Point of tangency of an inscribed circle divides a leg of an isosceles triangle into 3 cm and 4 cm line segments (considered from the vertex to the base). Find the perimeter of the triangle.

Answer:

96 deg

Step-by-step explanation:

Polygon ABCDE is a regular hexagon. The sum of the measures of the interior angles is (n - 2)180 = (6 - 2)180 = 4(180) = 720. Since it's a regular hexagon, each interior angle measures 720/6 = 120 deg.

For the interior angle, m<CDE = 120

On the exterior of the polygon, m<CDJ = 136

m<CDE + m<CDJ + m<EDJ = 360

120 + 136 + m<EDJ = 360

m<EDJ + 256 = 360

m<EDJ = 104 deg

Triangle EHG is regular. The sum of the measures of the angles of a triangle is 180. For a regular triangle, each angle measures 60 deg.

m<EGH = 60

For exterior angle m<HGJ = 220

m<HGJ(exterior) + m<EGH + m<EGJ = 360

220 + 60 + m<EGJ = 360

m<EGJ + 280 = 360

m<EGJ = 80

m<EGJ = m<GED, so

m<GED = 80

Polygon DEGJ is a quadrilateral. The sum of the measures of its interior angles is 360 deg.

m<EGJ + m<GED + m<EDJ + m<GJD = 360

80 + 80 + 104 + m<GJD = 360

m<GJD + 264 = 360

m<GJD = 96 deg

Answer:

The measure of angle GJD is 96°.

Step-by-step explanation:

It is given that HGJ=220° on the exterior of the polygon, EGJ is congruent to GED, and CDJ=136° on the exterior of the polygon.

Each side and each interior angle of a regular polygon are same.

It is given that ABCDEF and EHG are regular polygons. It means each interior angle of regular hexagon ABCDEF is 120° and each interior angle of regular triangle EHG is 60°.

[tex]\angle EGH+\angle EGJ+\angle HGJ(exterior)=360^{\circ}[/tex]

[tex]60^{\circ}+\angle EGJ+220^{\circ}=360^{\circ}[/tex]

[tex]\angle EGJ+280^{\circ}=360^{\circ}[/tex]

[tex]\angle EGJ=360^{\circ}-280^{\circ}[/tex]

[tex]\angle EGJ=80^{\circ}[/tex]

[tex]\angle GED=\angle EGJ=80^{\circ}[/tex]

[tex]\angle CDE+\angle EDJ+\angle CDJ(exterior)=360^{\circ}[/tex]

[tex]120^{\circ}+\angle EDJ+136^{\circ}=360^{\circ}[/tex]

[tex]\angle EDJ+256^{\circ}=360^{\circ}[/tex]

[tex]\angle EDJ=360^{\circ}-256^{\circ}[/tex]

[tex]\angle EDJ=104^{\circ}[/tex]

The sum of all interior angles of a quadrilateral is 360°.

[tex]\angle GED=\angle EGJ+\angle EDJ+\angle GJD=360^{\circ}[/tex]

[tex]80^{\circ}+80^{\circ}+104^{\circ}+\angle GJD=360^{\circ}[/tex]

[tex]264^{\circ}+\angle GJD=360^{\circ}[/tex]

[tex]\angle GJD=360^{\circ}-264^{\circ}[/tex]

[tex]\angle GJD=96^{\circ}[/tex]

Therefore the measure of angle GJD is 96°.

Answer:

D. Length = 9 cm; width = 6 cm

Step-by-step explanation:

Find 1/4 of the length and 1/4 of the width.

1/4 * 36 cm = 9 cm

1/4 * 24 cm = 6 cm

Answer: D. Length = 9 cm; width = 6 cm

The simulation design that has an appropriate device and a correct trial for this scenario is:

The correct option is C.

The simulation which involves using a table of random digits to select a digit between 0 and 9, letting 0 - 2 represent eating dessert and 3 - 9 represent not eating dessert, and then selecting three digits has an appropriate device and a correct trial.

This simulation design is given below:

To simulate the probability of eating dessert in 3 of the 7 days this week, we would select three digits from the table of random digits and count the number of 0s, 1s, and 2s. The number of 0s, 1s, and 2s would correspond to the number of days the children eat dessert, and the number of 3s, 4s, 5s, 6s, 7s, 8s, and 9s would correspond to the number of days the children do not eat dessert.

