Minnie is making tea. She knows that her tea tastes best if she lets her tea bag sit in the hot water for exactly fifteen minutes. However, depending how hot the water is, she may have to leave her tea bag in the water for 2 minutes more or less than usual. Write and solve an absolute value equation to describe this situation

Answer:

1/2

Step-by-step explanation:

Given that,

[tex]\lim_{n \to 1} (\dfrac{1+\cos\pi x}{\tan^2\pi x})[/tex]

Using L Hospital's rule to find it :

[tex]\lim_{n \to a} \dfrac{f(x)}{g(x)}= \lim_{n \to a} \dfrac{f'(x)}{g'(x)}[/tex]

We have,

a = 1, [tex]f(x)=1+\cos\pi x, \ \ g(x)=\tan^2\pi x[/tex]

[tex]f'(x)=\dfrac{d}{dx}(1+\cos\pi x)\\\\=-\pi \sin \pi x\ .....(1)[/tex]

[tex]g'(x)=\dfrac{d}{dx}(\tan^2\pi x)\\\\=2\tan\pi x\times \sec^2\pi x\times \pi\ .....(2)[/tex]

From equation (1) and (2) :

[tex]\lim_{n \to 1} \dfrac{f(x)}{g(x)}= \lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\\lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\=\lim_{n \to 1} \dfrac{-1}{2}\times\cos^3\pi x\\\\=\dfrac{-1}{2}\times \cos^3\pi \\\\=\dfrac{1}{2}[/tex]

So, the value of the given function is 1/2.

Answer:

B. 1/3

Step-by-step explanation:

The total number of sides in the cube are 6 (1,2,3,4,5,6). If Dimas only wants to roll either a 2 or 3 then that would mean that he has 2 chances out of the total 6 probable outcomes to roll one of those numbers. Therefore, in order to find the probability of this happening in a single roll we need to divide the number of times that his two choices appear on the dice by the total number of sides the dice has, like so...

2 / 6 = x

If we simplify it would give us [tex]\frac{1}{3}[/tex]

Answer:

60%

Step-by-step explanation:

add them all to 20

add 7 and 5 to get 12

12 over 20 is 60 percent

Answer:

The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.

Then one angle is marked as a right angle meaning it has a measure of 90 degrees.

Using this information and the labels on the diagram we can set up an equation:

x+3x+2+90=180

Now we can solve for x.

4x+92=180

4x=88

x=22 degrees

The measure of one of the acute angles is 22 degrees.

Now to solve for the measure of the other acute angle.

Subsitute the value of x first.

x=22

(3x+2)=?

3*22+2=68 degrees

The measure of the other acute angle is 68 degrees.

In the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

The triangle given is a right triangle having an angle tat is 90 degrees and two other acute angles given as: x and (3x + 2)

Thus:

[tex]x + (3x + 2) + 90 = 180^{\circ}[/tex] (sum of triangle)

[tex]x + 3x + 2 + 90 = 180[/tex]

[tex]4x + 92 = 180\\\\[/tex]

[tex]4x = 180 - 92\\\\4x =88[/tex]

x = 22

Measure of one of the acute angles is 22 degrees.

To find the second acute angle measure, substitute the value of x

3x + 2 = 3(22) + 2 = 68 degrees

Therefore, in the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

Learn more here:

https://brainly.com/question/347922

Answer:

Use an app called Cymath it tells you the answer and it shows you step by step on how to work it out. I used the app multiple times and it helps me a lot!

Step-by-step explanation:

Hope I helped! :)

Answer:

Speed = 25miles per hour

Step-by-step explanation:

Represent the time with x and the distance with y

So, from the attachment; we have the following details:

[tex](x_1,y_1) = (0.5,12.5)[/tex]

[tex](x_2,y_2) = (1,25)[/tex]

[tex](x_3,y_3) = (1.5,37.5)[/tex]

Required

Determine the constant speed

Because the train travelled at a constant speed, the speed can be calculated using:

[tex]Speed = \frac{y_3}{x_3}=\frac{y_2}{x_2}=\frac{y_1}{x_1}[/tex]

[tex]Speed = \frac{12.5}{0.5}=\frac{25}{1}=\frac{37.5}{1.5}[/tex]

[tex]Speed = 25=25=25[/tex]

Notice that the result of each division is the same.

Hence, the constant speed is:

Speed = 25miles per hour

Answer:

Check box 4 and 5

Step-by-step explanation:

We know there can only be up to 2 solutions for a quadratic equation.

5x^2-2x-9=0 is your equation, make sure to move that 1 to the left

Now we can use the quadratic formula

a=5

b= -2

c= -9

x= −1.15647

x=1.55647

Thus I would select the last 2 boxes. Both of them are solutions.

Answer:

11

Step-by-step explanation:

Answer:

13.44

Step-by-step explanation:

she is right...........

