Please solve and explain fully

Hello

What is the value of x?^

[tex]\frac{3x}{4x} = \frac{3x+7}{5x-8} \\\\\frac{3}{4} = \frac{3x+7}{5x-8}\\\\\frac{3}{4}(5x-8) = 3x+7\\\\\frac{3(5x-8)}{4} = 3x + 7\\\\\frac{15x-24}{4} = 3x + 7\\\\15x - 24 = 4(3x + 7)\\\\15x - 24 = 12x + 28\\\\15x - 12x = 28 + 24\\\\3x = 52\\\\\boxed{x = 52/3}[/tex]

We know the volume is 24, we can rearrange the formula to find the height: h = V/A. Plugging in the given values, we get h = 24/πr^2.

If the volume of a cylinder B2 is 24 cubic centimeters, there are a few things we can determine about the cylinder's dimensions. To find the radius of the cylinder, we first need to calculate the area of the base.

We can use the formula A = πr^2, where A is the area and r is the radius. If we know the volume of the cylinder, we can use the formula V = Ah, where V is the volume,

A is the area of the base, and h is the height of the cylinder. However, we do not have enough information to find the radius, as there are infinite combinations of radius and height that can give us a volume of 24 cubic centimeters.

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1). 140cm²

2). angle QRT

3). angle ACB= 65°

4). radian measure of d°

If the consumer raises their credit score by 60 points to 705, they will qualify for interest rate of 8.132%. The Option C

To know new interest rate, we have to get new credit score range and corresponding interest rate. The consumer's current credit score is 645, which falls within the range of 580-669.

To calculate the new credit score, we add 60 points to the current credit score:

= 645 + 60

= 705

The new credit score of 705 falls within the range of 670-739.  According to the given table, this range corresponds to a simple interest rate of 8.132%

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The linear graph that represents a proportional relationship is the graph that passes through the origin, which is the second option;

A graph that passes through the points (0, 0), (4, -1)

A proportional relationship is one in which the output value is a multiple of the input value, such that, the graph passes through the origin.

The options in the question are;

The first option; A graph that passes through the points (0, 2.5), (1, 4)

The second option; A graph that passes through the points (0, 0), (4, -1)

The third option; A graph that passes through the points (0, -1), (1, -1)

The fourth option; A graph that passes through the points (0, -3), (1, -2)

The first option; A graph that passes through the points (0, 2.5), (1, 4)

A proportional relationship is a function of the form; y ∝ x

y = k·x

k = y/x

The graph of a function that has a proportional relationship, passes through the point (0, 0), therefore, the option that represents a function that is a proportional relationship is the second option, such that we get;

The ratio of proportionality, k = -1/4

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Answer:

You have not provided a scatter plot for me to analyze. A scatter plot is a graph that shows the relationship between two variables by plotting data points on a coordinate plane. The relationship between the data points can be positive linear, negative linear, or nonlinear, or there may be no relationship. To determine the type of relationship between the data points in a scatter plot, I would need to see the plot itself. Could you please provide the scatter plot that you would like me to analyze?

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The angle pairs are given as follows:

a) Alternate exterior: <2 and <8.

b) Corresponding angles: <2 and <6.

c) Alternate interior: <3 and <5.

Item a:

Alternate exterior angles are two angles that are on the exterior of the two parallel lines, on opposite sides of the transversal line, hence they are given as follows, for item a:

Item b:

Corresponding angles are angles that are on the same position relative to the transversal line, but on different parallel lines, hence one example is given as follows, for item b:

<2 and <6.

Item c:

The two alternate interior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line, hence they are given as follows, for item c:

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The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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Answer:

1 South African Rand is equal to 100 cents. Therefore, 349 South African Rands is equal to 34900 cents.

Answer:

349 South African Rand equals

United States Dollar

17.95

South African Rand

349

Check the picture below.

so the part on the left is a template for transformations, and we can look at g(x) like this

[tex]{\Large \begin{array}{llll} g(x)=\stackrel{A}{-3} ~~ (\stackrel{B}{1}x+\stackrel{C}{4})^2 ~~ \stackrel{D}{-3} \end{array}}[/tex]

now, if you look at the template, we do +4 first, then -3 shift down, then 3 vertical shrink, and then the negative of -3, landing at g(x) from our parent f(x).

Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

The length of arc HK is approximately 3.86 units.

To find the length of arc HK, we need to know the circumference of circle J.

The formula for the circumference of a circle is C = 2πr,

where C is the circumference and r is the radius.

Since we don't have the radius directly given, we can find it using the given information.

We know that the measure of angle HJK is 48 degrees, and HJ is 11 units. The angle at the center of a circle is twice the angle at the circumference that intercepts the same arc.

Therefore, angle HJK at the center of the circle intercepts an arc HK with the same measure.

So, the circumference of the circle is C = 2πr = 2π(11 units).

To find the length of arc HK, we need to find the fraction of the circumference represented by the angle HJK.

We know that the total angle at the center of a circle is 360 degrees (the full circumference), so the fraction of the circumference represented by angle HJK is 48/360.

The length of arc HK is then calculated by multiplying the fraction of the circumference represented by the angle HJK by the total circumference of the circle:

Arc HK = [tex](48/360) \times 2\pi (11 units)[/tex]

Calculating this value, we get:

Arc HK ≈[tex](48/360) \times 2 \pi \times 11[/tex] ≈ 1.234π

To find the numerical value, we can approximate π as 3.14:

Arc HK ≈[tex]1.234 \times 3.14[/tex] ≈ 3.86 units (rounded to the nearest hundredth)

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Step-by-step explanation:

Volume  = 24 ft^3 = L x W x H

                  24 = 6 x 2 x H

                     H = 24 / ( 6 x 2) = 2 ft

Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

We have to given that;

Expressions are,

⇒ 12 - |2x + 15| > 3

And, (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

Now, We can simplify as;

⇒ 12 - |2x + 15| > 3

⇒ 12 - 3 > |2x + 15|

⇒ 9 > |2x + 15|

⇒ |2x + 15| < 9

⇒ - 9 < 2x + 15 < 9

This gives,

⇒ - 9 < 2x + 15

⇒ - 9 - 15 < 2x

⇒ - 24 < 2x

⇒ - 12 < x

And, 2x + 15 < 9

⇒ 2x < 15 - 9

⇒ 2x < 6

⇒ x < 3

Hence, Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Simplify the expressions ,

⇒ (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

⇒ (x - 3)² - x² + 3) ≥ 0

⇒ x² + 9 - 6x - x² + 3 ≥ 0

⇒ 12 - 6x ≥ 0

⇒ 12 ≥ 6x

⇒ 2 ≥ x

Hence, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

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To find the first four terms of the infinite sequence u_n = 1/(7n - 2), we substitute the values of n from 1 to 4 into the formula:

For n = 1:

u_1 = 1/(7(1) - 2) = 1/5

For n = 2:

u_2 = 1/(7(2) - 2) = 1/12

For n = 3:

u_3 = 1/(7(3) - 2) = 1/19

For n = 4:

u_4 = 1/(7(4) - 2) = 1/26

Therefore, the first four terms of the infinite sequence are:

u_1 = 1/5

u_2 = 1/12

u_3 = 1/19

u_4 = 1/26

To find the area of a sector, you can use the formula A = (θ/2π) × πr^2 = (θ/2) × r^2.

The area of a circle is given by the equation A = πr^2, where r is the radius of the circle. The arc length of a circle is given by the equation L = rθ, where θ is the central angle in radians and r is the radius of the circle.

To find the arc length of a portion of a circle, you can use the formula L = (θ/2π) × 2πr = (θ/2π) × C, where C is the circumference of the circle. This formula is useful when you have a fraction of a circle, such as a sector.

These equations are fundamental in geometry and are used in many applications such as architecture, engineering, and physics.

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Dian's family is 3 times old now.  

Let's call Dian's family's age" x" now.

 According to the problem,

Dian is 8 times aged than his family, so Dian's age is x 8 now.  

In 5 times, Dian's age will be x 8 5, and his family's age will be x 5.  

The problem also states that in 5 times, Dian will be  doubly as old as his family,

so we can set up the equation

 x+ 8+ 5 =  2( x +5)  

Simplifying the equation  x +13 =  2x+ 10  

Obtaining x from both sides  

13 =  x +10  

Obtaining 10 from both sides  

3 =  x  

thus,X=3

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Answer:

Let's call the three digits of the three-digit number "a", "b", and "c". Since the product of the digits is 135, we know that:

a * b * c = 135

We need to find the value of a + b + c. One way to approach this is to try out different combinations of digits that multiply to 135 and see which one adds up to the correct sum. The possible combinations are:

1 * 3 * 45 = 135 -> 1 + 3 + 45 = 49

1 * 5 * 27 = 135 -> 1 + 5 + 27 = 33

1 * 9 * 15 = 135 -> 1 + 9 + 15 = 25

3 * 5 * 9 = 135 -> 3 + 5 + 9 = 17

So, the only combination of digits that adds up to a three-digit number is 1, 3, and 45, which add up to 49. Therefore, the answer is 49.

