Finding the initial amount and rate of change given a table for a linear function

The properties used in the the simplification of the expression is:

step 1: Inverse multiplication property

step 2: Commutative property

step 3: Associative property

step 4:  Commutative property

step 5: Identity property

Given the expression is:

1 ÷ 2/3 × (₋5) × 3 ÷ (₋1/4)

step 1: 1 × 3/2 × (₋5)  × 3 × (₋4)

Inverse multiplication property is applied.

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

step 2: 1 × (₋4) × 3/2 × (₋5) × 3

Commutative property is applied.

Mathematical addition and multiplication operations are covered under the commutative property. In other words, adding or multiplying two integers does not change the outcome if the order or location of the numbers is changed.

step 3: 1 × [(₋4) × 3/2] × (₋5) × 3

Associative property is applied.

According to the associative feature of multiplication, the outcome of a multiplication problem is unaffected by the arrangement of the numbers in the problem's constituent parts.

step 4: 1 ×[-6] × (₋5) × 3

commutative property is applied.

step 5: (-6) × (₋5) × 3

Identity property is applied.

Multiplying 1 by any number yields the number itself, according to the Multiplicative Identity Property, commonly known as the Identity Property of Multiplication. This is because any time a number is multiplied by 1, it retains its identity and does not change.

Hence we have applied the above mentioned properties of multiplication.

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Answer: Yes, she can affort to rent the car.

Step-by-step explanation:

Main Answer:

Mars is bigger than Pluto by 27 times.

Explanation:

Given: Volume of Mars = [tex]1.31[/tex] × [tex]10^{21} m^{3}[/tex]

            Volume of Pluto = [tex]4.93[/tex] × [tex]10^{19} m^{3}[/tex]

To find: Determine how many times bigger is Mars than Pluto.

No. of times bigger = [tex]\frac{Volume of Mars}{Volume of Pluto}[/tex]

                              = [tex]\frac{1.31 * 10^{21} m^{3} }{4.93 * 10^{19}m^{3} }[/tex]

                              = [tex]\frac{131}{493} * 10^{2}[/tex]

                              =0.2657 × 100

                              = 26.57

                              =27

Final Answer:

Therefore, 27 times bigger is Mars than Pluto.

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Solution -:

By Using Pythagoras theorem-:

We know that,,

(Hypotenuse)²= ( Base )² + ( Perpendicular)²

than,,,, AC²= BC² + AB²

so,,,

[tex]( h) {}^{2} = ({15}^{2} ) + (\ {8}^{2} )[/tex]

[tex]AB = \sqrt{225 + 64} [/tex]

[tex]AB = \sqrt{289} [/tex]

then,,

[tex]AB \: = 17[/tex]

then,,, the value of sin a

[tex] \bold{= \frac{8}{17} }[/tex]

Thus option ( B ) is correct

Answer - put the dot on -1

(-2)-(-1) = -1

The total weight of the two animals is 1.2 x 10^5 lbs

The given parameters are

Animal 1 = 5.36 x 104 lbs.

Animal 2 = 6.2 x 104 lbs

Rewrite the parameters properly

Animal 1 = 5.36 x 10^4 lbs.

Animal 2 = 6.2 x 10^4 lbs

The total weight of the two animals is calculated as

Total weight = Animal 1 + Animal 2

This gives

Total weight = 5.36 x 10^4 lbs + 6.2 x 10^4 lbs.

Factor out 10^4 lbs

Total weight = (5.36 + 6.2) x 10^4 lbs.

Evaluate the sum

Total weight = 11.56 x 10^4 lbs.

Rewrite as

Total weight = 1.156 x 10^5 lbs.

Approximate

Total weight = 1.2 x 10^5 lbs.

Hence, the total weight of the two animals is 1.2 x 10^5 lbs

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The measure of the angle JL is 33 degrees

A bisection is a line that divides an angle into two equal portion. Using the addition postulate below:

<JKM = <JKL + <LKN + <NKM

If the line KN bisects <LKM then <LKN = <NKM = 22 degrees

Substitute the given parameters

<JKM = <JKL + <LKN + <NKM

77 = <JKL + 22 + 22

77 = <JKL + 44

<JKL = 77 - 44

<JKL = 33 degrees

Hence the measure of the angle JL is 33 degrees

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Answer:

$138

Step-by-step explanation:

%15 -> .15

120×.15=18

$120 + $18 = $138

Compare the two numbers √63, 7.5

[tex]\sqrt{63} =7.93[/tex]

So, √63  > 7.5

What is a square root?

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The restrictions on the variables x and y be

x = 0  ⇒  2/0  = ∞

y = 0  ⇒  2/0 = ∞

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)

(7x/4y³) × (8y/21x³) = (2/3x² y³)

What are the restrictions on the variables?

Here, x = 0  ⇒  2/0  = ∞

Similarly, y = 0  ⇒  2/0 = ∞

So , x, y ≠ 0

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The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.

