + y = 53

xy = 702

x = 702/y

702/y + y = 53

Multiply through by y

702 + y^2 = 53y

y^2 - 53y + 702 = 0

y^2 - 27y - 26y + 702 = 0

y(y - 27) - 26(y - 27) = 0

(y - 27) (y - 26) = 0

y = 26 or 27

Solve for x in x + y = 53

if y = 26,

x = 53 - 26 = 27

if y = 27,

x = 53 - 27 = 26

The numbers are 26 and 27

Whole numbers

Natural numbers

Real nunbers

The integral of sin(ax)sin(bx)dx evaluated using integration by parts is [- b cos(ax) sin(bx) - a cos(ax)sin(bx)] / [1 - ab] + C, where C is the constant of integration.

Let u = sin(ax), dv = sin(bx) dx, then du/dx = a cos(ax), v = - (1/b) cos(bx).

By integration by parts, we have:

∫sin(ax)sin(bx)dx = - (1/b) sin(ax) cos(bx) - ∫cos(ax)cos(bx) (a/b) dx

Next, let u = cos(ax), dv = cos(bx) dx, then du/dx = -a sin(ax), v = (1/b) sin(bx).

Using integration by parts again, we have:

∫sin(ax)sin(bx)dx = - (1/b) sin(ax) cos(bx) - [ (a/b)cos(ax)sin(bx) - (a/b^2) ∫sin(ax)sin(bx) dx]

Multiplying both sides by b^2 and rearranging, we get:

b^2 ∫sin(ax)sin(bx)dx = - b cos(ax) sin(bx) - a cos(ax)sin(bx) + a b ∫sin(ax)sin(bx)dx

Simplifying, we get:

[1 - ab] ∫sin(ax)sin(bx)dx = - b cos(ax) sin(bx) - a cos(ax)sin(bx)

Thus, we have:

∫sin(ax)sin(bx)dx = [- b cos(ax) sin(bx) - a cos(ax)sin(bx)] / [1 - ab]

Therefore, we have evaluated the given integral using integration by parts.

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Answer:

Step-by-step explanation:

Since the cannonball is fired at an angle of 45°, it will have the same horizontal and vertical velocities.

Let x be the distance it travels before it is 600 feet above ground. At this point, its vertical displacement will be 600 feet, and we can use the formula for vertical displacement:

y = v0*t + (1/2)at^2

Since there is no initial vertical velocity and we are ignoring gravity, a = 0 and the equation simplifies to:

y = 0*t + 0 = 600

Solving for t, we get:

t = sqrt(2y/a) = sqrt(2*600/0) = undefined

This means that the cannonball will never be 600 feet above ground if we ignore gravity. Since this is not realistic, we cannot answer this question without additional information or by assuming that gravity is acting on the cannonball.

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

B. f(x) = | x + 61 |

Step-by-step explanation:

An absolute value function is known by single vertical parenthesis demarcating the equation on both sides.

The only option with this indication is option B.

B. f(x) = | x + 61 |

This equation can be solved in two ways;

first; f(x) = - (x + 61)

second; f(x) = x + 61

Answer:

give a thanks first and then ill tell you

Step-by-step explanation:

Answer:

Maybe it's D) or c) if not i'm du.mb and sorry

Step-by-step explanation:

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

39.1 megabytes

Step-by-step explanation:

Percentages are out of a hundred, so 15.7% is 15.7 out of 100, aka 15.7/100, which is 0.157.

Now, you just need to multiple this number by 249 megabytes to get 0.157 * 249 = 39.093 which rounds to 39.1

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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