Drag the tiles to the correct boxes to complete the pairs.

Match the graphs with the functions they represent.

Answer:

  y = 11.2 in

Step-by-step explanation:

The square of the tangent length is equal to the product of the lengths of the secant from the intersection with the tangent to the near and far circle intersection points.

  9^2 = 5(5+y)

  16.2 = 5+y . . . . . divide by 5

  11.2 = y . . . . . . inches

Answer:

2nd one: AB = 6

Step-by-step explanation:

Because PQ is 4 (Pythagorean triples), you can prove that triangle PBQ is congruent to PAQ by HL. You can then say AQ is equal to 3 becasue of CPCTC. AQ+QB=AB, or 3+3=6. AB=6

Answer:

  5 times as large

Step-by-step explanation:

You can think of "10^5" as "green marbles" if you like. Then your question is ...

  5 green marbles is how many times as large as 1 green marble.

Hopefully, the answer is all too clear: it is 5 times as large.

_____

In math terms, when you want to know how many times as large y is as x, the answer is found by dividing y by x:

  y/x . . . . . tells you how many times as large as x is y.

Here, that looks like ...

  [tex]\dfrac{5\times 10^5}{1\times 10^5}\\\\=\dfrac{5}{1} \qquad\text{the factors of $10^5$ cancel}\\\\=5[/tex]

Answer:

5 times as large

Step-by-step explanation:

I did the question

Answer:

y = 700 (0.969)^t

Step-by-step explanation:

Using the depreciation formula after a given period of time.

A = P (1- r/100)^n

Where, A is the initial value

P is the original value

r is the rate of depreciation and

n is the time taken in years

Therefore;

A will be the new mass of the sample after decay,y

P is the original mass of the sample before decay, 700 mg

r is the rate of decay each year, 3.1% and

n is the number of years, t

Hence;

y = 700 (1- 3.1/100)^t

y = 700 (96.9/100)^t

y = 100(0.969)^t

The relationship between the mass of the radioactive sample (y) and the number of years since the start of the study (t) can be represented by the exponential function y = 700 * (1 - 0.031) ^ t.

This is a problem related to exponential decay. In general, the formula for an exponential decay is given as Y = A * (1 - r) ^ t where 'A' represents the initial amount, 'r' is the rate of decay (as a decimal), and 't' is the time period.

For this problem, the initial amount of the radioactive substance is 700 milligrams (A = 700), the rate of decay is 3.1% per year (r = 0.031), and 't' is represented as the number of years since the start of the study.

Using these values, we can write the exponential function showing the relationship between the mass of the sample 'y' and the number of years 't' as follows:

y = 700 * (1 - 0.031) ^ t

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ANSWER

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

EXPLANATION

We need to use the Pythagoras Theorem to find the height of the triangle.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] ({2 \sqrt{3}) }^{2} + {b}^{2} = {4}^{2} [/tex]

[tex]12 + {b}^{2} = 16[/tex]

[tex] {b}^{2} = 16 - 12[/tex]

[tex]{b}^{2} = 4[/tex]

Take positive square root to get;

[tex]b = \sqrt{4} = 2[/tex]

Area =½bh

[tex]Area = \frac{1}{2} \times 2\sqrt{3} \times 2[/tex]

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

Answer:

m∠DAB = 90°

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangent segments drawn from a point outside the circle, then

 the two tangent segments are equal in length

- The radius and the tangent perpendicular to each other at the point

 of contact

* Lets solve the problem

∵ AB and AD are two tangent segments to circle C at B and D

 respectively

∴ AB = AD ⇒ (1)

∵ CD and CD are two radii

∴ AB ⊥ BC and AD ⊥ DC

∴ m∠ABC = m∠ADC = 90°

∵ m∠BDC = 45°

∵ ∠BDC + m∠ADB = m∠ADC

∴ 45° + m∠ADB = 90° ⇒ subtract 45° from both sides

∴ m∠ADB = 45° ⇒ (2)

- In Δ ABD

∵ AB = AD ⇒ proved in (1)

∴ m∠ABD = m∠ADB ⇒ isosceles triangle

∵ m∠ADB = 45° ⇒ proved in (2)

∴ m∠ABD = 45°

- The sum of the measure of the interior angles of a Δ is 180°

∴ m∠DAB + m∠ABD + m∠ADB = 180°

∴ m∠DAB + 45° + 45° = 180° ⇒ simplify

∴ m∠DAB + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠DAB = 90°

Answer:

  a. 3 (see below for explanation)

  b. Ln = 4 + 3(n -1)

  c. 48

  d. dn = 6n +2

Step-by-step explanation:

a. The common difference is found by subtracting any given term from the next one: 7 -4 = 3, or 10 -7 = 3. The common difference is 3.

