A number cube for a game has a volume of 64 mm
What is the length of one side of the cube?
3.27 mm
4 mm
6.46 mm
8 mm

Answer:

3x

Step-by-step explanation:

Using the triangle sum theorem the following are the missing values:

x = 25

m∠B = 65°

m∠C = 50°

According to the triangle sum theory, all the interior angles of a triangle will add up to 180 degrees.

Given:

m∠A = 65°

m∠B = (3x - 10)°

m∠C = (2x)°

Therefore:

65 + 3x - 10 + 2x = 180

Combine like terms

55 + 5x = 180

5x = 180 - 55

5x = 125

x = 125/5

x = 25

m∠B = (3x - 10)° = 3(25) - 10 = 65°

m∠C = (2x)° = 2(25) = 50°

Therefore, using the triangle sum theorem the following are the missing values:

x = 25

m∠B = 65°

m∠C = 50°

Learn more about triangle sum theorem on:

https://brainly.com/question/7696843

The statement about the range of the logarithmic function F(x) = log_bx being positive real numbers is false; the range includes all real numbers.

The statement that the range of F(x) = logbx is the set of all positive real numbers is False. The range of a logarithmic function like F(x) = logbx, where b is the base and x is the argument, is actually all real numbers, not just the positive ones. This is because you can take the log of any positive number, but the result can be any real number, negative, positive, or zero (when x=1).

For example, if the base b is greater than 1, as x approaches zero from the positive side, logbx will approach negative infinity, illustrating how the range includes negative numbers.

Answer:

144°

If you look up 144° it matches exactly how it looks on a pie chart

I hope this helped

Answer:

5x - 2y - 23 = 0

Step-by-step explanation:

Line is passing through the points [tex] (3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2) [/tex]

Equation of line in two point form is given as:

[tex] \frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \: \frac{y -( - 4) }{ - 4 -1} = \frac{x -3 }{3 -5 } \\ \\ \therefore \:\frac{y + 4 }{ - 5} = \frac{x -3 }{ - 2 } \\ \\ \therefore \: \frac{y + 4 }{ 5} = \frac{x -3 }{ 2 } \\ \\ \therefore \: 2(y + 4) = 5(x - 3) \\ \therefore \: 2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\ \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \: \\ standard \: form.[/tex]

Answer:

6623.4375 feet²

Step-by-step explanation:

Distance is the radius

Area:

(135/360) × pi × r²

(135/360) × 3.14 × 75²

6623.4375 feet²

The area of the fairway watered by the sprinkler is 6,623.44 square feet

The shape of the golf course is a sector, Using the formula for calculating the area of a sector is expressed as:

[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]

Substitute the given parameters into the formula to have:

[tex]A=\frac{135}{360} \times 3.14 \times 75^2 \\A = \frac{2,384,437.5}{360}\\A= 6,623.4375ft^2[/tex]

Hence the area of the fairway watered by the sprinkler is 6,623.44 square feet

Learn more on area of a sector here: https://brainly.com/question/12792310

Answer:

y -1 = -4(x +3)

Step-by-step explanation:

The point slope form of a line is given by

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y -1 = -4(x --3)

y -1 = -4(x +3)

Answer:

36.3

Step-by-step explanation:

145.2/4 = length of each side

145.2/4 = 36.3

Answer:

Average speed = 15

Step-by-step explanation:

To find the speed of the body, we can take the position equation and take the derivative in relation to time:

Speed = dY/dt = 2*3*t = 6t

Then, we need to find the speed at t=0 and the speed at t=5:

Speed(t=0) = 6*0 = 0

Speed(t=5) = 6*5 = 30

Now, we just need to make the average of both speeds:

Average = (0 + 30) / 2 = 15

Answer:

17.043956

Step-by-step explanation:

Answer:

Step-by-step explanation:

17.043956 in decimal form

This is already in decimal form

Answer:

f(x) = - 4x² - 56x - 202

Step-by-step explanation:

We can simplify this quadratic function given in vertex form into standard form by simplifying the exponents and adding like terms.

f(x) = -4(x+7)^2 - 6

f(x) = -4(x^2 + 14x + 49) - 6

f(x) = -4x² - 56x - 196 - 6

f(x) = -4x² - 56x - 202

Answer: b

Step-by-step explanation: just took the quiz on egde.

