Calculate the perimeter. Round your answer to the tenthsas needed.

Answer:

1 and 1/3

Step-by-step explanation:

The absolute value means that you have a positive sign no matter what the value is. It is the distance in units from 0 on the number line to the point in question.

The number line is laid out in 1/6. Each tick is 1/6. Since the point is at 1 and 2/6, we have to reduce the fraction.  In 2/6 you can divide the bottom and top by 2 to reduce the fraction.

2 divided by 2 = 1

6 divided by 2 = 3

Therefore the 2/6 reduces to 1/3

You already know you had a 1, so you add 1/3 and it is 1 1/3.

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

f= 0

2(0) -4 = -4

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Answer:

\(distance = \sqrt{ {(8 - ( - 8))}^{2} + {( - 6 - ( - 6))}^{2} } \\ = \sqrt{256} \\ = 16 \: units\)

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

\(g(x) = -\sqrt{9(x - 1)} + 2\)

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Answer:

\(x=\frac{5}{2}\)

Step-by-step explanation:

In order to solve for "x" we proceed to raise both sides of the equal sign to the power 2 in order to eliminate the root:

\(\sqrt{2x-5} = 0\\(\sqrt{2x-5})^2 = 0^2\\2x - 5=0\\2x = 5\\x=\frac{5}{2}\)

Answer:

33 bags

Step-by-step explanation:

she has 4.5 ft³

she needs 54 ft³

she must get an additional

54 ft³ - 4.5 ft³ = 49.5 ft³

each bag has 1.5 ft³

(49.5 ft³)/(1.5 ft³) = 33

Answer: 33 bags

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

In linear equation ,242 total number of members within 5 weeks.

What is linear equation ?

a manual computation on how 1 member recruits his members until week 5. Then multiply the sum by 2.

                            old      new

1:   1

2:   1 x 3 = 3 ⇒        1         3       *only new members recruit 3 more

3:   3 x 3 = 9 ⇒        4         9

4:   9 x 3 = 27⇒     13       27

5: 27 x 3 = 81 ⇒    40       81

40 + 81 = 121. Total number of members under 1 founding member.

121 x 2 founding members = 242 total number of members within 5 weeks.

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Answer: Option C

Step-by-step explanation:

SOLUTION

Step 1 :

In the question, we would see clearly that angles 3 and 6 are same-side interior angles.

CONCLUSION:

They are same - side interior angles ...OPTION B

Answer:

1. Triangles HIJ and KML

2. Triangles RST and YXZ

3. Reflexive property and Congruent Property

Step-by-step explanation:

Step-by-step explanation:

for 1 and 2 to find which ones are congruent you have to look at the lines on the angles which show congruence

Answer:

A is the answer because the -T is right at 0

The matrix is 3 × 3 square matrix . Its values are:

\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)

Given,

Matrix A and Matrix B

Now,

According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.

So,

Apply multiplication rule,

\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)

Thus the values of the matrix can be calculated.

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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The required sum is 8.25

What is sum in mathematics?

A summation, also known as a sum, is the outcome of adding numbers or quantities arithmetically. A sum always has an even number of terms. There might be as few as two or as many as a hundred, thousand, or million phrases. Some sums have an unlimited number of terms.

\(6+4+\frac{3}{4}+(-2.5)\)

\(= 10+\frac{3}{4} -2.5\)

\(= \frac{40+3-10}{4}\)

\(=\frac{33}{4}=8.25\)

Hence the required sum is 8.25

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The expression \((\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}\) is an algebraic expression, and the result of simplifying the expression \((\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}\) is 1

The expression is given as:

\((\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}\)

Apply the power rule of indices

\((x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}\)

Expand the exponents of the expression

\(x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2\)

Apply the product rule of indices

\(x^{a^2-b^2+b^2 - c^2+c^2 - a^2\)

Collect like terms

\(x^{a^2- a^2-b^2+b^2 - c^2+c^2\)

Evaluate the differences

\(x^{0-0 - 0\)

This gives

\(x^{0\)

Evaluate the exponent

1

Hence, the result of simplifying the expression \((\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}\) is 1

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Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2

Answer:

it is a x= 40 degrees

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

100% on edge

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Answer:

The graph is in the pic

Step-by-step explanation:

The result of the row operation on the matrix is given as follows:

\(\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right]\)

The matrix in this problem is defined as follows:

\(\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right]\)

The row operation is given as follows:

\(R_1 \rightarrow \frac{1}{2}R_1\)

The meaning of the operation is that every element of the first row of the matrix is divided by two.

