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3 years ago

Find the measures of:all angles if 3(m∠1+m∠3) = m∠2+m∠4

Mathematics

1 answer:

slavikrds [6]3 years ago

4 0

Answer:

Part 1) m∠1=45°

Part 2) m∠3=45°

Part 3) m∠2=135°

Part 4) m∠4=135°

Step-by-step explanation:

we know that

m∠1=m∠3 -----> by vertical angles Equation A

m∠2=m∠4 -----> by vertical angles Equation B

m∠1+m∠2=180° ----> by supplementary angles (linear pair) Equation C

3(m∠1+m∠3) = m∠2+m∠4 ----> Equation D

Substitute equation A and equation B in equation D

3(m∠1+m∠1) = m∠2+m∠2

6(m∠1) = 2m∠2

3(m∠1) =m∠2 -----> equation E

Substitute equation E in equation C and solve for m∠1

m∠1+3(m∠1)=180°

4(m∠1)=180°

m∠1=45°

Find the measure of m∠3

Remember that

m∠1=m∠3 (equation A)

therefore

m∠3=45°

Find the measure of m∠2

Remember that

m∠2=3(m∠1) (equation E)

substitute the value of m∠1

m∠2=3(45°)=135°

Find the measure of m∠4

Remember that

m∠2=m∠4 (equation B)

therefore

m∠4=135°

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Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

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2 years ago

Among two supplementary angles, the measure of the larger angle is 44°

zhuklara [117]

Answer:

68° and 112°

Step-by-step explanation:

Supplementary angles sum to 180°

let the smaller angle be x then the larger angle is x + 44 , then

x + x + 44 = 180 , that is

2x + 44 = 180 ( subtract 44 from both sides )

2x = 136 ( divide both sides by 2 )

x = 68

Smaller angle = 68° and

larger angle = x + 44 = 68 + 44 = 112°

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3 years ago

What’s the quotient of 20 and 2

olasank [31]

the answer is 10 hoped this helped have a great day

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3 years ago

Read 2 more answers

A line m is perpendicular to an angle bisector of ∠A. The sides of ∠A intersect this line m at points M and N. Prove that △AMN i

Ray Of Light [21]

Answer:

Step-by-step explanation:

Given: A line m is perpendicular to the angle bisector of ∠A. We call this

intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.

AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.

To Prove: ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are

equal.

Solution: Now, In ΔADM and ΔADN

∠MAD=∠NAD ...(1) (∵Given)

AD=AD ...(2) (∵common side)

∠ADM=∠ADN ...(3) (∵Given)

Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN

( ∵ ASA congruence rule)

⇒ AM=AN

Now, In Δ AMN

AM=AN (∵ Proved)

Hence, ΔAMN is an isosceles triangle.

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