Plot the following points on the coordinate gria: A(0,-3),B(-2,0),C(-1,4),D(3,-4)

Answer:  2+n

Step-by-step explanation:

Tn=T1 + (n-1) d

3+(n-1)1

3+n-1

3-1+n

2+n

Answer:

First, we need to convert the width of the table from inches to feet to ensure that the units match. There are 12 inches in a foot, so:

42 inches ÷ 12 inches/foot = 3.5 feet

Let the length of the table be L feet. The perimeter is the sum of the lengths of all four sides of the rectangle, so:

2L + 2(3.5 feet) = 18 feet

Simplifying and solving for L:

2L + 7 feet = 18 feet

2L = 11 feet

L = 5.5 feet

Therefore, the length of the table is 5.5 feet.

Answer:

66

Step-by-step explanation:

the problem ask fr it draw out 2 rectangle

The volume of the right prism if bases are 15 cm apart is 405√3/2 cm^3.

The volume of a right prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a regular hexagon with one side measuring 6 cm and the height of the prism is 15 cm.

To find the area of the base, we can use the formula for the area of a regular hexagon: [tex]A = (3√3/2)s^2[/tex], where s is the length of one side.

Plugging in the value of s = 6 cm, we get:
[tex]A = (3√3/2)(6 cm)^2 = 54√3/2 cm^2[/tex]

Now we can plug this value into the formula for the volume of the prism:
V = Bh = ([tex]54√3/2 cm^2)(15 cm) = 405√3/2 cm^3[/tex]

So the volume of the prism is 405√3/2 cm^3.

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Answer: 1

Step-by-step explanation:

(6) + (8) ÷ 8 - 6
divide first then do left to right
6 + 1 - 6
7 - 6
1

Answer:

1

Step-by-step explanation:

t = 6 and d = 8

t + d ÷ 8 - 6 = 6 + 8 ÷ 8 - 6

6 + 1 - 6

6 + 1 - 6 = 1

The constant of proportionality, k, that relates the cost in dollars, y, to the number of tickets, x, is $62.30. The constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x, is 16. The circumference of the circle is approximately 23.876 feet.

1. To find the constant of proportionality, k, we need to divide the cost of the tickets by the number of tickets.
k = y/x = $498.40/8 = $62.30

Therefore, the constant of proportionality, k, is $62.30.

2. To find the constant of proportionality, k, we need to divide the number of cookies made by the number of cups of flour used.
k = y/x = 48/3 = 16

Therefore, the constant of proportionality is 16.

3. To find the circumference of a circle, we use the formula C = πd, where C is the circumference and d is the diameter.
C = π(7.6) = 23.876 feet

The measurement closest to the circumference of the circle in feet is 23.876 feet.

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After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).

The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).

Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).

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Answer:

Part A

a = 1

b = 3

c = -4

Part B

[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

Part D

Option B:   x = 1 and x = -4

Step-by-step explanation:

The standard form of the quadratic equation is [tex]ax^2 + bx + c=0[/tex]

1.The given equation is [tex]x^2 + 3x - 4 = 0[/tex]

Part A

Comparing the given equation with the generalized standard equation we see that

[tex]a[/tex]  = coefficient of [tex]x^2[/tex] = 1

[tex]b[/tex]= coefficient of [tex]x = 3[/tex]

[tex]c[/tex]= constant term = [tex]-4[/tex]

Part B.

The quadratic formula for the roots of the equation is:
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

Plugging in values for a, b and c from Part A:
[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

part D
Simplifying we get

[tex]x = \dfrac{ -3 + 5\, }{ 2 } = \dfrac{2}{2} = 1\\\\x = \dfrac{ -3 - 5\, }{ 2 } = \dfrac{-8}{2} = -4\\\\[/tex]

Correct answer for Part C:
B. x = 1 and x = -4

Answer:

Linear equation to represent the total cost:

Let x be the number of kgs of tomatoes Mail bought, and y be the number of kgs of potatoes Mail bought. The cost of x kgs of tomato at Rs. 50 per kg is 50x, and the cost of y kgs of potato at Rs. 20 per kg is 20y. Therefore, the total cost of the vegetables is:

Total cost = 50x + 20y

Substituting the value of total cost as Rs. 200, we get:

50x + 20y = 200

This is the required linear equation to represent the total cost.

