Using prime factorization what is the GCF of 42, 65

C. 3.16 is the right answer

Step-by-step explanation:

The distance formula used in coordinate geometry is derived from the Pythagorean theorem.

The distance formula is give by:

[tex]d=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]

Here (x1,y1) are the coordinates of first point and (y1,y2) are the coordinates of second point

Here,

(x1,y1) = (5,-3)

(x2,y2) = (6,0)

Putting the values in the formula

[tex]AB = \sqrt{(6-5)^2+(0-(-3))^2}\\=\sqrt{(1)^2+(0+3)^2}\\=\sqrt{(1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}\\=3.16\ units[/tex]

The distance between two points is 3.16 units.

Hence,

C. 3.16 is the right answer

Keywords: Coordinate geometry, Pythagorean Theorem

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Answer:

B

Step-by-step explanation:

-2x + 9 < x - 9 simplifies to x < 6

Answer:

A is the answer

Step-by-step explanation:

Solve the equation and the answer would come out to be 6

open dot that goes to the right

Answer:

1/2

Step-by-step explanation:

you put it in slope form which is y1-y2/x1-x2 to get 9-3/7+5 which simplifies to 1/2

Answer: x = 12

Step-by-step explanation:

First you must simplify:

x + (x + 4) = 28

Reorder the terms:

x + (4 + x) = 28

Remove parenthesis around (4 + x):

x + 4 + x = 28

Reorder the terms:

4 + x + x = 28

Combine like terms: x + x = 2x

4 + 2x = 28

Solving

4 + 2x = 28

Now we must solve for the variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.

4 + -4 + 2x = 28 + -4

Combine like terms: 4 + -4 = 0

0 + 2x = 28 + -4

2x = 28 + -4

Combine like terms: 28 + -4 = 24

2x = 24

Divide each side by '2'.

x = 12

Simplifying

x = 12

Hope this helps! :)

Answer:

1 and 2 answers are correct

Step-by-step explanation:

2x-y= -8

x-y = -4

ADD BOTH (y is cancelled)

3x= -12

x= -4

-8+y=-8

y=0

    -4-y = -4

     Multiply all by -1

4+y=4

y=0

i think u gotta multiply

Answer:

Use an app that can scan problems to solve

Step-by-step explanation:

Answer:

It is 3.5 x 10^2 and 9.4x10^4

Step-by-step explanation:

350 = 3.5 x 10^2

which implies 3 - hundred

5 - tens

0 - units

94000 = 9.4x10^4

which implies 9 - ten thousand

4 - thousand

0 - hundred

0 - tens

0 - units

Answer:

Repost: 350.94

Step-by-step explanation:

three hundred: 3__

fifty: _5_

And: Is for the decimal point

Ninety (Thousandths): ___.9_

Four (Thousandths): ___._4

Now just put it all together and you get 350.94

Hopes this helps in the future ^_^

Answer:

4*1/6=2/3

Step-by-step explanation:

we have 4 of 1/6

so 1/6 +1/6 +1/6 +1/6=4*1/6=4/6=2/3

To simplify the expression 12k + 5k - 11m + 13m, we can combine like terms by adding the coefficients of the like terms. The simplified expression is 17k + 2m.

The expression 12k + 5k - 11m + 13m can be simplified by combining like terms. Like terms have the same variables raised to the same powers. In this expression, the terms 12k and 5k are like terms because they both have the variable k. Similarly, the terms -11m and 13m are like terms because they both have the variable m.

To simplify, we can add the coefficients of the like terms:

12k + 5k - 11m + 13m = (12 + 5)k + (-11 + 13)m

Therefore, the simplified expression is 17k + 2m.

Answer:

At least 55 tickets must be sold to cover the remaining cost of the party.

Step-by-step explanation:

Total money needed for the party  = $350

The money already with the committee  = $75

Now, the money yet to be collected = Total Party Budget - Money present

                                                              = $350  = $75  = $275

Now, the cost of 1 ticket  = $5

Let us assume the number of tickets sold to cover the cost of party = m

⇒ The cost of m tickets   = 5 m

The renaming cost = Total cost of m tickets

or, 5 m =  $275

⇒ m = 275/5  = 55

or, m = 55

Hence, at least 55 tickets must be sold to cover the remaining cost of the

party by Josef.

Answer:

D) .h(x)= 6x+ 13

Step-by-step explanation:

We are given that,

Function representing number of students from A,

Function representing number of students from B,

It is required to find the total number of students in the fair.

