Mike and Jamal are 9 miles apart, and are planning to meet up. Mike is walking at an average speed of 3 miles per hour to meet Jamal. Jamal is driving at an average speed of 25 miles per hour to meet Mike.


Which equation can be used to find t, the time it takes for Mike and Jamal to meet?

25t – 3t = 0
25t – 3t = 9
25t + 3t = 1
25t + 3t = 9

The answer is:

The correct option is:

[tex]D.22\°[/tex]

We can calculate the angle of elevation of the rescue ladder (formed triangle) using the following trigonometric formula:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

Where,

y, is represented by the height where the person is located (50 feet) less the height of the top of the fire truck (10 feet)

hypothenuse, is represented by the length of the ladder (105 feet)

So, substituting and calculating we have:

[tex]Sin(\alpha)=\frac{y}{Hypothenuse}\\\\\alpha =Sin(\frac{Height}{LadderLength})^{-1}\\\\\alpha =Sin(\frac{50feet-10feet}{105feet})^{-1}=Sin(\frac{40feet}{105feet})^{-1}\\\\\alpha=Sin(\frac{40feet}{105feet})^{-1}=Sin(0.38)^{-1}=22.33\°=22\°[/tex]

Hence, we have that the correct option is:

[tex]D.22\°[/tex]

Have a nice day!

A reflection is a transformation where the mirror image of a figure is shown directly opposite its line of reflection.

To find an image that has been reflected across the line y = x, switch the x- and y-coordinates.

Therefore, the rule for reflecting an image across the line y = x can be described as (x, y) → (y, x).

Now, apply rule to coordinates ABC:

A': (2, 3)

B': (1, -4)

C': (-2, -3)

Answer:

got it right on odyssey

A'(2,3)

B'(1,-4)

C'(-2,-3)

Step-by-step explanation:

Answer:

  cos(B) = a/c

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Cos = Adjacent/Hypotenuse

The leg adjacent to angle B is "a". The hypotenuse is "c", so the desired cosine is ...

  cos(B) = adjacent/hypotenuse = a/c

Answer:

C. 1.12

Step-by-step explanation:

There are 60' (minutes) in a degree and 60" in a minute meaning that we have (60×60) seconds in a degree.

Therefore to convert seconds to degrees we divide by 3600. and minutes to degrees we divide by 60.

The angle 48°19'23'' can be converted into a decimal as follows

48°+(19/60+23/3600)°

=48.323°

Tan 48.323= 1.12

Answer:

Step-by-step explanation:

1^7 = 1

1^9 = 1

1= 1 x 1 or if they really want it 1^2

Answer:

Step-by-step explanation:

Your calculator knows all. You just have to know how to unlock it.

A graphing calculator is not necessary. A simple scientific one will work. The calculator on your computer will work (a PC) and my phone has one that will solve this as well.

2nd Function

Tan-1(

2

)

=

You should get 63.43

Make sure your calculator says degrees (DEG) at the top. Good luck.

Hello There!

The slope of a function is always in the form of "y=mx"

The slope for this function would be [tex]\frac{1}{6}[/tex] and the y intercept would be positive 7

Answer:

2nd answer

Step-by-step explanation:

For a linear equation in the form

f(x) or y = mx + b

m = slope

b = y - intercept

By observation, f(x) = [tex]\frac{1}{6}[/tex]x + 7

m = slope = [tex]\frac{1}{6}[/tex] (Answer)

b = y-intercept = 7 (answer)

Answer:

the answer is D

Step-by-step explanation: so you know that he can do 9 topics in 45 minutes. which is 1 topic every 5 minutes when you divide 45/9. if there is 60 minutes in an hour, and he does 1 topic every 5 minutes, he would do 12. hope this helps xd

A teacher can cover 12 topics in a 1-hour period. It is given that the number of topics he can cover is directly proportional to the length of the time he has to review. So, option D is correct.

Two variables are said to be directly proportional if one variable increases/decreases with respect to the increase/decrease in the other variable. They are related to each other by proportionality.

A ∝ B (A and B are two variables)

⇒ A2/A1 = B2/B1

The given variables are 'N - number of topics' and 'T - time period'.

It is given that they are directly proportional to each other.

So, we can write

N ∝ T

⇒ N2/N1 = T2/T1

Given that,

A teacher can cover 9 topics in a single 45-minute period.

