The vertex of the parabola represented by f(x)=x^2-2x+6 has coordinates (1,5). Find the coordinates of the vertex of the parabola defined by g(x)=f(x+3). Explain how you arrived at your answer

QUESTION POSTED AT 15/01/2020 - 03:08 AM

Related questions

The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage?

The point (-4, 7) is in the 2nd quadrant. The coordinate of the preimage of a -90 degrees rotation that resulted to point (-4, 7) will be in the third quadrant. (i.e. both x and y is negative). Hence, answer is (-7, -4).

ANSWERED AT 29/01/2020 - 05:41 PM


QUESTION POSTED AT 29/01/2020 - 05:41 PM

For every 10 fish you have, you need 5 gall how many gallons pf water do u have for 1 fish

10/5 = 1/x
cross multiply
10x = 5
x = 5/10
x = 1/2...u need 1/2 gallon per fish

ANSWERED AT 29/01/2020 - 05:40 PM


QUESTION POSTED AT 29/01/2020 - 05:40 PM

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?

Answer:

(3.95m) + (8.95b) = 47.65

Step-by-step explanation:

Hugh bought some magazines that cost = $3.95 each

the cost of each books = $8.95

He spent a total on purchase of books and magazines = $47.65

Let m represent the number of magazines and b represent the number of books.

Now the equation will be

(3.95m) + (8.95b) = 47.65

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 2x+7y=4 -4x -3y=14

2x + 7y = 4.....multiply by 2
-4x - 3y = 14
------------------
4x + 14y = 8 (result of multiplying by 2)
-4x - 3y = 14
----------------add
11y = 22
y = 2

2x + 7y = 4
2x + 7(2) = 4
2x + 14 = 4
2x = 4 - 14
2x = - 10
x = -5

solution is : (-5,2)

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

John wants to buy a new bike that costs $337 and he already has saved $103. Estimate to find about how much more John needs to save to buy the bike

John needs 234 dollars more for the bike.  About 235

336-103=234

ANSWERED AT 29/01/2020 - 05:35 PM


QUESTION POSTED AT 29/01/2020 - 05:35 PM

What is the circumference of circle p? Express your answer in terms of π (pi).

Whats the radius
of the circumfrence

ANSWERED AT 29/01/2020 - 05:35 PM


QUESTION POSTED AT 29/01/2020 - 05:35 PM

What is the circumference of circle p? Express your answer in terms of π (pi).

C = 2 * pi * r
C = 2 * pi * 29
C = 58(pi)

ANSWERED AT 29/01/2020 - 05:34 PM


QUESTION POSTED AT 29/01/2020 - 05:34 PM

A cylindrical container is packaged inside a prism-shaped box. The box has a volume of 96 cubic units. If the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? Round the answer to two decimal places.

Answer:

The volume of the empty space is 20.57 unit³.

Step-by-step explanation:

Given,

The volume of the box = 96 cubic units,

Also, the cylindrical container is packed inside the box.

We know that,

The volume of a cylinder is,

V=\pi (r)^2 h

Where r is the radius of cylinder,

h is its height,

Here, r = \frac{4}{2} = 2 unit   ( Radius = Diameter / 2 )

And, h = 6 units

Thus, the volume of the cylindrical container is,

V=\pi (2)^2(6)

=\frac{22}{7}\times 4\times 6 = \frac{528}{7}\text{ cubic unit}

Hence, the volume of the empty space between the cylinder and the box = Volume of the box - Volume of the container

= 96 - \frac{528}{7}

=\frac{672-528}{7}

=\frac{144}{7}=20.5714285714\approx 20.57\text{ cubic unit}

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

What is the circumference of circle p? Express your answer in terms of π (pi).

Equation: C = 2 \pi r
Step 1.) C = 2 * 3.1415 * 17
Solution: 106.814

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

The coordinates on the coordinate grid is (-1,5) the point is reflected across the x-axis to obtain a new point . The coordinate of the reflected point is?

1,5 I think because the x is negative so it would become positive and the y would stay the same.

ANSWERED AT 29/01/2020 - 05:32 PM


QUESTION POSTED AT 29/01/2020 - 05:32 PM

Question 1 of 8Fill in the blank: Type your answer in the box and then click "submit."What is the value of y?114Answer:

The value of 'y' is 57.

