Carlos calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?

Answer:

a(n) = 27*(2/3)^(n - 1)

Step-by-step explanation:

The first four terms are 27, 18, 12, 8.

Find the common ratio:

To do this, let that ratio = r, and write and solve 27r = 18.  Thus, r = 2/3.

The general explicit formula for this sequence is

a(n) = a(1)*(2/3)^(n - 1), or, since a(1) = 27, a(n) = 27*(2/3)^(n - 1)

Answer:

The sequence is A(n) = 27*(1.5)^(n-1)

Step-by-step explanation:

First, we need to see which type of sequence we have:

Differences:

27 - 18 = 9

18 - 12 = 6

the differences are different, let's try with the ratios.

27/18 = 1.5

18/12 = 1.5

12/8 = 1.5

So we have that this ratio is constant, then the sequence can be:

A(n) = 27*(1.5)^(n-1)

For n an integger number

where:

A(0) = 27*1.5^0 = 27

A(1) = 27*1.5^1 = 18

A(2) = 27*1.5^2 = 12

A(3) = 27*1.5^3 = 8

Answer:

heres the graph

Step-by-step explanation:

Answer:

1.The labels are switched.

2.The "partly cloudy" bar is the wrong length.

3.The "cloudy" bar is the wrong length

Step-by-step explanation:

In the bar graph, the labels are switched.The lable for the horizontal axis should read -----number of days------ and the label for the vertaical axis should read----type of weather----

The scale of the bar graph is good, where a unit distance in the x-axis represent a single day.However, the length for party cloudy is indicated as 7 instead of 8. This is wrong length. Similar mistake is observed in the length for cloudy which is indicated as 6 in the graph instead of 5 as shown in the table.

Answer:

1.The labels are switched.

2.The "partly cloudy" bar is the wrong length.

3.The "cloudy" bar is the wrong length

Step-by-step explanation:

The value of the given expression i.e. [tex]Log_864[/tex] is 2.

Given that,

Based on the above information, the calculation is as follows:

Let us assume [tex]Log_864[/tex] be n

So,

[tex]64= 8^n\\\\8^2 = 8^n[/tex]

n = 2

Therefore we can conclude that the value of the given expression i.e. [tex]Log_864[/tex] is 2.

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After the above expression has been evaluated, Log8 64 = 2.

To evaluate the expression "Log8 64," we need to determine the exponent to which the base 8 must be raised to obtain 64.

In this case, we are looking for the value of x in the equation 8ˣ = 64.

By observing that 8 is equal to 2³, we can rewrite the equation as (2³)ˣ = 64.

Using the property of exponentiation, we can simplify further: 2³ˣ = 64.

Since 64 is equal to 2⁶, we can equate the exponents - 3x = 6.

Solving for x, we find x = 2.

Therefore, Log8 64 = 2.

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Answer:

Angle C=35 degrees

Step-by-step explanation:

Angle C is an external angle. So, we can use the external angle theorem and get the equation

Angle C= 1/2(100-30)

Angle C=1/2(70)

Angle C=35 degrees

Answer:

35

Step-by-step explanation:

<C = 1/2 (large arc - small arc)

<C = 1/2 (100-30)

     =1/2(70)

       = 35

Answer:

m∠A=40°, m∠C=80°, m∠E=140°, m∠D=100°.

Step-by-step explanation:

Quadrilateral ACED is inscribed into the circle (see attached diagram).

Inscribed Quadrilateral Theorem: A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary (add up to 180°).

Since angle CAB has the measure of 40°, then opposite quadrilateral's angle CED has the measure of

180°-40°=140°.

Since angle ABC has the measure of 60°, then the third triangle's angle BCA has the measure

180°-40°-60°=80°.

Since angle BCA has the measure of 80°, then opposite quadrilateral's angle ADE has the measure of

180°-80°=100°.

So, in quadrilateral ACED,

m∠A=40°, m∠C=80°, m∠E=140°, m∠D=100°.

