a police car is located 40 feet to the side of a straight road. a red car is driving along the road in the direction of the police car and is 200 feet up the road from the location of the police car. the police radar reads that the distance between the police car and the red car is decreasing at a rate of 80 feet per second. how fast is the red car actually traveling along the road? the actual speed (along the road) of the red car is feet per second

Given,

Total distance [tex]=2\frac{1}{2}[/tex] miles

You run 1/3 of that distance on a hill.

Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles

You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles

Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles

Given that of the new books the new books the new liberian ordered;

-1/3 are science

-2/5 are biography

Let s, b and f represent the fraction of science, biography and fiction of the new book.

substituting the values of s and b given;

Answer: x < -6

Step-by-step explanation:

1) Bring 1 to the other side

x/-2 > 3

2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative

x < -6

Answer:

X+1

Step-by-step explanation:

x+1

Answer:

11 times

Step-by-step explanation:

-99/-9=11

The temperature in salt lake city will be 0° Celsius.

Temperature tells us about the degree of hotness or coldness of a body. According to the thermodynamics, temperature is a measure of the average kinetic energy of the atoms or molecules in the system.

Given is Salt Lake City where it is 8˚ colder than it is in Houston.

The degree of coldness on Celsius scale increase as the temperature tends to negative values and degree of hotness on Celsius scale increase as the temperature tends to positive values. The temperature in Houston is 8° Celsius. Since, the temperature is 8 degrees colder, we will subtract 8° from the temperature value in Houston. Therefore, temperature in salt lake city will be -

T[S] = + 8 - 8 = 0° Celsius

Therefore,  the temperature in salt lake city will be 0° Celsius.

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The correct answer is 0.4834

There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.

The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14

The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.

The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.

p = 0.14

q = 1 - p = 1 - 0.14 = 0.86

n = 12

x = 2

We need to find: P( x < 2)

Fewer than 2 tornadoes means either 1 or 0 tornado. So,

P(x < 2) = P(x=0) + P(x=1)

the likelihood of less than two tornadoes occurring in a 12-year period is 0.4834

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Answer:

see explanation

Step-by-step explanation:

(a)

common ratio r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{28}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5

(b)

to find the next term, multiply the previous term by r = 0.5

14 × 0.5 = 7

7 × 0.5 = 3.5

3.5 × 0.5 = 1.75

the next 3 terms in the sequence are 7 , 3.5 , 1.75

⇒In a geometric sequence to find the common ratio(r) we use the formula

[tex]r=\frac{T_{2} }{T_{1} }[/tex]

But in general we use the formula is [tex]r=\frac{T_{n+1} }{T_{n} }[/tex]

In this case we are going to use

[tex]r=\frac{14}{28} \\r=\frac{1}{2}[/tex]

⇒The common ratio of the sequence is [tex]\frac{1}{2}[/tex], to get the 3 consecutive terms you are going to multiply the current term by the common ratio which in this case is [tex]\frac{1}{2}[/tex]

[tex]T_{3} =T_{2} * r\\\\T_{3}=14(\frac{1}{2} )\\T_{3} =7[/tex]

[tex]T_{4} =T_{3} *r\\T_{4}=7(\frac{1}{2} )\\T_{4}=\frac{7}{2}[/tex]

[tex]T_{5}=T_{4} *r\\T_{5}=\frac{7}{2} *\frac{1}{2} \\T_{5}=\frac{7}{4}[/tex]

If you have any questions ask me as soon as possible.

GOODLUCK!!

Answer:

x = 12

Step-by-step explanation:

3/4x = 9

x = 9/1(4/3)

x = 12

Answer:

Jenny owes her sister 9.3 dollars.

Step-by-step explanation:

23.63 - 16.33 = 9.3

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (1500)(0.07)(8) \implies I = 840[/tex]

Answer:

4x²+2x-30

Step-by-step explanation:

(x+3) 2(2x-5)

(x+3) (4x-10)

4x²-10x+12x-30

4x²+2x-30

Answer:

[tex]23+4x(2+5)<15-5x(8-7)]2^5[/tex]

Answer: 49 degrees

Step-by-step explanation:

130+99=229

229-180=49

49 degrees

180 degrees is a straight line

1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:

2) Based on that, we can do the following to find the next two terms:

Thus, the next terms are -5 and 2

The probability that the father and son will obtain a kill if they both fired at an animal the same time is 0.9

The probability of an event is the likelihood of the occurrence of event.

The average number of animals the father kills every 5 shots he takes = 2

The average number of animals the son kills every 2 shots he takes = 1

[tex]Probability = \dfrac{Number \ of \ required \ items}{Number \ of \ possible \ outcomes}[/tex]

Which gives:

The probability that the father kills an animal = [tex]P(F) = \dfrac{2}{5} = 0.4[/tex]

The probability that the son kills an animal is; [tex]P(s) = \dfrac{1}{2} =0.5[/tex]

The probability that if the father and the son fires at the same animal, the probability that they will obtain a kill, which is the probability that the animal is killed , P(A) = The probability that the father kills the animal + The probability that the son kills the animal

Which gives: P(A) = 0.4 + 0.5 = 0.9

The probability that the animal will be killed is approximately 0.9

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That's it, do you have any question about the answer? my ple

The probability of a head and an even number is 1/4.

Probability is the occurrence of a certain event out of the total events than can occur in a given context.

Given event is a coin is tossed and then a die is rolled.

∴ The sample space (S) is = (H,1), (T,1), (H,2), (T,2), (H,3),(T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6).

So, the number of sample spaces N(S) = 12.

The number of heads and an even number N(H,E) = 3.

∴ The probability of a head and an even number is = N(H,E)/N(S).

= 3/12.

= 1/4.

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Hello!

To evaluate h(3)

 ==> must plug '3' into x's position in the equation:

    [tex]h(3)=3^2-4(3)+5\\h(3)=9-12+5=2[/tex]

Hope that helps!

Answer:

2

Step-by-step explanation:

substitute 3 for the x

3²-4(3)+5

9-12+5

2

Answer:

d=12

Step-by-step explanation:

8d+4+6d+8 = 180 (Straight angle = 180)

14d+12=180

14d=168

d=12

:]

Answer:

D =12

Step-by-step explanation:

8d+4+6d+8 =180 (being a linear pair)

14d+12=180

14d=180-12

14d=168

d= 168/14

d=12#

The value of the absolute value expression given; | 1.1n | for n > 1 as required in the task content can be classified as; Choice B; >1.

It follows from the task content that the best classification of the expression | 1.1n | for n > 1 be determined.

Since the domain of variable n is such that n > 1, it follows that 1.1 × n > 1.1.

There, it follows that; 1.1n > 1.1 > 1.

By definition; The absolute value |n| of any real number n is the non-negative value of x irrespective of its sign. For instance, the absolute value of 15 is 15, and also the absolute value of −15 is also 5.

Hence, the absolute value sign; | 1.1n | indicates positive values.

Ultimately, the correct classification of.the expression is; Choice B; > 1.

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ok it literally shows on the figure the length of the side AC is 6x + 7.

Answer:

AC = 25 units

Step-by-step explanation:

since ∠ A and ∠ C are congruent then the 2 legs BC and AB are congruent

BC = AB ( substitute values )

7x - 1 = 5x + 5 ( subtract 5x from both sides )

2x - 1 = 5 ( add 1 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Then

AC = 6x + 7 = 6(3) + 7 = 18 + 7 = 25

Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

[tex]f(x) = 2000(1+0.05)^{x}[/tex]

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

Answer: ask your teacher

Step-by-step explanation:u have to multiply

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-5}x-14\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {-5\implies \stackrel{slope}{\cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5}\implies \cfrac{1}{5}}}[/tex]

so we're really looking for the equation of a line whose slope is 1/5 and it passes through (10, -4)

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \implies {\large \begin{array}{llll} y +4= \cfrac{1}{5} (x -10) \end{array}}[/tex]

The solution to the equation is x = 5.24

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

(x - 3)^2 = 5

Take the square root of both sides

So, we have

x - 3 = 2.24

Add 3 to all sides of the equation

So, we have

x = 5.24

Hence, the solution is x = 5.24

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