1 .) 3 5/8 divided by 1/2
2.) 3 2/6 divided by 2/3
3. ) 4 1/2 divided by 3/4
4. ) 3 1/2 divided by 3/4
5. ) 3 2/9 divided by 3

Thank youu.

Answer:

Its 22

Step-by-step explanation:

By the mid segment theorem:-

3x + 32 = 2(5x + 2)

3x + 32 = 10x + 4

28 = 7x

x = 4

So mid segment = 5(4) = 2 = 22

Answer:

25 people

Step-by-step explanation: 6 x 5 = 30 30-5 = 25

Answer:

1,114 ft

Step-by-step explanation:

Answer: The answer is (A) ΔCBA similar to ΔFED, (D) ΔBAC similar to ΔEDF and (E) ΔABC similar to ΔDEF.

Step-by-step explanation:  We are given a figure in which two similar triangles are shown. We are to select all the correct similarity statements that describes the relationship between the two triangles.

In ΔABC, we have

∠B is the right angle, AC is the hypotenuse and AB is the shortest side.

Similarly, ΔDEF, we have

∠E is the right angle, DF is the hypotenuse and DE is the shortest side.

Therefore, the corresponding pairs of vertices in the two triangles will be

(A and D), (B and E) and (C and F).

Hence, the correct similarity statements are

ΔCBA similar to ΔFED,

ΔBAC similar to ΔEDF

and

(E) ΔABC similar to ΔDEF.

Thus, (A), (D) and (E) are the correct options.

Answer:

1.  x=6

2.  y=2

Step-by-step explanation:

If x=5, the line is vertical, so we need a vertical line so that we are parallel.  A vertical line is x= a constant

We can choose the value for x as long as it is not 5, that would make it the same line.  I will choose x=6

If y=-3=5, the line is horizontal, so we need a horizontal line so that we are parallel.  A horizontal line is y= constant

We can choose the value for y as long as it is not -3, that would make it the same line.  I will choose y=2

Answer:

The standard form would be 5x + 6y = 8

Step-by-step explanation:

To find the equation between these two points, start by finding the slope. You can do this using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (3 - -2)/(-2 - 4)

m = 5/-6

m = -5/6

Now that we have the slope, we can use that and a point in point-slope form. Once we have that we can solve for the constant and rationalize the denominator for the standard form.

y - y1 = m(x - x1)

y - 3 = -5/6(x + 2)

y - 3 = -5/6x - 5/3

5/6x + y - 3 = -5/3

5/6x + y = 4/3

5x + 6y = 8

Answer:

Its the 3rd choice.

Step-by-step explanation:

The general form  for this type of parabola is y^ = 4ax where a is the x coordinate of the focus.

So it is y^2 = 4*3 * x

= y^2 = 12 x

or x = 1/12 y^2

Answer:

mean: 27

median: 25

mode: 25

Step-by-step explanation:

Mean: 297/11 =27

Median: put the values in order; 22,23,24,25,25,25,28,29,31,32,33. the median is 25

Mode: 25

Final answer:

The mean of the data set is 27, the median is 25, the mode is also 25, and the range is 11.

Explanation:

To find the mean, you add up all the numbers and then divide by the number of values. The median is the middle value when the numbers are in order. The mode is the number that appears the most. The range is the difference between the highest and lowest numbers.

First, let's order the data from least to greatest: 22, 23, 24, 25, 25, 25, 28, 29, 31, 32, 33.

Now, we calculate each:

1.The mean is (22 + 23 + 24 + 25 + 25 + 25 + 28 + 29 + 31 + 32 + 33) / 11 which equals 297 / 11 which equals 27.
2.The median is the middle number, which is 25 because there are five numbers on each side of it in the ordered list.

3.The mode is the number that appears most frequently - that's 25, as it appears three times.

4.To find the range, subtract the smallest number from the largest: 33 - 22 equals 11.

Answer:

Marta is (2x)+6 older than Ella.

The three girl's average age is (w)+(w/2)+(w/2-6)/3

Step-by-step explanation:

Marta's Age: w

Felicia's Age: w/2

Ella's Age: (w/2)-6

The age difference between Marta and Elle is Felicia's age plus 6 years. The expression for the average age of the three girls is (2*w - 6) / 3, where w is Marta's age and Felicia's age is half of w.