Finding the value of x:

Let's assume that Mail bought x kgs of tomato and 2.5 kgs of potato. Using the equation derived above:

50x + 20(2.5) = 200

Simplifying the equation:

50x + 50 = 200

50x = 150

x = 3

Therefore, Mail bought 3 kgs of tomato.

Finding the point at which the graph of 5x+2y=20 cuts x-axis:

To find the point at which the graph of 5x+2y=20 cuts the x-axis, we need to set y = 0 in the equation and solve for x:

5x + 2(0) = 20

5x = 20

x = 4

Therefore, the point where the graph of 5x+2y=20 cuts the x-axis is (4,0).

The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.

The surface area of one tire making contact with the ground can be calculated as follows:

The diameter of the tire is 2 * radius = 2 * 21 in = 42 in

The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in

The width of the tire making contact with the ground is given as 12 in

Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches

Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.

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Answer:

16 + 24

Step-by-step explanation:

Answer:34

Step-by-step explanation:

The option that best describes the value 1.5 in the linear equation; u = 0.75·t + 1.5 is option D

D. y-intercept and the initial amount of rain, in inches at midnight

A linear equation is an equation of the form; y = m·x + c, where, m is the slope, and c is the y-intercept of the graph of the equation.

The time at which the analysis of the rainstorm by the meteorologist starts = 10 p. m.

The linear model for the accumulation of rain is; u = 0.75·t + 1.5

The number of hours, t after midnight where; t > 0

The model for the accumulation of rain, indicates that the coefficient of t, which is 0.75 is the rate at which the rain accumulates in inches per hour, therefore, the rain accumulates at a rate of 0.75 inches per hour

The constant term in the linear equation, u = 0.75·t + 1.5, which is the constant, 1.5, is the y-intercept of the graph of the equation.

The y-intercept is the value of the equation, when the input value, the time, t = 0, which is the time at midnight

The 1.5 therefore, indicates that the y-intercept, and the level of the accumulated rain at midnight, when the time, t = 0, which is the initial amount of rain at midnight is 1.5 inches.

The correct option is therefore;

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A) The Rational Root Theorem states that the only rational zeros of p(x) = x4+12x-5 must be a factor of -5 divided by a factor of 1. Therefore, the four possible rational zeros are -5, -1, 1, and 5.

B) The other three zeros is 1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)

A) The Rational Root Theorem states that if a polynomial with integer coefficients has a rational root r = p/q (where p and q have no common factors), then p must divide the constant term of the polynomial and q must divide the leading coefficient.

The constant term of p(x) = x^4 + 12x - 5 is -5, which has the factors ±1 and ±5. The leading coefficient is 1, which has the factors ±1. Therefore, the possible rational roots are:

±1/1, ±5/1, ±1/5, ±5/5 (which simplifies to ±1)

B) If r = 1 - 2i is a zero of p(x), then its complex conjugate r* = 1 + 2i is also a zero of p(x), since p(x) has real coefficients. Therefore, we can factor p(x) as:

p(x) = (x - r)(x - r*)(x²+ bx + c)

where b and c are the coefficients of the quadratic factor. We can expand this and compare coefficients to get:

x⁴ + 12x - 5 = (x - 1 + 2i)(x - 1 - 2i)(x² + bx + c)

Expanding the first two factors gives:

(x - 1 + 2i)(x - 1 - 2i) = x² - 2x + 5

Therefore, we have:

x⁴ + 12x - 5 = (x² - 2x + 5)(x² + bx + c)

Expanding the right side and comparing coefficients, we get:

b = -2 and c = -6

So the quadratic factor is:

x² - 2x - 6

We can find its roots using the quadratic formula:

x = [2 ± √(4 + 4(6))] / 2

x = 1 ± √(7)

Therefore, the four zeros of p(x) are:

1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)

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Step-by-step explanation:

To find the x-intercepts of the quadratic function f(x) = x^2 + 6x - 27, we need to set f(x) equal to zero and solve for x.

So we have:

f(x) = 0

x^2 + 6x - 27 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 1, b = 6, and c = -27.

Substituting these values into the quadratic formula, we get:

x = (-6 ± sqrt(6^2 - 4(1)(-27))) / 2(1)

x = (-6 ± sqrt(180)) / 2

x = (-6 ± 6sqrt(5)) / 2

x = -3 ± 3sqrt(5)

So the x-intercepts of the quadratic function are approximately -10.16 and 4.16.

