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3 years ago

13

describe how axioms about addition in particular could be helpful in developing theorems about multiplication.

1 answer:

Lady_Fox [76]3 years ago

8 0

The axioms in addition help in developing theorems about multiplication because multiplication, in simple terms, repeated addition.
As an example,
This addition operation
3 + 3 + 3 + 3 = 12
can be expressed as a multiplication operation
3 x 4 = 12
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Convert -2x+6y=-24 to slop intercept form

Firlakuza [10]

Answer:

y= 1/3x - 4

Step-by-step explanation:

hope this helps

3 0

3 years ago

A tree grows vertically on a hillside. The hill is at a 16° angle to the horizontal. The tree casts an 18-meter shadow up the hi

elixir [45]

The height of the tree is the sum of the part below the line parallel to the horizontal and the part above the line parallel to the horizontal.

Height of the part below the line parallel to the horizontal = 18 sin16° = 4.96 meters
Horizontal distance of the tip of the of the shadow from the tree = 18 cos16° = 17.30 meters
Height of the part above the line parallel to the horizontal = 17.3 tan68° = 42.83 meters

Height of the tree = 4.96 + 42.83 = 47.79 meters

8 0

3 years ago

The expression 148 – 24d gives the number of pizzas a store has in stock, where d is the number of days. How many pizzas will th

Feliz [49]

Explanation

A function is defined as a relation between a set of inputs having one output each,in this case our independent variable is the number of days( d) and the dependent variable would be the number of pizzas

so

Step 1

let the function

$\begin{gathered} P=148-24d \\ where\text{ P is the number of pizzas } \\ and\text{ d is the number of days} \end{gathered}$

therefore, to know the number of pizzas are in the stock after 5 days we need to evaluate the equation for d=3

so

$\begin{gathered} P=148-24d \\ let\text{ d=5 and evaluate} \\ P=148-24(5) \\ P=148-120=28 \\ P=28 \end{gathered}$

so, after five day there willbe 28 pizzas in stock

I hope this helpsyou

6 0

1 year ago

Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = x^2 - x + 1 text( on ) [1,8]; M = 21 c =

DanielleElmas [232]

Answer:

$c = 5$

Step-by-step explanation:

Given

$f(c) = M$

$f(x) = x^2 - x + 1$

$Interval: [1,8]$

$M = 21$

Required

Find c using Intermediate Value theorem

First, check if the value of M is within the given range:

$f(x) = x^2 - x + 1$

$f(1) = 1^2 - 1 + 1$

$f(1) = 1$

$f(x) = 8^2 - 8 + 1$

$f(x) = 57$

$1 \le M \le 57$

$1 \le 21 \le 57$

M is within range.

Solving further:

We have:

$f(c) = f(x) = M$

$f(x) = 21$

Substitute 21 for f(x) in $f(x) = x^2 - x + 1$

$21 = x^2 - x + 1$

Express as quadratic function

$x^2 - x + 1 - 21 = 0$

$x^2 - x - 20 = 0$

Expand

$x^2 + 4x - 5x - 20$

$x(x+4)-5(x+4)=0$

$(x - 5)(x+4) = 0$

$x - 5 = 0$ or $x + 4= 0$

$x = 5$ or $x = -4$

The value of $x = -4$ is outside the $Interval: [1,8]$

So:

$x = 5$

$f(c) = f(x) = M$

$f(c) = f(5) = 21$

By comparison:

$c = 5$

4 0

3 years ago

To determine the squirrel population in a city park, researchers tagged 90 squirrels. Later, they counted 630 squirrels, 42 of w

KonstantinChe [14]

Answer:

1350

Step-by-step explanation:

Initially 90 squirrels were tagged out of a total population of x squirrels.

Similarly, 42 squirrels out of a sample of 630 squirrels had tag

We can use ratio equality to find the total population x.

42:90=620:x

$\frac{42}{90} =\frac{630}{x}$

Cross multiplying

42 X x = 630 X 90

Dividing both sides by 42

$x=\frac{630 X 90}{42} \\=1350$

The total number of squirrels in the city park is 1350.

6 0

3 years ago