Answer:

4/3 ×π×r³

4/3 × 22/7 ×3³

88/21 ×27

There exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2.

To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use the concept of the longest path in a tree and the properties of odd integers.

First, let's consider the longest path in the tree T.

Since the tree has n vertices, the longest path can have at most n-1 edges.

Let's denote this longest path as P.

Since n is an odd integer, we have n = 2k + 1, where k is a non-negative integer.

This implies that n-1 = 2k, which is an even number.

Now, consider the middle vertex x of the longest path P.

If P has an odd number of vertices, then x is unique.

If P has an even number of vertices, then there are two possible middle vertices, but we can choose any one of them.

Next, let's consider the distance between v and x along the longest path P. Since x is the middle vertex, this distance can be at most (n-1)/2.

This is because the longest path P divides the tree into two parts, each containing (n-1)/2 vertices at most.

Now, let's consider the subtree rooted at x, which consists of all vertices that can be reached from x.

Since the distance between v and x is at most (n-1)/2, it implies that v is within this subtree.

Therefore, we have found a vertex u (in this case, x) in the subtree rooted at x such that the distance between u and v is at most (n-1)/2.

By proving the existence of such a vertex u, we have shown that for any vertex v in the tree T, there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

8

Step-by-step explanation:

(5² + 7) ÷ 4 ← evaluate terms in parenthesis

= (25 + 7) ÷ 4

= 32 ÷ 4

= 8

The number 5730 represents

(**the number of years it takes for half of the carbon-14 to decay.**)

It is the half-life of carbon-14, which is the amount of time it takes for half of the substance to undergo radioactive decay.

Answer:

If the height and radius of a cone are both 9 yards, then you can use the formula for the volume of a cone to calculate its volume. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Plugging in the values for r, h, and π gives us:

V = (1/3)πr^2h

 = (1/3)(3.14)(9 yd)^2(9 yd)

 = (1/3)(3.14)(81 yd^2)(9 yd)

 = (1/3)(254.34 yd^3)

 ≈ 84.78 yd^3

So, the volume of a cone with a height and radius of 9 yards is approximately 84.78 cubic yards, rounded to the nearest hundredth.

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The statement that the rational expression ( a − b ) / ( a + b ) always equals -1 is incorrect, it does not hold true for all values of a and b. Only specific values that satisfy ( a - b ) = -( a + b ) will lead to the result -1.

The statement in the question is not correct. That is, it is False. The rational expression in the form ( a − b ) / ( a + b ) does not always equal - 1. For example, if a = 5 and b = 3, the rational expression ( a − b ) / ( a + b ) becomes ( 5 - 3 ) / ( 5 + 3 ), which evaluates to 2 / 8 = 0.25, not -1. The statement would only be true if (a - b) = -(a + b), which is not an assumption we can make for all values of a and b. So, while simplifying a rational expression it is necessary to substitute the values and check it out.

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Answer:

A= 158

B=158

D=22

Step-by-step explanation:

An isosceles trapezoid has 2 pairs of equal angles.

A=B

C=D

Also A+C=180

So we have that A=158

B=158 and D=22

Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

Vicky uses 400 ml of lemon juice in the salad dressing.

Answer: All of the values for x would make the equation FALSE.

Step-by-step explanation:

To see if each value would fit x for this equation, we will need to check each of them.

If you said x = 1 would fit this equation, it would be 7 <  3 - 1. This would be false because when you evaluate this equation, it would be 2 is greater or equal to 7 which isn't true.

If you said x = 5 would fit this equation, it would be 7 <  3 - 5. This would be false because when you evaluate this equation, it would be -2 is greater or equal to 7 which also isn't true.

If you said x = -3 would fit this equation, it would be 7 <  3 - -3. This would be false because when you evaluate this equation, it would be 6 is greater or equal to 7 which is really close, but it isn't true.

Therefore, none of these values for x would fit this equation at all in any way. The value of x would have to be -4 or more to make this statement true. Hope this helps!

-From a Fifth Grade Honors Student