To solve the problem involving the ages of Elle, Felicia, and Marta, we use algebraic expressions. Marta is w years old.

Part a)

Let's denote Felicia's age as f. Since Elle is 6 years younger than Felicia, Elle's age is f - 6. Given that Marta is twice as old as Felicia, Marta's age, w, is equal to 2f. To find the age difference between Marta and Elle, we subtract Elle's age from Marta's age:

Age difference = w - (f - 6)

Since w = 2f, we can substitute 2f for w:

Age difference = 2f - (f - 6) = 2f - f + 6 = f + 6

Part b)

To find the average age of the three girls, we add their ages and divide by 3:

Average age = (Elle's age + Felicia's age + Marta's age) / 3

Average age = (f - 6 + f + 2f) / 3

Average age = (4f - 6) / 3

Since Marta's age is w and w = 2f, we can substitute 2f for each f in the equation:

Average age = (2*w - 6) / 3

Answer: C. [tex]\frac{7}{25}-\frac{24}{25}i[/tex]

Step-by-step explanation:

1. You have the following division:

[tex]\frac{4-3i}{4+3i}[/tex] (As you can see, to find the conjugate of  4-3i you must change the sign between the terms).

2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:

[tex]=\frac{(4-3i)}{(4+3i)}\frac{(4-3i)}{(4-3i)}=\frac{16-12i-12i+9i^{2}}{16-9i^{2}}[/tex]

3. Keeping on mind that [tex]i^{2}=-1[/tex], you have:

[tex]=\frac{16-12i-12i+9(-1)}{16-9(-1)}[/tex]

4. Simplifying:

[tex]=\frac{7-24i}{25}=\frac{7}{25}-\frac{24}{25}i[/tex]

5. The result is:

[tex]\frac{7}{25}-\frac{24}{25}i[/tex]

The quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

Given data:

The complex number is, 4 - 3i.

To find: The quotient when divided by conjugate of given complex number.

For a given complex number say, a + bi, the conjugate is given as,

a - bi

Then, the conjugate of the given complex number is, 4 + 3i.

Divide the given complex number with its conjugate as,

[tex]=\dfrac{ 4 - 3i}{4 + 3i}\\\\=\dfrac{ 4 - 3i}{4 + 3i} \times \dfrac{4-3i}{4-3i} \\\\=\dfrac{(4-3i)^{2}}{4^{2}-(3i)^{2}}[/tex]

Since, [tex]i^{2} =-1[/tex].

Solving further as,

[tex]=\dfrac{4^{2}+(3i)^{2}-2(4)(3i)}{16-9(-1)} \\\\=\dfrac{16+9(-1)-24)}{25}} \\\\=\dfrac{7}{25} -\dfrac{24}{25}i[/tex]

Thus, we can conclude that the quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

Learn more about the conjugate of complex number here:

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Answer:

14.  x=-2.5,  y = -7

15.  x=28  y = -20

Step-by-step explanation:

14.  Let's solve this system by elimination.  Multiply the first equation by -1.

-1*(4x-y)= -1*(- 3)

-4x +y = 3

Then add this to the second equation.

-4x+y = 3

6x-y= - 8

--------------

2x   = -5

Divide each side by 2

x = -2.5

We still need to find y

-4x+y =3

-4(-2.5) + y =3

10 +y =3

Subtract 10 from each side.

y = 3-10

y = -7

15.I will again use elimination to solve this system, because using substitution will give me fractions which are harder to work with.   I will elimiate the y variable.  Multiply the first equation by 11

11( 5x+6y)= 11*20

55x+66y = 220

Multiply the second equation by -6

-6(9x+11y)=32*(-6)

-54x-66y = -192

Add the modified equations together.

