Write an equation of the direct variation that includes the point (9, -12).

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

The point-slope form of the equation for a line with slope m and passing through a point (a, b) is given as;

[tex]y-b=m(x-a)[/tex]

The slope of the line is 5; the coefficient of x in the given equation. The point given is (–2, –13). We plug in these values into the above equation and simplify;

[tex]y-(-13)=5(x-(-2))\\\\y+13=5(x+2)[/tex]

Which is the equation of the line in point-slope form

Answer:

b

Step-by-step explanation:

Answer:

[tex]\large\boxed{(3+2i)(17+7i)=37+55i}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \bold{FOIL}\ (a+b)(c+d)=ac+ad+bc+bd,\ \text{and}\ i^2=-1:\\\\(3+2i)(17+7i)\\\\=(3)(17)+(3)(7i)+(2i)(17)+(2i)(7i)\\\\=51+21i+34i+14i^2\\\\=51+21i+34i+14(-1)\\\\=51+21i+34i-14\qquad\text{combine like terms}\\\\=(51-14)+(21i+34i)\\\\=37+55i[/tex]

Answer:

3y+4x=5

Step-by-step explanation:

step 1

Find the slope

we have

(–7, 11) and (8, –9)

m=(-9-11)/(8+7)

m=-20/15

m=-4/3

step 2

Find the equation of the line into point slope form

we have

m=-4/3

point (-7,11)

substitute

y-11=-(4/3)(x+7) ----> equation of the line into point slope form

Multiply by 3 both sides

3y-33=-4(x+7)

3y-33=-4x-28

3y+4x=33-28

3y+4x=5 -----> equation of the line into standard form

Answer:

I think that the answer is D

Answer:

Length [tex]14\ cm[/tex]

Width [tex]3\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of rectangle

y ----> the width of rectangle

we know that

The area of rectangle is equal to

[tex]A=xy[/tex]

[tex]A=42\ cm^{2}[/tex]

so

[tex]42=xy[/tex] ----> equation A

[tex]x=2y+8[/tex] ---> equation B

substitute equation B in equation A and solve for y

[tex]42=(2y+8)y\\ \\2y^{2}+8y-42=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=3\ cm[/tex]

see the attached figure

Find the value of x

[tex]x=2(3)+8=14\ cm[/tex]

therefore

Length [tex]14\ cm[/tex]

Width [tex]3\ cm[/tex]

The dimensions of the rectangle are: Width ( W = 3 ) cm and  Length ( L = 14 ) cm

We are given that the length L is 8 cm greater than twice its width W. This can be expressed as:

[tex]\[ L = 2W + 8 \][/tex]

The area  of the rectangle is given by the formula:

[tex]\[ A = L \times W \][/tex]

Given that the area is 42 cm², we can write:

[tex]\[ 42 = (2W + 8) \times W \][/tex]

Expanding the equation:

[tex]\[ 42 = 2W^2 + 8W \][/tex]

Rearranging the equation in standard quadratic form:

[tex]\[ 2W^2 + 8W - 42 = 0 \][/tex]

Now, let's solve this quadratic equation for ( W ). We can use the quadratic formula:

[tex]\[ W = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

-  a = 2

-  b = 8

-  c = -42

Now, let's substitute the values into the quadratic formula:

[tex]\[ W = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 2 \times (-42)}}}}{{2 \times 2}} \]\[ W = \frac{{-8 \pm \sqrt{{64 + 336}}}}{{4}} \]\[ W = \frac{{-8 \pm \sqrt{{400}}}}{{4}} \]\[ W = \frac{{-8 \pm 20}}{{4}} \][/tex]

Now, we have two possible values for \( W \):

[tex]\[ W_1 = \frac{{-8 + 20}}{{4}} = \frac{{12}}{{4}} = 3 \]\[ W_2 = \frac{{-8 - 20}}{{4}} = \frac{{-28}}{{4}} = -7 \][/tex]

Since the width cannot be negative, we discard [tex]\( W_2 = -7 \)[/tex]. Thus, the width of the rectangle is ( W = 3 ) cm.

Now, let's find the length using the equation ( L = 2W + 8 ):

[tex]\[ L = 2 \times 3 + 8 \]\[ L = 6 + 8 \]\[ L = 14 \][/tex]

1 pound = 16 ounces.

1 can weighs 8 ounces, so 2 cans weigh 8 +8 = 16 ounces, which is 1 pound.

Multiply total pounds by number of cans per pound:

25 pounds x 2 cans per pound = 50 total cans.

The number of cans each box hold will be 50.

In one pound there is a total of sixteen ounces.

So it means 1 pound = 16 ounces.

Given that the weight of the can is 8 ounces it means in 2 cans there are 16 ounces which are 1 pound.

