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3 years ago

The first four terms of an arithmetic sequence are -11,-5,1,7. what is the equation for an

Mathematics

1 answer:

mr_godi [17]3 years ago

7 0

Answer:

y = 6x - 11

Step-by-step explanation:

An arithmetic sequence is a linear function. This means it steadily increases or decreases through addition/subtraction by a constant amount. Here the sequence grows by adding 6 each time.

-11 + 6 = -5

-5 + 6 = 1

1 + 6 = 7

etc....

Since this is linear, its equation has the form y = mx + b where m is the slope and b is the y-intercept. The slope is m = 6 and b = -11.

y = 6x - 11

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How much is the number 727731000 in percent form

tankabanditka [31]

Answer:

72773100000%

Step-by-step explanation:

"Percent" means "per 100" or "over 100". So, to convert 727731000 to percent we rewrite 727731000 in terms of "per 100" or over 100.

Multiply 727731000 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

7277310001×100100=72773100000100

72773100000/100 is 72773100000 over 100 and means 72773100000 per 100. 72773100000 "per 100" means 72773100000 "percent" or 72773100000%

Therefore, we have shown that

727731000 = 72773100000%

Simplified Conversion:

Multiply by 100 and add the percent sign %

727731000 × 100 becomes 72773100000%

Shortcut Conversion:

Move the decimal point 2 places to the right and add the percent sign %

727731000 becomes 72773100000%

7 0

3 years ago

Read 2 more answers

The answer and how you got the answer

olasank [31]

Answer:

$\frac{34}{15}$

Step-by-step explanation:

we are asked to evaluate

$4\tfrac{1}{4}$ ÷ $1\tfrac{7}{8}$

Above we are given mixed fraction which can be converted in proper fraction using formula given below

$a\tfrac{b}{c}=\frac{a \times c +b}{c}$

Hence

$4\tfrac{1}{4}=\frac{4 \times 4 +1}{4}$

$4\tfrac{1}{4}=\frac{17}{4}$

Also

$1\tfrac{7}{8}=\frac{1 \times 8 +7}{8}$

$1\tfrac{7}{8}=\frac{15}{8}$

Hence

$4\tfrac{1}{4}$ ÷ $1\tfrac{7}{8}$

can be written as

$\frac{17}{4}$ ÷ $\frac{15}{8}$

Also we know the rule for dividing fraction is as given below

$\frac{a}{b}$ ÷ $\frac{c}{d}$ = $\frac{a}{b} \times \frac{d}{c}$

Hence

$\frac{17}{4}$ ÷ $\frac{15}{8}$ = $\frac{17}{4} \times \frac{8}{15}$

= $\frac{17 \times 2}{15}$

= $\frac{34}{15}$

8 0

3 years ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T

Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180 ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

$60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}$

$105^{\circ}+ m\angle B=180^{\circ}$

Simplify:

$m\angle B=75^{\circ}$

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

$\frac{\sin A}{BC} = \frac{\sin C}{AB}$

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

$\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}$

then,

$BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}$

$BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798$ unit

Similarly for AC:

$\frac{\sin B}{AC} = \frac{\sin C}{AB}$

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

$\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}$

then,

$AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}$

$AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283$ unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

$A = \frac{1}{2} \times AB \times AC \times \sin A$

Substitute the values in above formula to get area;

$A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}$

$A = 4 \times 10.9283 \times 0.86602540378$

Simplify:

Area of triangle ABC = 37.856 (approx) square unit

4 0

3 years ago

Which statement describes the translation of y=-1/2(x-2)^2-2 from standard position?

Masteriza [31]

Y = x^2 is the parent function.
y = (x - 2)^2 would translate 2 units to the right
y = (x - 2)^2 - 2 would translate 2 units to the right and also 2 units down
y = - (1/2) (x - 2)^2 - 2
would reflect the parabola upside down, and also make it wider

6 0

3 years ago

Help me please I will give brainiest

nadya68 [22]

8.a)
A= (1,1) A’= (3,3)
B= (4,6) B’= (12,18)
C= (6,1). C= (18,3)

8b.)

A= (1,1) A’(0,5,0.5)

B= (4,6) B(2,3)

C= (6,1). C(3,0.5)

Hope this helped ! :)

8 0

3 years ago