The figure below is dilated by a factor of centered at the origin. Plot the resulting
image.
Click twice to plot a segment.
Click a segment to delete it.

Answer:

[tex]3a^4b^2-2a^2b+9a[/tex]

Step-by-step explanation:

Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:

[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]

We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:

[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]

Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:

[tex]3a^4b^2-2a^2b+9a[/tex]

Answer:  Choice C

[tex]64m^3-32m^2+43m-15[/tex]

==================================================

Explanation:

Multiply out the expressions using the distribution rule as shown below.

[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]

I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.

Footnotes:

Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

Given that,

Luke asserts that since the shape is constant, two circles are always isometric.

We have to say is he accurate.

The answer is

No, an isometry keeps the size and shape intact.

Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.

Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

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The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.

Given that,

On one particular day, a waitress served 12 grilled salmon dinners and 19 ribeye steak dinners for a total of $581.52. She made $581.59 on another day by selling 24 ribeye steak dinners and 6 grilled salmon entrees.

We have to find what was the price of each kind of dinner.

So,

We take R as a ribeye steak dinner and S as grilled salmon dinners.

We get,

19R+12S=$581.52 ---> equation(1).

24R+6S=$581.59 ----> equation(2).

Now Take the equation (2)

24R+6S=$581.59

6S=$581.59-24R

Multiply 2 on both sides of equation.

12S=$1163.18-48R

Now take the equation(1)

19R+12S=$581.52

Take the 12S as 12S=$1163.18-48R

19R+$1163.18-48R=$581.52

-29R=$581.52-$1163.18

-29R=-581.66

29R=581.66

R=581.66/29

R= $20.05

Now substitute R in 12S=$1163.18-48R

We get,

12S=$1163.18-48($20.05)

12S=$1163.18-962.4

12S=200.78

S=200.78/12

S=$16.74

Therefore, The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.

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Answer:

3y + 4.1

Step-by-step explanation:

You can't add unlike terms, so you collect like terms:

9y - 6y + 4.1

= 3y + 4.1

Answer:

Step-by-step explanation:

You can use proportions to solve this.

You are paying $116.64 for 3 gallons of paint, so you could write this as:

\frac{116.64}{3}

Since the question is asking for price PER CUP, you want to convert 3 gallons to cups. 3 gallons = 48 cups. So now you can rewrite this as:

\frac{116.64}{48 cups}

In order to find the cost per cup, you can set up a proportion that solves for the price, x

\frac{116.64}{48 cups}  = \frac{x}{1 cup}

Solve for x by cross multiplying:

48x = 116.64

x = $2.43

It costs $2.43 per cup of paint

a. The smallest number of M & M's possible is 14.

b. The number of green is 24.

c. The ratio of green to yellow to red in 6: 15: 25.

a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:

= (2 × 2) + (2 × 5)

= 4 + 10

= 14

b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:

= 2 / (2 + 5) × 84

= 2/7 × 84

= 24 green

c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:

= Green : Yello : Red

= 24 : 60 : 100

= 6 : 15 : 25

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Answer:

y=9x

Step-by-step explanation:

For these x's and y's, we can notice that y is always equal to 9 times the value of x. 0 equals 9 * 0, 9 equals 9 * 1, 18 equals 9 * 2, 27 equals 9 * 3, and 36 equals 9 * 4.

We have just shown that y equals 9 times x, which is just y=9*x, or y=9x.

Answer:

-32

Step-by-step explanation:

-(4)^2 - -2^4 = -16 - 16 = -32

Answer:

A

Step-by-step explanation:

g(x) = f(x) + 3

Answer: 5x2x2x3x3 is the answer to your question

Answer: c

Step-by-step explanation:

The person is overwieght as his BMI is 31.00 (approx)

What is Proportion?

In general, proportion refers to a part, share, or quantity assessed in comparison to a total. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Solution:

Since, BMI is directly proportionate with weight and indirectly proportionate with square of height, we need to use a constant to make proportion to an equation.

According to the question,

BMI of a person who weighs 180 pounds and is 5 feet tall is 35.15.[tex]BMI = k*weight/height^{2}[/tex]

here, k is any constant value

35.15 = k*180/(60*60)

(35.15 * 3600)/180 = k

k = 703

Calculating BMI of a person weighing 210 pound and is 5 feet 9 inch tall.

First of all we need to convert 5 feet 9 inches into inches

5 feet = 60 inches

so, 5 feet 9 inch means 69 inches

BMI = 210*703/(69*69)

BMI = 31.00 (after rounding off)

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Answer:

Obtuse Angles

Step-by-step explanation:

Both < 3 and < 6 are visibly over 90° and less than 180°, so both are obtuse.

Examining the given graph the number of computers infected in

The graph shows that the function is an exponential function

represented as

The starting term of the function  f(x) = 4^t is 1, and base is 4

f(x) = number of computer infected

t = time in hours

90 minutes in hours

90 / 60 = 1.5 hours

for t = 1.5 hours

f(x) = 4^1.5

f(x) = 8

for t = 6 hours

f(x) = 4^6

f(x) = 4096

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The perimeter of the resulting hexagon is 60 meters.

In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

The perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):

p' = k · p

If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:

p' = (4 / 3) · (45)

p' = 60

The resulting hexagon has a perimeter of 60 meters.

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Answer:

[tex]\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}[/tex]

Step-by-step explanation:

[tex]\sf 3\left(s+1\right)-8=6s\left(2-4\right)[/tex]

Expand ( Apply the Distributive Property):-

[tex]\sf 3s-5=-12s[/tex]

Add 5 to both sides:-

[tex]\sf 3s-5+5=-12s+5[/tex]

Simplify:-

[tex]\sf 3s=-12s+5[/tex]

Add 12s to both sides:-

[tex]\sf 3s+12s=-12s+5+12s[/tex]

Simplify:-

[tex]\sf 15s=5[/tex]

Divide both sides by 15:-

[tex]\sf \cfrac{15s}{15}=\cfrac{5}{15}[/tex]

Simplify:-

[tex]\sf s=\cfrac{1}{3}[/tex]

___________________

Hope this helps!

Have a great day! :)

The key features of the graph of the exponential function are given as follows:

The y-intercept of a function gives the value of the function when it crosses the y-axis, that is, when x = 0, hence it is the initial number of mammals, which is of 120.

As x goes to infinity, the number of mammals will never be of zero but it will get very close to zero, hence the line y = 0 is the horizontal asymptote of the graph.

The graph is shown by the image given at the end of the answer.

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In the given coordinate plane, based on the given dilation the line r has slope 8 and coordinate (0,8)

Dilation:

Dilation refers the ratio of the given line to line by the scale factor.

Given

In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3).

Here we need to find the the slope and y-intercept of line r.

Here we know that scale factor is 3.

Let us consider the slope of the line r will not change and the intercept is the addition of their ordinate will be.

So, it can be written as,

=> Intercept = 5 + 3

=> Intercept = 8

Therefore, the line r has slope 8 and coordinate (0.8).

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with 100 flips, the outcome is very likely to be 45 heads or even less.

just because you have a 50% chance of getting heads, does not necessarily mean that you will get heads at exactly 50%.

100 coin flips will not always produce a 50-50 outcome of heads or tails. This is due to the fact that random events, while predictable in the long run, are not 100% predictable in small cases. For example, if we flipped a fair coin a quadrillion times, the variability in the outcomes caused by the coin's randomness would amount to a fractional value so small that calculators might even round the percentage of heads to 50%. However, with 100 flips, the outcome is very likely to be 45 heads or even less.

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Answer:

no, h=anything greater than 12

Step-by-step explanation

Answer:

No. It is false.