__

b. The general expression for an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 + d(n -1)

Here, the first term is 4 and the common difference is d. We choose to name the n-th term of Levy's sequence "Ln", so we can fill in the numbers to get ...

  Ln = 4 + 3(n -1)

__

c. We can call the terms of Zack's sequence Zn, so we have ...

  Zn = 3·Ln = 3·(4 + 3(n -1)) = 12 +9(n -1)

Putting 5 where n is in this equation, we find ...

  Z5 = 12 +9(5 -1) = 48

The 5th term of Zack's sequence is 48.

__

d. The difference of n-th terms of the two sequences is ...

  dn = Zn -Ln = (3·Ln) - Ln = 2Ln = 2(4 +3(n -1)) = 8 +6(n -1)

  dn = 6n +2

Answer:

$726.02 I had to guess cause I used a calculator but it didn't get to an exact number this is the closet

Answer:

$726.02

Step-by-step explanation:

Answer:

ΔADB~ΔCDB; SAS~

Step-by-step explanation:

Due to the tick marks on AD and DC, we know that those sides are congruent

We also know that the angle D is congruent due to the marks

As they share line BD, that side is also congruent.

This means that we have a side, an angle, and another side.

This leaves us with the last two options

The only difference between them is what angle corresponds to which

In the case of this triangle, A and C correspond with each other and B and D are shared. This means we are looking for when the locations of A and C, and B and D are matched

This would mean that the 4th option

ΔADB~ΔCDB; SAS~

Answer:

The value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Step-by-step explanation:

In figure, we are given a triangle

There is a 90 degree angle in the triangle. Therefore, the triangle is a right triangle.

In a right triangle,

[tex]Sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos\theta = \frac{Base}{Hypotenuse}[/tex]

[tex]Tan\theta = \frac{Perpendicular}{Base}[/tex]

In triangle, the side with right angle and given angle is called base, Therefore

Base = EF

The side opposite to the right angle is called the hypotenuse, so

Hypotenuse = DF

and

Perpendicular = DE

Therefore, the value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Final answer:

To find the time it took for Austin to catch up with Amber, we calculated the distance Amber had covered before Austin started, and then divided that distance by the difference in their speeds, yielding a catch-up time of 5.5 hours.

Explanation:

The question is asking after how many hours Austin will catch up with Amber if they are driving the same route, but start at different times and drive at different speeds. To solve this problem, we can use the concept of relative speed and the equation Distance = Speed × Time. Since Amber left 2 hours earlier, by the time Austin starts, Amber has already covered a certain distance. We can calculate this distance by multiplying Amber's speed (55 mph) by the time she drove alone (2 hours), which gives us 110 miles. Now, Austin catches up by covering the difference in the distance at a relative speed, which is the difference of their speeds. So, the relative speed is Austin's speed (75 mph) minus Amber's speed (55 mph), resulting in 20 mph.

Now we can find the time it took Austin to catch up by dividing the distance Amber covered alone (110 miles) by the relative speed (20 mph). This comes out to 5.5 hours. Thus, Austin catches up with Amber after driving for 5.5 hours.

Answer:

Hi ! I hope you're doing good

Here is your graph ...I hope it's helpful for you

Step-by-step explanation:

Answer:

Center: (-5,10)

Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the point (h,k)  is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

[tex]x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121[/tex]

Add 10x to both sides:

[tex]x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121[/tex]

Make two groups for variable "x" and variable "y":

[tex](x^2+10x)+(y^2-20y)=-121[/tex]

Complete the square:

Add [tex](\frac{10}{2})^2=5^2[/tex] inside the parentheses of "x".

Add  [tex](\frac{20}{2})^2=10^2[/tex]  inside the parentheses of "y".

Add [tex]5^2[/tex] and [tex]10^2[/tex] to the right side of the equation.

