An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?

Answer:

9x3 - 2x - 3.

Step-by-step explanation:

(6x3 − 8x − 5) + (3x3 + 6x +2)

=  6x3 − 8x − 5 + 3x3 + 6x + 2

= 6x3 + 3x3 - 8x + 6x - 5 + 2

= 9x3 - 2x - 3.

Answer:

9x-2x-3

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

Using the equation A(t) = 400e-.032t

a) replace t with 4 so A(4) = 400e((-.032)(4))

The hardest part about this is making sure to use order of operations. Be certain it works like this:

A(4) = 400e-.128

A(4) = 400(.8799)

A(4) = 351.9 grams

b) A(8) = 400e((-.032)(8)) = 309.7 grams

c) A(20) = 400e((-.032)(20)) = 210.9 grams

Note here that even after 20 years, not quite half of the original amount is gone. So, we can anticipate that in finding the half life, that our answer should be slightly greater than 20 years.

d) 200 = 400e(-.032t)

Divide both sides of the equation by 400.

.5 = e(-.032t)

Change this to logarithmic form.

Ln .5 = -.032t

-.6931≈ -.032t

t ≈ 21.7 years

Hope this helps!

The amount of radioactive lead,

(a).After 3 years is 454.23 grams

(b).After 8 years is 387.07 grams

(c).After 10 years is 363.07 grams.

(d). half life is 21.66 years.

The decay of radioactive lead is given by function,

                          [tex]A(t)=500e^{-0.032t}[/tex]

The amount of radioactive lead After 3 years is,

             [tex]A(3)=500e^{-0.032*3}=0.908*500=454.23g[/tex]

The amount of radioactive lead After 8 years is,

            [tex]A(8)=500e^{-0.032*8}=500*0.774=387.07g[/tex]

The amount of radioactive lead After 10 years is,

            [tex]A(10)=500e^{-0.032*10}=500*0.726=363.07g[/tex]

Half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

So,       [tex]250=500e^{-0.032t}[/tex]

            [tex]e^{-0.032t}=0.5\\\\-0.032t=ln(0.5)\\\\-0.032t=-0.693\\\\t=0.693/0.032=21.66 years[/tex]

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Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

The function is given :

f(x) = 4x + 15

For f(-3), the input for the function f(x) is -3.

Replace the x variable with -3.

f(-3) = 4(-3) + 15

Evaluate.

f(-3) = -12 + 15

f(-3) = 3

The output for f(-3) is 3.

Answer: f(-3) = 3

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(-3).

We find f(-3) by plugging -3 in for x,

everywhere that x appears in the function.

So we have 4(-3) + 15.

4(-3) is -12 so we have -12 + 15 which is 3.

So f(-3) is 3.

Answer:

44 degrees.

Step-by-step explanation:

The 3 small triangles are isosceles  so m < a = m < b , therefore

m < a = (180 - 92) / 2 = 44 degrees.

m < f = m < a ( they are both subtended on the circle by the same chord (cd)),

So m < f = 44.

Answer:

Surface area of the cone = 1306.24 square centimeters

Step-by-step explanation:

Surface area of a cone is determined from the formula,

Surface area of cone = πr(r + l)

where 'r' = radius of the circular base of the cone

l = lateral height of the cone

And π = 3.14

Surface area of the cone with 'r' = 13 cm and 'l' = 19 cm

Surface area = 3.14(13)(13 + 19)

                     = 3.14(13)(32)

                     = 1306.24 square centimeters

Answer:

Option (B).

Step-by-step explanation:

Since "measure of an angle formed between the tangent and a chord measure the half of the intercepted arc."

Therefore, x = 2 × (65)°

x = 130°

Since, measure of the inscribed angle is half of the measure of the intercepted arc.

Therefore, x = 2y

y = [tex]\frac{x}{2}[/tex]

y = [tex]\frac{130}{2}[/tex]

y = 65°

Therefore, Option (B). 65° will be the correct option.

Answer:

Number : 42

Step-by-step explanation:

This number will be a two - digit number, and hence we can say that it is yz. The ratio of the units digit to the tens digit is given by 1 / 2, so z / y = 1 / 2.

In addition the tens digit is 2 more than the units digit, so y = z + 2. We therefore have the following system of equations,

y = z + 2,

z / y = 1 / 2

Substituting the first equation into the second we receive z / z + 2 = 1 / 2. Using this we can solve for z.

z / z + 2 = 1 / 2 ( Cross - Multiply )

z + 2 = 2z, z = 2

And knowing z we can solve for y. y = z + 2 = 2 + 2 = 4. Therefore our number is 42.

