Which of these is the equation of the new function? ​

Answer:

The vertex form of the quadratic function, f(x) = a·(x - h)² + k

Step-by-step explanation:

The general form of a quadratic function is given as follows;

f(x) = a·x² + b·x + c

The vertex form of the quadratic function is f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex of the parabola

h = -b/2·a, k = f(h)

Answer:

30 seconds

Step-by-step explanation:

→ Work out how many floors it's going to travel

15 - 3 = 12 floors

→ Work out how many meters 12 floors is

12 × 5 = 60 meters

→ Work out how long that will take

60 ÷ 2 = 30 seconds

Answer:

[tex]\angle A=90-72[/tex]

[tex]\angle A=18[/tex]

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

[tex]sin~72=\frac{b}{11}[/tex]

[tex]11\times sin~72=6[/tex]

[tex]b=10.5[/tex]

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

[tex]11\times cos~72=a[/tex]

[tex]a=3.4[/tex]

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

ANSWER:

a=3.4

b=10.5

∠A=18

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

hope it helps...

have a great day!!

Answer:

[tex]4-6i[/tex]

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

Answer: C. (0, -3)

Step-by-step explanation:

You don't even need to find the function, just mentally graph every point in the options on the graph.

The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.

Answer:

(12, 2 )

Step-by-step explanation:

Given (x, y ) on the graph of f(x) , then on the inverse function

(x, y ) → (y, x ), then

(2, 12 ) → (12, 2 ) ← point on g(x) the inverse function

Answer:

1)  [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Answer:

parallel

Step-by-step explanation:

Let's rewrite each equation into the slope-intercept form so that we can easily identify the slope of each line.

slope-intercept form: y= mx +c, where m is the gradient and c is the y-intercept.

9x +3y= 12

3x +y= 4 (÷3 throughout)

y= -3x +4 -----(1)

24x +8y= 35

8y= -24x +35 (-24x on both sides)

[tex]y = - 3x+ 4 \frac{3}{8} [/tex] -----(2)

Thus, the slopes of the lines are both -3. Since both lines have the same gradient, they are parallel to each other.

Notes:

• parallel lines have the same gradient

• the product of the gradients of two perpendicular lines is -1

• gradient and slope has the same meaning and can thus be used interchangeably

Answer:

The population of Fun City after 171 years would be 214563.

Step-by-step explanation:

The statement depicts a case of exponential growth, whose model is described below:

[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)

Where:

[tex]p_{o}[/tex] - Initial population, no unit.

[tex]p(t)[/tex] - Current population, no unit.

[tex]r[/tex] - Growth rate, no unit.

[tex]t[/tex] - Time, in years.

[tex]T[/tex] - Growth period, in years.

If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:

[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]

[tex]p(t) = 214563[/tex]

The population of Fun City after 171 years would be 214563.

[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]

Hope it helps!!!

Thanks!!!

Answer:

[tex]j = - 0.45[/tex]

Step-by-step explanation:

Combine like terms and apply the rules of algebra.

[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1[/tex]

[tex] - 5.5 - 9.5j = 0.5j - 1[/tex]

[tex] - 9.5j = 0.5j + 4.5[/tex]

[tex] - 10 j= 4.5[/tex]

[tex]j = - 0.45[/tex]

Answer: j = -0.45

Step-by-step explanation:

Step 1: Combine like terms

2.25 - 11j - 7.75 + 1.5j = 0.5j - 1

-5.5 - 9.5j = 0.5j - 1

Step 2: isolate your variable

-5.5 - 9.5j = 0.5j - 1

Subtract 0.5j from both sides

-5.5 - 10j = -1

Add 5.5 to both sides

-10j = 4.5

Divide both sides by -10

j = -0.45

Answer:

1 and 2.....then 3 is a different question

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 1)² + (y - 12)² = 25 ← is in standard form

with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct .

Answer:

[tex] \frac{ \frac{3}{x - 1} - 4 }{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1) - 2}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2 - 2 } \\ \frac{7 - 4x}{2(x - 2)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]

Answer:

y=X²-4x+5

Step-by-step explanation:

substitute all the left side values to get the outputs..

y=(5)²-4(5)+5 =10

Answer:

A

Step-by-step explanation:

In fact, if we try to substitute, we have:

10 = 5^2 -4(5) +5

10 = 25 - 20 + 5

10 = 10 (ok)

17 = -2^2 - 4(-2) + 5

17 = 4 + 8 + 5

17 = 17 (ok)

and so on

Answer:

OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

To know more about scale factors follow

https://brainly.com/question/25722260

#SPJ2

Answer:

Let's define the high temperature as T.

We know that:

"four times T, was more than 2*T plus 66°C"

(i assume that the temperature is in °C)

We can write this inequality as:

4*T > 2*T + 66°C

Now we just need to solve this for T.

subtracting 2*T in both sides, we get:

4*T - 2*T > 2*T + 66°C - 2*T

2*T > 66°C

Now we can divide both sides by 2:

2*T/2 > 66°C/2

T > 33°C

So T was larger than 33°C

Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.

