The expression is 3 (x+4)-(2x+7) what is that equivalent too

Answer:

A president, a vice president, and a secretary can be selected in 60 ways.

Step-by-step explanation:

The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

3 students from a set of 5, so:

[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]

A president, a vice president, and a secretary can be selected in 60 ways.

Answer:

[tex]\displaystyle 51[/tex]

General Formulas and Concepts:

Algebra I

Algebra II

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

-3w-6p when w=2 and p=-7

-3(2)-6(-7)

= -6 + 42

= 36

Answer:

48

Step-by-step explanation:

-3w-6p when w=2 and p--7

you want to plug in the numbers to their letters

-3(2)-6(-7)

then you want to times the numbers.

-6-42

=48

Answer:

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]

Step-by-step explanation:

Given

[tex]8x^{-10}y^6 - 2x^2y^{-8}[/tex]

Required

Simplify

Rewrite as:

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6}{x^{10}} - \frac{2x^2}{y^8}[/tex]

Take LCM

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6*y^8 - 2x^2 * x^{10}}{x^{10}y^8}[/tex]

Apply law of indices

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]

9514 1404 393

Answer:

  (f -g)(x) = |2x +3| -12

Step-by-step explanation:

The difference of the functions is ...

  (f -g)(x) = f(x) -g(x) = |2x +3| -5 -7

  (f -g)(x) = |2x +3| -12

Answer:

35

Step-by-step explanation:

y = 35x+23 is in the form

y = mx+b  where m is the slope and b is the y intercept

The slope can also be called the rate of change

35 is the slope

Answer:

To obtain a "B", Rita needs to score between 76.7 and 100.

Step-by-step explanation:

Chapter tests mean:

[tex]M = \frac{70 + 76 + 86 + 87 + 85}{5} = 80.8[/tex]

Grades:

80.8 worth 60% = 0.6

85 worth 10% = 0.1

x worth 0.3.

So her grade is:

[tex]G = 80.8*0.6 + 85*0.1 + 0.3x = 56.98 + 0.3x[/tex]

What scores can Rita earn on the final  exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90?

G has to be greater than or equal to 80 and less than 90, so:

[tex]80 \leq G < 90[/tex]

Lower bound:

[tex]G \geq 80[/tex]

[tex]56.98 + 0.3x \geq 80[/tex]

[tex]0.3x \geq 80 - 56.98[/tex]

[tex]x \geq \frac{80 - 56.98}{0.3}[/tex]

[tex]x \geq 76.7[/tex]

Upper bound:

[tex]G < 90[/tex]

[tex]56.98 + 0.3x < 80[/tex]

[tex]0.3x < 90 - 56.98[/tex]

[tex]x < \frac{90 - 56.98}{0.3}[/tex]

[tex]x < 110[/tex]

Highest grade is 100, so:

To obtain a "B", Rita needs to score between 76.7 and 100.

9514 1404 393

Answer:

  -2/3

Step-by-step explanation:

The slope of the given line can be found by solving for y.

  2y -3x = 8

  2y = 3x +8 . . . . add 3x

  y = 3/2x +4 . . . . divide by 2

The slope is the coefficient of x: 3/2. For the perpendicular line, the slope is the opposite reciprocal of this:

  -1/(3/2) = -2/3

The slope of a perpendicular line is -2/3.

Answer:

Following are the response to the given question:

Step-by-step explanation:

For question 1:

Following are the regression equation:

[tex]price = 2044.03 - 28.35 \ \ (weight)[/tex]

[tex]\sigma = 94.353\\\\R^2 = 0.7647\\\\R^2\ (adj.) = 0.75\\\\[/tex]

For question 2:

Test of connection importance at 5 percent significance:

[tex]p-value < 0.000001\\\\p-value< 0.05[/tex]

Two variables could be said to be connected.

For question 3:

[tex]R^2 = 0.7647[/tex]

The computed equations of the regression fit well.

Answer:

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Step-by-step explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

[tex]V(x,y)[/tex] - Original point.

[tex]V'(x,y)[/tex] - Translated point.

[tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:

[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]

[tex]A'(x,y) = (3, 0)[/tex]

[tex]B'(x,y) = (0,1) + (6, -4)[/tex]

[tex]B'(x,y) = (6, -3)[/tex]

[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]

[tex]C'(x,y) = (2, -3)[/tex]

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Answer:

In picture.

Step-by-step explanation:

To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.

The picture below is the answer.

Answer:

C

Step-by-step explanation:

The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

Answer:

A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

Step-by-step explanation:

Answers:

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

Explanation:

Imagine that we have point A as a buoy in the water. So the horizontal line through 1 on the y axis is the water line. How much should the water line go up so that points A and B are on the same horizontal level? That would be 1 unit up. This is the vertical change. Another term for this is "rise".