So, we have,

Total number of students =

i.e. Total number of students =

i.e. Total number of students =

i.e. Total number of students =

Hence, the function representing the total number of students in the fair is .

Thus, option D is correct.

Answer:

6x + 13.

Step-by-step explanation:

That is the sum of R(x) and g(x)

= 4x + 5 + 2x + 8

= 6x + 13.

Answer:

The length is 52 units

Step-by-step explanation:

we know that

The length of the path. is equal to the perimeter of polygon A.B.C.D.E.F

[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance A.B

we have

[tex]A(-7,7),B(6,7)[/tex]

substitute in the formula

[tex]d=\sqrt{(7-7)^{2}+(6+7)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(13)^{2}}[/tex]

[tex]d_A_B=13\ units[/tex]

step 2

Find the distance B.C

we have

[tex]B(6,7),C(6,-2)[/tex]

substitute in the formula

[tex]d=\sqrt{(-2-7)^{2}+(6-6)^{2}}[/tex]

[tex]d=\sqrt{(-9)^{2}+(0)^{2}}[/tex]

[tex]d_B_C=9\ units[/tex]

step 3

Find the distance C.D

we have

[tex]C(6,-2),D(3,-2)[/tex]

substitute in the formula

[tex]d=\sqrt{(-2+2)^{2}+(3-6)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(-3)^{2}}[/tex]

[tex]d_C_D=3\ units[/tex]

step 4

Find the distance D.E

we have

[tex]D(3,-2),E(3,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6+2)^{2}+(3-3)^{2}}[/tex]

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

[tex]d_D_E=4\ units[/tex]

step 5

Find the distance E.F

we have

[tex]E(3,-6),F(-7,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6+6)^{2}+(-7-3)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(-10)^{2}}[/tex]

[tex]d_E_F=10\ units[/tex]

step 6

Find the distance A.F

we have

[tex]A(-7,7),F(-7,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6-7)^{2}+(-7+7)^{2}}[/tex]

[tex]d=\sqrt{(-13)^{2}+(0)^{2}}[/tex]

[tex]d_A_F=13\ units[/tex]

step 7

Find the perimeter

[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]

substitute the values

[tex]P=13+9+3+4+10+13[/tex]

[tex]P=52\ units[/tex]

Answer:

N = 14

Step-by-step explanation:

Let the number be N.  Then:

N + 7 = 21

Now solve this equation for N:

Subtract 7 from both sides.  We get:

N = 14

Answer:

1. n = 14

2. n = 3

3. n - 7 = 21; n = 28

Answer:

I would line up the numbers in order

The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.

We have,

To calculate the coefficient of skewness and kurtosis, we first need to organize the data into a frequency distribution table.

Age | Frequency

10 | 3

12 | 2

13 | 4

14 | 5

15 | 5

16 | 5

17 | 4

18 | 6

19 | 4

20 | 3

22 | 4

24 | 4

25 | 1

27 | 3

28 | 1

30 | 2

31 | 4

32 | 3

34 | 3

35 | 3

37 | 1

38 | 1

40 | 1

43 | 1

44 | 2

To calculate the coefficient of skewness, we use the formula:

Coefficient of Skewness = (mean - mode) / standard deviation

Mean = (10 * 3 + 12 * 2 + 13 * 4 + ... + 44 * 2) / 100 ≈ 20.49

Mode = 18 (the most frequent value in the dataset)

Standard Deviation

= √[((10 - mean)² * 3 + (12 - mean)² * 2 + ... + (44 - mean)² * 2) / 100]

≈ 9.63

Coefficient of Skewness = (20.49 - 18) / 9.63 ≈ 0.26

To calculate the kurtosis, we use the formula:

Kurtosis = ∑[((x - mean) / standard deviation)⁴ * frequency] / (n * standard deviation⁴) - 3

Kurtosis = [((10 - mean) / standard deviation)⁴ * 3 + ((12 - mean) / standard deviation)⁴ * 2 + ... + ((44 - mean) / standard deviation)⁴ * 2] / (100 * standard deviation⁴) - 3 ≈ -0.84

Interpretation:

Coefficient of Skewness:

The coefficient of skewness is positive (0.26), indicating that the data is slightly skewed to the right (positively skewed). This means that there is a longer tail on the right side of the distribution.

Kurtosis:

The kurtosis value is approximately -0.84. Since it is less than 3, the distribution is considered platykurtic. This means that the distribution has lighter tails and is flatter compared to a normal distribution.

Thus,

The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.

