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il63 [147K]
3 years ago
6

Amanda increased the amount of protein she eats everyday from 48g to 54g . by what percentage did Amanda increase the amount she

eats
A. 12.5%
B.6%
C.112.5%
D. Not here
Mathematics
1 answer:
Mandarinka [93]3 years ago
8 0
The answer should be A
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F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?
Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

The ratio by which the point F divides the line = 3:1

The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) =  (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

l_{HF} = \sqrt{\left (4-7  \right )^{2}+\left (1-(-11)  \right )^{2}} = \sqrt{\left (-3  \right )^{2}+\left (12  \right )^{2}} = 3\cdot \sqrt{17}

Similarly, we check the length of HJ, to get;

l_{HF} = \sqrt{\left (3-7  \right )^{2}+\left (5-(-11)  \right )^{2}} = \sqrt{\left (-4  \right )^{2}+\left (16  \right )^{2}} = 4\cdot \sqrt{17}

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

7 0
3 years ago
Which number line represents the solution set for the inequality -4(x + 3) S-2 - 2x?
Basile [38]

Answer:

Which number line represents the solution set for the inequality -4(x + 3) S-2 - 2x?

-7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

+ + +

-7 -6 -5 -4 -3 -2 -1 0

+

1

+

2

+

3

0 1 2

Step-by-step explanation:

5 0
3 years ago
Help with this question please!
Anton [14]

∠1 and ∠2 are alternate exterior angles where transversal BE crosses parallel lines AC and DF, therefore they are equal. ∠2 and ∠3 are opposite angles of a parallelogram, therefore they are equal.

... ∠1 = ∠2

... 3x -5 = 2x +15 . . . . substitute the given values

... x = 20 . . . . . . . . . . . add 5-2x

The measures of angles 1, 2, and 3 are 2·20+15 = 55 . . . degrees.

5 0
3 years ago
The roots of a quadratic function are x = -3 and x = 2/3. Which of the following would be the constant term of the equation in s
Alla [95]

Answer:

-2

Step-by-step explanation:

Since the roots are known and the function is a quadratic function, we can write down the function:

y = (x+3)(x-2/3) since when the roots are plugged in, the function gives 0.

Standard form means that the function has to be expanded:

y = (x+3)(x-2/3) = x^{2}+3x - 2x/3 - 3*2/3

y = x^{2}+ 7x/3 - 2

The constant term is -2.

7 0
3 years ago
Replace ∗ with a monomial so that the derived expression may be represented as a square of a binomial: * +14b+49
anyanavicka [17]

Answer:

  * = b²

Step-by-step explanation:

You know that the square of a binomial is of the form ...

  (x + y)² = x² + 2xy + y²

Matching given terms, we have ...

  49 = y²

  2xy = 14b

Solving the first of these relations for y, we have

  y = √49 = 7

Putting that in the second relation and solving for x, we find ...

  2x·7 = 14b

  14x = 14b

  x = b

Then the first term of the expansion, x², will be b².

The missing term is b².

7 0
3 years ago
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