as the first step in solving 3x-1=8, Stella multiplies by 1/3 on both sides. what advice would you give her about the procedure for solving equations

The original image and the resulting image are consistent if the scale factor is 1.

In the given question, we have to explain would it make sense to state a dilation has a scale factor of 1.

The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation.

The image stretches if the scaling factor is greater than 1.

The image contracts if the scale factor is between 0 and 1.

The original image and the resulting image are consistent if the scale factor is 1.

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SOLUTION

The given equation is

To graph the equation find the x and y intercepts

To find the x intercept, substitute y =0 into the equation

Therefore the x intercept is at (2,0)

To find the y intercept, substitute x =0 into the equation

Therefore the y intercept is at (0,3)

Plot the x and y intercepts

Draw a line through the plotted points to get the required graph of the line

The graph of the equation is shown.

Answer:

10 ; 10

Step-by-step explanation:

( 1 , 0 )

( 5 , 40 )

m = \(\frac{40-0}{5-1}\) = 10

y = 10x - 10

( 2 , 10 )

( 10 , 90 )

Answer:

\( - 8(45) + 482 = - 360 + 482 = 122\)

Answer:

1272.2 units²

Step-by-step explanation:

This problem requires several steps.

1. The shaded area is the area of the circle minus the area of the triangle.

2. The area of the circle can be found using the radius. We are not given the radius, but using the right triangle, we can fond the diameter. Then the radius is half of the diameter.

3. The area of the triangle is base × height / 2. The base and the height are the given lengths of the legs.

Let's use the Pythagorean theorem with the triangle to find the diameter. The diameter is the hypotenuse of the right triangle.

a² + b² = c²

40² + 9² = c²

1600 + 81 = c²

c² = 1681

c = √1681

c = 41

The diameter of the circle is 41.

radius = diameter/2 = 41/2 = 21.5

The radius of the circle is 21.5

shaded area = area of circle - area of triangle

area of circle = πr²

area of triangle = bh/2

shaded area = πr² - bh/2

shaded area = (3.14159)(21.5)² - (40)(9)/2

shaded area = 1452.2 - 180

shaded area = 1272.2 units²

Since both x + 1 and x - 1 are factors of f(x), we have the factorization

x³ + 2ax + b = (x + 1) (x - 1) (x - b)

where the last root must be x = b in order that b is the constant term in the cubic.

Expanding the right side and equating coefficients gives

x³ + 2ax + b = x³ - bx² - x + b

which tells us

-b = 0   ⇒   b = 0

2a = -1   ⇒   a = -1/2

Then we have

f(x) = x³ + 2 (-1/2) x + b = x³ - x

or

f(x) = x (x + 1) (x - 1)

The cost of the entrance ticket is $6.

The equation that can be used to represent the information in the question is:

Total cost = (number of students x entrance fee) + (cost to rent a skate x number of students)

$81 = 9t + ($3 x 9)

$81 =9t + $27

In order to determine the value of t, the following steps would be taken:

Combine similar terms

$81 - $27 = 9t

Subtract similar terms

54 = 9t

Divide both sides of the equation by 9

t = $6

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Answer:

C

Step-by-step explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ)  = cos²θ/1 * sin²θ/cos²θ = sin²θ

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

We have,

In set theory, a proper class is a class that is not a set.

A class is a collection of objects, and a set is a class that can be a member of other classes.

On the other hand, a proper class cannot be a member of another class.

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

This means that V cannot be an element of any other class or set within the context of the set theory being considered.

The concept of proper classes is used to prevent paradoxes and contradictions that can arise when unrestricted comprehension is allowed in set theory.

Thus,

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

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Answer:

1 ½ feet

Step-by-step explanation:

The shortest lizard is ½ a feet

The longest lizard is 2 feet

To find the difference in length:

2-½ = 1½ feet

For the given triangles:

There are 3 pairs of congruent angles

the triangles can not be proved using the congruent angles

the congruent angles used to prove the similarity of the triangles

So, the answer will be:

For the given triangle, we can not prove they are congruent.

Answer:

Yes because no same x-value resulted in different y-values.

Answer:

Yes

Step-by-step explanation:

The measurements are precise. Therefore, the correct option is D.

It should be noted that precision simply means how close a test is when it's repeated.

On the other hand, it should be noted that accuracy simply means how close the results are to the standard value.

Therefore, when the student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees, they're precise.

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Answer: 12.5 or 12 1/2

Step-by-step explanation:

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Step-by-step explanation:

1). 1

2). 36

3). 16

sorry I can't explain it properly, all you have to do is to dive the coefficient of x by 2 and square the result

Answer:

300

Step-by-step explanation:

450 / 9 = 50

50 x 6 = 300

300 is your answer

Hope this helps!

