If you increase your bicycle speed by 5.6 miles per hour, the speed will be 17.9 miles per hour. What is your bicycle speed now?

Answer:

[tex]z=13(\cos 157\degree +i\sin157\degree)[/tex]

Step-by-step explanation:

The given complex number is

[tex]z=-12+5i[/tex]

The polar form of this complex number is;

[tex]z=r(\cos \theta +i\sin \theta)[/tex], where

[tex]r=\sqrt{(-12)^2+5^2}[/tex]

[tex]r=\sqrt{144+25}=\sqrt{169}=13[/tex]

and

[tex]\theta =\tan^{-1}(\frac{5}{-12})[/tex]

This implies that;

[tex]\theta=157\degree[/tex] to the nearest degree.

Hence the polar form is

[tex]z=13(\cos 157\degree +i\sin157\degree)[/tex]

Answer:

SA: 62in

Step-by-step explanation:

make it into a net and find the area of each piece

Answer:

It's d. 0.

Step-by-step explanation:

The log (to any base) of 1 = 0, so log8 1 = 0, and the whole expression is equal to 0:

 0 * log3 27 = 0.

The expression log8 1 * log3 27 evaluates to 0, so the equivalent expression from the options is d - 0.

The expressions we need to evaluate are log8 1 * log3 27. The log of 1, no matter what the base, is always 0. This is because any number raised to the power of 0 is 1. So, log8 1 is equal to 0. Now, evaluate log3 27. The log base 3 of 27 is 3 because 3 cubed (or 3 to the power of 3) is 27. So, log3 27 equals 3. Thus, log8 1 * log3 27 = 0 * 3 = 0. Comparing with the given options, we find that the only equivalent expression is option d - 0.

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Answer:

Expression: 2x-3

Martina's height if her little brother is 28 inches: 53 inches

Step-by-step explanation:

To write the expression, first read the problem. Martina is twice as tall as her little brother, minus 3. If x represents Martina's little brother's height, the equation will be 2x-3, since she's 3 inches shorter than twice the height of her little brother.

The question says that her little brother is 28 inches tall. Since x represents Martina's little brother's height, simply plug x into our expression.

2x-3

2(28)-3

56-3

53

Therefore, if Martina's little brother was 28 inches tall, Martina would be 53 inches tall. i hope this helps! :)

This answer involves the creation of a mathematical expression based on the given information and substituting the known value to find the unknown variable. The mathematical expression is 'Martina's Height = 2 * (Brother's height) - 3 inches.' When the brother's height is 28 inches, we get Martina's height as 53 inches.

The question relates to writing and solving expressions in Mathematics. To find how tall Martina is, we need to first write down an expression depicting the statement. According to the given statement, we can write:

Martina's Height = 2 * (Brother's height) - 3 inches

If her little brother is 28 inches tall, we substitute 28 into the expression:

Martina's Height = 2 * (28) - 3 inches

This implies:

Martina's Height = 56 - 3 inches = 53 inches

Therefore, Martina is 53 inches tall if her little brother is 28 inches tall.

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two ratios are equal and form a proportion.

Answer:

they form a proportion.

Answer:

d. 53.1°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

Cos = Adjacent/Hypotenuse

You are given the lengths of t (hypotenuse) and r (adjacent to S), so you can find the angle from ...

cos(S) = r/t = 12/20

S = arccos(12/20) ≈ 53.1° . . . . . use the inverse cosine function

Answer:

d. 53.1

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

I would assume that they want a cosine value that would give the same answer. sin(30°) is equal to 1/2

Therefore cos(×) = 1/2

x = arccos(1/2)

x=60

cos(60°)

Answer:

cos60°

Step-by-step explanation:

Using the cofunction identity

sinx° = cos(90 - x)°

sin30° = cos(90 - 30)° = cos60°

Answer:

150

Step-by-step explanation:

Final answer:

Miss Balcon would work 150 hours in 4 weeks as a secretary at a Christian school.

