find the area of the shape below
​

Answer:

  y = (x +1)(x -3)

Step-by-step explanation:

You want the equation in factored form for the parabola shown in the graph with x-intercepts at -1 and +3, and a vertical scale factor of 1.

If p is a zero (x-intercept) of the graphed polynomial function, then (x-p) is a factor. The graph shows x-intercepts at x=-1 and x=3. This means (x-(-1)) and (x -3) are factors.

The equation of the graph may also have a vertical scale factor. That can often be determined easily from the graph by looking at the vertical distance from the vertex of points 1 unit either side of the vertex.

Here, the vertex is (1, -4) and points at x=0 and x=2 have the value -3, which differs from the vertex by 1 unit. Hence the scale factor is 1. It multiplies the other factors.

The equation of the graphed parabola is ...

  y = (x +1)(x -3)

The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center is the midpoint of the chords, hence:

The radius is half the distance between the chords, hence:

[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].

Hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]

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Answer:

13

Step-by-step explanation:

Since triangles CBA and DBA are equal, their lengths would also be equal, thus, DB = 13 as CA = 13

Answer:

CAB = DAB

CA is equivalent to BD

Answer:

7.5 ft

Step-by-step explanation:

1st drop = 60 ft

2nd drop = 60/2 = 30 ft

3rd drop = 30/2 = 15 ft

4th drop = 15/2 = 7.5 ft

The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like

[tex]a, ar , ar^2, ar^3, \ldots[/tex]

and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].

For this particular sequence, the first term is

[tex]a=3[/tex]

and the fourth term is

[tex]ar^{4-1} = ar^3 = 1029[/tex]

Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].

[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]

Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are

[tex]ar = 3\times7 = \boxed{21}[/tex]

and

[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]

Answer:

Term 2 is 21, and term 3 is 147.

Step-by-step explanation:

The geometric sequence is 3, 3r, 3r^2, 1029.

[tex]r = \sqrt[3]{ \frac{1029}{3} } [/tex]

[tex]r = \sqrt[3]{343} = 7[/tex]

So we have 3, 21, 147, 1029.

Answer:

15/50...may be/may not be......,,

The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

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.

As we can see in the picture, we have given a function:

We have a function:

g(x) = 4log(x) + 4

To find x-intercept plug g(x) = 0

0 = 4logx + 4

x = 0.1

(0.1, 0)

The vertical asymptote:

x = 0

The range of a function:

(-∞, ∞)

Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

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Answer:

If the distance from the origin to a given point is 5, then that point lies on circle C is true.

Step-by-step explanation:

The correct statement about given circle is "If the distance from the origin to a given point is 5, then that point lies on circle C"

In mathematics, the circle is a two dimensional rounded figure which has no corner edges.

Standard form = (x - a)² + (y - b)² = r²

Given that,

The center of a circle is on origin and the radius is 5 unit.

And point p lies on the circle,

So, according to definition of circle the distance  between center and any point on the circle is always constant and which is known as radius.

Therefore, the distance between center end given point will be equal to 5 then it will lies on a circle.

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Answer:

She needs the starting amount of money to create an equation.

Step-by-step explanation:

The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.

t=time

b=percent

P=starting value

The formula with the information given is: f(6)=P(1+3.75)^6

Hope this helps!

If not, I am sorry.

Answer:

Principal

Step-by-step explanation:

Since, the amount in the simple interest is,

Where, P is the principal amount,

r is the annual rate,

t is the time ( in years ),

Here, r = 3.75 %, t = 6 years,

Thus, By the above explanation,

It is clear that, we need the value of P, that is, principal to find the amount.

Answer:

3 < x < 13

Step-by-step explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let x be the length of the unknown side.

Therefore, x will either be the longest side or one of the shorter sides.

Therefore:

   x < 5 + 8

⇒ x < 13

And:

   8 < 5 + x

⇒ 3 < x

So the range of possible values of the third side is greater than 3 and less than 13:   3 < x < 13

Answer:

We will use a combination formula to determine how many ways the prizes could be given out.

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

The formulas nCk is popularly known as counting formula.

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The desired linear functions are given as follows:

a) x = a.

b) y = b.

A linear function is modeled by:

y = mx + b

In which:

A vertical line has undetermined slope, hence it is defined by x = a, containing point (a,b).

A horizontal line has slope of 0, hence it is defined by y = b, containing point (a,b).

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[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Given -}}}}}}[/tex]

Four points which lie at (0,0) ; (0,2) ; (2,2) ; (2,0)

[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{To \: Find-}}}}}}[/tex]

What is the figure formed?What is the area of the figure?

[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Solution-}}}}}}[/tex]

The given points lie on graph as per the order given in the attachment.

Which shape?

As the points lie 2 units apart from their adjacent sides. It can be a square or rhombus.

The opposite pairs of sides are also parallel to each other. The adjacent sides of the figure formed are also perpendicular to each other.

Hence! the figure formed is a square.

What is the area?

[tex]\large{\sf{ \longmapsto Area_{(square)} = s \times s}}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = {s}^{2} }}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = {(2)}^{2} }}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = 4 \: sq. \: units}}[/tex]

The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)

The height from D is perpendicular to EF

The slope of EF = (8 - 2)/(1 - 1) = ∞

Therefore, the side EF is parallel to the y-axis.

Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)

The median is the midpoint of the side EF

The coordinates of the midpoint is found as follows;

[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]

Therefore;

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The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.