W=500lb

m=?

W=mg(m=W÷g)

500=m×10

500÷10=m

50=m

In the English Engineering system, the unit slug is used to measure mass. The mass of an object in slugs can be calculated by dividing its weight in pounds (lb) by the acceleration due to gravity (32.2 [tex]ft/s^2[/tex]). Therefore, a body weighing 500 lb would have a mass of about 15.53 slugs.

In physics, the unit slug is used in the English Engineering system where force is expressed in pounds (lb). The relationship between slug and lb is tied to the acceleration due to gravity on Earth which is approximately 32.2 [tex]ft/s^2[/tex]. To convert the weight of an object in lb to its mass in slugs you divide the weight by the acceleration due to gravity.

Thus, if an object weighs 500 lb, its mass in slugs can be found by dividing 500 lb by 32.2 [tex]ft/s^2[/tex]. So, the equation is:

Mass = 500 lb / 32.2 [tex]ft/s^2[/tex] = 15.53 slugs

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This is the graph of x-2y=5 start by writing it into y=mx+b format then plug in numbers for x then graph!

Answer:

8 metres long

Step-by-step explanation:

28 = 2l + 12

2[6]

16 = 2l

8 = l

I am joyous to assist you anytime.

Answer:

The correct option is b $81.00

Step-by-step explanation:

Interest earned can be found simply by multiplying the interest rate into the principal amount.

Our Interest rate is = 3%

and principal amount = $2,700

Interest earned = $2700 * 3/100

Interest earned =$ 81

So, the correct option is b $81.00.

Answer:

$ 81.00.

Step-by-step explanation:

Answer:

The answer is $960

Step-by-step explanation:

A = P(1 + rt)

[A] is Answer

[600] is P

[6%] is r

[10] is time

Answer:

true

Step-by-step explanation:

Answer:

I'm really sorry I can't tell you the answer because you have to measure the angle by yourself using a protractor. But I gave you information about types of angles if you got the degree of angles ( e.g 90 degrees). Hope it helped.

Step-by-step explanation:

acute angle-an angle between 0 and 90 degrees  

right angle-an 90 degree angle  

obtuse angle-an angle between 90 and 180 degrees  

straight angle-a 180 degree angle  

For this case we have that by definition:

Sharp angle: It is less than 90 degrees.

Flat angle: Measures 180 degrees.

Obtuse angle: Measures more than 90 degrees

The figure shows a pair of angles, each measuring 77 degrees. Now they enter the definition of acute angles.

To find the angle CEB we subtract:

[tex]180-77 = 103[/tex] degrees

This is the same measure of angle AED.

These would be obtuse angles.

Answer:

Sharp angles (77 degrees)

Obtuse angles (103 degrees)

Answer:

75%

Step-by-step explanation:

Because if 10 is half and 5 is half of 10 its 75%

Jane has saved 75% of the radio cost

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency.

The radio Jane wants to purchase costs $20 but she has saved only $15. The fraction of the amount Jane has saved to the total cost of the radio is [tex]\frac{15}{20}[/tex]. This fraction would have to multiplied by 100 to convert it to a percentage.

Percentage of the radio cost she has saved = (amount Jane has saved / cost of the radio) x 100

[tex]\frac{15}{20}[/tex] x 100 = 75%

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Answer:1:15 P.M

Step-by-step explanation:just substract it 230-115 and you get your time

If she rode for 1.5 hours and caught a flat @ 2:30 pm she had to have started at 1:15

Which one? The fractions to the right?

Answer:

The explicit formula

[tex]a_n = 3 +0.25 (n-1)[/tex]

The recursive formula

[tex]a_1 = 3[/tex]                            for [tex]n=1[/tex]

[tex]a_n = a_ {(n-1)} +0.25[/tex]     if [tex]n>1[/tex]

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

[tex]3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25[/tex]

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

[tex]a_n = a_1 + d (n-1)[/tex]

Where d is the constant difference between the terms.

