8-109. Solve each equation.
.
a. 6x+12=-x-2

9514 1404 393

Answer:

  (x, y) ⇒ (y+1, 7-x) . . . rotation 90° CW about (4, 3)

or

  (x, y) ⇒ (y+1, x+1) . . . glide reflection across y=x; and translation (1, 1)

Step-by-step explanation:

The figure is apparently rotated 90° clockwise. This can be accomplished a couple of ways: (1) rotation 90° CW about some center; (2) reflection across the line y=x. Because of the symmetry of the figure, we cannot tell which of these is used.

Rotation

The center of rotation can be found by looking at the perpendicular bisectors of the segments joining a vertex and its image. One such segment has endpoints (1, 6) and (7, 6), so is a horizontal line with midpoint (4, 6). The perpendicular bisector of that is x=4.

Another segment joining a point with its image has endpoints (5, 6) and (7, 2). Its midpoint is (6, 4), and the slope of the bisector through that point is 1/2. It intersects the line x=4 at (4, 3), the center of rotation.

Rotation 90° CW about the origin is the transformation (x, y) ⇒ (y, -x), so rotation of (x, y) 90° about the point (4, 3) will be the transformation ...

  (x, y) ⇒ ((y -3) +4, (-(x -4) +3) = (y +1, 7 -x)

The transformation A to B is rotation 90° CW about (4, 3):

  (x, y) ⇒ (y +1, 7 -x).

__

Reflection

Simple reflection across the line y=x is the transformation (x, y) ⇒ (y, x). Applying that transformation, we see that an additional translation of 1 unit right and one unit up is required. The complete transformation is a "glide reflection", a reflection followed by a translation.

The transformation A to B is a glide reflection across the line y=x with a translation up 1 and right 1:

  (x, y) ⇒ (y +1, x +1).

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer:

Last graph that slopes upwards from left to right and that has an y-intercept of -1

Step-by-step explanation:

let us pick some points!(you can chose any two)

when x =3 , y = 14 : helps us get points (3,14)

when x =1 , y = 4 : helps us get points (1,4)

so we find the gradient using the two points:

\(gradient \ =\frac{14-4}{3-1} =\frac{10}{2} \\\)

we now use gradient 10/2 and point (1,4) to find the equation  of the line:

\(\frac{10}{2} =\frac{y-4}{x-1} \\2(y-4)=10(x-1)\\2y-8=10x-10\\2y=10x-10+8\\2y=10x-2\\y=5x-1\)

from the equation of the line found we are able to find the y- intercept of the line is -1 and that the line has a positive gradient thus should slope upwards from left to right.

From the pictures you posted, we pick the last graph as it seem to slope upwards from left to right and has the line cutting y axis at around -1

Answer:

32

Step-by-step explanation:

the cofactor of 24 is then subtracted by the diameter of pi and then sent to the power of 2 after that divide by 2 and multiply by 6

Answer:

The whole thing is wrong. In order to find radius of a circle its 6(piesymbol) mini 2

Step-by-step explanation:

Answer:

The error of this problem is that 6^3 is supposed to be 216 not 18. The volume is not about 75.4 cubic inches, but it is actually about 904.3

Step-by-step explanation:

When you evalulate 6^3 it is supposed to look like 6 x 6 x 6, which equals 216. However in this problem, the student does it as 6 x 3 = 18, which makes the whole answer wrong.

So the actual volume of the soccer ball is 904.3 cubic inches. A strategy to prevent from getting the problem wrong is to write 6^3 out as 6 x 6 x 6.

Note that where the conditions above subsist the height determined by the other colleague is not the same so the answer is No. To solve this problem, you need to be conversant with the Pythagorean Theorem, and Angle Bisector Theorems.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The formula for the Pythagorean Theorem is:

c² = a² + b²

where "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides (the legs) of a right triangle.

With this, we can find the c for the lower Right angle triangle on the left and B for the lower right angle triangle on the right.

Since C² = A² + B²

B = √( A²- C²)

B = √( 9.5²- 6²)

B \(\approx\) 7.36546


To determine c on the right angle to the left,

c² = a² + b²

c = √(a² + b²)

c = √(5.5² + 7.2²)

c = 9.060353194

c \(\approx\) 9.06

With the postulate of the Angle Bisector Theorem, we can begin to find the height of the two upper right angle triangles.

The Angle Bisector Theorem states that in a triangle, an angle bisector of a vertex of the triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

In other words, if a line segment bisects an angle of a triangle and intersects the opposite side or the extension of the opposite side, then the ratio of the lengths of the segments on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

As seen from the image, the right angles where each lady is holding is bisected. This means that we have for each Triangle Two angles and one side.

Right Angle on the Left:

90°

45°; and

7.2ft

Given the above, Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.2 = 1/1.

Therefore, the height of the right triangle is:

h = 7.2 × 1

h = 7.2 ft

So the height of the right triangle is 7.2 feet.

Right Angle on the Right :

90°

45°; and

7.36546ft

Given the above, we can use the trigonometric ratios of the angles in the right triangle.

Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.36546 = 1/1.

