Match each expression with its value 2,-9,-1, or undefined
G(-0.0001)
G(0)
G(0.0001)
G(9)

Answer:

EF = 2.9

Step-by-step explanation:

The geometric figures are similar so we can use the similarity ratio to calculate the length of EF:

GF/ CB = EF/AB

5/29 = EF/17 cross multiply expressions

29EF = 85 divide both sides by 29

EF = 2.9 approximately

Let's take this problem step-by-step:

Let's convert the equation back into the standard form:

     ⇒ standard form: (x-h)² +(y-k)² = r²

       [tex]x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2[/tex]

Based on the equation found

  ⇒ center: (4, -5)

   ⇒ radius: 2

Answer:

Hope that helps!

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The coordinate of the point P will be (6/5, -7/5). Then the correct option is C.

The complete question is attached below.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divide the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Given the points X(-2, 5) and Y(2, -3).

Then the coordinates of the point P on directed line segment XY that partitions segment XY such that the ratio of XP to PY is 4:1.

(x₁, y₁) = (-2, 5)

(x₂, y₂) = (2, -3)

m = 4

n = 1

Then the point will be

x = [4 × 2 + 1 × (-2)] / (4 + 1)

x = 6 / 5

y = [4 × (-3) + 1 × 5] / (4 + 1)

y = -7 / 5

The coordinate of the point P will be (6/5, -7/5).

Then the correct option is C.

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The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N

Resolving forces in the y direction gives us;

T₁ sin 29° + T₂ sin 53° = 210  ------(eq 1)

Resolving forces in the horizontal direction gives;

T₁ cos 29° = T₂ cos 53°   ----(eq 2)

T₁ = T₂ cos 53°/cos 29°

Thus;

(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210  

0.3336T₂ + 0.7986T₂ = 210

T₂ = 210/1.1322

T₂ = 185.48 N

Thus;

T₁ = 185.48 cos 53°/cos 29°

T₁ = 127.63 N

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Answer: I love the picture example

Step-by-step explanation:

We will first find the heigh of the kite from his hand to a point in the air.

Then, we will add 3 feet to the result.

So, how to find the vertical line of the right triangle?

Well, we have the vertical line = x

We also got the hypothenuse, equal to 100 feet

And also theta, equal to 25 degrees.

We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse

sin(25) = x/100 feet

multiply 100 feet on both sides, to cancel to 100 feet on the right side.

100sin(25) = x

100(0.442) = x

x = 42.2  feet

Height = 42.2 + 3 feet (the yoda's hand =) =  45.2 feet (total)

Rounded to the nearest tenth.

I also did the verification, so it is the correct answer.

Easy as that =]]

Height of the kite from 3ft above the ground

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]

[tex]\\ \rm\Rrightarrow P=100sin25[/tex]

[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]

Height from the ground

Answer:

True

Step-by-step explanation:

Step 1: We can plug 106 into x in the equation x - 62 = 44.

Step 2: Check if 106 - 62 = 44. It’s correct, so the answer is TRUE!!

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:True [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: x - 62 = 44[/tex]

[ add 62 on both sides ]

[tex]\qquad \tt \rightarrow \: x - 62 + 62 = 44 + 62[/tex]

[tex]\qquad \tt \rightarrow \: x = 106[/tex]

The proved value is same as that of statement, hence the statement is correct.

Answer:

a] 38.5$
b] 118.71$

Step-by-step explanation:

A)35$ was increased by 10%
So:
10% of 35$
10/100 x 35 ($)
3.5$
So 35$ was increased by 3.5$ and the new price is 38.5$
B)105.99$ was increased by 12%
So:
12% of 105.99$
12/100 x 105.99$
=12.7188$
Let's round it to the nearest hundredths:
12.72$

So 105.99$ was increased by 12.72$ and the new price is 118.71$

HOPE IT HELPS :D
Tip: "of" means multiplication in Maths.

Answer:

333.333 Tiles and 333.333 Square Foot

Step-by-step explanation:

3X <= 1000

X <= 1000/3

X <= 333.333 Tiles

Then

333.333* 1sqt2 = 333.333 Square Foot

I don't understand your question

The number of goats sold is 4 and hens sold is 8.

An equation is a mathematical statement which equates two algebraic expression with an equal sign.

Let the total number of goats sold be g

Let the total number of hens sold is h

g + h = 12

The total no. of legs of a goats sold will be 4g

and the total number of legs of a hens sold will be 2h

and it is given that

4g +2h = 32

The system of equation formed is

g + h = 12

4g +2h = 32

Multiplying equation (1) by 2 and then (1) - (2)

-2g = -8

g = 4

Therefore the number of goats sold is 4 and hens sold is 8.

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Answer:

1

Step-by-step explanation:

Via calculator inputs.....

The substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.125t}[/tex]

Solving for t:

t = 5.54 ≈ 5.5 days

Thus, the substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

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The graph first represents the provided piecewise function option first is correct.

The graph of a piecewise function contains numerous curve components. It signifies that it has a plethora of definitions based on the value of the input. In other words, a piecewise function behaves differently depending on the input.

We have a piecewise function shown in the picture.

