Which theorem or postulate proves that △ABC and △DEF are similar?


-SAS Similarity Theorem

-SSS Similarity Theorem

-AA Similarity Postulate


ANSWER ASAP!

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Answer:

144 out of 180 days.

Step-by-step explanation:

180/30 is 6. That means that 30 * 6 = 180. So, 24 * 6 = 144, which is our answer.

Answer:

To calculate exponential growth, use the formula y(t) = a__ekt, where a is the value at the start, k is the rate of growth or decay, t is time and y(t) is the population's value at time t.

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To calculate the time for exponential growth, use the formula n = ln(M) / ln(b) for a specific multiple (M) and growth rate (b), or the Rule of 70 for estimating doubling time.

Understanding Exponential Growth

The formula to calculate the time for exponential growth depends on the growth rate and the factor by which a quantity increases. If the growth rate is constant and represented as a percentage or fraction, the growth is exponential. For example, if a bacterial population doubles every hour, starting with 1000 bacteria, it will grow to 2000 after one hour, 4000 after two hours, and so on.

Calculating Time for Exponential Growth

One formula to find the time (n) to reach a certain multiple (M) of the original amount at a specific growth rate (b) is:

n = ln(M) / ln(b)

For instance, to calculate the time to increase by a factor of 1000 with an annual growth rate of 7% (b = 1.07):

n = ln(1000) / ln(1.07) ≈ 102 years

This equation shows that it would take approximately 102 years for the quantity to grow by a factor of 1000.

The Rule of 70

t = 70 / growth rate

t = 70 / 2.9 ≈ 24 years

The time it takes for exponential growth can vary significantly based on the growth rate and the factor of increase desired.

Answer:

Step-by-step explanation:

First, let's look at the pie-shaped segment defined by the 123° angle and the 18.6 m radius.

The area of the entire circle is given by A = πr² = 3.14159(18.6 m)², or A = 1086.865 m².

The area of the "pie slice" is (123/360) of that, or 371.346 m².

Next, we must find the area of the triangle and subtract this area from this 371.346 m²:

Use the Law of Cosines to find the area of this triangle.  The Law of Cosines in appropriate form is

c² = a² + b² -2ab*cos C.

In this case C is 123° and a and b are both 18.6 m in length.  Thus,

c² = (18.6 m)² + (18.6 m)² - 2(18.6 m)(18.6 m)*cos 123°

Thus,

c² = 691.92 m² - 691.92*cos 123°, or

    = (691.92 m²)(1 - cos 123°)

     =  (691.92 m²)(1 - [-0.5446] ) = (691.92 m²)(1.5446) = 1068.767

Taking the square root of this result, we get c = +32.6920 m.

Subdivide the triangle shown to form a new triangle with hypotenuse 18.6 m, adjacent side 32.6920 m  / 2, or  16.3460 and opposite side h.

Then 18.6² = h² + 16.3460², which leads to h²2 = 18.6² - 16.346², or 78.768.

Then h = √78.768 = 8.875 (m).

We now use this info to find the area of the illustrated triangle, using the formula A = (1/2)(base)(height).  That comes out to:

A = (1/2)(16.3460 m)(8.875 m) = 72.535 m²

Finally, we subtract twice that from the area of the 'pie' to get the area of the yellow (shaded) area:

pie area - area of triangle shown in the diagram =

371.346 m² - 145.071 m² = 226.3 m² (to the nearest tenth)

Answer:

226.4

Step-by-step explanation:

NOT 226.3 !!

The answer of the question is A

Answer: The answer to ur question is 60.84

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Answer:

x=17

Step-by-step explanation:

Answer:

x=5   x=-3

Step-by-step explanation:

x - 15/x = 2

Multiply each term by x to get rid of the fraction

x(x - 15/x) = 2*x

x^2 -15 = 2x

Subtract 2x from each side

x^2 -2x -15 = 2x-2x

x^2 -2x-15 = 0

Factor the left hand side

(x-5) (x+3) =0

Using the zero product property

x-5=0      x+3 =0

x=5   x=-3

Answer:

Table 2

Step-by-step explanation:

The given frequency distribution table is

X  :   1           2           3            4           5

f   :   11          1            2           4           2

The sum of frequencies is

[tex]\sum f=11+1+2+4+2=20[/tex]

The formula for probability is

[tex]P_i=\frac{f_i}{\sum f}[/tex]

where, [tex]f_i[/tex] is frequency and [tex]\sum f[/tex] in the sum of frequencies.

For X=1,

[tex]P_1=\frac{11}{20}=0.55[/tex]

For X=2,

[tex]P_2=\frac{1}{20}=0.05[/tex]

For X=3,

[tex]P_3=\frac{2}{20}=0.1[/tex]

For X=4,

[tex]P_4=\frac{4}{20}=0.2[/tex]

For X=5,

[tex]P_5=\frac{2}{20}=0.1[/tex]

The probability distribution table corresponds with the given frequency distribution table is

X  :   1           2           3            4           5

P   :   0.55    0.05    0.1          0.2       0.1

Therefore, the correct option is 2.