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The combined volume of both tanks is: Option A: 15x^2

Step-by-step explanation:

Given

Volume of larger tank = V_L =  [tex]8x^2+2x-1[/tex] in^3

Volume of smaller tank = V_S= [tex]7x^2-2x+1[/tex] in^3

To find the combined volume, we have to add both volumes

[tex]V = V_L+V_S\\=8x^2 + 2x - 1 + (7x^2 - 2x + 1)\\=8x^2+2x-1+7x^2-2x+1\\Combining\ like\ terms\\=8x^2+7x^2+2x-2x-1+1\\=15x^2[/tex]

Hence,

The combined volume of both tanks is: Option A: 15x^2

Keywords: Expressions, Polynomials

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Answer:

She can make 10 pizzas.

Step-by-step explanation:

8 1/3=25/3

(25/3)/(5/6)=(25/3)(6/5)=150/15=10

Final answer:

The value of the discriminant is 36, which means that the quadratic equation -2x = -8x + 8 has two distinct real solutions.

Explanation:

The given equation -2x = -8x + 8 can be rearranged into a quadratic equation: -8x + 8 + 2x = 0. Combining like terms gives: -6x + 8 = 0. To find the discriminant of this quadratic equation, we look at the coefficient of x^2, which is 0. Since the discriminant D = b^2 - 4ac, where a = coefficient of x^2, b = coefficient of x, and c = constant term, in this case, a = 0, b = -6, and c = 8. Plugging these values into the formula, we have: D = (-6)^2 - 4(0)(8) = 36 - 0 = 36.

The value of the discriminant is 36. The discriminant tells us about the number of real number solutions the equation has. If the discriminant is positive (D > 0), then the equation has two distinct real solutions. If the discriminant is zero (D = 0), then the equation has one real solution. If the discriminant is negative (D < 0), then the equation has no real solutions.

In this case, since the discriminant is positive (D = 36), the quadratic equation has two distinct real solutions.

Answer:

sqrt(x+3)

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

A hexagon has 6 sides, thus

sum = 180° × 4 = 720°

To find the measure of each interior angle divide by 6, that is

interior angle = 720° ÷ 6 = 120°

Answer: 120°

Step-by-step explanation: Let's start by finding the sum of the measures of the interior angles. The sum of the measures of the interior angles of a polygon can be found using the formula 180 (n - 2) where n represents the number of sides in the polygon.

Since a regular hexagon has 6 sides, we can plug a 6 in for n in our formula and we have 180 (6 - 2) where 6 represents the number of sides. We can simplify this by subtracting 2 from 6 inside the parentheses to get 180 (4) which is 720.

So the sum of the measures of the interior angles of a regular hexagon is 720°.

However, we want to know the measure of each interior angle. Since the angles of a regular hexagon are all congruent, we simply divide the sum of the measures of the angles which is 720 by the number of angles or sides which is 6 to get 120.

So the measure of each interior angle of a regular hexagon is 120°.

So the formula for finding the measure of each interior angle of a regular polygon is simply the sum of the interior angles 180 (n - 2) divided by the number of sides which is n.

Image provided.

Answer:

Step-by-step explanation:

CH3Cl is polar while CCl4 is non polar.

When we consider whether something is polar or not we have to consider the following:

-Molecular symmetry

-Polar bonds (based on Electronegativity)

-Whether or not all the bonds are equal in magnitude

So for CCl4:

-All of the bonds are equal, in that all the electronegativity differences (delta EN) are the same.

-There are polar bonds as the delta EN between Cl (EN = 3.0) and C (EN=2.5) is 0.5 which means the bond is polar covalent

But when we look at the symmetry of the molecule (by drawing the lewis structure) there are no lone pairs, meaning that the molecule is symmetrical and therefore, it is non polar.

For CH3Cl:

-There are polar bonds here whether between C-H or C-Cl like above, both delta EN are greater than or equal to 0.5

-But, all of the bonds are not equal in strength. Cl (3.0) atoms have much higher electronegativity values than H (2.1) and there for they will "pull" the electrons closer and polarize the molecule. Therefore, the differences in bonds causes this molecule to be asymmetrical, and hence polar.

CH3Cl is polar due to an uneven electron distribution and net dipole moment, due to the different atoms attached. In contrast, CCl4 is nonpolar because it's symmetrical with the dipole moments cancelling out.

