A 12 pack of cola costs $5.46. How much does one can of cola cost?

Answer:

  C.  The field will be covered 25% of the way in 2014.

Step-by-step explanation:

Since the field was completely covered in 2016, and the blueberries doubled in size in one year to do that, the field was half-covered in 2015. Similar reasoning tells you the field was 1/4 covered in 2014.

Answer:

No

Step-by-step explanation:

You cannot work negative 3 hours, it's impossible. One possible solution would be to work 50 hours a week at dog walking for 7 dollars an hour, and 10 hours a week at Computers & More, Inc. for 12 dollars a week. This would give you 350 dollars from dog walking, and 120 dollars from Computers & More, Inc. This would be a total of 470 dollars.

Answer:

No, this is not a possible solution because it does not satisfy all inequalities of the system.

Step-by-step explanation:

Let x represents the number of hours spent on dog walking and y represents the number of hours spent on sales job at Computers & More Inc.,

Given,

Total hours can not be no more than 60 hours,

⇒ x + y ≤ 60

Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour.

Thus, the total earning = 7x + 12y

According to the question,

Total earning ≥ $ 450

⇒ 7x + 12y ≥ 450

Also, hours can not be negative,

⇒ x ≥ 0; y ≥ 0

Hence, the system of inequalities that shows the given situation is,

7x + 12y ≥ 450;  

x + y ≤ 60;

x ≥ 0; y ≥ 0

Since, -3 ≥ 0 ( False ),

Thus, the point is not satisfying all inequalities of the system,

Hence, it can not be the solution.

Answer:

  92

Step-by-step explanation:

Assuming your (f*g)(2) is the product f(2)*g(2), you have ...

  f(2) = 8*2 +7 = 23

  g(2) = 2+2 = 4

  (f*g)(2) = f(2)*g(2) = 23*4 = 92

Answer:

Step-by-step explanation:23

Answer:

First question C

C) after drawing the shape

Second question C

C). Solved the equation and then put 6 in place of X

x+17=3x+5. 3x-x= 17-5. 2x=12. 2x/2=12/2. x=6

NM=6+17= 23. OL=3(6)+5=23

Step-by-step explanation:

hope this helps and mark me as brainliest

A = {3, 4, 7, 9}

B = {8, 9, 10, 11}

C = {4, 9, 11, 13, 15}

A∩(B∪C)

First let's solve parentheses, we want the union between B and C.

B∪C = {4, 8, 9, 10, 11, 13, 15}

Now we want the interception between A and this, which means we want just the value which appears in both.

A∩{4, 8, 9, 10, 11, 13, 15} = {4, 9}

Final answer:

To determine A∩(B∪C), first calculate the union of B and C which is {4, 8, 9, 10, 11, 13, 15}. Then find the intersection of this union with set A, which results in {4, 9}.

Explanation:

To find the intersection of set A with the union of sets B and C, denoted as A∩(B∪C), we first identify the union of sets B and C. The union of two sets contains all elements that are members of either set, without duplicates. Therefore, the union of set B = {8, 9, 10, 11} and set C = {4, 9, 11, 13, 15} is the set that contains all distinct elements from both, which is {4, 8, 9, 10, 11, 13, 15}.

Next, we identify the intersection of set A with this union. The intersection of two sets contains only the elements that are members of both sets. Set A = {3, 4, 7, 9}. We check which elements in set A are also in the union of B and C. The elements 4 and 9 appear in both set A and the union of B and C. Consequently, the intersection A∩(B∪C) is {4, 9}.

Answer: OPTION B

Step-by-step explanation:

Since the base is a square, you need to use the following formula:

[tex]V=\frac{s^2h}{3}[/tex]

Where "s" is the lenght of any side of the base and "h" is the height of the pyramid.

 You can identify in the figure that:

[tex]s=12units\\h=8units[/tex]

Then you can substitute these values into the formula to calculte the volume of this pyramid. Therefore, the result is:

[tex]V=\frac{(12units)^2(8units)}{3}=384units^3[/tex]

Answer:

The correct answer is option B.   384 units³

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

To find the volume of given pyramid

Here a = 12 units  and h = 8 units

Volume =  (a²h)/3

  =  (12² * 8)/3

  = (12 * 12 * 8)/3

  = (4 * 12 * 8) = 384 units³

Therefore the correct answer is option B.   384 units³

BA and BD are radii of the circle, so triangle ABD is isosceles. Then angles BDA and BAD are congruent, and the remaining (central) angle ABD has measure

[tex]m\angle ABD=(180-2\cdot20)^\circ=140^\circ[/tex]

Angles ABD and CBD are supplementary, so

[tex]m\angle CBD=(180-140)^\circ=40^\circ[/tex]

and the answer is E.

The measure of the angle CBD is 40°.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

According to the given problem,

BA and BD are radii of the circle.

Triangle ABD is isosceles.

Angles BDA and BAD are congruent.

m∠ABD = (180 - 2*20)

              = 140°

Angles ABD and CBD are supplementary, so,

∠CBD = 180 - 140

           = 40°

Hence, the measure of the angle CBD is 40°.

Learn more about circles here: https://brainly.com/question/11833983

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[tex]\bf P(\stackrel{x}{1},\stackrel{y}{-3})\qquad \qquad cot(\theta )=\cfrac{\stackrel{\stackrel{adjacent}{x}}{1}}{\stackrel{\stackrel{opposite}{y}}{-3}}[/tex]

The value of Cotangent or cot is: [tex]cot \;\theta= \frac{1}{-3}[/tex]

Trigonometric ratios are the ratios of the length of sides of a triangle.

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.

Given ordered pair P(1, -3).

As we know that Cotangent is ratio of base : perpendicular i.e.,

adjacent of x: opposite y

So, [tex]cot \;\theta= \frac{1}{-3}[/tex]

Now, Hypotenuse = [tex]\sqrt{base^{2}+perpendicular^{2} }[/tex]

                              = [tex]\sqrt{1^{2} + (-3)^{2}} =\sqrt{10}[/tex]

and,

[tex]sec\;\theta= \frac{\sqrt{10} }{1} \\cosec\;\theta =\frac{\sqrt{10} }{(-3)}[/tex]

Learn more about Trigonometric ratios here:

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Answer:

64

Step-by-step explanation:

Answer:

The second graph represents the system of inequalities

[tex]y\geq-3x + 1\\\\y\leq\frac{1}{2}x + 3\\[/tex]

Step-by-step explanation:

Let us first consider how the graphs of the inequalities will look like.

For the inequality  [tex]y\geq-3x + 1[/tex] all the values "above" the line [tex]y=-3x + 1[/tex] are its solutions (because of the [tex]\geq[/tex] sign).

And for the inequality [tex]y\leq\frac{1}{2}x + 3[/tex] all the values the "below" the line [tex]y=\frac{1}{2}x + 3[/tex]  are its solutions  (because of the [tex]\leq[/tex] sign).

Together these system of inequalities have the solutions as shown in the second figure.

Answer:

The second graph.

Yr Welcome

Step-by-step explanation:

Answer:

Step-by-step explanation:

6/4=1.5 (price per can)

10/8=1.25 (price per can)

1.25 is cheaper than 1.5

the second one is the better buy

The better buying option is 8 cans for $10 and this can be determined by using the unitary method and the given data.

Given :

4 cans for $6 or 8 cans for $10.

The following steps can be used in order to determine the correct buying option:

Step 1 - The unitary method can be used in order to determine the better buying option.

Step 2 - If the value of 4 cans is $6 then the value of 1 can is:

4 cans = $6

1 can = [tex]\rm \dfrac{6}{4}[/tex]

= $1.5

Step 3 - If the value of 8 cans is $10 then the value of 1 can is:

= $1.25

So, the best buying option is 8 cans for $10.

For more information, refer to the link given below:

https://brainly.com/question/12116123

Answer:

The area of a sector GHJ is [tex]36.3\ cm^{2}[/tex]

Step-by-step explanation:

step 1

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=8\ cm[/tex]

substitute

[tex]A=\pi (8)^{2}[/tex]

[tex]A=64\pi\ cm^{2}[/tex]

step 2

Remember that the area of a complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 65 degrees

[tex]\frac{64\pi}{360}=\frac{x}{65}\\ \\x=64\pi (65)/360[/tex]

Use [tex]\pi =3.14[/tex]

[tex]x=64(3.14)(65)/360=36.3\ cm^{2}[/tex]

Answer:

[tex]\$7,204.85[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$6,000\\ r=0.0183\\n=365[/tex]  

substitute in the formula above  

[tex]A=\$6,000(1+\frac{0.0183}{365})^{365*10}=\$7,204.85[/tex]  

The investment will be worth approximately $6,960.47 after 10 years.