Then:

[tex](x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4[/tex]

Rewriting, you get that the equation of the circle in center-radius form is:

 [tex](x+5)^2+(y-10)^2=2^2[/tex]

You can observe that the radius of the circle is:

[tex]r=2[/tex]

And the center is:

[tex](h,k)=(-5,10)[/tex]

Answer:

Step-by-step explanation:

x²+y²+121-20y=-10x

(x²+10x)+(y²-20y)+121=0

(x²+10x+25)-25+(y²-20y+100)-100+121=0

(x+5)² + (y-10)²= 2²

the center is : A(-5;10)  and radius : r = 2

Some simplification:

[tex]\dfrac{x^{-1}}{x^{-1}+1^{-x}}=\dfrac{x^{-1}}{x^{-1}+1}=\dfrac1{1+\frac1{x^{-1}}}=\dfrac1{1+x}[/tex]

Then

[tex]f(2)=\dfrac1{1+2}=\dfrac13[/tex]

Answer:

13

180-125-42=13

You can find the measure of the missing angle by identifying the fraction of the total circle that the time period represents. For example, the movement from 12 to 3 on a clock represents a quarter of the clock's cycle, which corresponds to a 90 degrees angle.

To find the measure of the missing angle, we must first identify the type of problem it is. Based on the information shared, it seems like it's a problem involving angles in a circle, specifically, how the hour hand of the clock moves.

When the hour hand moves from 12 to 3, we are looking at a quarter (1/4) of a 360 degrees circle, which is identified by 90 degrees.

So, if you're trying to find the measure of a missing angle over a certain period, you can use the fraction of the total circle that the period represents. For example, the quarter period from 12 to 3 on the clock would represent a 90 degrees angle.

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Answer:

  x = 12 cm

Step-by-step explanation:

The product of lengths from the secant intersection point to the "near" and "far" circle intersection points is the same for both secants. When one "secant" is a tangent, the lengths to the circle intersection points are the same (so their product is the square of the tangent segment length).

  8^2 = 4·(4 +x) . . . . . . measures in centimeters

  16 = 4 +x . . . . . . divide by 4

  12 = x . . . . . . . . . subtract 4

De l'Hospital rule applies to undetermined forms like

[tex]\dfrac{0}{0},\quad\dfrac{\infty}{\infty}[/tex]

If we evaluate your limit directly, we have

[tex]\displaystyle \lim_{x\to 0}(1+2x)^{-\frac{3}{x}} = 1^\infty[/tex]

which is neither of the two forms covered by the theorem.

So, in order to apply it, we need to write the limit as follows: we start with

[tex]f(x)=(1+2x)^{-\frac{3}{x}}[/tex]

Using the identity [tex]e^{\log(x)}=x[/tex], we can rewrite the function as

[tex]f(x)=e^{\log\left((1+2x)^{-\frac{3}{x}}\right)}[/tex]

Using the rule [tex]\log(a^b)=b\log(a)[/tex], we have

[tex]f(x)=e^{-\frac{3}{x}\log(1+2x)}[/tex]

Since the exponential function [tex]e^x[/tex] is continuous, we have

[tex]\displaystyle \lim_{x\to 0} e^{f(x)} = e^{\lim_{x\to 0} f(x)}[/tex]

In other words, we can focus on the exponent alone to solve the limit. So, we're focusing on

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) [/tex]

Which we can rewrite as

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) = -3\lim_{x\to 0}\frac{\log(1+2x)}{x}[/tex]

Now the limit comes in the form 0/0, so we can apply the theorem: we derive both numerator and denominator to get

[tex]\displaystyle -3\lim_{x\to 0}\frac{\log(1+2x)}{x} = -3 \lim_{x\to 0}\dfrac{\frac{2}{1+2x}}{1} = -3\cdot 2 = -6[/tex]

So, the limit of the exponent is -6, which implies that the whole expression tends to

[tex]e^{-6}=\dfrac{1}{e^6}[/tex]

By applying L'Hospital's rule to the given expression, the limit is found to be 1 as x approaches 0.

L'Hospital's rule can be applied to find the limit of the expression (1+2x)^(-3/x) as x approaches 0. This rule states that if we have an indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.

After simplifying the expressions and substituting x = 0, we find that the limit is equal to 1.

