The headlights of an automobile are set such that the beam drops 5.00 in for each 28.0 ft in front of the car. What is the angle between the beam and the road

Answer:

0.5

Step-by-step explanation:

first you must solve addition and subtraction, to find x you must do the opposite of what it says

you must add 5 from both sides

10x -5 = 0

     +5 = +5

 then you must solve multiplication and division, for example here it says that 10 is being multiplied with x so you must do division  

you must divide 10 to both sides

10x =5

10/10 = 5/10          

after dividing 5 by 10 it will give you 0.5

so the check is

10x . 0.5 - 5 = 0

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The factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression will be solved as:-

f(x) = x³ + 10x² + 31x + 30

f(x) = ( x³ + 7x² + 10x + 3x² + 21x + 30

f(x) = ( x² + 7x + 10 ) ( (x + 3 )

f(x) = ( x²+ 5x + 2x + 10 ) ( x + 3 )

f(x) =[ x ( x+ 5 ) +2 ( x+ 5) ] ( x + 3 )

f(x) = ( x + 5 ) ( x + 2 ) ( x + 3 )

Therefore factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

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The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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The x-intercepts of the given equation 4x^2-12x+4 is -3/2

What is Quadratic equation ?

Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where c is a constant.

Given equation ,

y = 4x^2+12x+4

so we have to find the x-intercept , make y = 0

and we have to solve for the given quadratic equation

so,

we get

4x^2+12x+4 = 0

(2x)^2 + 9 + 12x = 0

(2x+3)^2 = 0

x = -3/2

There is double root unique intercept or tangent at  x  = -3/2

Therefore, The x-intercepts of the given equation 4x^2-12x+4 is -3/2

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Answer:

C

Step-by-step explanation:

the .1 is how much it increases per mile

so .10 a mile increase

Complete Question

In response to concerns about nutritional contents of fast foods, McDonald's has announced that it will use a new cooking oil for its French fries that will decrease substantially trans fatty acid levels and increase the amount of more beneficial polyunsaturated fat. The company claims that only 3 out of 100 people can detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion), what is the approximate probability that in a random sample of 1000 individuals who have purchased fries at McDonald's, at least 40 can taste the difference between the two oils? (2.5 pts.)

Answer:

The probability is  \(P(\^ p \ge 0.04 ) = 0.03216\)

Step-by-step explanation:

From the question we are told that

   The population proportion is  \(p = \frac{3}{100} = 0.03\)

    The sample size is  n  = 1000

 Generally the mean of this sampling distribution is  \(\mu_{x} = 0.03\)

Generally the standard deviation of this sapling distribution is  mathematically evaluated as  

        \(\sigma = \sqrt{\frac{p (1 - p)}{n} }\)

=>      \(\sigma = \sqrt{\frac{0.03 (1 - 0.03)}{1000} }\)

=>      \(\sigma = 0.0054\)

Generally the sample proportion when the number of those that can taste the difference is 40  is mathematically represented as

      \(\^ p = \frac{40}{1000} = 0.04\)

Generally the approximate probability that in a random sample of 1000 individuals who have purchased fries at McDonald's, at least 40( \(\^ p = 0.04\)) can taste the difference between the two oils is mathematically represented  as

     \(P(\^ p \ge 0.04 ) = 1 - P(\^ p < 0.04 )\)

Here

      \(P(\^ p < 0.04 ) = P(\frac{ \^ p - \mu_{x}}{\sigma } < \frac{0.04 - 0.03}{0.0054} )\)

\(\frac{\^ p -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \^ p )\)

=>   \(P(\^ p < 0.04 ) = P(Z < 1.85 )\)

From the z table the probability of  (Z < 1.85  ) is

      \(P(Z < 1.85 ) = 0.96784\)

So

    \(P(\^ p < 0.04 ) = 0.96784\)

So

   \(P(\^ p \ge 0.04 ) = 1 - 0.96784\)

=> \(P(\^ p \ge 0.04 ) = 0.03216\)

To solve this equation, we can follow the next steps:

First

Subtract - x from each side of the equation:

x - x -2y = 12 - x

x

Answer:

78°

Step-by-step explanation:

angle on a straight line : 180° - 126° = 54°

Therefore, 48° + 54° = 102°

total angle in a triangle = 180°

So, 180° - 102° = 78°

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Recall that proportion is partitive if the word problem can be modeled by an equation of the form:

Where k is a constant. The above equation means that as one variable increases the other one increases too.

In the case of inverse proportion, when one varibale

Answer:

34 degrees

Step-by-step explanation:

The equation that represents this situation is

2t - 7 = 61

to solve, start by adding 7 to both sides

2t = 68

then divide both sides by 2

t = 34

Answer:

(x-3)^2+(y-4)^2=6^2

Step-by-step explanation:

(x-3)^2+(y-4)^2=6^2

Answer:

x = 5 - 2a

Step by step explanation:

2x + 4a = 10

So, 2x = 10 - 4a

=> x = (10 - 4a)/2

=> x = 5 - 2a

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Thank you.

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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the graph of the equation y = 2 x - 2 is being obtained.

We are given the equation:

y = 2 x - 2

We need to make the graph of the equation.

We will first find some points on this equation:

x              y

0             -2

1               0

2              2

3              4

4              6

5              8

Now, we will plot these points on the graph and join them with a dark line to obtain the graph of the equation y = 2 x - 2.

Therefore, the graph of the equation y = 2 x - 2 is being obtained.

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Answer:

x = 11

Step-by-step explanation:

23 = 3x-10

1. Add 10 to both sides of the equation. -10 plus 10 is equal to zero so it cancels out to nothing, and 23 plus 10 is 33.

2. The new equation is now 33 = 3x.

3. Now you want to divide both sides by 3 to make x by itself since that is what you are trying to solve for.

4. 33/3 is equal to 11 so x = 11.

The value of the unknown number is 11

Inequality is a concept in mathematics that shows the comparison between two non-equal numbers.

From the given information

∴

3x - 10 = 23

Collect like terms

3x  = 23 + 10

3x = 33

Divide both sides by 3

\(\mathbf{\dfrac{3x}{3}= \dfrac{33}{3}}\)

x = 11

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Answer:

49b^10 -16b^2

Step-by-step explanation:

(7b^5)^2 -(4b)^2=

49b^10 - (4b)^2=

49b^10 - 16b^2

The given expression is equivalent to 49b¹⁰ - 16b².

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

(7b⁵ - 4b) (7b⁵ + 4b)

We have to expand this.

(7b⁵ - 4b) (7b⁵ + 4b) = (7b⁵ × 7b⁵) - (4b × 7b⁵) + (4b × 7b⁵) - (4b × 4b)

                                = 49b¹⁰ - 28b⁶ + 28b⁶ - 16b²

                                = 49b¹⁰ - 16b²

Hence the given expression is equivalent to 49b¹⁰ - 16b².

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Answer:

There is a difference of 10%

Step-by-step explanation:

In this situation, the theoretical probability, the probability of something based on logic, is 10%. This means that if the spinner was spun 10 times it would land on 1 once. However, the experimental probability, the probability determined by the results of an experiment, is 20%. This number can be found by finding how many times the spinner actually landed on 1. Out of 5 spins, the spinner landed on 1 once. So the experimental probability is 1/5, which is equal to 20%. Therefore, there is a 10% difference in the prediction and simulation.

The domain and range of the function are {-4, -2, 0, 4} and {-3, -1, 0, 1} respectively.

The domain of the function is defined as the value of the independent function for which the function exist.

The range of the function is defined as the value of the dependent function for which the function exist.

From the given table, the domain are the values in the x-column which the range in the y-column are the values in the y-axis.

From the table, the domain are D = {-4, -2, 0, 4} while the range is R = {-3, -1, 0, 1}.

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Answer:

c=pie r squared is the equations and the answer is 50.27

Step-by-step explanation:

Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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Answer:

1.8

Step-by-step explanation:

divide

The three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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Answer:

smaller angle - 40.4 degrees

larger angle - 49.6 degrees

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Given:

Costing = $400

Simple interest = 6%

Finance charge = $48

Simple interest formula is:

For 2 year.

(b)

Monthly payment is:

Monthly payment is $18.66

Complete Question

The complete question is shown on the first  and second uploaded image

Answer:

a

  \(\= HK = \= t + \= u\)

b

  \(\= GL = \= s - \= t\)

c

\(\= JH = \= u + \= s\)

Step-by-step explanation:

Now looking at the diagram

Following the direction of the unit vectors \(\= u , \= s, \= t\)

     \(\= {HK} = \= {KI} + \= KL\)

=>   \(\= HK = \= t + \= u\)

And  

    \(\= GL = \= GH + \= GF\)  jjj

=>   \(\= GL = \= s - \= t\)

Also

    \(\= JH = \= JG + \= JI\)

=>  \(\= JH = \= u + \= s\)

Answer:

6 donuts

Step-by-step explanation:

total donut = 6 + 8 + 4

= 18

\( \frac{1}{3} \times 18 = 6\)

Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.