Explanation:

In order to find out how many hours Miss Balcon would work in 4 weeks, we need to first calculate the number of hours she works in a week. She works 7 1/2 hours each day, and since there are 5 days in a week, she works a total of 7 1/2 x 5 = 37 1/2 hours in a week.

Now, to find out how many hours she would work in 4 weeks, we can multiply the number of hours she works in a week by 4. So, 37 1/2 x 4 = 150 hours.

Therefore, Miss Balcon would work 150 hours in 4 weeks.

Answer:

1190

Step-by-step explanation:

35× 34 = 1190...._ hope it help ....have a nice day

Answer:

1190

Step-by-step explanation:

Since the dot means "X" or multiply, we multiply 35 by 34.

So 35*34 = 1190.

A way to quickly multiply 35 snd 34, is to split 34 into 2*17 and multiply the 2 by 35 first to get 70*17. Since 17*7=119, we get 70*17 to be 1190.

Answer:

The number of females is 288.

Step-by-step explanation:

Let the number of females be x.

5:4 = 360:x

We can write the equal ratios as a proportion.

5/4 = 360/x

Cross multiply:

5x = 360 * 4

5x = 1440

x = 288

Answer: The number of females is 288.

Answer:

288 females

Step-by-step explanation:

We can write a proportion to solve, putting males over females

males         5                  360

------------ = ------------ = -------------

females         4                  x

Using cross products

5x = 360*4

5x =1440

Divide by 5

5x/5 = 1440/5

x = 288

There are 288 females

Step-by-step explanation:

[tex]19.\\2x^2=(2)\bold{(x)}(x)\\x=(1)\bold{(x)}\\2x^2+x=\bold{x}(2x+1)\\\\20.\\12x^5=\bold{(3)(4)(x)}(x)(x)(x)(x)\\36x=\bold{(3)(4)}(3)\bold{(x)}\\12x^5-36x=\bold{(3)(4)(x)}(x^4-3)=\bold{12x}(x^2-3)\\\\21.\\15x=(3)\bold{(5)}(x)\\5y^2=\bold{(5)}(y)(y)\\15x-5y^2=\bold{5}(3x-y^2)[/tex]

Step-by-step explanation:

62.56

9.2 * 6.8 = about 63

Since you are estimating, first round the numbers.

Change 9.2 to 9 and change 6.8 to 7. This leaves you with 9 * 7, which is 63, and since you are estimating, your answer doesn’t need to be exact.

Let the number be x.

4x - 8 =12

4x =12 +8 ( you bring the eight over to the 12, it becomes positive )

4x = 20

x = 20÷4

x = 5

The problem is a basic algebra equation. It translates to 4x - 8 = 12, which can be solved by adding 8 to both sides and then dividing by 4 to get x=5. The answer is 5.

The subject of this question is Mathematics, specifically algebra. To solve this equation, start by translating the problem into a mathematical expression. This can be done as follows: 4 times a number is represented as 4x, then decreased by eight is -8 and the equation equals twelve (12).

Therefore, the equation is 4x - 8 = 12. To solve for x, you can start by adding 8 to both sides of the equation obtaining 4x = 20. Lastly, divide both sides by 4 to find x, which gives x = 5.

Therefore, the number that meets the condition '4 times a number, decreased by 8 equals 12' is 5.

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Hi, hope you’re having a good day!

Could you please add the picture?

Thanks, have a good day! ❤️❤️

The picture is not shown, if you could add it, I would be happy and try and answer as best I can! Have a good day! :)

Answer:

1. 31/99 2. 215/999 3. 6704/9999

Answer:

31/100, 215/100, 419/1250

Answer:

I recommend the work that pays  $45,000 a year because the monthly income is greater than the other job

Step-by-step explanation:

we know that

The first work pays $45,000 a year

so

The monthly income is equal to

$45,000/12=$3,750 per month

The second work pays $20.50 an hour

Remember that

1 year= 52 weeks

so

In one year pays -----> (8)*(5)*(52)($20.50)=$42,640 a year

The monthly income is equal to

$42,640/12=$3,553.33 per month

I recommend the work that pays  $45,000 a year because the monthly income is greater than the other job

Answer:

a. 12/13

Step-by-step explanation:

For a right triangle, sin theta = opposite side/ hypotenuse

sin C = 24/26

Sin C = 12/13

Answer:

A. 10 fluid ounces

Step-by-step explanation:

One fluid ounce is equal to one quart. This means she had 64 fluid ounces in her jug. She poured 6 3/4 fluid ounces in 8 mugs, so you would multiply 6 3/4 by 8 to get 54. Now you go back to the original amount, 64, and subtract 54 from that. 64 minus 54 equals 10. I hope this helped!

the answer is d i think

Answer:

94.1 m²

Step-by-step explanation:

Use the sine rule to find BC

[tex]\frac{BC}{sin82}[/tex] = [tex]\frac{12}{sin40}[/tex]  ( cross- multiply )

BC × sin40° = 12 × sin82° ( divide both sides by sin40° )

BC = [tex]\frac{12sin82}{sin40}[/tex] ≈ 18.487

Area = [tex]\frac{1}{2}[/tex] × 12 × 18.487 × sin58° ≈ 94.1

Answer:

The answer is 754.4 cm²

Step-by-step explanation:

a = r²π

a = (31/2)²π

a ≈ 754.4

The area of the clock face is 754.4 cm²

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

The area of the clock will be calculated as:-

a = r²π

a = (31/2)²π

a ≈ 754.4

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Answer:

4.4721

Step-by-step explanation:

Answer:

the explicit formula for the geometric sequence  2,6,18,54 is [tex]a_{n}=a_{1}.r^{n-1}[/tex]

2,6,18,54

Step-by-step explanation:

In the sequence given: 2,6,18,54

The common ration is 3 because

a₁ = 2

a₂= 2*3 =6

a₃ = (2*3)*3 = 2*3^2 = 18

a₄= (2*3*3)*3 =2*3^3 = 54

Here we see for a₂ 3 has power 1, for a₃ 3 has power 2 and so on.

So, the formula will be

[tex]a_{n}=a_{1}.r^{n-1}[/tex]

Here aₙ is the no of term.

a₁ is the first term of the sequence

and r is the common ratio among the sequence.

Answer:

b(n)=2⋅3 ^n−1

Answer:she would have at least gotten a 75 to pass.

Step-by-step explanation:76+82+71+75=304

304÷4= a solid 76%

Answer:

k-3

Step-by-step explanation:

Eliminate the opposites

K-k+k3

= k-3

The given algebraic expression simplifies to k - 3. This means, for any value of 'k', the result would be 'k' minus 3.

The problem provided is k-k+k-3. In this case, 'k' is a variable, which is essentially an unknown number. When you subtract a variable (k) from itself, you get zero. Therefore, k - k equals zero. Adding k back again, we return to k itself. Hence, k - k + k - 3 simplifies to k - 3. That is, whatever value 'k' is, you have to subtract 3 from it to solve this equation.

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16

absolute value is always positive

i want to say 16 or 1/16. i’m sure it’s not a negative though.

the answer is A.) 3/10

Option: B is the correct answer.

            [tex]B.\ \ \dfrac{7}{10}[/tex]

We know that P(A or B) i.e. P(A∪B) is calculated by using the formula:

[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]

( The students are: Fran, Juan , Ian and Ella )

( The students are: Mickey, Mai, Marcus , Ian and Ella)

( since those students are: Ian and Ella)

Hence, we have:

[tex]P(A)=\dfrac{4}{10}\\\\\\P(B)=\dfrac{5}{10}\\\\\\P(A\bigcap B)=\dfrac{2}{10}[/tex]

Hence, we have:

[tex]P(A\bigcup B)=\dfrac{4}{10}+\dfrac{5}{10}-\dfrac{2}{10}\\\\\\i.e.\\\\\\P(A\bigcup B)=\dfrac{4+5-2}{10}\\\\\\i.e.\\\\\\P(A\bigcup B)=\dfrac{7}{10}[/tex]

Answer:

Final answer is [tex]a_0=-9[/tex]

Step-by-step explanation:

Given equation is [tex]5-a_0=14[/tex]

Now we need to solve the given equation 5-a_0=14 for the unknown variable  [tex]a_0[/tex] .

We can do that by isolating [tex]a_0[/tex]

To isolate a_0, let's subtract 5 from both sides

[tex]5-a_0-5=14-5[/tex]

[tex]-a_0=9[/tex]

multiply both sides by -1

[tex]-a_0(-1)=9(-1)[/tex]

[tex]a_0=-9[/tex]

Hence final answer is  [tex]a_0=-9[/tex]

Answer: If you take 6 in and multiply by 12 You would get 72 inches

*Step By Step explanation* 6 Multiplied by 12 equals 72

Rounding would not be necessary.

Answer:

The correct option is B. 226 inches³

Step-by-step explanation:

The diameter of the cone is given to be 12 inches

So, The radius of the cone will be 6 inches

Also, The height of the cone is given to be 6 inches'

Now, we need to find the volume of the cone.

So, Volume of the cone is given by the formula :

[tex]Volume=\frac{1}{3}\pi\times radius^2\times height[/tex]

[tex]Volume=\frac{1}{3}\times 3.14\times 36\times 6[/tex]

[tex]Volume=226.08[/tex]

[tex]Volume\approx 226.08\:inches^3[/tex]

Therefore, the correct option is B. 226 inches³

Answer:

[tex]|A'B'|=\sqrt{5}[/tex]

Step-by-step explanation:

The points A and B have coordinates at (0,4) and (4,2) respectively.

The distance formula can be used to find the length of AB.

[tex]|AB|=\sqrt{(4-0)^2+(2-4)^2}[/tex]

[tex]|AB|=\sqrt{(4)^2+(-2)^2}[/tex]

[tex]|AB|=\sqrt{16+4}[/tex]

[tex]|AB|=\sqrt{20}[/tex]

[tex]|AB|=2\sqrt{5}[/tex]

Since quadrilateral ABCD was enlarged with  a scale factor of [tex]\frac{1}{2}[/tex].

The length of A'B' is

[tex]\frac{1}{2}|AB|[/tex]

[tex]=\frac{1}{2}\times2\sqrt{5}[/tex]

[tex]\therefore |A'B'|=\sqrt{5}[/tex]

The quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So, after the dilation the length of A'B' is [tex]\sqrt{5}[/tex] and this can be determined by using the formula of length between two points.

Given :

Given that the quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So the points of the quadrilateral ABCD becomes:

[tex]\rm A(0,4) \to A'(0\times \dfrac{1}{2},4\times \dfrac{1}{2}) = A'(0,2)[/tex]

[tex]\rm B(4,2) \to B'(4\times \dfrac{1}{2},2\times \dfrac{1}{2}) = B'(2,1)[/tex]

[tex]\rm C(4,-4) \to C'(4\times \dfrac{1}{2},-4\times \dfrac{1}{2}) = C'(2,-2)[/tex]

[tex]\rm D(-2,-2) \to D'(-2\times \dfrac{1}{2},-2\times \dfrac{1}{2}) = D'(-1,-1)[/tex]

Now, the length of A'B' is given by:

[tex]\rm AB=\sqrt{(4-0)^2+(2-4)^2}[/tex]

[tex]\rm AB=\sqrt{4^2+(-2)^2}[/tex]

[tex]\rm AB=\sqrt{20}[/tex]

[tex]\rm AB = 2\sqrt{5}[/tex]

[tex]\rm A'B' = \dfrac{1}{2}AB[/tex]

[tex]\rm A'B' = \sqrt{5}[/tex]

Therefore, the correct option is a).

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