The compounds CH3Cl and CCl4 vary in their polarities due to their molecular geometry, leading to different symmetries. CH3Cl has a tetrahedral shape but is polar because of the presence of the electronegative Chlorine atom and three Hydrogen atoms, creating an uneven distribution of electrons and thereby, a net dipole moment. On the other hand, CCl4 is also tetrahedral, but it's nonpolar due to its symmetry. As it has four Chlorine atoms evenly distributed around the Carbon atom, the dipole moments cancel out each other leading to no net dipole moment.

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Answer:

Step-by-step explanation:

5, 39, 24 just finished it

Answer:

[tex]SU=5\\\angle WXY = 24\°\\\angle SYW = 39 \°[/tex]

Step-by-step explanation:

According to the graph,

[tex]\angle WXT \cong \angle YXT[/tex]

So, [tex]m\angle YXT =12 \°[/tex]

By sum of angles we have

[tex]\angle WXY = \angle WXT + \angle YXT\\\angle WXY = 12 \° + 12\° = 24 \°\\\therefore \angle WXY 24\°[/tex]

By given, we know that

[tex]\angle UYS \cong \angle SYW\\\therefore \angle SYW = 39 \°[/tex]

By given, we know that side SU is a leg of the right triangle SUX, where the hypotenuse is 13 units, and the opposite angle is 12°. However, if you look closer, you would find that side ST is 5 units, and by GIven we know that ST = SU.

Therefore, SU = 5.

Answer:

x=-61/5

Step-by-step explanation:

-5=1/(x+12)

x+12=-1/5

x=-1/5-12

x=-1/5-60/5

x=-61/5

Total area of the field is 160 ft^2

Step-by-step explanation:

Given

Total workers = 4

Each worker's share of area = 5*8 feet

We will find the area for each worker and then multiply the area with four to find the whole area of field as it was evenly distributed to workers

so,

[tex]Area\ given\ to\ one\ worker = 5*8\\= 40\ ft^2[/tex]

[tex]Total\ area = 40*4 = 160\ ft^2[/tex]

Total area of the field is 160 ft^2

Keywords: Area, Measurement

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Final answer:

The total area of the field being harvested by four workers, each with a plot of 5 by 8 feet, is 160 square feet.

Explanation:

The subject of this question is Mathematics, specifically, it involves calculating the total area of land worked by four workers. Each worker is given a plot that is 5 feet by 8 feet. To find the total area of the field that the four workers are harvesting, you multiply the area of one plot by the number of workers.

To calculate the area of one plot: Area = length * width = 5 feet * 8 feet = 40 square feet.
Now, since there are four workers each with a plot of this size, you multiply the area of one plot by the number of plots/workers:
Total area = 40 square feet/plot  imes 4 plots = 160 square feet.

Therefore, the total area of the field being harvested by the four workers is 160 square feet.

Answer:

D. 47 square units

Step-by-step explanation:

The area of the piece of red paper after the hole for the photograph has been cut is the difference between the area of large square and are of small square.

Area of large square:

The length of the side of large square is

[tex]EF=|-4-4|=8\ units[/tex]

Area of large square [tex]=8^2=64\ un^2.[/tex]

Area of small square:

The length of the side of large square is

[tex]AB=\sqrt{(-3-(-2))^2+(-2-2)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}\ units[/tex]

Area of small square [tex]=\sqrt{17}^2=17\ un^2.[/tex]

Difference:

[tex]64 \ un^2-17\ un^2=47\ un^2[/tex]

Answer:

width =4.5ft

length=6ft

Step-by-step explanation:

w = x

L = 2x-3

area = L*w

27 = x(2x-3)

[tex]27=2x^{2} -3x[/tex]

[tex]2x^{2} -3x-27=0[/tex]

[tex]2x^{2} +6x-9x-27=0[/tex]

2x(x+3)-9(x+3)=0

(2x-9)(x+3)=0

2x-9=0

2x=9

x=9/2

x=4.5

L=2x-3=2*4.5-3 =9-3=6

The dimensions of the rectangle are; width = 4.5ft and length = 6ft.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The length of the rectangle is 3ft less than twice the width.

Let width = x

Length = 2x - 3

The area of the rectangle = length × Width

27 = x(2x-3)

2x² - 3x = 27

2x² - 3x - 27 = 0

2x(x + 3) - 9(x + 3) = 0

(2x-9)(x+3)=0

The solutions are;

2x-9=0

2x=9

x=9/2

x = 4.5

(x+3) = 0

x = -3

The width cannot be negative.

So,

Length = 2x-3 = 2*4.5-3 = 9 - 3

Length = 6

Hence, The dimensions of the rectangle are; width = 4.5ft and length = 6ft.

