2.6.4 practice modeling pendulums and bridges

Answer: x = -2, \(\frac{2 }{3}\)

Step-by-step explanation:

     Given:

0 = –3x² – 4x + 4

    The quadratic formula:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

    Substitute known values:

* a = -3, b = -4, c = 4

\(\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-3)(4)} }{2(-3)}\)

    Simplify with multiplication:

\(\displaystyle x=\frac{4\pm\sqrt{16+48} }{-6}\)

    Simplify:

\(\displaystyle x=\frac{4\pm\sqrt{64} }{-6}\)

\(\displaystyle x=\frac{4+8 }{-6}\),    \(\displaystyle x=\frac{4-8 }{-6}\)

\(\displaystyle x=\frac{12 }{-6}\),    \(\displaystyle x=\frac{-4 }{-6}\)

Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

Learn more about Isosceles Trapezoid Angle Measure here:

https://brainly.com/question/32850813

#SPJ11

Answer:

Step-by-step explanation:

4/4

8/6

4/6

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Know more about the term mixed fractions:

https://brainly.com/question/1055953

#SPJ1

Answer: The answer is 49

Step-by-step explanation:

i got it right

The amount of soil that is needed to cover the garden with a layer of soil is 49 ft². The correct option is C.

An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally in the triangle.

Therefore, an isosceles right angled triangle will be a right angle triangle with both legs of the triangle measuring exactly the same.

The given triangle is an isosceles right angle triangle. Let the length of the legs of the right-angle triangle be represented by x. Therefore, using the Pythagoras theorem we can write the length as,

x² + x² = 14²

2x² = 14²

√2 · x = 14

x = 14/(√2)

Now, the area of the isosceles right-angle triangle can be written as,

Area of the triangular field

= (1/2) × Height of the triangle × base of the triangle

=  (1/2) × 14/(√2) × 14/(√2)

= (14 × 14)/(2 ×√2 × √2)

= 196/4

= 49 ft²

Hence, the amount of soil that is needed to cover the garden with a layer of soil is 49 ft².

The complete question is mentioned in the image below.

Learn  more about Isosceles Right Angled triangle here:

https://brainly.com/question/27190025

#SPJ5

Answer:

EF = 3.16

Step-by-step explanation:

Assume the triangles are similar.

BC/EF = BA/ED

7.9/EF = 11/4.4

11(EF) = 4.4 × 7.9

EF = 0.4 × 7.9

EF = 3.16

The response to these questions is "7",  but first we need to explain the  instantaneous rate, and its further calculation can be defined as follows:

Given:

at \(\bold{x=3 }\)

\(\bold{y=21 }\) from the given graph

Solution:

Therefore for the instantaneous rate of changes at the \(\bold{x=3 }\)

that is\(\bold{ =\frac{y}{x}}\)

So, the instantaneous rate of change is\(\bold{=\frac{y}{x}=\frac{21}{3}=7}\)

Therefore, the final answer is "7".

Learn more:

brainly.com/question/17107065

Answer:

The answers will placed according to the order that they were given

6.93

15.75

17.64

6.93

Step-by-step explanation:

Answer:

\(\displaystyle d = \sqrt{74}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (6, 2) → x₁ = 6, y₁ = 2

Point (1, -5) → x₂ = 1, y₂ = -5

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

132 cm

I hope this helped!

Answer:

74 Degrees

Step-by-step explanation:

How i got it was we already know a triangle equal 180 degrees so you have to just add 69 degrees by 37 degrees and once you get the answer to the subtract it by 180 degrees and you get 74 degrees.

The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

Learn more about function on:

brainly.com/question/1415456

#SPJ1

Answer:

3:14

Step-by-step explanation:

Answer:

3:14

Step-by-step explanation:

The original ratio of width to length originally is 6:28, 6 being the width and 28 being the length. Then, you simplify to reach the final answer.

In this case you would divide each term by 2 and reach the final answer.

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

D

When you have the vexter, the axis of symmetry is automatially known.

But, then you only have 1 point.

A parabola, can open upwards from here, downwards, skinny, obese etc.

So, there are infinitely many parabolas that can go through that vertex.

Hence,

The vertex and axis of symmtery are not sufficient. With the intercepts (x and y) and some additional sample points falling on the parabola, there can be infinite parabolas going through the vertex.

Correct answer is D

The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:

C) Translation (x,y) -> (x + 7, y), and reflection over the x-axis.

The glide reflection is a combination of a reflection with a translation.

The vertices of the original triangle are given as follows:

A(-3,-2), B(-6,-5) and C(-1,-4).

The vertices of the reflected triangle are given as follows:

A'(4,2), B'(1,5) and C'(6,4).

The composite rule for these two transformations is given as follows:

(x,y) -> (x + 7, -y).

The transformation y -> -y is a reflection over the x-axis, hence the correct option is given by option C.

More can be learned about glide reflections at brainly.com/question/5612016

#SPJ1

Answer:

the domain is the input or the x value, while the range consists of y values or the output of an input output table.

Step-by-step explanation:

Answer:

middle set of data

Step-by-step explanation:

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

x = 1.1

Step-by-step explanation:

First multiply by x on both sides in order to cancel it from the left side of the equation. After doing this we get 18.15 = 16.5x, from there we can divide by 16.5 on both sides in order to get x alone on the right side of the equals sign. After dividing we get 1.1 = x

The value of the expression  18.15/x = 16.5 is, 1.1

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

To find the value of x in the equation 18.15/x = 16.5, we need to isolate x on one side of the equation. We can do this by multiplying both sides of the equation by x:

18.15/x × x = 16.5 × x

On the left-hand side of the equation, the x's cancel out, leaving:

18.15 = 16.5 × x

To solve for x, we can divide both sides of the equation by 16.5:

18.15/16.5 = x

Using a calculator, we can simplify this expression to get:

x ≈ 1.1

Therefore, the value of x is approximately 1.1.

To know more about Expressions check:

brainly.com/question/16804733

#SPJ7

The value of x, considering the similar triangles in this problem, is given as follows:

x = 27.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

(x + 8)/(2x - 5) = 10/14

Applying cross multiplication, the value of x is given as follows:

10(2x - 5) = 14(x + 8)

6x = 162

x = 162/6

x = 27.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

Answer: 678

Step-by-step explanation: ii

Answer:

Since they're similar rectangles

p/h = m/g

48/12 = m/5

m = 48 x 5/(12)

m = 20.

OPTION B✅

Answer:

answer b.

Step-by-step explanation:

if h=12 and p=48

so 12×4=48

g=5

so m= 5×4=20

Answer:

D

Step-by-step explanation:

I just know it plz mark me Brainlyist

Answer:

Step-by-step explanation:

When you are taking off percentages from numbers, you first want to make the percent a number. This step is super simple. Just divide the 18 by 100

This gets you 0.18

Now multiply

84 * 0.18 = 15.12

So 15.12 is the discount

Then take 84 and subtract 15.12

84 - 15.12 = 68.88

So 68.88 is the sell price

Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

Answer: A

Step-by-step explanation:

Goes down to the integer 1. B is the only one that makes sense subtracting doesn't work 87654321 goes from the 2 half line.