We would repeat this process many times (e.g., 1000 times) to obtain an estimate of the probability of eating dessert 3 of the 7 days this week.

Learn more about simulation and probabilities at: https://brainly.com/question/1231005

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1. simply: h+245

2. your answer is right

3. 2+1/3n (i believe)

4. 29+5m

5. I’m pretty sure the answer is 29

Answer:

Commutative Property

Step-by-step explanation:

"Changing the order but not the result"

Answer:

The correct answer is C. g(x) = 1/4x^2

Step-by-step explanation:

In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.

(2, 1)

g(x) = 1/4x^2

1 = 1/4(2)^2

1 = 1/4(4)

1 = 1 (TRUE)

Answer:

[tex]y-0=-1(x-8)[/tex]

Step-by-step explanation:

The given line passes through (0,8) and (8,0).

The slope of this line is [tex]m=\frac{8-0}{0-8} =-1[/tex].

The point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the slope and the point (8,0) to get:

[tex]y-8=-1(x-0)[/tex]

We substitute the slope and the point (0,8) to get:

[tex]y-0=-1(x-8)[/tex]

Answer:

[tex]c=15[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]a^2+b^2=c^2 \\ \\ 9^2+12^2=c^2 \\ \\ 81+144=c^2 \\ \\ c^2=225 \\ \\ c=\sqrt{225} \\ \\ c=15[/tex]

Answer:

n-2

Step-by-step explanation:

Difference means subtraction

n-2

Answer:

[tex]A=452.39\ cm^2[/tex]

Step-by-step explanation:

The formula to calculate the surface area of a sphere is the following:

[tex]A=4\pi r^2[/tex]

Where A is the area of the sphere and r is the radius of the sphere.

In this case we know that the diameter d of the sphere is:

[tex]d = 12\ cm[/tex]

The diameter is:

[tex]d = 2r[/tex].

Thus

[tex]r = \frac{d}{2}\\\\r = \frac{12}{2}\\\\r=6\ cm[/tex]

Then the surface area of the sphere is:

[tex]A=4\pi (6)^2\\\\A = 144\pi\ cm^2\\\\A=452.39\ cm^2[/tex]

Answer is provided in the image attached.

Answer:

Step-by-step explanation:

This has a very brief answer when you know what it means.

f(x) + g(x) = abs(x) + 9 - 6

f(x) + g(x) = abs(x) + 3

Answer:

f + g)(x) = |x| + 3

Step-by-step explanation:

Add the two functions together:

f(x) = |x| + 9

+g(x) = - 6

------------------------

f(x) + g(x) = |x| + 9 - 6

               = |x| + 3

The label  f(x) + g(x)  can be rewritten as (f + g)(x).  

Thus, f + g)(x) = |x| + 3

Answer:

rectangle. trapezoid. triangle. A sphere is sliced so that the cross section does not intersect the center of the sphere

Answer:

sorry im late to this but it is a triangle

Step-by-step explanation:

because when you cut it horizontally and look at the top it is a rectangle so that is wrong trapezoid is when you look at it from the side when cut horizontally so that is wrong there is no square so that instantly becomes wrong because it is a rectangular pyramid  when  perpendicular it will provide you with a triangle  

ANSWER

AB=76 BC=357 AC=365 This triangle is a right triangle.

EXPLANATION

We use the Pythagoras Theorem to determine whether the triangles are right triangles.

According to this theorem, the square of the hypotebuse is equal to the sum of the squares of the two shorter legs.

We have:

AB=76 BC=357 AC=365

[tex] {365}^{2} = {76}^{2} + {357}^{2} [/tex]

133225=5776+127449

133225=133225

For the second triangle, we have;

B) Triangle ABC: AB=123 BC=836 AC=845

845²=123²+826²

714025=15129+682276

714025≠697405

The first triangle is a right triangle

Answer:

the firsst one

Step-by-step explanation:

Answer:

Step-by-step explanation:

16x^4+56x^2+49

(4x^2+7)^2

7200. Because 1.2 *30 *200=7200

To estimate the mouse population after 30 days using the given model, M(t)=200(1.2)^t, evaluate the expression with t=30, which results in approximately 47,475 mice.

