SAT/ACT Mitsu travels a certain distance at 30 miles per hour and returns the same route at 65 miles per hour. What is his average speed in miles per hour for the round trip?
A 32.5
B 35.0
C 41.0
D 47.5
E 55.3

The maximum​ displacement, the​ frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.

A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

Therefore, the instantaneous speed is different from velocity, which is the rate at which the distance traveled along a particular path changes over time. The temporal rate of change of the position vector can also be used to describe velocity.

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The formula for estimating the nth term of an arithmetic sequence is:

a n = a₁ + (n-1)d

The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7

A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.

A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.

The formula for estimating the nth term of an arithmetic sequence exists:

a n = a₁ + (n-1)d

The four quantities in the formula exist a n, a₁, n, d.

The first 5 terms are a n = -2n + 3

a₁ = -2 + 3 = 1

a2 = -4 + 3 = -1

a3 = -6 + 3 = -3

a4 = -8 + 3 = -5

a5 = -10+3 = -7

Therefore, the first 5 terms of the sequence  be 1, -1, -3, -5, -7.

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Answer:

Lucia is 12 years old now

Answer: 7+8y

Step-by-step explanation:

for the first one x = 12

second one is 2

Answer:

x = 12

x = 2

Step-by-step explanation:

Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.

Answer:

Step-by-step explanation:

W-8=6x

W-6x=8

 The rationalized expression in general term is given by: (-8 -4√2) / 3

  Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

  As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

(8√2 / 6-3√8 ) Multiply by  ( 6+3√8)/( 6+3√8)

(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)

8√2(6+3√8) / (6-3√8)²  Expand the denominator using the FOIL method.

8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)

8√2(6+3√8) / -36

48√2 + 24√2√8 / -36  ::::.   √8 = 2√2

48√2 + 96 / -36

-12(4√2 + 8) / 12x3

(-8 -4√2) / 3 is the result.

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The equation of the line in standard form of 2y = -4x - 12 is 4x + 2y = -12.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.

Given the equation 2y = -4x - 12, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

2y = -4x - 12

4x + 2y = -12

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Answer:

B(5, -1)

Step-by-step explanation:

"When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative." - https://calcworkshop.com/

B(-1, -5), -1 = x, -5=y

B(y, x) = B(-5, -1)

B(-y, x) = B(5, -1)

B(5, -1)

Answer:

35, the population size is 2.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months}\dotfill &10 \end{cases} \\\\\\ A=50\left(1+\frac{0.03}{1}\right)^{1\cdot 10} \implies A=50(1.03)^{10}\implies A \approx \text{\LARGE 67.20}[/tex]

well, let's check how long till you'd have $100 first

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months} \end{cases}[/tex]

[tex]100=50\left(1+\frac{0.03}{1}\right)^{1\cdot t} \implies 100=50(1.03)^t\implies \cfrac{100}{50}=1.03^t \\\\\\ 2=1.03^t\implies \log(2)=\log(1.03^t)\implies \log(2)=t\log(1.03) \\\\\\ \stackrel{\textit{about 23 months and 13 days}}{\cfrac{\log(2)}{\log(1.03)}=t\implies \text{\LARGE 23.45}\approx t}[/tex]

Answer:

0.744-0.741-0.7412-0.7041-0.70411

Step-by-step explanation:

Answer:

Step-by-step explanation:

Decending order- From greatest to least

To order them start with the dight with the highest number in the place that isn't equal. In this case it the 4 in the hundredths place so are top 3 numbers are 0.741, 0.7412, and 0.744. As this point you continue to look at the greatest number when the dights aren't equal so the top three would be ordered 0.744,0.7412

0.744,0.7412, and 0.741. As for the bottom 2 numbers you do the same thing with the top three numbers so the rest of the list is 0.70411 and 0.7041

The equation written in standard form is expressed as 3x - y = -11

The standard form of a linear equation is expressed as Ax + By = C

Given the equation below;

y - 8 = 3(x+1)

Expand

y- 8 = 3x + 3

Collect the like terms

y-3x = 3 + 8

y - 3x = 11

-3x + y = 11

3x - y = -11

Hence the equation written in standard form is expressed as 3x - y = -11

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Answer:

ok

Step-by-step explanation:

-2x+9=2

dive answer is 3

Answer:

x = 6 and y = 10

Step-by-step explanation:

Substract (-5x+3y=0) from (7x-4y=2)

[tex] \sf \: - 5x + 3y = 0 \\ \sf \: \: \: \: 7x - 4y = 2 \\ = = = = = = = = \\ \sf2x - 1y = 2 \\ = = = = = = = = =[/tex]

Let's solve your system by elimination.