After the water goes up, and A and B are on the same level, the question is now: how far to the right do we go from A to B? That would be 2 units. This is the horizontal change. Another term for this is "run".

Using those two values, we can compute the rate of change aka slope.

slope = rise/run = 1/2 = 0.5

So each time we go up 1 (rise) we move to the right 2 (run).

The slope is positive since we're moving uphill while moving to the right.

Answer:

BẠN BỊ ĐIÊN À

Step-by-step explanation:

CÚT

Answer:

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this question:

We have to derivate V and r implicitly in function of time, so:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 3 mm/s.

This means that [tex]\frac{dr}{dt} = 3[/tex]

How fast is the volume increasing when the diameter is 60 mm?

Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

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Answer:

  9

Step-by-step explanation:

The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.

The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.

Then the sum is ...

  (F+G)(2) = F(2) +G(2) = 4 +5

  (F+G)(2) = 9

Answer: Commutative Property of Addition

Explanation: The problem 3 + 2 = 2 + 3 demonstrates the commutative property of addition. In other words, the commutative property of addition says that changing the order of the addends does not change the sum.

For example here, we can easily see that the sum of 3 + 2,

which is 5, is equal to the sum of 2 + 3, which is also 5.

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

Answer:

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{0.61}{\sqrt{103}} = 0.2[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 98.5 - 0.2 = 98.3ºF.

The upper end of the interval is the sample mean added to M. So it is 98.5 + 0.2 = 98.7ºF.

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.

Answer:

The answer is 17

Step-by-step explanation:

-15-2= -17

Answer:

The slope of this line is 1 and the equation for the line is y=x+1

Step-by-step explanation:

So take 2 points passing through the the line (0,1), (-1,0)

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=1.

Also, let's call the second point you gave, (-1,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m=

0 - 1

-1 - 0

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,1). When x of the line is 0, y of the line must be 1.

(-1,0). When x of the line is -1, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=x+b. b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,1) and (-1,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,1). y=mx+b or 1=1 × 0+b, or solving for b: b=1-(1)(0). b=1.

(-1,0). y=mx+b or 0=1 × -1+b, or solving for b: b=0-(1)(-1). b=1.

In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,1) and (-1,0)

is

y=x+1

Answer:

where is the question? please attatch the angle

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]4=6+2x[/tex]

Flip the equation:

[tex]2x+6=4[/tex]

Subtract 6 from both sides:

[tex]3x+6-6=4-6[/tex]

[tex]2x=-2[/tex]

Divide both sides by 2:

[tex]2x/2=-2/2[/tex]

[tex]x=-1[/tex]

Answer:

x= -1

Step-by-step explanation:

firstly group the like terms

4-6=2x

-2=2x

divide both sides by 2

-2/2=2x/2

-1=x

therefore x is -1

Answer:

25/3 ft/s

Step-by-step explanation:

Height of pole , h=15 ft

Height of man, h'=6 ft

Let BD=x

BE=y

DE=BE-BD=y-x

All right triangles are similar

When two triangles are similar then the ratio of their corresponding sides are equal.

Therefore,

[tex]\frac{AB}{CD}=\frac{BE}{DE}[/tex]

[tex]\frac{15}{6}=\frac{y}{y-x}[/tex]

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

[tex]5y-5x=2y[/tex]

[tex]5y-2y=5x[/tex]

[tex]3y=5x[/tex]

[tex]y=\frac{5}{3}x[/tex]

Differentiate w.r.t t

[tex]\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}[/tex]

We have dx/dt=5ft/s

Using the value

[tex]\frac{dy}{dt}=\frac{5}{3}(5)=\frac{25}{3}ft/s[/tex]

Hence, the tip of  his shadow moving  with a speed 25/3 ft/s when he is 45 feet from the pole.

Answer:

The tip pf the shadow is moving with speed 25/3 ft/s.

Step-by-step explanation:

height of pole = 15 ft

height of man = 6 ft

x = 45 ft

According to the diagram, dx/dt = 5 ft/s.

Now

[tex]\frac{y-x}{y}=\frac{6}{15}\\\\15 y - 15 x = 6 y \\\\y = \frac{5}{3} x\\\\\frac{dy}{dt} = \frac{5}{3}\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{5}{3}\times 5 =\frac{25}{3} ft/s[/tex]

We have to,

Simplify the expression,

→ (3x + y²)

Now remove brackets in expression,

→ (3x + y²)

→ 3x + y²

Therefore, 3x + y² is simplest form.

Answer:

10x8=80 that would be the area for the picture 14x11=154 for the boards area

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26