55x+66y = 220

-54x-66y = -192

---------------------------

x = 28

We still need to solve for y

5x+6y = 20

5*28 + 6y =20

140 + 6y = 20

Subtract 140 from each side

6y = -120

Divide by 6

y = -20

Answer:

Mass of one penny = .005 pounds

10 pounds of pennies = 10 / .005 = 2,000 pennies

Step-by-step explanation:

Final answer:

To calculate the number of pennies, divide the total weight of the pennies in the jar (10 pounds) by the weight of one penny (0.005 pounds), resulting in approximately 2000 pennies.

Explanation:

To determine the number of pennies in Ian's jar, we need to use the weight of one penny and the total weight of pennies in the jar. The question states that one penny weighs about 5*10^-3 pounds, which can also be represented as 0.005 pounds.

Next, we divide the total weight of pennies in the jar, which is 10 pounds, by the weight of one penny:

Convert the weight of one penny to pounds: 5*10^-3 pounds.

Divide the total weight of the pennies by the weight of one penny: 10 pounds \/ 0.005 pounds per penny = 2000 pennies.

Hence, there are approximately 2000 pennies in Ian's jar.

Answer: The scale factor is 3

Divide the two volumes (larger over small) to find that (21870pi)/(810pi) = 27. This means that the larger volume is 27 times bigger than the smaller volume.

From here, you apply the cube root to this result to get 3. Note how 3 cubed = 3^3 = 3*3*3 = 27.

The linear scale factor is 3. The larger figure has a radius 3 times larger than its counter part in the smaller cone. The same applies to the heights as well.

Answer:

domain = real numbers, range = positive real numbers

Step-by-step explanation:

f(x) = a^x

Domain is the set of all real numbers whose values are defined.

Here x is the exponent. There is no restriction for x

So x  can take any value. x  can be positive or negative

Hence, domain is all real numbers.

For range we consider the value of f(x)

For positive x  values , f(x) will be positive

For negative x  values , f(x) will be positive

so , range is positive real numbers

Answer:

118

Step-by-step explanation:

simple:

59.50 - 30.00=29.50

29.50 divided by 0.25= 118

in equation form

y=mx+b

59.50=0.25(x)+30.00

so the output (y) is the total money owed (59.50) and the 0.25 cents is the slope or unit rate and the 30.00 in this context is the monthly fee. So to find x= number of texts sent, you have to firstly get rid of the monthly fee, you subtract 30.00 by itself so it cancels out and you gotta do the same to the other side (the output), ( 59.50 - 30.00)= 29.50 and after that you have the remaining of 29.50=0.25x , now you have to divide 0.25 to both sides so 0.25/0.25=1 and basically 1x=x , now you divide 29.50/0.25=118    now you solved for x! The amount of texts sent=118

Answer: B

Step-by-step explanation:

[tex]P=100e^{(.70)t}[/tex]

[tex]300=100e^{.7t}[/tex]

[tex]3=e^{.7t}[/tex]

[tex]ln3=lne^{.7t}[/tex]

[tex]ln3=.7t[/tex]

[tex]\dfrac{ln3}{.7}=t[/tex]

1.6 = t

Answer:

Option B. 1.6 Hours

Step-by-step explanation:

The model for the population of bacteria is growing by :

[tex]P=100e^{(0.70)t}[/tex]

Where P = Number of colonies

and t = time in hours.

So, now put  the value of  P = 300 in the given model and obtain the value of t.

⇒ [tex]300=100e^{(0.70)t}[/tex]

⇒ [tex]3=e^{(0.7)t}[/tex]

Taking the natural log in on both the side

⇒ [tex]In3=Ine^{(0.7)t}[/tex]

⇒ [tex]In3=0.7t[/tex]

⇒ [tex]t=\frac{In3}{0.7}[/tex]

⇒ t = 1.6 hours

Therefore, The correct option is B). 1.6 hours

Answer:

It was part of an exam that someone recognized apparently. It's for the best, trust me. Maybe its just because it may have been asking for answers, not help.

Step-by-step explanation:

They did that to me and took everything from me! I was ranked expert and it was all gone! My answer wasn't even wrong! I have 83 answered questions and they took it all... FOR NO REASON

I answered someones questioned and they deleted it and gave me warning

Answer: The equation will be set up as y=mx+b. Mrs. Jones charges $35 per hour, so we can substitute m for 35 with x representing the number of hours. The $35 for pool usage fee will be substituted for b.

