Mark can dig a ditch in 4 hours. Greg can dig the same ditch in 3 hours. How long would it take them to dig it together?

Answer:

[tex]\boxed{\sqrt[3]{16} }[/tex]

Step-by-step explanation:

=> [tex]\sqrt[3]{16}[/tex] is an irrational number because it cannot be written as the form [tex]\frac{p}{q}[/tex] which is the basic requirement of being a rational number.

=> [tex]\sqrt{100}[/tex] = 10 (A rational number because it's a whole number)

=> 1/8 (Rational as it is in the form p/q)

=> -2.2675 (Rational because it is an integer)

Answer:

[tex]\boxed{\sqrt[3]{16} }[/tex]

Step-by-step explanation:

An irrational number cannot be expressed in the form p/q, where p and q are whole integers.

[tex]\sqrt{100} =10[/tex]

[tex]\frac{1}{8} =0.125[/tex]

[tex]-2.2675= - \frac{907}{400}[/tex]

[tex]\sqrt[3]{16} \approx 2.51984209979... \neq \frac{p}{q}[/tex]

[tex]\sqrt[3]{16}[/tex] is an irrational number.

Answer:

its not a right triangle

Step-by-step explanation:

Answer: [tex]\frac{7}{12}.[/tex]

Step-by-step explanation:

Given table:

X            f(X)

-1                -2

0                 -1

1                  [tex]-\dfrac{1}{2}[/tex]

2                 [tex]-\dfrac{1}{4}[/tex]

3                 [tex]-\dfrac{1}{8}[/tex]

i.e. , f(-1) = -2

f(2) = [tex]-\dfrac{1}{4}[/tex]

The rate of change between [tex]f(a)[/tex] and [tex]f(b)=\dfrac{f(b)-f(a)}{b-a}[/tex]

Then, the rate of change between f(-1) and f(2) = [tex]\dfrac{-\dfrac{1}{4}-(-2)}{2-(-1)}[/tex]

[tex]=\dfrac{-\dfrac{1}{4}+2}{3}=\dfrac{\dfrac{-1+8}{4}}{3}\\\\=\dfrac{\dfrac{7}{4}}{3}\\\\=\dfrac{7}{12}[/tex]

Hence, the rate of change between f(-1) and f(2) is [tex]\frac{7}{12}.[/tex]

Answer:

A. 85

Step-by-step explanation:

SInce nickels are worth 5 cents, the number of pennies must end with an 8 or a 3 in order for the total to end with a 3 ($9.83)

Answer:

40 degrees

Step-by-step explanation:

90 degrees + 50 degrees = 140 degrees

there are 3 angles that total at 180 degrees in every  triangle

180 degrees - 140 degrees = 40 degrees

Let

A = location of buoy 1

B = location of buoy 2

C = location of buoy 3

True north is 0 degrees on a compass bearing. Turning to 135 degrees means you turn to the south east direction exactly. Then we can break the angle down as shown in the diagram below. We have the angles 90+45+45 = 180 along the right side of location A.

Due to the fact we have parallel lines, specifically the north/south parallel lines going through A and B, we know that the green angles in the diagram are congruent. Both of which are 45 degrees. The purple angle of 45 degrees is to indicate turning to the bearing 045 degrees when you get to location B.

The green and purple angles add to 45+45 = 90, so angle ABC is 90 degrees. Triangle ABC is a right triangle.

We can use the tangent ratio to compute the angle ACB which will help us find the bearing from location 3 to location 1.

tan(angle) = opposite/adjacent

tan(C) = AB/BC

tan(C) = 4.2/2.8

C = arctan(4.2/2.8)

C = 56.3099324740202

Make sure your calculator is in degree mode

This is angle ACB. It combines with the purple angle of 45 degrees that is adjacent to point C. So we have 45+56.3099324740202 = 101.30993247402

Then this adds to 180 as this is the measure of the red arc near point C.

So, 101.30993247402+180 = 281.30993247402

The bearing is approximately 281.30993247402 degrees

Round this however you need to.

Answer:

(13,15)

Step-by-step explanation:

If the trapezoid were to be reflected over the line segment BC, the new coordinates of point A would be (13,15) as it moves to right 5 points from BC sides.

