Identify the restrictions on the variable







​

Answer:

v=3i+8j

Step-by-step explanation:

The given the vector v has an initial point (-2,-6) and a terminal point of (1,2).

To find the components of vector v, we subtract the terminal points from the initial point to obtain.

v=<1,2>-<-2,-6>

v=<1--2,2--6>

v=<1+2,2+6>

v=<3,8>

As a linear combination of the standard unit vectors.

v=3i+8j

pretty much by simply solving for "y".

[tex]\bf 3x+2y=6\implies 2y=-3x+6\implies y=\cfrac{-3x+6}{2} \\\\\\ \underset{\textit{distributing the denominator}}{y=\cfrac{-3x}{2}+\cfrac{6}{2}~\hfill }\implies y=-\cfrac{3}{2}x+3\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

y = -3/2 x +3

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

3x+2y = 6

Subtract 3x from each side

3x-3x+2y = -3x+6

2y = -3x+6

Divide each side by 2

2y/2 = -3x/2 +6/2

y = -3/2 x +3

This is in slope intercept form where the slope is -3/2 and the y intercept is 3

Answer:

[tex]y=\pm i \sqrt{7}[/tex]

Step-by-step explanation:

Given equation is [tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}[/tex]

Factor denominators then solve by making denominators equal

[tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}[/tex]

[tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}[/tex]

[tex]\frac{y\left(y+4\right)-4\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}[/tex]

[tex]y\left(y+4\right)-4\left(y-4\right)=9[/tex]

[tex]y^2+4y-4y+16=9[/tex]

[tex]y^2=9-16[/tex]

[tex]y^2=-7[/tex]

take squar root of both sides

[tex]y=\pm \sqrt{-7}[/tex]

[tex]y=\pm i \sqrt{7}[/tex]

Hence final answer is [tex]y=\pm i \sqrt{7}[/tex].

Answer:

16cm

Step-by-step explanation:

To find the diameter we must first find the radius and multiply by 2.

The isosceles triangle that has the length of a leg to be 8cm and a vertex angle of [tex]120\degree[/tex] that has been circumscribed is shown in the attachment.

We draw a line from the vertex of the isosceles triangle that bisects the base through the center O of the circle.

This implies that [tex]m\angle OAC=60\degree[/tex].

Based on this [tex]m\angle ACO=60\degree[/tex] because the two radii are equal.

It follows that:[tex]m\angle AOC=60\degree[/tex] because sum of angles in a triangle must be 180 degrees.

This means that, triangle AOC is an equilateral triangle, hence all sides are equal.

One side of this equilateral triangle happens to be the side of the leg of the isosceles triangle which is 8cm.

It follows that, the radius of the circle is 8cm.

Therefore the diameter of the circle is 16cm

Answer:

Tj should write 5.75 hours on her time card.

Step-by-step explanation:

We have been given, Tj worked for 5 hours and 45 minutes.

We will convert 45 minutes to hours by dividing 45 by 60 as one hour has 60 minutes.

[tex]\frac{45 minutes }{60} \times\frac{hour}{minutes}[/tex]

=0.75 hours

Hence, Tj should write 5.75 hours on her time card.

Answer:

The length of the arc shown in red is [tex]\frac{22}{9}\pi\ in[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=4\ in[/tex]

substitute

[tex]C=2\pi (4)[/tex]

[tex]C=8\pi\ in[/tex]

step 2

Find the length of the arc in red

Remember that the length of the circumference subtends a central angle of 360 degrees

so

by proportion find the length of the arc by a central angle of 110 degrees

[tex]\frac{8\pi}{360}=\frac{x}{110}\\ \\x=8\pi*110/360\\ \\x=\frac{880}{360}\pi\ in[/tex]

Simplify

[tex]\frac{880}{360}\pi=\frac{22}{9}\pi\ in[/tex]

Answer:

1. y=0.25x+9

2. The graph that starts at 9 and the highest number is 11.

NOT THE ONE WITH THE HIGHEST NUMBER 15

Step-by-step explanation:

I got it right on edmentum

The equation that correctly models this situation y=0.25x+9.

solving this we will get the valve of Y if x is given.

calculation:-

⇒pickup charges of the cap company= $9

⇒charge for per mile = $0.25

⇒let the total distance traveled is X

⇒total amount George pays (y)=  0.25x+9.

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Answer: The answer to your question is C. (7*5) - (7*3)

Step-by-step explanation: because when you have an expression or equation in parentheses, you apply the distributive property to get rid of the parentheses:

The problem will now look like this:

[tex]7(5-3)= (7*5) - (7*3)[/tex]

And if they asked you for the answer in a whole number, it would be 14 because

7*5=35 and 7*3=21

35-21=14

So, therefore, the expanded form would be (7*5) - (7*3)

Answer: hypothesis

Step-by-step explanation:

Answer:

The correct word is hypothesis.

Step-by-step explanation:

If a conditional statement is true and its HYPOTHESIS is true, then the conclusion is true.

The conditional statement is written in the following form -

If p is true, then q is true.

Here p is the hypothesis and q is the conclusion.

The opposite can be defined as - if the hypothesis is true and the conclusion is false, then the conditional statement is false.

Answer:

1000 years

Step-by-step explanation:

1x10^11 is basically 100 billion

1x10^8 is basically 100 million

so 100 billion divided by 100 milllion is basically 1000

so 1000 years

Answer:

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps: Step 1: Work out the missing lengths around the edge of the compound shape.

Step-by-step explanation:

Answer:

Acceleration = 2 meters /second^2.

Step-by-step explanation:

Use Newton's Second Law of Motion:

Force = mass * acceleration.

0.5 = 0.25 * a

a = 0.5 / 0.25

a = 2 meters /second^2.

Answer: 10

a=27-5-12=10

A= (27-5)=22-12=10

A=10

Answer:

The maximum possible area of the triangle is 36 units²

Step-by-step explanation:

Let

x, y the legs of the right triangle

Applying the Pythagoras Theorem

[tex]12^{2}=x^{2}+y^{2}\\\\144=x^{2}+y^{2}[/tex]

[tex]y=\sqrt{144-x^{2}}[/tex] ----> equation A

The area of the right triangle is equal to

[tex]A=\frac{1}{2}xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=\frac{1}{2}x(\sqrt{144-x^{2}})[/tex]

Using a graphing tool

The vertex of the graph is a maximum

That means

The x-coordinate of the vertex is the value of x for the maximum possible area of the triangle

The y-coordinate of the vertex is the maximum possible area of the triangle

The vertex is the point (8.485,36)

see the attached figure

therefore

The maximum possible area of the triangle is 36 units²

well, the assumption is that is a rectangle, namely it has two equal pairs, so we can just find the length of one of the pairs to get the dimensions.

hmmmm let's say let's get the length of the segment at (-1,-3), (1,3) for its length

and

the length of the segment at (-1, -3), (-4, -2) for its width

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{length}{L}=\sqrt{[1-(-1)]^2+[3-(-3)]^2}\implies L=\sqrt{(1+1)^2+(3+3)^2} \\\\\\ L=\sqrt{4+36}\implies L=\sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{width}{w}=\sqrt{[-4-(-1)]^2+[-2-(-3)]^2}\implies w=\sqrt{(-4+1)^2+(-2+3)^2} \\\\\\ w=\sqrt{9+1}\implies w=\sqrt{10} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{A=Lw}\implies \sqrt{40}\cdot \sqrt{10}\implies \sqrt{400}\implies \boxed{20}[/tex]

the answer is c. 16.4 feet in 5 meters

Answer:

16.4 ft

Step-by-step explanation:

We are given that Yvette measured the length of her driveway to be 5 meters long.

We have to find that which is equivalent to  given length in given options.

Measurement of length = 5 m

We know that 1 meter =3.28 foot

1 meter=1.09 yard

1 meter =39.37 inches

5 m= [tex]5\times 3.28=16.4  ft[/tex]

5 m=[tex]5\times .109=5.45 yard[/tex]

5 m=[tex]5\times 39.37=196.85 inches[/tex]

Hence, measurement of length =5 m =16.4 ft

Answer:

y = -2

Step-by-step explanation:

We have a point (-1,y) on the graph of y = 3x + 1

When x = -1 then,

y = 3(-1) + 1

y = -3 + 1 = -2

Answer:

If the question is  "If (-1, y) lies on the graph of y = 3^x+1, then y = 1"

So the answer is 1

Step-by-step explanation:

Answer:

[tex]\large\boxed{\text{The slope}\ m=-\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-3, 5) and (-1, 4). Substitute:

[tex]m=\dfrac{4-5}{-1-(-3)}=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]

Answer:

[tex]29\sqrt{5}[/tex]

Step-by-step explanation:

We want to simplify:

[tex]11\sqrt{45}-4\sqrt{5}[/tex]

We need to simplify the first radical before we can subtract

[tex]11\sqrt{9\times5}-4\sqrt{5}[/tex]

[tex]11\sqrt{9} \times\sqrt{5}-4\sqrt{5}[/tex]

This implies that:

[tex]11\times 3\times\sqrt{5}-4\sqrt{5}[/tex]

[tex]33\sqrt{5}-4\sqrt{5}[/tex]

We have now obtained like surds.

We simplify to get:

[tex]29\sqrt{5}[/tex]

Answer:

the answer is d and please accept my friend request

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The answer is C.

Hope this helps :)

Answer: [tex](2g+h)[/tex] and [tex](2g-h)[/tex]

Step-by-step explanation:

The area of a rectangle is obtained by multiplying its lenght by its width.

You know that the area of this rectangle is [tex]4g^2- h^2[/tex], then you need to apply the Difference of squares to find the dimensions of this rectangle.

