a box has a length of 6x inches. the width equals one third the length, and the height equals half the length. if the volume equals 972 cubic inches, what does x equal?

Using the Pythagorean theorem:

Hypotenuse = sqrt( 20^2 + 15^2)

Hypotenuse = sqrt( 400 + 225)

Hypotenuse = sqrt(625)

Hypotenuse = 25

Answer: 25 inches

Answer:

25 inches

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

20^2 + 15^2 = c^2

400 +225 = c^2

625=c^2

Taking the square root of each side

sqrt(625) = sqrt(c^2)

25 = c

Answer:

x = 17

Step-by-step explanation:

The angles are same side interior angles and they will add to 180 when the lines are parallel

6x+8  + 4x+2 = 180

10x+10 = 180

Subtract 10 from each side

10x+10-10 =180-10

10x = 170

Divide by 10

10x/10 = 170/10

x = 17

Answer:

x = 17

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.

For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.

6x + 8 + 4x + 2 = 180

10x + 10 = 180

10x = 170

x = 17

Answer:

[tex] \displaystyle a = \frac{1+vh}{v}[/tex]

Step-by-step explanation:

we want to figure out a value of a for the following condition

[tex] \displaystyle va - vh = 1[/tex]

to do so factor out v;

[tex] \displaystyle v (a - h )= 1[/tex]

divide both sides by v which yields:

[tex] \displaystyle \frac{(a-h) \cancel{(v)}}{ \cancel{v}}= \frac{1}{v} [/tex]

therefore,

[tex] \displaystyle a-h = { \frac{1}{v}}[/tex]

now,add h to both sides:

[tex] \displaystyle a = \frac{1}{v}+h[/tex]

further simplification if necessary:

[tex] \displaystyle a =\boxed{ \frac{1+vh}{v}}[/tex]

factor out of v

Dividing both sides by (v)

cancel out (v)

add h in both sides

cancelout h

[tex]\sf{ }[/tex] [tex]\sf{ }[/tex]

the value of a if va- vh is equals to 1 is [tex]\bold{\dfrac{1+vh}{v} }[/tex]

Answer: 4x + 0.5y

Step-by-step explanation:

Concept:

Here, we need to understand the idea of the mean (average).

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

**Disclaimer** I assume the question is asking for the arithmetic mean instead of geometric. If it was, then you can refer to my answers. If it was not, then you can point it out and I will redo the question.

Terms: 2x-5y, 5x+2y, 8x+6y, x-y

Number of terms: 4

 [(2x-5y) + (5x+2y) + (8x+6y) + (x-y)] / 4

=[2x + 5x + 8x + x + 2y - 5y + 6y - y] / 4

=[16x + 2y] / 4

=4x + 0.5y

Hope this helps!! :)

Please let me know if you have any questions

Answer:

points D and B. Answer choices D and E.

Step-by-step explanation:

The point, C, is at -1 1/4. Count over 2 points of either B or D, and you have your answer.

Step-by-step explanation:

= 1/2x^2.12x^2 - 1/2x^2.4x + 1/2x^2.2

= 6x^4 - 2x^2 + x

Answer:

1

Step-by-step explanation:

no exponent

Answer: [tex]24^{\circ}[/tex]

Step-by-step explanation:

Given

River is flowing from south to North with a velocity of [tex]u=1\ m/s[/tex]

Motor boat traverses the river from east to west at a speed of [tex]v=2.5\ m/s[/tex]

South component of boat velocity must compensate the river velocity in order to travel in west direction.

[tex]\therefore v\sin \theta=u\\\\\Rightarrow 2.5\sin \theta=1\\\\\Rightarrow \sin \theta=\dfrac{2}{5}\\\\\Rightarrow \theta=23.57^{\circ}\approx 24^{\circ} \text{south of west}[/tex]

Answer:

36 units

Step-by-step explanation:

this is a walk around problem

the sides of the triangle will be 10, 13, and 13

so the perimeter = 10 + 13 + 13

p = 36 units

Answer:

perimeter = 36

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, then

perimeter = (5 + 5) + (8 + 8) + (5 + 5)

                = 10 + 16 + 10

               = 36

Answer:

<CAB  

Step-by-step explanation:

Since CAD is equal to DAB

AD bisects CAB  

Answer:

FALSE. isn't it supposed to be 3 : 4.

Step-by-step explanation:

Simplified would be 27÷ 9 =3 and 36 ÷ 9 =4

============================================================

Explanation:

The ratio 4:3 has the first part (4) larger than the second part (3)

The ratio 27:36 has it flipped around, where the second part is the larger item this time.