ANSWERED AT 29/01/2020 - 05:32 PM


QUESTION POSTED AT 29/01/2020 - 05:32 PM

Find the zeros of the function. f(x)= 3x^3- 12x^2- 15x a. 0, 1, and -5 b. -1 and 5 c. 0, -1, and 5 d. 1 and -5

F(x) = 3x³ - 12x² - 15x

1) Factor Outside: 3x( x² - 4x - 5)

Factor Inside: 3x(x + 1)(x - 5)

2) Set Equal To 0:
3x = 0
x + 1 = 0
x - 5 = 0

3) Solve:
x = 0, -1, 5

ANSWERED AT 29/01/2020 - 05:31 PM


QUESTION POSTED AT 29/01/2020 - 05:31 PM

The legs of a right triangle have lengths of 4 and 5 units. Find the length of the hypotenuse.

Answer:

\text{Length of hypotenuse is }\sqrt{41}units

Step-by-step explanation:

Given the legs of right angled triangle 4 and 5 units. we have to find the length of hypotenuse.

By Pythagoras theorem,

In right angled triangle the square of the length of the hypotenuse is equal to sum of squares of the lengths of other two sides

Hypotenuse&^2=Base^2+Height^2\\\\Hypotenuse^2=4^2+5^2\\\\H^2=16+25\\\\H=\sqrt{41}units=6.4units

Hence, \text{length of hypotenuse is }\sqrt{41}units

ANSWERED AT 29/01/2020 - 05:29 PM


QUESTION POSTED AT 29/01/2020 - 05:29 PM

How many significant figures will there be in the answer to the following 403.7*4.03

7 :). The answer is 1626.911. None of these digits are a zero, so therefore all 7 are sig figs :)

ANSWERED AT 29/01/2020 - 05:27 PM


QUESTION POSTED AT 29/01/2020 - 05:27 PM

The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage? A.(–7, –4) B.(–7, 4) C.(4, –7) D.(7, –4)

The point (-4, 7) is in the 2nd quadrant. The coordinate of the preimage of a -90 degrees rotation that resulted to point (-4, 7) will be in the third quadrant. (i.e. both x and y is negative). Hence, answer is (-7, -4).

ANSWERED AT 29/01/2020 - 05:27 PM


QUESTION POSTED AT 29/01/2020 - 05:27 PM

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so what is the hight of the dam

The height of a dam:
h = x + 1.65 m,
where:
x = 90 m · tan 26°
x = 90 · 0.4877
x = 43.90
h = 43.90 m + 1.65 m = 45.55 m
Answer:
The height of the dam is 45.5 m.

ANSWERED AT 29/01/2020 - 05:23 PM


QUESTION POSTED AT 29/01/2020 - 05:23 PM

Honora started an insect collection. By the fourth week,she collected 32 insects. Week Number of Insects 1 4 2 8 3 16 4 32 5 ? If the pattern continued, how many insects did Honora collect by Week 5?

Weeks                    :     1       2     3        4      5
number of insects  :     4      8     16     32     64

each week ur insect collection doubled...so by week 5, u had 64 insects in ur collection

ANSWERED AT 29/01/2020 - 05:22 PM


QUESTION POSTED AT 29/01/2020 - 05:22 PM

Find the slope of the line whose equation is 15 + 3x = 2y.

15+3x=2y
2y=3x+15
y= \frac{3}{2} x+ \frac{15}{2}
Gradient, m=  \frac{3}{2}

ANSWERED AT 29/01/2020 - 05:22 PM


QUESTION POSTED AT 29/01/2020 - 05:22 PM

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?

To get the x-intercepts of the function, f(x) = 4x2 – 24x + 20

It has to be equated to zero and the values of x are the x-intercepts. So,

4x2 – 24x + 20 = 0

The resulting equation is a quadratic equation which can be solved by different methods. The solution is

x = 5, 1

The average therefore is:

(1+5/)2 = 3

ANSWERED AT 29/01/2020 - 05:22 PM


QUESTION POSTED AT 29/01/2020 - 05:22 PM

QT bisects ∠PQR. find ∠PQR if ∠RQT = (10x-13) and ∠PQT = (6x+1) i need to know angle PQR and the value of X.

The answer might be 
<PQR = 6x+1
X=3.5

ANSWERED AT 29/01/2020 - 05:21 PM


QUESTION POSTED AT 29/01/2020 - 05:21 PM

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image? A.(–5, –4) B.(–4, 2) C.(2, 2) D.(2, 4)

Hint:
r_{y=k): (x,y)->(x,-(y-k)+k)
or simplified,
r_{y=k): (x,y)->(x,2k-y)

So in this case, k=-1, x=2, y=-4
(2,-4) -> (2, 2(-1)-(-4)
(2,-4) -> (2, -2+4)
(2,-4) -> (2, 2)

ANSWERED AT 29/01/2020 - 05:19 PM


QUESTION POSTED AT 29/01/2020 - 05:19 PM

Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 3. (Input decimals only, such as 12.71, as the answer.)