The only probability distribution table that corresponds with the frequency distribution table is; Second table

From the given frequency distribution table, let's find the sum of the given frequencies. Thus;

Σf = 11 + 1 + 2 + 4 + 2

Σf = 20

Now,the probability for each value of x will be;

P_x = f_x/Σf

Where f_x represents the frequency of the given value of x.

Thus;

P_1 = 11/20

P_1 = 0.55

P_2 = 1/20

P_2 = 0.05

P_3 = 2/20

P_3 = 0.1

P_4 = 4/20

P_4 = 0.2

P_5 = 2/20

P_5 = 0.1

Looking at the tables in the options, in conclusion the only tables that have their P value corresponding with those we got for each value of x is Option B which is the second table.

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Answer:

Step-by-step explanation:

[tex]\frac{4^{10}}{4^2} = 4^{10 - 2} = 4^8[/tex]

Alternative A

I hope I helped you.

Answer:

A. 4^8

Step-by-step explanation:

When you divide powers with the same base, use the same base, and subtract the exponents.

Here is the rule:

[tex] \dfrac{a^m}{a^n} = a^{m - n} [/tex]

Here is your problem:

[tex] \dfrac{4^{10}}{4^2} = 4^{10 - 2} = 4^8 [/tex]

Answer: 50

To find the surface area of any prism, you multiply the base by the height.

10 x 5 = 50

Answer:

Step-by-step explanation:

first solve the volume of the rectangular prism

V = l x w x h

where l is the length

w is the width

h is the height

V = 7 x 4 x 2.5

v = 70 cu cm

then solve the volume of the box

v = e^3

v = 0.5^3

v = 0.125

number of cubes = 70 / 0.125

number of cubes = 560 cubes

Answer:

The number of cubes are needed to fill the rectangular prism = 448 cubes

Step-by-step explanation:

It is given that,

A rectangular prism has a length of 7 cm, a width of 4 cm, and a height of 2 cm. The prism is filled with cubes that have edge lengths of 1/2 cm

To find the volume of rectangular prism

Volume of rectangular prism = Length x Width X Height

Length = 7 cm, Width = 4 cm and height = 2cm

Volume = 7 x 4 x 2 = 56 cm³

To find the volume of small cubes

Volume of cube = a³

a = 1/2 cm = 0.5³ = 0.125

To find the number of cubes needed to fill prism

Number of cubes = Volume of prism/  volume of cube

 = 56/0.125 = 448 cubes

Therefore the correct answer is 448 cubes

Answer:7 is an irrational number.

Step-by-step explanation: it can be expressed as the quotient of two integers: 7÷ 1.

Answer:

Number 7 is A and Number 8 is D.

Answer:

The correct answers are

A) 2+10h

D) 40

Factor the polynomial

7(x-3)(x+5)

Answer:

V=a^3 is the answer

The value of the volume of a cube with an edge of 6cd³ is,

⇒ V = 216c³d⁹

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

We have to given that;

An edge of cube is,

⇒ 6cd³

Since, We know that;

Volume of cube is,

⇒ V = side³

Hence, The value of the volume of a cube with an edge of 6cd³ is,

V = (6cd³)³

V = 216c³d⁹

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Answer:

215 seconds

Step-by-step explanation:

120 words : 100 seconds = 258 words : x seconds

x = 258*100/120 = 258*5/6 = 43*5/1 = 215 seconds

Answer: 120+120+ 18= 258

You know that it takes 100 seconds for 120 words

120=100 120=100 now we have to find now how many seconds does it take to make 18 words

Answer:

Step-by-step explanation:

The formula fo an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

b - base

h - height

We have

x - base

6x - height

Substitute:

[tex]A=\dfrac{(x)(6x)}{2}=\dfrac{6x^2}{2}=3x^2[/tex]

Answer: 4 hours

Step-by-step explanation:

10+6=16

16+6=22

22+6=28

28+6=34

Step-by-step explanation:

Given

The measure of the length of the triangular prism is 5.3, height is 1.26, and width is 3.3,

Surface area triangular prism;

The surface area of a triangular prism is the total area covered by its surface in a three-dimensional plane.

The surface area of a triangular prism is given by;

Where a, b, and c are the sides of triangular bases and H is the height of the prism.

The measured side a is 5.3, b is 3.6, and c is 2.3.

Substitute all the values in the formula;

Hence, the surface area of this triangular prism is 43.6 square meters.

Answer:

See below  

Step-by-step explanation:

Integer exponents are a subset of rational exponents

Integer exponents

An integer exponent is an exponent that is an integer. For example, in the expression y = 5³, the 3 is an integer exponent.

An integer exponent is a power. Thus, 5³ = 5× 5× 5.

Rational exponents

Rational exponents can be expressed as a ratio of integers with nonzero denominators.

Thus, in the expression [tex]y = 5^{\frac{ 2}{3 }}[/tex], the fraction ⅔ is a rational exponent.

A rational exponent is both a power and an nth root. The numerator is the power, and the denominator is the root. Thus,

[tex]5^{\frac{ 2}{ 3}} = \sqrt[3]{5^{2}} = (\sqrt[3]{5}})^{2}[/tex]

The product after multiplying 8 x 1/5 in the simplest form is 1.6.