Answer:

A. 10

Step-by-step explanation:

This is a right triangle with a hypotenuse between the vertices (-4,-2) and (4,4). You can now solve for the length to get 10.

Answer:

  10.  D. 5 1/3

  11.  C. 285 cm

  12.  A. 42 units

Step-by-step explanation:

The first two are simple addition problems. (In problem 11, you can replace the addition of 5 identical numbers with a multiplication by 5.) The last problem is also an addition problem, but figuring out what to add can take a little effort.

___

10. The segment addition theorem tells you that for R between S and T:

  ST = SR + RT

  ST = 3 2/3 + 1 2/3 = (3 +1) + (2/3 +2/3) = 4 + 4/3 = 4 + 1 1/3

  ST = 5 1/3

__

11. The definition of a regular polygon is that all of its sides and angles are congruent. A "pentagon" is 5-sided polygon, so your regular pentagon will have 5 sides, each of measure 57 cm. The perimeter is the total length of the sides, so is ...

  P = 57 cm +57 cm +57 cm +57 cm +57 cm

  P = 5×57 cm

  P = 285 cm

__

12. Again, the perimeter is the sum of the side lengths. Here, the length of the top side is easily figured by the difference of x-coordinates (6 units). The length of the left side is recognizable as double the length of the hypotenuse of a 3-4-5 right triangle (10 units). The lengths of the other two sides can be found using the distance formula with the end point coordinates:

  MN = √((-10-8)^2 +(-6-(-3))^2) = √(324 +9) = √333 ≈ 18.248

 LM = √((8-2)^2 +(-3-2)^2) = √(36 +25) = √61 ≈ 7.810

So, the perimeter is ...

  P = 6 + 10 + 18.248 +7.810 = 42.058 ≈ 42 units

_

Here, it is helpful to be familiar with the 3-4-5 right triangle. It has several interesting properties, one of which is that it shows up in algebra problems a lot. Any triangle with this ratio of side lengths is also a right triangle.

In this problem, the difference in coordinates K - N = (-4-(-10), 2-(-6)) = (6, 8) which we recognize as having the ratio 3:4. We could continue with the distance formula:

  NK = √(6^2 +8^2) = √100 = 10

or, we can simply recognize this will be the result based on our familiarity with this triangle.

_

An alternate approach to this problem will also work. You can estimate the length of the perimeter.

The distance between two points is more than the maximum difference of their coordinates and less than the sum of differences of their coordinates. For example, the distance between points N and K will be more than 8 and less than 8+6=14.

If you need to refine this very crude estimate further, you can add 40% of the smallest difference to the largest difference. In this case, that would be ...

  8 + 0.40·6 = 10.4 . . . . . we already know the length is actually 10, so we see this estimate is within 4% of the real length.

For the coordinates in this problem, we can see that the perimeter will be more than the sum of the longest coordinate differences: 6+6+18+8 = 38. This is an important fact, because it eliminates all of the answer choices except 42. If there were any remaining ambiguity as to the answer, we could refine our estimate by adding 40% of the sum of the shortest coordinate differences: 0.40·(0+5+3+6) = 5.6. That would bring our estimate to 38+5.6 = 43.6, within 4% of the actual value of the perimeter.

The first one u circled is a single rotation

Answer:

The upper left figure has a single rotation.

Step-by-step explanation:

In math and geometry single rotation is what we call a figure that has been rotated by only 90º from an original point and it is usually measured to the right, so in this case from the option the figure that has been rotated only 90º is the one in the upper left corner of the image.

Answer:

The area of the circle is [tex]36\pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle subtends a central angle of [tex]2\pi[/tex] radians

so

By proportion find the area of the circle

[tex]\frac{33\pi }{(11\pi /6)}=\frac{x}{2\pi}\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^{2}[/tex]

Answer:

its just 36 pi

Step-by-step explanation:

just did this one

The scale factor of the lengths of two similar octagons with areas 4 m² and 9 m² is obtained by taking the square root of the ratio of their areas, yielding a scale factor of 1.5.

The subject of this question is Mathematics, particularly dealing with geometry and scale factors. For two similar shapes, the ratio of their areas is equal to the square of the scale factor of their lengths.

