find the length represented by x for each pair of similar triangles 12in x 20in 15in 40in 25in

The solutions to the equations are:

x = 6, x = 4, x = 7.

1. 8x² + 11 = 191 + 3x²

Rearranging the equation:

8x² - 3x² = 191 - 11

5x² = 180

Dividing both sides by 5:

x² = 36

Taking the square root of both sides:

x = ±6

Checking the solution:

8(6)² + 11 = 191 + 3(6)²

288 + 11 = 191 + 108

299 = 299

The solution x = 6 satisfies the equation.

2. 7x² - 15 = 49 + 3x²

Rearranging the equation:

7x² - 3x² = 49 + 15

4x = 64

Dividing both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Checking the solution:

7(4)² - 15 = 49 + 3(4)²

112 - 15 = 49 + 48

97 = 97

The solution x = 4 satisfies the equation.

3. 14x² - 157 = 333 + 4x²

Rearranging the equation:

14x² - 4x^2 = 333 + 157

10x² = 490

Dividing both sides by 10:

x² = 49

Taking the square root of both sides:

x = ±7

Checking the solution:

14(7)² - 157 = 333 + 4(7)²

686 - 157 = 333 + 196

529 = 529

The solution x = 7 satisfies the equation.

Therefore, the solutions to the equations are:

x = 6, x = 4, x = 7.

Learn more about Quadratic Equation here:

https://brainly.com/question/30098550

#SPJ1

The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]

To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:  

[tex]4p(y - k) = (x - h)^2[/tex]  

where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.

In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).

The directrix is given as y = 1.

First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.

Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.

Now that we have the value of p, we can substitute it into the equation:

[tex]4p(y - k) = (x - h)^2[/tex]

Plugging in the values (h, k) = (3, 4) and p = 3, we get:

[tex]4(3)(y - 4) = (x - 3)^2[/tex]

Simplifying further:

[tex]12(y - 4) = (x - 3)^2[/tex]

Expanding the equation:

[tex]12y - 48 = x^2 - 6x + 9[/tex]

Bringing all terms to one side:

[tex]x^2 - 6x - 12y + 57 = 0[/tex]

For similar question on parabola.

https://brainly.com/question/29635857  

#SPJ8

Answer:

Step-by-step explanation:

the answer is 69 the if we round of

Answer:

79

Step-by-step explanation:

add this you have easily find answer

The number that belongs in the green box is 32.8

From the question, we have the following parameters that can be used in our computation:

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 37 - 64

Evaluate

Third angle = 79

If the number that belongs in the green box is x, then we have

x/sin(79) = 30/sin(64)

This gives

x = sin(79) * 30/sin(64)

Evaluate

x = 32.8

Hence, the number that belongs in the green box is 32.8

Read more about law of sines at

https://brainly.com/question/30974883

#SPJ1

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

An example of an extension of a function f is adding additional input-output pairs beyond the original domain and range of f.

The extension of a function f means new function that preserves the properties and behavior of the original function on its domain while adding new values or expanding its domain.

For example, we will consider the function f(x) = x^2 defined on the interval [0, 1]. An extension of this function could be g(x) = x^2 for x in [0, 1] and g(x) = 0 for x outside [0, 1].

This extension maintains the quadratic behavior of f on [0, 1] while assigning a constant value of 0 to points outside that interval.

Read more about function

brainly.com/question/11624077

#SPJ1

Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.

We have,

The number of different homework sets Mrs. Brown could assign can be calculated using the combination formula.

In this case, she wants to choose 8 problems out of 11 available problems. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of items to choose from and r is the number of items to be chosen.

Using this formula:

C(11, 8) = 11! / (8! x (11 - 8)!)

C(11, 8) = 11! / (8! x 3!)

Simplifying the factorial expressions:

C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)

The factorial terms cancel out:

C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)

C(11, 8) = 165

Therefore,

Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.

Learn more about combination here:

https://brainly.com/question/14355408

#SPJ1

Answer:

1.67% approx

Step-by-step explanation:

To determine the experimental probability of landing on a number less than two when a number cube is tossed 60 times, we need to count the number of times the number on the cube is less than two and divide it by the total number of tosses.

Let's denote the event of landing on a number less than two as "A." We'll count the number of successful outcomes, where the number on the cube is less than two.

Assuming the number cube is fair and unbiased, it has six sides numbered from 1 to 6. Out of these, only one side has a number less than two, which is one.

Now, we can calculate the experimental probability using the formula:

Experimental Probability (P(A)) = Number of successful outcomes / Total number of tosses

In this case, the number of successful outcomes is the number of times the cube lands on a number less than two, which is one. The total number of tosses is given as 60.

