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what do the coefficients of a quadratic function in standard form reveal about its graph?

Answer:

[tex]f(x) = 2000 * 1.05^x[/tex]

Step-by-step explanation:

The key to this question is interpreting the graph and then modelling it into an exponential function.

You are given 2 key characteristics of this graph. 1 characteristic being that it intercepts the y-axis at (0,2000), and another characteristic being that it goes through the point (1,2100)

Now refer to the standard form of an exponential function.

[tex]y = a * b^x[/tex]

Since you know that when x = 0, y = 2000, a must be 2000. Because [tex]b^0 = 1[/tex], 2000 * 1 = 2000

So you got your a value. Sub it into the equation and now you got.

[tex]y = 2000 * b^x[/tex]

You still need to solve for b, so this is where you do some algebra. Pick your key point, (1,2100), sub in those values for x and y, and solve for b.

[tex]2100 = 2000 * b^1\\\frac{2100}{2000} = b\\ 1.05 = b[/tex]

Now you have your a and b values. Now you can express using a function:

[tex]f(x) = 2000 * 1.05^x[/tex]

Answer:

a. 1

b. 1

Step-by-step explanation:

by looking at the graph you can deduce the answer.

The equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is,

g(x) = x²-3

The graph of a quadratic function that has something bowl-shaped. Any equation of the form ax²+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

To find the value of g (2) the value of the function is,

g(2) = 2²-3

g(2) =8-3

g(2) =5

Thus, the equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.

Learn more about the function here:

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Step-by-step explanation:

First box =25

Second Box = 0.25

Answer:

If you want to multiply then,

3/5 × 1/2 = 3/10 or 0.3

If you want to Add then,

3/5 + 1/2 = 6 + 5/5 × 2 = 11/10 or 1.1

If you want to subtract then,

3/5 – 1/2 = 6 – 5/5 × 2 = 1/10 or 0.1

If you want to Divide then,

3/5 ÷ 1/2 = 3/5 × 2/1 = 6/5

Answer:

132 cm³

Explanation:

[tex]\sf volume \ of \ cone = \dfrac{1}{3} \pi r^2h[/tex]

put radius: 3 cm, height: 14 cm, π as 22/7

[tex]\sf \rightarrow \dfrac{1}{3} *\dfrac{22}{7} * (3)^2(14)[/tex]

[tex]\sf \rightarrow 132 \ cm^3[/tex]

Answer:

Step-by-step explanation:

9.23

Answer:

i can't see the multiple choice

Step-by-step explanation:

angle c and b are equal

angle a and d are equal

and you have a common angle o

and ab = cd

The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

It is given that AB || CD. The side AB is congruent to the side CD.

The line AD and BC intersect at the mid-point. Then the line segment AO and OD will be congruent and the line segment CO and OB will be congruent.

And the angle ∠AOB and ∠COD will be congruent because they are vertically opposite angles.

The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.

More about the triangle link is given below.

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Answer:

Step-by-step explanation:

According to angle bisector theorem we get the following ratio:

Substitute the lengths and solve for x:

Use angle bisector theorem

Answer:

64 cm^3

Step-by-step explanation:

V = lwh

V = 4 x 4 x 4

V = 64 cm^3

Hope this helps!

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]

[tex] \mathsf \pink{v = {4}^{3} }[/tex]

[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]

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Answer:

The answer is, Jimmy, fed the horses 3 apples each.

27 apples divided into the 9 horses

27 ÷ 9 = 3

If you had 27 seven apples and you individually gave one apple to each of the 9 horses each horse would end up having 3.
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Answer:

Division property of equality

Step-by-step explanation:

If you have an equation with the variable not equal to one you want it to equal one so you would divide to get the variable to 1 so 5/5 and then you would do the same to the other side(75/5) d=15.

Answer:Division property of equality

Step-by-step explanation:If you have an equation with the variable not equal to one you want it to equal one so you would divide to get the variable to 1 so 5/5 and then you would do the same to the other side(75/5) d=15.

Answer:

6

Step-by-step explanation:

4 time one is 1

plug in 1 for m

and you got 4 - -2

witch both negatives make a positive

1hour=600

2hour=600+600

=1200words

Answer:

D) 130

Step-by-step explanation:

So there are three arc sections in this problem,

The first one is given: 158

To find the arc between S and R, you can use the angle of point T and double it.

