A triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m. A second
triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m. What must the interior angles of the second triangle
be for the two shapes to be similar?

Answer: c/bd = a

Step-by-step explanation:

What we need to do is isolate a on one side of the equal side. Now, remember that multiplication and division cancel each other out, so if we divide b and d on the right side by b and d then we cancel those values and get a by itself. Now, we have to do this on the left side as well in order to keep the equation balanced. When we do this, we get c/bd = a. Keep working hard! You're doing great!

The number of pages read by her will be 36.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Marion read 616 pages in 14 days, The number of pages each day will be calculated as,

N = 616 / 17

Divide the number 616 by 17,

N = 36.23

N = 36

Therefore, the number of pages read by her will be 36.

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Answer:

X=30

Step-by-step explanation:

[tex](4x + 30) + (2x - 30) = 180 \\ 4x + 2x + 30 - 30 = 180 \\ 6x = 180 \\ x = 30[/tex]

Answer:

x = 30

Step-by-step explanation:

We are told that:

• m∠A =  (4x + 30)°

• m∠B = (2x - 30)°,

and that these two angles are supplementary to each other.

When two angles are supplementary to each other, it means that they add up to 180°.

Therefore:

∠A + ∠B = 180°

⇒ (4x + 30)°  +  (2x - 30)° = 180°

⇒ 4x + 30 + 2x - 30 = 180

⇒ 4x + 2x + 30 - 30 = 180      [Combining like terms]

⇒ 6x = 180

⇒ [tex]\frac{6}{6}x = \frac{180}{6}[/tex]     [Dividing both sides of the equation by 6]

⇒ x = 30

Answer: [tex]h=\frac{S}{2πrh}[/tex]

Step-by-step explanation:

= Solve S = 2πrh:

= [tex]h=\frac{S}{2πrh}[/tex]

The line with no slope will be a horizontal line the correct option is line b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that on a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.

The line with no slope will be line b because the line is a horizontal line.

Therefore, the line with no slope will be a horizontal line the correct option is line b.

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Answer:

C. Line C

Step-by-step explanation:

Edge 2023

Poisson Distribution along with Binomial Distribution is applied for Discrete Random variable.

What is discrete variable and example?

What is discrete and continuous random variable?

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Answer:

x = 10

Step-by-step explanation:

48 = x + 8 + 2x + x

    48 = 4x + 8

   -8           -8

40 = 4x

divide both sides by 4

10 = x or x =10

The fifth graders are read for total 180 minutes.

What do you mean by minutes?

A 60-second interval of time. In an hour, there are 60 minutes. For illustration, the time 10:35 is 35 minutes after 10 o'clock. A minute is equivalent to 1/60th of a degree in terms of angles.

According to the given question,

First 5 students read for 100 minutes.

Then, next 25 studenda read for 50 minutes.

And the rest of the fifth graders read for 30 minutes.

Now, we will adding all the minutes to obtain the answer or total minutes of fifth grader read,

Total minutes of fifth graders read= 100+50+30

                                                        =180 minutes.

Therefore, the fifth graders take 180 minutes to read.

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Answer:

y = [tex]\frac{1}{5}[/tex] x - 5

Step-by-step explanation:

y = mx +b  You have to find the slope and the y intercept

slope:

I used the two points on the graph (0,-5) and (5,-4)  The slope is the change in y over the change in x.  An ordered pair is given in the form (x,y)

[tex]\frac{- 4 - - 5}{5-0}[/tex] = [tex]\frac{-4 + 5}5}[/tex] = [tex]\frac{1}{5}[/tex]

or you could just look at the two points.  If you start at (0,-5) and go straight up one and the then go right 5 spaces, you will be at the point (5,-4) [tex]\frac{1}{5}[/tex]

The y intercept for the b is where the line crosses the x axis.  It crosses at the point (0,-5)  The -5 is the b part.

The height of the triangle is 15 feet.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the interior angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.

The formula for the area of a right-angle triangle is A = (½)×b×h square units.

Let the height of the triangle be h

Given:- The area (A) of the triangle is 120 ft^2.

            The base (b) of the triangle is 16 feet.

From the formula, we know that area of the triangle is:-

A = (½)×b×h

By substituting the values of A and b

[tex]120=\frac{1}{2}*16*h\\ h=(120*2)/16\\h=15[/tex]

Hence the height of the triangle is 15 feet.

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The function g(-1) has its value to be (c) g(-1) =  1

The definition of the function is given as

g(x)=x³+6x² + 12x+8

Rewrite the above function properly

So, we have the following representation

g(x) = x³ + 6x² + 12x + 8

To find the function g(-1), we set the value of x in the equation g(x) = x³ + 6x² + 12x + 8 to -1

This is represented by

Calculate g(x), when x = -1

Substitute -1 for x in the equation g(x) = x³ + 6x² + 12x + 8

So, we have the following equation

g(-1) = (-1)³ + 6(-1)² + 12(-1) + 8

Evaluate the exponents

This gives

g(-1) = -1 + 6(1) + 12(-1) + 8

Evaluate the products

This gives

g(-1) = -1 + 6 - 12 + 8

Evaluate the sum

g(-1) =  1

Hence, the value of the function is g(-1) =  1

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Answer:

the domain is the x values: -5,-4,-2,0,1

The range is the y values: -1, 1, 3, 4

Step-by-step explanation:

Step-by-step explanation:

they are parabolas.

their line of symmetry is exactly in the middle between their x-intercepts (when y = 0).

these x-intercepts we get from the factors : y can only be 0, when at least one of the factors is 0.

y = (x + 14)(x + 16)

means y = 0, when x = -14 or x = -16.

so, the line of symmetry is

x = -15

y = (x - 12)(x - 18)

y = 0, when x = 12 or x = 18

line of symmetry is

x = 15

y = (x + 13)(x - 17)

x = -13 or x = 17

line of symmetry

x = 2 (again, the middle between -13 and +17)

y = (x - 10)(x + 20)

x = 10 or x = -20

line of symmetry

x = -5

Answer:

The area of the dount is about 35.325 in²

Step-by-step explanation:

In order to find the area of a donut with a hole on the center we need to find the area of the center and the area of the circle of the donut (as if the donut was whole)

*The radius is half of the diameter or r = d/2

The area of a circle is A = n(3.14) r² or pi(3.14)× radius

Answer:

26

Step-by-step explanation:

4⅓×6

=13/3 × 6

=26

smash as brainliest

The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is a plane figure which is referred to as a quadrilateral and has four right angles. The area is calculated by the following below:

Area = Length × breadth.

In cases where the algebra tile rectangles is used , it is ideal to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 7cm and the breadth is 6cm then the area will be  7cm × 6cm = 42cm²

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We need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

As per the question statement, we are provided with a binomial (n² - 18n),

And we are required to add a proper constant to the above mentioned binomial so that the resulting trinomial is a perfect square, and then factorise the resulting trinomial.

To answer question, first we need to know the standard form of expanding a perfect square into a trinomial, which goes as,

[(a - b)² = {(a)² + (b)² - (2 * a * b)]

Here, if we compare our concerned binomial (n² - 18n), or, [(n)² - (2 * n * 9)], with the above mentioned standard expansion of a perfect square into a trinomial, we get, (a = n) and (b = 9), and the (b²) term is missing.

Adding [(b²) = (9²) = 81] which is a constant term, to our concerned binomial (n² - 18n), we get, (n² - 18n + 81),

Or, [(n)² + (9)² + (2 * n * 9)],

Which is a trinomial and matches with the standard expansion of a perfect square into a trinomial, and hence,

[(n² - 18n + 81) = (n - 9)²]

That is, we need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

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Read the left colum top to bottom then the right column top to bottom, hope this helps

The unit rate for the given situation is 29 students per classroom.

What is the unit rate?

A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.

Given situation is 87 students in 3 classrooms.

So, the unit rate  [tex]= \frac{87}{3}[/tex]  students/classroom

                            [tex]= 29[/tex] students per classroom

Hence, the unit rate for the given situation is 29 students per classroom.

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The value of the expression when z = -19 is 25.

Here we have the expression:

(33 + 2z)²

And we want to evaluate this on z = -19

Evaluating just means that we need to replace the variable in the expression by the given number.

By doing that we will get:

(33 + 2*(-19))^2

(33 - 38)^2

(-5)^2 = 25

The expression is equal to 25.