Based on this alone, we can see that there's no way that 4:3 is the same as 27:36

--------------

Another way you can look at it is to divide both parts of 27:36 by the GCF 9

The ratio 27:36 fully reduces to 3:4 and not 4:3. The order matters.

--------------

Or you could go in verse of the previous section. Multiply both parts of 4:3 by 9

So the ratio 4:3 is equivalent to 36:27 which is not the same as 27:36. Again, the order is important.

--------------

Yet another approach:

Treat the ratios like fractions. If they were equal, then 27/36 = 4/3 would be true.

Cross multiplying leads to 27*3 = 36*4 and that becomes 81 = 144 which is false. So saying 27:36 reduces to 4:3 is also false

Answer:

D

Step-by-step explanation:

first of all, what is mode: it is the highest occuring number in a set of numbers.

now since 12 is supposed to be the mean and it occurs twice but 9 also occurs twice so for 12 to be the mode, we must add one more 12.

therefore the answer is 12

Answer: 1/2x + 2

Step-by-step explanation:

To get the slope you can look at the image. I got the y intercept by graphing the line and manually finding it. I forget how to solve for it

Answer:

Sa / Va = time traveled by bus a

Sb  / Vb + 3/4  = time traveled by van b

Sa / Va = Sb  / Vb + 3/4      times traveled are the same

            = (220 - Sa) / Vb + 3/4

Sa ( 1 / Va + 1 / Vb) = 220 / 80 + 3/4

Sa (140 / 4800) = 3.5

Sa = 120 km

Check: 120 km / 60 km/hr = 2 hr = Ta

Sb = 1.25 * 80 = 100 km   traveling for 1.25 hrs

Answer:

15

Step-by-step explanation:

The given parameters are represented by drawing the triangle with the details given using MS Visio

The point Q is located between points M and N in ΔMNP

The point R is located between points N and P in ΔMNP

The incenter of the triangle = H

Line HQ is perpendicular to side MN on ΔMNP

Line HR is perpendicular to side NP on ΔMNP

The length of the segment QN = 36

The length of the segment HN = 39

By Pythagoras' theorem, HQ = √((HN)² - (QN)²)

∴ HQ = √(39² - 36²)  = 15

HQ = 15

Given that H is the incenter of ΔMNP, the lengths of the perpendicular from H to the sides of the triangle are equal to the radius of the inscribed circle of the triangle

Therefore, the radius lengths are HQ, and HR

∴ HR = HQ = 15

HR = 15.

Answer:

Step-by-step explanation:

There are several ways in which to express this ratio. First and according to the size the model is to the real car:

m = .03c or [tex]m=\frac{3}{100}c[/tex] or conversely, you could state the expression according to the size of the real car as compared to the model:

c = 33 1/3m (the car is 33 and a third times the size of the model).

Answer: 300

Step-by-step explanation:

Based on the information given in the question, the number of participants in the study will be calculated thus:

The number if letters in the set are 8 from A - H. This means that there are 8 ways to choose 3 letter when the ordering matters.

This will be:

= 8!/(8 - 3)!

= 8 × 7 × 6

= 336

Since 36 sequences were not assigned, therefore the numbers that were assigned will be:

= 336-36

= 300.

There were 300 participants.

Answer:

[tex]y = - \frac{1}{5} x + 7[/tex]

Step-by-step explanation:

Slope -intercept form:

y= mx +c, where m is the slope and c is the y- intercept.

Since the given equation is already in the slope-intercept form, we can identify its slope by looking at the coefficient of x.

Slope of given line= 5

The product of the gradients of two perpendicular lines is -1.

m(5)= -1

[tex]m = - \frac{1}{5} [/tex]

Substitute the value of m into the equation:

[tex]y = - \frac{1}{5} x + c[/tex]

Substitute a pair of coordinates to find the value of c.

when x= 0, y= 7,

[tex]7 = - \frac{1}{5} (0) + c[/tex]

c= 7

Thus, the equation of the line is y= -⅕x +7.

Answer:

[tex](x-\frac{1}{2})^2=\frac{81}{4}[/tex]

Step-by-step explanation:

Hi there!