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Answer:

$48

Step-by-step explanation:

A pair of jeans= $12

Two pair of jeans= $12*2= $24

A shirt= $8

3 shirts= $8*3= $24

So it would be $24+$24= $48.

They made their mistake when calculating the cost of the jeans by getting $26 instead of $24.

Answer:

[tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]

Step-by-step explanation:

Assume that the deposited amount C dollars earn r% simple interest annually.

If after t years the deposited amount C dollars grows to D dollars, then we are asked to write a relation using the given terms to calculate t.

Now, using the formula of simple interest we can write

[tex]D = C(1 + \frac{t\times r}{100})[/tex]

⇒ [tex]1 + \frac{t \times r}{100} = \frac{D}{C}[/tex]

⇒ [tex]\frac{t \times r}{100} = \frac{D}{C} - 1[/tex]

⇒ [tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]

So, this is the expression for t. (Answer)

Answer:

t= 100/r [d/c-1]

Answer:

200 ft.

2 jumps

Step-by-step explanation:

The slide is placed at coordinates (-2,0) and the fountain is placed at coordinates (-2,-2).

(A) Therefore, using the distance between two known points formula, the distance from the slide to the fountain is given by  

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

Now, given that each unit on the grid represents 100 ft.

So, the distance from slide to the fountain is (100 × 2) = 200 ft. (Answer)

(B) Now, if each jump = 100 ft, then the slide is 2 jumps apart from the fountain. (Answer)

We know the distance between two known points on the coordinate plane ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by the following formula

Distance = [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2}  )^{2}}[/tex]

The distance from the slide to the fountain is sqrt(29) units on the grid or 100*sqrt(29) feet. If each unit represents 100 ft, the distance is 100*sqrt(29) feet.

To find the distance from the slide to the fountain, we need to determine the coordinates of both points on the grid. Let's assume the slide is located at point A (2,4) and the fountain is located at point B (7,6).

Using the distance formula, d = sqrt(([tex]x2 - x1)^2 + (y2 - y1)^2)[/tex], we can plug in the coordinates:

d = [tex]sqrt((7 - 2)^2 + (6 - 4)^2)[/tex] = sqrt(25 + 4) = sqrt(29).

So, the distance from the slide to the fountain is approximately sqrt(29) units on the grid or 100*sqrt(29) feet.

To determine the distance in feet if each unit on the grid represents 100 ft, we can simply multiply the distance by 100:

Distance = sqrt(29) * 100 = 100*sqrt(29) feet.

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Answer:

Domain f(x)={y:6≥y≤0}

Range of f(x)={x:x≤69}

Cross-check the location of point on your graph this is roughly estimation

The total number of boxes will be 60 that the girls have sold in one hour.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have to determine the total number of boxes will the girls have sold in one hour

Let Kate sold x boxes in 60 minutes

As per the given situation, we can write the ratio would be as:

27 boxes : 45 minutes = x boxes :  60 minutes

⇒ 27/45 = x/60

Apply the cross-multiplication operation,

⇒ x = (60×27)/45

⇒ x = 36

Let Miley sold y boxes in 60 minutes

⇒ 12/30= y/60

Apply the cross-multiplication operation,

⇒ y = (12×60)/30

⇒ y = 24

So, the total number of boxes = x + y = 36 + 24 = 60

Thus, the total number of boxes will be 60 that the girls have sold in one hour.

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Final answer:

Kate sells 36 boxes and Miley sells 24 boxes in one hour. So, they will have sold a total of 60 boxes in one hour.

Explanation:

To find the total number of boxes sold by both Kate and Miley in one hour, we need to calculate the rate at which each of them sells boxes. Kate sells 27 boxes in 45 minutes, which can be converted to 0.6 boxes per minute (27 boxes / 45 minutes = 0.6 boxes per minute). Miley sells 12 boxes in 30 minutes, which can be converted to 0.4 boxes per minute (12 boxes / 30 minutes = 0.4 boxes per minute).

To find the total number of boxes sold in one hour, we add the number of boxes each of them sells in one minute and multiply it by 60 (the number of minutes in an hour). Kate sells 0.6 boxes per minute, so in one hour she would sell 0.6 boxes/minute * 60 minutes = 36 boxes. Miley sells 0.4 boxes per minute, so in one hour she would sell 0.4 boxes/minute * 60 minutes = 24 boxes. Therefore, the total number of boxes sold by both Kate and Miley in one hour would be 36 + 24 = 60 boxes.