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1 year ago

Please help! ! ( please answer all)

Mathematics

1 answer:

hoa [83]1 year ago

6 0

17) AB = 26

18) ∠1 and ∠2 are supplementary angles.

19) ∠1 and ∠2 are vertical angles.

20) x = 7

21) 10.125° = ∠GEF

22) x = 14

23) x = 25

<h3>How to find congruent angles?</h3>

17) AC is congruent to CE.

DE = 7x - 1

BC = 9x - 2

CE = 10x + 18

DE + DE = CE

2DE = CE

2(7x - 1) = 10x+18

14x-2 = 10x+18

14x-10x = 18+2

4x = 20

x = 20/4

x = 5

Thus; AC = CE = 10x + 18

CD = 10x + 18 - 7x + 1

CD = 3x + 19

AB = 10x + 18 - (9x - 2)

AB = 10x + 18 - 9x + 2

AB = x + 18 + 2

AB = x + 20

Since x = 5

AB = 5 + 21

AB = 26

18) ∠1 and ∠2 are supplementary angles.

19) ∠1 and ∠2 are vertical angles.

20) ∠TUV = ∠TUW + ∠WUV

7x - 9 + 5x - 11 = 9x + 1

12x - 20 = 9x + 1

3x = 21

x = 21/3

x = 7

21) Let ∠DEG = x. Thus;

∠GEF = 5x - 13

Thus;

x + 5x - 13 = 149

6x = 162

x = 162/6

x = 10.125° = ∠GEF

22) 7x - 1 + 6x - 1 = 180

13x = 182

x = 14

23) 5x + 4 = 8x - 71

3x = 75

x = 25

Read more about Congruent Angles at; brainly.com/question/1675117

#SPJ1

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The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

$\displaystyle \frac{dl}{dt} = 4 \ m/day$

$\displaystyle w = 23 \ meters$

$\displaystyle \frac{dw}{dt} = 1 \ m/day$

Step 2: Differentiate

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Step 3: Solve

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

8 0

3 years ago

Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the

scoray [572]

9514 1404 393

Answer:

7 forks
20 spoons

Step-by-step explanation:

Let x and y represent the numbers of forks and spoons made, respectively.

The cost of materials is ...

1.70x + 1.30y = 37.90

The revenue from sales is ...

5.60x + 5.40y = 147.20

You can solve these by any of your favorite methods. A graph is attached. It shows the solution is (x, y) = (7, 20).

They made 7 forks and 20 spoons.

_____

Additional working out

The equation coefficients are not "nice" multiples of each other, so elimination and substitution will require multiplying both equations by some numbers. If we're going to that trouble, we may as well use Cramer's Rule or a variation of the "cross multiplication method". The latter is relatively straightforward and can be easy to remember. It tells you the solution to ...

ax +by +c = 0

dx +ey +g = 0

is ...

1/(ae-db) = x/(bg-ey) = y/(cd-ga)

Here, that becomes ...

1/(1.70·5.40-5.60·1.30) = x/(1.30·(-147.20)-5.40·(-37.90))

= y/(-37.90·5.60-(-147.20·1.70))

1/1.9 = x/13.3 = y/38

x = 13.3/1.9 = 7 . . . number of forks

y = 38/1.9 = 20 . . . number of spoons

The above solution formula may be more easily remembered in terms of the cross-multiplication pattern that gives the method its name. When the coefficients are written in two rows of four, with the last being a repeat of the first:

a b c a
d e g d

each of the three denominators (of 1, x, and y) is the difference of products in adjacent columns, formed in an X fashion: ae-db, bg-ec, cd-ga. Note that the equations are written in "general" form, which is similar to "standard" form, but with all of the non-zero terms on the left of the equal sign. (This has the effect of changing the sign of the constants: 1.7x+1.3y=37.9 ⇒ 1.7x+1.3y-37.9=0)