Step-by-step explanation:

h - 2 > 10; h = 12

Substitute 12 in place of h.

12 - 2 >? 10

Simplify.

10 >? 10

10 is NOT > 10

10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.

Answer:

3/32-pound cheese in 1 serving

Step-by-step explanation:

(3/8)/4=3/32 or 0.09375 lbs

The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].

What are Exponents?

What are the Laws of Exponents?

There are major seven Laws of Exponents as follows:

From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex]    -----(1)

Here, we can use the power of a power rule to simplify the expression.

The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]

Solving expression (1) using the power of a power rule, we get

[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

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Well the domain is the number of tickets and the range is the cost for those tickets.

So x = 1 when y = 125 (1 ticket is 125 dollars). Here is a reasonable domain and range comparision:

x = 1 , y = 125

x = 2, y = 250

x = 3, y = 375

x = 4, y = 500

ect...

The lower limit of the domain is 0 because you cannot have less than 0 tickets.

I hope this helps!

In the given geometric sequence

a) The expression of the common ratio r = -6 and (m+8)/2

b) The possible value of m = -28

c) The possible value of r = -6

The geometric sequence is

-1 , 6, m+8

The the common ratio = second term / first term

= 6 / -1

= -6

The common ratio = third term /  second term

= (m+8)/6

The two expressions of common ratio is -6 and (m+8)/6

Part b

The third term = second term × common ratio

= 6 × -6

= -36

Then,

m +8  = -36

m = -36 + 8

m = -28

The possible value of m = -28

Part c

The possible value of r = -6

Hence, in the given geometric sequence

a) The expression of the common ratio r = -6 and (m+8)/2

b) The possible value of m = -28

c) The possible value of r = -6

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Answer:

A. Yes, they have the same slope and a different y-intercept.

Step-by-step explanation:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Rearrange 3x + y = 6 to y = mx + c form.

y = -3x + 6

Parallel lines have the same slope.

Since slope of both lines is -3, the lines are parallel.

The x value for each of the equation.

1)The x is 10 when the equation is 8=x-2

2)If x+2=-2, then the value of x is -4.

3)If 2=x+8, then the value of x is -6.

4)The x is -10 when the equation is x+8=-2

Given that,

The given equation are

1) 8=x-2

2) x+2=-2

3) 2=x+8

4)x+8=-2

We have to find the x value for each of the equation.

Take the equations,

1) 8=x-2

Adding 2 on both sides

8+2=x-2+2

10=x

The x is 10 when the equation is 8=x-2

2) x+2=-2

Adding 2 on both sides

x+2+2=-2+2

x+4=0

Adding -4 on both side

x+4-4=0-4

x=-4

If x+2=-2, then the value of x is -4.

3) 2=x+8

Subtracting 8 on both sides

2-8=x+8-8

-6=x

x=-6

If 2=x+8, then the value of x is -6.

4)x+8=-2

Adding -8 on both sides

x+8-8=-2-8

x=-10

The x is -10 when the equation is x+8=-2

Therefore, the x value for each of the equation.

1)The x is 10 when the equation is 8=x-2

2)If x+2=-2, then the value of x is -4.

3)If 2=x+8, then the value of x is -6.

4)The x is -10 when the equation is x+8=-2

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The mean of this distribution is 0.55

The standard error of this distribution is 0.0384

We have the following:

p=0.55

sample size, n=168

Mean of distribution:

Mean=true proportion of voters who support a restaurant

Mean=p=0.55

Hence, the mean of distribution is 0.55

Standard error of the distribution:

[tex]=\sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]=\sqrt{\frac{0.55(1-0.55)}{168} }[/tex]

=0.0384

Hence, the standard error is 0.0384

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The questions was incomplete, the complete question is given below:

Suppose the true proportion of voters in the county who support a restaurant tax is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 168.

What is the mean of this distribution?

What is the standard error of this distribution?