So, N1 = 9 topics and T1 = 45 minutes

And T2 = 1 hour

We need to find N2 =?

Thus, from the above equation

N2/N1 = T2/T1

⇒ N2/9 = (1 hour)/45 minute

1 hour = 60 minutes

⇒ N2/9 = (60/45)

⇒ N2 = 9 × 4/3

∴ N2 = 12 topics

So, he can cover 12 topics in 1 hour. Thus, option D is correct.

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Answer:

  about 18.8°

Step-by-step explanation:

The depth of the tumor (1.8 cm) is the leg of the right triangle that is opposite the angle of interest. The offset distance (5.3 cm) is the adjacent leg of the triangle.

We know that ...

  tan(angle) = opposite/adjacent = (1.8 cm)/(5.3 cm) = 18/53

Then the angle is found from ...

  angle = arctan(18/53) ≈ 18.76°

_____

The arctangent, or inverse of the tangent function, is also written tan⁻¹. It may be a "second function" of your calculator's tan key.

The angle to aim the gamma ray source to hit the tumor 1.8cm beneath the skin without damaging the vital organ, while moving the source over 5.3cm, can be determined by calculating the inverse tangent (arctan) of the ratio 1.8cm / 5.3cm.

In physics, this problem involves the concept of triangles and trigonometry. Since a right triangle can be formed in this configuration with the distance beneath the patient's skin being one side (1.8cm), the distance over which the radiologist moves the gamma ray source being the second side (5.3cm), the angle required would be an inverse tangent (arctan) of the ratio between these two lengths.

The calculation is thus as follows:

Firstly, set up the ratio of the opposite over the adjacent side of the triangle. This equates to 1.8cm / 5.3cm.

Next, compute the inverse tangent (arctan) of this ratio. You can compute this using a scientific calculator. The answer will be in degrees.

Thus, the required angle to aim the gamma ray source to hit the tumor without damaging the vital organ will be the result of the above calculation.

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let's bear in mind that Y is a bisecting point, so it's really cutting XZ into two equal halves.

[tex]\bf \underset{\textit{\Large 18x-6}}{\boxed{X}\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}} Y\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}}\boxed{Z}} \\\\\\ 12x+12x = 18x-6\implies 24x=18x-6 \\\\\\ 6x=-6\implies x=\cfrac{-6}{6}\implies x=-1[/tex]

If segment XZ is bisected by point Y and XY=12x and XZ=18x-6 then the value of x=-1.

Bisection means division of a line segment into two equal parts by  other line or line segment.

We know that bisector cuts line into equal parts so 2XY=XZ

2(12x)=18x-6

24x=18x-6

6x=-6

x=-1

Hence the value of x is -1 if  XZ is bisected by point Y.

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Final answer:

To convert a whole number to a percent, multiply the number by 100. This process turns the whole number into a fraction with a denominator of 100, which can then be written as a percent. This simple multiplication can be done on most calculators.

Explanation:

Converting Whole Numbers to Percent

To convert a whole number to a percent, you simply need to think of the whole number as a fraction with a denominator of 1 and then convert it to an equivalent fraction with a denominator of 100. Once you have this fraction, you simply write it as a percent. Here is a step-by-step process using a calculator:

Since a whole number is over 1, multiply this number by 100. (5 * 100).

The result will be the whole number as a percent (e.g., 500%).

It's important to remember that calculating percents is essentially finding out how many parts out of a hundred the number represents. When using a calculator, this process may involve additional steps or functions, depending on the calculator's design.

For example, with some calculators, you can enter the number, press the multiplication key, enter 100, and then press the equals key to get the percent (e.g., 5 * 100 = 500%).

Remember that calculating percents can be further applied to situations where you have a 'part' and you want to find out what percentage that 'part' is of a 'total'. In such cases, you would divide the 'part' by the 'total' and multiply by 100 to get the percentage. For instance, if 13 out of 35 students in a class wear sandals, the percentage of students wearing sandals can be calculated as (13/35) * 100 which equals approximately 37%.

Answer:

Step-by-step explanation:

The range is 6 to 10 inches per month; 6 is the least amount of rain, whereas 10 is the most, for these four months.

Find the median by rearranging these four measurements in ascending order:  6 6 8 10.  Since four is an even number (of measurements), we find the median by averaging the middle two measurements:  (6 + 8) /2 = 7 in.