To solve this problem, we can use the formula for compound interest, which is:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:

-  A  is the amount of money accumulated after n years, including interest.

-  P  is the principal amount (the initial amount of money).

-  r  is the annual interest rate (decimal).

-  n  is the number of times that interest is compounded per year.

-  t  is the time the money is invested for, in years.

 Given:

[tex]- \( P = $6,000 \) \\-( r = 1.83\% = 0.0183 \) (as a decimal) \\- \( n = 365 \) (since the interest is compounded daily) \\- \( t = 10 \) years[/tex]

Plugging these values into the compound interest formula, we get:

[tex]\[ A = 6000 \left(1 + \frac{0.0183}{365}\right)^{365 \times 10} \][/tex]

Now, we calculate the value inside the parentheses first:

[tex]\[ \frac{r}{n} = \frac{0.0183}{365} \approx 0.000050137 \][/tex]

[tex]\[ 1 + \frac{r}{n} = 1 + 0.000050137 \approx 1.000050137 \][/tex]

[tex]\[ (1.000050137)^{365 \times 10} \] \[ = (1.000050137)^{3650} \][/tex]

Using a calculator or a software tool to compute this value, we find:

[tex]\[ (1.000050137)^{3650} \approx 1.1600785 \] \[ A = 6000 \times 1.1600785 \approx 6960.47 \][/tex]

Therefore, the investment will be worth approximately $6,960.47 after 10 years.

Answer:

The correct answer is the first one listed.

Step-by-step explanation:

First you have to determine what the equation for that circle is.  The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex] where h and k are the coordinates of the center and the radius is squared.  Using the given info, our equation will look like this:

[tex](x-5)^2+(y+1)^2=25[/tex]

Now we use the coordinates given and plug in 2 for x and 3 for y and do the math and see if the 2 sides are equal.

[tex](2-5)^2+(3+1)^2=25[/tex]

and 9 + 16 = 25, right?  So that's how you can check the other coordinate pairs to verify that they DON'T work out!

The point Y(5, -4) lies on the circle with center O(5, -1) and radius 5, as per the distance formula and the equation of a circle.

To determine which point lies on the circle with center O(5, -1) and radius 5, we can use the distance formula to check if any of the given points are exactly radius 5 units away from center O. The distance formula, which is derived from the Pythagorean theorem, states that the distance between two points (x₁, y₁) and (x₂, y₂) in a 2-dimensional plane is given by √[(x₂ - x₁)² + (y₂ - y₁)²].

Thus, if a point (x, y) is on the circle, the following must be true: (x - 5)² + (y + 1)² = 52.

Checking for each point:

For point V(2, 3), we find (√[(2 - 5)² + (3 + 1)²]) which does not equal 5.

For point X(-3, -2), we calculate (√[(-3 - 5)² + (-2 + 1)²]) which does not equal 5.

For point Y(5, -4), we get (√[(5 - 5)² + (-4 + 1)²]) which equals to 5, hence Y lies on the circle.

For point Z(6, 9), we determine (√[(6 - 5)² + (9 + 1)²]) which does not equal 5.

Therefore, the point Y(5, -4) is on the circle.

Using the numbers in the given equation:

a =-2, b = 6 and c = -5

The vertex form is written as : a(x+d)^2 + e

we need to find d and e:

d = b/2a = 6/2(-2) = -3/2

e = c-b^2/4a = -5 - 6^2/4(-2) = -1/2

Now substitute the letters for their values in the vertex form formula above:

-2(x-3/2)^2 -1/2

The vertex is (3/2, -1/2)

2. The formula begins with a negative number ( -2) so the Parabola opens downwards.

3. To find the intercept replace x with 0 and solve for y:

the intercept is (0,-5)

Answer:

Step-by-step explanation:

The first thing you should do is get a graph of this quadratic. The graph will answer the location of the vertex and it will also tell you if it opens up or down. It (finally) shows the intercept although that is easily found.

