To get system B, the
equation. The solution to system B
equation in system A was replaced by the sum of that equation and
v times the
v the same as the solution to system A

Answer:

463mi

Step-by-step explanation:

Answer:

(a) The zeroes of f(x) are rational numbers

(b) The smallest integer value of a is 3

Step-by-step explanation:

In the quadratic function f(x) = ax² + bx + c, we can know the number and the types of its roots using the discriminant  Δ, where Δ = b² - 4ac

Note: In the first case if Δ is a perfect square number then the zeroes are rational, if not then the zeroes are irrational

(a)

∵ The equation function is f(x) = ax² + 11x + 12

∵ a = 2

∴ a = 2, b = 11 and c = 12

→ Substitute them in the rule of Δ

∵ Δ = (11)² - 4(2)(12) = 121 - 96

∴ Δ = 25

∵ Δ > 0

∴ f(x) has two different real zeroes

∵ 25 is a perfect square number

→ That means the zeroes of the function are rational numbers

∴ The zeroes of f(x) are rational numbers

(b)

∵ f(x) ha imaginary zeroes

→ By using the third rule above

∴ Δ < 0

∵ a = a, b = 11 and c = 12

→ Substitute them in the rule of Δ

∴ (11)² - 4(a)(12) < 0

∴ 121 - 48a < 0

→ Add 48a to both sides

∵ 121 - 48a + 48a < 0 + 48a

∴ 121 < 48a

→ Divide both sides by 48

∴ 2.52083 < a

∴ a > 2.52083

∵ The smallest integer greater than 2.52083 is 3

∴ The smallest integer value of a is 3

Answer:

1 1/2 quarts per hour

Step-by-step explanation:

To do this you would divide 3/4 by 1/2 to do divide you flip 1/2 to 2/1 then multiply.

3/4*2/1=6/4 which is also equal to 1.5 quarts of paint per hour.

Answer:

Start at the y-intercept, (0,-1). Next, go up one and to the right 2, plot a point. Keep going up one and to the right 2 until you reach the end of the graph. Next, go back to your y-intercept. Go down one and to the left 2. Keep going down and to the left until you reach the end of the graph. Connect all points.

Step-by-step explanation:

Start at the y-intercept, (0,-1). Next, go up one and to the right 2, plot a point. Keep going up one and to the right 2 until you reach the end of the graph. Next, go back to your y-intercept. Go down one and to the left 2. Keep going down and to the left until you reach the end of the graph. Connect all points.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The coordinates that we can plot on the graph are:

(1, -1/2), (2, 0), (3, 1/2), and (4, 1)

The graph is given below

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The equation of a line y = (1/2)x - 1

We will find some coordinates from the equation.

When x = 1,

y = 1/2 - 1

y = -1/2

When x = 2,

y = 1/2 x 2 - 1

y = 1 - 1 = 0

When x  = 3,

y = 1/2 x 3 - 1

y = 3/2 - 1

y = 1/2

When x = 4.

y = 4/2 - 1

y = 2 - 1

y = 1

The coordinates that we can plot on the graph are:

(1, -1/2), (2, 0), (3, 1/2), and (4, 1)

The graph is given below

Thus,

The coordinates that we can plot on the graph are:

(1, -1/2), (2, 0), (3, 1/2), and (4, 1)

The graph is given below

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ2

Answer:

Rs. 3923.08

Step-by-step explanation:

First principal invested = Rs. 10000

Interest rate = 5%

The interest is compounded yearly.

Time = 1 year

1 year compound interest is equal to simple interest.

Formula for simple interest:

[tex]SI = \dfrac{PRT}{100}[/tex]

Interest on first sum = [tex]\frac{10000\times 5\times 1}{100} = Rs\ 500[/tex]

Another sum is on fixed deposit 8% compounded half yearly.

Let the sum = Rs [tex]x[/tex]

Formula for compound interest is given as:

[tex]CI = P(1+\frac{R}{100})^T - P[/tex]

It is compounded half - yearly, therefore T = 2

[tex]CI = x (1+\frac{8}{100})^2 - x\\\Rightarrow CI = x(1.08)^2-x = 0.1664x[/tex]

As per question statement:

[tex]0.1664x - 500 = 152.80\\\Rightarrow x = \dfrac{652.80}{0.1664} = Rs\ 3823.08[/tex]

Answer:

2y + 4z = x

Step-by-step explanation:

Given

[tex]x = -4[/tex]

[tex]y = -8[/tex]

[tex]z = 3[/tex]

Required

Write an equation that which is true for the above parameters

This question will be answered using trial by error method and the solution is not limited to one equation.

One equation that matches the values above is:.

[tex]2y + 4z = x[/tex]

To check:

Substitute the values of x, y and z in the above equation.

[tex]2y + 4z = x[/tex]

[tex]2 * -8 + 4 * 3 = -4[/tex]

[tex]-16 + 12 = -4[/tex]

[tex]-4 = -4[/tex]

Hence,

Because both sides of the equation are one and the same (-4), [tex]2y + 4z = x[/tex] is true for the above values of x, y and z.

Answer:

9

Step-by-step explanation:

18/2=9

Answer:

-9 feet per second

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

2 is the correct answer

Answer:

$5.25

Step-by-step explanation:

23.75-2.75= is the price of four cheeseburgers, which is 21. 21/4 is the price of one. So its 5.25

Answer:

379.94

Step-by-step explanation:

area of a circle is, pi times radius powered by 2, with this in mind-

r= 11, pi=3.14

3.14(11)^2

3.14(121)

=379.94

Answer:

Divide the percentage by 100 to get a decimal number. Use that number as the numerator (top) of a fraction. Put a 1 in the denominator (bottom) of the fraction. Convert the decimal to a whole number: Count how many places are to the right of the decimal.