7x−4y=2;2x−1y=2

Multiply the second equation by -4, then add the equations together.

(7x−4y=2)

−4(2x−1y=2)

Becomes:

7x−4y=2

−8x+4y=−8

Add these equations to eliminate y:

−x=−6

Then solve−x=−6for x:

−x=−6

−x/−1 = −6/−1

(Divide both sides by -1)

x=6

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

7x−4y=2

Substitute6forxin7x−4y=2:

(7)(6)−4y=2

−4y+42=2(Simplify both sides of the equation)

−4y+42+−42=2+−42(Add -42 to both sides)

−4y=−40

−4y/−4 = −40/−4

(Divide both sides by -4)

y=10

Answer:

Associative.

Step-by-step explanation:

The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.

e.g

[tex](a - b) \times c = c \times (b-a)[/tex]

Answer:

It will take 22 hours

Step-by-step explanation:

10925 ÷ 500 = 21.9 = 22 hours

Answer:

3/7.

Step-by-step explanation:

1/3 / 7/9

Invert the 7/9 and multipliply:

= 1/3 * 9/7

= 9 / 21

= 3/7

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

Answer: y = -22

Step-by-step explanation:

a variable can't be negative, and there is always a 1 by a variable, so divide each side by -1

Answer:

-22

Step-by-step explanation:

-y=22

-y/-1 = 22/-1

y= -22

The equation of the line in point-slope form, with slope equal to -1 and passing through the point located at (-3 , 5), is (y - 5) = -1(x + 3).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = -1 and (x1 , y1) = (-3 , 5)

(y - 5) = -1(x - -3)

(y - 5) = -1(x + 3)

In slope-intercept form, the equation of the line is:

(y - 5) = -1(x + 3)

y - 5 = -x -3

y = -x + 2

In standard form, the equation of the line is:

y = -x + 2

x + y = 2

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Answer: Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.

Step-by-step explanation:

Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.

The following volume quantities are listed below:

a) 2 pints, 1 qt

b) 12 pints, 6 qt

c) 5 pints, 2.5 c

d) 6.75 pints, 3.375 fl oz

In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.

Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:

Now we proceed to convert each quantity to pints and quarts by cross multiplication:

a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt

b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt

c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c

d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz

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It is not a function. which is the correct answer would be option (B)

Given that,

A function is shown in the figure with its domain and range.

To determine the inverse function.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

Since the two preimages of the value 5 are present in the domain

So that is why the inverse function of a given function is not possible.

Therefore, It is not a function.

Hence, the correct answer would be option (B)

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The equation of line is:

y = (5/2) x - 11

Given,

Points (x₁, y₁) = (2, 4) and (x₂, y₂) = (-4, -11)

We can find the slope using the equation for slope

m = (y₂ - y₁) / (x₂ - x₁)

   = (-11 -4) / (-4 -2)

   = -15 / - 6

    = 5/2

We know the slope and a point, so we can use point slope form to make an equation

y-y₁ = m(x-x₁)

y - (-4) = 5/2 (x-2)

Distribute

y+4 = 5/2x – 5/2 x 2

y+4 = 5/2x - 5

Add -4 to each side

y +4 -4 = 5/2x – 5 - 4

y = 5/2x - 11

This is in slope intercept form (y= mx-b)

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The probability that the chosen marble will be red is, 0.27.

Probability:

Probability is calculated by using the formula,

P(A) = n(A)/n(S)

Where,

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes.

n(S) is the total number of events in the sample space.

Given,

A box contains 7 blue marbles, 6 red marbles, 2 white marbles, and 3 black marbles.

Here we need to find  If one marble is chosen at random, then what is the probability that it will be red.

According to the formula,

number of favorable outcomes = 6

total number of events in the sample space = 7 + 6 + 2 + 3 = 22.

Then the probability of getting red marbles is,

=> P(A) = 6/22.

It can be simplified as,

=> P(A) = 3/11

=> P(A) = 0.27

Therefore, the probability of getting red marble is 0.27.

Here in the options, the option 0.27 is not present.

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The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.

The circumcenter, centroid, and orthocenter are all collinear.

The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1

i.e, CSOC = 21.

Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.

The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.

Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.

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