So:

36 * 2 = 72

The second arc is 72

Now for the one that they want you to find, you have to add the two arcs that you have and substract it from 360, which is the angle of a whole circle

Like so:

360 - (158 + 72) = 130

Answer:

130

Step-by-step explanation:

Answer:

centre (5, 6 ) , r = [tex]\sqrt{37}[/tex]

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 the radius

given

x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )

x² - 10x + y² - 12y = - 24

using the method of completing the square

add ( half the coefficient of the x / y terms)² to both sides

x² + 2(- 5)x + 25 + y² + 2(- 6)y + 36 = - 24 + 25 + 36

(x - 5)² + (y - 6)² = 37 ← in standard form

with centre (h, k ) = (5, 6 ) and r = [tex]\sqrt{37}[/tex]

Answer:

1.732i (complex form)

its weird, at high-school level complex shouldn't come, its considered mistake in the question. But the mathematically its all correct

Step-by-step explanation:

Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.

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

Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.

Find out more on transformation at: https://brainly.com/question/4057530

Given is an A.P. in which -

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1[/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2 [/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5[/tex]

nth term of an A.P ,is given by-

[tex]\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}[/tex]

where

Putting n = 46

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, the 46th term is 227

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given sequence is

[tex]2,7, 12,...[/tex]

Here,

[tex]a=2[/tex]

[tex]d=a_2-a_1\\d=7-2\\d=5[/tex]

The general formula of the sequence is

[tex]a_n=a+(n-1)d[/tex]

where,

[tex]a_n=[/tex] nth term

[tex]a[/tex] is the first term

[tex]d[/tex] is the common difference

[tex]n[/tex] is the number of terms

Now substituting the values in general formula is

[tex]a_{46}=2+(46-1)5\\\\a_{46}=2+(45)5\\\\a_{46}=2+225\\\\a_{46}=227\\[/tex]

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

To know more about the sequence

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Answer:X = 13

Step-by-step explanation:

An exterior angle is equal to the sum of the two opposite interior angle

⇒95=4x+3 + 3x+ 1

95=4x + 3x + 3 + 1

95=7x + 4

95-4=7x

91=7x

91/7=x

13=x

This implies that X= 13

Step-by-step explanation:

the distance of a vertex on the 2 outgoing sides to the touching points with the inscribed circle is the same for both sides.

and that applies to all 3 vertexes.

so, we know for the top left vertex the distance to both touching points is 4.

that means the distance to the touching points from the bottom left vertex is 7-4 = 3.

and that means that the distance to the touching points from the bottom right vertex is 16-3 = 13.

so, x = 13

it is the distance to one of the touching points for the bottom right vertex.

and the perimeter of the triangle is therefore

7 + 16 + (13 + 4) = 40

Answer:

6 6

---- ÷ ---

16 10

Step-by-step explanation:

equals 5/8

Step-by-step explanation:

3 blue

4 red

2 yellow

in total 9 marbles.

when looking at the 3 blue marbles that leaves 9-3 = 6 others (red and yellow).

so, the ratio is

3:6 = 1:2

remember, a ratio is a fraction and follows the same rules of calculation, simplification, ...

Answer:

No, I do not agree. This is because 10⁰ is equivalent to 1.

Step-by-step explanation:

any number to the power of 0 is equal to 1

Answer:

5

Step-by-step explanation:

19-14=5

for the Tape diagram just make 19 boxes and fill in 5.

Answer:

Step-by-step explanation: 737/ 11= 67

sooooo 67 x 5= 335

Answer:

Circumference = 7.68 cm

Area = 113.04 cm²

Step-by-step explanation:

First, let us find the radius of the given circle.

d = 2r

r = d / 2

r = 12 / 2

r = 6 cm

And now, let us find the circumference of the circle using the below formula.

C = 2 π r

C = 2 × 3.14 × 6

C = 37.68 cm

And now let us find the area of the circle using the below formula.

A = π r²

A = 3.14 × 6 × 6

A = 113.04 cm²

Answer:

  (3√26, 0)

Step-by-step explanation:

Finish your work by evaluating the sine and cosine. The imaginary part corresponds to the y-coordinate in (x, y) form.

  3√26(cos(360°) +i·sin(360°)) = 3√26(1 +0i)

In rectangular form, that is ...

  (3√26, 0)