Whats 32% of 80???????????

What is the slope of the line that passes the points (3, 1) and (2, 4).

aliya0001 [1]

Answer:

(x1, y1) = (3, 1)

(x2, y2) = (2,4)

the slope is

m= y2−y1/x2−x1 = 4-1/2-3 = 3/-1 = <u>-3</u>

5 0

2 years ago

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.

natka813 [3]

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

Let x be the amount of time in hours

Let y be the heoght of a candle in centimeters

The two points are then as (9,24.5) and (23,17.5).

$\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(9,\:24.5\right)\mathrm{,\:}\left(23,\:17.5\right)$

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)$

$m=\frac{17.5-24.5}{23-9}$

$m=-0.5$

$\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b$

$y=\left(-0.5\right)x+b$

$\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5$

$24.5=\left(-0.5\right)\cdot \:9+b$

$-4.5+b=24.5$

$b=29$

$\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29$

$y=-0.5x+29$

Now plug in x=21, we get

$y=-0.5*21+29=18.5$

Thus the height of the candle after 21 hours is 18.5 centimeters.

7 0

3 years ago

Trapezoids and kites

lisov135 [29]

QUESTION 3

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 36\degree +70\degree+m$ .

$\Rightarrow 106\degree+m$ .

$\Rightarrow m$ .

But the two remaining opposite angles of the kite are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

QUESTION 4

RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.

Using the Pythagoras Theorem, we obtain;

$|RH|^2=12^2+20^2$

$|RH|^2=144+400$

$|RH|^2=544$

$|RH|=\sqrt{544}$

$|RH|=4\sqrt{34}$

QUESTION 5

The given figure is an isosceles trapezium.

The base angles of an isosceles trapezium are equal.

Therefore $m$

QUESTION 6

The measure of angle Y and Z are supplementary angles.

The two angles form a pair of co-interior angles of the trapezium.

This implies that;

$m$

$\Rightarrow m$

QUESTION 7

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 48\degree +110\degree+m$ .

$\Rightarrow 158\degree+m$ .

$\Rightarrow m$ .

But the two remaining opposite angles are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

QUESTION 8

The diagonals of the kite meet at right angles.

The length of BC can also be found using Pythagoras Theorem;

$|BC|^2=4^2+7^2$

$\Rightarrow |BC|^2=16+49$

$\Rightarrow |BC|^2=65$

$\Rightarrow |BC|=\sqrt{65}$

QUESTION 9.

The sum of the interior angles of a trapezium is $360\degree$ .

$\Rightarrow m$ .

But the measure of angle M and K are congruent.

$\Rightarrow m$ .

6 0

3 years ago

It would be great if someone could help me with this problem

GaryK [48]

Y-intercept (0, 1)
Equation of asymptote y=0

Equation of asymptote can also be called horizontal asymptote.
It means the place where the line almost meets but actually not touching the place. The line almost touches y=0 but it actually does not touch it.

7 0

2 years ago

Find the product. Simplify your answer.<br> -5 • 9t<br> 7s 7

Sauron [17]

Answer:

-13

——— = -0.20635

63

Step-by-step explanation:

Step 1 :

7

Simplify —

9

Equation at the end of step 1 :

4 7

— - —

7 9

Step 2 :

4

Simplify —

7

Equation at the end of step 2 :

4 7

— - —

7 9

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : 7

The right denominator is : 9

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

7 1 0 1

3 0 2 2

Product of all

Prime Factors 7 9 63

Least Common Multiple:

63

Calculating Multipliers :

3.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 9

Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 4 • 9

—————————————————— = —————

L.C.M 63

R. Mult. • R. Num. 7 • 7

—————————————————— = —————

L.C.M 63

Adding fractions that have a common denominator :

3.4 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4 • 9 - (7 • 7) -13

——————————————— = ———

63 63

Final result :

-13

——— = -0.20635

63

8 0

2 years ago

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