Adam’s sister wants to watch her intake of fat per day. He estimates that the dinner will have 48 grams of fat. What percentage of her total daily allowance of fat will the dinner be

Answers

Answer 1

Answer: Since she wants to watch her intake of fat, let's say she has a daily intake of 58 grams of fat per day. That's about 83% of 58.

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Normal line to the curve y=ln(2x+a) at x=1 is perpendicular to x-4y+2 = 4ln3. Find the value of a.

Answers

Hello,

The normal perpendicular to x-4y+2=4ln(3) or y=(x+2-4ln(3))/4
has as slope -4

So y'=(ln(2x+a))'=1/(2x+a) *2 if x=1 , y'=1/(2+a)
Thus
1/(2+a)=-4 ==>2+a=-1/4==>a=-1/4-2==>a=-9/4

Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets. Find the total cost of producing 8 widgets. Write your answer in quadratic equation.

Answers

The answer is Incorrect

Latrell is packing boxes that can contain two types of items. Board games weigh 3 pounds and remote controlled cars weigh 1.5 pounds. The box can hold no more than 25 pounds.Let x represent the number of board games. Let y represent the number of remote controlled cars.

Enter an inequality that represents the situation.

Answers

The correct answer is:

3x + 1.5y ≤ 25

Explanation:

The variable x represents the number of board games. Each one weighs 3 pounds, which gives us the expression 3x.

The variable y represents the number of remote control cars. Each one weighs 1.5 pounds, which gives us the expression 1.5y.

The sum of their weights gives us the expression 3x+1.5y.

Since the box can hold no more than 25 pounds, the inequality must be less than or equal to:

3x+1.5y≤25

Answer:

THE ANSWER IS 3x+1.5y ≤ 25

Step-by-step explanation:

What are the solutions to the equation x-7/x=6? a. x=-7 and x=1
b. x=-6 and x=-1
c. x=-1 and x=7
d. x=1 and x=6

Answers

$x - (7)/(x) = 6$
$(x^(2))/(x) - (7)/(x) = 6$
$(x^(2) - 7)/(x) = 6$
$x^(2) - 7 = 6x$
$x^(2) - 6x - 7 = 0$
$x^(2) - 7x + x - 7 = 0$
$x(x) - x(7) + 1(x) - 1(7) = 0$
$x(x - 7) + 1(x - 7) = 0$
$(x + 1)(x - 7) = 0$
$x + 1 = 0$ $or$ $x - 7 = 0$
$x = -1$ $or$ $x = 7$

Answer:

Step-by-step explanation:

The equation is $x-(7)/(x)=6$

LCM of the denominator on the left side gives us:

$(x^(2)-7)/(x)=6$

Cross multiplying and arranging gives us:

$x^(2)-7=6x\nx^(2)-6x-7=0$

This is a binomial, to factor this, we have to think of 2 numbers that multiplied gives us $-7$ [the constant term] and added gives us $-6$ [the coefficient of x].

The two numbers are: $-7$ and $1$ .

Now we can write:

$x^(2)-6x-7=0\n(x-7)(x+1)=0$

Hence, either $(x-7)=0$ OR $(x+1)=0$ . This gives us two solutions, $x=7$ and $x=-1$ . Answer choice C is correct.

8.92*10^9 in standard notation

Answers

8,920,000,000

Basically just add 9 0's to that number, using the first few to get rid of the decimal places.

What is the area of a rectangle with vertices at (4, 3), (11, 3), (11, 9), and (4, 9)?

Answers

Answer:

The area of a rectangle is 42 units ².

Step-by-step explanation:

As the diagram is given below.

Distance Formula

$Distance\ formula = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}$

As the rectangle with vertices at A (4, 3), B(11, 3),C (11, 9), and D (4, 9).

Take A (4, 3) to B(11, 3)

$AB = \sqrt{(11-4)^(2)+(3-3)^(2)}$

$AB = \sqrt{(7)^(2)+(0)^(2)}$

$AB = √(49)$

$√(49) =7$

AB = 7 units

As take B(11, 3) to C (11, 9).

$BC = \sqrt{(11-11)^(2)+(9-3)^(2)}$

$BC = \sqrt{(0)^(2)+(6)^(2)}$

$BC = √(36)$

$√(36) =6$

BC = 6 units

As take C (11, 9) toD (4, 9).

$CD = \sqrt{(4-11)^(2)+(9- 9)^(2)}$

$CD = \sqrt{(7)^(2)+(0)^(2)}$

$CD = √(49)$

$√(49) =7$

CD = 7 units

As take D (4, 9) to A (4, 3)

$DA = \sqrt{(4-4)^(2)+(3-9)^(2)}$

$DA = \sqrt{(0)^(2)+(-6)^(2)}$

$DA = √(36)$

$√(36) =6$

DA = 6 units

Thus

AB = DC= 7 units

AD = BC = 6 units

Formula

Area of rectangle = Length × Breadth

Length = 7 units

Breadth = 6 units

Put value in the above

Area of rectangle = 7 × 6

= 42 units ²

Therefore the area of a rectangle is 42 units ².

This is rectangle ABCD, where coordinates of the vertices are: A ( ( 4, 3 ); B ( 11, 3 ); C ( 11, 9 ) and D ( 4, 9 ). The area of the rectangle is: A = L x W ( L - length and W - width ). Length = AB = 11 - 4 = 7. Width = BC = 9 - 3 = 6. Finally: A = 7 * 6 = 42. Answer: The area of a rectangle is 42. Hope this helps. Let me know if you need additional help!

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