1. If two nonvertical lines are parallel, what do we know about their slopes? If two lines are perpendicular and neither is parallel to an axis, what do we know about their slopes? Why must the lines be nonvertical?

The length of flag is 760 feet and width of flag is 320 feet

Solution:

A seed company planted a floral mosaic of a national flag

Since, the flag is generally of shape rectangle, we can use the formula of rectangle

Let "a" be the length of rectangle

Let "b" be the width of rectangle

The length is 440 ft greater than the width

Length = 440 + width

a = 440 + b ----- eqn 1

The perimeter of the flag is 2,160 ft

The perimeter of rectangle is given as:

Perimeter = 2(length + width)

Substituting the given values, we get

2160 = 2(440 + b + b)

2160 = 880 + 4b

4b = 2160 - 880

4b = 1280

b = 320

Substitute b = 320 in eqn 1

a = 440 + 320

a = 760

Thus the length of flag is 760 feet and width of flag is 320 feet

Answer:

Therefore the correct option is A. 7^11/4^11

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Step-by-step explanation:

Given:

[tex](\dfrac{7}{4})^{11}[/tex]

Solution:

We know the Identity For Law of Indices

[tex](\dfrac{x}{y})^{a}=\dfrac{x^{a}}{y^{a}}[/tex]

So here we have,

x = 7

y = 4

a = 11 , then

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Therefore the correct option is A. 7^11/4^11

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Answer:

4/5

Step-by-step explanation:

Because slope=rise/run.

Answer: slope = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

The formula for finding slope is given by

slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

From the graph give :

[tex]x_{1}[/tex] = -3

[tex]x_{2}[/tex] = 3

[tex]y_{2}[/tex] = 4

[tex]y_{1}[/tex] = -1

substituting into the formula , we have

slope = [tex]\frac{4-(-1)}{3-(-3)}[/tex]

slope = [tex]\frac{4+1}{3+3}[/tex]

slope = [tex]\frac{5}{6}[/tex]

Answer:

Therefore the value of n is

[tex]n=-9[/tex]

Step-by-step explanation:

Given:

[tex]x^{12}y^{-13}x^{-5}y^{4}=x^{m}y^{n}[/tex]

To Find:

n = ?

Solution:

Using identity

[tex]1.\ x^{a}x^{b}=x^{a+b}[/tex]

[tex]2.\ x^{a}x^{-b}=x^{a-b}[/tex]

[tex]3.\ x^{-a}x^{b}=x^{-a+b}[/tex]

Therefore

[tex]x^{(12-5)}y^{(-13+4)}=x^{m}y^{n}[/tex]

[tex]x^{7}y^{-9}=x^{m}y^{n}[/tex]

Now on Comparing and Equality Property we get

[tex]m =7\\n=-9[/tex]

Therefore the value of n is

[tex]n=-9[/tex]

The final expression is  [tex]x^{7}[/tex] [tex]y^{-9}[/tex] , making n = -9.

The given expression is([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]). We want to find the equivalent expression in the form [tex]x^{m}[/tex] [tex]y^n[/tex], where m and n are exponents that we need to determine.

Here's how to simplify it step by step:

[tex]x^{12}[/tex] * [tex]x^{-5}[/tex] = [tex]x^{12-5}[/tex] = [tex]x^{7}[/tex]

    2.  Combine the exponents of y:

[tex]y^{-13}[/tex] *[tex]y^{4}[/tex] = [tex]y^{-13+4}[/tex] = [tex]y^{-9}[/tex]

Therefore, the expression simplifies to [tex]x^{7}[/tex] [tex]y^{-9}[/tex]. This means that m = 7 and n = -9. Thus, the value of n is -9.

Question-The expression ([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]) is equivalent to [tex]x^m y^n[/tex].

What is the value of n?

Answer:

36

Step-by-step explanation:

10% of 360=10/100*360=1/10*360=360/10=36

Answer:

$36 or  $360

Step-by-step explanation:

Answer:

the middle sequentially in a list of numbers (sorted from lowest to highest)

Step-by-step explanation:

for example, in the dataset 2, 4, 6, 8, 10, 6 would be the median because it is in the middle when sorted properly

Answer: The median is the middle value in the list of numbers

Step-by-step explanation:

For example: 5,3,7,10,22,12,15,100,98

The median is 22 because it is in the middle of all the number displayed

there is no acute angle.......

Answer:

angle CPB is an acute angle cause it's measure is less than 90°

Answer:

The base of the tree from a stake anchoring the wire is 18.67 feet far.