Answer:

The answer is C.

Step-by-step explanation:

h(x) = 3x + 2 - 1

Step-by-step explanation:

|14- c| = 15

=> 14 - c = 15 or 14 - c = -15

=> c = -1 or c = 29.

Answer:

Speed = 25miles per hour

Step-by-step explanation:

Represent the time with x and the distance with y

So, from the attachment; we have the following details:

[tex](x_1,y_1) = (0.5,12.5)[/tex]

[tex](x_2,y_2) = (1,25)[/tex]

[tex](x_3,y_3) = (1.5,37.5)[/tex]

Required

Determine the constant speed

Because the train travelled at a constant speed, the speed can be calculated using:

[tex]Speed = \frac{y_3}{x_3}=\frac{y_2}{x_2}=\frac{y_1}{x_1}[/tex]

[tex]Speed = \frac{12.5}{0.5}=\frac{25}{1}=\frac{37.5}{1.5}[/tex]

[tex]Speed = 25=25=25[/tex]

Notice that the result of each division is the same.

Hence, the constant speed is:

Speed = 25miles per hour

Answer:

−11n + 10

Step-by-step explanation:

(4-n) + 2 (-5n+3)

4 - n + -10n + 6

-11n+4+6

The answer:-11n+10

Answer:

x = 106°

Step-by-step explanation:

sum of interior opposite angles of a triangular is equal to a exterior angle

= x +22= 40 +88

= x = 128- 22

x = 106 °

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Answer:

can you state what point I is?

Complete question :

A parachutist's speed during a free fall reaches 162 kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 20 seconds of free fall? Do not round your answers.

Answer:

45 m/s ; 900 meters

Step-by-step explanation:

Given that :

Speed = 162 kilometers per hour ;

The speed in meters per second can be found by:

162 km/hr = (162 * 1000)m / (60 * 60) second

162 km/hr = 162000m / 3600 s

162 km/hr = 45 m/s

At this speed, how many meters will the parachutist fall during 20 seconds of free fall?

Speed of free fall = 45m /s

Distance in meters after 20 seconds :

(45 m/s * 20s) = 900 meters

Answer:

0.5

Step-by-step explanation:

Distance of OL = 0 - (-5)

                         = 0 + 5

                         = 5

Distance of OK = 2(5)

                          = 10

Gradient = [tex]\frac{rise}{run}[/tex]

               = [tex]\frac{0-(-5)}{10-0}[/tex]

               = [tex]\frac{5}{10}[/tex]

               = 0.5

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

The distance between two points on the coordinate plane is given as:

[tex]Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6[/tex]

In triangle STU:

[tex]|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2[/tex]

|QR| / |TU| = 4/2 = 2

|PR| / |SU| = 6/3 = 2

|PQ| / |ST| = 2√13 / √13 = 2

Hence:

|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|

Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.

Similar triangles may or may not be congruent

Triangles PQR and STU are similar by SSS theorem.

The vertices of triangle PQR are given as:

[tex]P= (4, 4)[/tex]

[tex]Q= (-2, 0)[/tex]

[tex]R = (-2, 4)[/tex]

The vertices of triangle STU are given as:

[tex]S = (2, -4)[/tex]

[tex]T = (-1, -2)[/tex]

[tex]U =(-1, -4)[/tex]

Start by calculating the side lengths of the two triangles, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

For triangle PQR, we have:

[tex]PQ = \sqrt{(4 --2)^2 + (4 -0)^2} = \sqrt{52}[/tex]

[tex]PR = \sqrt{(4 --2)^2 + (4 -4)^2} = 6[/tex]

[tex]QR = \sqrt{(-2 --2)^2 + (0 -4)^2} = 4[/tex]

For triangle STU, we have:

[tex]ST= \sqrt{(2 --1)^2 + (-4 --2)^2} = \sqrt{13}[/tex]

[tex]SU= \sqrt{(2 --1)^2 + (-4 --4)^2} = 3[/tex]

[tex]TU= \sqrt{(-1 --1)^2 + (-2 --4)^2} = 2[/tex]

Check if the side lengths of both triangles are similar, by dividing corresponding sides

[tex]k = \frac{PQ}{ST} = \frac{\sqrt{52}}{\sqrt{13}} = 2[/tex]

[tex]k = \frac{PR}{SU} = \frac{6}{3} = 2[/tex]

[tex]k = \frac{QR}{TU} = \frac{4}{2} = 2[/tex]

Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.

Read more about similar triangles at:

https://brainly.com/question/8691470

Answer:

i hope this helps you

7.4+(-2)

28-2

26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Plug 4 in for y and -2 in for z giving you: 7(4)+(-2). 7*4=28 giving you 28+(-2). the portion +(-2) is the same as -2. This gives you 28-2 which is 26.

Answer:

No because if you set them equivelent to each other you get 12=0

Step-by-step explanation:

1/4(12x + 24) - 9x = -6(x + 1)

3x + 6 - 9x = -6x - 6

-6x + 6 = -6x - 6

12 = 0x

I hope this helps

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, but I would show how to solve.

Transformation is the movement of a point from its initial location to a new location. Types of transformation is reflection, translation, rotation and dilation.

Dilation is the enlargement or reduction of the size of an object by a factor.

If a point A(x, y) is dilated by a factor k with a center of dilation at (a, b), then the new point is:

A'(x, y) = [k(x - a) + a, k(y - b) + b]

Let us assume that point A(2, 0) dilation with a scale factor of 2 centered at (1, 2). Hence the new point is:

A'(x, y) = [2(2 - 1) + 1, 2(0 - 2) + 2]  = (3, -2)