Question 3

You find the intercept by making x = 0

When you do that y becomes

y = - 2(0)^2 + 6(0) - 5

y = 0 - 5

y = - 5

Question 2

This too, is just a visual answer. Just look at the number in front of x^2

y = ax^2

if a < 0 then the graph always opens down

if a > 0 then the graph always opens up

In this case, y = - 2x^2. The graph opens down. The 6x + 5 does not affect the answer at all.

Question 1

This part is the tricky part and you have to complete the square.

Put brackets around the first 2 terms.

y = ( - 2* x^2 + 6x ) - 5    Pull out the common factor of - 2

y = -2 (x^2 - 3x) - 5         divide - 3 by 2 and square. Add inside the brackets.

y = -2(x^2 - 3x +  (3/2)^2  ) - 5   Add 2 times the squared amount outside the brackets.

y = -2(x^2 - 3x + (3/2)^2 ) - 5 + 2*(3/2)^2

y = -2(x^2 - 3x  + 9/4)     - 5 + 9/2     Show what is inside the brackets as a perfect square. Combine - 5 and 9/2

y = -2(x - 3/2)^2 - 5 + 4.5

y = -2(x - 3/2)^2 - 0.5

The vertex should be at (3/2, - 0.5)

Answer: The graph confirms (3/2, - 0.5) as the vertex.

Answer:

w = 13.3, x= 10.3

First option is correct.

Step-by-step explanation:

In triangle ABC, we have

[tex]\tan42^{\circ}=\frac{AB}{BC}\\\\\tan42^{\circ}=\frac{12}{w}\\\\w=\frac{12}{\tan42^{\circ}}\\\\w=13.3[/tex]

Now, in triangle ABD

[tex]\tan27^{\circ}=\frac{AB}{BD}\\\\\tan27^{\circ}=\frac{12}{w+x}\\\\13.3+x=\frac{12}{\tan27^{\circ}}\\\\13.3+x=23.6\\\\x=10.3[/tex]

Thus, we have

w = 13.3, x= 10.3

First option is correct.

Answer:

A = $12831.8

Step-by-step explanation:

We know that the formula for compound interest is given by:

[tex]A=P(\frac{1+r}{n} )^{nt}[/tex]

where [tex]A[/tex] is unknown which is the amount of investment with interest,

[tex]P=9000[/tex] which is the initial amount,

[tex]r=12/100=0.12[/tex] is the interest rate,

[tex]n=4[/tex] which is the number of compoundings a year; and

[tex]t=3[/tex] which is the number of times that interest is compounded per unit t.

So substituting these values in the above formula to find A:

[tex]A=P(\frac{1+r}{n} )^{nt}[/tex]

[tex]A=9000(\frac{1+0.12}{4} )^{(4.3)}[/tex]

[tex]A = 9000(1 + 0.03)^{12}[/tex]

A = $12831.8

Answer:

The amount after 3 years = $12381.85

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t - number of times compounded yearly

n  number of years

To find the amount

Here,

P = $9000.00, n = 3 years, t = 4, n = 3 and R = 12% = 0.12

A = P[1 +R/n]^nt

 = 9000[1 + 0.12/4]^(3 * 4)

 = 9000[1 + 0.03]^12

 = 12831.85

Therefore the amount after 3 years = $12381.85

Answer:

Part 1) Sphere The surface area is equal to [tex]SA=196\pi\ m^{2}[/tex] and the volume is equal to [tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]

Part 2) Cone The surface area is equal to [tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex] and the volume is equal to [tex]V=\frac{112}{3}\pi\ units^{3}[/tex]

Part 3) Triangular Prism The surface area is equal to [tex]SA=51.57\ mm^{2}[/tex] and the volume is equal to [tex]V=17.388\ mm^{3}[/tex]

Step-by-step explanation:

Part 1) The figure is a sphere

a) Find the surface area

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter

substitute

[tex]SA=4\pi (7)^{2}[/tex]

[tex]SA=196\pi\ m^{2}[/tex]

b) Find the volume

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (7)^{3}[/tex]

[tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]

Part 2) The figure is a cone

a) Find the surface area

The surface area of a cone is equal to

[tex]SA=\pi r^{2} +\pi rl[/tex]

we have

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

[tex]h=7\ units[/tex]

Applying Pythagoras Theorem find the value of l (slant height)

[tex]l^{2}=r^{2} +h^{2}[/tex]

substitute the values

[tex]l^{2}=4^{2} +7^{2}[/tex]

[tex]l^{2}=65[/tex]

[tex]l=\sqrt{65}\ units[/tex]

so

[tex]SA=\pi (4)^{2} +\pi (4)(\sqrt{65})[/tex]

[tex]SA=16\pi +4\sqrt{65}\pi[/tex]

[tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex]

b) Find the volume

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

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

[tex]h=7\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (4)^{2}(7)[/tex]

[tex]V=\frac{112}{3}\pi\ units^{3}[/tex]

Part 3) The figure is a triangular prism

a) The surface area of the triangular prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the prism

Find the area of the base B

[tex]B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2.7*3=8.1\ mm[/tex]

we have

[tex]L=5.6\ mm[/tex]

substitute the values

[tex]SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}[/tex]

b) Find the volume

The volume of the triangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular base

L is the length of the prism

we have

[tex]B=3.105\ mm^{2}[/tex]

[tex]L=5.6\ mm[/tex]

substitute

[tex]V=(3.105)(5.6)=17.388\ mm^{3}[/tex]

Answer:

[tex]\large\boxed{a=10.92\ and\ b=14.52}[/tex]

Step-by-step explanation:

Step 1:

Calculate a measure of angle C.

We know: The sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

[tex]m\angle C+43^o+115^o=180^o[/tex]

[tex]m\angle C+158^o=180^o[/tex]          subtract 158° from both sides

[tex]m\angle C=22^o[/tex]

Step 2:

Use the law of sines to calculate the length a:

[tex]\dfrac{6}{\sin22^o}=\dfrac{a}{\sin43^o}[/tex]

[tex]\sin22^o\approx0.3746\\\\\sin43^o\approx0.6820[/tex]

[tex]\dfrac{6}{0.3746}=\dfrac{a}{0.6820}[/tex]          multiply both sides by 0.6820

[tex]a\approx10.92[/tex]

Step 3:

Use the law of sines to calculate the length b:

[tex]\dfrac{6}{\sin22^o}=\dfrac{b}{\sin115^o}[/tex]

[tex]\sin22^o\approx0.3746[/tex]

To calculate sin115°, use the formula:

[tex]\sin(180^o-\theta)=\sin\theta[/tex]

[tex]\sin115^o=\sin(180^o-65^o)=\sin65^o[/tex]

[tex]\sin65^o\approx0.9063[/tex]

[tex]\dfrac{6}{0.3746}=\dfrac{b}{0.9063}[/tex]         multiply both sides by 0.9063

[tex]b\approx14.52[/tex]

Answer:

76.9 in²

Step-by-step explanation:

The area (A) of any sector in a circle is

A = area of circle × fraction of circle

   = πr² × [tex]\frac{77}{360}[/tex]

   = π × 10.7² × [tex]\frac{77}{360}[/tex]

   = [tex]\frac{10.7^2(77)\pi }{360}[/tex] ≈ 76.9 in²

Answer:

The most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.

Step-by-step explanation:

Consider the provided information.

A random sample of 50 subscribers to Auto Wheel magazine about the number of cars that they own. Of the subscribers surveyed, 15 own fewer than 2 vehicles.

We need to find the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles if there are 340 subscribers.

Here, the sample used is 50 and the population size is 340.

Now use the formula to find the reasonable estimate.

[tex]\frac{Part}{Sample}=\frac{x}{Population}[/tex]

Substitute the respective values in the above formula as shown;

[tex]\frac{15}{50}=\frac{x}{340}[/tex]

[tex]\frac{15}{50}\times 340=x[/tex]

[tex]x=3\times 34[/tex]

[tex]x=102[/tex]

Hence, the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.

Let's call the left side of this tirangle y and downside z.