[tex]x^2-x-20=0[/tex]

This equation is written in the form [tex]ax^2+bx+c=0[/tex]. First, use partial factoring:

[tex](x^2-x)-20=0[/tex]

For x^2-x, the b value is -1 in [tex]ax^2+bx+c[/tex]. To complete the square, take the square of half of 1 and add it in the parentheses as the c value:

[tex](x^2-x+\frac{1}{2}^2 )-20=0[/tex]

However, when adding values to one side of the equation, we must to the same to the other side:

[tex](x^2-x+\frac{1}{2}^2 )-20=\frac{1}{2}^2[/tex]

Complete the square:

[tex](x-\frac{1}{2})^2-20=\frac{1}{4}[/tex]

Move 20 to the other side

[tex](x-\frac{1}{4})^2=\frac{1}{4}+20\\(x-\frac{1}{2})^2=\frac{81}{4}[/tex]

I hope this helps!

Answer:

The product of 1/3(2/5) represents the number of hot dogs that were served on sesame buns WITH ketchup

Step-by-step explanation:

Answer:

[tex]162.07[/tex]

Step-by-step explanation:

An image that creates represents this situation has been attached to this answer. As one can see, the diagram models the situation, the angle of depression represents the angle between the horizon line and the line of sight. The horizon line and the tower form a right angle (a (90) degree angle). This means that the angle of depression is complementary to the angle of sight. Therefore, one can state the following:

[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]

Substitute,

[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]

[tex](m<ABD)+(m<DBC)=90[/tex]

[tex]42+(m<DBC)=90[/tex]

Inverse operations,

[tex]42+(m<DBC)=90[/tex]

[tex]m<DBC=48[/tex]

Now one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are a series of ratios that describe the relationship between the sides and angles in a right triangle. These ratios are as follows:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Bear in mind, the terms (opposite) and (adjacent) are subjective, and change depending on the reference angle. However, the term (hypotenuse) refers to the side opposite the right angle and is constant regardless of the reference angle.

In this case, one has found an angle in the triangle, one is given the measure of the side opposite this angle, and one is asked to find the side adjacent to this angle. Therefore, it would make the most sense to use the ratio tangent (tan).

[tex]tan(\theta)=\frac{opposite}{adjacnet}[/tex]

Substitute,

[tex]tan(48)=\frac{180}{adjacent}[/tex]

Inverse operations,

[tex]tan(48)=\frac{180}{adjacent}[/tex]

[tex]adjacent=\frac{180}{tan(48)}[/tex]

[tex]adjacent=162.07[/tex]

Answer:

$7 is his Hourly Wage.

Step-by-step explanation:

We can start by finding out how much money Jada started with by adding the amount of money he had after buying the cake with how much he spent on the cake, 86 + 12 = 98.

We now know how much money he had before buying anything. Now we can just divide the total amount of money by how long he worked.

98 ÷ 14 = 7

Answer:

x = 29.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos x = adj side/ hypotenuse

cos x = 67/77

Taking the inverse cos of each side

cos^-1( cos x) = cos^-1 (67/77)

x = 29.52626525

To the nearest tenth

x = 29.5

Step-by-step explanation:

The depth of the water is increasing by 2 feet each minute.

Answer:

La ingeniería es la opción más preferida y la contabilidad es la opción menos preferida entre los diferentes estudios.

Step-by-step explanation:

Los resultados obtenidos de la encuesta a estudiantes que siguen diferentes carreras luego de completar su 4 grado en la escuela secundaria. Cuando los estudiantes terminan sus estudios de secundaria, prefieren dedicarse más a la ingeniería. La escala salarial de los ingenieros es alta y también la demanda de ingenieros es alta en el país. La segunda mejor opción para los estudiantes serán los estudios comerciales, luego elegirán medicina, contabilidad y otros estudios. Las opciones están disponibles para que los estudiantes elijan su carrera preferida en la que identifiquen su interés.

Answer:

Step-by-step explanation:

a) 1200≥25x+45y

b) YES, because:

1200≥25(15)+45(15)

1200≥375+675

1200≥1050

Answer:

c = 18 - 3d

Step-by-step explanation:

d =  days after birthday

Answer:

C = 18 - 3t

Step-by-step explanation:

18 - 9 = 9

9 / 3  = 3

18 = chocolates at the beginning.

C = 18 - 3t

The answer is C = 18 - 3t.

Answer:

-2/8

Step-by-step explanation:

All you need to do is to find the common denominator which is 8

so 4/8 is good to go and remains as it is

For 3/4 you have to multiply the fraction by 2, both numerator and denominator

you will get 6/8

so 4/8-6/8 would give you -2/8 or -1/4