Need help with a math question

You need to find the least common multiple of 24 and 20.

[tex]24=2^3\cdot3\\20=2^2\cdot5\\\\\text{lcm}(20,24)=2^3\cdot 3\cdot 5=120[/tex]

120 min = 2 h

9:00 + 2:00=11:00

So, the answer is at 11:00

Final answer:

To find the next time both the Manchester and Birmingham buses leave London Victoria bus station at the same time, calculate the Least Common Multiple (LCM) of their departure intervals, which is 120 minutes. The buses will next leave together 2 hours after their 09:00 departure, at 11:00.

Explanation:

The question involves finding a common multiple of the times buses to Manchester and Birmingham leave the station. Since Manchester buses leave every 24 minutes and Birmingham buses leave every 20 minutes, we need to calculate the Least Common Multiple (LCM) of 24 and 20. To find the LCM of 24 and 20, we can list the multiples of each number until we find the smallest multiple they have in common.

The smallest common multiple is 120 minutes, which is 2 hours. Since both buses leave at 09:00, the next time both buses will leave at the same time will be 2 hours later, at 11:00.

Answer:

horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer A

Step-by-step explanation:

* Lets revise some transformation

- A vertical stretching is the stretching of the graph away from

 the x-axis

# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

  by multiplying each of its y-coordinates by k.

# If k should be negative, the vertical stretch is followed by a reflection

  across the x-axis.  

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally

  compressed by dividing each of its x-coordinates by k.

* Lets solve the problem

∵ y = cos x

∵ y = -2 cos 3x

- At first cos x multiplied by -2

∵ y multiplied by -2

∵ 2 > 1

∴ y = cos x is stretched vertically by factor 2

∵ The factor 2 is negative

∴ y = cos x reflected across the x-axis

∴ The function y = cos x stretched vertically with factor 2 and then

  reflected across the x-axis ⇒ (1)

∵ cos x changed to cos 3x

∵ x multiplied by 3

∵ 3 > 1

∴ y = cos x compressed horizontally by factor 3

∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)

- From (1) and (2)

* The function y = cos x has horizontal compression by factor 3,

  vertical stretch by factor 2, then reflection across the x-axis to

  produce y = -2 cos 3x

Answer:

It is A

Step-by-step explanation:

AP3x

Answer:

  see below

Step-by-step explanation:

The answer is a list of arcs. That means you can ignore the answer choices that are lists of angles or line segments.

The only requirement is that the end points of the arc lie on the circle. Points M, N, P, Q, R are all on the circle, and all are at the end of line segments that intercept them. Any combination of these letters will define an intercepted arc.

Answer:

10/3

Step-by-step explanation:

|x+3|=4x-7

So |-(x+3)|=|x+3|

We are going to try out two cases:

-(x+3)=4x-7                              and    x+3=4x-7

-x-3=4x-7                                               3=3x-7

 -3=5x-7                                               10=3x

  4=5x                                                   x=10/3

  x=4/5

We are going to test out both because we could something that isn't actually a solution, this is called extraneous.

First thing I'm going to check is 4x-7 for it being positive.

4(4/5)-7=20/5-7=-15/5=-3 so 4/5 will not work because absolute value result can't be negative

4(10/3)-7=40/3-7=19/3 which is positive

checking |x+3| to see if is 19/3 for x=10/3 we see that is so that is the answer

Answer:

  4

Step-by-step explanation:

The problem statement tells you the constant of proportionality is y/x. The graph shows y=4 for x=1. Then y/x = 4/1 = 4.

The constant of proportionality is 4.

_____

Caveat

Before you copy this answer, be certain the graph in your problem statement is identical to this graph. If your marked point has different coordinates than (1, 4), your constant of proportionality may be different. It will still be computed as y/x, but you need to use the x and y values of the marked point on your graph (or those of any other point whose coordinates you can read).

Answer:

12

Step-by-step explanation:

12-3>8and 12+1<14

9>8 and 13<14

Answer:

4/9

Step-by-step explanation:

Answer:

In brief, apply the pythagorean theorem to show that the distance between the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and the origin is [tex]1[/tex].

Step-by-step explanation:

The pythagorean theorem can give the distance between two points on a plane if their coordinates are known.

A point is on a circle if its distance from the center of the circle is the same as the radius of the circle.

On a cartesian plane, the unit circle is a circle  

Therefore, to show that the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle, show that the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex] equals to [tex]1[/tex].

What's the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex]?

[tex]\displaystyle \sqrt{\left(\frac{\sqrt{2}}{2}-0}\right)^{2} + \left(\frac{\sqrt{2}}{2}-0\right)^{2}} = \sqrt{\frac{1}{2} + \frac{1}{2}}= \sqrt{1}= 1[/tex].

By the pythagorean theorem, the distance between [tex](\sqrt{2}/2,\sqrt{2}/2) [/tex] and the center of the unit circle, [tex](0,0)[/tex], is the same as the radius of the unit circle, [tex]1[/tex]. As a result, the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle.

Answer:

  the three angle measures are 35°, 29°, 26°

Step-by-step explanation:

The sum of the angle measures will be 90°, assuming the sections do not overlap. Then ...

  ( 7x - 49) + ( 2/3x + 21) + ( 3/4x + 17) = 90

  (8 5/12)x -11 = 90 . . . . . simplify

  x = 101/(8 5/12) = 12 . . . divide by the coefficient of x

Then the angles are ...

  7x -49 = 7·12 -49 = 35

  2/3x + 21 = 2/3·12 +21 = 29

  3/4x +17 = 3/4·12 +17 = 26

The angle measures are 35°, 29°, 26°.

_____

Check

  35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°

_____

We assume you can manage addition of fractions and division by a mixed number or improper fraction. If not, convert all of the coefficients of x to multiples of 1/12. Instead of dividing by the coefficient of x, multiply by the inverse of the coefficient of x.

To find the angle measures of each of the three sections at home plate, the equation (7x - 49) + (2/3x + 21) + (3/4x + 17) = 90 is solved to find that x equals 12. Substituting 12 for x, the angle measures are calculated to be 35 degrees, 29 degrees, and 26 degrees.

Since the angle at home plate is 90 degrees, the sum of the angles for the sections must also be 90 degrees. This allows us to set up the following equation:

(7x - 49) + (2/3x + 21) + (3/4x + 17) = 90

To solve this equation, we combine like terms. First, find a common denominator for the x terms, which is 12. So, we convert all terms into twelfths:

Combining these we get:

(101/12)x - 11 = 90

Add 11 to both sides to isolate the variable term:

(101/12)x = 101

Now, divide both sides by (101/12):

x = 12

Now we will substitute this value for x into the original expressions to get the angle measures:

Therefore, the angle measures for the sections are 35 degrees, 29 degrees, and 26 degrees.

Answer:

7/17

Step-by-step explanation:

16 inches of concrete plus 4 inches of limestone come to 20 inches of concrete and limestone combined.  Subtracting 20 inches from 34 inches yields 14 inches.  14 inches of the total wall thickness (34 inches) is brick.  This fraction is 14/34, or 7/17.

The fraction of the wall made up of brick is found by subtracting the concrete and limestone widths from the total width of the wall. The fraction is 14/34, which simplifies to 7/17.

The question is asking us to find the fraction of the wall made up of brick. The total width of the wall is 34 inches. Substrating the concrete and limestone widths from the total width (34 inches - 16 inches for concrete - 4 inches for limestone) we get a result of 14 inches for the brick portion. To express this as a fraction of wall's total width, we place the number 14 (the width of the brick portion) over 34 (the total width of the wall). Therefore, the fraction of the wall that is brick is 14/34, which simplifies to 7/17 when reduced to lowest terms.

Learn more about Fractions here:

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Answer:

two or zero positive real roots, one or zero negative real roots

Step-by-step explanation:

f(x) = 9x³ − 2x² − x + 5

There are 2 sign changes, so the number of positive real zeros is 2 or an even number less than that.  So there are two or zero positive real roots.

f(-x) = 9(-x)³ − 2(-x)² − (-x) + 5

f(-x) = -9x³ − 2x² + x + 5

There is 1 sign change, so the number of negative real zeros is 1 or an even number less than that.  So there is exactly 1 negative real root.

Your answer is correct.

Answer:

Option A (x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates).

Step-by-step explanation:

There are two inequalities. One is 110 < 2x + 10 and 2x + 10 < 310. x is the amount of carbs consumed in grams, the first inequality is the lower limit, and the second inequality is the upper limit. The question requires to solve the two inequalities.

1)

110 < 2x + 10.

100 < 2x.

50 < x (or x > 50).

2)

2x + 10 < 310.

2x < 300.

x < 150.

Now combining the two inequality gives:

50 < x < 150.

So Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates. Therefore, Option A is the correct answer!!!

Answer:

a

Step-by-step explanation:

Answer:

  (1000, 179°)

Step-by-step explanation:

In rectangular coordinates, where east is the +x direction and north is the +y direction, the woman's final position is (1000 yards west, 20 yards north) or (-1000, 20).

This is translated to polar coordinates (r, θ) using ...

  r = √(x² +y²)

  θ = arctan(y/x) . . . . with attention to quadrant

The magnitude of the distance (r) is ...

  r = √((-1000)² +20²) = √1000400 ≈ 1000.2 ≈ 1000

  θ = arctan(20/-1000) in quadrant 2, so is 180° -1.15° = 178.85° ≈ 179°

In polar coordinates, the final position is (1000, 179°).

Answer:

[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].

Step-by-step explanation:

[tex]\displaystyle \theta\in \left(\pi, \frac{3\pi}{2}\right)[/tex],

such that

[tex]\displaystyle \frac{\theta}{2} \in \left(\frac{\pi}{2}, \frac{3\pi}{4}\right)[/tex].

As a result,

[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\sin{\displaystyle \frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex],

such that

Let

[tex]\displaystyle t = \tan{\frac{\theta}{2}}[/tex].

[tex]t < 0[/tex].

By the double angle identity for tangents.

[tex]\displaystyle \frac{\displaystyle 2\tan{\frac{\theta}{2}}}{1-\displaystyle \left(\tan{\frac{\theta}{2}}\right)^{2}} = \tan{\theta}[/tex].

[tex]\displaystyle \frac{2t}{1 - t^{2}} = \frac{5}{12}[/tex].

[tex]24t = 5 - 5t^{2}[/tex].

Solve this quadratic equation for [tex]t[/tex]:

Discard [tex]t_1[/tex] for it is not smaller than zero.

Let [tex]\displaystyle s = \sin{\frac{\theta}{2}}[/tex].

[tex]0 < s <1[/tex].

By the definition of tangents:

[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\displaystyle \sin{\frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex].

Apply the Pythagorean Algorithm to express the cosine of [tex]\displaystyle \frac{\theta}{2}[/tex] in terms of [tex]s[/tex]. Note that [tex]\displaystyle \cos{\frac{\theta}{2}}[/tex] is expected to be smaller than zero.

[tex]\displaystyle \cos{\frac{\theta}{2}} = -\sqrt{1 - \left(\sin{\frac{\theta}{2}}\right)^{2}}= - \sqrt{1 - s^{2}}[/tex].

Solve for [tex]s[/tex]:

[tex]\displaystyle \frac{s}{- \sqrt{1 - s^{2}}} = -5[/tex].

[tex]s^{2} =25(1 - s^{2})[/tex].

[tex]\displaystyle s = \sqrt{\frac{25}{26}} = \frac{5\sqrt{26}}{26}[/tex].

Therefore

[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].

[tex]\bf \cfrac{5x+50}{x+5}\cdot \cfrac{1}{x+10}\implies \cfrac{5~~\begin{matrix} (x+10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{x+5}\cdot \cfrac{1}{~~\begin{matrix} x+10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{5}{x+5}[/tex]

Answer:

The correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].

Step-by-step explanation:

We are given the following expression and we are to simplify it:

[tex] \frac { 5 x + 5 0 } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]

We would take the common terms out and then cancel any like terms present in the expression to get the simplest form.

[tex] \frac { 5 ( x + 1 0 ) } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]

[tex] \frac { 5 } { x + 5 } [/tex]

Therefore, the correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].

Explanation:

Divide the frequency numbers by their total to get the relative frequency. Plot that on your graph.

P(0 heads) = 4/80 = 0.05

P(1 head) = 8/80 = 0.10

P(2 heads) = 36/80 = 0.45

P(3 heads) = 20/80 = 0.25

P(4 heads) = 12/80 = 0.15

From the graph, when x = 1, y = 57,000.

Replace x with 1 in the equations and see if any of the Y 's equal 57,000 :

y = -2610.82(1) + 47860.82 = 45,250

y = 219(1)^2 - 6,506.78(1) + 59,385 = 219 - 6506.78 + 59385 = 53,097.22

y = 54041.5(0.9)^1 =  48,637.35

y = 10,504.6 (1.1)^1 = 11,555.06

The second equation is the closest. so try another x value to see if it is close to the Y value:

Let's try x = 14:

y = 219(14)^2 - 6506.78(14) + 59,385 = 42924 - 91094.92 + 59385 = 11,214.08

This is close to Y = 12,00 shown on the graph

SO the closest equitation is y = 219x^2 - 6506.78x + 59385

Answer:

Option D.  18.75 cm3

Step-by-step explanation:

we know that

The Boyle's law (Ideal gas law) states that Where temperature remains constant, the pressure is inversely proportional to volume.

so

[tex]P1 *V1 = P2 *V2[/tex]  

In this problem we have

P1=150 kPa

P2=200 kPa

V1=25 cm³

substitute and solve for V2

[tex](150)(25)= 200*V2[/tex]

[tex]V2=(150)(25)/200=18.75\ cm^{3}[/tex]    

Answer:

Option D.  18.75 cm3

Step-by-step explanation:

MARK ME PLS

A - rolling exactly one six

[tex]P(A)=\dfrac{1}{5}\cdot\dfrac{4}{5}+\dfrac{4}{5}\cdot\dfrac{1}{5}=\dfrac{4}{25}\cdot \dfrac{4}{25}=\dfrac{16}{625}[/tex]

Answer:

A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A

Step-by-step explanation:

* Lets revise the properties of the rectangle

# Each two opposite sides are parallel

# Each two opposite sides are equal in length

# Its two diagonals bisect each other  and equal each other

# Its four angles are right angles

- The parallelogram can be a rectangle if:

# Two adjacent sides are perpendicular to each other means one

  angle of its four angles is a right angle

- OR

# Its two diagonals are equal in length

* Lets solve the problem

- We will study the answers to chose the best one

# Answer A

- A rectangle is a parallelogram with at least one right angle

∵ Each tow opposite angles are equal in the rectangle

∵ One of the is right angle means its measure is 90°

∴ The measure of the opposite angle is also 90°

∵ The sum of the measures of the four angles is 360°

∴ The sum of the measures of the other two angles is;

   360 - (90 + 90) = 180°

∵ They are equal to each other (opposite angles)

∴ The measure of each one = 180 ÷ 2 = 90°

∴ The measure of the four angles are 90°

∴ The four angles of the rectangle are right angles

* A rectangle is a parallelogram with at least one right angle is the

 best choice

Answer:it is A

Step-by-step explanation:

Answer:

$50/day

Step-by-step explanation:

If 90% of 150 beds are occupied, the .90 × 150 are occupied, or 135 beds.  The total expenses for ALL the residents for the month is 202,500.  We need the cost per day for all the residents, then when we know that we can find the cost per day of one resident.

202,500 ÷ 30 = $6750 for one day for ALL residents

$6750 ÷ 135 = $50 for one day for a single resident

To find the average cost per resident per day for a facility with an average 90% occupancy rate, multiply the number of beds by the occupancy rate to find the average daily occupancy, then multiply by the number of days in the month to get total resident-days. Finally, divide the total monthly expenses by the total resident-days to get the average daily cost per resident.

To calculate the average cost per resident per day in a 150 bed facility with a 90% average occupancy rate over a 30-day month with total expenses of $202,500, we can follow these steps:

So, first we find the average number of occupied beds per day:
150 beds × 90% = 135 occupied beds per day.

Next, we calculate the total number of resident-days for the month:
135 occupied beds × 30 days = 4050 resident-days.

Finally, we find the average cost per resident per day:
$202,500 total expenses ÷ 4050 resident-days = $50 per resident per day.

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Answer:

A. 3

Step-by-step explanation:

see attached for the tableau

___

As you know, the number on the bottom row is multiplied by the divisor to get the next middle-row number to the right. Top and middle rows are added to get the bottom row.

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {x} {x-1}} {\frac {1} {x + 1}}[/tex]

Applying double C we have the following expression:

[tex]\frac {x (x + 1)} {x-1} =[/tex]

Applying distributive property to the terms within the parentheses of the numerator we have:

[tex]\frac {x ^ 2 + x} {x-1}[/tex]

Thus, the quotient is given by option A

Answer:

Option A

Answer:

The answer is option A. (x^2 + x)/(x-1)

Step-by-step explanation:

To solve this problem, we must first understand how to divide fractions.  When dividing fractions, the first fraction is unchanged and is multiplied by the reciprocal of the second fraction.  If we apply this knowledge to this problem, we get:

x/x-1 * x+1/1

When we multiply fractions, we simply multiply both of the numerators together and both of the denominators together to create a single fraction.

In this case we get:

x(x+1)/x-1

When we simplify this single fraction by using the distributive property, we get the following:

(x^2 + x)/(x-1)

Therefore, your answer is option A.

Hope this helps!

Answer: 6 pounds of apples

Step-by-step explanation:

See photo attached. (:

Her first visit and follow up 60 mins + 30 mins

The limit is 8 follow ups per day

The hospital has 8 hrs available for appointments

Her first visit cost $120 (60 mins) as her follow up was $70 (30 mins)

X = Visits

Y = Follow-ups

And since her first visit and follow up equals to an hour and 30 mins, meaning for it to all add up into the 8 hrs for the appointment, it'll be... 1 hr, 30 mins/ 3 hrs/ 4 hrs, 30 mins/ 6 hrs/ 7 hrs, 30 mins/ 9 hrs

Eight hours is the limit so that means it equals to 5 visits and 6 follow ups, due to if you want it to be the whole 8 hours.

Claude is so Brainy his brain's nickname is Brainly

Answer:

A

120

Step-by-step explanation:

With all the parallel lines involved, the central figure is a parallelogram.  These 4 sided figures have the odd property of having their opposite angles equal.

What that means, in plain English is that <NRL = <NML

Both of these angles = 120

Here's the cruncher. <NRL and <PRK are vertically opposite. They are therefore equal.

The answer to your question is 120 which is A

the answer is A good luck !

Answer:

C.

Step-by-step explanation:

[tex]\cos x+\sqrt{2}=-\cos x \\ 2\cos x = -\sqrt 2 \\ \cos x = -\dfrac{\sqrt 2}{2}\\ \\ \Rightarrow x = \pm \arccos\Big(-\dfrac{\sqrt 2}{2}\Big)+2k\pi,\quad x\in \mathbb{Z}\\ \Rightarrow x =\pm\dfrac{3\pi}{4}+2k\pi\\ \\ \\k = -1 \Rightarrow x < 0\\\\ k=0 \Rightarrow x<0 \quad \text{or}\quad \boxed{x = \dfrac{3\pi}{4}} \\ \\k = 1 \Rightarrow x=-\dfrac{3\pi}{4}+2\pi \Rightarrow \boxed{x= \dfrac{5\pi}{4}}\quad \text{or}\quad x > 2\pi[/tex]

Answer:

C

Step-by-step explanation:

Given

cos x + [tex]\sqrt{2}[/tex] = - cosx ( add cosx to both sides )

2cosx +[tex]\sqrt{2}[/tex] = 0 (subtract [tex]\sqrt{2}[/tex] from both sides )

2cosx = - [tex]\sqrt{2}[/tex] ( divide both sides by 2 )

cosx = - [tex]\frac{\sqrt{2} }{2}[/tex]

Since cosx < 0 then x is in the second/ third quadrant

x = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] )

  = [tex]\frac{\pi }{4}[/tex] ← related acute angle

Hence

x = π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex] ← second quadrant

or

x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] ← third quadrant

Explanation:

The purpose of trigonometry and the trigonometric ratios sine, cosine, and tangent is to help you calculate angles based on the ratios of side lengths of triangles they are found in.

Answer:

A.) 19.5

Step-by-step explanation:

Answer:

64 sq feet

Step-by-step explanation:

Given:

Rectangle Length = 10 feet

Rectangle Width = 6 feet

Triangle Base = 4 feet

Triangle Height = 2 feet

Area of rectangle = Length x Width = 10 x 6 = 60 sq feet

Area of triangle = [tex]\frac{1}{2}[/tex] x Base x Height = [tex]\frac{1}{2}[/tex] x 4 x 2 = 4 sq feet

Total area

= Area of Rectangle + Area of Triangle

= 60 + 4 = 64 sq feet

Answer:

64 ft^2

Step-by-step explanation:

The rectangular area is 10 ft by 6 ft, which comes to 60 ft².

The triangular area is A = (1/2)(base)(height) = (1/2)(4 ft)(2 ft) = 4 ft²  

The total area of tile will be 4 ft² + 60 ft², or 64 ft².