Therefore, the experimental probability of landing on a number less than two is:

P(A) = 1 (successful outcomes) / 60 (total number of tosses)

= 1/60

≈ 0.0167 or 1.67%

So, the experimental probability of landing on a number less than two is approximately 0.0167 or 1.67%.

obove answer is correct i think

Given statement solution is :- The given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are real numbers.

To find the complex number in the form w = a + bi, where a and b are real numbers, we can solve the given expression.

Let's solve √(-8 + 6i) step by step:

First, we can express -8 + 6i in the form a + bi:

-8 + 6i = -8 + 6i + 0i = -8 + 6i + [tex]0i^2[/tex]

Now, we can take the square root of -8 + 6i:

√(-8 + 6i) = √((-8) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-8 + 6i) = √(-8 - 6 + 6i)

= √(-14 + 6i)

Now, we want to express -14 + 6i in the form a + bi:

-14 + 6i = -14 + 6i + 0i = -14 + 6i +[tex]0i^2[/tex]

Taking the square root, we have:

√(-14 + 6i) = √((-14) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-14 + 6i) = √(-14 - 6 + 6i)

= √(-20 + 6i)

Now, we want to express -20 + 6i in the form a + bi:

-20 + 6i = -20 + 6i + 0i = -20 + 6i + [tex]0i^2[/tex]

Taking the square root, we have:

√(-20 + 6i) = √((-20) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-20 + 6i) = √(-20 - 6 + 6i)

= √(-26 + 6i)

Now, we want to express -26 + 6i in the form a + bi:

-26 + 6i = -26 + 6i + 0i = -26 + 6i +[tex]0i^2[/tex]

Taking the square root, we have:

√(-26 + 6i) = √((-26) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-26 + 6i) = √(-26 - 6 + 6i)

= √(-32 + 6i)

We continue this process until we reach a point where the expression simplifies. However, in this case, we encounter an expression that cannot be simplified further, as the square root of a negative number is not defined in the set of real numbers.

Therefore, the given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are real numbers.

For such more questions on real numbers.

https://brainly.com/question/30592734

#SPJ8

The horizontal slice of a rectangular prism will always be a rectangle. Therefore, the correct answers are options A, B and C.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

The horizontal cross section of a rectangular prism will always be a rectangle.

Therefore, the correct answers are options A, B and C.

To learn more about the rectangular prism visit:

https://brainly.com/question/27812749.

#SPJ1

Answer:

Step-by-step explanation:

a. 2r + 5 = b because you have you have 5 more blue marbles than double the red *r= red and b=blue

b. to do the substitution you know that the red marbles plus the blue marbles add up to 77 so

b + r=77

now we can isolate for b and then substitute that value into the first equation

b=77-r and then this goes to 2r+5=77-r

c. now you just have to get like terms to their side of the equal sign

add r to both sides: 2r+r+5=77-r+r=  3r+5=77

and then you subtract 5 from both sides which makes 3r=72

to find r, divide both sides by 3

r=24

there are 24 red marbles

The angle m∠HAT in the line segment is 54 degrees.

When line segment intersect, angle relationships are formed such as

vertical angles, linear angles etc.

Therefore,  the angle ∠HAT can be found using the relationship of the angles as follows:

m∠MAH = 3x + 14

m∠HAT = 2x + 6

Therefore,

m∠MAH + m∠HAT = 90 degrees

3x + 14 + 2x + 6 = 90

5x + 20 = 90

5x = 90 - 20

5x = 70

x = 24

Therefore,

m∠HAT = 2x + 6 = 2(24) + 6 = 48 + 6 = 54 degrees

learn more on angles here: https://brainly.com/question/26243305

#SPJ1

When you know the volume of a prism and some dimensions, you can solve for an unknown dimension.

When armed with knowledge about the volume of a prism alongside certain known dimensions, the possibility emerges to determine an elusive dimension within the prism. By leveraging the given information, the missing dimension can be unearthed, unraveling the intricacies of the prism's complete set of measurements.

This calculation empowers us to gain a comprehensive understanding of the geometric structure, further enriching our grasp of its spatial characteristics. The interplay between the volume and the known dimensions acts as a gateway to unlocking the enigma of the unknown dimension.

Find out more on volume of prism at https://brainly.com/question/23575161

#SPJ1

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find

The area of the figure as shown in the diagram is 30.64 cm².

