Point C is midpoint of segment AB for A (1, -2) and B (7,2). What is the length of segment AC? Round to the nearest tenth.

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

The equation in general form for the total amount spend on tickets is  13A + 10C = 859 and if the number of adults was 53, the  number of children was 17.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Given that,

The cost of each ticket for an adult is $13,

The cost of each ticket for an child $10,

And, the total amount spend on tickets is $859.

Suppose the number of adult tickets be A and the number of child tickets be C.

Then the amount spend on tickets for adults is 13A,

And, the amount spend on tickets for children is 10C.

As per the question the equation for total amount spend on tickets is given as,

13A + 10C = 859

Now if the number of adults was 53, the number of children can be calculated by substituting A = 53 in the above equation as,

13 × 53 + 10C = 859

⇒ 10C = 859 - 689

⇒ 10C = 170

⇒ C = 17

Hence, the equation in general form for the given situation is 13A + 10C = 859 and if the number of adults was 53, the  number of children was 17.

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The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

8(x² + 2x + 1) = -3 + 8

8(x² + 1) = 5

(x² + 1) = 5/8

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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The midpoints are not the same, indicating that the diagonals PR and QS do not bisect each other.Based on these calculations, we can conclude that the quadrilateral formed by the given points P, Q, R, and S is not a parallelogram.

To determine if the quadrilateral formed by the points P(-4, 2), Q(6, 4), R(11, -2), and S(2, -3) is a parallelogram, we need to examine its properties.

A quadrilateral is a parallelogram if opposite sides are parallel. In addition, we can also check if the diagonals bisect each other.First, let's calculate the slopes of the sides PQ, QR, RS, and SP:

Slope of PQ = (4 - 2) / (6 - (-4)) = 2/10 = 1/5

Slope of QR = (-2 - 4) / (11 - 6) = -6/5

Slope of RS = (-3 - (-2)) / (2 - 11) = -1/9

Slope of SP = (2 - (-3)) / (-4 - 2) = 5/6

We observe that the slopes of opposite sides are not equal. Therefore, the sides PQ and RS are not parallel, and the sides QR and SP are not parallel.Additionally, we can calculate the midpoint of the diagonals PR and QS:

Midpoint of PR = ((-4 + 11) / 2, (2 - 2) / 2) = (3.5, 0)

Midpoint of QS = ((6 + 2) / 2, (4 - 3) / 2) = (4, 0.5).

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Given:

The degree of polynomial = 9

Leading coefficient is negative.

To find:

The end behavior of the polynomial.

Solution:

Let the polynomial be P(x).

We have,

Degree of polynomial = 9, which is odd.

Leading coefficient is negative.

If the degree of a polynomial is odd and leading coefficient is negative, then

\(P(x)\to \infty\text{ as }x\to -\infty\)

\(P(x)\to -\infty\text{ as }x\to \infty\)

Therefore, the end behavior of the given polynomial is \(P(x)\to \infty\text{ as }x\to -\infty,P(x)\to -\infty\text{ as }x\to \infty\).

Answer:

3.5 yd is your answer

Step-by-step explanation:

First, change in. to ft. Note that the measurement given to you is that 1 ft = 12 in.

Divide the amount of inches you have with 12.

126/12 = 10.5

Next, solve for yards. It is given to you that 1 yard = 3 feet.

Divide the amount of feet you have with 3.

10.5/3 = 3.5

3.5 yd is your answer

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

Answer:

[0.184, 0.266]

Step-by-step explanation:

Given:

Number of survey n =280

Number of veterans = 63

Confidence interval = 90%

Computation:

Probability of veterans = 63/280

Probability of veterans =0.225

a=0.1

Z(0.05) = 1.645 (from distribution table)

Confidence interval = 90%

So,

p ± Z*√[p(1-p)/n]

0.225 ± 1.645√(0.225(1-0.225)/280)

[0.184, 0.266]

Answer:

1/2

Step-by-step explanation:

-3/4 + (1/10 ÷ 2/5)

1/10 ÷ 2/5 = 1/10 x 5/2 (Keep. Change. Flip. [KCF])

1/10 x 5/2 = 5/20 (or simplify to 1/4)

1/4 - 3/4 = 0.25 - 0.75 = -0.5 (or 1/2)

Open the bracket on LHS by multiplying with -1/3 and RHS by multiplying with -5 with quantity inside the bracket.