Answer:

1.7x-2=8+2x

Step-by-step explanation:

collect like terms

7x-2x=8+2

5x=10

divide 5 both sides to get the value of x

5x/5=10/5

x=2

Answer:

1. x = 2

2. a = 2

4. a = 5.

Step-by-step explanation:

1. 7x - 2 = 8 + 2x

7x - 2x = 8 + 2

5x = 10

x = 2.

2.  4 ( 3a + 1 ) = 3a + 22

12a + 4 = 3a + 22

12a - 3a = 22 - 4

9a = 18

a = 2.

4. a - 3(2a) = -25

a - 6a = -25

-5a = -25

a = 5.

( I couldn't do number 3 because there is no variable in the equation).

Answer:

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

I think this is right

the unit vector e which is collinear to vector a = (6,8) , and has the same direction is  [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .

Step-by-step explanation:

Here we have ,  vector a = (6,8)  . We need to find  the unit vector e which is collinear to vector a = (6,8) , and has the same direction. Let's find out:

We know that for a vector [tex]a = (x,y)[/tex] the unit vector is given by :

⇒ [tex](\frac{x}{|a|} ,\frac{y}{|a|} )[/tex] , where |a| is modulus of vector a . So , Modulus of vector a is :

⇒ [tex]|a| = \sqrt{x^2+y^2}[/tex]

⇒ [tex]|a| = \sqrt{6^2+8^2}[/tex]

⇒ [tex]|a| = \sqrt{36+64}[/tex]

⇒ [tex]|a| = \sqrt{100}[/tex]

⇒ [tex]|a| =10[/tex]

Hence , unit vector is given by [tex](\frac{6}{10} ,\frac{8}{10})[/tex] or ,  [tex](\frac{3}{5} ,\frac{4}{5})[/tex] . Vector is already collinear as it's in same direction of original vector as :

⇒ [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex]

Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is  [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .

a) 18.68 minutes

b) 2.34%

c) 9.96 km/h

Step-by-step explanation:

a)

The velocity of Surya in the 1st segment (swimming part) is

[tex]v_1=4 km/h[/tex]

So, the distance covered by Surya in the swimming part is

[tex]d_1=4t_1[/tex]

where [tex]t_1[/tex] is the time taken to cover this part.

The velocity of Surya in the 2nd segment (biking part) is

[tex]v_2=40 km/h[/tex]

So the distance covered in the biking part is

[tex]d_2=40t_2[/tex]

where [tex]t_2[/tex] is the time taken to cover this part.

We know that the total distance covered in these 2 segments is

[tex]d=d_1+d_2=43.29[/tex]

So it can be rewritten as

[tex]4t1+40t_2=43.29[/tex] (1)

The total time taken to cover these two parts is

[tex]t=t_1+t_2=81.75 min =1.36 h[/tex]

So we have

[tex]t_2=1.36-t_1[/tex]

And substituting in (1) we can find t1:

[tex]4t_1 + 40(1.36-t_1)=43.29\\36t_1=11.21\\t_1=\frac{11.21}{36}=0.31 h = 18.68 min[/tex]

b)

The total distance covered in all 3 segments is

[tex]d=d_1+d_2+d_3=52.95 km[/tex]

where

where

d1 is the length of the swimming part

d2 is the length of the biking part

d3 is the length of the running part

We know that the distance covered in part 1 (swimming part) is

[tex]d_1=v_1 t_1 = (4)(0.31)=1.24 km[/tex]

Therefore we can find the percent that the swimming part correspond to the total race as:

[tex]\frac{d_1}{d}=\frac{1.24}{52.95}=0.0234 = 2.34\%[/tex]

c)

Here the total time taken by Surya for the race must be

[tex]t=140 min = 2.33 h[/tex]

And this is the sum of the times of the 3 segments:

[tex]t=t_1+t_2+t_3[/tex]

where

t1 is the time taken to complete the swimming part

t2 is the time taken to complete the biking part

t3 is the time taken to complete the running part

We know already that

[tex]t_1=0.31 h[/tex]

and

[tex]t_2=1.36-t_1=1.36-0.31=1.05 h[/tex]

So the time for the 3rd section must be

[tex]t_3=t-t_1-t_2=2.33-0.31-1.05=0.97h[/tex]

The distance to cover in the last part is

[tex]d_3=d-d_1-d_2=52.95-43.29=9.66 km[/tex]

So the average velocity of the last segment must be:

[tex]v_3=\frac{d_3}{t_3}=\frac{9.66}{0.97}=9.96 km/h[/tex]

Answer:

-12

Step-by-step explanation:

-6 times 3 is -18 and 2/3 of -18 is -12

Answer:

He would walk 1 1/2 a mile. Hope that helps

Step-by-step explanation:

According to the given question, the length of AC on the number line is 5 units

The length of AC on the number line can be determined by subtracting the coordinate of point A from the coordinate of point C. Let's say point A is located at coordinate 2 and point C is located at coordinate 7. To find the length of AC, we subtract the coordinate of A from the coordinate of C: 7 - 2 = 5

Therefore, the length of AC on the number line is 5 units. Another way to think about this is by considering the distance between the two points. In this case, the distance between point A and point C is the same as the length of AC. If you have any further questions, please, let me know.

To know more about  length here

https://brainly.com/question/2217700

#SPJ2

Answer:

18x^5y

Step-by-step explanation:

Divide 36 by 2 first : 18

since you are dividing, you subtract the exponents:

x^8 - x^3= x^5

y^4-y^3= y^1 but you usually just write y

Dividing exponents in this equation  [tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex] is [tex]18x^{5} y[/tex]

How can the expression be simplified?

A mathematical action called an exponent, sometimes referred to as a power, is the result of repeatedly multiplying a base number by itself. A little number or variable to the right and above the basic number serves as a symbol for it. For instance, in the notation 2^3, the base and exponent are 2 and 3, respectively, denoting three times the product of 2 and itself: 2^3 = 2 x 2 x 2 = 8.

Given that;

[tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex]

Divide 36 by 2 first : 18

[tex]\frac{18x^{8}y^{4} }{x^{3} y^{3} }[/tex]

=[tex]18x^{5} y[/tex]

Answer:

73/10

Step-by-step explanation:

7*10+3/10=

70+3/10=

73/10

Your answer would be 73/10.

Think of it this way, each whole number counts as 10/10. So by using that, just do 10 * 7 / 10...

So you would get 70/10.

Then you would add on the left over 3/10 that you had at the beginning.

70/10 + 3/10 = 73/10

This would get your final answer of 73/10.

Answer:

4.968 cm

Step-by-step explanation:

Given area of prism = 31.3 cm

This problem can be solved by using formula to calculate area of trapezium which is given below

Formula to calculate area of prism =( sum of parallel sides * perpendicular distance between parallel side )/2

let the perpendicular distance between parallel side = X

sum of parallel sides = 7.3+5.3 = 12.6 cm

Therefore by using formula

31.3 = (7.3+5.3)*X/2

=> 31.3 * 2 = 12.6*X

=> X = 62.6/12.6 = 4.968

Hence perpendicular distance between parallel side  is 4.968 cm

Answer: 384

Step-by-step explanation: 12x8x4=384

Answer:

V =384 inches^3

Step-by-step explanation:

The volume of a box is given by

V = l*w*h

V = 12*8*4

V =384 inches^3

Final answer:

To solve this problem, we set up a system of equations representing the amount of oil in each tank. Using the fact that all three tanks end up with the same amount of oil, we determine that Tank A must have started with 1000 litres of oil.

Explanation:

You need to find the value of n which represents the amount of oil initially in Tank A, given that 500 litres are pumped from Tank A to Tank C, and that Tanks A, B, and C eventually contain the same amount of oil.

After transferring 500 litres from Tank A to Tank C, Tank A will have n - 500 litres left. Since tank C was empty and now has 500 litres, Tank B must also transfer enough oil to Tank C such that both B and C have the same amount of oil. Tank B started with n + 150 litres and must end up with the same amount as tank C, which we will refer to as x.

Therefore, we need to solve the following system of equations:

Tank A: n - 500 = x

Tank B: n + 150 - x = x

Tank C: 500 = x

From Tank C's equation, we know that x = 500. Substituting this into the equations for Tanks A and B gives us:

Tank A: n - 500 = 500

Tank B: n + 150 - 500 = 500

From Tank A's equation, we see that  n = 1000  litres.

Answer:

mean id 45.6

we get it by adding then subtracting

Answer:

-3

Step-by-step explanation:

-15 divided by 5= -3

Answer:

The answers are options A, C, and D

Step-by-step explanation:

Final answer:

To find Bethany's expanded garden dimensions, we factored the quadratic equation x² + 8x - 48 = 0 to find that the original dimension is 4 feet, resulting in the new dimensions of 4 feet by 12 feet.

Explanation:

The student is tasked with finding the possible dimensions of Bethany's expanded garden, which will have an area of 48 square feet. The side lengths of the new garden are related by the fact that one side will be 8 feet longer than the other. We can use the given quadratic equation x² + 8x - 48 = 0 to model this situation.

Step-by-Step Factoring

First, we identify the coefficients in the equation, which are A=1 (coefficient of x²), B=8 (coefficient of x), and C=-48 (constant term).

To factor the quadratic equation, we look for two numbers whose product is A*C (-48) and whose sum is B (8). These numbers are 12 and -4.

Rewrite the middle term (8x) using the numbers found: x² + 12x - 4x - 48 = 0.

Factor by grouping: (x² + 12x) - (4x + 48) = 0 becomes x(x + 12) - 4(x + 12) = 0.

Factor out the common factor: (x - 4)(x + 12) = 0.

Solve for x: x = 4 or x = -12. Since a garden's dimensions must be positive, we disregard the negative solution. This leaves us with x = 4 feet as the original dimension and x + 8 = 12 feet as the expanded dimension.

Thus, the dimensions of Bethany's new garden are 4 feet by 12 feet.

Answer:

69.08 inches

Step-by-step explanation:

Circumference of the wheel

= 2 pi r

Given

Pi = 3.14

Radius r = diameter/2 = 22/2

= 11

Therefore

Circumference = 2 x 3.14 x 11

= 69.08 inches

The probability of choosing a blue marble is 2/5 or 0.4.

It is given that the jar contains 3 red marbles, 10 blue marbles, 8 green marbles, and 4 yellow marbles.

It is required to find the probability of choosing a blue marble.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We have:

Number of total marbles = 3+10+8+4 ⇒25

Number of blue marble = 10

From the definition of the probability:

[tex]\rm Probability = \frac{Favourable \ outcomes}{Total \ outcomes}[/tex]

[tex]\rm Probability = \frac{10}{25}[/tex]

[tex]\rm Probability = \frac{2}{5 } \Rightarrow 0.4[/tex]

Thus, the probability of choosing a blue marble is 2/5 or 0.4.

Learn more about the probability here:

brainly.com/question/11234923

The answer is 440 in²

Here is what I added up!

25 + 4(40) + 4(20) + 100 + 75

I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!

Answer:

y=-3x^2+12x+63

Step-by-step explanation:

y=-3(x-7)(x+3)

y=-3(x^2-4x-21)

y=-3x^2+12x+63