5. In each of the following figures, AB// CD. Find the value of the unknown.
Note: Don't give wrong answer. Give answer by step by step explanation ​

[tex]\cfrac{1}{6}+\cfrac{3}{4}-\cfrac{2}{3}\implies \cfrac{(2)1~~ + ~~(3)3~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{2+9-8}{12}\implies \cfrac{3}{12}\implies \cfrac{1}{4}[/tex]

Answer:

Step-by-step explanation:

If the price of the jacket increases 2.5% each year for 10 years, we can think of the price increase as the interest earned on an initial investment of $100 with an annual percentage yield (APY) of 2.5%. We can use the formula for compound interest to calculate the future value of the investment after 10 years:

FV = PV x (1 + r)^n

where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (as a decimal), and n is the number of compounding periods (years).

In this case, PV = $100, r = 0.025 (2.5% expressed as a decimal), and n = 10. Plugging these values into the formula, we get:

FV = $100 x (1 + 0.025)^10

FV ≈ $128

Therefore, the jacket that costs $100 today will cost approximately $128 in 10 years if the price increases 2.5% each year.

Answer: (2,0) = (-2,-2) (2,2) = (-2,0) (1,0) = (-3,-2) (0,2) = (-4,0)

Step-by-step explanation:

Answer:

No, rhombuses are not necessarily rectangles. While both shapes are quadrilaterals with opposite sides parallel, there is an additional requirement for a rectangle that is not present in a rhombus. Specifically, a rectangle must have all interior angles measuring 90 degrees, while a rhombus can have any angle between 0 and 180 degrees.

On the other hand, all rectangles are parallelograms, while not all parallelograms are rectangles. Similarly, all squares are both rhombuses and rectangles, but not all rhombuses or rectangles are squares. In summary, a rhombus is a quadrilateral with four equal sides, while a rectangle is a quadrilateral with four right angles. While there is some overlap between the definitions, they are not equivalent.

Answer:

Rhombuses are not rectangles

Step-by-step explanation:

This is because rhombuses do not have 4 right angles.

A square would be a rectangle because its a quadrilateral with 4 right angles

while a rectangle wouldn't be a square because it doesn't have 4 equal sides

A rhombus is a quadrilateral that has 4 equal sides but doesn't have 4 right angles, making it not a rectangle

Based on the information, we can infer that the expression that tells us how many slices the entire pizza had is x = 4 * 3 (option D).

To find the correct expression we must take into account the information that the statement gives us:

Based on the above, if Ben ate 1/3 of the pizza, we must multiply 4 * 3 to find the total number of slices on the pizza.

So the pizza had 12 slices. To check this result we can divide it by 3 to find out if 1/3 of 12 is equal to 4.

Note: This question is incomplete. Here is the complete information:

4. A pizza was cut into equal slices. Ben ate 4 of the slices. The amount Ben ate was 1/3 of the whole pizza. Which equation represents a way to find the total number of slices that were in the whole pizza?

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As this is when it hits the ground, the projectile is in the air for 6 seconds.

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

Objects that are thrown, shot, or launched with a certain initial velocity and then move against the forces of gravity and air resistance are known as projectiles. Projectiles can be anything from arrows and bullets to rocks and water balloons. Typically, a bow, slingshot, gun, or cannon is used to fire them. When projectiles are launched, gravity, air resistance, and other forces influence their trajectories.

from the question:

We must discover the moment the missile strikes the ground in order to calculate how long it was in the air. The height of the missile above the earth would be zero at that point.

Thus we must resolve the following equation:

y = -3x² - 12x + 96 = 0

We can use the quadratic formula to solve this equation in the quadratic form:

x = (-b ± √(b² - 4ac)) / 2a

where a = -3, b = -12, and c = 96.

Plugging in these values, we get:

x = (-(-12) ± √((-12)² - 4(-3)(96))) / 2(-3)

x = (12 ± √(144 + 1152)) / (-6)

x = (12 ± √1296) / (-6)

x = (12 ± 36) / (-6)

So, the solutions are:

x = -2 or x = 6

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

As a result, the missile is in the air for 6 seconds before it strikes the earth.

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According to the above, the figure rotated 180° would remain as shown in the image in the fourth quadrant of the Cartesian plane (+ , -)

To rotate the figure 180 degrees we must take into account its initial position. Additionally, we must remember that each quadrant is equivalent to 90°, so we would have to rotate it two quadrants. In this case it is not important to know if it rotates counterclockwise or clockwise because we know it will be in quadrant #4.

In this case, we must be guided by the coordinates that the figure has to draw it again. From the above we can see that it has four coordinates at the top. In the case of the figure rotated in quadrant #4, these four coordinates would be at the bottom because the figure has been rotated 180°.

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Therefore , the solution of the given problem of rational numbers comes out to be 92 and 95 are the numbers that, when rounded to the closest 10, will equal 90.

Any number that can be expressed as a ratio (not a portion) of two integers is considered rational. A reasonable fraction is one that has a nonzero denominator. 1/2, 1/5, but also 3/4 are a few examples of rational integers. "0" may additionally be expressed in a variety of forms as an actual function, like 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. It makes logical that there are seven. When two parameters are divided, a rational number results.

Here,

We glance at the digit in the ones spot to round a number up to the nearest 10. In that case, we round down to the prior multiple of 10 if the digit is 0, 1, 2, 3, or 4. We round up to the following multiple of 10 if that number is 5, 6, 7, 8, or 9.

Finding numbers with a ones place digit between 5 and 9 will enable us to round to the closest 10 and arrive at 90. The figures that would round to 90 are as follows:

=>92

=> 95

As a result, 92 and 95 are the numbers that, when rounded to the closest 10, will equal 90.

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a. Rogue Imperial Stout (11.6) is an extreme outlier.

b. This suggests that there may be more beers with lower alcohol percentages in the sample than higher percentages.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.

To determine if there are any outliers in the sample, we need to calculate the interquartile range (IQR), which is the difference between the upper quartile (Q3) and lower quartile (Q1).

IQR = Q3 - Q1

= 5.95 - 4.35

= 1.6

We then use the following rule to identify outliers:

Mild outliers: values that are less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR).

Extreme outliers: values that are less than Q1 - 3(IQR) or greater than Q3 + 3(IQR).

Using this rule, we have:

Mild outliers: None.

Extreme outliers: Rogue Imperial Stout (11.6) is an extreme outlier.

b. The boxplot below shows the distribution of alcohol percentage for the sample of 25 beers. The box represents the interquartile range (IQR), with the lower and upper whiskers extending to the smallest and largest values within 1.5 times the IQR from the lower and upper quartiles, respectively. Any values beyond the whiskers are considered outliers.

Another interesting feature of the boxplot is that the distribution appears slightly skewed to the right, with the median (5) closer to the lower quartile (4.35) than the upper quartile (5.95). This suggests that there may be more beers with lower alcohol percentages in the sample than higher percentages.

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Answer:

perimeter of first ️

2(100+150) = 500 m

In response to the query, we can state that The p-value, rounded to four probability decimal places, is 0.0056.

Mathematicians use probability theory to determine the chance that an event will occur or a statement is true. A probability of about 0 reflects how probable an event appears to occur, whereas a risk is a value between 0 and 1, where 1 suggests certainty. Probability is a mathematical representation of the likelihood that a specific event will take place. Other ways to express probabilities are as integers between 0 and 1 or as percentages between 0% and 100%. the ratio of events among equally likely options that lead to a certain event to all other outcomes.  

The sample proportions for the first and second populations are respectively p1 = 0.25 and p2 = 0.223. The samples had n1 = 587 and n2 = 251 respectively.

For this sample, the test statistic is provided by:

z is equal to (p1 - p2) / sqrt(p hat * (1 - p hat) * (1/n1 + 1/n2)).

where p hat is the pooled sample proportion and n1 + n2 is the sample size.

When we change the values, we obtain:

z = (0.25 - 0.223) / sqrt(0.236 * (1 - 0.236) * (1/587 + 1/251)) = 2.541

The test statistic, rounded to three decimal places, is 2.541.

, we hunt for the region in the standard normal distribution's right tail that corresponds to a z-score of 2.541. We calculate this area to be 0.0056 using a calculator or a table.

The p-value, rounded to four decimal places, is 0.0056.

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Answer:

To divide by a fraction, we can multiply by its reciprocal.

So,

4/9 /8 = 4/9 x 1/8 = 4/72 = 1/18

Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).

Slope is a mathematical term that describes how steep a path is. It gives an explanation of the rate of rise or decline of the line as it moves horizontally along the x-axis. The percentage of the difference in the y-coordinate to the change in the x-coordinate at all between the two locations on a line is known as the slope of the line. In other terms, it is the line's "rise" over its "run". The letter "m" stands for slope, and the following formula is used to determine it:

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

given

In slope-intercept form, a line's equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Given that the y-intercept is (0, -4) and the slope is 4/5, we can enter these numbers into the slope-intercept form to obtain:

y = (4/5)x - 4

Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).

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The only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

What is a valid triangle?

A valid triangle is a three-sided polygon that satisfies the following conditions:

The sum of the lengths of any two sides of the triangle is greater than the length of the third side.

The lengths of all three sides of the triangle are greater than zero.

Adam should use the dimensions 40 in., 44 in., 58 in. for a triangular frame to form a right triangle.

To determine if a right triangle can be formed, we need to check if the Pythagorean theorem is satisfied, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse).

Let's check each set of dimensions:

For 25 in., 60 in., 65 in.:

25^2 + 60^2 = 625 + 3600 = 4225

65^2 = 4225

The Pythagorean theorem is satisfied, so a right triangle can be formed. However, this triangle is not a valid option for Adam because the lengths are too short for building walls.

For 40 in., 44 in., 58 in.:

40^2 + 44^2 = 1600 + 1936 = 3536

58^2 = 3364

The Pythagorean theorem is not satisfied, so a right triangle cannot be formed using these dimensions.

For 50 in., 110 in., 130 in.:

50^2 + 110^2 = 2500 + 12100 = 14600

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

For 130 in., 50 in., 60 in.:

50^2 + 60^2 = 2500 + 3600 = 6100

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

Out of the options given, only the dimensions 50 in., 110 in., 130 in. and 130 in., 50 in., 60 in. satisfy the Pythagorean theorem, but both are too large for building walls.

Therefore, the only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

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The approximate diameter of the tin would be 12.9 centimeters.

Diameter is a straight line passing through the center of a circle, or any other curved shape, and connecting two points on the circumference. It is the longest line that can be drawn within a circle and its length is twice the radius. It is also used in measuring the size of objects and distances in the universe. The term is also used in geometry to refer to the size or width of a triangle, square, or other shapes.

To measure the diameter of a tin which is 750 gram, one needs to use a ruler or measuring tape. First, one needs to weigh the tin using a scale or balance. Once the weight is known, it can be used to calculate the approximate diameter of the tin.

To find the diameter, one needs to use the formula: Diameter = 2 x (cube root of volume). The volume of the tin can be calculated by multiplying the weight of the tin (in grams) by 0.52.

Therefore, for a tin weighing 750 grams, the approximate volume would be 390 cubic centimeters. To find the diameter, one needs to take the cube root of 390, which is 6.47.

Therefore, the approximate diameter of the tin would be 12.9 centimeters.

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Answer:

200 x 20% = 200 x 20/100 = 40.

Answer is 40.

Answer:

C.  [tex]\frac{n+4}{2}[/tex]

Step-by-step explanation:

"the sum of a number (n) and 4" --> n + 4

"divided by 2" --> this means the whole expression will be divided by 2

Therefore, the final answer is the third option!

Hope this helps!! :)

Answer:

ehhhhhhhhhhh

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Arrange the 4 set of numbers above each other and add the corresponding numbers.

9 and 5, 16 and 16, 9 and 5, 16 and 16

Answer:

the sum of 9 16 9 15 and 5 16 5 16 is 14 32 14 32 which is (A)

Step-by-step explanation:

9 16 9 16+

5 16 5 16

14 32 14 32

The width of the rectangle is calculated as: 11 inches

The formula for area of a rectangle is:

A = l*w.  

Since the area is 33 in², then;

33 = x(x + 8) would be the equation to solve for x.

Now, you need to put the equation in standard form.  

x² + 8x - 33 = 0.

To complete the square you need to add 33 to both sides.  

Now you have x² + 8x = 33  

Take the coefficient for the x term (8) and divide by 2.  Now square it.  That would be 4², so 16.  

Now you have x² + 8x + 16 = 49

(x + 4)² = 49

Take  the square root of both sides and you have;

x + 4 = 7.  

Therefore, x = 3 (the short side) and 11 is the long side.

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Answer:

10.3

Step-by-step explanation:

Let's say

a leg = 9

b leg = 5

The formula to find the hypotenuse is [tex]\sqrt{a^{2}+b^{2} } = \sqrt{9^{2} +5^{2} } = \sqrt{81+25} = \sqrt{106} = 10.246\\[/tex]

Round [tex]10.246[/tex] to get [tex]10.3[/tex]

Answer:

Solving a word problem is similar to specific tasks we do in various areas of our lives, such as school, home, or job, in that it requires critical thinking, attention to detail, and logical reasoning. In school, we solve math problems to understand different concepts, and in our job, we solve various problems related to our work to improve efficiency and productivity. Similarly, in our personal lives, we encounter problems and challenges that require problem-solving skills.

Addition problems are crucial in almost every job. For example, in accounting, addition is necessary when calculating profit and loss or taxes. In the retail sector, addition is necessary when calculating inventory or the total amount of sales. Even in fields such as medicine, addition is necessary when calculating dosages and other related calculations.

Knowing how to problem solve in this way can be incredibly helpful in the real world. Being able to identify the problem, analyze it, and find a suitable solution can make us more effective and efficient in our personal and professional lives. The ability to solve problems can also help us develop critical thinking skills, which can be useful in various situations.

In conclusion, solving word problems is an essential skill that can be applied to various areas of our lives. Being proficient in addition problems is essential for success in most jobs. Developing problem-solving skills can make us more effective and efficient in our personal and professional lives, and critical thinking skills can help us analyze problems and identify the best solutions.

Answer:

d

Step-by-step explanation:

The equation that represent the whole slices is as follows:

2 / 3 x = 4 .

Therefore, the answer is A.

A pizza was cut into equal slices. Ben ate 4 of the slices.  The amount Ben ate was 2/3 of the whole pizza.

Therefore, the equation that represent a way to find the total number of slices that were in the whole pizza can be calculated as follows:

Let

x = amount of the whole pizza

Therefore,

2 / 3 x = 4

cross multiply

2x = 4(3)

2x = 12

x = 12  /2

x = 6

Therefore, the whole slice is 6.

Hence, the equation is 2 / 3 x = 4

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Let me solve it down for you :)

The shape is a cuboid, so its dimensions will be:

[tex] \sf \: Surface \: area \: of \: cuboid = 2(lb + bh + hl)[/tex]

[tex] \sf \: S.A. = 2(12 \times 5 + 5 \times 10 + 12 \times 10)[/tex]

[tex] \sf \: S.A. = 2(60+ 50 + 120)[/tex]

[tex] \sf \: S.A. = 2(230)[/tex]

[tex] \sf \: S.A. = 460 \: {m}^{2} [/tex]

Dimensions of the cuboid:

[tex] \sf \: Volume = l \times b \times h[/tex]

[tex] \sf \: Volume = 12\times 5 \times 10[/tex]

[tex] \sf \: Volume = 600 \: {m}^{3} [/tex]

Convert m to cm, according to the question:

600 Cubic meter =

600,000,000 Cubic Centimeters

No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.

YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.

No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.

Thus, correct options are-

No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.

YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.

No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.

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Answer:

The answer is C.)

Step-by-step explanation:

The correct solution for the given absolute function |x/5| = 1 is: x = 5 and x = -5.

The variable inside this absolute value bars makes up an essential algebraic function known as the absolute value function.

The given function is-

|x/5| = 1

Solving the bars will give:

x/5 = 1 and x/5 = -1

So,

x = 5 and x = -5 are the solution of the absolute function.

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Answer:

the solution to the equation 2x + 18 = 42 is x = 12.

Step-by-step explanation:

To solve for x in the equation 2x + 18 = 42, you can follow these steps:

Subtract 18 from both sides of the equation:

2x + 18 - 18 = 42 - 18

2x = 24

Divide both sides of the equation by 2:

2x/2 = 24/2

x = 12

Therefore, the solution to the equation 2x + 18 = 42 is x = 12.

Answer:

[tex] \sf \: x = 12[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 18 = 42

Then the value of x will be,

→ 2x + 18 = 42

→ 2x = 42 - 18

→ 2x = 24

→ x = 24 ÷ 2

→ [ x = 12 ]

Hence, the value of x is 12.