Given a multiplication expression, 8 x 1/5.

We have to find the product of this in the simplest form.

Here 8 and 1/5 are the numbers which are to be multiplied.

The simplest fractional form of the product is,

8 x 1/5 = 8/5

This fraction cannot be simplified further.

Now we have to find the result in decimal form.

8 x 1/5 = 1 3/5 = 1 + 0.6 = 1.6

Hence the product is 1.6.

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Answer:

9 12 15

Step-by-step explanation:

9²+12²=15²

81+144=225

Answer:

Step-by-step explanation:

Hello, this is a factorization algebra case:

a) 7(X+6)

b) 11y + 7

Best regards

Answer:

= [tex]\dfrac{1}{5^{9}}[/tex]

Step-by-step explanation:

When dividing values with exponents, we simply need to subtract the numerators exponent to the denominators exponent.

So we have:

[tex]\dfrac{5^{-6}}{5^{3} }[/tex]

= [tex]5^{-6 - 3}[/tex]

= [tex]5^{-9}[/tex]

Now since we have a negative exponent, we can get the reciprocal of the value to make it positive.

= [tex]\dfrac{1}{5^{9}}[/tex]

Answer:

The answer is 1 / 5^(9)

Step-by-step explanation:

We just need to divide both numbers and find the result

(5)^-6 / (5)^3

(5)^(-6-(3)) =

(5)^(-9) =

1 / 5^(9) = 5,120 .10^(-7)

There is a 150% increase.

Work is attached in the image provided.

Have a great day!

Hi. if you have acces to a ti-84 plus or a virtual to plug it into Y= and click 2nd and graph which will take you to the data table

Answer:

The correct option is 1.

Step-by-step explanation:

The system of equations is

[tex]f(x)=2(3)^x[/tex]

[tex]g(x)=10\log (x+3)[/tex]

Using graphing tool we can draw the graph as shown below.

From the below graph it is clear the graph of f(x) and g(x) intersect at (-1.944,0.236) and (1.004,6.025).

[tex](-1.944,0.236)\approx (-2,0.2)[/tex]

[tex](1.004,6.025)\approx (1,6)[/tex]

The approximate solutions of the given system of equations are (-2,02) and (1,6). Therefore only option 1 is correct.

The area of a semi-circle with a diameter of 18in is 127.17 inches squared

Answer:

I have the same question connections academy? it is so hard i still dont know

Step-by-step explanation:

Answer: Right (Last option)

Step-by-step explanation:

As you can see in the figure, the parallel lines AD and GJ are intersected  by two lines.

The line EL intersects the parallel lines and there are two angles that are formed by this intersections which are located on the exterior of AD and GJ, but  on opposite sides of EL, (these angles are called "Alternate exterior angles" and they are congruent), which are:

 ∠LHJ and ∠EBA

You can observe that the angle ∠EBA is indicated with a square. This means that the measure of that angle is 90° (Right angle).

Therefore, if ∠EBA=90°, then ∠LHJ =90°

Answer:

The correct answer is last option Right

Step-by-step explanation:

From the figure we can see that,

AD ║ GJ and LE is the traversal.

And also given <ABE = 90°

Fro figure we get <ABE and <GHB are corresponding angles. Corresponding angles are equal.

Therefore <GHB = 90°

To find the <LHJ

From figure we can see that <LHJ and <GHB are vertically opposite angles.

Vertically opposite angles are  equal.

Therefore <LHJ = <GHB = 90°

Answer:  6

Step-by-step explanation:

x⁶ + x³ + 1 = 0

The only possible rational roots are ± 1.

Use synthetic division to see if either root is valid:

1 |  1     0     0     1     0     0     1

  |  ↓     1      1     1     2     2     2  

     1      1     1      2    2     2      3   ← Remainder ≠ 0 so not a factor

-1 |  1     0     0     1     0     0     1

  |  ↓    -1      1    -1     0     0     0  

     1     -1     1      0    0     0      1   ← Remainder ≠ 0 so not a factor

Since there are no real roots, all 6 roots must be imaginary (complex). You can graph the equation to confirm (see attached). None of the roots cross the x-axis so they are all imaginary.

Answer:

Step-by-step explanation:

1. Add 1 to both the sides

2. 3x=12

3. Divide both the sides by 3

4. X=4

Answer:

Step-by-step explanation:

[tex]3x-1=11\qquad\text{add 1 to both sides}\\\\3x-1+1=11+1\\\\3x=12\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{12}{3}\\\\\boxed{x=4}[/tex]

Answer:

A) 0.2  

Step-by-step explanation:

From least to greatest, the data points are

6, 6, 6, 7, 7, 7, 8, 8, 8, 9

To find the mean, we find the sum of the data points and divide by the number of data points, 10.  The sum of the data points is

6+6+6+7+7+7+8+8+8+9 = 72

Dividing by 10, the mean is 72/10 = 7.2.

The median is the middle number in the set.  This is 7.

The difference between the mean and the median is

7.2-7 = 0.2.

Answer:

0.2

Step-by-step explanation:

just got it right