Answer:

The correct unit price is $1.12 per pair. The error comes from dividing $67.20 by only 5 pairs (instead of 60 pairs).

Step-by-step explanation:

The contractor should have calculated the unit price as $67.20 divided by 60 pairs. Five dozen pairs is 5x12=60. This results in $67.20/60=$1.12 per pair. The error comes from dividing $67.20 by only 5 pairs (instead of 60 pairs).

Answer: I Believe 15%, But I'd Double Check.

Answer:

x=-2, 2.

Step-by-step explanation:

5x^2-20=0

factor out the 5

5(x^2-4)=0

5(x+2)(x-2)=0

(x+2)(x-2)=0/5

(x+2)(x-2)=0

x+2=0, x-2=0

x=0-2=-2,

x=0+2=2.

Answer: 1,120 frogs

Step-by-step explanation:

If 12 out of every 180 frogs in the population have spots on their backs, the number that do not are;

= 180 - 12

= 168 frogs

168 frogs out of every 180 do not have spots. Out of 1,200 that would be;

= 168/180 * 1,200

= 1,120 frogs

Answer:

good job its very good

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

The equation is

x×2=285-x

3x=285

x=95

Answer:

x = 75°

Step-by-step explanation:

There are many Circle Geometry Rules. We will be using the following:

The angle at the centre of the circle is twice the angle at the circumference.

x = the angle opposite 285 - x.

This means that 360 - (285 - x) = 2x

360 - 285 + x = 2x

75 + x = 2x

We can simplify this by taking away x from both sides.

75 = x

We can check this by substituting x into the orginal equation.

360 - (285 - x) = 2x

360 - (285 - 75) = 2 * 75

360 - 210 = 2 * 75

150 = 2*75

150 = 150

Answer:

x = -1

Step-by-step explanation:

i multiplied the first equation by 2 to eliminate the fractions and got:

-4x + y = 3

used substitution method:  y = 3 + 4x

x - 3(3 + 4x) = 2

x - 9 -12x = 2

-11x = 11

x = -1

Answer:

The image of the point (2, 3) after the reflection across the y-axis will be: (-2, 3)

Step-by-step explanation:

We know that when a point, let say P(x, y), is reflected across the y-axis, the sign of x-coordinate is reversed but y-coordinate remains the same.

In other words, the rule is:

P(x, y) → P'(-x, y)

Here, P'(x, y) is the image of the original point P(x, y) after the reflection across the y-axis.

Considering the point

Let us reflect the point A(2, 3) across the y-axis.

We know the rule:

P(x, y) → P'(-x, y)

so

A(2, 3) → A'(-2, 3)

Thus, the image of the point (2, 3) after the reflection across the y-axis will be: (-2, 3)

Answer:

first one

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x-intercept is (-4,0)

y-intercept is (0,-3)

Answer:

B.x<0 cs u useing easy steps

Answer:

P = 50.39 cm

Step-by-step explanation:

It is given that,

The side of a square, a = 5∛16 cm

We need to find the perimeter of the square.

Perimeter = sum of all sides.

All sides of a square are equal. Its perimeter is given by :

P = 4a

[tex]P=4\times 5\sqrt[3]{16} \\\\P=50.39\ cm[/tex]

So, the exact perimeter of the square is 50.39 cm.

Answer:

A Positive

Step-by-step explanation:

If we input the fraction given to us by using the text editor, we have:

\dfrac{b}{c}

OUTPUT:

[tex]\dfrac{b}{c}[/tex]

The sign before that fraction term is known as positive.

Answer:

a. postive

Step-by-step explanation:

Answer: Dried apricots are less expensive they are $8.75

Step-by-step explanation: I divided 21.98 by 2 and got 10.99 then I divided 26.25 by 3 and 8.75 which makes dried apricots less expensive

Answer:

Olivia's puppy, it weighed 5 pounds.

Step-by-step explanation:

Answer:

800 > x + 375

x < 425

Step-by-step explanation:

800 > x + 375

425 > x

Answer:

2 bags of topsoil.

Step-by-step explanation:

The attached figure shows a flower bed.

One bag of topsoil covers 15 square meters.

We need to find how many bags of topsoil does Tom need to cover his flower bed.

The area of the flower bed is :

[tex]A=\dfrac{1}{2}\times 12\times 5\\\\=30\ m^2[/tex]  

Let he has to cover x bags of topsoil. So,

x = Area of flower bed/Area of 1 bag of top soil

x = 30/15

x = 2

Hence, he will need 2 bags of topsoil to cover his flower bed.

Answer:

-1

Step-by-step explanation:

Given the equation :

2(3x – 1) > 4x – 6

Open the bracket :

6x - 2 > 4x - 6

Collect like terms

6x - 4x > - 6 + 2

2x > - 4

Divide both sides by 2

2x /2 > - 4/2

x > - 2

Since x > - 2

-10, - 5, - 3 are all < - 2

Hence, the only option greater than - 2 is - 1