Please help me with this Problem!

[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]

Answer:

To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:

distance = speed * time

Rearranging the formula, we get:

time = distance / speed

Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.

Now we can plug in the values for distance and speed into the formula:

time = 30 feet / 58.8 fps

time = 0.5104 seconds

Rounding to the nearest second, we get:

time = 0.51 seconds

So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.

Step-by-step explanation:

The conditional probability P(B|F) of the two way table is; P(B|F) = 0.37 given that the students prefer to write with block letters, there is a 0.37 probability that they have fair dancing skills

Two-way tables are a way of sorting data so that the frequency of each category can be seen quickly and easily.

Conditional probability is defined as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

Now, from the given two way table,

B = the student prefers writing in block letters.

F = the student's dancing skills are fair.

Thus;

P(B|F) = 17/45

P(B|F) = 0.37

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Answer:because angles in a triangle add up to 180 degrees.

Step-by-step explanation:

A=40

C=30

So 180-40-30=110

The measure that changes the most is the mean and the new value is 74.33°

If a value of 71° is changed to 93°, we have:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

Mean = (58+ 61+ 93+77+ 91+ 100+ 105+ 102 + 95 + 82+ 66+ 57)/12 = 74.33°

To find the median, arrange the data in order of size and pick the middle number. That is:

57, 58, 61, 66, 77, 82, 91, 93, 95, 100, 102, 105

Median = (82+91)/2 = 86.5°

Range = 105 - 57 = 48°

IQR = 97.5 - 63.5 = 34°

Therefore, the measure that changes the most is the mean and the new value is 74.33°

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Answer: it is 86.5 i got the answer correct on test trust me i want to help you guys out.

Step-by-step explanation:

The reasons for (1) and (2) are added below

One reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.

One reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.

This means that the candle's height is bounded and cannot continue to decrease linearly forever.

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The value of x in the diagrams are 14 and 99 respectively

Note the following points;

From the information given in the diagram

56 degrees and 4x degrees are corresponding

Then,

4x = 56

Make 'x' the subject

x = 14

From the second image

Add the angles and equate to 360 degrees, we have;

3x + 2 + 36 + x - 74 = 360

collect like terms

4x = 360 + 36

4x = 396

Make 'x' the subject

x = 99

Hence, the values are 14 and 99

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The percentage of gratuity paid is 20%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount for the bill = $50

Amount paid = $60

The amount of gratuity.

= 60 - 50

= $10

Now,

The percentage of gratuity.

= 10/50 x 100

= 20%

Thus,

The percentage of gratuity is 20%.

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Answer:

4,233,000

Step-by-step explanation:

4,232,000                 4,4232,852                  4,233,000

4,4232,852 is between 4,232,000 and 4,233,000.  It is closer to 4,233,000.

The rule is to look a the digit in the hundreds' place.  That number is 8.  If the digit in the hundreds' place is 5 or larger, you round up.

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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The value of k is given as follows:

k = 2x.

The exponential function that models the growth of the first virus is given as follows:

y = P(3)^x.

The exponential function that models the growth of the second virus is given as follows:

y = P(9)^x = P(3)^k.

We have that 9 is the second power of 3, hence we have that:

y = P(3²)^x = P(3)^k.

Applying the power of power rule, we have that:

y = P(3)^(2x) = P(3)^k.

Hence the value of k is given as follows:

k = 2x.

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1) the rule for the graph is y=3x+3

2) the rule for the graph is y=4x+10

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

1)  slope, m = change in y/change in x = 3/1 = 3

y-intercept = b = 3  

A line's slope intercept form is y=mx+b

Thus, the rule for the graph is y=3x+3

2)  slope, m = change in y/change in x = 4/1 = 4

y-intercept = b = 10

A line's slope intercept form is y=mx+b

Thus, the rule for the graph is y=4x+10

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Answer:

Flase, no real numbers (2+-8)

Step-by-step explanation:

First, you conjoined the equations (-6x+2=-6x-8).  Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.

The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.

We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of

y² = x, x = 3y.

=> x = 3y --(1)

=> y² = 3y

=> y² - 3y = 0

=> y( y - 3 ) = 0

=> y = 0 or y - 3 = 0

=> y = 0 , y = 3

from (1), x = 3y => x = 0, x = 9

Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is

[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]

where R = 3y , r = y²

[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]

[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]

[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]

[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]

[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]

Hence, the required volume is 162π/5 cubic units.

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To find the mean (average) of a set of numbers, you add up all the numbers and then divide by the number of items in the set.

Mean = (79g + 88g + 116g + 109g + 93g) / 5

Mean = (475g) / 5

Mean = 95g

So, the mean of the set of numbers is 95g.

The value of mean of the data set is,

⇒ Mean = 97 g

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Data set is,

79g, 88g, 116g, 109g, 93g

Now, We get;

The mean of data set is,

⇒ Mean = 79g + 88g + 116g + 109g + 93g / 5

⇒ Mean = 485g / 5

⇒ Mean = 97 g

Thus, The value of mean of the data set is,

⇒ Mean = 97 g

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The value of x for the given circle will be going to be 50°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr

where r is the radius of the circle.

Angles of Intersecting Chords Theorem

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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Answer:

Below

Step-by-step explanation:

Rectangular area = L x W =  10 x 20 = 200 ft^2

  PLUS triangular area = 1/2 b h = 1/2 * 10 * 10  = 50 ft^2

      TOTAL = 250 ft^2

The coordinates of the fourth vertex D = (3,−1.5).

A parallelogram has the following property AB=DC

AB=OB−OA=(3,3)−(1,5)=(2,−2)

DC=OC−OD=(8,3)−(a,b)=(2,−2)

OD=OC−DC=(8,3)−(2,−2)=(6,5)

Turn them into vectors. Position vector of point d

should be 6,5

To get the 2nd point, just do AD=BC

BC=OC−OB=(8,3)−(3,3)=(5,0)

AD=OD−OA=(a,b)−(1,5)=(5,0)

OD=OA−AD=(1,5)−(5,0)=(−4,5)

As long as the shape has four sides and two of them are parallel, and you know the length, this should work. For instance, a trapezium where AB=2DC/2CD:

A=(0,0),B=(2,0),C=(2,−1.5),D=(a,b)

AB=(2,0)DC=(2,−1.5)−(a,b)=12(2,0)(a,b)=(1,−1.5)

OR

AB=(2,0)CD=(a,b)−(2,−1.5)=12(2,0)(a,b)=(3,−1.5)

Thus, The coordinates of the fourth vertex D = (3,−1.5).

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Let's call the smaller integer "x". Then the larger integer would be "x + 3".

The sum of the reciprocal of the smaller integer and twice the reciprocal of the larger integer is 9/10, so we can write that as:

1/x + 2/(x + 3) = 9/10

Expanding and simplifying the right side:

1/x + 2/(x + 3) = 9/10

(x + 6)/(x * (x + 3)) = 9/10

10(x + 6) = 9x * (x + 3)

10x + 60 = 9x^2 + 27x

9x^2 - 83x + 60 = 0

Now we have a quadratic equation that we can solve using the quadratic formula or by factoring. Since the coefficients are integers, we can try factoring:

(3x - 20)(3x - 3) = 0

So either 3x - 20 = 0 or 3x - 3 = 0, which means either x = 20/3 or x = 3. Since x must be a positive integer, the only solution is x = 3.

So the two integers are 3 and 3 + 3 = 6.

Answer:

- It is a parallelogram

Step-by-step explanation:

- The interior angle sum of a quadrilateral is 360°

Considering the four angles;

[tex]{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( \frac{3}{2} x - 15) + ( \frac{7}{3} x - 12) = 360}} \\ \\ { \tt{(x + 2x + \frac{3}{2}x + \frac{7}{3}x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ \frac{41}{6} x - 9 = 360}} \\ \\ { \tt{ \frac{41}{6}x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}[/tex]

- Therefore, substitute in x and find the angles.

[tex] { \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( \frac{3}{2}x - 15) = \{( \frac{3}{2} \times 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( \frac{7}{3}x - 12) = \{( \frac{7}{3} \times 54) - 12 \} = 114 \degree }}[/tex]

If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Inequality

x is the integer

First step is to formulate the inequality

40x≤ 25,500-6,400

Now let determine the x by using the inequality

40x≤ 25,500-6,400

40x≤19,100

x=≤19,100/40

x=≤ 477.5

Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

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Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.

To solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.

So the length of the metal strip available for the 12 holes is:

3414 - 2 - 2 = 3410 inches

Dividing this length by the number of holes gives us:

3410 ÷ 12 = 284.166666... inches

To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:

284.166666... ÷ 11 = 25.833333...

Rounding this to the nearest hundredth of an inch, we get:

25.83 inches (to the nearest hundredth)

Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.

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The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.

The new coordinates of B will be:

x-coordinate: 4 x (-2) = -8

y-coordinate: 4 x (-1) = -4

So the new vertex B' is (-8, -4).

The new coordinates of C will be:

x-coordinate: 4 x (2) = 8

y-coordinate: 4 x (-2) = -8

So the new vertex C' is (8, -8).

The new coordinates of D will be:

x-coordinate: 4(1) = 4

y-coordinate: 4(2) = 8

So the new vertex D' is (4, 8).

Therefore, the image of the resultant figure is given in the image below.

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The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.

In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.

Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.

Options;

A. -0.28

B. -0.82

C. -4/5

D. -1/5

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The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

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The solution to the system of equations is x = -1 and y = 1.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The system of equation is given as:

2x - 3y = -5 .........(1)

3x + y = -2 ........(2)

Equation 2 can be written as:

y = -2 - 3x

Substituting the value of y in equation 1 we have:

2x - 3(-2 - 3x) = -5

2x + 6 + 9x = -5

11x + 6 = -5

11x = -5 -6

11x = -11

x = -1

Substituting the value of x in equation 2 we have:

3x + y = -2

3(-1) + y = -2

-3 + y = -2

y = -2 + 3

y = 1

Hence, the solution to the system of equations is x = -1 and y = 1.

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The numbers could be:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Shawn rounded a number to the nearest tenth and got 6.5.

When he rounded it to the nearest whole number, he got 6.

Now,

The number = 6.45

Rounded to the nearest tenth = 6.5

Rounded to the nearest whole number = 6

The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

Thus,

The possible numbers are:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

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The range is the set of y-coordinates of the function.

As per graph we can see:

Add all together to get the range:

As interval the range is:

Based on the information, it can be inferred that the area of the figure is 310 yards²

To calculate the surface area of this figure we must find the area of all the faces of the figure:

Then we must multiply the area of each face by the number of faces with that area.

Finally we must add the areas of the faces

According to the above, the total surface area of this figure is 310 yards ²

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