[tex]\rm y=\left\{x\le-2:\sqrt{-x-2}\right\}[/tex]

[tex]\rm y=\left\{-2 < x < 1:\dfrac{x}{x^{2}+x-2}\right\}[/tex]

[tex]\rm y=\left\{x\ge1:\log_{2}\left(x+1\right)\right\}[/tex]

After plotting all the pieces of a function on the coordinate plane we will get a graph the same as shown in the first option.

Thus, the graph first represents the provided piecewise function option first is correct.

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The value of y for the given equation at x=81 is 87.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, given equation;

       y = x + 6

     Put x = 81, we get

       y = 81 + 6

      y = 87

Thus, the value of y for the given equation at x=81 is 87.

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When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.

First Method:

∠1  + ∠2 = 180° {Supplementary angles because both lies on the line q}

∠2 = (180° - ∠1)

Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,

∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}

∠7 = 180° - ∠6

∠7 = 180° - (180° - ∠1)

∠7 = 180° - 180° + ∠1

∠7 = ∠1

OR

Second Method:

∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}

∠3 = ∠5 {Alternate Interior angles}

∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}

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Answer:

5sqrt3

Step-by-step explanation:

You can use trigonometry to figure out the answer

TOA is tan(any angle) = opposite/adjacent

Tan(30) = 5/x

tan(30) = sqrt3/3

x = tan inverse (30) multiplied by 5

x = 5sqrt3

Answer:

[tex]-75x^{7}y^{9}[/tex]

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. ΔAKE and ΔCKP are congruent.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔABC, since AB≅BC, therefore, the triangle will be an isosceles triangle, and the measure of ∠A ≅ ∠C, using the base angle theorem.

Now In ΔAKE and ΔCKP,

∠A ≅ ∠C {Proved above}

∠AKE ≅ ∠CKP {Given}

AK ≅ KC {Given }

Since two angles and a side of the triangle are equal, therefore, we can write the two triangle are congruent using the Side-angle-side or Angle-Side-Angle congruence.

Hence, ΔAKE and ΔCKP are congruent.

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A ray is a part of a line that starts at a point (called the endpoint) and extends infinitely in one direction. An angle is formed when two rays share a common endpoint (vertex).

A ray has one endpoint: A ray is a one-dimensional figure that starts at a single point (the endpoint) and extends infinitely in one direction. On the other hand, an angle is formed by two rays, each with its own endpoint, meeting at a common vertex.

An angle is two rays: As mentioned earlier, an angle is created when two rays share a common endpoint. The two rays are referred to as the sides of the angle, and the endpoint they share is called the vertex.

The measure of an angle is determined by the amount of rotation: The measure of an angle is not dependent on the lengths of its sides but rather on the amount of rotation between its two rays. To measure an angle, we compare it to a standard unit of angle measurement, usually degrees. One full rotation (360 degrees) corresponds to a complete circle, and angles are measured based on the fraction of a full circle they represent.

The measure of an angle remains the same at all distances from its vertex: The measure of an angle is independent of the length of its sides or how far away an observer is from the vertex. For example, a 60-degree angle remains a 60-degree angle whether you look at it from up close or from a distance. This is because the measure of an angle depends only on the relative positions of its two rays, not on the size of the shape it forms.

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The only option that cannot be used to prove that the diagonals of parallelogram abcd intersect at point e is; Option C

A) The sum of the interior angles of any quadrilateral is 360° and so this is true about the parallelogram.

B) AB = CD and BC = DA from opposite sides of a parallelogram are equal. Also AC = CA because of reflexive property of congruence. Thus, ∠ABC ≅ ∠CDA

C) This is not true because ∠ABC ≅ ∠CDA instead of ∠ABC ≅ ∠CDE.

D) This is true because of the definition of a transversal.

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Answer:

19/54

Step-by-step explanation:

- 7/27 + 11/18

LCM of the 27, 18 is 54

- 7/27 * (2/2) + 11/18 * (3/3)

- 14/54 + 33/54

33 - 14/54

19/54

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The answer choice which best uses the associative and commutative properties is; Choice C; [-1/3+(-10)]+[7+2/3+5].

It follows from the answer choices that the best application of the associative and commutative properties is that which sums up all negative numbers and sums up all positive numbers and hence, choice C is the correct answer choice.

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Answer:

B

Step-by-step explanation:

This is quite a trial and error question.

Given from the table

$1 cost of item = $0.08 tax on item

$2 cost of item = ($0.08x2) tax on item = $0.16 tax on item

$3 cost of item = ($0.08x3) tax on item = $0.24 tax on item

$8.50 cost of item = ($0.08x8.50) tax on item =  $0.68 tax on item

$10 cost of item = ($0.08x10) tax on item = $0.80 tax on item

The only one that is different is the incorrect value therefore $0.64 is the incorrect one.

Answer:

The translation is [tex]X+0[/tex]

Step-by-step explanation:

A translation means the transformation that moves every point in a figure at the same distance in the same direction.

The translation can be described using words like moved up 3 and over 5 to the left or with the notation.

As for the given, there can be no rule described. so the translation is [tex]X+0[/tex]

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The translation is [tex]X+0[/tex]

A translation means the transformation that moves every point in a figure at the same distance in the same direction.

The translation can be described using words like moved up 3 and over 5 to the left or with the notation.

As for the given, there can be no rule described. so the translation is[tex]X+0[/tex]

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Answer:

-96

Step-by-step explanation:

(20-25)(16+4)-8+(3x4)

=(-5)(20)-8+12

=-100-8+12

=-96