Answer:

(B) 13,15

Step-by-step explanation:

If we look at point A in relation to point B, we see that it's 5 units to the left and 3 units down from point B, therefore making it at (3,15). Now, if we reflect across line BC (which is a y-axis) then we change the X value, not the y value. If the line BC is located at X=8, then the X value will be 8+5, since point A is 5 units away from the line BC. The y value will stay the same because we are reflecting over only one axis. 8+5 = 13, and the y stays at 15, so the new point value of A would be (13,15).

Hope this helped!

Answer:

10

4

Step-by-step explanation:

Purple: This makes two trapezoids. A=(a+b)/2 times h

1st = (4+1)/2 x 1 = 2.5  

2nd = (4+1)/2 x 3 = 5/2 x 3 = 2.5x3=7.5

Total = 2.5+7.5=10

Green: if you draw a line down the center, you can divide these into two more manageable triangles. A=1/2bh

1st = 1/2x2x2 = 2

2nd = 1/2x2x2 = 2

Total = 2+2=4

Answer:

Purple : 10 sq. un

Green : 4 sq. un

Step-by-step explanation:

Answer:

The valueof x is root under 41.

Hope this helps.

Answer:

[tex]f^{-1}(x) = \frac{cos(2x+6)}{\pi }[/tex]

Step-by-step explanation:

[tex]y = \frac{1}{2} cos^{-1} (\pi x)-3[/tex]

Firstly, we've to interchange the variables.

[tex]x = \frac{1}{2} cos^{-1}(\pi y)-3[/tex]

Solving for y

[tex]x = \frac{cos^{-1} \pi y}{2} -3[/tex]

Adding 3 to both sides

[tex]x+3 = \frac{cos^{-1}(\pi y)}{2}[/tex]

Multiplying 2 to both sides

[tex]2(x+3) = cos^{-1} (\pi y)\\2x+6 = cos^{-1} (\pi y)[/tex]

Taking cosine on both sides

[tex]\pi y = cos (2x+6)[/tex]

Dividing both sides by y

[tex]y = \frac{cos(2x+6)}{\pi }[/tex]

Replace y by [tex]f^{-1}(x)[/tex]

=> [tex]f^{-1}(x) = \frac{cos(2x+6)}{\pi }[/tex]

Answer:

[tex]\large \boxed{f^{-1}(x)=\frac{cos(2x+6)}{\pi} }[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{cos^{-1} (\pi x)}{2} -3[/tex]

Swicth variables.

[tex]\displaystyle x=\frac{cos^{-1} (\pi y)}{2} -3[/tex]

Solve for y.

Add 3 to both sides.

[tex]\displaystyle x+3=\frac{cos^{-1} (\pi y)}{2}[/tex]

Multiply both sides by 2.

[tex]\displaystyle 2(x+3)=cos^{-1} (\pi y)[/tex]

[tex]\displaystyle 2x+6=cos^{-1} (\pi y)[/tex]

Take the cos of both sides.

[tex]\displaystyle cos(2x+6)=\pi y[/tex]

Divide both sides by [tex]\pi[/tex].

[tex]\displaystyle \frac{cos(2x+6)}{\pi} =y[/tex]

Answer: NO

Step-by-step explanation:

The functions that models the height of the ball is given as

h(t) = -5t2 + 40t + 100

Where

a = -5, b = 40, c = 100

The time the ball will reach the maximum height will be the vertex of the parabola. At the line of symmetry, the time t will be:

t = -b/2a

Substitute b and a into the formula above.

t = - 40 / -5 = 8

Substitute 8 for t in the function f(t)

h(t) = - 5(8)^2 + 40(8) + 100

h(t) = -5(64) + 40(8) + 100

Open the bracket

h(t) = -320 + 320 + 100

h(t) = 100

The maximum height of the ball is 100m

Given that the power lines is 185 metres above the ground. The golf ball will therefore not hit power lines because the maximum height the ball can go is 100 metres

Answer:

2/6 (1/3)

12 gallons

Step-by-step explanation:

3) 1/2x1/3=1/6, so he'd used 1/6 of a tank.

1/2-1/6=

3/6-1/6=2/6.  So the tank was 2/6 full, or 1/3 full when he got home.

4) If it's 1/3 full and has 4 gallons, it can hold 12 gallons.  (4x3)

Answer:

the smallest possible perimeter is 6

Step-by-step explanation:

since the smallest possible prime number is 2 it would make since if each side is 2 which makes the smallest perimeter possible. i really hope this helped :)

Answer:

6

Step-by-step explanation:

the smallest possible number will be 2.

2 inches/centimeters of each 3 sides of the triangle

Answer:

Step-by-step explanation:

A(1) = 9

A(n+1) = A(n) - 5

n = 1 ;     A(1+1) = A(1) - 5

             A(2) =  9 - 5

             A(2) = 4

n = 2 ;     A(2+1) = A(2) - 5

             A(3) =  4 - 5

             A(3) = 1

n = 3 ;     A(3+1) = A(3) - 5

             A(4) =  1 - 5

             A(4) = -4

n = 4 ;     A(4+1) = A(4) - 5

             A(5) =  -4 - 5

             A(5) = -9

First four terms are: 9 , 4 , 1 , -4 , - 9

Answer:

1.Quantifying measurement error

2.Measurement Error (also called Observational Error) is the difference between a measured quantity and its true value. It includes random error (naturally occurring errors that are to be expected with any experiment) and systematic error (caused by a mis-calibrated instrument that affects all measurements)

3.statical unit

Step-by-step explanation:

[tex]f(x) = \dfrac{x-2}{2}\\\\\\f(f(x)) = \dfrac{\dfrac{x-2}{2}-2}{2}\\\\\\f(f(x)) = \dfrac{\dfrac{x-2-4}{2}}{2}\\\\\\f(f(x)) = \dfrac{x-6}{4}[/tex]

Answer:

i think its the first one-

Step-by-step explanation:

Answer:

the answer is the second one to the right on the top.

Step-by-step explanation:

i got it right on the quiz

Answer:

The answer is given below

Step-by-step explanation:

The statements are not given but from this definition, you should be able to select the correct statement.

Triangles are said to be congruent if they have the same size and shape. A triangle is made up of six (three sides and three angles) but only three is usually needed to prove triangle congruence. These are:

a) Side - Side - Side (SSS): Two triangles are congruent if the length of their three sides are equal to each other.

b) Side- angle- side (SAS): If two sides and one angle of a triangle is equal to two sides and a angle of another triangle then the two triangles are congruent to each other.

c) Angle - side - angle (ASA): If two angles and a side of a triangle are equal to a corresponding two angles and a side of another triangle then the two triangles are congruenr.

d) Right angle - hypotenuse - side (RHS): If for two right angled triangles, their hypotenuse and a side (leg) are equal, then the two triangles are congruent.

Answer:

Step-by-step explanation:

The Volume is given by the following equation: V= Base x Height

Therefore,  [tex]V = 16\frac{1}{4} * \frac{1}{2} = \frac{65}{4} * \frac{1}{2} = \frac{65}{8} = 8\frac{1}{8}[/tex] units

Answer:

1: 18

2: P

Step-by-step explanation:

1: each number in the second row is the square of the number in the first row but it's kinda backwards! for example 4×4=16 writing it backwards would be 61.

now: 9×9=81 and the backwards would be 18

2:the code for each letter is the number of its ends! like: A has 2 ends. S has 2 Ends. O doesn't have any ends.

now: the only letter left with 1 end is P

Answer: pretty tricky question, the answer would be 18

Step-by-step explanation:

each number is multiplied by itself so

4x4=16

and then reverse the writing of the product

16 to 61

9x9=81

81 to 18

Answer:

(x+ (b/2a))^ 2 = (b/2a) ^2 + c/a

Step-by-step explanation:

ax²+bx=c

first we know the form of a square

(x+a)^2 = x^2 + 2ax +  a^2

we have to write the given ax²+bx=c in the above form

for that we bring c on LHS

for the we subtract c from both sides

ax²+bx -c =c - c

=> ax²+bx - c = 0

now we see that in x^2 + 2ax +  a^2 , term x^2 does not have any coefficient,

so in our equation we get rid of coefficient a from  ax²+bx - c = 0

for that we divide both LHS and RHS by a

(ax²+bx - c)/a = 0/a

x²+bx/a - c/a = 0

now we have to write (b/a)x in form of 2ax

for we divide and multiply (b/a)x by 2

thus we have

x²+2 (b/2a)x - c/a = 0

now comparing above equation with x^2 + 2ax +  a^2

we see that 2ax is same 2 (b/2a)x

thus (b/2a) is same as a in standard form of quadratic equation  x^2 + 2ax +  a^2

now we have to get   a^2

as (b/2a)  is same as a

we add and subtract square of (b/2a) on LHS

x²+2 (b/2a)x - c/a + (b/2a) ^2 - (b/2a) ^2 = 0

rearranging it

x²+2 (b/2a)x  + (b/2a) ^2 - (b/2a) ^2 -c/a = 0

=> x^2 + (b/2a)x + (b/2a) ^2 -(b/2a) ^2 -c/a = 0

=> (x+ (b/2a))^ 2 - ((b/2a) ^2 + c/a ) = 0

=> (x+ (b/2a))^ 2 = (b/2a) ^2 + c/a  answer

Answer:

y= x^2 + 6

Step-by-step explanation:

y= x2 + 6 (which should be written as y= x^2 + 6) has the form y - k = a(x - h)^2.  For y= x^2 +  6, h = 0 and k  = 6.  Thus the vertex is (0, 6)

Answer:

B and E

Step-by-step explanation:

For every 3 minutes she spend running, she spends 5 minutes lifting weight so that would be [tex]\frac{3}{5}[/tex] as fraction.

So, therefore, the answers are B and E.

For the entirety of this problem, p will represent a pair of pants and b will represent a bracelet.

Step 1) Set up equations for Destiny and Guadalupe

Destiny: 178 = 2p + 6b

Guadalupe: 155 = 3p + 2b

I will be using substitution to solve this problem, but elimination can also be used.

Step 2) Solve Destiny's equation for p

178 = 2p + 6b

178 - 6b = 2p

89 - 3b = p

Step 3) Substitute the found value of p from Destiny's equation into Guadalupe's equation and solve for b

155 = 3(89 - 3b) + 2b

155 = 267 - 9b + 2b

155 = 267 - 7b

-7b = -112

b = 16

Step 4) Use the value of b found in step 3, plug that back into our equation from step 2 and solve for p

89 - 3(16) = p

89 - 48 = p

p = 41

one pair of pants = $16

one bracelet = $41

Hope this helps!! :)

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]

Required

[tex]a + b[/tex]

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex](x_1,y_1) = A(0,1)[/tex]

[tex](x_2,y_2) = B(3,4)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]

[tex]AB = \sqrt{( - 3)^2 + (-3)^2}[/tex]

[tex]AB = \sqrt{9+ 9}[/tex]

[tex]AB = \sqrt{18}[/tex]

[tex]AB = \sqrt{9*2}[/tex]

[tex]AB = \sqrt{9}*\sqrt{2}[/tex]

[tex]AB = 3\sqrt{2}[/tex]

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

[tex](x_1,y_1) = B (3,4)[/tex]

[tex](x_2,y_2) = C(4,3)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]

[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]

[tex]BC = \sqrt{1 + 1}[/tex]

[tex]BC = \sqrt{2}[/tex]

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

[tex](x_1,y_1) = C(4,3)[/tex]

[tex](x_2,y_2) = D (3,0)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]

[tex]CD = \sqrt{(1)^2 + (3)^2}[/tex]

[tex]CD = \sqrt{1 + 9}[/tex]

[tex]CD = \sqrt{10}[/tex]

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

[tex](x_1,y_1) = D (3,0)[/tex]

[tex](x_2,y_2) = A (0,1)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]

[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]

[tex]DA = \sqrt{9 + 1}[/tex]

[tex]DA = \sqrt{10}[/tex]

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

[tex]Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}[/tex]

[tex]Perimeter = 4\sqrt{2} + 2\sqrt{10}[/tex]

Recall that

[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]

This implies that

[tex]a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}[/tex]

By comparison

[tex]a\sqrt{2} = 4\sqrt{2}[/tex]

