Jai left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Jai is xx minutes after he left his house, until he got back home. How many blocks is it from the store to the bank?

The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.

Let:

x be  the distance from the bottom of the ladder to the base of the wall

y  be the distance from the top of the ladder to the bottom of the wall

When the ladder is still, apply the Pythagorean Theorem,

x² + y² = 13²

5² + y² = 13²

y² = 169 - 25 = 144

y = 12 ft

When the ladder slides, apply the differential equation:

x² + y² = 13²

2x . dx/dt + 2y . dy/dt = 0

Substitute x = 5, dx/dt = 1, y = 12

2 . 5 . 1 + 2 . 12 . dy/dt = 0

24 dy/dt = -10

dy/dt = -5/12 = - 0.417 ft/s

The minus sign indicates that the ladder is sliding downward.

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The function that can be used to represent the total amount that will be paid for the room is 100 + 55h.

A function simply means the expression that. an be used to show the relationship between the variables or the data given.

In this case, the interior designer charges $100 to visit a site, plus $55 to design each room.

Let the number of rooms be represented as r.

The function that represents the total amount will be:

= 100 + (55 × h)

= 100 + 55h

This illustrates the concept of functions.

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the number of sales by b must be 150 to make the same amount of salesman B.

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.

given that :

Salesman A gets paid $300 a month plus $8 for every sale he makes :

let the no. of sales A made be : x

then, in order to make the same amount of salesman b we equate btoth the amount :

300 + 8x = 1500

8x = 1500-300

8x = 1200

x = 1200/8

x = 150

Therefore, the number of sales by A must be 150 to make the same amount of salesman b.

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The perimeter of the given triangle is the sum of the following segments:

Perimeter = PD + DO + OP

based on the given graph, you have that the coordinates of the points PDO are:

P: (1,-6)

D: (4,3)

O: (7,-6)

use the following formula for the distance in between two points:

d = √((x2 - x1)²+(y2 -y1)²)

where (x1,y1) and (x2,y2) are two points on the cordinate system.

For segement PD you have:

PD = √((1-4)²+(-6-3)²) = √(100) = 10

For segemtn DO:

DO = √((4-7)²+(-6-3)²) = √(100) = 10

For segment OP:

OP = √((1-7)²+(-6+6)²) = √36 = 6

then, the perimeter of the triangle is:

perimeter = 10 + 10 + 6 = 26

Answer:

21

Step-by-step explanation:

120*7/10= 84  french
15 are chinese
84+15=99
120-99=21

Answer:

21

Step-by-step explanation:

Answer: 48 ft

Step-by-step explanation:

The height gap between the balloons is 60 -40 = 20 feet. That gap is being closed at the rate of 2 + 3 = 5 ft/s, so will be gone in ...

 (20 ft)/(5 ft/s) = 4 s

At that time, the red balloon will have risen (2 ft/s)(4 s) = 8 ft to a height of ...

 40 ft +8 ft = 48 ft

The blue balloon will have descended (3 ft/s)(4 s) = 12 ft to a height of ...

 60 ft -12 ft = 48 ft

The balloons at at 48 ft when they are both the same height.

_____

Time and speed and distance are related by the formula you see on every speed limit sign:

 speed = distance/time . . . . . . . (on the sign, it's "miles per hour")

or

 time = distance/speed

or

 distance = speed × time

_____

If you want equations, you can write them as ...

 h = 40 +2t

 h = 60 -3t

where h is the altitude the balloons have when they are at the same height, and t is the number of seconds it takes to get there.