Answer:

I got 65.94

Step-by-step explanation

3 x 3=9

3 x 4=12

12+9= 21

21 x 3.14 = 65.94

ANSWERED AT 29/01/2020 - 05:18 PM


QUESTION POSTED AT 29/01/2020 - 05:18 PM

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image? A.(–5, –4) B.(–4, 2) C.(2, 2) D.(2, 4)

The coordinates of the image are : C ) ( 2, 2 )

ANSWERED AT 29/01/2020 - 05:17 PM


QUESTION POSTED AT 29/01/2020 - 05:17 PM

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +

Hello,

u_{1}=72\\&#10;&#10;u_{2}=\dfrac{72}{6}\\&#10;&#10;u_{3}=\dfrac{72}{6^{2}}\\&#10;&#10;u_{15}=\dfrac{72}{6^{14}}\\&#10;&#10;&#10;s=72*(1+\dfrac{1}{6^{1}}+\dfrac{1}{6^{2}}+\dfrac{1}{6^{3}}++...+\dfrac{1}{6^{14}})\\&#10;=72*(\dfrac{\frac{1}{6^{15}}-1}{\frac{1}{6}-1}})\\&#10;=72*(\dfrac{470184984576-1}{78364164095*5})\\&#10;&#10;=86,400...&#10;&#10;&#10;

ANSWERED AT 29/01/2020 - 05:16 PM


QUESTION POSTED AT 29/01/2020 - 05:16 PM

The ordered pairs below represent a relation between x and y.(-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11)Could this set of ordered pairs have been generated by a linear function?A. No, because the distance between consecutive y-values is different than the distance between consecutive x-valuesB. Yes, because the distance between consecutive x-values is constantC. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate itD. No, because the y-values decrease and then increase

Answer:

The correct answer is C.

Step-by-step explanation:

Notice that the difference between consecutive values of x is always 1, and the difference between consecutive values of y is always 2. This means that

\frac{x_{1}-x_{0}}{y_{1}-y_{0}} = 2

where x_0 and x_1 stands for two consecutive values of x, and the same goes to y.

Now, notice that this is the definition of the slope of the equation of a line. Then, a line can be characterized by this condition, and that is why C is the correct answer.

Anyway, you can check that this set of point is generated by a linear function in other way. Suppose that it can be done, and the linear function has the form

y=mx+n.

From the pair (0,7) we deduce that  7 =m*0+n, then n=7. Now, substituting the pair (-3,1) we get 1=-3*m+7 and as consequence m=2. Thus, if the points are generated by a linear function, its expression would be y=2x+7.

Now, substitute the different values of x and check that the same values of y are obtained.

ANSWERED AT 29/01/2020 - 05:16 PM


QUESTION POSTED AT 29/01/2020 - 05:16 PM

1.Which is an equation of a circle with center (-5, -7) and radius 6? 2.Which is an equation of a circle with center (5, 0) that passes through the point (1, 1)? 3.What is the center and radius of the circle with equation (x - 5)2 + (y + 3)2 = 16? 4.Which point is on the circle described by (x - 2)2 + (y + 3)2 = 4?

1. Equation of circle = (x - a)^2 + (y - b)^2 = r^2; where (a, b) is the centre of the circle and r is the diameter.
(x - (-5))^2 + (y - (-7))^2 = 6^2
(x + 5)^2 + (y + 7)^2 = 36
x^2 + 10x + 25 + y^2 + 14y + 49 = 36
x^2 + y^2 + 10x + 14y + 38 = 0

ANSWERED AT 29/01/2020 - 05:15 PM


QUESTION POSTED AT 29/01/2020 - 05:15 PM

The ordered pairs below represent a linear relation between x and y. (-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20) Which of the following is a correct statement about this relation? A. The slope of the line represented by this table is -4 and the y-intercept is -3. B. The slope of the line represented by this table is 4 and the y-intercept is 12. C. The slope of the line represented by this table is 4 and the y-intercept is -3. D. The slope of the line represented by this table is -4 and the y-intercept is 12.

Answer:

The correct option is B.

Step-by-step explanation:

It is given that the ordered pairs below represent a linear relation between x and y. (-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20).

At y-intercept the value of x is 0. From the given points we can say that the y-intercept of the function is (0,12).

If a line passing through the two points, then the slope of the function is

m=\frac{y_2-y_1}{x_2-x_1}

The slope of the function is

m=\frac{4-0}{-2-(-3)}=\frac{4}{1}=4

Therefore the slope of the line represented by this table is 4 and the y-intercept is 12. Option B is correct.

ANSWERED AT 29/01/2020 - 05:15 PM


QUESTION POSTED AT 29/01/2020 - 05:15 PM