Which values of a, b , and c correctly represent the answer in the simplest form?

Answer:[tex]30 i -473 j -3 k[/tex]

Step-by-step explanation:

We are given two velocity vectors with its three components in unit notation:

Airplane's velocity:

[tex]\vec{p}=30i-492j+42k[/tex]

Crosswind velocity:

[tex]\vec{t}=0i+19j-45k[/tex]

Now, if we want to know the velocity of the airplane when it is affected by the wind, we have to add these two velocity vectors:

[tex]\vec{p} + \vec{t}=(30i-492j+42k) + (0i+19j-45k)[/tex]

Adding both vectors:

[tex]\vec{p} + \vec{t}=30i-473j-3k[/tex]

Answer:

D edge

Step-by-step explanation:

Step-by-step explanation:

Wooden Cars = 2 × Wooden Trains

Ratio is

2 : 1

In total there are 3 parts

228 ÷ 3 = 76 (1 part)

Wooden Cars = 2 × 76 = 152

Wooden Trains = 1 × 76 = 76

To find the number of wooden trains made, we can set up an equation and solve for 'x'.

To solve this problem, let's represent the number of wooden trains as 'x'.

According to the given information, there are twice as many wooden cars as wooden trains. So, the number of wooden cars can be represented as '2x'.

We are also given that the total number of wooden vehicles made is 228.

Therefore, the equation that represents the given information is: x + 2x = 228

Simplifying the equation, we get: 3x = 228

Dividing both sides by 3, we find that x = 228/3 = 76

So, they made 76 wooden trains.

Answer:

None of these

Step-by-step explanation:

A perpendicular bisector is a segment which intersects a given segment at a 90° angle, and passes through the given segment's midpoint. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a perpendicular bisector.

A median of the triangle is a segment joining a vertex to the midpoint of the opposite side. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a median.

An altitude of the triangle is a segment passing through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). The diagram doesn't show the right angle at point T (VT is not perpendicular to SU), then VT is not an altitude.

Thus, option None of These is true.

Answer:

719

Step-by-step explanation:

ones place is 8 and we add 1 if the right hand number is 5 or greater than 5.

Answer:

The answer is 719

Step-by-step explanation:718.521 when rounded up to the nearest one be comes 719 because .5 is converted to 9. Thanks

Answer:

The amount of electricity bill is $52.60.

Step-by-step explanation:

Given:

Victoria whit used 578 kwh of electricity.

The rate is 9.1 cents per kw-hr.

Now, to find the amount of her electric bill.

Electricity used = 578 kwh.

Rate of electricity = 9.1 cents per kw-hr.

So, to get the amount we multiply the electricity used by the rate of electricity:

[tex]Amount\ of\ electric\ bill=Electricity\ used\times rate\ of\ electricity[/tex]

[tex]Amount\ of\ electric\ bill=578\ kwh\times 9.1\ cents[/tex]

[tex]Amount\ of\ electric\ bill=5259.8\ cents.[/tex]

Thus, the amount of electricity bill = 5259.8 cents.

Now, converting the amount from cents to $ by dividing:

$1 = 100 cents.

So, 5259.8 cents ÷ 100 = $52.60 .

therefore, the amount of electricity bill is $52.60.

Answer:

Answer:

5/12x

Step-by-step explanation:

Answer:

y = 5/12x - 2

Step-by-step explanation:

5x - 12y = 24

We get -12y = -5x + 24

Divide all of the equation by -12

You get y = 5/12x -2

Answer:13/24

Step-by-step explanation:

Answer:

13/24

Step-by-step explanation:

3/8+1/6=9/24+4/24=13/24

Answer:

y-2=2(x-9)

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-2=2(x-9)

Answer:

4875

Step-by-step explanation:

100%-84%=16%

16%x=780

x=4875

Answer:

hi there!

the equation for this dot plot will be: y=15x

Step-by-step explanation:

if you look at the dots on the graph (2, 30) and (4,60) they both satisfy the equation

Answer:

B. (-4,5)

Step-by-step explanation:

a function cannot have any repeating x values....it can have repeating y values, just not the x values

so..going by ur answer choices, u can remove (-4,5) and it would be a function. The reason is because u have two sets of points with the same x value...so it is not a function unless u take out either (-4,5) or (-4,3)...because they both have the same x value.

To find the missing number so that the equation has infinitely many solutions, subtract -2x from both sides to eliminate x and find that the missing number can be any real number.

To find the missing number so that the equation has infinitely many solutions, we need to look at the given equation: -2x - 10 = -2x + c. Since the variable x is present on both sides, we can subtract -2x from both sides to get rid of it. This leaves us with -10 = c. In order for this equation to have infinitely many solutions, the missing number c can be any real number.

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Answer:

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Step-by-step explanation:

The complete question is

The angle θ1 is located in Quadrant 1, and cos (θ1)=10/17.

What is the value of sin(θ1)?

we know that

[tex]sin^2(\theta_1)+cos^2(\theta_1)=1[/tex] ---> trigonometric identity

we have

[tex]cos(\theta_1)=\frac{10}{17}[/tex]

The angle [tex]\theta_1[/tex] is located in Quadrant I, that means the sine of angle [tex]\theta_1[/tex] is positive

substitute the given value in the trigonometric identity

[tex]sin^2(\theta_1)+(\frac{10}{17})^2=1[/tex]

[tex]sin^2(\theta_1)+\frac{100}{289}=1[/tex]

[tex]sin^2(\theta_1)=1-\frac{100}{289}[/tex]

[tex]sin^2(\theta_1)=\frac{189}{289}[/tex]

take square root both sides

[tex]sin(\theta_1)=\pm\frac{\sqrt{189}}{17}[/tex]

Remember that the sine is positive (Quadrant I)

so

[tex]sin(\theta_1)=\frac{\sqrt{189}}{17}[/tex]

Simplify

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Answer:

x ÷ 15

Step-by-step explanation:

quotient is division

Option A is correct, A shows a mapping diagram which represents a function from x → y

A relation is a function if it has only One y-value for each x-value.

A mapping diagram that represents a function from x to y is a diagram that shows a set of ordered pairs (x, y), such that each x-value has exactly one corresponding y-value

For option A, the ordered pairs are (4, 5)(5,5),(6,1),(8,2).

For each value of x there is only one value of y or else the values of x are not repeated so the diagram represents a function.

In other option the x has 2 values of y.

Hence, option A is correct, A shows a mapping diagram which represents a function from x → y

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A mapping diagram that represents a function from x → y include the following: A. mapping diagram A.

In Mathematics, a function is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).

Based on the mapping diagram shown above, we can reasonably infer and logically deduce that the inputs (4, 5), (5, 5), (6, 1), and (8, 2) are ordered pairs that represents a function because they indicate unique mappings of each input value to an output value.

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Answer:

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation: To obtain number 28, we will find the factors of this number.

Factors of this number are: 1, 2, 4, 7, 14, 28

From the given factors, we can find the combinations which will givs us the product as 28

We are asked to find the multiplication ( times) of two number that will yield a number 28. So, the combinations will be

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation:

Final answer:

To find numbers that multiply to 3.75, we can identify factor pairs like 1.5 and 2.5, or 1 and 3.75. Multiplying these pairs will result in 3.75.

Explanation:

To find which numbers multiplied together equal 3.75, we can look for factor pairs of the number 3.75. A factor pair is a set of two numbers that, when multiplied together, result in the given number. Since 3.75 can also be expressed as the fraction ⅓75/100 (or 15/4 in simplest form), we can find factor pairs by considering both whole numbers and decimals that multiply to give us the fraction equivalent.

