Calculate the distance between (3 + i) and (3 − i).

Answer:

Total length of running track is 371.24 m .

Step-by-step explanation:

Total running track = Running track around straight region + running track around curved region.

Running track around straight region = 2 × length of straight region

= 2×82 m

= 164 m

Running track around curved region = 2 × length of curved region

= 2 × π × radius of curved region

= 2 × 3.14 × 33 m

= 207.24 m

Therefore , total length  of running track = 164 + 207.24 m

= 371.24 m

Answer:

The estimated result is 680, which suggests the calculator is incorrect.

Final answer:

The estimated result when rounding to the nearest ten is 130, while the exact calculator result is 159. Therefore, the given options for estimation are all incorrect. The calculator is accurate, but the estimate is lower.

Explanation:

The calculator results for the expression 56 + 7 * (34 - 17) u2013 16 can be checked by estimation. To estimate, we round the numbers to the nearest ten and perform the operations. Here are the steps for estimation:

Round 56 to the nearest ten: 60

Round 34 to the nearest ten: 30

Round 17 to the nearest ten: 20

Perform the rounded operation: 60 + 7 * (30 - 20) u2013 10

The simplified expression would be 60 + 7 * 10 u2013 10

This simplifies further to 60 + 70 u2013 10, which is 130

The exact calculator result would be:

Calculate the parentheses first: 34 - 17 = 17

Multiply by 7: 7 * 17 = 119

Add 56: 56 + 119 = 175

Subtract 16: 175 u2013 16 = 159

The estimated result is 130, and the accurate calculator result is 159. Therefore, none of the options provided are correct as the estimate should be 130, suggesting that while the calculator is accurate, the given estimate options are incorrect.

Answer:

Step-by-step explanation:

20 km to 95 minutes = x km to 285 minutes

20 / 95 = x / 285.....cross multiply

(95)(x) = (20)(285)

95x = 5700

x = 5700/95

x = 60 km <======

Answer:

The value of cos y° is -1

Step-by-step explanation:

Given as Trigonometrical functions as :

sin y° = - 1

tan y° = 1

Let The value of cos y° = x

Now, As we know

tan [tex]\theta[/tex] = [tex]\dfrac{sin \theta }{cos \theta }[/tex]

So, tan y° = [tex]\dfrac{sin y^{\circ}}{cos y^{\circ}}[/tex]

∴ cos y° =  [tex]\dfrac{sin y^{\circ}}{tan y^{\circ}}[/tex]

Or,  x = [tex]\dfrac{-1}{1}[/tex]

i.e, x = - 1

So, The value of cos y° = x = -1

Hence, The value of cos y° is -1  Answer

Answer:

The minimum is 9, meaning he continued to score an avg of 9 points per game. The maximum could be infinity, because not enough info is given.

Step-by-step explanation:

Original: 9

Possible: 9, infinite

Answer:

14.3

Step-by-step explanation:

percent: 14.3%

decimal: 14.3

fraction: 14 3/10

Answer:

I got 143/10 ;-;

But as a decimal it's 143.0 and percent is 14.3%

Answer:

The signa notation to represent the first five ten f(x) is given by [tex] f(x)=\sum\limits^{5}_{n=1}a_n[/tex]

Step-by-step explanation:

Given sequence is -5, -9, 13...

Let f(x) be the given sequence and is denoted by

[tex]f(x)=\{-5,-9,-13,...\}[/tex]

Let the first term be [tex]a_1, 2^{\textrm{nd}}[/tex]  term be [tex]a_3,...[/tex]

ie, [tex]a_1=-5,a_2=-9, a_3=-13,...[/tex]

To find the common difference d:

[tex]d=a_2-a_1[/tex]

[tex]=-9-(-5)[/tex]

[tex]=-9-(+5)[/tex]

[tex]d=-4[/tex]

[tex]d=a_3-a_2[/tex]

[tex]=-13-(-9)[/tex]

[tex]=-13+9[/tex]

[tex]d=-4[/tex]

Therefore the common difference d is -4 for given sequence f(x) with [tex]a_1=-5[/tex] and d=-4, the seqence f(x) is an arithmetic sequence

By defintion of arithmetic sequence

[tex]a_n=a+(n-1)d\hfill(1)[/tex]

Now to find [tex]a_4, a_5[/tex]:

put n=4 in equation (1)

[tex]a_4=a+(4-1)d[/tex]

[tex]a_4=-5+(3)(-4)[/tex]        [since a=-5, d=-4]

[tex]=-5-12[/tex]

[tex]a_4=-17[/tex]

in equation (1)

[tex]a_5=a+(5-1)d[/tex]

[tex]a_5=-5+(4)(-4)[/tex]       [since a=-5, d=-4]

[tex]=-5-16[/tex]

[tex]a_5=-21[/tex]

Therefore [tex]a_4=-17[/tex] and [tex]a_5=-21[/tex]

Therefore [tex]f(x)=\{-5,-9,-13,-17,-21,...\}[/tex]

Now to represent the sum of the first five terms of f(x) using sigma notation as below

[tex]f(x)=\sum_{n=1}^5 a_n[/tex]

where [tex]\sum_{n=1}^5 a_n=a_1+a_2+a_3+a_4+a_5[/tex]

           [tex]-5-9-13-17-21[/tex]

[tex]\sum_{n=1}^5 a_n=-65[/tex]

Answer:

The unknown number is 12.

Step-by-step explanation:

Let the unknown number be 'x'

Given:

A number increased by 5 is equivalent to twice the same number decreased by 7.

So, 'x' increased by 5 means add 5 to 'x'. This gives [tex]x+5[/tex]

Now, [tex]x+5[/tex] is equivalent to twice of 'x' decreased by 7.

Twice of 'x' means 2 times of 'x' which is [tex]2x[/tex]

'2x' decreased by 7 means subtract 7 from '2x'. This gives,

[tex]2x-7[/tex]

Now, [tex]x+5[/tex] and [tex]2x-7[/tex] are equivalent meaning they are equal. So,

[tex]x+5=2x-7\\5+7=2x-x\\12=x\\x=12[/tex]

Therefore, the unknown number is 12.

Answer:

x = 9, y = 2

Step-by-step explanation:

Given the 2 equations

x + 10y = 29 → (1)

x - y = 7 → (2)

Subtracting (2) from (1) term by term will eliminate the term in x

(x - x) + (10y - (- y)) = (29 - 7), that is

11y = 22 ( divide both sides by 11 )

y = 2

Substitute y = 2 in either of the 2 equations

Substituting in (2)

x - 2 = 7 ( add 2 to both sides )

x = 9

Answer:

730

Step-by-step explanation:

Answer:

350+160+220 = 730

Step-by-step explanation:

There were 730 boxes. After moving 350 boxes out of 730 boxes, there were left 380 boxes. Again after moving 160 boxes out of 380 boxes, there were remained 220 boxes.

Answer:

The in the calculation the step 3 is the first incorrect step.

Step-by-step explanation:

The function [tex]f(x) = 800(1.09)^{3x}[/tex] shows the growth due to interest that Jim earns on an investment.

To get an equivalent function we are given the following steps:

[Step 1] [tex]f(x) = 800(1.09)^{3x}[/tex]

[Step 2] [tex]f(x) = 800(1.09^{3}) ^{x}[/tex]

[Step 3] [tex]f(x) = 800(1.09 \times 3)^{x}[/tex]

[Step 4] [tex]f(x) = 800(3.27)^{x}[/tex]

The in the calculation the step 3 is the first incorrect step.

And this will be [tex]1.09^{3} = (1.09)^{3} = 1.295 \neq   3.27[/tex] (Answer)

Step 3

It is multiplying three instead of doing 9x9x9 she did 9x3

Answer:

Step-by-step explanation:

-3(c-1) = 33

c - 1 = 33/ -3

c -1 = -11

c = -11 +1

c = -10

Answer:

-10

Step-by-step explanation:

-3 (c-1 ) = 33

Divide both sides by -3

c-1 = -11

Add 1 to both sides

c = -10

Nevermind someone already answered it.

Answer:

Therefore,

[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]

Step-by-step explanation:

Consider a Δ ABC with

m∠ A = 45°

m∠ C = 30°

AB = c = 5√2

To Find:

BC = a = ?

AC = c = ?

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

[tex]\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°[/tex]

We know in a Triangle Sine Rule Says that,

In Δ ABC,

[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]

substituting the given values we get

[tex]\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}[/tex]

∴ [tex]\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units[/tex]

Similarly for 'b',

[tex]\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\[/tex]

Therefore,

[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]

By using the Law of Sines, side BC of the triangle is found to be approximately 10 m, and AC is approximately 8.66 m. These calculations take into account the given lengths and angles of triangle ABC.

To find the lengths of sides BC and AC in triangle ABC with given angles and side AB, we will employ trigonometry and the properties of triangles. Since the sum of the angles in any triangle is 180 degrees, we know that m∠B = 180° - 45° - 30° = 105°. With this information, we can use the Law of Sines, which states:
[tex]\(\frac{AB}{\sin(C)} = \frac{BC}{\sin(A)} = \frac{AC}{\sin(B)}\)[/tex]

From the given, AB = 5√2 m, m∠A = 45°, and m∠C = 30°, we know that:

[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{BC}{\sin(45°)}\)[/tex]

[tex]Knowing \ that\ \(\sin(30 ) = 0.5\) and \(\sin(45) = \frac{\sqrt{2}}{2}\), we can find BC:[/tex]

[tex]BC = \(\frac{5\sqrt{2}}{0.5} \times \frac{\sqrt{2}}{2}\) = 5√2 \times \sqrt{2} = 10 m[/tex]

Now, to find AC, we set up the ratio:

[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{AC}{\sin(105°)}\)[/tex]

Solving for AC, we get:

[tex]AC = 5\sqrt{2} \times \frac{\sin(105°)}{0.5}[/tex]
 Since \(\sin(105°)\) is not a standard angle, we can use the sine sum identity where [tex]\(\sin(105) = \sin(60 + 45\),[/tex]which gives us:

[tex]AC = 10 \times (\(\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2} + \frac{1}{2}\times\frac{\sqrt{2}}{2}\)) = 10 \times (\(\frac{\sqrt{6} + \sqrt{2}}{4}\))[/tex]

AC ≈ 8.66 m

The acceleration of the object is 5 m/s^2

Step-by-step explanation:

Given

Mass of object = m = 40 kg

Force = F = 200 N

Newton's 2nd law states that:

[tex]F = ma[/tex]

As we have to find the acceleration

[tex]a = \frac{F}{m}[/tex]

Putting the values

[tex]a = \frac{200}{40}\\a = 5\ ms^{-2}[/tex]

The acceleration of the object is 5 m/s^2

Keywords: Force, acceleration

Learn more about force at:

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To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Using the given force of 200 N and mass of 40 kg, we can determine that the acceleration of the object is 5 m/s^2.

To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

Therefore, the acceleration of the object is 5 m/s^2.

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Answer:

Therefore the expression is option A)

[tex]2x-8[/tex]

Step-by-step explanation:

Given:

Statement as ' 8 less than two times X'

To Find :

Expression for the statement

'8 less than two times X'

Solution:

[tex]Two\ times\ 'x'\ means=2\times x[/tex]

Now 8 less than two times X  means Subtract 8 from '2x'

[tex]2x-8[/tex]

Therefore the expression is option A)

[tex]2x-8[/tex]

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time = [tex]\frac{Distance}{Speed}[/tex]

Time = [tex]\frac{396}{180}[/tex]

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

Learn more about distance at:

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The two trains will take approximately 2.2 hours to meet.

To find the time it takes for the two trains to meet, we can use the formula:

Time = Distance/Speed

In this case, the distance between the two trains is 396 miles. The combined speed of the two trains is 95 mph + 85 mph = 180 mph. Substituting these values into the formula, we get:

Time = 396/180 = 2.2 (rounded to the nearest tenth)

So it will take approximately "2.2 hours" for the two trains to meet.

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Answer:

r=39.75

Step-by-step explanation:

7(5*9.5-R)+3r=173.5

7(47.5-R)+3r=173.5

332.5-7R+3r=173.5

332.5-4r=173.5

4r=332.5-173.5

4r=159

r=159/4

r=39.75

Step-by-step explanation:

7 (5x - R) + 3r = 173.5

let x = 9.5 as given

solve for R

substitute the value of x=9.5 into the equation:

7 (5 * 9.5 - R) + 3R = 173.5

7 (47.5 - R) + 3R = 173.5   expand

332.5 - 7R + 3R = 173.5    combine similar terms

332.5 - 173.5 = 7R - 3R     simplify

159 = 4R                            divide 4 on each side

R = 159/4                           simplify

R = 39.75

Answer:

63

Step-by-step explanation:

85 * .75 = 63 hats

Answer:

The length of a side of the original square is 6 meters

Step-by-step explanation:

Let

x ----> the length side of the original square

The area of a square is equal to

[tex]A=b^2[/tex]

where

b is the length side of the square

In this problem

The new length side of the square is [tex]b=(x+3)\ m[/tex] and the area is [tex]A=81\ m^2[/tex]

so

[tex](x+3)^2=81[/tex]

solve for x

take square root both sides

[tex](x+3)=9[/tex]

[tex]x=9-3=6\ m[/tex]

Answer:

The current flowing through the circuit is 180 ampere .

Step-by-step explanation:

Given as :

The measurement of load = p = 1800 watt

The voltage of the circuit= v = 10 volts

Let the current = i amperes

Now, As we know

Power = The electric power is define as the voltage drop at the terminal of electric circuit and the product of electric current passing through the circuit

i.e power = voltage × current

where power in watt

voltage in volt

current in ampere

Or, p = v × i

Now, From the definition of power

i = [tex]\dfrac{p }{v}[/tex]

Or, i = [tex]\dfrac{1800}{10}[/tex]

∴ i = 180 ampere

So, The current flowing through the circuit = i = 180 ampere

Hence, The current flowing through the circuit is 180 ampere . Answer

Answer:

There were 9 cats at the shelter on Wednesday.

Step-by-step explanation:

Given:

An animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.

Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday.

Nick found a record showing that there were a total of 34 cats and dogs on Wednesday.

Now, to find the number of cats at the shelter on Wednesday.

Let the number of cats be [tex]x[/tex].

And let the number of  dogs be [tex]y[/tex].

So, total number of dogs:

[tex]x+y=34.[/tex]

[tex]y=34-x.[/tex]......( 1 )

As given animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.

Now, total money animal shelter spent on Wednesday:

[tex]3x+5.50y=164.50[/tex]

Putting the value of equation ( 1 ) in the place of [tex]y[/tex] :

⇒ [tex]3x+5.50(34-x)=164.50[/tex]

⇒ [tex]3x+187-5.50x=164.50[/tex]

⇒ [tex]187-2.50x=164.50[/tex]

Adding [tex]2.50x[/tex] on both the sides we get:

⇒ [tex]187=164.50+2.50x[/tex]

Subtracting 164.50 on both sides we get:

⇒ [tex]22.50=2.50x[/tex]

Dividing by 2.50 on both sides we get:

⇒ [tex]9=x[/tex]

⇒ [tex]x=9.[/tex]

The number of cats = 9.

Therefore, there were 9 cats at the shelter on Wednesday.

Answer: 3

Step-by-step explanation:

Given :

[tex]Log_{7}[/tex] 343

We need to write 343 in index form of 7.

343 is the same as [tex]7^{3}[/tex] , replacing 343 with [tex]7^{3}[/tex] , we have

[tex]Log_{7}[/tex] [tex]7^{3}[/tex]

Recall one on the law of Logarithm :

[tex]Log_{a}[/tex][tex]b^{c}[/tex] can be written as c [tex]Log_{a}[/tex]b

So, [tex]Log_{7}[/tex] [tex]7^{3}[/tex] can be written as ;

3[tex]Log_{7}[/tex] 7

Also from the laws of Logarithms , [tex]Log_{a}[/tex] a = 1

so , Log_{7}[/tex] 7 = 1

The solution then becomes

3 x 1 = 3

Therefore :

[tex]Log_{7}[/tex] 343 = 3

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

(x-7)(x+2)=0

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

Answer:

x = - 2, x = 7

Step-by-step explanation:

Given

x² - 5x = 14 ( subtract 14 from both sides )

x² - 5x - 14 = 0 ← in standard form

Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)

The factors are - 7 and + 2, since

- 7 × 2 = - 14 and - 7 + 2 = - 5, thus

(x - 7)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 7 = 0 ⇒ x = 7

Answer:

-1/2

Step-by-step explanation:

The format your equation in is called slope-intercept form:

y=mx+b

m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.

Your equation is:

y= -1/2x+1/4

y=   m x+ b

Answer:

Can I please have more details on what your question is?

Step-by-step explanation:

Answer:

$7.6825

Step-by-step explanation:

65%=0.65

0.65*21.95=14.2675

21.95-14.2675=7.6825

Answer:

7.6825

Step-by-step explanation:

Answer:

a. 2² * 3² * 5; b. All numbers with a zero in the ones place is even.

Step-by-step explanation:

Final answer:

The prime factorization of 180 is 2 × 2 × 3 × 3 × 5. Every natural number with a zero in the ones place is a composite number because it can be divided evenly by 2 and at least one other number.

Explanation:

a. Prime factorization of 180:

To find the prime factorization of 180, we need to find the prime numbers that divide 180 evenly. Start by dividing 180 by the smallest prime number, 2. We get 180 ÷ 2 = 90. Then divide 90 by 2 again: 90 ÷ 2 = 45. Now, divide 45 by 3: 45 ÷ 3 = 15. Finally, divide 15 by 5: 15 ÷ 5 = 3. Therefore, the prime factorization of 180 is 2 × 2 × 3 × 3 × 5.

b. Explanation of why every natural number with a zero in the ones place is a composite number:

A composite number is a number that has more than two factors. Any natural number with a zero in the ones place can be divided evenly by 2 and at least one other number, making it a composite number. For example, 10 is divisible by 2 and 5, and 20 is divisible by 2 and 10. So, every natural number with a zero in the ones place is a composite number.