[tex]x = 11\frac{42}{99} [/tex]

Step-by-step explanation:

[tex]11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \: (2) \: \\ 100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x = \frac{1131}{99} \\x = 11\frac{42}{99} \\ [/tex]

Answer: C

Step-by-step explanation: I did the test

Answer:

D

Step-by-step explanation:

It's d because it has the highest x value. The higher x value is the farther it is from the y-axis

Answer:

Degrees- 40°

Minutes- 46'

Seconds- 48.00"

Step-by-step explanation:

40° + 46'/ 60 + 48.00"/ 3600= 40.78°

Answer:

Step-by-step explanation:

40.78°=40°+0.78°=40°+(78/100)×60=40°+46.8'=40°+46'+0.8'=40°46'+(8/10)×60=40°46'48''

Answer:

When two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°

Step-by-step explanation:

Based on the Inscribed Angles Theorem, the measure of an intercepted arc is twice the measure of the inscribed angle that intercepts it in a circle.

Consequently, the theorem also Holds that the measure of two inscribed angles intercepting the same arc, are congruent. In other words, both angles together are the same, and their sum would give you the measure of the arc they both intercept.

In the diagram shown in the attachment below, we have 2 inscribed angles, angle A and B. They both intercept the same arc of 75°.

Therefore, we can conclude that the measure of both angles equal 75°, which is the same as the measure of the arc they intercept.

Angle A = Angle B

m<A + m<B = measure of intercepted arc = 75°

Answer:

-9

Step-by-step explanation:

Hey there!

Well, to simplify,

5 - 2(3 + 4)

Wel need to use PEMDAS,

3+4=7

7 * -2 = -14

5 - 14 = -9

Hope this helps :)

Answer:

-9

Step-by-step explanation:

[tex]5 - 2(3+4)\\5 - 2(7)\\5 - 14\\-9[/tex]

Answer:

5-46i

Step-by-step explanation:

1. Multiply (10-4i) and (4-5i), I recomnd using foil:

40-50i-16+20i^2 + (-15+20i)

2. Remove the parenthesis around -15+20i

*we can do this since there is a "+":    

40-50i-16+20i^2 + (-15)+20

3. Simplify i^2

* i^2 is -1 by textbook defination:

40-50i-16+20(-1) + (-15)+20

4. Simplify

40-50i-16-20 + (-15)+20

6. Combine like terms:

-5-50i-16i+20i

5-46i

And the problem is done

Answer:

if im understanding right the answer should be x = -1

Step-by-step explanation:

5x - 11 = 3x - 9

subtract 3x

2x -11 = -9

add 11

2x = -2

divide by 2

x = -1

Answer:

Well the correct answer is −4x+28... But I don't

see that as one of your options. :/

Simplify:

18−2(x+x−5)

Distribute:

=18+(−2)(x)+(−2)(x)+(−2)(−5)

=18+−2x+−2x+10

Combine Like Terms:

=18+−2x+−2x+10

=(−2x+−2x)+(18+10)

=−4x+28

Answer:

−4x+28

Answer:

Option D is the correct option.

Step-by-step explanation:

18 - 2 [ x + ( x - 5 ) ]

Remove the unnecessary Parentheses

⇒18 - 2 [ x + x - 5 ]

Collect like terms

⇒18 - 2 [ 2x - 5 ]

Distribute 2 through the parentheses

⇒18 - 4x + 10

Add the numbers

⇒28 - 4x

Hope I helped!

Best regards!!

Answer:

x=3

Step-by-step explanation:

5/2 ( 3x-1) = 20

Multiply each side by 2/5

2/5 ( 5/2 ( 3x-1) )= 20 *2/5

3x-1 = 8

Add 1 to each side

3x-1+1 = 8+1

3x = 9

Divide each side by 3

3x/3 = 9/3

x =3

Answer:

50 cars

Step-by-step explanation:

Let's define p as the number of people and c the number of cars.

We know that p / c = 3/5 or in other words, there are 5 cars every 3 people. If we have 30 people means that p = 30 which implies 30/c = 3/5 which implies c = 5/3 * 30 = 50.

Answer:

Step-by-step explanation:people=30=3/5

30/5=6*3=18

car=30=5/3

30/3=10

10*5=50

so there are 50 cars there

Answer:

2x - 7y + 17

Step-by-step explanation:

Subtracting the 2 expressions

2x - 4y + 6 - (3y - 11) ← distribute parenthesis by - 1 )

= 2x - 4y + 6 - 3y + 11 ← collect like terms

= 2x - 7y + 17

Answer:

0

Step-by-step explanation:

2x_4y +6_3y_11

2x_7y=17

2x _7y+17=0

Answer:

THEY ARE COMPLIMENTARY BUT NOT NECESSARILY CONGRUENT.

Step-by-step explanation:

This is so because their lines don't meet.

Answer:

8

Step-by-step explanation:

rows=x

each row=(x+5) tomatoes

she increased the number of rows by 3

and doubled the number of tomatoes in each row

3multiplied by x=3x

(2x+10) because she doubled them

3x+10÷2x

=8

I've tried I hope this helps

Answer:

I agree with the other person that Line S is the one parallel to line R.

Step-by-step explanation:

This is because they do not intersect each other and if they were to continue to go on forever, the lines would never intersect. Lines are parallel when they never intersect. Also, there are indication lines that show that the two lines are parallel, you see the arrows that are in the lines.

The line which is parallel to the line r will be line b

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Parallel lines are those line which has the same slope or we can say the angle between the parallel line is always zero.

A parallel line is also called for the lines which do not intersect.

From the given question it is clearly visible that line q p t all are intersecting the line r and line s are not intersecting hence, line s will be parallel to the line r.

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Answer:

p=(-0.0125n) + 42.5

Step-by-step explanation:

Let p= price

n = number of shirts

m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

There are two points which are (1000, $30) and (3000, $5)

Our slope m = (p1-p2)/(n1-n2)

Filling in from our points m = (30-5)/(1000-3000)

m = 25/-2000

m = -0.0125

Since we have determined our slope, we can now find our equation

p-p1=m(n-n1)

p-30=(-0.0125)(n-1000)

p-30= (-0.0125n) + 12.5

p=(-0.0125n) + 42.5

Then, we can double check with the other point there:

p=(-0.0125n) + 42.5

5? (-0.0125x 3000) + 42.5

5= 5

Therefore,linear equation in the form p(n) is

p=(-0.0125n) + 42.5

Answer:

A. x > -1 or x < -1

Step-by-step explanation:

5x - 29 > -34                     or                   2x + 31 < 29

Add 29 to both sides.                             Subtract 31 from both sides.

5x > -5                              or                    2x < -2

Divide both sides by 5.                          Divide both sides by 2.

x > -1                                 or                    x < -1

Answer: x > -1 or x < -1

Answer:

[tex]\huge \boxed{17}[/tex]

Step-by-step explanation:

Point M is on the line segment LN.

LM = 7

MN = 10

LN = LM + MN

LN = 7 + 10 = 17

The value of the line segment LN is 17.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that point, M is the online segment LN. Given LM=7 and MN=10,

The value of the line segment will be calculated as:-

Point M is on the line segment LN.

LM = 7

MN = 10

LN = LM + MN

LN = 7 + 10 = 17

Therefore, the value of the line segment LN is 17.

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Answer:

Step-by-step explanation:

Hello, when you try to find the intersection point(s) you need to solve a system like this one

[tex]\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}[/tex]

So, you come up with a polynomial equation like.

[tex]ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0[/tex]

And then, we can estimate the discriminant.

[tex]\Delta=(b-m)^2-4*a*(c-p)[/tex]

If [tex]\Delta<0[/tex] there is no real solution, no intersection point.

If [tex]\Delta=0[/tex] there is one intersection point.

If [tex]\Delta>0[/tex] there are two real solutions, so two intersection points.

Hope this helps.

Answer:

Step-by-step explanation:

[tex](1,5)=(x_1,y_1)\\(9,0) = (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d = \sqrt{(9-1)^2 +(0-5)^2}\\ \\d = \sqrt{(8)^2+(-5)^2}\\ \\d = \sqrt{64+25}\\ \\d = \sqrt{89}\\[/tex]

The distance between the points (1, 5) and (9, 0) is √89 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points (1, 5) and (9, 0) into the distance formula, we have the following;

Distance = √[(9 - 1)² + (0 - 5)²]

Distance = √[(8)² + (-5)²]

Distance = √[64 + 25]

Distance = √89 units.

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Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio m:n is given by:

[tex]x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1[/tex]

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

[tex]x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7[/tex]

Therefore the coordinates of point X is at (-13, -7)

Answer:

24 kilometers per hour

Step-by-step explanation:

15 kph x 8 h = 120 kilometers

120km/5 hours = 24 kph

Step-by-step explanation:

Hi, there!!!

According to the question,

1st case

At the speed of 15 km/ hr, it takes time 8 hrs to reach a point.

Then, we must find the distance first to calculate your speed in 2nd case,

So, let's find the distance first,

now,

distance (d) = s×t

or, d= 15km/ hr × 8hrs

Therefore, the distance is 120 km.

now,

In 2nd case,

As the question has asked to find speed on same point, it will have same distance covered.

time( t) = 5hrs.

distance (d)= 120km

now,

speed = distance/time taken

or, s= 120 km/5 hrs

or, s = 24km/ hr.

Therefore, your speed in 2nd case will be 24km/hr.

Hope it helps...

Answer:

Hey there!

x=95

This is because x and the angle of 95 degrees are vertical angles, and vertical angles are congruent to each other.

Let me know if this helps :)

Answer:

[tex]\large \boxed{4}[/tex]

Step-by-step explanation:

[tex]\sf The \ sum \ of \ -5, \ -10, \ and \ -9 \ is \ divided \\ by \ the \ product \ or \ multiplication \ of \ 2 \ and -3.[/tex]

[tex]\displaystyle \frac{-5+-10+-9}{2 \times -3}[/tex]

[tex]\displaystyle \frac{-24}{-6}[/tex]

[tex]=4[/tex]

Answer:

4

Step-by-step explanation:

-5+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4