For example, one obvious pair is 1.5 and 2.5. If we multiply 1.5 by 2.5, we get 3.75:

1.5 × 2.5 = 3.75

Another pair could be 1 and 3.75 as any number multiplied by 1 equals the number itself.

1 × 3.75 = 3.75

These are just two examples of factor pairs for 3.75, but there can be other combinations as well, particularly if we consider fractions or more decimal places.

Answer:

It's C.

Step-by-step explanation:

x + y + x + y + 3(y + 5)

= x + y + x + y + 3y + 15

= 2x + 5y + 15.

Answer:

2x + y + 30

C.

Answer:

38 [tex]ft^{2}[/tex]

Step-by-step explanation:

We can see this figure as

WHOLE RECTANGLE - PORTION OF RECTANGLE CUT OUT

We know area of a rectangle is length * width

If this was the WHOLE RECTANGLE, the area would have been:

5 * 10 = 50 sq. ft.

The portion cut out is also a rectangle with dimensions:

Length = 6

Width = 5 - 3 = 2

Thus,

Area = 6 * 2 = 12 sq. ft.

So, the area of the figure is 50 - 12 = 38 sq. ft.

Answer:

it is 4,000

Step-by-step explanation:

since you are rounding it to the nearest thousand, you loo at the 4, and the 2, the 2 is blow five, so it doesn't change the thousands place, but everything else becomes a 0

Answer: 4,000

Explanation: To round 4,279 to the nearest thousand, we first locate the digit in the rounding place which in this case is the 4 in the thousands place.

Next, we look at the digit to the right of the 4 which is 2. The rules of rounding tell us that if the digit to the right of the rounding place is less than 5, we round down and if the digit to the right of the rounding place is greater than or equal to 5, we round up.

In this problem, the digit to the right of the rounding place is less than 5 so we round down. This means that the 4 in the rounding place stays the same and all digits to the right of the 4 become zero.

Therefore, 4,279 rounded to the nearest thousand is 4,000.

Answers:

a) [tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) 0.299 s

Step-by-step explanation:

a) We are given the following equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

If we divide by 2 both the numerator and the denominator, we will have:

[tex]t=\sqrt{\frac{2d/2}{(9.8)/2}}[/tex]

[tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) From this equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

[tex]t[/tex] is the reaction time in seconds

[tex]d=44 cm \frac{1 m}{100 cm}=0.44 m[/tex] is the distance

[tex]9.8 m/s^{2}[/tex] is the acceleration due gravity

Solving:

[tex]t=\sqrt{\frac{2(0.44 m)}{9.8 m/s^{2}}}[/tex]

[tex]t=0.299 s[/tex] This is the reaction time

Answer:

equation: y = -2x + 7

Step-by-step explanation:

y = mx + b   M: slope     b: y intercept

m = -2

x = 3 and y = 1

b = y - mx = 1 - (- 2) x 3 = 7

equation: y = -2x + 7

check:     ( 3,1)     -2 x 3 + 7 = 1

Answer:

The equation of the required line is,

y = -2x + 7

Step-by-step explanation:

We know that equation of a line passing through the point (x₁, y₁) and having slope 'm' is given by

(y - y₁) = m(x - x₁)

Now, the required line passes through the point (3, 1) and has a slope of -2.

So, (x₁, y₁) = (3, 1) and m = -2

So, equation of the line passing through (3, 1) and having a slope of -2 is given by,

  y - 1 = -2(x - 3)

⇒y - 1 = -2x + 6

⇒y = -2x + 6 + 1

⇒y = -2x + 7

So, the required equation of line in point-slope form is,

y = -2x + 7

Answer:

4

Step-by-step explanation:

10 - 2 = 8

4 x 2 = 8

4 x 3 = 12

Final answer:

The answer explains how to find a number given that two-thirds of it increased by two equals ten, using clear step-by-step instructions.

Explanation:

The subject of the question is Mathematics.

The question states that two-thirds of a number increased by two is equal to ten. To solve this equation:

Let the number be represented by x.