We're only interested in h, so we can cancel t by multiplying the first equation by 3 and adding that to the second equation multiplied by 2:

 3(h) + 2(h) = 3(40 +2t) +2(60 -3t)

 5h = 120 +6t +120 -6t

 h = 240/5 = 48 . . . . the height in feet at which the balloons are the same height

Volume of a cone is given by;

From the queston,

h = 414

diameter = 416, this implies r = d/2 = 416/2 = 208

π = 3.14

substitute the values into the formula

We want to know what's the probability of spinning a number greater than two

There are 2 spinnings greater than two, of a total of 8. therefore, the probability I will be

The probability is 1/4

Answer:

C (0,3)

Step-by-step explanation:

Plot the two equations and the points.  See the attached graph.  The blue area reflects the inequality of y+3x<=8:  many points satisfy this equation and they are all blue.

The red line is equation y-3=x.  There is only one point on this line that is also in the blue area:  (0.3).  The other three points (A, B, and D) do not satisfy either equation.  The metric term for them is losers.

The two consecutive odd integers are -7 and -5, then the greater integer is -5.

Let's say that the smaller integer is x and the larger one is y.

Such that if both of these are odd and consecutive, then y = 2 + x.

We can now write:

8*y - x = -33

Replacing y by x + 2 we get:

8*(x + 2) - x = -33

8x + 16 - x = -33

7x = -33 - 16  = -49

x = -49/7 = -7

that is the smaller integer, then the next one is:

y = x + 2 = -7 + 2 = -5

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The required value of the greater integer among the two consecutive odd integers is - 5.

An integer is a real number that has no decimal part.

suppose we have specified a particular odd no. 'O' then the consecutive odd integers are those numbers that arrive after every two numbers.

Given, an integer is subtracted from 8 times the next consecutive odd integer, the difference is -33.

Assuming the first odd integer to be 'n'.

So, the next consecutive odd integers are (n + 2), (n + 4)...

∴ 8(n + 2) - n = - 33.

8n + 16 - n = - 33.

7n = - 33 - 16.

7n = - 49.

n = - 49/7.

n = - 7.

So, the two integers are -7 and (-7 + 2) = - 5.

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The factors of the given monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The factors of the monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The midpoint of (-2, 11) and (18, -1) is:

Point (8,5)

EXPLANATION

Replacing the given functions into the following:

Removing the parentheses and simplifying:

Simplifying like terms:

Hence,

Answer:  1 1/2x−1 3/4

Step-by-step explanation: i took the test on k12

The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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Wherever you see the letter [tex]x[/tex] in the equation, you write [tex]4[/tex], [tex]0[/tex] or [tex]-4[/tex] and perform arithmetic operations. Good luck!

Answer:

p(-1) = 7

p(2) = -2

Step-by-step explanation:

We have p(x) = 4 - 3x

p(-1) = 4 - 3(-1) = 4 + 3 = 7

p(2) = 4 - 3(2) = 4 - 6 = -2

The proper test statistic has a value of 13.21.

As a result, repeated measurements of cholesterol levels from the same blood sample are taken to assess a lab technician's consistency.

The desired accuracy is a measurement variance of 2.78 or less. In the event that the lab technician conducts 16 measurements, and the sample's measurement variance is 2.45.

1) n=16 samples were used.

The desired accuracy is a measurement variance of 2.78 or less.

The sample's measurements' variance is 2.45 or less.

We list both the null and alternative hypotheses in response to the query.

Null hypothesis [tex]H_{0}[/tex] = [tex]var^{2} \geq[/tex]  2.78

Alternative hypothesis [tex]H_{a}[/tex] = [tex]var^{2} <[/tex]  2.78

We claim the alternative hypothesis.

2)Calculate the appropriate test statistic's value.

Using Chi-square,

X= ((n-1)(2.45)/(2.78)

X= 15(2.45)/(2.78)

X=36.75/2.78

X= 13.21

Therefore, The value of the appropriate test statistic is 13.21

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Answer: Well, yes. It's more like p = s + s + s + s. "S" = side. "P" = perimeter.

So, this is theoretically true if your variable for a side just happened to be "n".

You also put, "The perimeter of a square", A simpler way to put this is

P = s4   or in your case P = n4.

Because this shape is a square all side lengths and angles will be congruent, and therefore will all be the same (which is why we are able to multiply one side by four.)

Hope this helps. :)

Answer: I'm not sure what your options are, but a line the passes through -3,1, and is parallel to y=4, would be y=1

Step-by-step explanation:

We paint with:

• red the regions where the function is decreasing,

• green the regions where the function is increasing.

From the graph, we see that the function is:

• decreasing in the intervals (-∞, -1.5) and (2, ∞),

• increasing in the interval (-1.5, 2).

Answer

• Increasing on the interval(s): ,(-∞, -1.5), (2, ∞)

• Decreasing on the interval(s): ,(-1.5, 2)

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

With this in mind we conclude that:

There are 8 values in the data set which are greater than or equal to 20 and less than or equal to 29. This comes from the fact that we have to count how many leafs are in the stem 2.

There are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. This comes from the fact that we have to count how many leafs are in the stem 1.

There are 14 values in the data set which are greater than or equal to 40 and less than or equal to 49. This comes from the fact that we have to count how many leafs are in the stem 4.

Answer:

6

Step-by-step explanation:

Trust

Answer:

[tex](f \circ g)(2)=2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-2x+8\\g(x)=\sqrt{x+7}\end{cases}[/tex]

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(2) means to substitute the result of g(2) in place of the x in the function f(x).

[tex]\begin{aligned}\implies (f \circ g)(2) &=f[g(2)]\\&=f(\sqrt{2+7})\\&=f(\sqrt{9}) \\& = f(3)\\& = -2(3)+8\\&=-6+8\\&=2\end{aligned}[/tex]

Given the question

To resolve this, we can follow the steps below

Step1: Apply the logarithm rule

This will give=>

Since we have been given that

Step2: Substitute the given values into the equation

=>

Answer = 13

Answer:

y > -1

Step-by-step explanation:

8y+9 > 1

   -9    -9

8y > -8

/8    /8

y > -1

Answer: The slope is -0.7, the rise is -1.4, and the run is 2

Answer:

D. Negative

Step-by-step explanation:

Always read the graph from left to right

The graph is going down thus it is negative

Answer: Negative.

Step-by-step explanation: The graph of the line falls from left to right which makes it negative.

Answer:

  20 cm

Step-by-step explanation:

Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.

The missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:

  b² = c² +a²

  10² = 8² +a² . . . . . . . use given lengths

  a² = 100 -64 = 36 . . . . subtract 8², simplify

  a = 6 . . . . . . . . . . . . . length of side BC

The area of the right triangle base is ...

  A = 1/2bh . . . . . . . . b is the triangle base; h is its height

  A = 1/2(6 cm)(8 cm) = 24 cm²

The volume of the prism is ...

  V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height

  480 cm³ = (24 cm²)h . . . use known values

  h = 20 cm . . . . . . . divide by the coefficient of h

The height of the prism is 20 cm.

The most appropriate choice for ascending order will be given by-

[tex]-\sqrt{25}[/tex], 4.79, [tex]4\frac{19}{28}[/tex], [tex]4.\bar{8}[/tex] is in ascending order

What is ascending order?

Suppose there is a series of numbers. The numbers will be in ascending order if the numbers are arranged from their least value to their greatest value.  

The sorting of numbers in ascending order plays a very important role in statistics for calculation of median, quartiles, decile and percentile.

Here,

4.79 = 4.79

[tex]4\frac{19}{28} = 4 + \frac{19}{28} = 4.68\\[/tex]

[tex]4,\bar{8} = 4.8888..... = 4.89[/tex]

[tex]-\sqrt{25} = -5[/tex]

-5< 4.68< 4.79< 4.89 is in ascending order

So, [tex]-\sqrt{25}[/tex]< [tex]4\frac{19}{28}[/tex]< 4.79, [tex]4.\bar{8}[/tex] is in ascending order.

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