Then the range of possible temperatures is:

(33°C, ...)

Where we do not have an upper limit, so we could write this as:

(33°C, ∞°C)

(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)

Given:

The statement is: If 2 angles are both right angles then they are congruent.

To find:

The converse of the given statement and then check whether it is true or not.

Solution:

We know that,

Statement: If p, then q.

Converse : If q, then p.

The statement is: If 2 angles are both right angles then they are congruent.

So, the converse of this statement is:

If 2 angles are congruent then both are right angles.

This statement is not true because if 2 angles are congruent then it is not necessary that the angles are right angles.

Therefore, the converse of this statement is not true.

k<28

Step 1: Simplify both sides of the inequality.

−k+28>0

Step 2: Subtract 28 from both sides.

−k+28−28>0−28

−k>−28

Step 3: Divide both sides by -1.

−k /−1  >  −28 /−1

k<28

Answer:

k < 28

Step-by-step explanation:

Given inequality :-

Last Option is correct .

Hello,

Imagine Algebra does not exist .

Let's suppose all tickets are children's tickets

The sum should be 5$*375=1875$

Not enough, we must have $2153: 2153-1875=278 ($) must be found.

Let's replace a children ticket with an adult one,

we get one dollar more.

We must thus exchange 278 tickets

There are 278 adult tickets and 375-278=97 children tickets

Proof:  278*6+97*5=2153

Answer:

[tex] ({x}^{2} + 4 )( {x}^{2} - 4) \\ 1)( {x}^{2} - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^{2} + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^{2} + 8x + 16 \\ {x}^{2} + (4 + 4)x + 16 \\ {x}^{2} + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^{2} - 8x - 16 \\ {x}^{2} - (4 + 4)x - 16 \\ {x}^{2} - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)[/tex]

Answer:

1/2 + 2/3 + 5/4 = 29/ 12 = 2 5/  12  ≅ 2.4166667

Step-by-step explanation:

Add: 1/ 2  + 2/ 3  = 1 · 3/ 2 · 3  + 2 · 2/ 3 · 2  = 3/ 6  + 4/ 6  = 3 + 4/ 6  = 7/ 6

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one half plus two thirds = seven sixths.

Add: the result of step No. 1 + 5/ 4  = 7/ 6  + 5/ 4  = 7 · 2/ 6 · 2  + 5 · 3/ 4 · 3  = 14/ 12  + 15/ 12  = 14 + 15/ 12 = 29/ 12

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seven sixths plus five quarters = twenty-nine twelfths.

hope it helps...

correct me if I'm wrong...

Answer:

x = -1, y = -1

Step-by-step explanation:

x = 4y + 3

2x + y = -3

We have the value of x in terms of y, so we substitute that in 2x + y = -3:

2(4y+3)+y = -3

8y+6+y = -3

9y = -9

y = -1

Now we substitute the value of y in x = 4y + 3:

x = 4(-1)+3

x = -1

Answer:

y = -1 & x = -1

Step-by-step explanation:

x = 4y + 3 .... ( 1)

2x + y = -3 ........(2)

substitute the 4y + 3 as x in the second equation

2( 4y + 3) + y = -3

simplify and solve for y

8y + 24 + y = -3

9 y + 24 = -3

9y = -3 -24

9y = -27

y = -27 / 9

y = -1

Now, substitute the value of y -1 in first equation

x = 4y + 3

solve for x

x = 4 ( - 1 ) + 3

x = -4 + 3

x = -1

Answer:

The domain and range is (as inequalities):

[tex]x\leq 3\text{ and } -\infty < y < \infty[/tex]

Or in interval notation:

[tex]D=(-\infty, 3]\text{ and } R=(-\infty, \infty)[/tex]

Step-by-step explanation:

Recall that the domain is simply the set of all x-values of the function.

From the graph, we can see that the function is defined for all x-values less than or equal to 3.

Therefore, the domain is:

[tex]x\leq 3[/tex]

The range is the set of all y-values of the function.

From the graph, we can see that the range will extend infinitely in both directions.

Therefore, the range is all real numbers. As an inequality:

[tex]-\infty < y < \infty[/tex]

Or in interval notation, the domain is:

[tex](-\infty, 3][/tex]

And the range is:

[tex](-\infty, \infty)[/tex]

Answer:

7.1

Step-by-step explanation:

We used SOHCAHTOA because it's a right angle triangle

So because we have an angle with an adjacent of 6.3 and hypotenuse of x

We will use

Cos=adjacent /hypotenuse

Answer:

There are 39 seats I think.

Step-by-step explanation:

548 divided by 14 is a decimal but rounded it to the nearest full number.

the answer is in the picture