Select three ratios that are equivalent to 11:1.

A(1:11
B(22:2
C(55:5
D(9:99
E(110:10

Considering the linear functions, the coordinates of B and C are given as follows:

The slope-intercept representation of a linear function is given below:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

The equation of line AC is given as follows:

2y = x + 4

y = 0.5x + 2.

When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of line BD is:

0.5m = -1

m = -1/0.5

m = -2.

Then:

y = -2x + b

Considering point D, when x = 10, y = -3, hence the intercept is obtained as follows:

-3 = -20 + b

b = 17.

Point B is the intersection of these two lines, hence:

0.5x + 2 = -2x + 17

2.5x = 15

x = 15/2.5

x = 6

y = 0.5 x 6 + 2 = 5.

Point B is the midpoint of AC, that is, it's coordinates are the mean of the coordinates of A and C, hence the x-coordinate of C is obtained as follows:

6 = (0 + x)/2

x = 12.

The y-coordinate is obtained as follows:

5 = (2 + y)/2

2 + y = 10

y = 8.

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Answer:

221mile per day

Step-by-step explanation:

Mean=total distance her car traveled/days

11477-10150=1327

1327/6=221.167≈221mi

Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

Answer:

i think 6 5/8

Step-by-step explanation:

So distribute

-2*-4+-2*1/2=7 1/2

1/4*-4+1/4*1/2=-7/8

7 4/8 - 7/8 is 6 5/8

Answer:

8

Step-by-step explanation:

Answer:

x =2

Step-by-step explanation:

4x - 2x = 9-5

2x = 4

x = 4

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)

\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)

⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)

⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)

⤑ \( \sf{ \sqrt{100 - 64}} \)

⤑ \( \sf{ \sqrt{36}} \)

⤑ \( \boxed{ \sf{6\: units}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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Answer:

6

hope this helps

have a good day :)

Step-by-step explanation:

Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

The average rate of change for the function f(x)= 3^x + 25 using the intervals of x=2 to x=6 is 6.75

The function is given as:

f(x) = 3^x + 25

The interval is given as:

x = 2 to 6

Start by calculating f(2) and f(6)

f(2) = 3^2 + 25 = 34

f(6) = 6^2 + 25 = 61

The average rate of change is then calculated as:

\(m = \frac{f(6) - f(2)}{6 -2}\)

This gives

\(m = \frac{61 - 34}{6 -2}\)

\(m = \frac{27}{4}\)

m = 6.75

Hence, the average rate of change is 6.75

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Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

We conclude that the set of numbers x satisfying -7 ≤ x ≤ 4 is an interval that contains -7, 4, and all numbers in between.

Thus, the domain of g is: -7 ≤ x ≤ 4

Step-by-step explanation:

We know that the domain of a function is the set of inputs or argument values for which the function is defined.

From the given graph, it is cleared that the function g starts from the x-value x = -7 and ends at x = 4.

It means the function is defined for the set of input values from x = -7 to x = 5 for which the function is defined.

Therefore, we conclude that the set of numbers x satisfying -7 ≤ x ≤ 4 is an interval that contains -7, 4, and all numbers in between.

Thus, the domain of g is: -7 ≤ x ≤ 4

Answer: √(1 - x^2)

Step-by-step explanation: The inverse cosine function, cos^-1(x), gives the angle whose cosine is x. So, cos^-1(x) = θ where cos(θ) = x.Using the identity sin(cos^-1(x)) = √(1 - x^2), we can simplify the expression sin(cos^-1(x)) as:sin(cos^-1(x)) = √(1 - x^2)So, the algebraic expression equivalent to sin(cos^-1(x)) is √(1 - x^2).

this is simply a quick addition to the superb reply above by "MastG"

\(\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)\implies \sin(\theta)=\boxed{\sqrt{1-\cos^2(\theta)}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(sin( ~~ \underset{\theta }{cos^{-1}(x)} ~~ )\implies sin(\theta ) \\\\[-0.35em] ~\dotfill\\\\ cos^{-1}(x)=\theta \implies cos(\theta )=x\implies cos^2(\theta )=x^2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{so then we can say that}}{sin( ~~ cos^{-1}(x) ~~ )\implies sin(\theta )}\implies \sqrt{1-\cos^2(\theta)}\implies \boxed{\sqrt{1-x^2}}\)

Answer:

Step-by-step explanation:

If Elena walk 12 miles, and then 0.25 that distance

0.25=1/4

12*1/4=3 miles is 1/4 of the distance

she walked in total 12+3=15 miles

choice A =12+12*1/4

Elena walked a total 12(1+0.25) distance.

The distance is the total movement of an object without any regard to direction.

First Elena walked 12 miles.

Then walked 0.25 or (1/4)th of 12 miles

i.e. 12 * (1/4) = 3

The total distance Elena walked is

12+3 = 15 miles or

12 + (1/4)*12 = 12(1+0.25)

Hence, 12(1+0.25) is the total distance walked by Elena.

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Answer:

Step-by-step explanation:

R=21

Answer: 15cm

Step-by-step explanation: If the length of the model on the top is 6 cm, then the length of the model on the bottom must be 15 cm

The true statement is "the line that can be drawn through points D and E is contained in plane Y".

option B is the correct answer

The points x and y and points C,D,E and f are shown in the figure, the true statement is determined as follows;

We know that, if two points lie in a plane, then the line drawn through the points will contained in the same plane.

The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contained in plane Y.

So, option (A) is NOT correct.

The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contained in plane Y.

So, option (B) is CORRECT.

Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.

So, option (C) is NOT correct.

Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.

So, option (D) is NOT correct.  

Thus, the correct option is;

The line that can be drawn through points D and E is contained in plane Y.

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The complete question is below:

Points x and y and points C,D,E and f are shown what is true about points

(A) The line that can be drawn through points C and D is contained in plane Y.

(B) The line that can be drawn through points D and E is contained in plane Y.

(C) The only point that can lie in plane X is point F.

(D) The only points that can lie in plane Y are points D and E

Answer:

x = 2.4

Step-by-step explanation:

4 = 1/6 (5x - 12)

4 = 5/6x -2

5/6x - 2 = 4

5/6x = 2

x = 2.4

Answer:

Step-by-step explanation:

These equations are all written in slope-intercept form, so the question is relatively easy to answer. These rules apply.

1. y=-6x-2; y=-6x-2 --- infinitely many

2. y=0.5x+5; y=0.5x+1 --- zero

3. y=0.25x-2; y=5x-4 --- one

4. y=2x+3; y=4x-1 --- one

5. y=2x+1.5; y=2x+1.5 --- infinitely many

6. y=-x-3; y=-x+3 --- zero

_____

Slope-intercept form is ...

  y = mx +b

m is the slope

b is the y-intercept

Answer:

Step-by-step explanation: 1. y=-6x-2; y=-6x-2 --- infinitely many

2. y=0.5x+5; y=0.5x+1 --- zero

3. y=0.25x-2; y=5x-4 --- one

4. y=2x+3; y=4x-1 --- one

5. y=2x+1.5; y=2x+1.5 --- infinitely many

6. y=-x-3; y=-x+3 --- zero

Answer:

875 inches

Step-by-step explanation:

almost 73 feet!

Answer:

4.5

Step-by-step explanation: