Modeling with Two- and Three-Dimensional Figures: Practice
Question 1 of 5
Select the correct answer.
A solid metal cylindrical rod has a diameter of 4 centimeters and a length of 100 centimeters. The rod weighs between 10 and 11 kilograms.
What type of metal was used?
O
O
O
Yellow brass with a density of 8.47 g/cm³
Stainless steel with a density of 7.48 g/cm³
Iron with a density of 7.87 g/cm³
Nickel with a density of 8.90 g/cm³
dhy

The function that describes the car's distance from little rocks would be option A; y = 45x + 280

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Point 1:

(x, y) = (0, 280)

Since we are told the car's initial position is 280 miles in the time 0 h

Point 2:

(x, y) = (4, 100)

Since we are told the car's final position is 100 miles after 4h.

Let's find the Slope :

m = 45

Now, the equation of the line is:

y = mx + b

y = 45x + 280

Then, The function that describes the car's distance from little rocks would be option A; y = 45x + 280

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The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Given the following expression

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

In order to find the equivalent proportion, we will find the LCM of the right side expression to have:

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

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Answer: For the next part

✔ x = 1 and x = 8

✔ x = 0

The length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

We have:

Georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1.

The length DC = 12 inches

DC/UT = 4/1

12/UT = 4/1

UT = 12/4 = 3 inches

Thus, the length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,

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Answer:

3 in.

Step-by-step explanation:

Keep it simple :)

Answer:

the graph of y=x^2-4x is parabola as shown in the image

Step-by-step explanation:

The graph of [tex]y = x^{2} -4x[/tex] by drawing the line y=x-4

so this gives us that the line  y=x-4 satisfies the equation  [tex]y = x^{2} -4x[/tex]

To get points put y = x - 4 in the equation  [tex]y = x^{2} -4x[/tex]

so we get x -4 = x( x- 4)

x =1 and x - 4 = 0

from here we get x = 1,4

now put these values in y = x -4

From here we get y = -3,0

so the points are (1 , -3) and ( 4 , 0)

Plot these on graph and we get the straight line .

For equation  [tex]y = x^{2} -4x[/tex]

As we know it is of type of parabola with shifted centre.

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The coordinates for point B are (a) (7,0)

Point B is located 7 units right of the origin. What are the coordinates for point b?

The origin is located as:

(0,0)

From the question, we understand that:

B ⇒ 7 unit right of origin

This means that:

B = (0 + 7, 0)

Evaluate the sum

B = (7,0)

Hence, the coordinates for point B are (a) (7,0)

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Answer:a

Step-by-step explanation:

From the given options the options B and C are correct for the given equation.

we have given the equation,

70=10+12r

We have to determine the correct option

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Therefore from the given options the options B and C are correct for the given equation.

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Answer:

46,57/4

Step-by-step explanation:

area = π.r^2 = π.(d^2)/4

d^2 = AB^2= 5,6^2+3,9^2 =46,57

----> area = π.46,57/4

Part (c)

[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]

Part (d)

[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]

Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.

= Sum of sample mean absolute deviation / Number

= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9

= 2

First find the population mean:

= (10 + 11 + 19) / 3

= 13.3

Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))

= 3.8

We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.

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The variation equation is xy = a^3

An inverse variation is represented as:

xy = k

Where k is the constant of variation

When y = a and x =a^2, we have:

k = a * a^2

Evaluate

k = a^3

Substitute k = a^3 in xy = k

xy = a^3

Hence, the equation is xy = a^3

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Answer:

Step-by-step explanation:

Do you have any options or a graph?

A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,

25% of $40.00 is,

0.25 × $40 = $10

After using the coupon, the sale price is,

$40 - $10 = $30

The 10% tax on the sale price is,

0.10 × $30 = $3

The final price is $

$30 + $3 = $33

Hence, the amount that Kelly will pay for the dress is $33.

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Answer:

x = 26

y = 72°

Step-by-step explanation:

(4x - 16)° = (3x + 10)°

Subtract 3x to both sides

4x - 3x - 16 = 10

x - 16 = 10

Add 16 to both sides

x = 10 + 16

x = 26

(4x - 16)° + y° = 180°

4x - 16 + y = 180

4(26) - 16 + y = 180

104 - 16 + y = 180

88 + y = 180

Subtract 88 to both sides

y = 180 - 88

y = 72°

[tex]\rule[225]{225}{2}[/tex]

if a/b and c/d are rational expressions,a/b / c/d = a*b/c*d is false.

