A dilation produces a smaller figure. Which is a possible scale factor?

Answer:

If KE = OS then we can deduce that the trapezoid is constructed of 3 equilateral triangles and thus we can easily work out the angles.

OSK = 60

SKE = 120

KEP = 120

EPO  = 60

We can also easily work out the perimeter since we can deduce that PE = SK = KE and thus the perimeter is 5 * 8 = 40

The measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively.  While the perimeter of EPSK is 40 units.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

Given KE=OS=8, but OS is the radius of the circle, therefore, it can be written as,

OS = OP = KE = OK = OE = radius of the circle = 8 units.

Since in ΔOEK all sides are equal it is an equilateral triangle therefore, the measure of the angle ∠EOK is 60°.

As the measure of the angle, ∠EOK is 60°, the measure of the angle, ∠KOS and ∠EOP will be 60° each.

Also, in ΔSOK and ΔPOE, the sides OS = OP = KE = OK = OE are equal, they are equilateral triangles as well.

Therefore, the measure of ∠KSO and ∠EPO will be 60° each.

The angles at the end of the non-parallel sides of a trapezium are supplementary. Therefore, we can write,

∠KSO + ∠SKE= 180°

∠SKE = 120°

Similarly, the measure of the ∠PEK is 120°.

Further, it is known that the measure of the sides OS=OP=PE=EK=KS = 8 units, therefore, the perimeter of the trapezium is,

Perimeter = OS + OP + PE + EK + KS = 8+8+8+8+8 = 40 units.

Hence, the measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively.  While the perimeter of EPSK is 40 units.

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Answer:

maximum value of the given function is = 3

Step-by-step explanation:

Given function is [tex]F(x)=-4(x-6)^2+3[/tex].

Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.

Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].

Comparing both we get: h=6, k=3

We know that maximum value occurs at the vertex where maximum value is given by "k"

Hence maximum value of the given function is = 3

Answer:

18

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change = [tex]\frac{75-3}{5-1}[/tex] = [tex]\frac{72}{4}[/tex] = 18

Answer:18

Step-by-step explanation:

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change =  =  = 18

Answer:

A, B, D

Step-by-step explanation:

Use the LCM to help...

To achieve 204 gallons of 5% butterfat milk, one would need 136 gallons of 6% butterfat milk and 68 gallons of 3% butterfat milk by solving a system of linear equations.

How to Mix Butterfat Percentages for Milk

To solve the problem of mixing two different butterfat percentages of milk to achieve a certain amount of milk with a desired fat content, we will use a system of equations.

Let x represent the gallons of 6% butterfat milk, and y represent the gallons of 3% butterfat milk.

To achieve 204 gallons of 5% butterfat milk, we have the following equations:

Equation 1: x + y = 204 (total gallons of milk)

Equation 2: 0.06x + 0.03y = 0.05(204) (total butterfat content)

Solving these equations simultaneously, we find:

From equation 1, we can express y as y = 204 - x.

Substituting this into equation 2 gives us 0.06x + 0.03(204 - x) = 10.2.

Simplifying this, we get 0.06x + 6.12 - 0.03x = 10.2, which leads to 0.03x = 4.08.

Hence, x = 136 gallons of 6% butterfat milk and y = 68 gallons of 3% butterfat milk.

No. You cannot use the Pythagorean theorem to find the missing side, because you can only use The Pythagorean theorem when you are dealing with a right triangle.

All you have to do is divide 150 by 18 and that will get you how many meters Pete drives per second

150 ÷ 18

8.3333333333333333333

so...

8.3 m/s (B)

Hope this helped!

~Just a girl in love with Shawn Mendes

Speed is defined as quotient of distance and time.

[tex]

s=\frac{d}{t}=\frac{150}{18}=8.33\dots

[/tex]

Speed is a scalar value therefore we cannot determine its vector. Speed with vector is known as velocity and that is where we specify its vector because velocity is a vector value.

So the answer is 8.3 m/s.

Hope this helps.

r3t40

Answer:

sin 40/x =sin 60/12

Step-by-step explanation:

The question is on law of sines

Given a triangle with sides a, b, c and angles A, B, C respectively, the sine law states that; a/sin A = b/sin B = c/sin C

In the question x=a, b=12 feet, A=40° , B=60° and C=80°

Finding value of x;

x/sin 40° = 12/sin 60°

x sin 60° =12 sin 40°

x=12 sin 40 / sin 60

x=29.33 ft

Answer:

The length of the pole is 9.90 feet.