The answer then is y=35x+35

Answer: C. (x+1) is a factor

Step-by-step explanation:

First we need to factor the polynomial x^2 - x - 2.

It is written in the form ax^2 + bx + c

a = 1

b = -1

c = -2

Since the coefficient in front of x^2 is 1 we can start with (x + _) (x + _).

Now we need to find a pair of numbers that when multiplied together equal -2 (c) and when added together equal -1  (b).

The only pairs of numbers that multiply to make -2 are: -2 and 1, -1 and 2

The pair must also equal -1 when added together.

-1 + 2 = 1

-2 + 1 = -1

Therefore, to fill in the blanks for (x+_)(x+_) we should use -2 and 1.

x^2 - x - 2 factored becomes: (x-2)(x+1)

As you can see, (x+1) is a factor of x^2 - x - 2, so you can select c.

An icosahedron have 20 faces. So the correct Option is D.  

An icosahedron is a three-dimensional geometric shape known as a polyhedron. It is characterized by having 20 faces, making it an interesting and unique structure in geometry.

An icosahedron is one of the five Platonic solids, which are regular polyhedra with equal faces and angles. To understand why an icosahedron has 20 faces, we can break down its construction.

1. Vertices (V): An icosahedron has 12 vertices. Each vertex is a point where three edges of the polyhedron meet.

2. Edges (E): There are 30 edges in an icosahedron. These are the straight lines connecting the vertices.

3. Faces (F):  Now, to find the number of faces, we can use Euler's formula, which states that for any polyhedron, V - E + F = 2. This formula relates the number of vertices, edges, and faces of a convex polyhedron.

  Plugging in the values, we get: 12 (vertices) - 30 (edges) + F (number of faces) = 2

  Solving for F, we get: F = 20

Thus, an icosahedron has 20 faces, represented by 20 flat surfaces, each of which is an equilateral triangle. Each vertex is shared by five triangles, and each edge is shared by two triangles.

The keyword "icosahedron" refers to the specific three-dimensional shape with 20 faces, while "Platonic solids" refers to the family of regular polyhedra with equal faces and angles. Euler's formula is essential for understanding the relationship between vertices, edges, and faces of polyhedra.

To know more about Icosahedron here

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Answer:

3V / (pi*r^2) = h

Step-by-step explanation:

V = 1/3 *pi * r^2 h

We want to solve for h so we need to get it alone

Multiply each side by 3.

3*V =3* 1/3 *pi * r^2 h

3V = pi * r^2 h

Divide each side by pi r^2

3V / (pi*r^2) = pi * r^2 h/ (pi *r^2)

3V / (pi*r^2) = h

Answer:

Equation of midsegment line: y = (-1/4)x + 2.

Step-by-step explanation:

If the parallel sides of a trapezoid are contained by the lines:-

y = (-1/4)x +5 and y = (-1/4)x - 1

Midsegment of any trapezoid is the line segment

1. that is parallel to pair of parallel side of trapezoid and

2. that passes through the middle of the trapezoid and cuts the other two sides into equal-half.

It means the midsegment would have same slope as the parallel lines and y-intercept would be in the middle of intercepts of parallel lines.

So y = mx + b

where m = -1/4 and b = (5 - 1)/2 = 4/2 = 2.

Hence, the equation of midsegment would be y = (-1/4)x + 2.

Answer:

c. 345 calories

Step-by-step:

We need to create a ratio

There are 230 calories in 4oz

230/4

How many calories are in 6oz

x/6

Let's equate them to solve for x

230/4 = x/6       cross multiply

4x = 1380           isolate x

x = 345

There are 345 calories in 6oz of said icecream

Answer:

Step-by-step explanation: by Saturday,, he would have read 25 + 32 +  39 +46 +53 +60 =255 pages. Note the number of pages read increases by 7 each day

Answer:

x=36

Step-by-step explanation:

We know the three angles of a triangle add to 180 degrees

x + 65+ 79 = 180

Combine like terms

x+144 = 180

Subtract 144 from each side

x+144-144 = 180-144

x = 36