(|5 - 3x | - 1) - ( 1 - 3x ) = 0

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:

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.

Answer:

(x + 14)² + (y – 21/2)² = 1

Step-by-step explanation:

The equation of a circle can be written as seen below

(x – h)² + (y – k)² = r²

Where (h,k) is at the center and r = radius

We are given that the radius is 1

We are also given that the center is at (-14,21/2)

So we know that r = 1, h = -14, and k = 21/2

So to find the equation of the circle we simply substitute these values into the equation of a circle

Equation of a circle: (x – h)² + (y – k)² = r²

r = 1, h = -14, and k = 21/2

Substitute values

(x – (-14))² + (y – 21/2)² = 1²

1^2 = 1

The two negative signs before the 14 cancel out and it changes to + 14

The equation of a circle with a center at (-14,21/2) and a radius of 1 is (x + 14)² + (y – 21/2)² = 1

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

Step-by-step explanation:

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

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:

1. Cos θ = 6√2 / 11

2. Tan θ = 7 / 6√2

3. Cosec θ = 11 / 7

4. Sec θ = 11 / 6√2

5. Cot θ = 6√2 / 7

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine θ = 7 / 11

Next, we shall determine the adjacent of the right triangle. This can be obtained as follow:

Sine θ = 7 / 11

Sine θ = Opposite / Hypothenus

Opp = 7

Hypo = 11

Adj =?

Hypo² = Opp² + Adj²

11² = 7² + Adj²

121 = 49 + Adj²

Collect like terms

Adj² = 121 – 49

Adj² = 72

Take the square root of both side

Adj = √72

Adjacent = 6√2

1. Determination of Cos θ

Adjacent = 6√2

Hypothenus = 11

Cos θ =?

Cos θ = Adjacent / Hypothenus

Cos θ = 6√2 / 11

2. Determination of Tan θ

Opposite = 7

Adjacent = 6√2

Tan θ =?

Tan θ = Opposite / Adjacent

Tan θ = 7 / 6√2

3. Determination of Cosec θ

Sine θ = 7 / 11

Cosec θ =?

Cosec θ = 1 ÷ Sine θ

Cosec θ = 1 ÷ 7 / 11

Cosec θ = 1 × 11/7

Cosec θ = 11/7

4. Determination of Sec θ

Cos θ = 6√2 / 11

Sec θ =?

Sec θ = 1 ÷ Cos θ

Sec θ = 1 ÷ 6√2 / 11

Sec θ = 1 × 11 / 6√2

Sec θ = 11 / 6√2

5. Determination of Cot θ

Tan θ = 7 / 6√2

Cot θ =?

Cot θ = 1 ÷ Tan θ

Cot θ = 1 ÷ 7 / 6√2

Cot θ = 1 × 6√2 / 7

Cot θ = 6√2 / 7

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:

B. 9k^2 + 5k - 1

Step-by-step explanation:

4k^2 + 5k - 3 + 5k^2 + 2

= 4k^2 + 5k^2 + 5k - 3 + 2

= 9k^2 + 5k - 1

Answer: (B) [tex]9k^2+5k-1[/tex]

Step-by-step explanation:

Add [tex]4k^2 + 5k^2[/tex]

Then [tex]-3+2[/tex] and you get -1

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

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

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.

Answers:

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

Explanations:

Answer:

1: gets steeper

2: gets less steep

3: negative

Step-by-step explanation:

"As the value of m changes from 1 to 3, the graph gets steeper."

m is the slope of the line, and when it increases, there's more "rising" then "running", so it becomes more steep.

"As the value of m changes from -6 to -1, the graph gets less steep."

When the value of m increases, it gets more steep. It makes sense since -6 is less than -1. However, in this scenario, the negative sign doesn't "affect" the slope of the graph. It just flips the graph over the y-axis.

So you have to think of it as if the negative signs were gone and it was 6 to 1.

In that case, the slope is decreasing, so it's getting less steeper.

"If the value of m is negative, the slope of the line is negative."

The m variable represents the slope in slope-intercept form, so if m is negative, that's the same as saying the slope is negative.

Hope this helps (●'◡'●)

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:

$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

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: 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:

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: [tex]\$100[/tex]

Step-by-step explanation:

Given

T-shirt cost 5 times as much as a singlet

Suppose the price of a singlet [tex]x[/tex]

Price of a T-shirt is [tex]5x[/tex]

According to the question, for $800, trader can buy 32 more singlet than T-shirt

[tex]\Rightarrow \dfrac{800}{x}=\dfrac{800}{5x}+32\\\\\Rightarrow \dfrac{800}{x}-\dfrac{160}{x}=32\\\\\Rightarrow 800-160=32x\\\\\Rightarrow x=20[/tex]

Thus, the price of a T-shirt is [tex]5x=\$100[/tex]

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:

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

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

[tex]\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}[/tex]

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

[tex]\bf\implies a^m \times b^m = (ab)^m [/tex]

Using this property , we have ,

[tex]\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}[/tex]

This can be written as ,

[tex]\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}[/tex]

Simplifying using ( a+b)(a-b) = a² - b² ,

[tex]\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1} [/tex]

Subtracting the numbers inside the brackets ,

[tex]\rm\implies (-1)^{2n - 1 }[/tex]

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the power is odd .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

[tex]\rm\implies\boxed{\quad \red{ -1 }\quad }[/tex]

Hence the required answer is (-1) .

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:

(5/3)(5/3)(5/3) = 125/27

Step-by-step explanation:

Answer:

[tex]4\frac{17}{27}[/tex]

Step-by-step explanation:

5/3³

5/3 × 5/3 × 5/3

5 × 5 × 5 = 125

3 × 3 × 3 = 27

[tex]\frac{125}{27}[/tex]

[tex]4\frac{17}{27}[/tex]

Step-by-step explanation:

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

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

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:

<CAB  

Step-by-step explanation:

Since CAD is equal to DAB

AD bisects CAB