two people start from the same point. one walks east at 4 mi/h and the other walks northeast at 5 mi/h. how fast (in mi/h) is the distance between the people changing after 15 minutes? (round your answer to three decimal places.)

The standard form of the line that contains a slope of -3/2 and y-intercept of 6 is y = (-3/2)x + 6.

The slope intercept form of a line is:-

y = mx + c

Where,

m represents the slope of the line,

(x,y) represents the ordered pair of coordinates of each point on the line, and

c is the y-intercept

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

Hence, we have,

m = -3/2

c = 6

Hence, the standard form of the line that contains a slope of -3/2 and y-intercept of 6 is given by:-

y = (-3/2)x + 6

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Answer:

b

Step-by-step explanation:

angle 3 and angle 6 are alternate interior angles which makes the congruent

This is the right response: T F- F.

What is the explanation:

If the answer to the following question is p, then 2 + 2 = 4.

which is accurate, meaning that this statement has a truth value of True.

The following assertion q illustrates q: 7 + 1 Equals 7.

This is untrue, making the statement's truth value Untrue

As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.

The truth table reveals that the truth value of pq will be False

So T F → F

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From the given quadratic function, it is found that:

a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.

b) The number of bacteria will be minimal for a temperature of 0.5 ºC.

c) The minimum number of bacteria is of 115.

d) The graph that models the situation is sketched at the end of the answer.

The quadratic function is given as follows:

N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.

In which:

The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.

For a concave up quadratic function, the minimum value happens when the input is of:

Tm = -b/2a.

For this problem, the coefficients of the quadratic function are as follows:

b = -20, a = 20.

Hence the temperature in which the number of bacteria will be minimal is of:

Tm = 20/40 = 0.5 ºC.

The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:

N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.

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the whole answer to the differential equation used to model the statement. The relationship between the rate of change of n and n is (dN/dt)=kN.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

According to given data;

The derivative of N with respect to t, or (dN)/(dt), represents the rate of change of N.

dN/dt = kN, where k is the proportionality constant, if the rate of change of N is proportional to N. We must solve this differential equation.

To solve it, separate the variables:

(dN)/N = kdt

Integrating both sides results in

ln N = kt + C , where C is another constant.

This can be rewritten in exponential form as

N = e^(kt + C)

= N_0e^(kt) .

Here, N_0 = e^C

and it equals N(t) when t = 0.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{3}{4} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Slope (m) of a line can be calculated by using this formulae :

[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]

Considering two points [ (10 , 10) and (50 , 40) ]

[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{40 - 10}{50 - 10} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{30}{40} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{3}{4} [/tex]

So, slope of given line is 3/4

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

To find the slope of a graph you need to look for 2 pairs of accurate xand y values

First value which is accurate is:

x = 10 and y= 10

Second pair which is accurate is :

x = 50 and y = 40

Gradient = rise/run = y2-y1/x2-x1

im taking y2 as 40, x2 as 50, y1 as 10 and x1 as 10

40-10/50-10

= 30/40

=3/4

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The number of groups of 5/7 that are in 1 is 1 2/5.

when 8 is divided by 5/7, the quotient is 11 1/5.

A proper fraction is a non-integer in which the numerator is less than the denominator. The numerator is the number above and the denominator is the number below. An example of a proper fraction is 5/7.

In order to determine the groups of 5/7 are in 1, divide 1 by 5/7. Division is the process of determining the quotient of two or more numbers.  Division is the process of grouping a number into equal groups using another number.  The sign that denotes division is ÷.

1 ÷ 5/7

1 x 7/5 = 7/5 = 1 2/5

8 ÷ 5/7

8 x 7/5 = 56 / 5 = 11 1/5

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2.622e+14

                                                    OR

262200000000000x^2

Answer:

2.622e+14

Step-by-step explanation:

10^8=100000000

100000000x3.8=380000000

10^5=100000

100000x6.9= 690000

380000000x690000= 2.622e+14

The line segment NO of the triangle MNO, that is similar to the triangle QRS, has a length of 25 meters.

In this problem we have a system of two similar triangles. Two triangles are proportional when the sides of a triangle are proportional to the corresponding sides of the other triangle. Herein we find the following relationship:

MN / QR = NO / RS = MO / QS

If we know that QR = 1 m, MN = 5 m and RS = 5 m, then the length of the line segment NO is:

NO = (MN / QR) · RS

NO = (5 m / 1 m) · 5 m

NO = 25 m

The line segment NO has a length of 25 meters.

There is a typing mistake in the statement, correct form is introduced below:

Given ΔMNO and ΔQRS are similar triangles. If QR = 1 meters, MN = 5 meters and RS = 5 meters. What does line NO equal to?

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Isaac's statement that T will be located at (4, 20) is correct

The coordinates of the triangle are given as

V (2,2) U(6,2) T(2,10)

The transformation is given as

Scale factor of 2, across the origin

The transformation can be described by (x, y) --> (2x, 2y)

There are four types of transformation, and they are:

The representation of the types of transformation are:

By comparing the rules of the above types of transformation, we have

(x, y) --> (2x, 2y)

For point T, we have

(2, 10) --> (2 x 2, 2 x 10)

Evaluate

(2, 10) --> (4, 20)

When the above is compared to the student's result, we have

Isaac = (2, 10) --> (4, 20)

Hence, the correct statement about the transformation is Isaac's statement is correct

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Answer:

B

Step-by-step explanation:

When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.

Based on the number of batches of cupcakes, the pounds of sugar in each batch can be found to be 3 / 16 pounds

Find out more below

The total number of pounds of sugar that Polly used was 15/16 pounds of sugar and she used these to make 5 batches of cupcakes.

Each of this batches of cookies used the same amount of sugar so the amount of sugar per batch of cookie is:

= Total number of pounds of sugar used / Number of batches of sugar

Solving for the pounds of sugar gives:

= 15/16 ÷ 5

= 15/16 x 1/5

= 15 / 80

= 3 / 16 pounds

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Answer:

Using inverse operations to isolate teh variable 'X'.

Step-by-step explanation:

THE FIRST STEP IS TO MULTIPLY EACH AND EVERY TERM IN THE BRACKETS BY 5

[tex]5(2x) + 5(7) - 15 = 15 \\ 10x + 35 - 15 = 15[/tex]

THEN GROUP THE LIKE TERMS TOGETHER. WHEN TERMS MOVE ACROSS THE EQUAL SIGN THEY CHANGE SIGNS.

[tex]10x = 15 - 35 + 15 \\ 10x = - 5[/tex]

[tex] \frac{10x}{10} = \frac{ - 5}{10} \\ x = \frac{ - 5}{10} \\ x = - \frac{1}{2} [/tex]

ATTACHED IS THE SOLUTION

Answer:

false

Step-by-step explanation:

The missing statements in the given paragraph proof are:

1)  corresponding angle postulate

2) angles 3 and 1

3) transitive property of parallel lines

In this question, we have been given  a paragraph proof.

we need to complete this proof.

We have been given L || K and M || K

To prove: L || M

Since L || K, ∠2 ≅ ∠1 by the corresponding angle postulate

Since M || K, angles 3 and 1 are congruent for the same reason.

By the transitive property of congruence, ∠2 ≅ ∠3

By the transitive property of parallel lines, L || M

Therefore, the missing statements in the given paragraph proof are:

1)  corresponding angle postulate

2) angles 3 and 1

3) transitive property of parallel lines

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The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.

The graph of the solution is shown below.

From the question, we are to solve the given inequalities

The given inequalities are

3 < 2p - 3 ≤ 12

We will solve  the inequalities separately

That is

3 < 2p - 3  and 2p - 3 ≤ 12

Solve 3 < 2p - 3

3 < 2p - 3

3 + 3 < 2p

6 < 2p

6/2 < p

3 < p

Solve 2p - 3 ≤ 12

2p ≤ 12 + 3

2p ≤ 15

p ≤ 15/2

p ≤ 7.5

Hence,

Joining the two solutions together, the solution is 3 < p ≤ 7.5.

The graph is shown below.

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When two dice are rolled one time, the probability of getting a sum of 11 is 1/18.

From the information, two dice are rolled one time. There are 6 different possibilities and the outcomes of rolling the dice will be:

= 6 × 6 = 36

It should be noted that the sum of 11 can be gotten as (6, 5) and (5, 6). That's 2 out of 36.