Let's assume that the height and radius are 14cm and 7cm. The volume will be:

= πr²h

= 3.14 × 7² × 14

= 2154.04cm³

When the radius and height are reduced to 5cm and 9cm, the volume will be:

= πr²h

= 3.14 × 5² × 9

= 706.5cm³

This illustrates that the volume reduces when the height and radius reduces.

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Answer:

x =7

Step-by-step explanation:

2x+6 = 20

To solve this equation, you first need to subtract 6 from each side

2x+6-6 = 20-6

2x = 14

Then divide each side by 2

2x/2 = 14/2

x = 7

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{z^{2}-8 }-\sqrt{6z-17}=0 \end{gathered}$}[/tex]

Simplify the left side. Yes n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-\sqrt{6z-17}=0 } \end{gathered}$}[/tex]

If n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-(6z-17)^{\frac{1}{2}} =0 } \end{gathered}$}[/tex]

Draw each side of the equation. The solution is the x value of the point of intersection.

[tex]\red{\underbrace{\overbrace{\boxed{\boldsymbol{\sf{\green{z=3}}}}} \ \ \to \ \ \ Answer}}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{z^2-8} -\sqrt{6z-17} =0\\\sqrt{z^2-8} =\sqrt{6z-17} \\6z > 17\\z > \frac{17}{6} \\z^2-8=0\\z^2 > 8\\so \\z < -\sqrt{8} \\or\\z > \sqrt{8} \\combining\\z > \frac{17}{6} \\again\\z^2-8=6z-17\\z^2-6z-8+17=0\\z^2-6z+9=0\\z^2-3z-3z+9=0\\z(z-3)-3(z-3)=0\\(z-3)(z-3)=0\\z=3[/tex]

The most economic way to purchase health insurance for the family would be to insure Patrick with his employer and Susie and the twins with her employer (Option c).

Reason behind the Choice

Patrick's employer pays for 100% of his monthly health insurance premium of $378

In this case, additional beneficiary for the twins = $280*2 = $560

Susie's employer pays 63% of her $403 monthly premium, and is ready to pay 32% of the $310 monthly premium for each additional beneficiary.

Total money to be paid in this case = 37% of $403 +2*(68% of $310)

= $570.71

Considering that Patrick's health insurance cost is lower than Susie's, it makes sense for him to get health insurance via Patrick's company.

For the twins, Susie's employer offers to pay 68% of $310 for each additional beneficiary. So, the most viable deal would be to buy Patrick's health insurance from his employer and Susie and the twin's health insurance from her employer.

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Answer:

C. Insure Patrick with his employer and Susie and the twins with her employer.

Answer:

Step-by-step explanation:

The formula for circumference is 2πr

First, lets find the radius

3.14 * 2 = 6.28

56.52 / 6.28 = 9

The diameter = 2r

2 * 9 = 18

The diameter is 18 feet

Hope this helps!

Answer:

Hence, 87,50,000 can be expressed as [tex]$8.75 \times 10^{6}$[/tex].

Step-by-step explanation:

- Given 87,50,000

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 87,50,000.

8.75

So, 8.75 lies between 1 & 10 .

Now, Decimal moved to 6 places at left.

[tex]$8.75 \times 10^{6}$[/tex]

So, [tex]$87,50,000=8.75 \times 10^{6}$[/tex].

The x-coordinate of the point which divide the line segment is 3.

Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.

When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.

To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.

Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).

Now, we will substitute these values in the formula, we get

x=(1/(1+3))(9-1)+1

x=(1/4)(8)+(1)

x=8/4+1

x=3

Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.

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Answer:

b. 3

Step-by-step explanation:

got it correct

Answer:

43°

Step-by-step explanation:

Calculating for the measure of angle C using

[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]

Answer:

√12×(-1)+√12×√5

-√12+√12×5

= -2√3+2√15

The area of the given composite figure is 74.24cm^2

The figure is made up of semi circle and rectangle

Area = area of semicircle + Area of rectangle

Area = 3.14(4)^2 + 3(8)

Area = 50.24 + 24

Area. = 74.24cm^2

Hence the area of the given composite figure is 74.24cm^2

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Hello,

[tex]$$\sum_{n=0}^4$$(\frac{1}{2})^{n} =(-\frac{1}{2})^{0}+(-\frac{1}{2})^{1}+(-\frac{1}{2})^{2}+(-\frac{1}{2})^{3}+(-\frac{1}{2})^{4}=1-\frac{1}{2} +\frac{1}{4} -\frac{1}{8}+\frac{1}{16}[/tex]

The value of x is 126.87° and the value of y is 53°.

An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.

From the given information:

sin x° = 0.8

x = sin⁻¹ (0.8)

x = 53.13°

x + 53.1° = 180°

x = 180° -53.13°

x = 126.87°

If cos 127° = -cos y°,

-cos y = -0.6018

cos y = 0.6018

y = cos⁻¹ (0.6018)

y = 53°

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Answer:

64 girls

Step-by-step explanation:

Number of boys in a classroom: 4

Total no. of students in the classroom: 12

Number of girls in 1 classroom: 12-4 = 8

Number of girls in 8 such classrooms: 8 × 8 = 64

See attached plots.

The top one shows all three pieces plotted simultaneously, independent of their domains.

The bottom plot takes into account the domains and removes parts of each piece (the dashed gray parts) outside their respective domains.