2 cans = 1 pound

Since, the box can hold only 25 pounds Hence,

25 × 2 = 50 cans so a box can hold up to 50 cans.

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Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{\log_84a\left(\dfrac{b-4}{c^4}\right)=\log_84+\log_8a+\log_8(b-4)-4\log_8c}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a(bc)=\log_ab+\log_ac\\\\\log_a\left(\dfrac{b}c{}\right)=\log_ab-\log_ac\\\\==============================[/tex]

[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)=\log_84+\log_8a+\log_8\dfrac{b-4}{c^4}\\\\=\log_84+\log_8a+\log_8(b-4)-\log_8c^4\\\\=\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex]

Answer:

answer is A

Step-by-step explanation:

bc

Answer:

r= C over 2π

Step-by-step explanation:

C =  2πr

To solve for r, divide each side by  2π

C/  2π =  2πr/  2π

C/  2π =  r

Answer: r= C over 2π or [tex]r=\dfrac{C}{2\pi}[/tex]

Step-by-step explanation:

Formula to find the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle .

To find the formula for r , we need to divide both sides by [tex]2\pi[/tex], we get

[tex]r=\dfrac{C}{2\pi}[/tex]

Hence, an equivalent equation solved for r will be :-

[tex]r=\dfrac{C}{2\pi}[/tex] i.e. r= C over 2π

Answer:

He did not test it against anyone who did not drink milk before bed and he tested it on a relatively small number of people. In order to have more accurate results he should include more people in the study and should test it against the same number of people who haven't drank milk before bed. He should also take into account the amount of milk that they drank before going to bed.

Answer:

No comparision and repeatibility

Step-by-step explanation:

Firstly, this total number of hours each friend sleeps is not specified and therefore can vary each night. What is constant is that they drank milk before they slept and for one month the analysis was made. Secondly, he never made a comparison between milk drinkers and non-milk drinkers and therefore the analysis is just one sided and open to other effects such as exercise, eating habits etc. Furthermore, no repeatability was conducted to determine if the same results would be obtained. Lastly, the ages of the friends are unknown so making a conclusion of teenagers is inaccurate.

Answer:

The factors of x^3+2x^2+5x+10 are (x^2+5)(x+2)

Step-by-step explanation:

x^3+2x^2+5x+10

Group the expression by two:

=(x^3+2x^2)+(5x+10)

Factor out GCF in each group.

=x^2(x+2)+5(x+2)

Note:(The binomials in parentheses should be the same, if not the same... there is an error in the factoring or the expression can not be factored.)

Now factoring out the GCF which basically has you rewrite what is in parentheses and place other terms left together:

=(x^2+5)(x+2)

Thus the factors of x^3+2x^2+5x+10 are (x^2+5)(x+2)....

Answer:

35.8333 (3 repeated) in^3

Step-by-step explanation:

Just Multiply 2, 5 1/3, and 10 3/4 all together (you'll get 107.5) and divide it by 3 to get your answer.

Answer:

A: 270 ,':)

Step-by-step explanation:

Answer:

the answer is A:  270

Step-by-step explanation:

Op= 360

AB= 90

Op(360)-AB(90) = 270

The solution to the system of equations y = -(1/3)x + 6 and y = (1/3)x—6 is (18, 0) option fourth (18,0) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

y = -(1/3)x + 6 and

y = (1/3)x—6

Add both the equations

2y = 0

y = 0

Plug y = 0 in the first equation:

x = 18

Thus, the solution to the system of equations y = -(1/3)x + 6 and y = (1/3)x—6 is (18, 0) option fourth (18,0) is correct.

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Answer:

It is D

Step-by-step explanation:

The equation equivalent to r = 1 + 2 is mathematically given as

(x^2+y^2-2y)^{2}=x^2+y^2

Question Parameter(s):

r = 1 + 2

Generally, the equation for the polar cordinates  is mathematically given as

[tex]x=rsin\theta\\\\y=rcos\theta[/tex]

Therefore

[tex](sin^{2}\theta + cos^{2}\theta) = 1[/tex]

Hence

[tex]r=\sqrt{x^2+y^2}[/tex]

In conclusion

[tex]\sqrt{x^2+y^2} = 1+2\frac{y}{\sqrt{x^2+y^2}}\\\\x^2+y^2-2y= \sqrt{x^2+y^2}[/tex]

(x^2+y^2-2y)^{2}=x^2+y^2

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The easiest way to solve this question is to write out both equations in the form y = mx + c, where m is the gradient and c is the y-intercept.

a) Thus, if we start with 9x - 10y = 21, then we get:

9x - 10y = 21

(9/10)x - y = 21/10 (Divide both sides by 10)

(9/10)x = y + 21/10 (Add y to both sides)

(9/10)x - 21/10 = y (Subtract 21/10 from both sides)

Thus, our first equation may be written as y = (9/10)x - 21/10

b) Now if we take the second equation, (3/2)x - (5/3)y = 7/2, we can follow the same process to get:

(3/2)x - (5/3)y = 7/2

(9/10)x - y = 21/10 (Multiply each side by 3/5)

(9/10)x = y + 21/10 (Add y to each side)

(9/10)x - 21/10 = y (Subtract 21/10 both sides)

Thus, the second equation may be written as y = (9/10)x - 21/10.