Therefore, the height of the right triangle is:

h = 7.36546 × 1

h = 7.36546 ft

So the height of the right triangle is 7.36546 feet.

So both heights approximated to the nearest tenth:

Since 7.2 ≠ 7.4, the heights are not equal.

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Answer:

The distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units

Step-by-step explanation:

The distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units[1].

To find the distance between two points on a coordinate plane, we use the distance formula based on the Pythagorean theorem. The distance formula is:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the coordinates of the two points are (-3,10) and (-3,-9). Substituting these values into the distance formula, we get:

d = sqrt((-3 - (-3))^2 + (-9 - 10)^2)

 = sqrt(0^2 + (-19)^2)

 = sqrt(361)

 = 19

Therefore, the distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units.

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Answer:

The recursive formula is given below as

Step 1:

To figure out the value of the forurth term, we will substitute the value of

By substituting the n=4, we will have

Step 2:

Calculate the second term and the third term

Step 3:

Substitute the value of the third term in the equation below

Hence,

The final answer is

OPTION C is the right answer

Answer:

Step-by-step explanation:

Formula: Area=(a+b)/2 * h

72=(16+8)/2*h

72=24/2*h

72=12*h

h=72/12

h=6

It will be nice if you give me brainlies.Good luck!

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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Answer:

x = 36.2851

Step-by-step explanation:

5.9l -> 100km

x -> 615km

615km*5.9l = x/100km

x=36.285l

Answer:

61500

Step-by-step explanation:

i think this help

Answer:

43

Step-by-step explanation:

angle sum property of quadrilateral

87+ 103 + 127+ x = 360

317 + x = 360

x= 360-317

x = 43

The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

Now you can solve the question from a math tool - Rule of three. Thus,

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

\(100 \ \text{km/h}= \text{x mi/h}\)

\(\text{x}= 100 \times 0.6\)

\(\text{x}=33 \ \text{mi/h}\)

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If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π\(/180*5\)

=70π\(/36\)

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π\(/36\)

=(360π-70π)\(/36\)

=290π\(/36\)

Put π=3.14

=290*3.14\(/36\)

=910.6\(/36\)

=25.29m

Hence the length of arc LNM is 25.29 m.

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Answer:

Option B

Step-by-step explanation:

Given quadratic equation is,

y = 2x² + 5x - 7

By comparing this equation with y = ax² + bx + c

a = 2, b = 5 and c = -7

Solution of the polynomial (2x² + 5x - 7) can be determined by the quadratic formula,

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Substitute the values of a, b and c.

\(x=\frac{-5\pm \sqrt{5^2-4(2)(-7)}}{2(2)}\)

   \(=\frac{-5\pm \sqrt{25+56} }{4}\)

Therefore, Option B will be answer.

Step-by-step explanation:

250 i think sorry if im wrong solution it said 2/5 of students have hearing problems. so since there is 450 students and it said 2/5 that means 2/5 will be 250 hope if i could help.

When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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Answer:

25.8

Step-by-step explanation:

divide

Answer:

divide like i said

Step-by-step explanation:

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The total number of coins that were in Kay's bank are 137 coins.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since she has 11 less dimes than nickels, an equation which models this situation is given by;

n = d + 11     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 10 dollars;

0.1d + 0.05n = 10 ....equation 2.

By solving both equations simultaneously, we have:

0.1d + 0.05(d + 11) = 10

0.1d + 0.05d + 0.55 = 10

0.15d = 9.45

d = 63 dimes.

For nickels, we have:

n = d + 11

n = 63 + 11

n = 74

Now, we can determine the total number of coins;

Total number of coins = n + d

Total number of coins = 74 + 63

Total number of coins = 137 coins.

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Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

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

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / \((N\sum X^2 - (\sum X)^2)\)

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

\(\sum X^2\) = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

\(\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144\)

Now, substitute these values into the formulas to find b1 and bo:

\(b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)\)

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 \(\times\) 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

Answer:

Step-by-step explanation:

The correct order of the quadrilaterals are : Polygons → Quadrilaterals →Parallelograms → Rhombus → Rectangle → Squares

A quadrilateral is a closed shape that is formed by joining four points, among which any three points are non-collinear.

Given that, a partially complete chart,

The complete chart will be

Polygons → Quadrilaterals →Parallelograms → Rhombus → Rectangle → Squares

Hence, The correct order of the quadrilaterals are : Polygons → Quadrilaterals →Parallelograms → Rhombus → Rectangle → Squares

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Step-by-step explanation:

n = 52

x bar = 122.31

standard deviation sd = 38.75

1. the hypothesis:

null hypothesis

h0: μ ≤ 35

alternative hypothesis

h1: μ > 35

2.

we have been given the sd of the sample but not that of the population. so what we are supposed to use here is the t test and not the z test. the following conditions have to be met.

3.

= \(\frac{122.31-35}{38.75/\sqrt{52} }\)

= 87.31/5.37

= 16.26

using the T distribution function in excel, the p value was calculated and found to be approximately equal to 0.

TDIST(16.26, 51, 1)

since p value is very small we reject the null and accept the alternate hypothesis.

4. from the result above the answer to this question is yes

Answer:

31

Step-by-step explanation: