The point p on the graph means that the car can travel ___ miles(s) per ____ gallon(s) of gasoline.



1 3 10. 30

The distance between the lines L1 and L2 given by √293/7.

The distance is the angular separation between any two points on one line. Eventually, the smallest distance between these lines is zero. The distance between the lines is the same length as the perpendicular between them.

Finding two locations P1 and P2 on L1 and L2 separately will help us determine the shortest path between them. We then need to project P1P2 in the direction n that is perpendicular to both L1 and L2 to arrive at the answer. To put it another way, L1 - L2 distance = COMPN (P1P2).

Let the two points be

[tex]$$\begin{aligned}& \vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \\& \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})\end{aligned}$$[/tex]

These two lines pass through the points having position vectors [tex]$\overrightarrow{a_1}=\hat{i}+2 \hat{j}-4 \hat{k}$[/tex]and [tex]$\overrightarrow{a_2}=3 \hat{i}+3 \hat{j}-5 \hat{k}$[/tex] are parallel to the vector [tex]$\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$[/tex]

Now, [tex]$\overrightarrow{a_2}-\overrightarrow{a_1}=3 \hat{i}+3 \hat{j}-5 \hat{k}-\hat{i}-2 \hat{j}+4 \hat{k}=2 \hat{i}+\hat{j}-\hat{k}$[/tex] and [tex]$\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}=(2 \hat{i}+\hat{j}-\hat{k}) \times(2 \hat{i}+3 \hat{j}+6 \hat{k})$[/tex]

[tex]$$\begin{aligned}& =\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\2 & 1 & -1 \\2 & 3 & 6\end{array}\right| \\& =\hat{i}(6+3)-\hat{j}(12+2)+\hat{k}(6-2) \\& =9 \hat{i}-14 \hat{j}+4 \hat{k}\end{aligned}$$[/tex]

[tex]$$\left|\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}\right|=\sqrt{9^2+(-14)^2+4^2}=\sqrt{81+196+16}=\sqrt{293}$$\pi[/tex]

and [tex]$|\vec{b}|=\sqrt{2^2+3^2+6^2}=\sqrt{4+9+36}=7$[/tex]

The shortest distance between the two lines exists given by [tex]$\frac{\left|\left(\overrightarrow{\mathrm{a}_2}-\overrightarrow{\mathrm{a}_1}\right) \times \overrightarrow{\mathrm{b}}\right|}{|\overrightarrow{\mathrm{b}}|}=\frac{\sqrt{293}}{7}$[/tex]

Therefore, the distance between the lines L1 and L2 given by √293/7.

The complete question is;

Find the distance between the lines L1 and L2 given by

[tex]$$\vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \text { and } \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})$$[/tex]

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Answer: 1

Step-by-step explanation: Find the total number of colors in the trays. There are 5 colors in each tray. Then Find the number of colors in the purple tray. There is only one color in the purple tray, so the number is 1.

The front door is twice as long as the bedroom door.

A bedroom door in the house has the same dimensions and length and all at the front door. The length is 30 in rather than 63. If the bedroom door has a length of 30 inches, and the front door has the same dimensions but is longer, we can compare the two lengths using a proportion.

We can write the proportion as 30 inches / x inches = 1/2, where x is the length of the front door. To find the length of the front door, we can cross-multiply and solve for x: x = 30 inches * 2 = 60 inches. So the front door is 60 inches long, which is twice as long as the bedroom door.

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The line segment which is divided into the ratio 2 : 3 represents that line is divided into 5 equal parts.

As given in the question,

Let the given line segment be represents as AB .

And point C be the points which divide AB in the ratio 2 : 3.

The given ratio represents from AC is divided into 2 equal parts.

And BC is divided into 3 equal parts.

Total number of parts AB is divided into the ratio 2 : 3 is equal to

= 2 + 3

= 5 equal parts

Therefore, the line segment divided into the ratio 2 : 3 represents 5 equal parts.

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Option 1 is Correct. For the line connecting the two locations, an equation in slope-intercept form is. y = x + 3

A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively. The linear relationship between two variables is defined by the slope and intercept, which can be used to calculate the average rate of change.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

y=mx+c

y= (6+3)/(4+2)

y= 9/6

y= 3/2

equation = y+6 =3/2(x-2)

2y+12=3x-6

y=x-3

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Correct Question:

Write an equation in slope-intercept form for the line passing through the pair of points. (2, –6), (–4, 3) Question 1 options:

1. y = x + 3

2. y = x – 3

3. y = x – 3

4. y = x + 3

The four main steps of division are dividend, divisor, quotient and remainder.

Dividend: The number that is being divided.

Divisor: The number by which the dividend is being divided.

Quotient: The result of the division, which is the number of times the divisor can "fit into" the dividend.

Remainder: The amount left over after the division is complete. It is the part of the dividend that is not "fit" into the divisor.

For example, when dividing 16 by 3, the dividend is 16, the divisor is 3, the quotient is 5, and the remainder is 1.

It can be written as:

16 ÷ 3 = 5 with a remainder of 1.

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Answer:

(a)  5/12

Step-by-step explanation:

to solve this problem you can make all fractions equivalent with 12 as the denominator

a) 5/12

b) 2/3 = 8/12      Multiply top and bottom by 4

c) 5/6 = 10/12     Multiply top and bottom by 2

d) 3/4 = 9/12       Multiply top and bottom by 3

if you compare numerators, the smallest one is the closest to zero, which would be (a) 5/12

Answer:

A 5/12

Step-by-step explanation:

first you need to round these all to /12 so a is 5/12

12/3 is 4 so multiply 4 by two which means b is 8/12

12/6 is 2 so multiply 5 by two which gives us c = 10/12

12/4 is 3 and multiply 3 x 3 which is 9 so d is 9/12

5 is the lowest decimal/fraction which makes it the closest to 0

The rank of object according to acceleration from greatest to least is:

C = B > A

In the given question, we have to rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.

The acceleration is given by:

a = [tex]\frac{dv}{dt}[/tex]

where, dv represents change in velocity and dt represents change in time.

Also, Acceleration = slope of velocity - time graph

For object A acceleration is 0 because velocity is constant.

Now for object B:

[tex]a_{B}=\frac{5-0}{10-0}[/tex]

[tex]a_{B}=\frac{5}{10}[/tex]

[tex]a_{B}=\frac{1}{2}[/tex]

[tex]a_{B}[/tex] = 0.5 m/s square

Now for the object C:

[tex]a_{C}=\frac{-5-0}{10-0}[/tex]

[tex]a_{C}=-\frac{5}{10}[/tex]

[tex]a_{C}=-\frac{1}{2}[/tex]

[tex]a_{C}[/tex] = -0.5 m/s square

As we know that magnitude cannot be negative, so

[tex]a_{C}[/tex] = 0.5 m/s square

As we can see that acceleration of object B and C is same although the acceleration of object A is 0 which is smaller than the acceleration of B and C.

So the rank of object according to acceleration from greatest to least is:

C = B > A

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The complete question is:

The figure below shows velocity versus time graphs for objects. Rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.

The total amount of money molly will pay for the skirt after the total discount is $14.5

Original price of the skirt = $29

Percentage discount = 30%

Additional percentage discount = 20%

Total percentage discount = 30% + 20%

= 50%

Total amount molly paid for the skirt not counting the sales tax = $29 - (50% of $29)

= 29 - (0.50 × 29)

= 29 - 14.5

= $14.5

Hence, Molly will pay a total of $14.5 after deducting the discount.

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Answer:

the equivalent ratio to 240 is 10.

When the blue ribbon measures 10 inches, the red ribbon measures 3 inches, when the blue ribbon measures 27 inches, the red ribbon measures 20 inches, and when the blue ribbon measures 'x' inches, the red ribbon measures (x - 7) inches.

According to craft project instructions, a piece of red ribbon should be 7 inches longer than a piece of blue ribbon.

To find the length of the red ribbon given the length of the blue ribbon, we can subtract 7 inches from the length of the blue ribbon.

a) The length of the blue ribbon is 10 inches.

Red ribbon length = 10 - 7 = 3 inches

b) The length of the blue ribbon is 27 inches.

Red ribbon length = 27 - 7 = 20 inches

c) The length of the blue ribbon is x inches.

Red ribbon length = (x - 7) inches

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The question seems to be incomplete the correct question would be:

Instructions for a craft project say that the length of a piece of red ribbon should be 7 inches than the length of a piece of blue ribbon. How long is the red ribbon the length of the blue ribbon is: 10 inches. 27 inches? x inches?

Let f: A→B be a function. The inverse of f, denoted by [tex]f^{-1}[/tex], is the set of ordered pairs {(b, a) ∈ B×A | f(a)=b}. That is, f−1 = {(b,a) ∈ B×A | f(a) = b}.

The inverse of a one-to-one function f: A → B, is the function g: B → A, having the following property

f(x) = y ⇔ g(y) = x

The function f is named invertible if its inverse function g exists.

When is a function from set S to set T then the inverse of f will be a function g from T to S such that each of f and g unties the other: for every s ∈ S we have g(f(s)) = s and for every t ∈ T we have f(g(t)) = t. A function f may or may not carry an inverse. When it does we can represent it as [tex]f^{-1}[/tex].

