Walter used the iterative process to determine that √13 is between 3.61 and 3.62.Analyze Walter’s estimation. Is he correct? If not, what was his mistake?
A-Yes, Walter is correct.
B-No, 3.612 is less than 13.
C-No, both 3.612 and 3.622 are greater than 13.
D-No, both 3.612 and 3.622 are less than 13.
i need the right answer

Answer:

See below

Step-by-step explanation:

Here is one way .... I showed you how to use Law of cosines in another Q

 use this to find  CB

CB^2 = 13^2 + 21^2 - 2(13)(21) cos 91      <==== solve for CB

THEN use law of SINES to find angle B

sin B / 21  =  sin 91 / CB           (CB you found using law of cosines above)

Answer:

m∠B = 57.5°

Explanation:

Use cosine rule:

a² = b² + c² - 2bc cos(A)

  inserting values

a² = 21² + 13² - 2(21)(13) cos(91)

a² = 619.529

a = √619.529

a = CB = 24.89 km

Then use sine rule:

sin(A)/a = sin(B)/b

sin(91)/24.89 = sin(B)/21

sin(B) = 21sin(91)/24.89

sin(B) = 0.843583...

B = sin⁻¹(0.843583) = 57.52° ≈ 57.5°

The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ [tex]9x^{n} x^{n}[/tex]

We have to find the values of x for which the series converges.

We know,                

∑ [tex]ar^{n-1}[/tex]    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ [tex](9x)^{n}[/tex] is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

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The logarithmic equation is:

log₂128 = x

So the correct option is the third one

Here we have the expression.

2ˣ = 128

Now, if we apply the natural logarithm to both sides, we can get:

ln(2ˣ) = ln(128)

Because of the property of natural logarithms, we can write the left side as:

ln(2ˣ) = x*ln(2) = ln(128)

Now, if we isolate x, we get:

x = ln(128)/ln(2)

And remember that:

ln(k)/ln(n) = logₙ(k)

Then we can rewrite the logarithmic equation as:

x = log₂(128)

Which is the third option.

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Answer:

13

Step-by-step explanation:

w^2 = -2^2 = 4

-v = -1*-8 = 8

Put it together: w^2-v+1 --> 4+8+1 = 13

Answer:

Son: 26 yrs. Dad: 58 yrs.

Step-by-step explanation:

Let s equal to the present age of the son and let d equal to the present age of the dad. We can make two equations based on the information given to us. The first is about the fact that the dad is 32 yrs. older than the son:

d = s+32

the second is about the fact that 10 yrs. ago, he was triple his son's age.

d-10 = 3(s-10)

We can use the distributive property and we have:

d-10 = 3s-30

Then, let's add 10 to each side:

d = 3s-20

We can substitute the first equation into the second, resulting in:

s+32 = 3s-20

Adding 20 to both sides:

s+52 = 3s

2s = 52

s = 26

Now that we have the son's age, the dad's age is 26+32 = 58.

Son's age: 26

Dad's age: 58

Answer:

  (d)  71°

Step-by-step explanation:

The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.

Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.

  sin(W/2) = Opposite/Hypotenuse

  sin(W/2) = (35/2)/(30) = 7/12

Using the inverse sine function, we find ...

  W/2 = arcsin(7/12) ≈ 35.685°

  W = 2×36.684° = 71.37°

  W ≈ 71°

The law of cosines tells you ...

  w² = u² +v² -2uv·cos(W)

Solving for W gives ...

  W = arccos((u² +v² -w²)/(2uv))

  W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°

  W ≈ 71°

The smallest positive integer having exactly 5 different positive integer divisors is 60.

To find the smallest positive integer having exactly 5 different positive integer divisors:

Therefore, the smallest positive integer having exactly 5 different positive integer divisors is 60.

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Answer:

option 4

Step-by-step explanation:

F = [tex]\frac{kxy}{z}[/tex]

k is the constant of variation

• if the variables are on the numerator they vary directly

• if the variables are on the denominator they vary inversely

In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )

Answer:

Use this equation to find out!

Step-by-step explanation:

Since you didn't specify the n-gon, you have to use this equation to find out!

Number of Diagonals = n(n-3)/2

Hope this helps! :)

Answer:

∠a=40°, ∠b=50°, ∠c=115°.

Step-by-step explanation:

∵The opposite vertex angles are equal,

∴∠a=40°.

∴∠b=90°-∠a=90°-40°=50°.

∠c=180°-65°=115°.

The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

From the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point

Lines that are parallel to each other will have the same slope.

First, we will determine the slope of the line in the given equation.