Add '5x' to LHS (Left-hand side) and RHS (Right-hand side) of the above expression to eliminate the 5x in the RHS.

Substract '7' from both RHS and LHS of the above expression.

Divide '3' from the RHS and LHS of the above expression.

Thus, the value of x is -4.

Answer: Yes

Step-by-step explanation:

Yes, dilations preserve angle measures like similar shapes and there pre-image and current image side lengths are in proportion like similar shapes

Answer:

\(4\sqrt{x} - 7\)

Step-by-step explanation:

Required

Express the given statement, mathematically;

We start by taking the statement in bits:

\(Root\ of\ x = \sqrt x\)

\(4\ times\ root\ of\ x = 4 * \sqrt x\)

\(4\ times\ root\ of\ x = 4 \sqrt x\)

\(7\ less\ than\ 4\ times\ root\ of\ x = 4 \sqrt x - 7\)

Hence;

The algebraic equivalent of the statement is \(4\sqrt{x} - 7\)

Answer:

eight two point baskets

Step-by-step explanation:

3 points = 9 points

1 points = 5 points

9+5= 14

30-14= 16

= 16/2

=8

Check the picture below.

The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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5² × 2⁵ = 25 × 32 =. 800

Hope this helps

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

Answer:

1116units²

Step-by-step explanation:

area of trapezium= (a+b)h all over 2

a=38

b=55

h=24

area= (38+55)*24 allover 2

area= 1116units²

Answer:

Step-by-step explanation:

To check whether both equations are balanced, we will simplify

6+6 -n =12 - n

Add n to both sides of the equation using additive property

6+6-n+n = 12-n+n

6+6 +0 = 12+0

6+6 = 12 (This gives the other equation)

Since they are both equal, this shows that the equations are balanced

Answer: x= −0.357142857142857

Step-by-step explanation: don’t count me on it

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Answer:

119.32

Step-by-step explanation:

\(A = 2 * 3.14 * 19 = 119.32\)

As per the perimeter the length of the shorter side is 10.5 feet and the length of the longer side is 73.5 feet.

The perimeter of a rectangle is the sum of the lengths of all its sides. If we know the perimeter of a rectangle and some information about the relationship between its sides, we can use that information to find the lengths of the sides.

Let's call the length of the shorter side "x".

The other side is seven times as long, so it is 7x.

The perimeter of the rectangle is 168 feet, so we have

=> 2x + 14x = 168.

Simplifying the equation, we have

=> 16x = 168.

Dividing both sides of the equation by 16, we find

=> x = 10.5.

So, the length of the shorter side is 10.5 feet and the length of the longer side is

=> 7x = 7 * 10.5 = 73.5 feet.

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Answer: the predictive value positive of the test is 0.7

Step-by-step explanation:

Given that;

                                              Predicted

                                             Diesease                No-Diesease                Tt

Actual              Diesease           225                           75                         300

No-Diesease         25                175                            200

                                                  250                           250                       500

so finding the predictive value positive of the test,

predictive negative value = (175 / (75+175) )

= 175 / 250

= 0.7

Therefore the predictive value positive of the test is 0.7

Answer:

B. (-12,-3,4,6)

Step-by-step explanation:

The above question is asking the domain

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

P(h, k) → P'(k, -h)

Step-by-step explanation:

Rule to be followed,

If a point P(h, k) is rotated 90° clockwise about the origin, coordinates of the image point P' will be,

P(h, k) → P'(k, -h)  

Similarly, all vertices of the parallelogram PQRS will follow the same rule when rotated 90° about the origin to form P'Q'R'S'.