Answer:

Step-by-step explanation:

The answer is 11.61

The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.

Plugging in the given values, we get:

\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)

Simplifying, we get:

\( s = \frac{11\pi}{2} \mathrm{in} \)

Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).

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The equation is now in the form y=mx+b, where m is 2 and b is -4. The second equation is now in the form y=mx+b, where m is -0.5 and b is -2.

An equation is an expression that shows the relationship between two or more variables. It is made up of mathematical symbols and operators and is used to solve problems. Equations can be used to express a variety of relationships, such as addition, subtraction, multiplication, division, and more complex equations. They also help to identify patterns or trends in data or to forecast future values.

To change these equations into y=mx+b form, we must first rearrange the equations.

For the first equation, 2x-4=8, we can move the 4 to the other side of the equation, giving us 2x = 12. We can then divide both sides by 2, giving us x = 6. So the equation is now in the form y=mx+b, where m is 2 and b is -4.

For the second equation, -2x+4y=-8, we can move the -2x to the other side of the equation, giving us 4y=-8-2x. We can divide both sides by 4, giving us y=-2-0.5x. So the equation is now in the form y=mx+b, where m is -0.5 and b is -2.

Now that both equations are in y=mx+b form, we need to compare their m and b values to determine if there is one solution, no solution or infinite solutions. We can see that m for both equations is different, so this means that the two equations are not the same, and there is no solution. This means that the two equations have no solution.

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The account will be growing by $741.87 per year 11 years from now.

To find the answer, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.03, n = 1, and t = 11. Plugging these values into the formula gives us:
A = $2000(1 + 0.03/1)^(1*11)
A = $2000(1.03)^11
A = $2741.87
To find out how fast the account will be growing 11 years from now, we need to subtract the principal amount from the final amount:
$2741.87 - $2000 = $741.87

Therefore, the account will be growing by $741.87 per year 11 years from now.

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Taking into account the definition of molarity, the mass of MgBr₂ in 215 mL of a 0.350 M solution of MgBr₂ is 13.85 grams.

Molarity is a measure of the concentration of a solution expressed in the number of moles dissolved per liter of solution.

This is, the molarity indicates the number of moles of solute that are dissolved in a given volume.

The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:

molarity= number of moles of solute÷ volume

Molarity is expressed in units moles/L.

The molar mass of substance is a property defined as the amount of mass that a substance contains in one mole.

In this case, you have:

Replacing in the definition of molarity:

0.350 M= number of moles of solute÷ 0.215 L

Solving:

0.350 M× 0.215 L= number of moles of solute

0.07525 moles= number of moles of solute

Being the molar mass of MgBr₂ 184.11 g/mole, the mass of the compound is calculated as:

mass of MgBr₂= 0.07525 moles× 184.11 g/mole

mass of MgBr₂= 13.85 grams

Finally, the mass of MgBr₂ is 13.85 grams.

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Answer:29 1/4

Step-by-step explanation:

Because the formula for the volume of a rectangular prism is (w)(h)(l).

Answer:

1/4

Step-by-step explanation:

you can plug it into a calculator

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

Therefore, the answer is 1.

In HTML format, the answer would be:

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

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Answer:

2

Step-by-step explanation:

The coordinates of R are (-15, 8). The solution has been obtained by using Mid point formula.

What is Mid point formula?

The centre point of a straight line can be located using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.

We are given that Q is the midpoint of segment PR and point P is (11,-2) and point Q is (-2,3).

Let the coordinates of R be (x₂, y₂)

Using Mid point formula, we get

⇒Point Q = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

⇒(-2,3) = ((11 + x₂) / 2, (-2 + y₂) / 2)

So,

⇒-2 = (11 + x₂) / 2

⇒-4 = 11 + x₂

⇒x₂ = -15  

Similarly,

⇒3 = (-2 + y₂) / 2

⇒6 = -2 + y₂

⇒y₂ = 8

Hence, the coordinates of R are (-15, 8).

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a)CD and AA

b)CD + AA = 190,000

c)0.06CD + 0.11AA = 18,900

d)AA = 187,333.17.

(a) Let CD be the amount invested in Certificates of Deposit and AA be the amount invested in AA bonds.

(b) The total amount invested is given by the equation CD + AA = 190,000.

(c) The total amount earned from the investment is given by the equation 0.06CD + 0.11AA = 18,900.

(d) To solve this system of equations using elimination, we multiply the first equation by 0.11 and the second equation by 0.06 and add the resulting equations together, yielding the equation 12.06CD + 10.11AA = 214,084. We then subtract the original equation from this new equation to get 9.06CD = 24,084. Solving for CD, we get CD = 2,666.83. We can then substitute this value into either of the original equations to get AA = 187,333.17.

(e) Sally should invest $2,666.83 in Certificates of Deposit and $187,333.17 in AA bonds to earn exactly $18,900 per year.

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To construct a 3x3 linear system whose solution is (x,y,z)=(3,5,-2) using Gauss-Jordan's Elimination, we will first create an augmented matrix for the system.

This matrix will contain the coefficients for the variables x, y, and z, as well as the values for the constants. For example:
ax + by + cz = d

We can then plug in the values for x, y, and z, and choose values for a, b, c, and d that will make the equation true. For example:

2(3) + 3(5) - 4(-2) = 29

This gives us one equation in our system:

2x + 3y - 4z = 29

We can repeat this process two more times to get two more equations:

-5(3) + 2(5) + 3(-2) = -19

-5x + 2y + 3z = -19

4(3) - 6(5) + 2(-2) = -24

4x - 6y + 2z = -24

So our 3x3 linear system is:

2x + 3y - 4z = 29

-5x + 2y + 3z = -19

4x - 6y + 2z = -24

To solve this system using Gauss-Jordan's Elimination, we can write the system as an augmented matrix:

| 2  3 -4 | 29 |

|-5  2  3 |-19 |

| 4 -6  2 |-24 |

We can then use elementary row operations to reduce the matrix to reduced row echelon form:

| 1  0  0 | 3  |

| 0  1  0 | 5  |

| 0  0  1 |-2  |

This gives us the solution (x,y,z)=(3,5,-2), as desired.

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Answer:

csc(0)= 25/7

sec(0)= 25/24

cot(0)= 24/7

Step-by-step explanation:

Answer:

csc Θ = 25/7

sec Θ = 25/24

cot Θ = 24/7

Step-by-step explanation:

csc Θ = 1/sin Θ

sin Θ = opp/hyp

csc Θ = hyp/opp

csc Θ = 25/7

sec Θ = 1/cos Θ

cos Θ = adj/hyp

sec Θ = hyp/adj

sec Θ = 25/24

cot Θ = 1/tan Θ

tan Θ = opp/adj

cot Θ = adj/opp

cot Θ = 24/7

31, 87, 90 are the numbers which are considered possible outliers.

An outlier is an observation or data point that is significantly different from other observations in a dataset. In other words, it is an unusual or extreme value that is much higher or lower than most other values in the data.

A box and whisker plot is used to easily detect outliers. In this figure, the outliers are shown as black circles or dots. These are the data points that are distant from other observations.

Therefore, the numbers which are considered possible outliers are 31, 87, and 90.

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Answer:

60

Step-by-step explanation:

Colton is 60 because Polly is 21 and plus 39 is 60.

The values of x and y are determined by solving the equation

The values of x and y can be found by solving the equation x(23) + y(-10) = (106). This can be done by isolating one variable and solving for the other. For example, isolating x gives us x = (106 + 10y)/23. We can then plug this value of x back into the original equation and solve for y. Once we have the value of y, we can plug it back into the equation for x to find the value of x.

The value of −2p2s2v​−qtw​−rux​​ can be found by plugging in the given values of p, s, v, q, t, w, r, and u into the equation and simplifying.

The value of ∣3AB∣ can be found by using the properties of determinants of matrices. Specifically, the determinant of a product of matrices is equal to the product of the determinants of the individual matrices. Therefore, ∣3AB∣ = ∣3∣∣A∣∣B∣ = 3(-1)(3) = -9.

So, the values of x and y are determined by solving the equation x(23) + y(-10) = (106), the value of −2p2s2v​−qtw​−rux​​ is found by plugging in the given values and simplifying, and the value of ∣3AB∣ is found by using the properties of determinants of matrices.

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