Solve for x in terms of y
4x+2y=7

Answer: 8/5

Step-by-step explanation:

To calculate the geometric mean, we take their product instead: 1 x 5 x 10 x 13 x 30 = 19,500 and then calculate the 5-th root of 19,500 = 7.21. This is equivalent to raising 19,500 to the 1/5-th power. Another way to calculate the geometric mean is with logarithms, as it is also the average of logarithmic values converted back to base 10.

The value of the expression  is 3 using the concept of the logarithm.

A base must be raised to a certain exponent or power, or logarithm, to produce a specific number. If bˣ=n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.

Given the expression log₂√(2+14)(1+3)

Solving the square root we obtain,

[tex]log_{2} \sqrt{(16)(4)}\\[/tex]

Simplifying further we get,

[tex]=log_{2} (4)(2)[/tex]

[tex]=log_{2} (8)[/tex]

We know that the logarithm of 8 with base 2 is 3.

Hence, the given expression can be simplified as 3.

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Answer:

47

Step-by-step explanation:

6(7)+5=42+5=47

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The slope of the line through each pair of points (1,2) and (2,3) is 1.

Find the coordinates of two points along the selected line.

Find the difference in these two locations' y-coordinates (rise).

Find the difference in these two locations' x coordinates (run). Add the difference in x-coordinates (rise/run or slope) to the difference in y-coordinates.

The formula to calculate slope is -

m = y2 - y1 / x2 - x1

m = 3 - 2 / 2 - 1

m = 1  

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The value of the equation cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Now , the value of cos A + cos B = 2 cos ( A + B / 2 ) cos ( A - B / 2 )

Substituting the values in the equation , we get

cos x + cos ( x + 2π/3 + x + 4π/3 / 2 ) cos ( x + 2π/3 - x - 4π/3 / 2 )

On simplifying the equation , we get

cos  x + 2cos ( 2x + 2π / 2 ) cos ( -π/3 )

cos x + 2cos ( x + π ) ( -1/2 )

cos x + ( -cos x ) = 0

So , 0 = 0

Hence , the equation is solved

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Answer:

Approximately [tex]0.7\; {\rm ft}[/tex].

Step-by-step explanation:

If the current bounce is of height [tex]h\; {\rm ft}[/tex], the next bounce would be of height [tex](78\%\, h)\; {\rm ft}[/tex], which is equal to [tex](0.78\, h)\; {\rm ft}[/tex].

It is given that the first bounce is of height [tex]6.5\; {\rm ft}[/tex]. Relative to this first bounce:

In general, the [tex]n[/tex]th bounce would have been dampened [tex](n - 1)[/tex] times. The height of that bounce would be [tex]((0.78)^{n - 1}\, 6.5)\; {\rm ft}[/tex].

Thus, the [tex]10[/tex]th bounce would have been dampened [tex](10 - 1) = 9[/tex] times. The height of that bounce would be [tex]((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}[/tex] (rounded to the nearest tenth, one digit after the decimal point.)

Answer:

No decimal: 905

One decimal: 905.3

Using supplementary angles, it is found that the value of x is of x = 10.75.

Supplementary angles are angles whose measures add to 180º.

An entire pizza is 360º, hence half the pizza is 180º, meaning that angles AOB and BOD are supplementary.

Their measures are given as follows:

Since they are supplementary, they add to 180º and we can add their measures and solve for x as follows:

2x - 4 + 14x + 12 = 180

16x = 172

x = 172/16

x = 10.75.

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The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.

From the given options;

Consider option D; 15 + 40 = 5(3 + 8).

It is the case of distributive addition.

where

5(3 + 8) = 5×3 + 5×8

5(3 + 8) = 15 + 40

Thus, the option D is the correct representation of the distributive law.

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The total number of seats are there is row 16 is 65.

In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come along through a few specific terms in AP that had been labeled as:

As shown below, the AP can also be referred to in terms of common differences.

Now, as the values given in the question;

There are total 16 rows in the arena.

Thus, n = 16.

There are 20 seats present in row 1.

Consider the first term as 'a₁' = 20.

Similarly, there are 23 seats present at row 2.

Consider 'a₂' = 23 is the second term.

Now, calculate the common difference;

d = a₂ - a₁  

Put the values in the 'd'.

d = 23 - 20 = 3.

Now, compute the total number of seats in 16th row bu nth formula.

n-th term:  an = a + (n − 1) × d

a₁₆ = a₁ + (n - 1)d

a₁₆ = 20 + (16 - 1)3

a₁₆ = 20 + 45

a₁₆ = 65

Therefore, the total number of seats present in the 16th row is 65.

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The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-6 - 0)^2 + (-4 - 0)^2

radius= √36 + 16

radius = √52

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

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

where (h , k) = (0 , 0)

r = √52

(x - 0)^2 + (y - 0)^2 = (√52)^2

x^2 + y^2 = 52

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The words that are needed to complete the proof has been added below:

a. AE ≅ BD a. Given

b. A C=C E, B C=C D b. definition of midpoint

c. A E = B D c. definition of congruent segments

d. A C + C E = A E d. Segment Addition Postulate

e. A C + C E = B C + C D e. definition of congruent segments

f. A C + A C = C D + C D f. substitution

g. 2 A C  = 2 C D g. Simplify.

h. A C  = C D h. Division Property

i. AC ≅ CD i. definition of congruent segments

step I is the required proof

This is a term to compare segments that they are have similar properties such as equality in length. For instance using the line asked in the question, line AC is congruent to line CD means that the two lines are equal in length

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The total area of all the faces of the cube is square feet

The given parameter is

Side length, l = 2 feet

The total area of all the faces of the cube is calculated as

So, we have

Total area = 6 * Side length^2

This gives

So, we have

Total area = 6 * 2^2

Evaluate the exponent

So, we have

Total area = 6 * 4

Evaluate the product

So, we have

Total area = 24

Hence, the total area of all the faces of the cube is 24 square feet

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A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.