Some of the Translation are,

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.

Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

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The complete question image is attached.

Answer: All answers are correct

Step-by-step explanation: ur really smart congrats

Since 0.004 is 4/1000, muiltiply the numerator and denominator by 1000.

That is: (0.86×1000)= 860

(0.004×1000) = 4

860/4= 215

Answer:

215

Step-by-step explanation:

0.86 ÷ 0.004 = 215

Answer: 3(m+3n)

Step-by-step explanation:

3m + 9n=

3*m + 3*3n=3(m+3n)

There are a two solutions of the given quadratic equation.

According to the statement

We have to find that the number of solutions of the equation.

So, For this purpose, we know that the

Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power

From the given information:

The given equation is a:

-16=16x^2

It becomes

16x^2 = -16

Then solve it with the help of the rearrange the terms

x^2 = -16/16

x^2 = -1

x = (-1)^1/2

x = +i , -i

There is a two solutions of the quadratic equation.

So, There are a two solutions of the given quadratic equation.

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The equation x = 2

is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

It is given that, the line is passing through two points (2, -1) and (2, 6)

The formula to find the equation of a line in two point form is

(y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

where m = [tex]\frac{y2 - y1}{x2 - x1 }[/tex] is the slope of the line

Slope is the measurement of the level of steepness of the line

We need to find the Two- Point form of the line

Using the above formula we get, where

x1 = 2 , x2 = 2, y1 = -1, y2 = 6

m = [tex]\frac{(6-(-1))}{(2-2)}[/tex]= [tex]\frac{7}{0}[/tex]

The equation of the line = (y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

[y - (-1)] = [tex]\frac{7}{0}[/tex] (x - 2)

0. [y - (-1)] = 7(x-2)

7x - 14 = 0

x = 2

Hence, x =2 is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

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Answer:

first to get a 60 sided figure we know there if 360 degrees in a full rotation so let's simply divide it by 60

360÷60= 60 degrees

A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).

BD is an altitude here because is it perpendicular to AC.

A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).

An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.

A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.

BD is an altitude here because is it perpendicular to AC.

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The statement can be proved by the law of syllogism.

A formal logical framework used to infer a conclusion from a series of premises is referred to as a syllogism, also known as a rule of inference.

The law of syllogism in conditional statement is given as:

if p then r and if r then q , then we can state that if p then q , where p , q, and r are statements.

Now in the given conditional statements we can write it as:

let p = You go camping

r = you will need a flashlight

q = you will need extra batteries.

Now it is given the if p then r and again if r then q , so by using the law of syllogism we can state that if p then q , that is

If you camping you will need extra batteries.

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The conclusion follows from the law of syllogism .

Law of Syllogism : The Law of Syllogism allows to squeeze together the conditional statements and draw a conclusion .

In general ,

If

p → q

q → r

Then , p → r .

In the given case ,

p =  if you go camping

q = then you will need a flashlight

r = then you will need extra batteries

Hence , since p → r

if you go camping → then you will need extra batteries .

Therefore , the conclusion follows from the law of syllogism .

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the independent variable is the one that's squared, namely the "x", that means that the parabola is a vertically opening parabola, so its axis of symmetry will simply be the equation of the vertical line that passes through the vertex, hmmm what's its vertex anyway?

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-38} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 12}{2(-1)}~~~~ ,~~~~ -38-\cfrac{ (12)^2}{4(-1)}\right) \implies \left( - \cfrac{ 12 }{ -2 }~~,~~-38 - \cfrac{ 144 }{ -4 } \right) \\\\\\ (6~~,~~-38+36)\implies (\stackrel{x}{6}~~,~~-2)~\hfill \stackrel{\textit{axis of symmetry}}{x=6}[/tex]

Check the picture below.

Answer:

Below in bold.

Step-by-step explanation:

81^2/3

= 81^2 = 6561

6561^1/3

= ∛(6561)

= 18.72

√18.72

= 4.33 to nearest hundredth.

Answer:

Step-by-step explanation:

x= -2

y=2

We can conclude that ΔWXZ ≅ ΔXZY under ASA condition.

So,

To Prove: ΔWXZ ≅ ΔXZY

So, ΔWXZ ≅ ΔXZY under ASA consition.

Therefore, ΔWXZ ≅ ΔXZY.

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Answer:

[tex]\sqrt{17} }[/tex]

Step-by-step explanation:

To find the distance between these points in the Cartesian Plane, apply the distance formula (aka pythagorean theorem).

(x1-x2)^2+(y1-y2)^2= d^2 , where d is distance.

(-5-3)^2+(1-0)^2 -> (-8)^2+(1)^2 ->

16+1 -> 17

Find square root of d^2 to find d, which gives you the exact answer of [tex]\sqrt{17}[/tex].

Answer

i.d.k anformation in the table and i.d.k maria's worth

Step-by-step explanation:

Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

2

Step-by-step explanation:

just did it on khan acadmey.