Given the areas of the two similar octagons as 4 m² and 9 m², we find the square root of the ratio of the areas to obtain the scale factor of the lengths. That is, √(9/4) = √2.25 = 1.5.

Therefore, the scale factor of the lengths of the two similar octagons is 1.5.

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The scale factor of the lengths of the two similar octagons is 1.5.

To find the scale factor of the lengths of two similar octagons, we can use the formula:

Scale factor = sqrt(Area2 / Area1)

Where Area1 is the area of the first octagon, and Area2 is the area of the second octagon.

Plugging in the given values, we get:

Scale factor = sqrt(9 m² / 4 m²) = sqrt(2.25) = 1.5

Therefore, the scale factor of the lengths of the two octagons is 1.5.

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The answer is -- 10 days

The answer is 4. Any absolute value of a negative number is positive

Answer: 4

Step-by-step explanation: It's important to understand what absolute value really means and that is the absolute value of a number represents that numbers distance from zero on a number line.

The absolute value of -4 is 4. The reason the absolute value of -4 is 4 is that if we graph -4 down here on the number line, you can see that its distance from zero is 4 units.

I have attached a number line below showing the absolute value of -4

Answer:

6.9

Step-by-step explanation:

12 x 4 = x^2

48 = x^2

x = 6.9

Answer:

6.9

explanation:

I did the test.

hope this helps you!

:D

The solution to the equation -3(h + 5) + 2 = 4(h + 6) - g is h = -12 and g = -18.

Distribute the negative signs:

-3(h + 5) + 2 = -3h - 15 + 2

Combine constant terms:

-3h - 15 + 2 = 4(h + 6) - g

-3h - 13 = 4h + 24 - g

Isolate h on one side:

-7h - 13 = 24 - g

-7h = 37 - g

h = (37 - g) / -7

Substitute h back into the original equation to solve for g:

-3(h + 5) + 2 = 4(h + 6) - g

-3((37 - g) / -7 + 5) + 2 = 4((37 - g) / -7 + 6) - g

-3(-12 - g + 35) + 2 = 4(-12 - g + 42) - g

Simplify both sides:

11g + 66 = -36g + 108

47g = 42

g = -18

Therefore, the solution is h = -12 and g = -18.

Answer:

  58 in^2

Step-by-step explanation:

The area of one face of the 3" cube is (3 in)^2 = 9 in^2. Then the 6 faces of that will have an area of ...

  6·9 in^2 = 54 in^2

The area of the top of the paperweight is unaffected by the area of the added cube: the area the smaller cube covers is exactly the same as its exposed top area. So, the net effect of the added 1" cube is to increase the total area by that cube's lateral area: 4 faces at 1 in^2 for each face, a total of 4 in^2.

Then the total surface area of the paperweight is ...

  54 in^2 + 4 in^2 = 58 in^2

Answer:$76

Step-by-step explanation:

JEANS: (5x8)= 40

SHIRTS:(4x6)= 24

SHOES BUY ONE GET ONE FREE: (12x2 - 12)= 12

40 + 24 + 12 = 76

Multiply the first bracket by -4. Multiply the second bracket by -2

-8x+12y+4x-2x-12

Negative and Negative = Positive

Negative and Positive = Negative

Then do -8x+4x-2x

= -6x+12y-12

Answer is D. -6x+12y-12

D. -6x + 12y - 12

First, distribute the -4 and the -2.

-8x + 12y + 4x - 2x - 12

Now, rearrange the expression so the like terms are easier to combine.

-8x + 4x - 2x + 12y - 12

Now, combine the like terms.

-6x + 12y - 12

This is as simple as the expression can get without knowing what the variables are.

Answer:

a. The snow is accumulating at about 3/2 inches per hour.

Step-by-step explanation:

Since the description of the dependent variable is "inches of snow accumulated" and the description of the independent variable is "hours", the meaning of the slope of a line on the graph of inches versus hours is "inches of snow accumulated per hour." In my opinion this best matches answer choice "a" because of the use of the words "accumulated" and "accumulating".

In plain English, the wording of answer choice "d" means the same thing: snow accumulation means snow height. I believe it can reasonably be argued that choice "d" is also a correct answer to this question.

_____

Please note that the slope of a line on *any* graph has the meaning (unit of dependent variable) per (unit of independent variable).