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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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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:

Step-by-step explanation:

It looks like you are using the sine law.

23/Sin(85) = x /  sin(55)     Cross multiply

23*sin(55) = x * sin(85)

23*sin(55)/sin(85) = x

None of these answers look correct. One thing you could try is

sin(85) = cos(90 - 85)

sin(85) = cos(5)

That would give you

x = sin(55)*cos(5)

If that is not among  your choices you have no answer.

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.

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]

Answer:y=\frac{1}{2} x-4

Step-by-step explanation:

Slope intercept form of the equation of a line is y = mx+b where m is the slope and b is the y intercept. Plugging in 1/2 for m and -4 for b gives y = 1/2x + (-4) then simplifying adding a negative means subtracting.

The equation of the line is y = (1/2)x - 4, where the slope is 1/2 and the y-intercept is -4.

Explanation:

The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the slope is 1/2 and the y-intercept is -4, so the equation of the line is y = (1/2)x - 4.

The slope of 1/2 means that for every increase of 1 on the horizontal axis, there is a corresponding increase of 1/2 on the vertical axis.

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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:

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! :)

Answer:

Step-by-step explanation:

If it is Tanya and 3 friends, there are 4 people in total. If they all contributed the saem amount, you would do 75/4= 18.75 dollars each

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°

16

absolute value is always positive

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

B. 712.50

40hrs x $15/hr= $600

5hrs OT x time & a half pay ($22.50)= $112.50

$600 + $112.50= $712.50

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:

$7.40

Step-by-step explanation:

https://sciencing.com/calculate-cost-per-pound-7595889.html

use this

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

You will need 721 centimeters of paper. This is because you take 11 and multiply it by 11 because a cube is equal in the length and the height. To find the total area of wrapping paper for one side you have to find the area. 11x11=121. Then you have 6 sides of the cube so you multiply 121x6=721 inches of wrapping paper to wrap the cube

Least amount of wrapping paper you need to wrap the gift = 726 cm²

The total surface area of a cube is equal to six times the area of one side of the cube.

Given,

Side length of the cube = 11 cm

Area of one side of the cube = side²

Therefore, area of one side of the cube =  11² cm²

                                                                   = 121 cm²

Total surface area of a cube = 6 × side²

                                                = 6 × 121 cm²

                                                = 726 cm²

Hence, least amount of wrapping paper you need to wrap the gift is 729 cm².

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the answer is d i think

Answer:

Option C

Step-by-step explanation:

Option C. Is the correct option.

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. For that reason, if we multiply the number (2^1/4)(2^1/4)(2^1/4)(2^1/4) the result will be 2^(1/4+1/4+1/4+1/4) = 2^(4/4) = 2.

two ratios are equal and form a proportion.

Answer:

they form a proportion.

Answer:

SA: 62in

Step-by-step explanation:

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

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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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:

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:

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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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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B. -4-1. -4-1=-5, which is the amount of you count the spaces in between.

Hope this helps!

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:

59 2/4

Step-by-step explanation:

Answer: 14.33 in³

Step-by-step explanation:

the volume of the box= L * W * H

V = 2 * 16/3 * 43/4 = 114.67 in³

114.67 takes up 8 servings

hence each serving will take up a volume of 114.67 in³/8 = 14.33 in³

Answer:

10

Step-by-step explanation:

If a board is 3.75 inches wide and he wants the table to be at least 36 inches wide, then we need to use the rule of three:

If a 1 board ---------------------------> 3.75 inches wide

    x             ---------------------------> 36 inches wide

x = (36 inches wide * 1 board)/3.75

x= 9.6 boards.

Like we cannot buy 9.6 boards, then we conclude that the least number of boards he can use is 10.

Answer:

The team from the second league would be more likey to win becasue teams in taht league have more consistent, and mostly greater, numbers of home runs and winning games. Data for teams in the second league also do not show any outliers.

Comparing the data of wins and home runs for the 2 leagues given in the table, we can predict that;

The second league will be more likely to win a game than the first league.

This is about data comparisons and interpretation.

Now, from the 2 tables, we see 2 columns namely HR and W;

HR; This means Home Runs. This is gotten by hitting the ball in a baseball game over the outfield fence that stands in-between the foul poles and does not touch the ground first before going over the outfield fence. This means more home runs denotes more points.

W; This is the number of wins each team possesses. The more the games won, the more the points and the more chances of winning the league.

Now, from the above analysis, we have seen that More HR( Home runs) and more W(Wins) means more points and better chances of winning the league.

Comparing the two leagues, it is clear that second league has teams with more Home runs and more Wins than the first League.

In conclusion, we can say that The second league will be more likely to win a game than the first league.

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