Translate the given information into an equation: (2/3)x + 2 = 10.

Solve for x: (2/3)x = 8, x = 12. Therefore, the number is 12.

Answer:

They can never be both either increasing or decreasing.

Step-by-step explanation:

If the rate of change i.e. the slope of one linear function is positive, that means the graph of the linear function makes angle which varies between 0° to 90° with respect to the positive direction of the x-axis.

Therefore, the function must be increasing.

Again, if the rate of change i.e. the slope of one linear function is negative, that means the graph of the linear function makes angle which varies between 90° to 180° with respect to the positive direction of the x-axis.

Therefore, the function must be decreasing.

Hence, if the rate of change of one linear function is positive and for another is negative, they can never be both either increasing or decreasing. (Answer)

The value of x when y = 9 is x = 2 or x = -2

Solution:

Given that value of y varies inversely as the square of x, and y=4, when x=3.

Therefore the initial statement is:

[tex]y \propto \frac{1}{x^{2}}[/tex]

To convert to an equation, multiply by k, the constant  of variation

[tex]y = k \times \frac{1}{x^2}[/tex]

[tex]y = \frac{k}{x^2}[/tex]  --- eqn 1

Given that,

y = 4 when x = 3

Now find value of k

[tex]4 = \frac{k}{3^2}\\\\4 \times 9 = k\\\\k = 36[/tex]

Find the value of x when y = 9

x = ?

y = 9

From eqn 1,

[tex]9 = \frac{k}{x^2}\\\\9 = \frac{36}{x^2}\\\\x^2 = 4\\\\x = \pm 2[/tex]

Thus value of x is found

Final answer:

To find the value of x when y=9 for a scenario where y varies inversely as the square of x, and given y=4 when x=3, we first determine the constant of variation and then solve for x, resulting in x=2.

Explanation:

The student's question concerns an inverse variation where the value of y varies inversely as the square of x, with an initial condition that when x=3, y=4. To find the value of x when y=9, we recall that an inverse variation can be expressed as y = k/x², where k is a constant. Using the given condition, we can solve for k: 4 = k/3², leading to k = 36. To find x when y=9, we set up the equation 9 = 36/x² and solve for x, yielding x = 2.

Answer:

f(3)=3/7

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

Answer:

[tex]r=0.05[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

A is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$3,000\\I=\$450\\r=?[/tex]

substitute in the formula above

[tex]450=3,000(3r)[/tex]

solve for r

[tex]450=9,000(r)[/tex]

[tex]r=450/9,000[/tex]

[tex]r=0.05[/tex]

Answer:

There was a 15 among the 7 numbers. That is the number you removed.

Step-by-step explanation:

x/7 = 9                       (1)

(x -  y)/6 = 8               (2)

Multiply 1 by 7

x/7 * 7 = 9*7

x = 63

Put 63 for x into equation 2

(63 - y)/6 = 8         Multiply by 6

6*(63-y)/6 =8*6

63 - y = 48            Add y to both sides

63-y+y = 48+y

63 = 48 + y           Subtract 48 from both sides

63-48=48-48+y

y = 15

Final answer:

The number removed from the list to change the average from 9 to 8 is 15, calculated by finding the difference between the total sum of the original and remaining lists.

Explanation:

To find the number that was taken away from a list when the average changes, you can first calculate the total sum of the original list, then the sum of the list after the number is removed.

Initially, the average of the 7 numbers is 9. To find the total sum of all 7 numbers, you multiply the average by the number of values.

Total sum of original list = 7 (number of values) × 9 (original average) = 63

After removing one of the numbers, the average of the 6 remaining numbers is 8.

Total sum of the remaining list = 6 (remaining values) × 8 (new average) = 48

The number that was removed can be found by subtracting the sum of the remaining list from the sum of the original list.

Number removed = Total sum of original list - Total sum of the remaining list = 63 - 48 = 15

Therefore, the number that was taken away from the list is 15.