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The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.

Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.

Applying the distance formula, we have:

BC = √[(8−12)² + (10−13)²]

BC = √(−4)² + (−3)²]

BC = √(16+9)

BC = √25

BC = 5 units

Applying the scale factor:

Length of C'B' = 3(5) = 15 units.

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The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters

A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.

To find the distance, we will have to determine how much 1:4 represents in the total distance.

Total distance = 25 meters - 3 metes = 22 meters

Thus; 22 * 1/ 5 = 22/5 = 4.4

However, we also know they are three meters behind the start.

Thus, the meter mark at which Ario will be when Miguel starts the race

4.4 + 3 =7.4 meters

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Step-by-step explanation:

"integral" means here that the factors in the polynomial are integers.

we have 3 zeros.

the least degree of a polynomial with 3 zeros is 3.

and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).

or 4 zeros (at least 4th degree).

it in general n zeros (at least nth degree).

constructing this out of the given zeros is easy.

what happens, when I multiply something by 0 ? the total result will be 0.

and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.

what expression in x turns 0, when x = -1/3 ?

well : x + 1/3 or with integers 3x + 1 (multiplied by 3)

and for x = 2/3 ?

x - 2/3 or with integers 3x - 2

and for x = -1/4 ?

x + 1/4 or with integers 4x + 1

so, our polynomial function (of at least 3rd degree) is then

(3x + 1)(3x - 2)(4x + 1)

basically this could be already the result, depending on what your teacher wants.

for the fully extended form we need to do the multiplications :

(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2

(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =

= 36x³ - 3x² - 11x - 2

the requested polynomial function is

f(x) = 36x³ - 3x² - 11x - 2

Answer:

5*8 = 40

Step-by-step explanation:

2(3) -1 = 5

3 +5 = 8

area = 5*8 = 40

Answer:

formula-Area=l×b

Step-by-step explanation:

Length (l)=2x-1

Breadth(b)=x+5

We know that,

Area(A)=l×b

=(2x-1)×(x+1)

=(2×3-1)×(3+1)

=5×4

=20cm*2*

Answer:

1) Equation's:

2) Number of guest and the charge:

Part 1

Turn sentences into equation's (Let 'y' be total cost and x per meal) :

(i) charges $500 and $15 per meal

(ii) charges $350 and $18 per meal

Part 2

            y  =  y

500 + 15x = 350 + 18x

18x - 15x = 500 - 350

3x = 150

x = 150/3

x = 50

Charge at guest's 50 meal:

y = 500 + 15(50)

y = $1250

Point : (50, 1250)

If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.

Given Biologist catches and tags 32 bass, when sample of 55 bass is taken  then 5 are found tagged.

Population is basically number of living thing exists in a particular area.

Number of bass which are tagged in lake=32

Sample size=55

Number of bass found tagged=5

means percentage of tagged bas found is 5/32*100=1.6%

We have to calculate number of times 5 is multiplied to get 32 which is 6.4.

Number of bass in the lake=55*6.4

=352 basses.

Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.

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The distance would be 231 miles.

Speed can be calculated as the ratio of distance traveled to the time taken

Given information;

Time taken = 3 hours 30 minutes

Speed = 70 mph

We know that,

Distance = speed x time

Distance = 70 x 3.30

Distance = 231 miles

Thus, the distance would be 231 miles.

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Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

The dimensions in feet are given as follows:

Hence the area in square feet is given by:

A = 4.5 x 3.75 = 16.875 ft².

Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.

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Answer:

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

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.

Given 3y>2x+12 and 2x+y<=-5.

We are given two inequalities  3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.

2x-3y<-12

2x+y<=-5

Now assume these are equalities

2x-3y=-12

2x+y=-5

now subtract 2 from 1

2x-3y-2x-y=-12+5

-4y=-7

y=7/4

put the value of y in 2x-3y=-12

2x-3(7/4)=-12

2x-21/4=-12

2x=-12+21/4

2x=(-48+21)/4

2x=-27/4

x=-27/8

Now put the signs between the values

x<-27/8

y<7/4.

Hence the solution of the inequalities 3y > 2x + 12

2x + y ≤ -5 is the value of x<-27/8 and y<7/4.

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Answer:

43.2 m square is ur answer .

Answer:

43.2 m^2

Step-by-step explanation:

The area of a rectangle is the width times the length.

Area = (9.6 m)*(4.5 m)

Area = 43.2 m^2

1 atom of C has a mass of 12 amu (atomic mass unit).

1 atom of O has a mass of 16 amu.

1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.

C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.

Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.

Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.

Given we have, Initial amount of milk is [tex]2[/tex] liters.

The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.

Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters

[tex]\frac{3}{2}[/tex] liters used in half:

[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.

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Answer:

2x³+3x²-8x+3

Step-by-step explanation:

So we know x=½,x=1 and x=-3

Then (2x-1)(x-1)(x+3) are the factors

(2x-1)[(x²+3x-x-3)]

(2x-1)[(x²+2x-3)]

2x³+4x²-6x-x²-2x+3

2x³+3x²-8x+3

The side of the edge of the cube is 7. 07cm

Given that a  diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.

Let's find the edge of the face

Note that the face of the cube is in the shape of square .

The diagonal of the face is 10 cm.

The formula for  diagonal of square = [tex]\sqrt{2a}[/tex]

a is the side of the square face

We have that,

[tex]\sqrt{2a} = 10[/tex]

Make 'a' subject of formula

a = [tex]\frac{10}{\sqrt{2} }[/tex]

Find the surd of the equation, we have

a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

a = [tex]\frac{10\sqrt{2} }{2}[/tex]

a = [tex]5\sqrt{2}[/tex]

a = [tex]7. 07cm[/tex]

Thus, the side of the edge of the cube is 7. 07cm

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Answer:

A. 100

Step-by-step explanation:

Angle 1 = 40

Angles 1 and 2 are equal. Add the angles 1 and 2 together.

40+40=80

The last step is to subtract 80 from 180.

180-80=100.

∠3=100

Hope this helps!

If not, I am sorry.

The ratio of orange juice to apple juice to grape juice is 6: 3 : 2

A ratio says how much of one thing there is compared to another thing.

Therefore, we are comparing the numbers of juice produce by a bottling company.

Hence,

number of orange juice = 24

number of apple juice = 12

number of grape juice = 8

Therefore, the ratio of orange juice to apple juice to grape juice is as follows:

ratio = 24 : 12 : 8

divide through by 4

ratio = 6: 3 : 2

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Answer:

the answer is (x )

math  way  helps

Step-by-step explanation:

The requried function of function f(g(x)) is given as x² + 6x +5.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given functions,
f(x)=x²−4 and g(x)=x+3

In order to form a function of function we have to function g(x) in function f(x)

Now,

f(g(x)) =  f(x)=(g(x))²−4

f(g(x)) =  f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5

Thus, the requried function of function f(g(x)) is given as x² + 6x +5.

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Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.

Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.

The most simple example is given by:

[tex]f(x) = \frac{1}{x}[/tex].

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Answer: Reciprocal

Step-by-step explanation:

Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.

The price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

We know that the original price of the light is $375.

This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98

Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

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Answer:

All of these definitions are correct.

Answer:

Graph is below

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The value of x° + y° is 216°

Note that the shape is a regular pentagon

Sum of angle in a pentagon = 540

Angle on each side = 108°

x = 108°

y = 108°

x° + y° = 108 + 108

x° + y° = 216°

Thus, the value of x° + y° is 216°

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The value of x in the equation (x - 5)² = 25 is 10.

(x - 5)² = 25

Take the square root of both sides

Therefore,

√(x - 5)² = √25

x - 5 = 5

add 5 to both sides

x - 5 + 5 = 5 + 5

x = 10

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[tex]f(x)=x(x-3)(x+3)[/tex]

The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.

Given  function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].

Function is a relationship between two or more variables expressed in equal to form.

The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.

The polynomial function is given as:

[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]

factorize the above function

[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]

Now put the function f(x) equal to zero.

f(x)=(2x+9)(5x-3)(x-1)

split the function means put all the expressions equal to zero as under:

(2x+9)(5x-3)(x-1)=0

solve each for the value of x

x=-9/2,x=3/5,x=1

Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.

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Answer:

Step-by-step explanation:

Answer:

It is NOT a function

Step-by-step explanation:

No it is NOT a function.....each value of x can only have one y value....

  this has two y values for   x = 2 :    y = 2 and 4    therefore not a function

361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;

Volume of candy bag = 528 in.³

Number of lollipop candies the bag can hold = 361 candies

Number of gummy bear candies the bag can hold = 697 candies

Therefore;

[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]

[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]

Which gives the following equation;

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Answer:

l/361 + g/697= 1

Khan Academy Sat Practice

Answer:

Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

Parallel: [tex]y=3x-7[/tex]

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]