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After calculating the average of his last 4 years’ salaries and will give him 1. 9% of that average for each year he worked, the total pension is $2928.204.

In the given question, we have to calculate Henry pension.

Henry has worked for a factor for 31 years and will be retiring.

He earned salaries over the past 4 years of $38433, $37776, $39125, and $38782.

His employer calculates pension by finding the average of his last 4 years’ salaries and will give him 1.9% of that average for each year he worked.

His earning over the past 4 years = $38433, $37776, $39125, $38782

The average of Henry earning = Sum of his earning over 4 years / number of years

The average of Henry earning = ($38433 + $37776 + $39125 + $38782)/4

The average of Henry earning = $154,116/4

The average of Henry earning = $38,529

Hence, the average of Henry last 4 years’ salaries is $38,529.

The pension is 1.9% of the average salary. So,

Pension = $38,529×1.9%

Pension = $38,529×0.019

Pension = $732.051

He worked for total 4 years. So,

Total pension = $732.051×4

Total pension = $2928.204

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This is a linear system since it is a linear combination of the inputs x[n] and x[n-1].

A: y[n] = x[n] x x[n-1]

This is a linear system since it is a linear combination of the inputs x[n] and x[n-1]. We can represent this equation as:

y[n] = a * x[n] + b * x[n-1]

where a and b are constants.

For example, if x[n] = 2 and x[n-1] = 3 then y[n] = 2 x 3 = 6.

C: y[n] = x2[n]

This is also a linear system since it is a linear combination of the input x[n] and its squared value x2[n]. We can represent this equation as:

y[n] = c * x[n] + d * x2[n]

where c and d are constants.

For example, if x[n] = 2 then y[n] = c * 2 + d * 2² = c * 2 + d * 4.

Therefore, the correct answer is D: (a) and (c).

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your answer is in given picture just go through them

The work done in lifting a forty-pound crate three feet is forty-three foot-pounds

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Answer:

y = 154°

Step-by-step explanation:

Because angle z is a straight angle it is 180°.

26° + y = 180°

subtract 26.

y = 154°

Answer:

0.38

Step-by-step explanation:

Percentage is number/100 = 38/100 = 0.38

Cheers

The answer of 5 less than 10 is 5.

The answer of 5 less than 10 is 5 which can be derived using simple mathematical calculations.

To find 5 less than 10, you can subtract 5 from the original number 10.

10 - 5 = 5

It's a simple arithmetic operation where you subtract a specific number, in this case, 5, from the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 5 less than 10 is 5.

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Answer:

Yes, the ordered pair (-4, -22) satisfy

Step-by-step explanation:

y=5x-2

To see if it satisfies or not, we need to put the x and y in

-22 = 5(-4) - 2

-22 = -20 -2

-22 = -22

So, the ordered pair (-4, -22) satisfy

For r [tex]$\mathrm{k}=0$[/tex]or[tex]$\mathrm{k}=3$,[/tex] the given equation will be a perfect square.

[tex]$$(4-k) x^2+(2 k+4) x+8 k+1=0$$[/tex]

Here, [tex]$a=4+k, \quad b=2 k+4, \quad c=8 k+1$[/tex]

The given equation will be a perfect square, i.e., real and equal roots if

[tex]& \mathrm{D}=0 \\[/tex]

[tex]& \mathrm{~b}^2-4 \mathrm{ac}=0 \\[/tex]

[tex]& (2 \mathrm{k}+4)^2-4(4-\mathrm{k})(8 \mathrm{k}+1)=0 \\[/tex]

Then,

[tex]& 4 \mathrm{k}^2+16+16 \mathrm{k}-4\left(32 \mathrm{k}-8 \mathrm{k}^2+4-\mathrm{k}\right)=0 \\[/tex]

Simplifying,

[tex]& \mathrm{k}^2+4+4 \mathrm{k}-32 \mathrm{k}+8 \mathrm{k}^2-4+\mathrm{k}=0 \\[/tex]

[tex]& 9 \mathrm{k}^2-27 \mathrm{k}=0 \\[/tex]

[tex]& \mathrm{k}^2-3 \mathrm{k}=0 \\[/tex]

So,

[tex]& \mathrm{k}(\mathrm{k}-3)=0 \\[/tex]

Get,

[tex]& \mathrm{k}=0[/tex] or [tex]\mathrm{k}=3[/tex]

Hence for [tex]$\mathrm{k}=0$[/tex]or[tex]$\mathrm{k}=3$,[/tex] the given equation will be a perfect square.

The complete question is,

For what value of [tex]$\mathrm{k},(4-\mathrm{k}) \mathrm{x}^2+(2 \mathrm{k}+4) \mathrm{x}+(8 \mathrm{k}+1)=0$[/tex] is a perfect square:

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For  k=0 or k=3, the given equation will be a perfect square.

4−k)x 2 +(2k+4)x+8k+1=0

Here, a=4+k,b=2k+4,c=8k+1

The given equation will be a perfect square, i.e., real and equal roots if

D=0

b2 −4ac=0

(2k+4) 2 −4(4−k)(8k+1)=0

4k 2 +16+16k−4(32k−8k 2+4−k)=0

k 2+4+4k−32k+8k 2−4+k=0

9k 2−27k=0

k 2−3k=0

k(k−3)=0

k=0 or k=3

Hence for k=0 or k=3, the given equation will be a perfect square.

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Answer:182 is correct

Step-by-step explanation:

Answer: $16

Hope this helps :)

Step-by-step explanation:

Find the unit rate and multiply by 50

1 Dozen=12 Eggs

1 Dozen= $3.84

3.84/12= .32 per egg

.32*50= 16

Answer:

[tex]3x^2+4x+8[/tex]

Step-by-step explanation:

To find the value of [tex]7x^2+6x+9-4x^2-2x-1[/tex]

We need to combine like terms by grouping

[tex]7x^2-4x^2+6x-2x+9-1[/tex]

= [tex]3x^2+4x+8[/tex]

Hope this helps :)

Have a great day!

Two segments are of equal length indicates its measurable quantity where as when two segments are congruent they are equal in length and shape.

As given in the question,

Difference between two segments are of equal length and the two segments are congruent is given by :

Therefore, the main difference in the segment of equal length and congruent segment is overlapping and only measurable quantity.

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The solution to the system of equations is x = −2, y = ±√23.

Equation is a math statement that expresses two expressions with an equal sign. It is used to find the value of an unknown variable or unknowns. Equations are used in many branches of mathematics and science. For example, equations are used to calculate the force of gravity, the speed of light, the temperature of a gas, and the area of a triangle. Equations are also used to solve problems in physics, chemistry, engineering, and other disciplines. Equations are written in symbols and often involve multiple equations.

This system can be solved by solving the two equations separately.

For the first equation, xe^y+2e^y= 0, we can rearrange it to get xe^y = −2e^y. We can then divide both sides by e^y to get x = −2.

For the second equation, x² − 3x + y² = 19, we can plug in the value of x that we found previously, x = −2, and rearrange the equation to get y² = 23, and then solve for y by taking the square root of both sides, giving y = ±√23.

Therefore, the solution to the system of equations is x = −2, y = ±√23.

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The percentage of the marks scored by Kendall after combining both of her test scores is found out to be as 85.5% .

Her original score = 73 and her score in the second test = 98

Considering that the test is of 100 marks, the percentage can be calculated as follows.

percentage =  previous marks + current marks / 2

= 73 + 98 / 2

= 171/2

= 85.5

Therefore, Kendall's average score in both the test is found out to be 85.5% .

The percentage is calculated or is known as the average of a given set of numbers. To find the average we divide the sum of the given numbers by n , where n is the total numbers.

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To translate a function left or right, you need to shift the graph of the function horizontally. To move the graph to the left, you subtract the same amount from each x-coordinate. To move the graph to the right, you add the same amount to each x-coordinate.

To translate a function left or right, you need to shift the graph of the function horizontally. If you want to move the graph to the left, you need to subtract the same amount from each x-coordinate. This means that all the points on the graph will be shifted to the left by the same amount. For example, if the graph of the function is f(x) = x² and you want to move it left by two units, you need to subtract two from each x-coordinate so the new graph would be f(x) = (x-2)². Similarly, if you want to move the graph right, you need to add the same amount to each x-coordinate. For example, if the graph of the function is f(x) = x² and you want to move it right by three units, you need to add three to each x-coordinate so the new graph would be f(x) = (x+3)².

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The linear equation with a fraction in it can be solved by using y-intercept form method.

What are linear equations?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Now,

y-intercept form-

Make sure the linear equation is in the form y = mx + b. This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. The values in the equation do not need to be whole numbers. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b.[1]

m is called the "slope," or sometimes "gradient."[2] Slope is defined as rise over run, or the change in y over the change in x.

b is defined as the "y-intercept." The y-intercept is the point at which the line crosses the Y-axis.[3]

x and y are both variables. You can solve for a specific value of x, for example, if you have a y point and know the m and b values. x, however, is never merely one value: its value changes as you go up or down the line.

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