3² + 6² = y²

y² = 45

y² + z² = (3 + x)²

45 + z² = 9 + 6x + x²

x² + 6² = z²

45 + x² + 6² = 9 + 6x + x²

45 + x² + 36 = 9 + 6x + x²

45 + 36 - 9 = 6x

72 = 6x

x = 12

Answer:

The second graph.

Step-by-step explanation:

The second dotted graph represents viable values because the weights of cans are discrete data. We deal with a whole number of cans ( not parts of a can) so a continuous graph like the first one is not appropriate here.

Answer:

Step-by-step explanation:

The second graph represents viable values to these variables, because the independent variable, which it's the horizontal axis, represents cans of tomato past, and that it's only represented by a discrete variables, this means that cans can be counted only in natural numbers 1, 2, 3, 4, 5, ... and the second graph represent these discrete values, because it shows points for each can.

On the other hand, the first graph represents a continuous variable, which admits decimal numbers that cannot represent cans, because we cannot say "I have 2.345 cans", it's not possible, because each can is a whole, 1 can, 2 cans, and so on.

Therefore, the second graph is the viable.

Answer:

[tex]\boxed{ \text{B. }\frac{2}{ 3}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding sides of the two pyramids.

The ratio of the areas is the square of the scale factor.

[tex]\frac{A_{1}}{ A_{2}} =C^{2}\\ \\\frac{48 }{108} = C^{2}\\\\ \frac{4}{9} = C^{2}\\\\ C = \frac{2}{3}\\\\[/tex]

The scale factor is [tex]\boxed {\frac{2}{3}}[/tex].

Answer:

[tex]A'(10,-5)\\\\B'(15,20)\\\\C'(-35,10)[/tex]

Step-by-step explanation:

You know that the triangle ABC has these points:

A(2, -1), B(3, 4), C(-7, 2)

If the triangle ABC is dilated by a factor of 5 to create the triangle A'B'C', you can find the coordinates of this new triangle by multiplying by 5 the coordinates of the triangle ABC given.

Therefore, the coordinates of the triangle A'B'C' are:

[tex]A'=(2(5),\ -1(5))=(10,-5)\\\\B'=(3(5),\ 4(5))=(15,20)\\\\C'=(-7(5),\ 2(5))=(-35,10)[/tex]

Answer:

70%

Step-by-step explanation:

60+80=140

140/2=70

Answer:

when x=3, the answer is

f(3)=36

Step-by-step explanation:

You need to plug in 3 for x and then solve. :)

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Answer:

18

Step-by-step explanation:

Wherever you put a 3 in for the x's that are on the right.

f(x) = 2x^2 - 3x + 9

f(3) = 2*3^2 - 3(3) + 9

f(3) = 2*9 - 9 + 9

f(3) = 18

[tex]\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k[/tex]

[tex]\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z[/tex]

By the divergence theorem,

[tex]\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV[/tex]

I'll assume a sphere of radius [tex]r[/tex] centered at the origin, and that [tex]W[/tex] is bounded below by the plane [tex]z=0[/tex]. Convert to spherical coordinates, taking

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

Then

[tex]\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4[/tex]

Final answer:

The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.

Explanation:

The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.

To solve this, we need to apply the divergence theorem, which states that the integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by that surface. In this case, the volume is the upper half of the sphere and the divergence of the vector field is div(f) = ∂f/∂x + ∂f/∂y + ∂f/∂z.

By evaluating the divergence of the vector field and simplifying the expression, we can then use the divergence theorem to convert the surface integral into a volume integral, which can be evaluated using appropriate coordinates.

Answer:

[tex]a=\sqrt{c^2-b^2}[/tex]

Step-by-step explanation:

Subtract b² from both sides of the equation.

a² = c² -b²

Now, take the square root of both sides of the equation.

a = √(c² -b²)

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Please note that when writing the square root (or any function) in plain text, it only applies to the first operand after the function name. That is ...

square root [ ] - [ ]

is evaluated as ...

(square root [ ]) - [ ]

If you want an entire expression to be considered to be "under the radical", then it must be enclosed in parentheses:

square root ([ ] -[ ])

This is the interpretation demanded by the Order of Operations. It can only be modified by using parentheses.