Hence the resulting matrix is given as follows:

\(\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right]\)

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Answer:

a

\(\= x = 40.85\)

b

\(E = 5.85\)

Ca  

   \(t_c =  2.08 \)

Cb

   \( t_c  =   1.282 \)

Explanation:

From the question we are told that

     The sample size is n  =  100

     The upper limit of the 95% confidence interval is  b =  47.2 years

     The lower limit of the 95% confidence interval is   a =  34.5 years

Generally the sample mean is mathematically represented as

         \(\= x = \frac{a + b }{2}\)

=>    \(\= x = \frac{47.2 + 34.5 }{2}\)

=>    \(\= x = 40.85\)

Generally the margin of error is mathematically represented as

         \(E = \frac{b- a }{ 2}\)

=>      \(E = \frac{47.2- 34.5 }{ 2}\)

=>      \(E = 5.85\)

Considering question C a  

From the question we are told the confidence level is  90% , hence the level of significance is    

      \(\alpha = (100 - 90 ) \%\)

=>   \(\alpha = 0.10\)

The  sample size is  n =  22

Given that the sample size is not sufficient enough i.e \(n < 30\) we will make use of the student t distribution table  

Generally the degree of freedom is mathematically represented as

           \(df = n- 1\)

=>        \(df = 22 - 1\)

=>        \(df = 21\)

Generally from the student  t  distribution table the critical value  of  \(\frac{\alpha }{2}\) at a degree of freedom  of  21 is  

   \(t_c =t_{\frac{\alpha }{2} ,  21  } =  2.08 \)

Considering question C b

From the question we are told the confidence level is  80% , hence the level of significance is    

      \(\alpha = (100 - 80 ) \%\)

=>   \(\alpha = 0.20\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \( t_c  =Z_{\frac{\alpha }{2} } =  1.282 \)

Answer:

It intersects the y-axis at point (0, 2).

Step-by-step explanation:

x + 3y = 6

3y = -x + 6

y = -1/3x + 2

Answer:

4. (6,0)

Step-by-step explanation:

Plug the points into the equation.

6+3(0)=6

6+0=6

6=6

Correct option is A - Ellipse with center at (-5,4) ; B - Ellipse with center at (4,-5) ; C - Hyperbola with center at (4,-5) ; D - Hyperbola with center at (-5,4).

What is conic section ?

Conic sections are curves that are formed by the intersection of a plane and a double cone. The conic sections include circles, ellipses, parabolas, and hyperbolas. Each of these curves has a unique set of characteristics that can be described by mathematical equations.

Explanation of the correct matching :

A - The equation represents an ellipse with center at (-5,4). The values 100 and 225 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (-5,4) in this case.

B - The equation represents an ellipse with center at (4,-5). The values 16 and 9 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (4,-5) in this case.

C - The equation represents a hyperbola with center at (4,-5). The values 64 and 81 in the equation represent the squared distances between the center and the vertices on the y-axis and x-axis, respectively. The center of the hyperbola is (h,k), which is (4,-5) in this case.

D - The equation represents a hyperbola with center at (-5,4). The values 16 and 9 in the equation represent the squared distances between the center and the vertices on the x-axis and y-axis, respectively. The center of the hyperbola is (h,k), which is (-5,4) in this case.

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Answer:

C A D B

Step-by-step explanation:

on edge

the distance from the center of the circle to a point on the circle is simply its radius, thus

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(~~-4 - (-2)~~)^2 + (~~1 - 1~~)^2} \implies r=\sqrt{(-4 +2)^2 + (1 -1)^2} \\\\\\ r=\sqrt{( -2 )^2 + ( 0 )^2} \implies r=\sqrt{ 4 + 0 } \implies r=\sqrt{ 4 }\implies \stackrel{ radius }{r=2} \\\\[-0.35em] ~\dotfill\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~2^2\implies (x+2)^2 + (y-1)^2 = 4 \\\\\\ (x^2+4x+4) + (y^2 - 2y + 1) = 4\implies \boxed{x^2+4x +y^2 -2y + 1 = 0}\)

Answer:

Step-by-step explanation:

Answer: 500 + 30 + 1 + 0.2 + 0.04 + 0.006