is that true that r is the set of counting numbers from 7 to 12 is in a roster notation​

Hence, in answering the stated questiοn, we may say that We knοw they equatiοn are perpendicular tο each οther since the prοduct οf their slοpes equals -1.

A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο describe the relatiοnship between the twο sentences οn οppοsite sides οf a letter. In usually, the lοgο and the prοgramme are the same. Fοr instance, 2x - 4 equals 2.

The οld rοad has a slοpe οf 3, hence the new rοad will have a slοpe οf -1/3.

Let's name the new rοad's equatiοn y = mx + b, where m is the slοpe and b is the y-intercept.

We knοw that the new rοad must gο past pοint (1,1), therefοre

1 = (-1/3)(1) + b

b = 4/3

y = (-1/3)x + 4/3

We may cοmpute the prοduct οf their slοpes tο ensure that this new rοad crοsses the current rοad at a perpendicular angle.

Because the new rοad's slοpe is -1/3 and the present rοad's slοpe is 3, their prοduct is:

(-1/3) * 3 = -1

We knοw they are perpendicular tο each οther since the prοduct οf their slοpes equals -1.

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Answer:

Step-by-step explanation:

What is 3-3×6+2 please?

remember PEMDAS

3 - 3 × 6 + 2 =    (solve multiplication)

3 - 18 + 2 =         (solve addition)

3 - 16 =              (solve subtraction)

-13                     (result)

Answer:

f(x) = -5/81( x^2 -2x - 80)  

Step-by-step explanation:

The zeroes are -8 and 10 so we can write :

f(x) = -a(x - 10)(x + 8)  

( negative is because the parabola opens downwards).

The maximum value is at the vertex = 5.

f(x) = -a(x^2 - 2x - 80)

       =  a[(x - 1)^2 - 1 - 80)

        = a(x - 1)^2 - 81a

As the vertex is at f(x) = 5

81a = 5 so a = 5/81

So the equation is

f(x) = -5/81( x^2 -2x - 80)    

Answer:I'm pretty sure it would be C but that might be wrong

Step-by-step explanation:

Answer:

D. Not factorable

Step-by-step explanation:

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

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Answer:

-42

Step-by-step explanation:

Assuming you want the dot product,

(8)(-6)+(2)(3)= -42

The intersection consists of the elements that are contained in all of the intervals.

(5,6) is the answer

Please let me know if im wrong!

The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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Answer:

41.8°

Step-by-step explanation:

Opposite angles are equal.

Answer:

41.8 degrees

Step-by-step explanation:

They are vertical angles, meaning they are the same, just opposite one another.

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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The inequalities that can be used to represent the situation are:

Inequalities are mathematical statements showing that two or more mathematical expressions are unequal.

With inequalities, two or more values are compared to show that they are not equivalent.

Inequalities can be represented as follows:

The cost of small candles per unit = $3.50

The cost of large candles per unit = $5.00

The number of small candles = x

The number of large candles = y

The number of candles Jimmy needs to buy ≥ 20

The total amount Jimmy can spend on the candles ≤ $80

3.50x + 5y ≤ $80

x + y ≥ 20

Thus, with these inequalities, the total cost of small and large candles must not exceed $80 and the number can be 20 or more.

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Show the two inequalities representing the situation.

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

\(4x\)

Step-by-step explanation:

Step 1: Define

I will substitute delta x with h

\(\lim_{h \to 0} \frac{2(x+h)^2-2x^2}{h}\)

Step 2: Simplify function

Step 3: Evaluate limit

\(\lim_{h \to 0} 4x+2h=\lim_{h \to 0} 4x+2(0)\)

\(\lim_{h \to 0} 4x+2(0)=\lim_{h \to 0} 4x+0\)

\(\lim_{h \to 0} 4x+0 = 4x\)

Answer:

\(\left[\begin{array}{ccc}y=x&y=\frac{2}{3}x&y=\frac{2}{3}x +1 \\-6&-4&-3\\-3&-2&-1\\0&0&1\\3&2&3\\6&4&5\end{array}\right]\)

Step-by-step explanation:

-6: y = -6

y = \(\frac{2}{3}\) (-6)

y = -4

y = \(\frac{2}{3}\) (-6) + 1

y = -4 + 1

y = -3

-3: y = -3

y =  \(\frac{2}{3}\) (-3)

y = -2

y =  \(\frac{2}{3}\) (-3) + 1

y = -2 + 1

y = -1

0: y = 0

y =  \(\frac{2}{3}\) (0)

y = 0

y =  \(\frac{2}{3}\) (0) + 1

y = 1

3: y = 3

y =  \(\frac{2}{3}\) (3)

y = 2

y =  \(\frac{2}{3}\) (3) + 1

y = 2 + 1

y = 3

6: y = 6

y =  \(\frac{2}{3}\) (6)

y = 4

y =  \(\frac{2}{3}\) (6) + 1

y = 4 + 1

y = 5

7x + 3 = 9x - 3 - 2x

7x - 9x + 2x = -3 - 3

0 = -6

equation doesn't have any solution

If the pumpkins follow a normal distribution, then some behaviour of the data is expected:

- Approximately 50% of the data will be below the mean and the other 50% will be above the mean. This will be more precise as the sample size grows.

The fact that 75% of the pumpkins have weigths above the mean does not correspond to a normally-like distribution.

- The median is expected to be equal or around the mean value.

If the median is 10 lb or 35 lb, it may be an indication that the distribution is not normal, but skewed to the right or the left.

- 68% of the data is expected to fall within one standard deviation from the mean.

Then, the first 3 options correspond to clear signs that the distribution is not normal.

Answer:

Check:

- 75% of the pumpkins in the sample have weigths above the mean.

- The median pumpkin weight is 35 lb.

- The median pumpkin weight is 10 lb.

The traveler must walk 17 blocks to reach the State Building.

The traveler needs to walk 8 blocks from the intersection of Orovada Street and Washington Avenue to the State Building.

She also knows that the intersection of Orovada Street and Washington Avenue is 5 blocks from the intersection of Wyoming Street and Washington Avenue, so she needs to walk 5 blocks from the intersection of Wyoming Street and Washington Avenue to the intersection of Orovada Street and Washington Avenue.

Also, the traveler had to walk 4 blocks to get from the intersection of Wyoming Street and Green Avenue to the intersection of Orovada Street and Green Avenue.

Therefore, the traveler must walk 8 + 5 + 4 = 17 blocks to reach the State Building.

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Answer:

2

Step-by-step explanation:

because the outer line is one line and the triangle in other line

Answer:

3

Step-by-step explanation:

There is a line of symmetry from each vertex of the triangle through the square opposite it. I can't draw it out here but there's one going straight down the middle, another going from the triangles leftmost point through the right hand square and another from the triangles rightmost point through the left hand square.

Answer:

So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units like feet or inches.

Step-by-step explanation:

Answer:

D) 12 units

Step-by-step explanation:

Using the formula for the midpoint of the line with given points  A and B as the end points of the line, the coordinates of the point B is (6,-8).

To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.

What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.

Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line,  and using the midpoint formula for a line AB,

Midpoint(M) = \((\frac{x1+x2}{2},\frac{y1+y2}{2} )\)

where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B

so , (7,-7) = \((\frac{8+x2}{2} , \frac{-6+y2}{2})\)

equating the corresponding points,

7 =(8+x2)/2

therefore, x2 = 6

and , -7 = (-6+y2)/2

therefore , y2 = -8

Hence the coordinates of B is , (x2,y2 ) = (6,-8)

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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