The mean is found by summing up the four measurements and dividing the result by 4:

6+6+8+10

-------------- = 30/4 = 7.5

       4

Draw a histogram as two vertical bars, one of which is 3 units higher than the other.  We don't yet know the total number of cats that each boy has, so your markings of your histogram have to be algebraic expressions, for example:

x + 0 for the first vertical bar and x + 3 for the second.  Then, clearly, one boy has 3 more cats than does the other.

Corey has 3 more cats than Taylor.  Let t represent the number of cats owned by Taylor and c the number by Corey.

Then t = c + 3 (general relationship), and so

        6 = c + 3

We must isolate c to determine how many cats corey has.

Subtract 3 from both sides, which results in c = 3.  Corey has 3 cats and Taylor has 6.

Answer:

  5 m

Step-by-step explanation:

The perimeter is the sum of the lengths of the four sides. Opposite sides have the same length, so it is twice the sum of the lengths of adjacent sides.

The sum of adjacent sides is (32 m)/2 = 16 m. If one of them is 11 m long, the other is ...

  16 m - 11 m = 5 m

The "missing" side is 5 m long.

Answer:

26

Step-by-step explanation:

If the sides of a triangle are a, b, and c, the triangle inequality theorem tells us, about the sides possible to make up this NON-right triangle:

a + b > c

b + c > a and

a + c > b

Since we have 2 sides, we will call the third unknown side x.  Let a = 12 and b = 14:

12 + 14 > x

14 + x > 12 and

12 + x > 14.

The first inequality, solved for x, is that x < 26.

The second inequality, solved for x, is that x > -2.  We all know that the 2 things in math that will never EVER be negative are distance/length measures and time; therefore, we can safely disregard -2 as a side length of this, or ANY, triangle.

The third inequality, solved for x, is that x > 2.

We now have the solutions for the side length possibilities:

2 < x < 26

From this inequality statement, we see that the longest the side could possibly be and still make a triangle with the other 2 side lengths given, is 26

Answer:

C. 7 inches

Step-by-step explanation:

The Obtuse Triangle Inequality Theorem: c^2 > a^2 + b^2.

14^2 > 12^2 + b^2.

196 > 144 + b^2.

so b < 52. and the square root of 52 is 7.

Thank you and have a great day!

Answer: The answer is A, because if you subtract 1.3 from 9.2, you would get 7.9, and after that you would divide 7.9 by 4. After doing that, you would get an answer of 1.975, which rounds up to 2.

Step-by-step explanation:

1. Subtract 1.3 from 9.2

2. Take the Answer from Step 1, and divide it by 4

3. Round up your answer.

Answer:

  D:  -5(-6x^2 + x + 2)

  E:  5(2x + 1)(3x − 2)

Step-by-step explanation:

You want to identify the expressions equivalent to 30x² -5x -10.

The first two answer choices have incorrect constants (25 and -2 vs. -10).

A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:

  30x^2 -5x -10 = 5(6x^2 -x -2)

An additional x cannot be factored from the expression, so choice C can be eliminated.

Multiplying each of these factors by -1 will make the product correspond to answer choice D.

Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:

  E:  2x(-2) +1(3x) = -x, as required

  F:  2x(2) -1(3x) = x, wrong sign

The equivalent expressions are those of choices D and E.

ANSWER

[tex]y = 8x - 26 [/tex]

EXPLANATION

The given points are (3,-2) (4,6).

The slope formula is given by:

[tex] m= \frac{y_2-y_1}{x_2-x_1} [/tex]

We use the slope formula to get:

[tex]m = \frac{6 - - 2}{4 - 3} [/tex]

The slope is

[tex]m = 8[/tex]

We use the point-slope formula to get;

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y + 2 = 8(x - 3)[/tex]

We expand to get;

[tex]y = 8x - 24 - 2[/tex]

The slope-intercept form of the equation is:

[tex]y = 8x - 26[/tex]

Answer:

One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph.

Answer:

Step-by-step explanation:

8x+2=-2

Answer:

you would divide 25 by 5.

Step-by-step explanation:

each of the 5 officers would patrol 5 streets with a final of 5 x 5 = 25.

Answer:

5 streets

Step-by-step explanation:

Data:

The number of streets = 25

Number of officers = 5

Each officer will patrol = [tex]\frac{25}{5}[/tex]

                                      = 5 streets

Answer:

20√2=28.2842....

Step-by-step explanation:

special right traingles

a 45-45-90 states that the legs are congruent and the hypotenuse is leg√2

An extraneous solution is a solution that arises during the algebraic process of solving a radical equation but does not actually satisfy the original equation. It is essential to substitute the solution back into the original equation to determine its validity.

An extraneous solution to a radical equation refers to a solution that emerges from the process of solving the equation, but is not a valid solution to the original equation. When we solve radical equations, we often have to square both sides to remove the radical. This process can introduce solutions that aren't true for the original equation. To determine whether a solution is extraneous, we must always substitute it back into the original equation to verify its validity.

If during your process you encounter coefficient terms that correspond to variable-dependent outcomes in function theory, be mindful that the extraneous solutions can impact the interpretation of the solution set. The goal is always to reduce the equation to a state that is readily solvable—via algebraic normal equations in the case of more complex equations like the quintic equation, which sometimes involves elliptic functions for their solution, not to be confused with solutions by radicals.

Equations that are solvable by radicals mean they can be reduced to pure equations using algebraic processes, eliminating the need for other non-algebraic methods. However, during the solution process, extraneous solutions may appear, and thus, it is essential to substitute any found solution into the original equation to ensure it was not introduced during the algebraic manipulations.

Answer:

  3 runners

Step-by-step explanation:

The number of runners needed is the length of the race divided by the length each runner can run:

  (1/3 mi)/(1/9 mi/runner) = 9/3 runner = 3 runners

_____

There are a couple of ways you can divide fractions:

  → "invert and multiply." That is, multiply the numerator by the reciprocal of the denominator. Here, that is (1/3)(9/1) = 9/3 = 3

  → make the denominators the same and use the ratio of the numerators. Here that is (1/3)/(1/9) = (3/9)/(1/9) = 3/1 = 3

  → use a calculator (see attached)

Hello There!

The fuel efficiency of a car decreases as tire pressure decreases. The independent variable in the situation is: Tire pressure.

Answer:

A

Step-by-step explanation:

The Price per gallon goes with the fuel efficiency and the speed of the car determines how much gas you use so the answer is A Tire Pressure

Answer:

10/3 mph

Step-by-step explanation:

Obviously, (time going) + (time returning) = (total time spent en route) = 54 min.  Since time = distance / rate,

                           3 miles                3 miles

                    ----------------------- + --------------------- = 54 min

                     downhill speed      uphill speed

Let u = uphill speed and d = downhill speed; then d = u + 5 (all in mph)

Then we have:

                           3 miles                3 miles

                    ----------------------- + --------------------- = 54 min

                           u + 5                        u

and our task here is to determine the uphill speed, u.

The LCD is u(u + 5).  Thus we have:

                           3u                     3(u + 5) miles

                    ----------------------- + -----------------------  = 54 min = 0.9 hr

                           u(u + 5)                  u(u + 5)

so that:

             6u + 15

      -----------------------  = 0.9 hr     or      6u + 15 = 0.9(u)(u + 5), or

             u(u + 5)

             6u + 15 = 0.9u² + 4.5u

Combining the u terms, we get:

                      15 = 0.9u² + 4.5u,            or          0.9u² + 1.5u - 15 = 0

Eliminating the fractions, we get                         9u² + 15u - 150, or

                                                                               3u^2 + 5u - 50 = 0

This factors into (3u - 10)(u + 5) = 0.  The only positive root is u = 10/3.

Your average rate on the return trip (uphill) is 10/3 mph (3 1/3 mph).

R is approximately 6 mph.

Let's denote the average rate (speed) on the return trip as
r (in miles per hour, mph). Since it is given that the speed going to campus is 5 mph faster, the speed while going downhill would be r + 5 mph. We need to find the values of r.

The total distance for the round trip is 3 miles to campus and 3 miles back, adding up to 6 miles. The total time for the trip is given as 54 minutes, which we will convert to hours by dividing by 60, giving us 0.9 hours.