Therefore, the probability will be:

= 2 / 36

= 1 / 18

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well, first off let's convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}}[/tex]

now, let's use proportions to bind the sugar and flour that she'll be using, now if she were to use the 9 cups of flour, let's see how much will that be in sugar for this recipe

[tex]\begin{array}{ccll} \stackrel{cups}{sugar}&\stackrel{cups}{flour}\\ \cline{1-2} \frac{4}{3}&\frac{9}{4}\\[1em] S&9 \end{array}\implies \cfrac{~~ \frac{ 4}{3 } ~~}{S}~~ = ~~\cfrac{~~ \frac{ 9}{ 4} ~~}{9}\implies \cfrac{~~ \frac{ 4}{3 } ~~}{\frac{S}{1}}~~ = ~~\cfrac{~~ \frac{ 9}{ 4} ~~}{\frac{9}{1}}\implies \cfrac{4}{3S}=\cfrac{1}{4} \\\\\\ 16=3S\implies \cfrac{16}{3}=S\implies \boxed{ {\Large \begin{array}{llll} 5\frac{1}{3}=S \end{array}}}[/tex]

now, we know that 9/4 cups of flour gives Liz 18 muffins, well hell  how many for 9 cups of flour then?

[tex]\begin{array}{ccll} \stackrel{cups}{flour}&muffins\\ \cline{1-2} \frac{9}{4} & 18\\[1em] 9& M \end{array} \implies \cfrac{~~ \frac{ 9}{4 } ~~}{9}~~=~~\cfrac{18}{M}\implies \cfrac{~~ \frac{ 9}{4 } ~~}{\frac{9}{1}}~~=~~\cfrac{18}{M} \\\\\\ \cfrac{1}{4}=\cfrac{18}{M}\implies \boxed{M=72}[/tex]

The number of years when Dylan would have over £3,600 in his account is 18 June, 2021.

The time that If the account earns interest every 3 months, it means that the value increases quarterly or 4 times a year. The account would increase at an exponential rate. This means that both the amount invested and the interest that has already been earned would increase in value 4 times a year.

The formula that can be used to determine the time is:

Time = In(FV / PV) / r

Where:

FV = future value

PV = present value

r = interest rate

t = In (£3,600 / £3,000) / 0.0102

t = In 1.2 / 0.0102 = 17.87 / 4 = 4.468 years

4 years = 2017 + 4 = 2021

0.468 x 12 = 5.616 months

January + 5 months = June

0.616 x 31 = 19 days

18 June, 2021

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The unknown length is 28. the values of the six trigonometric functions for angle b that is tan B = 7/24

From the question,

we are given

a = 96 and c = 100, to get the unknown side 'b',

we will substitute the given values into the formula above;

c² = a²+b²

100²  = 96² +b²

b²  = 100²  - 96²

b²  = 10,000 - 9216b²

= 784b = √784b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity.

According to TOA,

tan B = opposite/adjacenttan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given, b = 28 and a = 96tan B = 28/96tan B = 4*7/4*24

tan B = 7/24

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The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Answer: So think of x to y cordinents. You have reguler numbers and negitive numbers where would you but the regulear numbers? and where would you put the negitve numbers? So what is range? Range is yo subtracting the largeest number form the littlest number.

Step-by-step explanation:

Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t. The x-intercept of the equation is (8,0). After 8 hours, Riley battery has no charge left in it ( since Riley left her house).

Given that,

Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t, where t is the number of hours since Riley left her residence, can be used to predict the percentage of charge still in Riley's battery.

We have to find what is the equation's x-intercept and how is it interpreted in the problem's context.

The equation B=40-5t can be used to model Lauren's battery charge remaining as a percentage when t is the number of hours since she left her home.

Put B = 0 to determine the x-intercept. (In this case, the independent variable is "t," as x signified the independent variable).

0=40-5t

5t=40

t=40/5

t=8

Therefore, the x-intercept of the equation is (8,0).

After 8 hours, Riley battery has no charge left in it ( since Riley left her house).

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Answer:

Obviously yes...

Step-by-step explanation:

Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.

Answer: =16

Step-by-step explanation:

 X-5=11

⇒X=11+5=16

⇒X=16

Answer: Where is the question I can help if you put in the question.

Step-by-step explanation:

Answer:

12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]

Step-by-step explanation:

the second term should not be -8x, it should be -8[tex]x^{4}[/tex]

The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex])  is 8 but then we add the exponents 2 + 2 = 4

Answer:

Step-by-step explanation:

B

Answer: 8

Step-by-step explanation:

180 degrees in a triangle, so 180 - 92 - 48 = 40

So, the missing angle is 40, which is equal to 5t, so

40 = 5t

t = 8