[tex]d = 0.25[/tex]

[tex]a_1[/tex] is the first term of the sequence.

[tex]a_1 = 3[/tex]

So

[tex]a_n = 3 +0.25 (n-1)[/tex]

Finally, the recursive formula is:

[tex]a_1 = 3\\\\a_n = a_ {(n-1)} +0.25[/tex]

Answer:

600

Step-by-step explanation:

200*3=600

Answer:

600 cocoa beans

Step-by-step explanation:

1×3=3, 200×3= 600

Answer:

zero (0)

when the exponent 0 is applied to a nonzero base, the result is always 1

Step-by-step explanation:

Acoording to the zero power rule, a non zero number raised to the power 0 is always 1:

[tex]a^{0} =1[/tex] whit [tex]a=0[/tex]

Let's check this property using an example:

We know that a quantity over itself is always 1:  [tex]\frac{2}{2} =1[/tex]

We also know that a base without exponent is always raised to the power 1: [tex]2=2^{1}[/tex]

Now, according to the division power rule [tex]\frac{a^{m} }{a^{n}} =a^{m-n}[/tex], so [tex]\frac{2}{2} =\frac{2^{1} }{2^{1} } =2^{1-1} =2^{0} =1[/tex]

Answer:

56.5

Step-by-step explanation:

The length of the paper around the can is equal the circumference of the base.

Circumference = πd

Circumference = 3.14 * 4

Circumference = 12.56

And since the height is 4.5 (which is also the width of the paper if you unwrap it), Multiply the circumference by 4.5.

12.56 * 4.5

= 56.52

The result follows from manipulating the conditional probability. By definition,

[tex]P(A_1\mid B)=\dfrac{P(A_1\cap B)}{P(B)}=\dfrac{P(B\mid A_1)P(A_1)}{P(B)}[/tex]

[tex]P(A_1\mid B)=\dfrac{0.05\cdot0.60}{P(B)}[/tex]

By the law of total probability,

[tex]P(B)=P(B\cap A_1)+P(B\cap A_2)=P(B\mid A_1)P(A_1)+P(B\mid A_2)P(A_2)[/tex]

So we have

[tex]P(A_1\mid B)=\dfrac{0.05\cdot0.60}{0.05\cdot0.60+0.10\cdot0.40}\approx0.4286[/tex]

the probability P(A1 | B) is approximately 0.42857

Bayes’ theorem formula is:

[tex]P(A1 | B) = \frac{[P(B | A1) \times P(A1)]}{P(B)}[/tex]

We first need to calculate P(B):

[tex]P(B) = P(B | A1) \times P(A1) + P(B | A2) \times P(A2)[/tex]

Substitute the given values:

[tex]P(B) = 0.05 \times 0.60 + 0.10 \times 0.40\\\\P(B) = 0.03 + 0.04\\\\P(B) = 0.07[/tex]

Next we use Bayes' theorem to find P(A1 | B):

[tex]P(A1 | B) = \frac{[0.05 \times 0.60]}{0.07}\\\\P(A1 | B) = \frac{0.03}{0.07}\\\\P(A1 | B) \approx 0.42857[/tex]

Therefore, the probability P(A1 | B) is approximately 0.42857.

Answer:

The domain is  -∞ < x < ∞ ⇒ answer B

Step-by-step explanation:

* lets revise the meaning of the domain

- The domain is the values of x

- The domain is all the values of x which make the function is defined

- If there are some values of x make the function undefined, we

 exclude these values from the domain

* Now lets look to the figure

- It is a straight line because its ends are arrow, that means the line

 is a straight line no starting point or ending point

- That means x can be any real number

- There is no value of x make the function undefined

∴ The domain of this function is all real numbers

∴ The domain is (-∞ , ∞)

OR

∴ The domain is {x I x all real numbers}

OR

∴ The domain is  -∞ < x < ∞

Answer:

it is b

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

a = -2

b = 4

a - ab + b

= (-2) - (-2)(4) + (4)

= -2 - (-8) + 4

= -2 + 8 + 4

= 14

Answer:

10

Step-by-step explanation:

[tex]a=-2 \\ \\ b=4 \\ \\ a-ab+b \\ \\ -2-(-2)(4)+4 \\ \\ -2-(-8)+4 \\ \\ -2+8+4 \\ \\ -2+12 \\ \\ 10[/tex]

Answer:

10+4x=26

Step-by-step explanation:

Answer:

Step-by-step explanation:

26-10 ÷ 4 = X

   ∨

  16 ÷ 4 = X

     x= 4

you can only rent the bike for 4 hours.

your down payment is $10 so you subtract it form the money you have now you are left with $16 dollars you divide it by four becuase 4 x 4 is 16 there for you know you can only go for 4 hours

Solutions just means the amount of times the lines intersect, so there are no solutions. Since the lines are parallel, they’re going the exact same direction forever and ever, never intersecting. Hope this helps!

Answer:

There is Zero solution to the system of equation.  

Step-by-step explanation:

Consider the provided graph.

The solutions for the system of equations are the values of the variables that simultaneously make both equations true.

Parallel lines are the lines on a plane that never meet. They are always apart from the same distance.

Now consider the provided graph.

From the above definition, it is clear that the parallel lines never intersect. Also, the line has no solution or we can say Zero solution because there are no such variables that simultaneously make both equations true.

Also, the lines never intersect each other. Thus there is zero solution.

Hence, there is Zero solution to the system of equation.

Answer:

A complementary angle is two angles whose sum add up to 90°

Step-by-step explanation:

To find x you have to add both angles.

x + 22° + x° = 90°

(x + x) + 22 = 90

Combine like terms.

2x + 22 = 90

Subtract 22 from both sides

2x = 68

Divide both sides by 2

x = 34

The value of x is 34°

Answer:

B

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = base × perpendicular height

base = DC = 4 and height = DB = 5, thus

A = 4 × 5 = 20 units² → B

The area of the parallelogram is 20 square units.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

We know, The area of a parallelogram is 2×(1/2)×base×height, As a parallelogram can be divided into two congruent triangles.

From the given information, If we draw an altitude to it will of 5 units and the base of the parallelogram is 4 units.

Therefore, The area of the parallelogram is, (5×4) = 20 square units.

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[tex]\bf (~~\stackrel{\stackrel{x}{\downarrow }}{-3}~~,~~ y~~)\qquad \qquad y=\left( \cfrac{1}{4} \right)^x\implies y=\left( \cfrac{1}{4} \right)^{-3}\implies y=\left( \cfrac{4}{1} \right)^{3} \\\\\\ y=4^3\implies y=64[/tex]

Final answer:

To find the value of y for the point (-3, y) on the function y = (1/4)^x, you substitute x with -3 and calculate y = (1/4)^(-3) = 1/64.

Explanation:

To find the value of y when the point (-3, y) lies on the graph of the function y = (1/4)^x, we need to substitute x with -3 in the given function.

So, we have y = (1/4)^(-3).

Now we find the value of y by calculating the inverse of 4 cubed, which will be:

y = 1/(4^3) = 1/64.

Therefore, y = 1/64.

The answer to this equation would be:

C=0

Answer:c=0

Step-by-step explanation:

Answer: x = 2 • ± √2 = ± 2.8284

Step-by-step explanation:

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!  

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  :

 x2 - 8  = 0  

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    x2-8 = 0  

Add  8  to both sides of the equation :  

                     x2 = 8  

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 8  

Can  √ 8 be simplified ?

Yes!   The prime factorization of  8   is

  2•2•2  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 8   =  √ 2•2•2   =

               ±  2 • √ 2  

The equation has two real solutions  

These solutions are  x = 2 • ± √2 = ± 2.8284  

Two solutions were found :

                  x = 2 • ± √2 = ± 2.8284

Not sure what you need help with, but I hope I helped you somehow.