The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

To calculate the area of the figure, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Learn more about area here: https://brainly.com/question/28470545

#SPJ1

b)50

since its a Equilateral triangle, then the two base angels have the same measure

abd since both triangles are symmetric, they have the same measurements

so 180-80 = 2x

x = 50⁰

The possible degrees of a function from it's graph are found with the sum of the multiplicities of each root of the function.

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

On the graph, these are the values of x for which the graph of the function crosses or touches the x-axis.

The multiplicity of each root is given as follows:

Hence the degree is found with the sum of the multiplicities of the zeros of the function.

More can be learned about the x-intercepts of a function at brainly.com/question/3951754

#SPJ1

The value of x is 33.4

To determine the value in the green box, we need to know that there are six different trigonometric identities.

These identities are enumerated as;

Using the sine identity, we have;

sin θ = opposite/hypotenuse

We have that;

θ = 64 degrees

Opposite = 30

Hypotenuse  = x

Substitute the values, we have;

sin 64 = 30/x

cross multiply

x = 30/0. 8987 = 33. 4

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

A function f is said to be one-to-one, or injective, if it has the property that for any two different inputs, it produces two different outputs.

More formally, a function f: X -> Y is one-to-one (or injective) if for every x1, x2 in X, if x1 ≠ x2 then f(x1) ≠ f(x2).

This means that no two different elements of the domain X map to the same element of the codomain Y. If you were to draw a horizontal line through any point on the graph of a one-to-one function in the Cartesian plane, that line would intersect the graph at most one time. This is known as the "horizontal line test" for one-to-one functions.

Read more on functions here:https://brainly.com/question/10439235

#SPJ1

Each of the other two angles in the roof gable measures approximately 34.8°.

If the roof gable on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a triangle is always 180°.

Let's denote the measure of the other two angles as x.

Since the two equal sides of the gable form an isosceles triangle, the two angles opposite those sides are equal.

Therefore, we have:

x + x + 110.4° = 180°

Combining like terms:

2x + 110.4° = 180°

Now, let's solve for x:

2x = 180° - 110.4°

2x = 69.6°

x = 69.6° / 2

x = 34.8°

Therefore, each of the other two angles in the roof gable measures approximately 34.8°.

Learn more about angles on

https://brainly.com/question/25716982

#SPJ1

The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

Learn more about equations here: https://brainly.com/question/9236233

#SPJ1

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

Read more about equations at

https://brainly.com/question/148035

#SPJ1

Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

You should leave at 7:34 to catch the bus that comes at 8:05.

We have,

To catch the bus that arrives at 8:05, you should leave with enough time to reach the bus stop 31 minutes before the bus's arrival time.

To catch the bus that arrives at 8:05, you need to be at the bus stop before the bus arrives. Since it takes you 31 minutes to get to the bus stop, you should leave your starting point early enough to allow for that travel time.

By subtracting 31 minutes from the bus's arrival time of 8:05, you determine the time at which you should depart.

In this case, subtracting 31 minutes gives you 7:34, meaning you should leave at 7:34.

To calculate the departure time, subtract 31 minutes from the bus's arrival time:

= 8:05 - 31 minutes

= 7:34

Thus,

You should leave at 7:34 to catch the bus that comes at 8:05.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The product of the expressions 19(x + 1 + 9z) is 19x + 19 + 171z

From the question, we have the following parameters that can be used in our computation:

19(x + 1 + 9z)

When the brackets are opened, we have

19(x + 1 + 9z) = 19 * x + 19 * 1 + 19 * 9z

Evaluate the products of the expression

So, we have the following representation

19(x + 1 + 9z) = 19x + 19 + 171z

Hence, the product of the expressions 19(x + 1 + 9z) is 19x + 19 + 171z

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

Learn more on quadratic equations ; https://brainly.com/question/30164833

#SPJ1

The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.

Area of the rectangle = Length * Width

Plugging in the given values:

Area = 3 cm * 2 cm

Multiplying 3 cm by 2 cm gives us:

Area = 6 cm²

Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).

For more questions on rectangle

https://brainly.com/question/25292087

#SPJ8

The expression that shows the volume of the prism is x³ - x² - 6.

The prism above is a rectangular prism. The volume of the prism can be found as follows:

The volume of the prism can be found as follows:

volume of the rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = (x - 3)(x)(x + 2)

volume of the rectangular prism = (x² - 3x)(x + 2)

volume of the rectangular prism = x³ + 2x² - 3x² - 6

volume of the rectangular prism = x³ - x² - 6

learn more on prism here: https://brainly.com/question/14886871

#SPJ1

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.