The given equation of the line is

8x − 3y = 1

Express the equation in the slope-intercept form of a line, y = mx + b

Where m is the slope and

b is the y-intercept

That is,

8x − 3y = 1

8x -1 = 3y

3y = 8x - 1

y = 8/3(x) - 1/3

By comparing,

∴ The slope of the line is 8/3

Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3

Now, find the equation of a line containing the point (-2, 0) and that has  a slope of 8/3

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -2

and y₁ = 0

∴ y - 0 = 8/3(x - -2)

y = 8/3(x +2)

3y = 8(x +2)

3y = 8x + 16

8x -3y = -16

Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

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Answer: 77 - 10 = 67, and the additive inverse of 77 - 10 is 77 + 10. 77 + 10 = 87.

Hope this helps! This question was kind of confusing for me, because I didn’t understand why you said to add 77 - 10… is this is the incorrect answer sorry your question was worded weird

Answer:0.333

Step-by-step explanation:4+8=12 so there is only 4 chances it can be male so 4/12=0.333

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

probability (P) is calculated as

P = (desired result ) ÷ ( number of possible results )

here desired result is choosing a male from 4 males

number of possible results = 4 + 8 = 12 , then

P( male) = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

(-4,0) , (0,9)

Step-by-step explanation:

x-intercept is the point where the line touches the x-axis, which means, y = 0.

So when y = 0,

-9x + 4(0) = 36

-9x = 36

x = [tex]\frac{36}{-9}[/tex]

x = -4

Therefore, the coordinates of the x - intercept is (-4,0)

y-intercept is the point where the line touches the y-axis, which means , x = 0.

so when x = 0,

-9(0) + 4y = 36

4y = 36

y = [tex]\frac{36}{4}[/tex]

y = 9

Therefore, the coordinates of the y - intercept is (0,9)

Answer:

x - intercept (-4,0)

y -intercept (0,9)

Step-by-step explanation:

Put in 0 for x.

-9(0) + 4y = 36

4y = 36  Divide both sides by 4

y = 9

(0,9) This is where the line will cross the y axis.

Put in 0 for y

-9y + 4(0) = 36

-9y = 36 Divide both sides by -9

Y = -4

Answer:

Step-by-step explanation:

since we know that the 50 degrees is one side of the line then the angle that is strait opposite from this angle is 50 degrees, so 50+60=110degrees and 180-110=70, so x=70 degrees

Answer:

8 Hours

Step-by-step explanation:

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

[tex]\frac{220}{5}x=352[/tex]

Multiply both sides by 5

[tex]220x=1760[/tex]

Divide both sides by 220

[tex]x=8[/tex]

Therefore it would take 8 hours.

8 Hours long would it take to travel 352 miles,

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

Multiply both sides by 5

Divide both sides by 220

Hence, it would take 8 hours.

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The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.

To find the step that is the part of the process of algebraically solving the given system of equations:

That would be:

(C) 4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substituted for y).

Proof:      

(E) 0 = x2 – 9x + 20  (liked terms are grouped and simplified).

Proof:      

Solving:

Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.

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The complete question is given below:
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.

(A) y = x2 + 5x + 10

(B) y + 5x = x2 + 10 + 4x – 10

(C) 4x – 10 = x2 – 5x + 10

(D) 0 = x2 – 9x

(E) 0 = x2 – 9x + 20

(F) One x-value of a solution to the system is 4.

a. Expressing y in terms of x, y = 20/(x + 3)

b. When x = 5, the value of y is 2.5

The question has to do with inverse variation.

Inverse variation is variation in which one quantity varies inversely as the other.

Given that y is inversely as x + 3 and that y = 4 when x = 2.

Since y varies inversely as x + 3, we have

y ∝ 1/(x + 3)

y = k/(x + 3)

When y = 4, x = 3. So

y = k/(x + 3)

4 = k/(2 + 3)

4 = k/5

k = 4 × 5

k = 20

So, y = k/(x + 3)

y = 20/(x + 3)

So, expressing y in terms of x, y = 20/(x + 3)

Since  y = 20/(x + 3)

Substituting x = 5 into the equation, we have

y = 20/(x + 3)

y = 20/(5 + 3)

y = 20/8

y = 5/2

y = 2.5

So, when x = 5, the value of y is 2.5

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

According to the given information ,there still 4 pockets to check .

Then

the possibility that the money will be in the next pocket :

[tex]=\frac{1}{4}[/tex]

Answer: Answer above me is correct

We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.

Using its position, explicit formulas can compute a(n).

Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

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Answer: (D)

Step-by-step explanation:

took quiz

Using the Fundamental Counting Theorem, it is found that the customer can put together 288 different outfits.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, hence the parameters are given as follows:

[tex]n_1 = 3, n_2 = 6, n_3 = 8, n_4 = 2[/tex]

Hence the number of different outfits is given as follows:

N = 3 x 6 x 8 x 2 = 288

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The approximate solution of this system of equations is

(x,y)=(-0.25,1.25)

Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account.

Given that,

y = |x − 1| and y = 3x+2

 y = |x − 1|

    = (x-1) ,    for  (x-1)>0 or x>1

and

y = -(x-1)  ,    for(x-1)<0  or x<1

y  = -x+1      

Now,   For x>1

y = x-1    ......(1)

y = 3x+2   ......(2)

Solving for x by equaliting's method:

 3x+2 = x-1

→ 3x-x = -1-2

→ 2x = -3

→ x = -3/2

→ x = -1.5 which is <1.

For x<1

y = -x+1    ......(1)

y = 3x+2   ......(2)

Solving for x by equaliting's method:

 3x+2 = -x+1

→ 3x+x = 1-2

→ 4x = -1

→ x = -1/4

→ x= -0.25 which is <1.

substitute the value of x = -0.25 in equation 1 for x<1.

y = -x+1

  = -(-0.25)+1

y  = 1.25

Hence, The approximate solution of this system of equations is

(x,y)=(-1/4,5/4)=(-0.25,1.25).

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Answer:

32 mm²

Step-by-step explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{Area=32~mm^2}[/tex]

Step-by-step explanation:

Given information

Rectangle A:

Rectangle B:

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

2) A = b × h

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

[tex]\Large\boxed{Area=32~mm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took [tex]f(-x) = - f(x)[/tex], which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].

A function f(x) is said to be odd or even when it completes the condition:

In the question, we are given that April was asked to determine whether  [tex]f(x) = x^3 - 1[/tex], is even, odd, or neither, and are shown her work.

We are asked whether April's work is correct, and if not, what is the first step where April made a mistake.

To check for a function is even or odd, we first calculate f(-x).

April's first step was also finding f(-x), which she found accurately as  [tex]f(-x) = -x^3 - 1[/tex].

Next, we need to check whether f(-x) is equal to f(x), -f(x), or neither, to check if the function is even, odd, or neither, respectively.

April, also choose the right step of checking, but did a mistake in checking, since f(-x) ≠ f(x), and also, f(-x) ≠ - f(x), since, [tex]- f(x) = -(x^3 - 1)[/tex] = [tex]-x^3 + 1[/tex], which is not equal to f(-x).

Thus, April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took f(-x) = - f(x), which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].

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Based on the task content; If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always. Option B

Based on the rule of inequality, whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

For instance,

-4x > 12

divide both sides by -4

x < 12/-4

x < -3

If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always.

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Answer:

a.9

b.36

Step-by-step explanation:

Blue beans + orange beans + red beans = 54

6x + 2x-3 + 15-x = 54

6x+2x-x=54+3-15

7x=42

divide both sides by 7

x=6

a. orange beans = 2x-3

but x=6

2(6)-3

12-3

=9

b.blue beans =6x

6(6)

=36

Answer:

11/18.

Dan is 8.

Step-by-step explanation:

The initial fraction is

x / 2x-4

Adding 3/3 we have

x+3 / 2x-1 = 2/3

Cross multiply:

3(x+3) = 2(2x-1)

3x + 9 = 4x - 2

9 + 2 = 4x - 3x

11 = x,

So the original fraction was 11 / 2(11) - 4

= 11/18.

If Dans age is d then Lois's age = 4d.

So 4d + d  = 40

5d = 40

d = 8.

So Dan is 8 years old.

The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

The expression is given as:

(2x+1)/(x²-3)

The above expression is a fraction and the numerator has 2 terms

For a fraction

A + B)/x

The fraction can be split as

A/x + B/x

Using the above as a guide, we have:

(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)

Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

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Considering the given function in the problem, it is found that:

a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.

b. At least 18 female rabbits are required for there to be 13 offspring.

The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:

[tex]R = 3 + \frac{350F}{F + 625}[/tex]

When there are 12 female rabbits, we have that F = 12, hence:

[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]

9.6 offspring survive to maturity when there are 12 female rabbits in the population.

For at least 13 offspring, we have that the number of rabbits needed is given as follows:

[tex]R \geq 13[/tex]

[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]

[tex]\frac{350F}{F + 625} \geq 10[/tex]

[tex]350F \geq 10F + 6250[/tex]

[tex]F \geq \frac{6250}{340}[/tex]

[tex]F \geq 18[/tex]

At least 18 female rabbits are required for there to be 13 offspring.

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