The student is asking how many mice will be in the building after 30 days according to the exponential growth model M(t) = 200(1.2)^t, where t is the time in days and M(t) is the population of mice at time t. To find the answer, we simply plug the value of 30 days into the model to get M(30) = 200(1.2)^30.

Calculating the expression:

First, calculate 1.2 raised to the power of 30, which gives us approximately 237.3769.

Then, multiply that by the initial population of 200 mice, yielding a result of approximately 47,475.38.

Therefore, after 30 days, assuming no mice die, there will be approximately 47,475 mice in the building.

Answer:

(a)

Step-by-step explanation:

To rationalise the fraction multiply the numerator/denominator by the conjugate of the denominator.

The conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{x}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{x}[/tex]

Hence

[tex]\frac{\sqrt{9}(\sqrt{3}-\sqrt{x} )  }{(\sqrt{3}+\sqrt{x} )(\sqrt{3}-\sqrt{x} )  }[/tex]

= [tex]\frac{3(\sqrt{3}-\sqrt{x}  }{3-x}[/tex]

= [tex]\frac{3\sqrt{3}-3\sqrt{x}  }{3-x}[/tex] → (a)

Answer:

In: 5, 4, 2, 3, 1, and 10.

Out: 40, 32, 16, 24, 8, and 80

Step-by-step explanation:

The first step you should do is to take notice of the pairs that have their "in" and "out" both answered.

The second step is to find out what you must multiply the "in" by to get the "out". In this answer, you must multiply the "in" by 8 to get the "out".

The third step is to do the same thing for all of the values until the chart is completely filled with values.

The fourth step is to check your work!

If you have any questions, please let me know!

The rule is 8

Bc 5 times 8 is 40

32/8 is 4

Either divide or multiply when needed

Answer:

A)

Step-by-step explanation:

We know that the expression (x^2 - a^2) can be written as (x-a)(x+a). So an expression of this type: (x^2 - a^2) wouldn't be completely factored because it could be factorized even more.

So we know that 36 = 6^2, 49= 7^2 and 81 = 9^2. So if we choose any of these options (Option B, C and D) it wouldn't be completely factored.

The correct is the option A, given that if a=12, it wouldn't be a perfect square, so it would be completely factored.

So I just did the problem and im pretty sure the answer is A

Answer:

a2+1)-(4+2a2)

Step-by-step explanation:

to solve this, we need to get rid of the brackets as follow:

3a2+1-4-2a2  

ading the common terms we have:

a2 - 3

that is all.

Plz mark  me brainlist!!!

Answer:

2b/3 * 2b/3 * 2b/3 * 2b/3

Good luck!!

Answer:

16b^4/81

Step-by-step explanation:

Answer:

1505 cubic centimeters

Step-by-step explanation:

Lengths are related by scale factor "k"

Volumes are related by scale factor "k^3"

From large to small:

What multiplied by 18, gives us 6? We can write:

18(k)=6

k = 6/18 = 1/3

So scale factor is 1/3

Now in terms of volume, the larger is given as 40, 635, so we can set up:

40,635 * k^3 = smaller volume

we know k = 1/3, so

40,635 * (1/3)^3 = smaller volume

Thus, smaller volume = 40,635 * (1/3)^3 = 1505

a)Each egg requires 0.5 cups of sugar in Grandma's recipe.

b)The ratio of baking powder to salt is 3:1.

a) The recipe uses 2 cups of sugar and 4 eggs. To find out how many cups of sugar are needed per egg, we divide the total cups of sugar by the number of eggs:

2 cups of sugar / 4 eggs = 0.5 cups of sugar per egg

So, 0.5 cups of sugar are needed for each egg.

b) Ratio of baking powder to salt

The recipe calls for 3/4 teaspoon of baking powder and 1/4 teaspoon of salt. To find the ratio of baking powder to salt, we divide the amount of baking powder by the amount of salt:

(3/4) teaspoon of baking powder / (1/4) teaspoon of salt = 3

Thus, the ratio of baking powder to salt is 3:1. This means there is three times as much baking powder as salt in the recipe, which aligns with your sister's observation.

