A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.

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

P1 = (12, -4)

P2 = (14, 8)

Substitution

Slope = (8 - - 4) / (14 - 12)

= (8 + 4) / 2

= 12/2

= 6

Result

Slope = 6

The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

To solve this problem, we simply need to factorize the polynomial given.

[tex]6x^2 + 15xy - 14x - 35y[/tex]

[tex]6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)[/tex]

This is the the reduced or factorized form of the given polynomial.

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3. 300

4. $180

5. $23.75

6. $102.6

Answer: 1 is 300 2 is 180 3 is 23.75 and the fourth one is 102.6

Step-by-step explanation: dont forget to add your $ signsss

a)Table is completed below.

b)The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.

What is proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

Given.

The proportion is: according to the first row of the proportional relationship

y = kx

28 = k*20

k = 28/20 = 1.4

the following is the function:

y = 1.4x

a) Fill in the following table:

Weight and distance (in centimeters) (newtons)

20 | 28

55 | 55*1.4 = 77

140/1.4 = 100 | 140

1 | 1*1.4 = 1.4

b) The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.

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The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

Isosceles triangle: What is it?

A triangle with two sides that have the same length is said to be isosceles.

Given,

Area of triangle = 64 sq.ft

Here, an isosceles triangle has two equal sides 

Let

x is equal to the length side of a right isosceles triangle's leg.

y is the area of a right isosceles triangle at position

Currently, the legs of a right isosceles triangle are equal.

Area of triangle = 1/2 ×  base × height

y = 1/2 × (x) × (x)

y = x²/2

64 = x²/2

128 = x²

x = √128

x = 8√2

The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

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Answer:

Step-by-step explanation:

first part: B.

second part: -11.3 or 11.3, 11.3

Answer:

Area is 314.2 cm²

Step-by-step explanation:

- Consider a circle whose radius is r, while calculating its area, the formula is derived from its circumference;

[tex]{ \rm{circumference = 2\pi r}}[/tex]

- but area is the integral of circumference;

[tex]{ \rm{area = \int circumference }} \\ \\ { \rm{area = \int2\pi r \: dr}}[/tex]

- Assume area is between the center to the edge from r = 0 to r = r

[tex] { \rm{area = 2\int^{r}_{0}\pi r \: dr}} \\ \\ { \rm{area = 2[\pi ( \frac{ {r}^{2} }{2} )]^{r} _{0} }} \\ \\ { \rm{area = \pi {(r)}^{2} - \pi {(0)}^{2} }} \\ \\ { \boxed{ \rm{area = \pi {r}^{2} }}}[/tex]

- From the question given, the circle has a radius of 10cm

[tex]{ \rm{area = 3.142 \times {10}^{2} }} \\ \\ { \bf{area = 314.2 \: {cm}^{2} }}[/tex]

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]

Step-by-step explanation:

the 2 triangles are similar.

that means their corresponding angles are equal, and their side lengths (and heights and so on) have all the same constant scaling factor.

so, we see that the side with the length 6 must corresponds to the side with the length 3 (factor 1/2).

as then the side with the length 5 corresponds to the side with the length 2.5, and the side with the length 4 corresponds to the side with the length 2 (all have the same factor 1/2).

a is the angle between 6 and 5 (the 2 longest sides).

the angle between the 2 longest sides in the smaller triangle (3 and 2.5) is d.

so, a and d correspond.

b is the angle between 6 and 4 (the longest and the shortest side).

the angle between the corresponding sides 3 and 2 is c.

so, b and c correspond.

therefore, the 4th and last answer choice is correct.

Answer: Choice A.  [tex](5\text{x}^2+2)(3\text{x}-1)[/tex]

==================================================

Work Shown:

[tex]15\text{x}^3-5\text{x}^2+6\text{x}-2\\\\(15\text{x}^3-5\text{x}^2)+(6\text{x}-2)\\\\5\text{x}^2(3\text{x}-1)+2(3\text{x}-1)\\\\(5\text{x}^2+2)(3\text{x}-1)\\\\[/tex]

Explanation:

The idea is to pair up the terms into two groups. Factor each group separately. Then we pull out the overall GCF (3x-1) to finish up the factorization. You can use the FOIL rule to expand out the answer to get the original expression again, which helps confirm the answer.

Answer:

Step-by-step explanation:

You want to know how many adults and children were admitted if there were twice as many children who paid $5.25 for admission as there were adults who paid $7.50, and total admission revenue was $378.

Let 'a' represent the number of adults admitted. Then 2a is the number of children. The total revenue is ...

  7.50a +5.25(2a) = 378

Collecting terms, we have ...

  18a = 378

  a = 21 . . . . . . . divide by 18

  2a = 2·21 = 42 . . . . . find the number of children admitted

21 adults and 42 children were admitted.

21 adults were admitted.

42 children were admitted.

Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.

Due to that,

Carnival earns a total of $378 in one hour.

Adult fees are $7.50.

Children's fees equal $5.25

Suppose that the carnival allows twice as many youngsters as adults.

If there are x adult, then

Children will thereafter be twice as many.

Since,

$378 is the total amount from both adults and children.

Then,

7.50x + 5.25(2x) = 378

7.50x + 10.50x = 378

18x = 378

x = 378 / 18

x = 21

As x was the total number of adults

Then, in an hour, 21 adults were admitted.

Since there were a total of two children,

Next, there were

42 kids were admitted in an hour (2(21)).

As a result, 42 kids and 21 adults were admitted in one hour.

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Answer:

(3, - 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(- 4, 3 ) → (3, - 4 )

Step-by-step explanation:

I assume we want ca miles/hour answer as speed.

but just formally, any distance per time unit is speed.

in that sense

12 miles / 20 minutes = 3 miles / 5 minutes

is the speed.

but now to convert this to miles/hour.

we want to multiply 3/5 or 12/20 by f/f, so that the denominator is 1 hour.

by multiplying the numerator by the same value we make sure the speed ratio remains the same.

so, what "f" do we need to multiply 20 with to get 60 (1 hour = 60 minutes) ?

right, f = 3

therefore, we get

12/20 × 3/3 = (12×3)/(20×3) = 36/60 = 36 miles / 1 hour

his brother's driving speed was 36 miles/h or 36 mph.

The other conjecture from A to C is true the only false conjecture is the option D.

Adjacent angles

Answer:

100.00

Step-by-step explanation:

it's 100.00 because the roof is being repaired and the person will have to pay after

Answer:

p = -9

Step-by-step explanation:

4p + 2 = 3p -7 subtract 3p to get p's on the same side

1p + 2 = -7 subtract 2 to get p alone

p = -9

Answer:

p = -9

Step-by-step explanation:

4p + 2 = 3p -7 subtract 3p to get p's on the same side

1p + 2 = -7 subtract 2 to get p alone

p = -9

Answer:

A

Step-by-step explanation:

a/b;

2/1=2;

5/4=1.25

that's why we can write it this way: 1.25 < a/b < 2

means the answer is A

Write an equation of the line in slope- point form

[tex]y- 6 = \frac{4}{5} (x+2)[/tex]

How to write the point- slope form of the equation?

We know, the point- slope formula is given by,

[tex]y-y_1=m(x-x_1)[/tex]

Given:

m= 4/5

[tex](x_1,y_1)= (-2,6)[/tex]

So, the equation of the line is,

[tex]y-y_1=m(x-x_1)\\\\y- 6 = \frac{4}{5} (x+2)[/tex]

It can also be written as ,

y- 6 = 0.8 (x+2)

What is point- slope form?

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The population that is most dense is the one for  5000 individuals per 200 square meters

Given the following information:

100 individuals per 100m^2

5000 individuals per200m^2

100,000 individuals per 20,000m^2

15,000 individuals per 10,000m^2

We find the population that is most dense using the formula:

Population density=(No. of people/Land area)

For 100 individuals per 100m^2,

Population density=100/100=1

For 5000 individuals per200m^2

Population density=5000/200=25

For 100,000 individuals per 20,000m^2

Population density=100,000/20,000=5

For 15,000 individuals per 10,000m^2

Population density=15,000/10,000=1.5

Hence, highest population density is 25 for 5000 individuals per200m^2  

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Yes

By drawing 36 little ones and 1 small one

Answer:

The first 4 terms are 3,9,15, and 21

Step-by-step explanation:

There's a image of all of the work above

The percent error of Ming’s estimate is 40%.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

here, it is given that :

Estimated number of members in his bicycle club by the end of summer = 21

Actual number of members in his bicycle club by the end of summer = 15

Now, the percent error of Ming’s estimate :

percent error = {(21-15)/15 } x 100

percent error = (6/15) x 100

percent error = 40%

Therefore, the percent error of Ming’s estimate is 40%.

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The probability that a day requires more water than is stored in city reservoirs will be; 0.965

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

Given that Water use in the summer is normally distributed with a mean of 310 million gallons and a standard deviation of 45 million gallons.

Let X be the random variable that shows the quantity of water required on a particular day.

Z-score :

[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]

Now, the probability that a day requires more water than is stored in city reservoirs will be;

[tex]Z = \dfrac{350 -310}{45},[/tex]

Z = 0.965

We can see that the above value to the given P(X > 350)= 1 - P(Z < b), we get the value of b is; 0.965.

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The common ratio of the Geometric sequence 19, 38, 76 ....  is 2.  

The distance between each number in a geometric series is known as the common ratio.

The reason it is common to all numbers and also the ratio between two consecutive numbers in the sequence is why it is known as the common ratio.

Divide the nth term by the (n-1)th term in a geometric series to find the common ratio.

The common ratio of the Geometric sequence 19, 38, 76 is

 common ratio = (38/19) = 2

or   common ratio  = 76/38 = 2

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Answer:

- 11s² + 2s + 9

Step-by-step explanation:

B = 2s + s²

A = 3 - 4s²

then

 2s + s² + 3(3 - 4s²)

=2s + s²+ 9 - 12s²

= - 11s² + 2s + 9

The value of x after solving the expression is 3.

What is an expression?

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numerals (constants), variable, operations, equations, brackets, punctuation, and grouping. Many writers differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical things. However, in modern mathematics, and particularly in computer algebra, formulae are considered as expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

Given expression 6x-7 = 4x-1

   or, 6x-4x = -1+7

   or, 2x = 6

   or, x = 6/2 = 3

Hence, the value of x after solving the expression is 3.

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Answer: 129

Step-by-step explanation: 180-51

Answer:

129.

Step-by-step explanation:

it's 129 believe me

The required allowance that Dan has prior is given as $11.6.

Given that,
Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0) is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the allowance Dan has be x,
According to the question,
x/2 + 8.90 = 14.70
x = 29.40 - 17.80
x = $11.6

Thus, the required allowance that Dan has prior is given as $11.6.

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The range of values that a bottle could contain to pass inspection will be 7.840 - 8.160 ounces.

It was stated that the toy company that makes bubbles fills its 8-ounce bottles using a machine.

The bottle passes inspection if the percent error of the amount is 2% or less. The minimum range will be:

= 8 ounces - (2% × 8 ounces)

= 8 ounces - 0.16 ounces

= 7.84 ounces

The maximum range will be:.

= 8 ounces + (2% × 8 ounces)

= 8 ounces + 0.16 ounces

= 8.16 ounces.

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The allowable range for the toy company is [7.84, 8.16].

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, the allowable percentage error is 2% or less.

Now, 2% of 8 ounces is,

= (2/100)×8.

= 0.16 ounces.

So, the allowable range is from (8 - 0.16) = 7.84 ounces to

(8 + 0.16) = 8.16 ounces.

As it is being given that it is 2% or less we'll use include the least value too.

So, the allowable range of the bottles is [7.84, 8.16].

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The piece of carpet on each side of the floor will be 10.8 feet.

From the information, Amber wants to put a carpet on the floor of her bedroom and the floor is a square with an area of 7.29 square feet.

It should be noted that the side will be

= ✓7.29

= 2.7 feet.

Therefore, the perimeter will be found and this will be:

= 4 × side

= 4 × 2.7

= 10.8 feet

This illustrates the length.

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If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .

In the question ,

it is given that

Commission of Danielle on everything she sells at electronic store = 7.75%

Base salary of Danielle = $725

amount of electronics merchandise sold by Danielle last week = $4500

So according to question

money earn = base salary + 7.75% of 4500

substituting the value of base salary as $725

= 725 + 0.0775*4500

= 725 + 348.75

= 1073.75

So, Danielle earns $1073.75 .

Therefore , If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .

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Not necessarily, because this was not an experiment.

In my opinion, Yet scientific evidence from case studies, surveys of meditator experiences, and historical studies is emerging to show that meditation can be associated with stress, negative effects, and mental health problems. Meditation can induce a state of deep relaxation and a calm mind. During meditation, you focus your attention and eliminate the stream of disorganized thoughts that can fill your mind and cause stress. This process can lead to increased physical and emotional well-being.

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