Y=1/3mx^3 – (m–1)x^2 + 3(m–2)x +1/3

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:

[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:

-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.

Answer:

D. Ana is 3 years older than Mark.

Step-by-step explanation:

We do not know how old Mark is.  That is the variable

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:

I'm sorry I'm not good at math

Step-by-step explanation:

sorry

Step-by-step explanation:

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

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

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:

A: Rewrite the expression on the left using the distributive property.

4/6

Mr. williams wants to buy 4/6

Answer:

there is some missing information  here

if the pas is a dozen brownies

1/2 of a pan is 6 2/3 of 6 would be "4"

how much mac-n-cheese are being made?

that information would be needed to solve this

Step-by-step explanation:

Answer:

[tex][-2.5,-2][/tex]

[tex][-2,-1.5][/tex]

[tex][1.5,2][/tex]

[tex][2,2.5][/tex]

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

Hope it helps...

Answer:

B, D, E

Step-by-step explanation:

The values in the answer choices are x-values, meaning on the x-axis.

B: [-2, -1.5]

From -2 to -1.5, the graph goes down from left to right, so it's decreasing.

D: [1.5, 2]

From 1.5 to 2, the graph goes down from left to right, so it's decreasing.

E: [2, 2.5]

From 2 to 2.5, the graph does down from left to right, so it's decreasing.

Hope that helps (●'◡'●)

[tex]\sf \: If \: the \: question \: is \: to \: convert \: - 0.6 \\ \sf \: to \: its\: equivalent \: fractional \: form \: then ⟹[/tex]

[tex]\sf \: - 0.6 \\ \sf= \frac{ - 6}{10} (direct \: fractional \: form) \\ \sf = \frac{ - 3}{5} (in \: simplified \: form)[/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

[tex]sp = 328 \\ p = 29 \\ cp = .... \\ \\ p = sp - cp \\ 29 = 328 - cp \\ cp = 328 + 29 \\ cp = 357[/tex]

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:

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:

1

Step-by-step explanation:

no exponent

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]

The true statements are A , B , E

It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here, In the synthetic calculation we use the coefficient of the dividend

with the factors of the function

∴ 2 , -2 , -12 are the coefficient of the dividend 2x² - 2x - 12

∵ The divisor is 3

∴ x = 3 is a root of F(x) = 2x² - 2x - 12

∵ x = 3 is the root of F(x) = 2x² - 2x - 12

- Subtract the two sides by 3

∴ x - 3 = 0

∴ (x - 3) is a factor of the dividend F(x) = 2x² - 2x - 12

- The quotient is the last line of the synthetic division

∴ The coefficients of quotient are 2 , 4

- The quotient is 1 degree less than the dividend

∵ The degree of the dividend is 2

∴ The degree of the quotient is 1

∴ The quotient is 2x + 4

* Lets check the answers to chose the write statements

A. The number 3 is a root of F(x) = 2x² - 2x - 12 ⇒ true

B. (x - 3) is a factor of 2x² - 2x - 12 ⇒ true

E. (2x² - 2x - 12) ÷ (x - 3) = 2x + 4 ⇒ true

Thus, the true statements are A , B , E.

Learn more about Division from:

https://brainly.com/question/21416852

#SPJ1

Answer:

Step-by-step explanation:

adjacent angles have a common vertex and a common ray

∠BEC and ∠AEB (common vertex E common ray EB)

Answer:

41/10

Explanation:

sqrt16 = 4

sqrt17 = 4.12

4.1 = 41/10 and 4<4.1<4.12

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]

Step-by-step explanation:

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

Answer:

The answer is "[tex]1\frac{1}{2}[/tex]"

Step-by-step explanation:

Please find the graph file of the question in the attachment.

Its first step is the lightest and heaviest evil. [tex]4 \frac{1}{4}[/tex] is the lightest bag, and [tex]5 \frac34[/tex] is the heaviest bag. To remove it now, it is not permissible to remove it as a mixed fraction, therefore convert each fraction into an improper fraction by multiplying the whole integer to the numerator, then adding a numerator to this amount, multiplied by the numerator. Follow those steps to find out [tex]4 \frac{1}{4}[/tex]  is the wrong part.

[tex](4\times 4+1=17) \ so\ 4\frac14=\frac{17}{4}.[/tex] The process is the same for [tex]5 \frac34 (5\times 4+3=23) \ so \ 5 \frac34= \frac{23}{4}.[/tex]

You now deduce the numerator but just not the negative, to deduct both. You subtract, as the question is raised far as[tex]\frac{23}{4}-\frac{17}{4} =\frac{6}{4}[/tex] is involved. The last stage is that this is transformed into blended families, dividing its count by the denominator, 6 divided by 4 is identical to 1.5. 1 is a full amount so you don't modify it, but you do need to change the 5 decimals to [tex]1.5=1 \frac{5}{10}[/tex] and the last step is [tex]1\frac{1}{2}[/tex]to reduce.

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:

4y2 - 12y

Step-by-step explanation:

2+4y-16y+32(Combine like-terms)

2−12y+32(Combine like-terms)

Answer:

The answer is [tex]4y^{2} -12y[/tex]

Step-by-step explanation:

To simplify the polynomial, start by combining like terms. Add [tex]y^{2}[/tex] and [tex]3y^{2}[/tex] to get [tex]4y^{2}[/tex]. Then, subtract [tex]16y[/tex] from [tex]4y[/tex] to get [tex]-12y[/tex]. Finally, the simplified answer is [tex]4y^{2} -12y[/tex].

Answer:

x = 60

Step-by-step explanation:

The single dashed line represents congruent side lengths.

If every side of a triangle has a single dashed line then all of the sides are congruent meaning that the triangle is an equilateral

Equilateral triangles have all congruent side lengths and angles

In an equilateral triangle each angle has a measure of 60 degrees

So x = 60

Answer:

Step-by-step explanation:

A parallelogram is divided into two triangles, both triangles having equal sides.

So triangles are equilateral..In equilateral triangles, the angles are also equal..the interior angles of a triangle are 180 degrees..

180 ÷ 3 = 60 degree---> x:60°