The time taken to go to campus is the distance divided by the speed, which is 3 / (r + 5) hours. The time taken for the return trip is 3 / r hours. Since both times add up to 0.9 hours, we can write the equation:

3 / (r + 5) + 3 / r = 0.9

Now we need to solve this equation for r. We find a common denominator and solve:

r(r + 5)(3 / (r + 5) + 3 / r) = r(r + 5)(0.9)

3r + 3(r + 5) = 0.9r(r + 5)

3r + 3r + 15 = 0.9r^2 + 4.5r

6r + 15 = 0.9r^2 + 4.5r

0.9r^2 - 1.5r - 15 = 0

Using the quadratic formula or factoring, we can find the root for r. The root that makes sense in this context (positive speed) gives us the average rate on the return trip.

After solving, we find that r is approximately 6 mph, which is the average speed of the student on their return trip.

Answer: $726 in interest is accumulated over a period of 6 months

Answer:

  $60.50

Step-by-step explanation:

Put the given numbers into the formula and do the arithmetic. 6 months is 1/2 year.

  i = Prt . . . . i is interest earned, P is principal amount, r is annual rate, t is number of years

  i = $2200×0.055×0.5 = $60.50

The amount of simple interest earned in 6 months is $60.50.

Answer:

The answer is :

A. (7x + 4)(7x - 4)

Answer:

The correct answer is first option

(7x + 4)(7x − 4)

Step-by-step explanation:

Points to remember

Identities

(a + b)(a - b) = a² - b²

It is given an expression,

49x² - 16

To factorize  the expression 49x² - 16

We know that 7² = 49 and 4² = 16

Therefore we can write the given expression as,

49x² - 16 = (7x)² - 4²

It is in the form of the above identity,

(7x)² - 4² = (7x + 4)(7x - 4)

The correct answer is first option

Answer:

4 is the greatest common factor

Step-by-step explanation

The factors of 44 are: 1, 2, 4, 11, 22, 44

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Answer:

B, D, E

Step-by-step explanation:

A. The vertex is (1, -9).

False.  The vertex is at (-1, -9).

B. The graph opens upward.

True.  The leading coefficient 6 is positive.

C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.

False.  It is shifted down 9 units.

D. The graph is steeper than the graph of f(x) = x².

True.  The absolute value of the leading coefficient |6| is greater than 1.

E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.

f(x) = 6(x² + 2x + 1) - 9

f(x) = 6x² + 12x + 6 - 9

f(x) = 6x² + 12x - 3

True.

The graph of f(x) = 6(x + 1)² -9 has its vertex at (-1,-9), opens upwards, is steeper than f(x) = x² and is not equal to f(x) = 6x² + 12x - 3. The graph is also shifted downwards by 9 units, not upwards.

The graph of f(x) = 6(x + 1)² -9 is a parabolic function. Let's check each of the given statements:

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Answer:

5.75t=p

Step-by-step explanation:

22p=126.50/22

p=5.75 per hour

5.75t=p

The $5.75 is earned for every hour worked.

Chance of seed growing into healthy plant:  0.65

Chance of seed NOT growing into a healthy plant:  0.35

To answer this question, we will use the nCr button on the calculator.

In this situation, n = 8   and r = 1.

If 1 seed doesn't grow, then 7 seeds will grow. So will raise 0.65 to the 7th power and 0.35 to a power of 1

7 seeds grow, so we use the 7th power

1 seed doesn't grow, so we use power 1 :

So the answer is:

⁸C₁ × (chance of successful growth)⁷ x (chance of Unsuccessful growth)¹

= ⁸C₁ × 0.65⁷ × 0.35¹

= 0.137   (3sf)

_____________________________

Answer:

Probability that exactly one seed doesn't grow is:

0.137

To calculate the probability in this case, we make use of the Binomial Probability formula. Here, we want to find out the probability that out of the 8 seeds planted, 7 sprout successfully and 1 fails to sprout.

The problem you're working out can be classified under the category of Binomial Probability. A binomial probability problem deals with yes-no scenarios repeated multiple times (like a seed either germinating or failing).

For this problem, we know that the probability of a seed sprouting (success) is 0.65 and therefore the probability of not sprouting (failure) is 0.35 (1 - 0.65). You have 8 seeds, and you want to find the probability that 7 succeed and 1 fails.

The formula for binomial probability is:

P(X=k) = C(n,k) * (p^k) * (q^(n-k))

Where:

By substituting the appropriate values into the formula, we would calculate the binomial probability of exactly 1 seed not sprouting.

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