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Answer:

1: [tex]2\sqrt{2}[/tex]

2: [tex]10\sqrt{55}[/tex]

Step-by-step explanation:

[tex]\sqrt{16-8}[/tex]

[tex]\sqrt{8}[/tex]

[tex]\sqrt{8}=2\sqrt{2}[/tex]

2:

[tex]\sqrt{\frac{11}{16+4}[/tex]

[tex]\sqrt{\frac{11}{20}[/tex]

[tex]\sqrt{.55}[/tex]

[tex]10\sqrt{55}[/tex]

Hopes this helps

Step-by-step explanation:

2.

it is a square !

what do we know about squares ?

first of all, they are a special rectangle, where length = width, and therefore all 4 sides are equally long.

and secondly, as they are a form of rectangle, every inner angle is 90°.

so,

6x - 12 = 90

6x = 102

x = 102/6 = 17

therefore,

CD = x + 15 = 17 + 15 = 32

many greetings to your teacher, CD is a side, a length, and NOT an angle, so it is NOT measured in degrees (°).

since it is a square and all sides are equally long,

AD = CD = 32

3.

it is a rectangle.

so, it has 4 sides consisting of 2 pairs of equally long sides. that means there are 2 equally long side we call length, and 2 equally long sides we call width.

these equally long sides are always opposite of each other.

that means

2x - 52 = x - 2

x - 52 = -2

x = -2 + 52 = 50

The equation D show the multiplication property of inequality if n+4 =11

What is inequality?

inequality, In mathematics if a statement of an order relationship—greater or greater than or equal to, less than, or less than or equal between two number or algebraic expressions.

An inequality show the relationship between two values in an algebraic equations that are not equal.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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The height of the tower is 9.24 feet. That is, the tower is 9.24 feet tall

From the question, we are to determine how tall the tower is

From the given information,

From a distance of 10 feet, the angle of elevation of the tower at a height 5 feet from the ground is 23 degrees.

Let x represent the length of the tower from a point 5 feet from the ground.

Thus,

The height of the tower will 5 + x feet

Now, we will determine x

Using SOH CAH TOA

tan 23° = x / 10

x = 10 × tan 23°

x = 4.24 feet

Height of the tower is 5 + x feet

Therefore,  

Height of the tower = 5 + 4.24 feet

= 9.24 feet

Hence,

The height is 9.24 feet

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Answer:

4,600,000,000

Step-by-step explanation:

Don't forget the order of operations

3.243 × 10⁸/7.05

= 46,000,000 × 10²

= 4,600,000,000

or 4.6 × 10⁹

Answer:

4.6x10 to the power of 5

Step-by-step explanation:

7.05×10

2

3.243×10

8

​

Divide them.

\frac{3.243}{7.05}\times \frac{10^8}{10^2}

7.05

3.243

​

×

10

2

10

8

​

Divide numbers and 10's separeately.

0.46\times 10^6

0.46×10

6

Subtract exponents.

(4.6\times 10^{-1})\times 10^6

(4.6×10

−1

)×10

6

Rewrite as a number bigger than 1

4.6\times (10^{-1}\times 10^6)

4.6×(10 −1 ×10 6 )

Associate

4.6\times 10^5

4.6×10 5

Add exponents

Answer:

6CO2 + 6H2O → C6H12O6 + 6O2.

Step-by-step explanation:

That's the equation for photosynthesis. let me know if you have any questions.

The solution to the inequality 6 + t ≤ 13 is given as follows:

t ≤ 7.

An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.

The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.

For this problem, the inequality is given as follows:

6 + t ≤ 13

Hence the solution for variable t is found isolating it as follows:

t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)

t ≤ 7.

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Answer:

  105 N

Step-by-step explanation:

You want the force exerted on an area 2 m by 1.25 m by a pressure of 42 N/m².

The area is ...

  A = LW

  A = (2 m)(1.25 m) = 2.50 m²

The force is the product of the pressure and the area:

  F = PA

  F = (42 N/m²)(2.5 m²) = 105 N

The box exerts a force of 105 N on the table.

Puzzle:

A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?

The initial  distance is 10 miles

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Puzzle:

A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?

Let x=  initial distance

x+12+2(x)=42

3x+12=42

3x=42-12=30

x=30/3=10 miles

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The maximum height covered is 32m and the time taken to reach maximum height is 1.25 seconds

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change = change in y / change in x. Rates of change can be positive or negative.

h(t) = -16[tex]t^{2}[/tex] +40t + 7

at maximum height the rate of change of h(t) with respect to t is zero.

so [tex]\frac{dh(t)}{dt}[/tex] = 0

but  [tex]\frac{dh(t)}{dt}[/tex] =  -32t + 40

so,

-32t + 40 = 0

32t = 40

t = 40/32

t = 1.25

to find h(t), we substitute t = 1.25 into the equation above

h(t) = -16[tex](1.25)^{2}[/tex] + 40(1.25) + 7

h(t) = 32m

In conclusion, the maximum height reached is 32m and the time taken to reach maximum height is 1.25 seconds

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