The general term for the geometric sequence is

an= a1 * r ^ (n-1)

where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.

where a₁ = 3 and r = 3/2

Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...

3rd value: 6.75.

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The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(0, 0) and C(3, -4).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(0 + 3) / 2, (0 - 4) / 2]

(x, y) = (3/2, -4/2)

(x, y) = (1.5, -2)

The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).

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The phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.

Given the phrase in the question;

"54 less than twice Chrissy's age"

Let variable 'c' represent Chrissy's age

Translation

Chrissy's age ⇒ x

Twice Chrissy's age ⇒ 2 × x = 2x

54 less than ⇒ -54

Now combine terms

2x and - 54

2x - 54

Therefore, the phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.

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Answer:

Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,

Step-by-step explanation:

Answer:

a) 13 = 2x - 5

Step-by-step explanation:

Given that,

→ Andrew ran 5 miles less than 2 times the no. of miles Bernadette ran.

→ Andrew ran a total of 13 miles.

Then the equation will be,

→ 13 = 2 times - 5

→ 13 = 2x - 5

Hence, option (a) is correct.

Parts of each Graph is,

a) Centre = C

   Radius = CA = CB = CD

   Diameter = BD

b) Centre = S

   Radius = SP = SQ = SR

   Diameter = PQ

The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle. Here, point P is the center of the circle.

The distance between the center of the circle to its circumference is the radius.

The diameter of a circle is the distance from a point on the circle to a point. radians away, and is the maximum distance from one point on a circle to another. The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere.

Therefore,

Parts of each Graph is,

a) Centre = C

   Radius = CA = CB = CD

   Diameter = BD

b) Centre = S

   Radius = SP = SQ = SR

   Diameter = PQ.

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Answer:

Answer C is correct

Step-by-step explanation:

We know that,

[tex] \sf \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ \sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \: \: \: \: \: \: \: \: [/tex]

[tex]\sf (x) ^{0} = 1 \rightarrow \: Any \: number \: to \: the \: power \: 0 \: is \: 1[/tex]

Let us solve it now.

[tex] \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times ( {b}^{5} {c}^{4} )^{0} \\ \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{3} \times {a}^{5} \times {b}^{12} \times {c}^{2} \times {c}^{2} \times 1\\ \sf {a}^{3 + 5} \times {b}^{12} \times {c}^{2 + 2} \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} \times {b}^{12} \times {c}^{4} \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} {b}^{12} {c}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

975 lbs.

Step-by-step explanation:

9 3/4 = 9.75

9.75 × 100 = 975

The isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

Draw an isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin.

The coordinate of the origin is (0, 0)

We can take the coordinate of point A and B as (-1, 1) and (1, -1)

The right angle triangle is shown in the attahced picture.

Thus, the isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.

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It has been proved that if the bisectors of ∠B and ∠C intersect each other at O, then; ∠BOC = 90°+  ¹/₂∠A

A △ ABC such that the bisectors of ∠ ABC and ∠ ACB meet at a point O.

To prove :

∠BOC = 90° + ¹/₂∠A

Proof :

In △BOC, we have

∠1 + ∠2 + ∠BOC = 180°

In △ ABC, we have, ∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

¹/₂∠A + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° -  ¹/₂∠A

Therefore, in equation 1,

90° -  ¹/₂∠A + ∠BOC = 180°

∠BOC = 90°+  ¹/₂∠A

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The length of MN is 68.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

LN = 6x-5, LM = x + 7, and MN = 3x + 20

As, M is in between L and N.

LM + MN = LN

x+7 + 3x+ 20 = 6x-5

4x + 27 = 6x -5

-2x = -32

x= 16

So, the length of MN = 3x + 20 = 3 * 16 + 20 = 68

Hence, the length of MN is 68.

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Answer:

Step-by-step explanation:

Let the number of miles be x.

Total amount of rental is:

Total amount of rental is:

Since A = B, substitute the values and solve the equation:

Regarding the piecewise curve and probabilities, we have that:

a) The figure is a value density curve because the area under the figure is of 1.

b) The probability is: P(0.6 ≤ X ≤ 0.8) = 0.2.

c) The probability is: P(0 ≤ X ≤ 0.4) = 0.6.

d) The probability is: P(0 ≤ X ≤ 0.2) = 0.3.

e) The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, to the left of x = 0.4, we have a linear curve with:

Then, considering the constant:

To represent a distribution, it's area over the entire interval has to be of 1. The area is composed by.

Hence the total area is:

A = 0.8 x 1 + 0.5 x 0.4 x 1 = 1.

Hence:

The figure is a value density curve because the area under the figure is of 1.

For itens b to d, the probabilities are also given by areas, hence:

For item e, we have that:

The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.

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