Round 0.977 to the nearest hundredth

Answers

Answer 1

Answer: .98 since the hundredth place is higher than a five it is rounded up

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Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. If q represents the number of quarters, then which of the following expressions represents the number of dimes that Thomas has? 3d + 3 3q + 3 6.35 - q 10(3q + 3)

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AA, BBB, and CCC are collinear, and BBB is between AAA and CCC. The ratio of ABABA, B to BCBCB, C is 1:21:21, colon, 2. If AAA is at (7,-1)(7,−1)left parenthesis, 7, comma, minus, 1, right parenthesis and BBB is at (2,1)(2,1)left parenthesis, 2, comma, 1, right parenthesis, what are the coordinates of point CCC?

Answers

Answer:

The coordinates of point C are (-8,5).

Step-by-step explanation:

It is given that A, B and C collinear and B is between A and C.

The ratio of AB to BC is 1:2. It means Point divided the line segments AC in 1:2.

Section formula:

$((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))$

The given points are A(7,-1) and B(2,1).

Let the coordinates of C are (a,b).

Using section formula the coordinates of B are

$B=(((1)(a)+(2)(7))/(1+2),((1)(b)+(2)(-1))/(1+2))$

$B=((a+14)/(3),(b-2)/(3))$

We know that point B(2,1).

$(2,1)=((a+14)/(3),(b-2)/(3))$

On comparing both sides we get

$2=(a+14)/(3)$

$6=a+14$

$6-14=a$

$-8=a$

The value of a is -8.

$1=(b-2)/(3)$

$3=b-2$

$3+2=b$

$5=b$

The value of b is 5.

Therefore, the coordinates of point C are (-8,5).

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

How to determine the location of a point within a line segment

According to the Euclidean geometry, a line is formed by two points on a plane and three points are collinear if all the three points go through a single line.

By definitions of vector and ratio we derive an expression to determine the coordinates of the point B:

$\overrightarrow{AB} = (1)/(1+2)\cdot \overrightarrow{AC}$

$\vec B - \vec A = (1)/(3)\cdot \vec C -(1)/(3)\cdot \vec A$

$(1)/(3)\cdot \vec C = \vec B - (2)/(3)\cdot \vec A$

$\vec C = 3 \cdot \vec B - 2\cdot \vec A$

If we know that A(x,y) = (7, -1) and B(x,y) = (2, 1), then the coordinates of point C is:

C(x, y) = 3 · (2, 1) - 2 · (7, -1)

C(x, y) = (6, 3) + (- 14, 2)

C(x,y) = (- 8, 5)

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

Remark

The statement is poorly formatted and reports mistakes. Correct form is shown below:

A, B and C are collinear and B is between A and C. The ratio of AB to BC is 1 : 2. If A is A(x, y) = (7, -1) and B(x, y) = (2, 1), what are the coordinates of point C?

To learn more on line segments, we kindly invite to check this verified question: brainly.com/question/25727583

3^x : write in terms of base e and simplify! ...?

Answers

The given function is exponential. Meanwhile $<b>change of base</b>$ has something to do with logarithms. So we convert the function to logarithm function, change to the required base and convert back to exponential function.

Let

$y = {3}^(x)$

Writing the above exponential equation as a logarithmic equation, we obtain;

$log_(3)(y) = x$

We can apply the change of base formula to obtain,

$( log_(e)(y) )/( log_(e)(3) ) = x$

Or

$( ln(y) )/(ln(3) ) = x$

We can cross multiply to obtain;

$ln(y) = x ln(3)$

Taking logarithm of both sides to base e, we obtain;

${e}^( ln(y) ) = {e}^(x ln(3) )$

This implies that,

$y= {e}^(x ln(3) )$
But we know that,
$y = {3}^(x)$
Hence
${3}^(x) = {e}^(x ln(3))$

3^x : write in terms of base e would

3x=e^ln3^x

=e^xln3

PLEASE HELP ME!!! ILL GIVE THE FIRST PERSON BRAINLIEST!!!

Answers

Problem 2

Midpoint: Think 1/2. A midpoint cuts a line segment in 1/2 (in this question). That means that the left segment = the right segment. Remember: midpoint means 1/2.

LN is given as 14.

LM is 1/2 the distance of 14

LM = 1/2 * 14

LM = 7

Problem 3

If the midpoint = the 1/2 way point, the two halves are equal. Remember a midpoint divides the 2 parts into 2 EQUAL parts.

4a - 2 = 18 Add 2 to both sides

4a = 18 + 2

4a = 20

a = 20 /4

a = 5

Problem 4

Remember that midpoint means 1/2. That a midpoint cuts a segment into 2 equal segments

Equation

2n + 2 = 5n - 4

Solve

2n + 2 = 5n - 4 Add 4 to both sides

2n + 2 + 4 = 5n Subtract 2n from both sides.

6 = 5n - 2n

6 = 3n Divide both sides by 3

6/3 = n

n = 2

Answer: B

Problem 5

And again the whole line segment is divided into 2 equal parts.

Equation

6p - 12 = 4p Add 12 to both sides

6p = 12 + 4p Subtract 4p from both sides.

6p - 4p = 12

2p = 12 Divide by 2

p = 12/2

p = 6 <<<<< Answer

13=-5/4a PLEASEE HELP ME WITH THIS

Answers

Move 4a to the other side.

13(4a) = -5

52a = -5

a = -5/52

hope this helped :D

Need some help doing this question, thanks!

Answers

Answer:

y = -5x + 6

Step-by-step explanation:

y = 1/5 x + 4/5

so that two lines are perpendicular, its slope must be opposite and reciprocal

y = m x + b

m: slope perpendicular -1/m

if our formula is y = 1/5 x + 4/5

m = 1/5

so the slope of our new formula will be

m' = -5/1

m' = -5

now if you tell us that you have to go through a certain point (1/1)

we just have to replace the values in the following formula and solve

y - y1 = m ( x - x1)

y - 1 = -5 ( x - 1)

y = -5x + 5 + 1

y = -5x + 6

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