Select all the correct answers.
Which statements are true about the graph of function f?
f(x) = log x

From the question,

The equation for the distance covered by the kids is d = 1 t + 34

The equation for the distance covered by the adults is d = 2t

Now, when the adults caught up with the kids was when : 2 t = 1 t + 34

Solving this equation, we have 2 t - 1 t = 34

t = 34

since d= 2 t , when t = 34

d = 2 x 34 = 68

It took ___34_ seconds for the adults to go _68___ meters and catch up to the kids.​

Real numbers contain the number zero and can be either positive or negative.

If x > y, then max (x, y) = x and min (x, y) = y.

So, max (x, y) + min (x, y) = x + y

Real numbers contain the number zero and can be either positive or negative. Because they exists not imaginary, which exists a separate type of number system, they are directed to as real numbers. Unquantifiable quantities, like the square root of -1, are referred to as imaginary numbers.

A "actual" and practical idea, infinity. Infinity, on the other hand, is not a number on the real number line since it is not a part of the mathematically defined set of "real numbers."

If x > y, then max (x, y) = x and min (x, y) = y.

So, max (x, y) + min (x, y) = x + y

If x ≤ y , then max (x, y) = y and min (x, y) = x.

And we have, max (x, y) + min (x, y) = y + x = x + y

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Answer:

  (6√13)/13

Step-by-step explanation:

You want the exact value of cot(arcsin(√13/7)).

The relevant trig ratios are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

  Cot = 1/Tan = Adjacent/Opposite

The Pythagorean theorem can be used to find the side adjacent to the angle whose sine is √13/7. Using the sine ratio, we can take the opposite side to be √13, and the hypotenuse to be 7. Then the adjacent side is ...

  adjacent² +opposite² = hypotenuse²

  adjacent² +(√13)² = 7²

  adjacent² = 49 -13 = 36

  adjacent = √36 = 6

Then the cotangent of the angle is ...

  cot(arcsin(√13/7)) = adjacent/opposite = 6/√13

  cot = (6√13)/13

Consider 9,168 ounces of spinach is 20% more than the amount of spinach of the last month. If x is such unknown amount of spinach, you can write:

where (2/100)x factor represents the 20% of x.

Simplify the pervious equation and solve for x:

Hence, last month the restaurant used 7,640 amount of spinach.

If we have the following number:

and we want to write it as a power of 10 in exponent, we just have to count the zeros of the number, in this case there are 5, and that would be our exponent, then, we have:

Answer:

20 hope this is helpful and also enjoy your day

I am 5 when you multiply me by 6, then divide the product by 3, the quotient is 10.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Assuming I am 'n'.

∴ When you multiply me by 6, which is 6n, then divide the product by 3, which is 6n/3 the quotient is 10 which is 6n/3 = 10.

6n/3 = 10.

2n = 10.

n = 5.

So, I am an odd number 5.

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In linear equation, value of x and y = ( 10 , 3 ).

What is linear equation with example?

3x + 5y = 45 ............1

2x + 4y  =32 .........2

Multiply by 2 in equation 1  and by 3 in 2

   6x + 10y = 90

   6x + 12y =  96

equation 2 - equation  1

          2y = 6

            y = 3

put value of y put in equation 1

   3x + 5y = 45

   3x + 5 * 3 = 45

  3x  = 45 - 15

     3x = 30

      x = 10

value of x and y = ( 10 , 3 )

the value of the objective function at each of the vertices to find the maximum.

I'll do one vertex, you do the rest.

(0,8)

F = 2x + y

F = 2 * 0 + 8

F = 8

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1) Considering that this is our parent function:

2) Then let's visualize what happens when we transform it to :

3) So now let's reflect that across the y-axis, and vertically shrink that by 1/3:

Answer:

No

Step-by-step explanation:

V/3 is -35, which is smaller than 5

Answer: 3 years

$60,000

Company B

Step-by-step explanation: Analyze the data on the graph

We are given a function, y = 2x + 11, where x is the number of miles driven. If we are told that the cab was driven 5 miles, x = 5. So, substitute 5 for x.

y = 2x + 11
= 2(5) + 11
= 10 + 11
= 21
y = 21

Answer:

C' = (10, 1)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units down.