Now you might have already realised this but the two equations are actually exactly the same; if they are the same line then they are said to be coincident.

Note that if the two lines are parallel, then their gradients (m) would be the same, but the y-intercepts (c) would be different (eg. y = 2x + 3 and y = 2x + 4 are parallel).

If they just intersect at a point, then the gradients of the lines would be different, but the y-intercepts could be the same or different (eg. y = 4x + 2 and y = 9x + 2 intersect at one point).

For them to be coincident however, both the gradient and y-intercept must be the same as only then would they be the same line.

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that:

[tex]r = 7\\h = 16[/tex]

Substituting the data we have:

[tex]V = \pi * (7) ^ 2 * 16\\V = \pi * 49 * 16\\V = 784 \pi[/tex]

So, the cylinder volume is[tex]784 \pi[/tex]

Answer:

[tex]784 \pi[/tex]

[tex]

L(x)=-2377+3\Longrightarrow L(x)=-2374 \\

V(x)=x

[/tex]

Both of the functions are linear. [tex]L(x)[/tex] is constant.

However we are required to determine the range of [tex](L\circ V)(x)[/tex]

[tex](L\circ V)(x)=L(V(x))=L(x)=-2374[/tex]

So the only possible solution that such notation gives is -2374 so therefore the answer in terms of range is [tex]x\in\{-2374\}[/tex]

Hope this helps.

r3t40

Answer:

3 cups of strawberries, 1 1/2 cups of grapes

Step-by-step explanation:

Basically you need 1 C of strawberries and 1/2 C of grapes for 2 people. Multiply those amounts by 3, for 6 people

This question requires us to use the cosine rule:

a^2 = b^2 + c^2 - 2bc*cos(A),

where A is the included angle between sides b and c, and a is the side of the triangle opposite to the angle.

In the context of the question, a is the length of the tunnel (let's call this t), b is 6 km, c is 7 km and A is 29°.

Given the values in the question and those we defined, we can rewrite the equation for the cosine rule as:

t^2 = 6^2 + 7^2 - 2(6)(7)cos(29)

Now, evaluating this we get:

t^2 = 36 + 49 - 84cos(29)

t^2 = 85 - 84cos(29)

t = sq.root (85 - 84cos(29))

= 3.40 km (rounded to two decimal places)

Answer:

3.40

Step-by-step explanation:

I checked the answer and it was right!!

Answer:

Let's solve for x.

5y=3x+b

Step 1: Flip the equation.

b+3x=5y

Step 2: Add -b to both sides.

b+3x+−b=5y+−b

3x=−b+5y

Step 3: Divide both sides by 3.

Answer:

x=

−1

3

b+

5

3

y

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

AC = 29.9

AB = 30.9

Step-by-step explanation:

for edg 2020

Answer:

Option B. Chef Andre used more than 3 1/2 cups of flour.

Step-by-step explanation:

we have

[tex]c > 3\frac{1}{2}[/tex]

The solution is all real number greater than [tex]3\frac{1}{2}[/tex]

therefore

Let

c -----> the number of cups

The statement that best represented by the inequality is

Chef Andre used more than 3 1/2 cups of flour

Answer:

The answer is B

Step-by-step explanation:

Answer:

A) -12x

Step-by-step explanation:

The linear portion has the variable x with power 1. It is the term -12x.

For this case we have by definition, that a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Where:

[tex]ax ^ 2[/tex]: It is the quadratic term

[tex]bx[/tex]: It's the linear term

c: It is the independent term

We have the following equation:

[tex]7x ^ 2-12x + 16 = 0[/tex]

So:

[tex]7x ^ 2:[/tex] It is the quadratic term

[tex]-12x:[/tex] It is the linear term

16: It is the independent term

Answer:

Option A

Answer:

y + 2 = - [tex]\frac{4}{5}[/tex](x - 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{4}{5}[/tex] and (a, b) = (3, - 2), hence

y - (- 2) = - [tex]\frac{4}{5}[/tex](x - 3), that is

y + 2 = - [tex]\frac{4}{5}[/tex](x - 3)

By using FOIL method and multiplying two parenthesis, we get the value of y as x² + 2x + 1

What is FOIL method?