Answer:

5 4/10 feet.

Step-by-step explanation:

A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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Answer:

for (a)

8m

(b)

1m

Step-by-step explanation:

(a) the area of a square =L*B

√64

=8m

(b)the perimeter of a square=4L

4*1=4m

(a) A square has an area of 64 m² . What is the length of each side .

As we know that area of square is equal to side² . So we have to equate the formula with given area . So :

Therefore , each side of square is of 8 m .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

(b) A square has a perimeter of 4 cm . What is the length of each side .

As we know that perimeter of square 4 cm , therefore we have to equate it with perimeter formula and then solve . So :

Therefore , each side of square is of 1 cm .

Answer:

I think it's 80!

Step-by-step explanation:

4x4 twice = 32

3x4 4 times = 48

so it should be 80

Answer:

  80 m²

Step-by-step explanation:

You want the surface area of a cuboid with dimensions 3 m, 4 m, and 4 m.

The area of the cuboid can be found using the formula ...

  A = 2(LW +WH +LH)

This can be simplified slightly to ...

  A = 2(LW +H(L +W))

For the given dimensions, we find the area to be ...

  A = 2(3·4 +4(3 +4)) = 2(12 +4(7)) = 80 . . . . square meters

The surface area of the cuboid is 80 square meters.

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Answer:

\( \frac{ {25}^{4} }{ {5}^{3} } \\ = \frac{ { {5}^{2} }^{4} }{ {5}^{3} } \\ = \frac{ {5}^{8} }{ {5}^{3} } = {5}^{5} \\ thank \: you\)

Answer:

Addition Property of Equality If AB = CD then AB + BC = BC +CD

Subtraction Property of Equality If AB + BC = BC + CD then AB = CD

Multiplication Property of Equality If m∢A = 90 then 2(m∢A) = 180

Division Property of Equaliity If 2(m∢B) = 180 then m∢B = 90

Substitution Property If m∢A + m∢B =180 and m∢B then m∢A + 90 =180

Distributive Property AB + AB = 2AB

Reflexive Property m∢B = m∢B

Symmetric Property If AB + BC = AC then AC = AB + BC

Transitive Property If AB ≅ BC and BC ≅ CD then AB ≅ CD

Segment Addition Postulate If C is between B and D, then BC + CD = BD

Angle Addition Postulate If D is a point in the interior of ∢ABC then m∢ABD + m∢DBC = m∢ABC

Linear Pair Postulate If two angles form a linear pair, then they are supplementary

Definition of Right Angle If ∢B is a right angle then m∢B = 90

Definition of Midpoint If P is the midpoint of segment AB then AP =PB

Definition of Segment Bisector If k intersects segment AB at M the Midpoint then k bisects segment AB

Definition of Perpendicular Lines If two lines are ⊥ they form right angles

Definition of Congruent Segments If AB = CD then segment AB ≅ segment CD

Definition of Congruent Angles If ∡A ≅∡ B then m∡A=m∡B

Definition of Angle Bisector If ray AB bisects ∡CAD then∡ CAB ≅ ∡ BAD

Definition of Complementary Angles If ∡ Z and ∡Y are complementary m∡Z +m∡Y =90

Definition of Supplementary Angles If ∡ S and ∡T are supplementary m∡S +m∡T = 180

Step-by-step explanation:

Answer:

11x +4

Step-by-step explanation:

Answer: 35% increase to the nearest whole percent

Step-by-step explanation:

65 / 100 = 0.65

0.65 x 135 = 87.75

135 - 100 = 35

or

88 / 65 = 1.35384615385......

100 x 1.35384615385 = 135....

135... - 100 = approximately 35

Answer:

C

Step-by-step explanation:

y = k * z , where k is any constant

x=4, z=9 , y=360

360 = k (4)(9)

360 = 36 k

k = 360/36

k = 10

y = 10 * z

when x=5 and z = 12

y = 10 (5)(12)

y = 600

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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The mean absolute deviation of given data set is 1.11.

Mean = (4 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 9

Mean = 63 / 9

Mean = 7

The absolute deviations from the mean are:

|4 - 7| = 3

|6 - 7| = 1

|6 - 7| = 1

|7 - 7| = 0

|7 - 7| = 0

|8 - 7| = 1

|8 - 7| = 1

|8 - 7| = 1

|9 - 7| = 2

The sum of absolute deviations is:

= 3 + 1 + 1 + 0 + 0 + 1 + 1 + 1 + 2

= 10

The mean absolute deviation will be:

= Sum of absolute deviations / Number of data points

= 10 / 9

= 1.11.

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