Step-by-step explanation:

If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.

Given vertices of triangle ABC:

To maintain similarity but not maintain congruence, dilate triangle ABC (since dilation keeps the corresponding angles of both triangles the same).

Given vertex of triangle A'B'C':

If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8).  If the triangle is then translated 3 units down, B' = (2, 5), which matches the given coordinate of point B'.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x, 2y - 3)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5), 2(2) -3) = (10, 1)

Answer:

t - 2 ≤ 0

Step-by-step explanation:

Given inequality
t- 2  ≤ 0

Add 2 on both sides of the inequality without changing the meaning

t - 2 + 2 ≤ 0 + 2

or

t ≤ 2

Looking at the number line given, we can see that all numbers to the left of 2 including 2 are part of the solution set

Hence the solution set graphed is t- 2  ≤ 0

Answer:

Step-by-step explanation:

Y = 22 - 2Z

22 - 2Z + Z = 16

22 - Z = 16

Z = 6

Y + Z = 16

Y + 6 = 16

Y  = 10

The expression we have is:

Step 1. To solve for x, we need to first apply the distributive property on the right-hand side of the equation. The distributive property is to multiply the number outside each pair of parenthesis by the terms inside it. We get the following:

Solving the multiplications on the right-hand side:

Step 2. Combine the like terms.

We start by combining the terms that contain x:

And then, combine the independent terms:

Step 3. Add 3x to both sides of the equation:

On the left side, we get that -3x+3x cancel each other:

As we can see, this is not true, which means that there is no solution for x.

Answer: There is no solution for x.

He will require 9 weeks to attend class, Based on given condition, 7.5 + 2.5x = 30.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

According to question,

The time he spend as instructor is 7.5 and 2.4 hour class.

total hours = 30

7.5 +2.5x = 30

2.5x = 30- 7.5

2.5x = 22.5

x= 22.5/2.5

x = 9

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To solve this problem we need to use the compound interest formula:

Where P is the initial deposit:

r is the interest rate in decimal form, since the interest rate is 11%, in the decimal form we have:

n is the number of times that the interest is compounded in a year, in this case, it is compounded quarterly, and since there are 3 quarters in a year, the interest will be compounded 3 times per year:

and t is the total time, in this case, 3 years:

Substituting all of these values into the formula to find the Amount "A" they will have after 3 years:

Solving the operations:

Answer: They will have $967.944 to spend

Explanation:

Part A:

The question is given below as

By putting x=0, we will have that

Hence,

The final answer for part A is

Part B:

add 4 to both sides

Hence,

The final answer for part B is

Part C:

Add 4 to both sides, we will have

Hence,

The final answer for part C is YES

Part D:

Hence,

The final answer for part D is given below as

We need to sketch the graph of V(t), with V in ml and t in seconds. Notice that:

because for t = 0, her lungs start with a volume of 2200 ml.

Since the period (of a complete breath) is 4 seconds, and the function is sinusoidal, the graph is:

b. Now, a sinusoidal function has the form:

where:

• A is the amplitude (half the difference between the smallest and the largest values of V);

• T is the period;

• b is the horizontal shift (the difference between the initial value of t and the value of t for which V(t) has the mean value);

• c is the vertical shift (the mean value of V(t)).

So, observing the graph, we see that:

Therefore, the equation representing the volume V, in ml, after t seconds is:

c. If Aira breathed more rapidly, the period and the horizontal shift of the function V(t) would be smaller. Thus, the graph would change more rapidly also, i.e., we would see more variations in the 20 seconds.