Divide both sides by [tex]\sqrt{2}[/tex]

[tex]a = 4[/tex]

By comparison

[tex]b\sqrt{10} = 2\sqrt{10}[/tex]

Divide both sides by [tex]\sqrt{10}[/tex]

[tex]b = 2[/tex]

Hence,

a + b = 2 + 10

a + b = 12

Answer:

a+b=6

Step-by-step explanation:

The tutor verified answer is mostly correct however, if you look under both by comperision sections you will see that it is:

[tex]4\sqrt{2}[/tex] and [tex]2\sqrt{10}[/tex] thus the answer is 4+2=6

Answer:

78 pounds

Step-by-step explanation:

Let's say Yolanda makes a pounds of Type A coffee and b pounds of Type B coffee. Since the total number of pounds is 130, we can write the equation:

a + b = 130

We know the cost of Type A coffee is $5.20/lb and the cost of Type B coffee is $4.05/lb, so since the total cost is $586.30, we can write:

5.20a + 4.05b = 586.30

We can now solve the system of equations:

a + b = 130

5.20a + 4.05b = 586.30

Manipulate the first equation by subtracting b from both sides:

a + b = 130

a = 130 - b

Substitute 130 - b for a in the second equation:

5.20a + 4.05b = 586.30

5.20 * (130 - b) + 4.05b = 586.30

676 - 5.20b + 4.05b = 586.30

Move the terms with b to one side:

1.15b = 89.70

b = 78

Thus, Yolanda used 78 pounds of Type B coffee.

~ an aesthetics lover

Answer:

29

Step-by-step explanation:

To find the lower quartile you need to split it into 2 by finding the median

Set A: 73, 75, 79, 81, 84, 85

Set B: 47, 49, 51, 51, 55, 56

Now you have to find the median of each

A: 80

B: 51

Lastly, you subtract and get 29

Answer:

6:11

Step-by-step explanation:

There are 12 grapes and 12 + 5 + 2 + 3 = 22 total fruits, so the ratio is 12:22 which simplifies to 6:11.

Step-by-step explanation:

Given:

Orange=5

Apple=3

Grape=12

Avocado=2

Formula:

Grape:Fruits

Answer:

Fruits= 5+3+12+2

Fruits=22

Grape/Avocado

12/2=6

Grape:Apple

12/3=4

Grape:Orange

12/5=2.4

Grape: All fruits

12/22=0.54

Hope it helps ;) ❤❤❤

You didn't attach a photo, so I am confused on what your question is. I am answering 3 problems that have the same intro.

If your question was not any of these, I can't help, sorry :)

Answer:

[tex]R' = 6[/tex]

[tex]S' = 7.5[/tex]

[tex]T' = 9[/tex]

Step-by-step explanation:

The question is incomplete; however the sides of the triangle are;

[tex]R = 8[/tex]

[tex]S = 10[/tex]

[tex]T = 12[/tex]

[tex]Scale\ Factor = \frac{3}{4}[/tex]

Required

Determine the sides of R'S'T'

The new sides of the triangle is calculated as thus;

[tex]New\ Side = Old\ Side * Scale\ Factor[/tex]

Calculating  R'

[tex]R' = R * Scale Factor[/tex]

Substitute 8 for R and 3/4 for Scale Factor

[tex]R' = 8 * \frac{3}{4}[/tex]

[tex]R' = \frac{24}{4}[/tex]

[tex]R' = 6[/tex]

Calculating  S'

[tex]S' = S * Scale Factor[/tex]

Substitute 8 for R and 3/4 for Scale Factor

[tex]S' = 10 * \frac{3}{4}[/tex]

[tex]S' = \frac{30}{4}[/tex]

[tex]S' = 7.5[/tex]

Calculating  T'

[tex]T' = T * Scale Factor[/tex]

Substitute 8 for R and 3/4 for Scale Factor

[tex]T' = 12 * \frac{3}{4}[/tex]

[tex]T' = \frac{36}{4}[/tex]

[tex]T' = 9[/tex]

Triangle RST was dilated with the origin as the center of the dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The lengths of the sides of the triangle RST are given. Enter the lengths of the sides of the triangle R'S'T' below.

Answer:

6

7.5

9