Step-by-step explanation:

From the figure, it is given that x is the length of the pole and the pole casts a shadow when the sun is at 40 degree angle.

Thus, using the sine law, we have

[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting the given values, we get

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}=\frac{c}{sin80^{\circ}}[/tex]

Taking the first two equalities, we have

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}[/tex]

[tex]x=\frac{12sin40^{\circ}}{sin60^{\circ}}[/tex]

[tex]x=\frac{12{\times}0.642}{0.866}[/tex]

[tex]x=8.90 feet[/tex]

Therefore, the length of the pole is 9.90 feet.

The smallest angle is a which is 35 and from 7 to 35 it X5 so times 18 and 11 by 5 as well which comes to the ratio 35:90:55 , you can tell this is right because angles in a triangle add up to 180 , 35+90+55 =180

Answer:

Step-by-step explanation:

ΔQTR and ΔRTS are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{RT}{TS}=\dfrac{TQ}{RT}[/tex]

We have

[tex]RT=x,\ TS=9,\ TQ=16[/tex]

Substitute:

[tex]\dfrac{x}{9}=\dfrac{16}{x}[/tex]              cross multiply

[tex]x^2=(9)(16)\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]

The statements about the functions that are true include:

A. f(x) and g(x) intersect at exactly two points.

B. The x-intercepts of f(x) are common to g(x).

In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).

By critically observing the table of values and graph shown in the image attached above, we can reasonably and logically deduce the following x-intercepts for both f(x) and g(x):

x-intercepts of f(x) = (-1, 0) and (1, 0).

x-intercepts of g(x) = (-1, 0) and (1, 0).

Therefore, the x-intercepts of f(x) are common to g(x), which means they intersect at exactly two points.

For the minimum value of f(x) and g(x), we have;

Minimum value of f(x) = -1

Minimum value of g(x) = -3

Therefore, the minimum value of f(x) is greater than the minimum value of g(x).

For the y-intercept of f(x) and g(x), we have;

y-intercept of f(x) = (0, -1).

x-intercepts of g(x) = (0, 1).

In conclusion, we can logically deduce that f(x) and g(x) have different y-intercept.

Answer:

Its the first one

Step-by-step explanation:

Final answer:

The rational expression[tex](r^2 - 4r + 5)/(r - 4)[/tex] is already in its simplest form, as the numerator cannot be factored to cancel out any terms with the denominator.

Explanation:

The question asks for the simplified rational expression for the quadratic equation [tex]r2 - 4r + 5[/tex] divided by the linear expression r - 4. Simplifying rational expressions often involves factoring the numerator and the denominator and then canceling out common factors. However, in this case, the numerator cannot be factored in a way that will cancel out terms with the denominator. Simplifying further requires either polynomial division or realization that the expression is already in its simplest form because there are no common factors. Therefore, the rational expression[tex]r2 - 4r + 5[/tex] over r - 4 is already simplified as no further reduction is possible.

Answer: The correct answer is 1/3x − 3 = −x + 1

Step-by-step explanation:

add 3 to both sides

simplify

add x to both sides

simplify

multiply both sides by 3

simplify

divide both sides by 2

simplify

The graph of the system of equations solves the equation -1/3x + 3 = x - 1.

The first step in solving a system of equations is to isolate one variable in one of the equations. We can begin by rearranging the first equation -1/3x + 3 = x - 1 to isolate x. First, multiply both sides of the equation by 3 to get rid of the fraction: -x + 9 = 3x - 3. Then, add x to both sides to bring all the x terms to one side: 9 = 4x - 3. Finally, add 3 to both sides to solve for x: 12 = 4x. Dividing both sides by 4 gives us x = 3.

Substitute this value of x into either of the original equations to solve for y. Let's use the second equation: (1/3)(3) - 3 = -3 + 1. Simplifying this equation, we get 1 - 3 = -2. This tells us that y = -2.

Therefore, the solution to the system of equations is x = 3 and y = -2, and it satisfies the equation -1/3x + 3 = x - 1.

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Answer:

Final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].

Step-by-step explanation:

given functions are [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].

Now we need to find about what is the value of [tex]g\left(x\right)*f\left(x\right)[/tex].

[tex]g\left(x\right)*f\left(x\right)[/tex] simply means we need to multiply the value of  [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].

[tex]g\left(x\right)\cdot f\left(x\right)=\frac{1}{2x\left(x+3\right)}\cdot\left(x-6\right)[/tex]

[tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex]

Hence final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].

Answer:

b)0, yes

Step-by-step explanation:

Given:

Vectors (4,8) . (6,-3)

Finding inner product of vectors:

= 4x6 + 8x-3

=24-24

=0

Now to check the angle between them using formula a.b=|a|.|b|cosθ

|a|= [tex]\sqrt{4^{2} +8^{2} } \\\sqrt{16+64}[/tex]

   =8.9

|b|=[tex]\sqrt{6^{2} +(-3)^{2} } \\\sqrt{36+9}[/tex]

   =6.7

Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,

0= 8.9(6.7)cosθ

cosθ =0

θ=90 degrees

Hence the two vectors are perpendicular !

Find the difference vertically( North and South) and the difference horizontally ( East and West)

Then use  the Pythagorean Theorem.

600 North - 200 South = 400 m

400 West - 100 East = 300 m

Now using the Pythagorean Theorem;

400^2 + 300^2 = total displacement^2

Total displacement^2 = 160,000 + 90,000

Total displacement^2 = 250,000

Total displacement = √250,000

Total displacement = 500 m

Answer:

22

Step-by-step explanation:

We know that 1 miles = 5280 ft  and 1 hour = 3600 seconds

15 miles         5280 ft         1 hour

--------------- * ------------- *   --------------        =

1 hour               1 mile        3600 second

The units cancel leaving us ft/s

22 ft/s

Answer:

3 minutes

Step-by-step explanation:

we know that

Pablo can put up a tent in 12 minutes

so

100% of the work Pablo can do in -------> 12 minutes

In one minute Pablo can do (100/12)%

His mom can put it up by herself in 4 minutes

so

100% of the work his Mon can do in -------> 4 minutes

In one minute his Mon can do (100/4)%

therefore

Pablo and his Mon together in one minute can do

(100/12)%+(100/4)%=(400/12)%

By proportion find how many minutes would they take to put up the tent working together

1/(400/12)%=x/100%

x=12*100/400=3 minutes

To find the slope, you should rearrange the equation into slope-intercept form, ie. y = mx + c, where m is the gradient.

y - 9 = 15(x - 5)

y = 15(x - 5) + 9 (Add 9 to each side)

y = 15x - 15*5 + 9 (Expand 15(x - 5))

y = 15x - 75 + 9

y = 15x - 66

Therefor, the slope of the equation is 15.

Answer:

Use the slope-intercept form  

y

=

m

x

+

b

 to find the slope  

m

.

m

=

15

Step-by-step explanation:

Cuz i know all that

For this case we must find the value of "b" of the following equation:

[tex]\frac {3} {2} + b = \frac {7} {4}[/tex]

Then, we subtract [tex]\frac {3} {2}[/tex] from both sides of the equation:

[tex]\frac {3} {2} - \frac {3} {2} + b = \frac {7} {4} - \frac {3} {2}\\b = \frac {7} {4} - \frac {3} {2}\\b = \frac {14-12} {8}\\b = \frac {2} {8}\\b=\frac{1}{4}[/tex]

Answer:

[tex]b = \frac {1} {4}[/tex]

Answer:

The answer is 1/4.

What are you solving for?

Use the vertex form, y=a(x−h)2+k y = a ( x - h ) 2 + k , to determine the values of a a , h h , and k k . Since the value of a a is positive, the parabola opens up. Find p p , the distance from the vertex to the focus. Find the distance from the vertex to a focus of the parabola by using the following formula.

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Answer:

Step-by-step explanation:

It is a first cousin to y=x^2. The only difference is the 2 in front of the x^2 which narrows x^2.

The vertex is at (0,0)

Answer:

(1,2)

Step-by-step explanation:

we know that

The rule of the transformation is equal to

(x, y)  ------> (x + 3, y + 1)

Pre-image -----> Image

(x, y)  ------> (4, 3)

so

x+3=4 ----> x=4-3=1

y+1=3 ---> y=3-1=2

therefore

The pre-image is the point (1,2)

Answer:

1.3 x 10^-5

Step-by-step explanation:

To convert 0.000013 to scientific notation, the decimal point is moved five places to the right, resulting in 1.3 × 10⁻⁵.