Step-by-step explanation:

Given:

the length of the wire  = 20 feet

Angle that the wire makes with the ground = 21 degrees

To Find:

The Distance from the base of the tree from the stake anchoring wire = ?

Solution:

We we construct a figure using the given data we end up with the right triangle as shown below

So now we can use the cosine ratio to find the distance from the base of the tree to the anchoring wire

Let d be the distance of  base of the tree from a stake anchoring the wire

[tex]Cos(angle) =\frac{\text{Adjacent side}}{Hypotenuse}[/tex]

On substituting the values we get

[tex]cos(21^{\circ}) =\frac{d}{20}[/tex]

[tex]d = cos(21^{\circ}) \times 20[/tex]

d = [tex]0.9335 \times 20[/tex]

d = 18.67 feet

The measure of angle y in the heptagon is 145 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

To find the measure of angle y in a heptagon, we can use the formula for the sum of the interior angles of a polygon, which is:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon.

For a septagon (a polygon with seven sides), we can substitute n=7 into the formula:

Sum of interior angles = (7-2) x 180 degrees = 5 x 180 degrees = 900 degrees

We can now find the value of angle y by adding up the measures of all the given angles and subtracting the sum from the total sum of the interior angles:

y = 900 - (129 + 116 + 120 + 130 + 135 + 125) = 145 degrees

Therefore, the measure of angle y in the Heptagon is 145 degrees.

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Complete question:

Step-by-step explanation:

Given,

The area of the yard = 6,756 square yards and

The width of the yard (b) = 12 yards

To find, the length of the yard (l) = ?

We know that,

Area of the rectangle =  Length(l) × Breadth(b)

⇒ l × 12 = 6,756

⇒ l =[tex]\dfrac{6,756}{12}[/tex]

⇒ l = 563 yards

Thus, the length of the yard was 563 yards.

Answer:

Therefore the Length of the yard is 563 yards.

Step-by-step explanation:

Consider  the yard as a Rectangle

Area of the Yard = 6756 square yards

Width of the yard = W = 12 yards

To Find :

Length of the yard = L =?

Solution:

WE know that

[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]

Substituting the values we get

[tex]\textrm{Area of Yard}=L\times W=L\times 12\\6756=L\times 12\\\\W=\dfrac{6756}{12}=563\ yard[/tex]

Therefore the Length of the yard is 563 yards.

Answer:

  (c)  10 cm, 9 cm, 9 cm

Step-by-step explanation:

You want to identify the set of side lengths that can form a triangle.

The triangle inequality requires a + b > c, for any assignment of a, b, c to side lengths. In effect, the sum of the two shortest sides must exceed the length of the longest side.

  6+6 = 12 < 15 . . . . not a triangle

  6+7 = 13 . . . . . . . . not greater; not a triangle

  9+9 = 18 > 10 . . . . forms a triangle

  4+8 = 12 < 14 . . . . not a triangle

The set of sides that will make a triangle is {10 cm, 9 cm, 9 cm}.

__

Additional comment

The semiperimeter (half the sum of side lengths) is always greater than any side length in a triangle. For example, if the perimeter is 20, the longest side must be less than 10.

By applying the Triangle Inequality Theorem, we find the only set of sides that could make a valid triangle is 10 cm, 9 cm, 9 cm.

The question is asking to identify which set of given lengths could make a valid triangle. To answer this question, it's important to remember the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this concept to each option.

Therefore, the only set of lengths that could make a valid triangle is 10 cm, 9 cm, 9 cm.

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Answer:

(4, 6).

Step-by-step explanation:

7x – 5y = -2

y = 7x – 22  

-7x + y = -22   Adding this to equation 1:

-4y = -24

y = 6.

Plug this into the second equation:

6 = 7x - 22

7x = 28

x = 4.

Sample 2 has least percent error

Step-by-step explanation:

We have to find the percent error in all samples to verify which sample had the least percent error

Percent error is given by:

[tex]Percent\ error = \frac{|actual\ amount-stated\ amount|}{Stated} * 100[/tex]

For sample 1:

Stated amount = 14 ounces

Actual amount = 13.7 ounces

[tex]Percent\ error = \frac{|13.7-14|}{14} * 100\\= \frac{|-0.3|}{14} * 100\\=\frac{0.3}{14} * 100\\= 0.021428*100\\=2.1428\%[/tex]

Sample 2:

Stated amount = 24 ounces

Actual amount = 24.4 ounces

[tex]Percent\ error = \frac{|24.4-24|}{24} * 100\\= \frac{|0.4|}{24} * 100\\=\frac{0.4}{24} * 100\\= 0.016666*100\\=1.666..\%[/tex]

Sample 3:

Stated amount = 25 ounces

Actual amount = 25.8 ounces

[tex]Percent\ error = \frac{|25.8-25|}{25} * 100\\= \frac{|0.8}{25} * 100\\=\frac{0.8}{25} * 100\\= 0.032*100\\=3.2\%[/tex]

Sample 4:

Stated amount = 39 ounces

Actual amount = 40.2 ounces

[tex]Percent\ error = \frac{|40.2-39|}{39} * 100\\= \frac{|-1.2|}{39} * 100\\=\frac{1.2}{39} * 100\\= 0.030769*100\\=3.0769\%[/tex]

Hence,

Sample 2 has least percent error

Keywords: Percent error, error

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It snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

Solution:

Given that, At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today

From given information,

[tex]\text{Snowed yesterday } = \frac{1}{2} \text{ foot }\\\\\text{Snowed today } = \frac{1}{5} \text{ foot }[/tex]

To find: how much more did it snow yesterday than today

So we have to find the difference between snowed yesterday and today

[tex]\text{Difference} = \text{Snowed yesterday } - \text{ snowed today }\\\\\text{Difference} = \frac{1}{2} - \frac{1}{5}\\\\\text{Difference} = \frac{1 \times 5}{2 \times 5}-\frac{1 \times 2}{5 \times 2}\\\\\text{Difference} = \frac{5}{10}-\frac{2}{10}\\\\\text{Difference} =\frac{3}{10}[/tex]

Hence it snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

They can not, there are only 2 sides and they probably flipped it different ways. They got 'lucky'.

Final answer:

Flipping a coin 100 times and getting 73 heads suggests a potential unbalanced coin. A chi-square statistical test is needed to determine if the deviation from the expected 50-50 ratio is significant. The large deviation in this scenario does suggest bias, but only a hypothesis test can confirm if the coin is unbalanced.

Explanation:

Intuitively, we might accept variations in coin flips as part of chance when the number of trials is small. However, as the number of trials increases, the expected 50-50 ratio of heads and tails should emerge. In the case where a person flipped a coin 100 times and obtained 73 heads, one could suspect an unbalanced coin, but to conclusively determine this, a statistical test, such as a chi-square, should be conducted to assess the significance of the deviation from the expected 50-50 ratio.

Flipping a coin 100 times should result in approximately 50 heads and 50 tails, according to the law of large numbers. A result of 73 heads is quite far from the expected outcome. The empirical observation suggests that there might be a bias towards heads, which indicates that the coin could be unbalanced.

To determine whether the coin is truly unbalanced or whether this was a fluke, one would perform a hypothesis test at a specified significance level to see if the observed results significantly differ from what is expected by random chance alone. If the results show a statistically significant difference, we could conclude that there is evidence to support the claim that the coin is unbalanced.

The correct statement about the system of equations y = x - 6 and y = -x - 2 is that the equations are independent because the lines intersect at one point, as they have different slopes.

The student is asking which statement about the system of equations is correct. The equations given are:

Let's analyze both equations:

Since the two lines have different slopes, they are not parallel and will intersect at a single point, making the system consistent and independent. Therefore, the correct answer is:

A. The equations are independent because the lines intersect in one point.

Answer:

0.0925 miles per second

Step-by-step explanation:

Answer:

16.9 seconds in 1 mile

Step-by-step explanation:

213miles => 3600s

1 mile => X

X=1*3600/213

X=16.9s

Answer:

p = (218-6)/4

Step-by-step explanation:

218-6 is in parenthesis because you want to remove the 6 people driving from the population you're dividing first, since they wont be on the buses. The divide that number by 4 to figure out how many people are on each bus. The answer to that is 53. There are 53 people on each bus.

Hope this helps! I would really appreciate it if you marked me brainliest!

Answer:

the answer is 55

Step-by-step explanation:

Answer: [tex]5\frac{3}{10}[/tex]

We first write them as improper fraction.

[tex]1\frac{7}{10}=\frac{17}{10}[/tex]

[tex]3\frac{3}{5}=\frac{18}{5}[/tex]

Then we find the LCM of the denominators. That is 10.

Using LCD we find the sum:

[tex]1\frac{7}{10}+3\frac{3}{5}\\=\frac{17}{10}+\frac{18}{5}\\=\frac{17}{10}+\frac{36}{10}\\=\frac{53}{10}\\=5\frac{3}{10}[/tex]

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The sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

To find the sum of the fractions [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \)[/tex], let's first convert them to a common denominator.

The least common denominator for 7, 3, and 5 is 105 (since it's the smallest number divisible by all three denominators).

So, we need to express each fraction with a denominator of 105:

[tex]- \( \frac{1}{7} \) becomes \( \frac{15}{105} \) (multiplied by 15)[/tex]

[tex]- \( \frac{10}{3} \) becomes \( \frac{350}{105} \) (multiplied by 35)[/tex]

[tex]- \( \frac{3}{5} \) becomes \( \frac{63}{105} \) (multiplied by 21)[/tex]

Now, we add these fractions:

[tex]\( \frac{15}{105} + \frac{350}{105} + \frac{63}{105} = \frac{15 + 350 + 63}{105} = \frac{428}{105} \)[/tex]

So, the sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

Answer:

6x+9

Step-by-step explanation:

add like terms

5x+x=6x

7+2=9

5x+7+x+2=6x+9

Answer:

1

Step-by-step explanation:

Answer:

2,325.58 Gallons

Step-by-step explanation:

20,000÷8.6=2,325.58

Answer:

100 minutes

Step-by-step explanation:

25 x 10 = 250

10×10=100

Answer:

u = 40° , v = 40° and x = 100°

Step-by-step explanation:

i) from the rule of triangle we know that the sum of all three angles = 180°

ii) 100° + 40° + y = 180°. Therefore y = 40°. where y is the angle adjacent to v.

iii) from theorem on parallel lines we can say that u = y =40°

iv) from the properties of parallel lines we get v = 40° as interior alternate angles are equal.

v) again from the properties of parallel lines we get u = 40°

vi) using the triangle property as in i) we can see that u + v + x =180° therefore 40° + 40° + x = 180°. Therefore x = 100°.

vii) Therefore u = 40° , v = 40° and x = 100°

Answer:

The speed of the bus after it decreased by 55% is now 27 miles per hour.

Answer: The speed of the bus inside city limits is... 27 mph

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Answer:

Explanation:

The theoretical probability, P (A), of an event, A, is:

For 10 cranberry and 15 strawberry juices, the number of outcomes for two strawberry juices are:

[tex]C^{15}_{2}=\frac{15!}{(15-2)!(2!)}=\frac{15!}{13!2!}=\frac{15\times 14}{2}=105[/tex]

The total number of possible outcomes is:

[tex]C^{25}_{2}=\frac{25!}{(25-2)!(2!)}=\frac{25!}{23!2!}=\frac{25\times 24}{2}=300[/tex]

Thus, the probability of randomly picking two strawberry juices is:

Note that you can obtain it as the product of the probabilities that the first juice is a strawberry juice and the second juice is also strawberry juice:

[tex]15/25\times 14/24=(15\times 25)/(14\times 24)=210/600=7/20[/tex]

Answer:

Option B is correct.

Step-by-step explanation:

Paul was asked to use the elmination to find the solution to the system of linear equations

What are the missing steps in his work below?

So, the step missing is multiplying equation 1 by 2 i.e

So, Option B is correct.

I'm going to assume that you want to know whether the coordinate satisfies the equation. Let's find out;

-3х - 6у = 17

-3(6) - 6(3) = 17

-18 - 18 = 17

-36 ≠ 17

The point (6, 3) does NOT satisfy the equation.

Best of Luck!

Answer:

Step-by-step explanation:

j + p = 178

j = p + 10

p + 10 + p = 178

2p + 10 = 178

2p = 178 - 10

2p = 168

p = 168/2

p = 84 <==== Phil's score

j = p + 10

j = 84 + 10

j = 94 <====Jerry's score

Final answer:

Jerry scored 94 and Phil scored 84.

Explanation:

To find Jerry and Phil's scores, we'll set up two equations based on the given information. Let's say Jerry's score is represented by 'J' and Phil's score is represented by 'P'. We know that Jerry scored 10 points higher than Phil, so J = P + 10. We also know that their scores combined equal 178, so J + P = 178. Now we can solve these two equations to find each student's score. Substituting the first equation into the second equation, we get (P + 10) + P = 178. Simplifying this equation gives us 2P + 10 = 178. Subtracting 10 from both sides gives us 2P = 168. Finally, dividing both sides by 2 gives us P = 84. So Phil's score is 84. Substituting this value back into the first equation, we get J = 84 + 10 which gives us J = 94. Therefore, Jerry's score is 94.