The complete question is:

Use the recipe shown in the table to answer the questions below. Use pictures, tables or number sentences to solve the task. Grandma's Recipe for Sugar Cookies 1/2 cups butter 2 cups sugar 4 eggs 34 teaspoon baking powder 1 % cups flour 14 teaspoon salt a) How many cups of sugar are needed for each egg? How do you know? Your sister notices that she needs three times as much baking powder as salt in this recipe. b)What is the ratio of baking powder to salt? Explain your reasoning in words.

Answer:

100

Step-by-step explanation:

The given equation is;

–m + 0.02 + 2.1m = –1.45 – 4.81m

The highest decimal places is 2.

This implies that, we must multiply each term of the equation by [tex]10^2=100[/tex] before solving in order to eliminate the decimal.

In that case the equation becomes;

–100m + 2 + 210m = –145 – 481m

Hence the number is 100

Answer:

easy answer 100

Step-by-step explanation:

Answer:

10 necklaces =  50 rocks

15 necklaces = 75 rocks

20 necklaces = 100 rocks

25 necklaces = 125 rocks

Step-by-step explanation:

A table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces:

| Number of necklaces | Number of shiny rocks used |

| 10 | 50 |

| 15 | 75 |

| 20 | 100 |

| 25 | 125 |

To calculate the number of shiny rocks used, we simply multiply the number of necklaces by the number of shiny rocks per necklace. For example, to calculate the number of shiny rocks used for 10 necklaces, we multiply 10 by 5:

10 necklaces * 5 shiny rocks/necklace = 50 shiny rocks

We can do the same calculation for 15, 20, and 25 necklaces to get the following results:

15 necklaces * 5 shiny rocks/necklace = 75 shiny rocks

20 necklaces * 5 shiny rocks/necklace = 100 shiny rocks

25 necklaces * 5 shiny rocks/necklace = 125 shiny rocks

Therefore, the table above shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces.

For such more question on number

https://brainly.com/question/30752681

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Answer:

- 3 is less than - 5 is not true

Step-by-step explanation:

Numbers to the right of numbers on the number line are greater.

Numbers to the left of numbers on the number line are less

- 3 is to the right of -5 on the number line and is greater than - 5

Answer:

[tex]\large\boxed{A.\ \dfrac{1}{2}x+\dfrac{11}{2}}[/tex]

Step-by-step explanation:

[tex]-3x-(x-1)+\dfrac{3}{2}(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left(\dfrac{3}{2}\right)(3x)+\left(\dfrac{3}{2}\right)(3)\\\\=-3x-x+1+\dfrac{9}{2}x+\dfrac{9}{2}\qquad\text{combine like terms}\\\\=\bigg(-3x-x+\dfrac{9}{2}x\bigg)+\bigg(1+\dfrac{9}{2}\bigg)\\\\=\bigg(\dfrac{-6}{2}x-\dfrac{2}{2}x+\dfrac{9}{2}x\bigg)+\bigg(\dfrac{2}{2}+\dfrac{9}{2}\bigg)\\\\=\dfrac{-6-2+9}{2}x+\dfrac{2+9}{2}=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]

Answer:

B.30

Step-by-step explanation:

This was picked because if u divide 18 by 3. You get 6 and if u multiply it by 2. You get 12 plus the 18 equals 30.

Answer:

±6

Step-by-step explanation:

Whenever you are finding the square root of something, it will ALWAYS result in a negative and positive number, or else depending on the situation of a problem.

Ex: Distance Formula → POSITIVE ANSWER ONLY

I am joyous to assist you anytime.

The area of that trapeziod is 28 inches.

Answer:

Step-by-step explanation:

The area is a+b/2

so the answer is 28

Answer:

Option D. [tex]272[/tex]

Step-by-step explanation:

we know that

To evaluate the sum , use the formula

[tex]S=\frac{1}{2}(a1+an)n[/tex]

where

a1 is the first term

an is the last term

n is the number of terms

In this problem

For n=1 ------> a1=2(1)=2

For n=16 ------> an=2(16)=32

n=16 terms

substitute in the formula

[tex]S=\frac{1}{2}(2+32)16[/tex]

[tex]S=272[/tex]