For example, if she breathed 2 times faster, the period would be 2 instead of 4, and the equation would be:

And the graph would be:

And if Aire took bigger breaths, the amplitude and the vertical shift of the function V(t) would increase. For example, if her lungs could reach the volume of 3000 ml, assuming the same period of 4 seconds, the equation would be:

And the graph would be:

The meaning of solving a formula for a variable is rewriting the formula in a way that the variable is "isolated" in one side of the formula, that is, one side of the equation has only the variable alone, without coefficients or other expressions.

For example, let's solve the formula below for the variable y:

We can see that in the formula above, the left side of the equation has only "y", this way it is solved for y.

Using proportions, it is found that the temperature after 8 hours is of -12.63 degrees.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using arithmetic operations such as multiplication or division considering the given rates in the function.

The temperature is of -12 degrees, and rises by 5/8 every hour for 3 hours, hence the temperature in 3 hours will be given by:

-12 + 3 x 5/8 = -12 + 15/8 = -10.13 degrees.

Then, for each of the next 5 hours, the temperature drops by 0.5 degrees, hence the temperature after 8 hours will be given by:

-10.13 degrees - 5 x 0.5 = -10.13 - 2.5 = -12.63 degrees.

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Solution:

Given:

Therefore, the probability of picking a number divisible by 3 is;

We can use the Pythagoras Theorem:

The hypotenuse is 10.63

Answer: 4 mph

Step-by-step explanation:

If woman can walk xmph, then she can ride {x + 10} mph (because she can ride 10 mph faster than she can walk)

Woman ride 28 miles by 28 hours, and can walk 8 miles by 8 hours.

                                        x+10                                                    x

28  =8                    [tex]28x=8%28x%2B10%2928x=8x%2B8020x=80x=80%2F20x=4[/tex]

x+10  x  

Based on the given graph, you can conclude:

A. Relative Maximum is f(x) = 1 where x = 2

(Because the relative maximum of a function is given by a point of the graph with a slope m = 0, but this point is not necessarily the absolute maximum. Furthermore, the concavity of the curve at this point is negative).

B. Relative minimum is f(x) = -8 where x = -3

C. Relative minimum is f(x) = 0 where x = 4

Both relative minima correspond to points in which the slope of the line is 0 and the concavity of the line is positive.

By proportion, Chris should mix 8/3 parts of the red paint in 2 fluid ounces of blue paint.

Purple paint is made using a combination of red paint and blue paint.

Now Allison made purple paint by mixing 3 parts red [aint and 4 parts blue paint.

Therefore, the ratio for the purple paint is :

= 4 parts blue paint / 3 red paint

Chris has 2 fluid ounces of blue paint.

Let the amount of red paint Chirs have to be x.

Then the proportion should be equal.

So,

4 / 3 = x / 2

By cross multiplication,

4 × 2 = 3 × x

8 = 3x

Dividing each side by 3,

x = 8/3

Chirs should mix 8/3 parts of the red paint with blue paint.

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Given:

Radius of circle r is 18 cm.

angle

Required:

We need to find the arc length in cm

Explanation:

The formula to find arc length is

Substitute the values in the formula

Final answer:

Arc length of given circle is 47.1 cm

Answer:

No Solution

Explanation:

Given the system of equations:

First, graph each equation using the x and y-intercepts.

Equation 1

Join the points (0,4) and (-2,0) as done below:

Equation 2

Join the points (0,5) and (-2.5, 0) as done below:

We observe that the two lines are parallel.

Therefore, the system of equations has No Solution.

The value of the height of the rectangle is 80 m.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: length and height. Due to its characteristics, the rectangle presents two length (L) and two heights (H).

The perimeter is the sum of all sides of a geometric figures. For a rectangle, the perimeter is 2L+2H.

The question gives:

From the perimeter, you can find the height, see below.

P=2L+2H

360=2*(20 + H) +2H

360= 40 +2H +2H

360-40 = 4H

320= 4H

320/4 = H

80=H

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