To multiply binomials, utilize the FOIL Method. First, Outside, Inside, and Last are represented by the letters, denoting the sequence of multiplying terms. For your answer, multiply the first word, the outside term, the inside term, the last term, and then combine like terms. The foil approach is a useful strategy since it allows us to manipulate numbers regardless of how ugly they may appear when mixed with fractions and negative signs.

The above question says," y = (x + 1)²

We can look it as ( x + 1) ( x+ 1)

Use concept of FOIL here,

So, y = (x+1)(x+1)

multiplying x with x and then with 1 and then multiplying 1 with x and then with 1.

y = x² + x + x +1

By combining the like term , we will get

x² +2x+1

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Final answer:

To simplify the expression y = (x + 1)² - 2, we need to expand the square and combine like terms.

Explanation:

To simplify the expression y = (x + 1)² - 2, we need to expand the square and combine like terms.

Square the binomial (x + 1)² using the formula for the square of a binomial:

(x + 1)² = x² + 2x + 1

Now substitute this expression back into the original equation:

y = x² + 2x + 1 - 2

Combine like terms:

y = x² + 2x - 1

Answer:

Step-by-step explanation:

[tex]Domain:\\\\x>0\ \wedge\ x-2>0\\\\x>0\ \wedge\ x>2\\\\\boxed{D:\ x>2}\\\\=============================[/tex]

[tex]2\log_9x=\log_98+\log_9(x-2)\\\\\text{use}\ n\log_ab=\log_ab^n\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_9x^2=\log_9\bigg(8(x-2)\bigg)\iff x^2=8(x-2)\qquad\text{use the distributive property}\\\\x^2=8x-16\qquad\text{subtract 8x from both sides}\\\\x^2-8x=-16\qquad\text{add 16 to both sides}\\\\x^2-8x+16=0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)(x-4)=0\\\\(x-4)^2=0\iff x-4=0\qquad\text{add 4 to both sides}\\\\x=4\in D[/tex]

Answer:

9.50x+12y<=60

Step-by-step explanation:

Answer:

186

Step-by-step explanation:

Cut it 6+7+11=24×5=120

6+11=66

120+66=186

Answer:  The correct option is (A) 186 sq. units.

Step-by-step explanation:  We are given to find the area of the polygon shown in the figure.

Let us divide the given polygon in two rectangles A and B as shown in the attached figure below.

The dimensions of rectangle A are

length, l = 11 units and breadth, b = 6 units.

So, the area of rectangle A is given by

[tex]AREA_A=l\times b=11\times6=66~\textup{sq. units}.[/tex]

And the dimensions of rectangle B are

length, l' = 7 + 11 + 6 = 24 units  and  breadth, b' = 5 units.

So, the area of rectangle B is given by

[tex]AREA_B=l'\times b'=24\times5=120~\textup{sq. units}.[/tex]

Therefore, the total area of the given polygon is given by

[tex]AREA=AREA_A+AREA_B=66+120=186~\textup{sq. units}.[/tex]

Thus, the required area of the given polygon is 186 sq. units.

Option (A) is CORRECT.

For this case we have that by definition, the mechanical power is given by:

[tex]P = \frac {W} {t}[/tex]

Where:

W: It is the work done

t: It's time

For its part:

[tex]W = F * d[/tex]

Where:

F: It is the applied force

d: It is the distance traveled

According to the data we have that the drag force of the tractor is [tex]F = 300lb[/tex], while the distance traveled is [tex]d = 80ft.[/tex]

Substituting:

[tex]P = \frac {300 * 80} {120}\\P = \frac {24000} {120}\\P = 200[/tex]

Finally, the power is:

[tex]\frac {200lb-ft} {s}[/tex]

Answer:

Option C

The correct option is 200 ft-lb/sec. The power output is 200 ft-lb/sec.

Determining the Power Output of a Tractor

To find the power output of the tractor dragging a 300 lb. concrete block over a distance of 80 ft. in 120 seconds, we need to use the formula for power:

Power = Work / Time

Step-by-step explanation:

 1. Calculate the Work Done: Work is calculated as the force applied times the distance moved by the force. Here, the force is the weight of the block (300 lb), and the distance is 80 ft.

   Work = Force x Distance

   Work = 300 lb x 80 ft = 24,000 ft-lb.

 2. Calculate the Time: The time given is 120 seconds.

 3.  Calculate the Power: Power is the rate at which work is done, given by dividing the work by the time.

Power = Work / Time

Power = 24,000 ft-lb / 120 sec = 200 ft-lb/sec.

Therefore, the power output of the tractor is 200 ft-lb/sec.