To express the number 0.000013 in scientific notation, follow these steps:

Therefore, the scientific notation for 0.000013 is 1.3 × 10⁻⁵. This notation is particularly useful for representing very small numbers in a compact and readable form.

Answer:

the answer is A.616.39

Step-by-step explanation:

Megan can withdraw $615.21 per month for 5 years from the new account.

Option B is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To solve this problem, we need to use the formula for the future value of an annuity:

[tex]FV = P [(1 + r/n)^{n\times t} - 1]/(r/n)[/tex]

where:

P = payment per period

r = interest rate per period

n = number of compounding periods per year

t = number of years

FV = future value of the annuity

First, we can calculate the future value of Megan's semiannual payments after 10 years:

P = $1,624.13

r = 1.5%/2 = 0.0075 (semiannual interest rate)

n = 2 (semiannual compounding periods)

t = 10 years

So,

[tex]FV = 1,624.13 \times[(1 + 0.0075/2)^{2\times10} - 1]/(0.0075/2)[/tex]

= $21,070.58

Next, we need to calculate the future value of this amount when transferred to the new account:

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

FV

[tex]= $21,070.58 \times (1 + 0.00191667)^{60}[/tex]

= $24,526.41

Finally, we need to calculate the monthly payment Megan can withdraw for 5 years from this account, assuming the balance is depleted at the end of the 5 years:

P = ?

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

Using the formula for the present value of an annuity:

[tex]P = FV \times (r/n) / [(1 + r/n)^{n\timest} - 1][/tex]

[tex]= $24,526.41 \times (0.00191667) / [(1 + 0.00191667)^{60} - 1][/tex]

= $615.21

Therefore,

Megan can withdraw $615.21 per month for 5 years from the new account.

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Answer:

2 4/20, which you can simplify as 2 1/5

Hope this helps if u can (thanks and brainliest) please. Have a good day!! Ask any questions if u need to!!

Answer:

The numbers are -9 and -7 or 13 and 15

Step-by-step explanation:

Let

x and x+2 ----> two consecutive odd integers

we know that

[tex]x(x+2)=3[x+x+2]+111[/tex]  

Solve for x

[tex]x(x+2)=3[x+x+2]+111\\ \\x^{2}+2x=6x+6+111\\ \\x^{2}-4x-117=0[/tex]

Solve the quadratic equation by graphing

The solution is x=-9, x=13

see the attached figure

First solution

x=-9

x+2=-9+2=-7

The numbers are -9 and -7

Second solution

x=13

x+2=13+2=15

The numbers are 13 and 15

ANSWER

{},{1},{3},{5},{7},{1,3},{1,5},{1,7},{3,5},{3,7},{5,7},{1,3,5},{1,3,7},{3,5,7},{1,5,7},{1,3,5,7}

EXPLANATION

The given set is {1,3,5,7}.

This set has

[tex] {2}^{n} = {2}^{4} = 16[/tex]

subsets.

Where n=4 is the number of elements in the set.

Recall that the null set is a subset of every set and every set is a subset of itself.

The subsets are:

{}

{1},{3},{5},{7}

{1,3},{1,5},{1,7},{3,5},{3,7},{5,7}

{1,3,5},{1,3,7},{3,5,7},{1,5,7}

{1,3,5,7}

For this case we have that by definition of trigonometric relations that, the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. So:

[tex]Sin (36) = \frac {5} {x}[/tex]

Clearing x:

[tex]x = \frac {5} {sin (36)}\\x =\frac {5} {0.58778525}\\x = 8.517887564 [/tex]

Rounding off we have to:

[tex]x = 8.51[/tex]

Answer:

Option D

I know the first 3 are c. I'm pretty sure the last one is a or d

Answer: 7. 2n + 162 = 424

              8. 3 hours

              9. K ≥ 18

7. The number of Delicious apples sold is represented by n. Because they  sold 162 more Empire apples than Delicious apples, the number of Empire apples sold can be represented by (n + 162). The total number of apples sold was 424, so the equation is Delicious apples + Empire apples = 424.

[tex]n + (n + 162) = 424\\\\n + n + 162 = 424\\\\2n + 162 = 424[/tex]

8. The equation is given for this problem. Simply solve for h in the equation.

[tex]55h + 275 = 440\\\\55h = 165\\\\h = 3[/tex]

9. The term "at least" generally means greater than or equal to. Thus, since Suzy scored at least 18 points, she scored 18 or more points.

[tex]K \geq 18[/tex]