Remember that the Difference of squares is:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Then, applying this, you get:

 [tex]4g^2- h^2=(2g+h)(2g-h)[/tex]

Therefore, now you know that the dimensions are:

[tex](2g+h)[/tex] and [tex](2g-h)[/tex]

the length and breadth of rectangle are [tex]2g - h[/tex] and [tex]2g + h[/tex] respectively

The given expression for the area of the rectangle is [tex]4g^2 - h^2[/tex]

This expression is a difference of squares, which can be factored using the formula: [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

Now by comparing both equations we can factor as follows:

[tex]4g^2 - h^2 = (2g)^2 - h^2\\\\4g^2 - h^2 = (2g+h)(2g-h)[/tex]

We know that area of a rectangle is a product of its length and breadth so we can say that:

Length: 2g - h

Breadth: 2g + h

So, the length and breadth of rectangle are [tex]2g - h[/tex] and [tex]2g + h[/tex] respectively

Answer:

8 units

Step-by-step explanation:

mid point of hypotenuse of right angled isosceles triangle is equidistant from three vertices.

length of altitude=16/2=8

The question is incomplete, here is a complete question.

Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.

What is the length of GJ?

A. 2 units

B. 4 units

C. 6 units

D. 8 units

Answer : The correct option is, (D) 8 units

Step-by-step explanation :

Given:

Length FH = 16 unit

As we know that a altitude between the two equal legs of an isosceles triangle creates right angles is a angle and opposite side bisector.

Thus,

Length FJ = Length HJ = [tex]\frac{16}{2}[/tex] = 8 units

As, the triangle is an isosceles. So, length GF = length GH = x unit

First we have to determine the value of 'x'.

Using Pythagoras theorem in ΔFGH :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](FH)^2=(GF)^2+(GH)^2[/tex]

Now put all the values in the above expression, we get :

[tex](16)^2=(x)^2+(x)^2[/tex]

[tex]256=2x^2[/tex]

[tex]x^2=128[/tex]

[tex]x=8\sqrt{2}[/tex]

Thus, length GF = length GH = x unit = [tex]8\sqrt{2}[/tex]

Now we have to determine the length GJ.

Using Pythagoras theorem in ΔGJH :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](GH)^2=(GJ)^2+(HJ)^2[/tex]

Now put all the values in the above expression, we get :

[tex](8\sqrt{2})^2=(GJ)^2+(8)^2[/tex]

[tex]128=(GJ)^2+64[/tex]

[tex](GJ)^2=128-64[/tex]

[tex](GJ)^2=64[/tex]

[tex]GJ=\sqrt{64}[/tex]

[tex]GJ=8[/tex]

Thus, the length of GJ is, 8 units.

-5(3)+13

=-15+13

=-2

Answer: g(3)= -2

ANSWER

g(3)=-2

EXPLANATION

The given function is

[tex]g(r) = - 5r + 13[/tex]

We want to find g(3).

We substitute r=3 into the given function to obtain:

[tex]g(3) = - 5 \times 3 + 13[/tex]

Multiply out the first term

[tex]g(3) = - 15 + 13[/tex]

Simplify the result to obtain:

[tex]g(3) = -2[/tex]

Answer

4.8/5

30

We are given 12 to the 3rd power over 12 to 7th power.

First we write given expression as exponent form and we get It looks ..

If base is same in division then their exponent subtract.

Thus, It would be 1 over 12 to the 4th.

[tex]\bf \sqrt{1764}~~ \begin{cases} 1764=&2\cdot 2\cdot 3\cdot 3\cdot 7\cdot 7\\ &2^2\cdot 3^2\cdot 7^2\\ &(2\cdot 3\cdot 7)^2\\ &42^2 \end{cases}\implies \sqrt{42^2}\implies 42[/tex]

Answer:

2(5+7)

Step-by-step explanation:

2 times any equation is 2(equation) and our equation is the sum of 5 and 7 which means 5 plus 7, therefore our equation is 2(5+7)

Answer

(5 + 7) · 2

Step-by-step explanation

If we take a look at PEMDAS or BEDMAS whichever one you were taught, multiplication comes before addition. (And unless you are in 2nd grade, you will know that "times" means multiplication, and sum is the result of an addition problem.)

P = Parentheses {|} B = Brackets/Parentheses

That means that anything in parentheses or brackets comes first, no matter what type of problem it is. So, if we add 5 and 7 and then multiply it by two and just rephrase that, we get 2 times the sum of 5 and 7.

Answer:−8x8y9z7

Step-by-step explanation:

Answer:

D (5,7.4)

Step-by-step explanation:

This is because all of the other (x,y) vales are close together in number and this is an outlier because it stands out from the group.

The answer is D. (5, 7.4)

284,000

(You would round up one because the number right before the thousands place is the hundred, which in our case, is above 4. As such, we are going to round up to 284,000.)

Hope I could help! :)

When rounding 283,657 to the nearest thousand, we look at the hundreds digit which is 6. Since it is greater than 5, we round up, resulting in a final rounded number of 284,000.

To round 283,657 to the nearest thousand, we look at the hundreds place to decide whether to round up or down. Since the hundreds digit is a '6' (which is greater than 5), we round up to the next thousand. Therefore, 283,657 rounded to the nearest thousand is 284,000.

Rounding rules dictate that if the digit to the right of the target rounding place is 5 or greater, we round up the target digit by one. In this case, we're rounding to the nearest thousand, so we look at the hundreds place which is a 6. Since it is greater than 5, we add one to the thousands place, changing 283,000 to 284,000, and set all the following digits to zero, giving us our final rounded number.

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