A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.

The given rational expression is;

a/b and c/d

Given relation;

[tex]\rm \frac{\frac{a}{b}}{\frac{c}{d}}\\\\ \frac{a d}{bc}[/tex]

When two fractions are divided the number got reversed and multiplied by the fraction.

Hence the given calculation is false.

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Answer: false

Step-by-step explanation: .

Answer: below! ^^

Step-by-step explanation:

Hii, do you need an answer to your question? Let me help you out! (;

Perpendicular lines have slopes that are opposite inverses of each other.

The slope (m) of the line that is perpendicular to y=-2x-7 is [tex]\sf -\cfrac{1}{2}[/tex].

[tex]\boldsymbol{y-y1=m(x-x1)}[/tex]

[tex]\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}[/tex]

[tex]\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}[/tex]

Voila! There's our answer, cheers! (:

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

/ = over

Step-by-step explanation:

a = 2, b=-9, c=8

x = −b±√b2−4ac/2a

x = −(−9)±√(−9)2−4(2)(8)/2(2)

x = 9±√17/4

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

Answer:

-x² + 3x + 7

Step-by-step explanation:

(f-g)(x) = f(x) - g(x) = (3x+1)-(x²-6) = -x² + 3x + 7

The value of (f - g)(x) is -x² + 3x + 7.

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given functions are;

   f(x) = 3x + 1

   g(x) = x² - 6

Now,

 (f - g)(x) = f(x) - g(x)

              = (3x + 1) - (x² - 6)

              = 3x + 1 - x² + 6

(f - g)(x)  = -x² + 3x + 7

Thus, the value of (f - g)(x) is -x² + 3x + 7.

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The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid GHJK that was rotated 180° about the origin.

The rule for 180-degree rotation about the origin:

(x, y) → (-x , -y)

From the graph:

Coordinate of H' is (-3, -2)

(-3, -2) → (3, 2)

Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

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Answer:

Step-by-step explanation:

Hi, let me help you out.

First I'm going to turn the verbal phrase into an algebraic phrase...

21+n=37. here n is the unknown number

Next, I believe you need to find what n equals.

This can be done by subtracting 21 from both sides.

n=37-21

n=16

Thus the number we need is 16.

_________________

Hope I helped. Best wishes.

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

Answer:

answer is B

Step-by-step explanation:

We know,

Opposite of a big arm has a big angle....the same way you can find the next two....

as 18>16>14

Answer:

x = 20°

Step-by-step explanation:

(4x-10)+x=90

4x-10+x=90

4x+x-10=90

5x-10=90

5x=100

x=20

Answer:

20

Step-by-step explanation:

Straight line angles:

     Angles on a straight line add up to 180°.

 90 + 4x - 10 + x = 180

 90 - 10 + 4x + x = 180

Combine like terms.

         80 + 5x     = 180

Subtract 80 from both sides,

                 5x    = 180 - 80

                    5x = 100

Divide both sides by 5

                      x = 100 ÷ 5

                      [tex]\sf \boxed{x = 20^\circ}[/tex]

Answer:

36.2

Step-by-step explanation:

Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2

33^2+15^2=c^2

1089+225=c^2

1314=c^2

Square root of 1314 = square root of c^2

36.2 aapproximately c

Answer:  $30

Step-by-step explanation:

So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30

(I'm assuming what you mean by "how much money he will have" is profit)

Answer:

The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.

Step-by-step explanation:

     125

×    24

  --------

    500

+ 2500

-----------

  30.00

The equation is written as 3(x+12)²+20.The formula for ax² + bx + c is (Ax + B)² + C.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

3x^2+12x+20

The equation is compared the equation with,ax²+bx+c

After comparing the equation we get;

a=3

b=12

c=20

The equation is written in the form as;

⇒a(x+b)^2+c

⇒3(x+12)²+20

The formula for ax² + bx + c is (Ax + B)² + C.

Hence the equation is written as 3(x+12)²+20.

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Answer:

5, 8, 11, ...

Step-by-step explanation:

f(n)=3n+2

the first three terms will be f(1), f(2), and f(3).

f(1)=3(1)+2=5

f(2)=3(2)+2=8

f(3)=3(3)+2=11

Hope this helps!

If not, I am sorry.

Answer:

A).

Step-by-step explanation:

The numbers should be in consecutive order e.g. - 6.2 6.3 6.4

Answer:

Step-by-step explanation: