1) John spent $36 to buy 4 basketballs. What was the price per basketball?

If [tex]x[/tex] and [tex]y-1[/tex] have the same sign, then either

[tex]x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9[/tex]

or

[tex]x<0,y<1 \implies 2|x| + 3|y-1| = -2x - 3(y-1) = 6 \implies 2x + 3y = -3[/tex]

If [tex]x[/tex] and [tex]y-1[/tex] have opposite sign, then

[tex]x>0,y<1 \implies 2|x| + 3|y-1| = 2x - 3(y-1) = 6 \implies 2x -3y = 3[/tex]

or

[tex]x<0,y>1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9[/tex]

This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set

[tex]R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}[/tex]

The area of [tex]R[/tex] is given by the double integral

[tex]\displaystyle \iint_R dx\,dy[/tex]

To compute the area, change the variables to

[tex]\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}[/tex]

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}[/tex]

with determinant [tex]\det(J) = -\frac1{12}[/tex]. Then the integral transforms to

[tex]\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du[/tex]

which is 1/12 the area of a square with side length 12. Hence the integral evaluates to

[tex]\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}[/tex].

Answer:

the answer is D- 9/k

Answer:

D- 9/k

Step-by-step explanation:

The Fall (drop)  of drainage piping is: A. 5".

In order to determine the fall (drop) of drainage piping we would need to multiply the drainage piping by the inch per feet.

Hence:

Using this formula

Fall (drop) of drainage piping = Drainage piping× inch per feet

Where:

Drainage piping=20

Inch per feet=1/4"

Let plug in the formula

Fall (drop) of drainage piping =20×1/4"

Fall (drop) of drainage piping =5"

Therefore the correct option is A. 5".

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Probability is 17.5% that 3 of them entered a profession closely related to their college

According to the statement

we have given that survey of 300 college graduates, 46% reported that they entered a profession closely and

We know that  For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major, or they have not. The probability of a college graduate having entered a profession closely related to their college major is independent of other college graduates, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

This is P(X = 3) when n = 8. and the value of p is 0.46 put the value in the binomial formula then the outcome of answer will 17.5%

So, Probability is 17.5% that 3 of them entered a profession closely related to their college

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The vertices of the parabolae are:

Parabolae are represented by quadratic equations. In this problem we have parabolae in standard form and we need to determine its vertex form to find the needed information. Now we summarize the forms of quadratic equations:

Standard form

y = a · x² + b · x + c     (1)

Vertex form

y - k = C · (x - h)²     (2)

Please notice that (x, y) = (h, k) represents the vertex of the parabola.

To change quadratic equations from standard form into vertex form we need to apply algebraic handling:

y = x² + 6 · x + 8

y + 1 = x² + 6 · x + 9

y + 1 = (x + 3)²

(h, k) = (- 3, - 1)

y = x² - 2 · x - 8

y + 9 = x² - 2 · x + 1

y + 9 = (x - 1)²

(h, k) = (1, - 9)

y = - x² + 8 · x - 15

y = - 1 · (x² - 8 · x + 15)

y - 1 = - 1 · (x² - 8 · x + 16)

y - 1 = - 1 · (x - 4)²

(h, k) = (4, 1)

y = - 4 · x² + 6 · x

y = - 4 · [x² - (3/2) · x]

y + (- 4) · (9/16) = - 4 · [x² - (3/2) · x + 9/16]

y - 9/4 = - 4 · (x - 3/4)²

(h, k) = (3/4, 9/4)

y = x² + 6 · x + 11

y - 2 = x² + 6 · x + 9

y - 2 = (x + 3)²

(h, k) = (- 3, 2)

y = - x² + 36

y - 36 = - x²

(h, k) = (0, 36)

y = - x² + 7 · x - 10

y = - (x² - 7 · x + 10)

y + (- 1) · (9/4) = - (x² - 7 · x + 49/4)

y - 9/4 = - (x - 7/2)²

(h, k) = (7/2, 9/4)

y = x² - 10 · x + 24

y + 1 = x² - 10 · x + 25

y + 1 = (x - 5)²

(h, k) = (5, - 1)

y = 2 · x² - 4 · x - 1

y = 2 · (x² - 2 · x - 1/2)

y + 2 · (3/2) = 2 · (x² - 2 · x + 1)

y + 3 = 2 · (x - 1)²

(h, k) = (1, - 3)

y = - 4 · x² - 2 · x

y = - 4 · [x² + (1/2) · x]

y + (- 4) · (1/4) = - 4 · [x² + (1/2) · x + 1/4]

y - 1 = - 4 · (x + 1/2)²

(h, k) = (- 1/2, 1)

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Answer: 7

Step-by-step explanation:

By the triangle proportionality theorem,

[tex]\frac{?}{21}=\frac{3}{9}\\\\?=7[/tex]

Answer:

5 cm

Step-by-step explanation:

When two chords are equidistant from the center of the circle, the two chords have equal length. Therefore, the length of chord AB, 4x - 6, is equal to the length of chord CD, 6x - 12.

4x - 6 = 6x - 12

6 = 2x

x = 3

Now that we know x = 3, we can substitute the value back into the original expression, 4x - 6, to find the length of chord AB.

AB = 4x - 6 = 4*3 - 6 = 12 - 6 = 6 cm

When measuring the distance between a line and a point, we create a segment through the point perpendicular to the line. In Geometry, we also learn that the perpendicular bisector of a chord in a circle contains the center of the circle.

In this case, the gray line perpendicularly bisects segment AB. PX is 4 cm long and AX is 3 cm long (because AX is half the length of AB). Notice that triangle AXP is a right triangle, so we can use Pythagorean Theorem to find AP.

[tex]AP^{2} = AX^{2} +PX^{2}[/tex]

[tex]AP = \sqrt{3^{2} +4^{2} }[/tex]

[tex]AP =\sqrt{9+16}[/tex]

[tex]AP = \sqrt{25}[/tex]

[tex]AP = 5[/tex]

Answer:

Ans: (4,-1)

Step-by-step explanation:

Lets keep:

2x+y=7 --- equation 1

x - 2y=6 ----- equation 2

equation 2 x 2: 2x - 4y=12 -------equation 3

now subtract equation 1 from equation 3

  2x - 4y = 12

(-) 2x + y = 7

----> -5y = 5 [ Divide both sides by -5 ]

------> y= -1

Substitute y= -1 into eqaution 1

----> 2x + -1 = 7 [ add 1 to both side]

----> 2x = 8 [Divide by 2 on both sids]

----> x=4

Ans: (4,-1)

Answer:

the answer is 8

Step-by-step explanation:

thats what i got

The difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11

Given the expression

(5. 29 × 10^11) - (3. 86 × 10 ^11)

First, find the common factor

10^11 ( 5. 29 - 3. 86)

Then substract the values within the bracket

10^11 (1. 43)

Multiply with the factor, we have

⇒1. 43 × 10^11

Thus, the difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11

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Answer:

A

Step-by-step explanation:

Find the difference. Express the answer in scientific notation.

(5.29 times 10 Superscript 11 Baseline) minus (3.86 times 10 Superscript 11 Baseline)

1.43 times 10 Superscript 11

9.15 times 10 Superscript 11

1.43 times 10 Superscript 22

9.15 times 10 Superscript 22

Answer:

946

Step-by-step explanation:

Let's make an equation :

34% of x = 321.8

Covert 34% into decimal by dividing by 100 :

34 ÷ 100 = 0.34

Rewrite equation with decimal form :

0.34x = 321.8

Divide both sides by x to make x the subject :

x = 321.8 ÷0.34

x = 946.470588235

To the nearest whole number will be 946 as 4 rounds it down

So our final answer will be 946

Hope this helped and have a good day

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{34}{100} \sdot x = 321.8[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{(321.8) \sdot(100)}{34} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 946.47[/tex]

Round off to nearest whole number :

[tex]\qquad \sf  \dashrightarrow \: x = 946[/tex]

Answer:

7.8g/cm

Step-by-step explanation:

One of the numbers would be 321. Hence option B is true.

Used the concept of the Number system that states,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Given that,

The ratio of the two numbers is 2/3, and their sum is 535.

Let us assume that,

The two numbers are x and y.

Hence we have;

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]  .. (i)

And, [tex]x + y = 535[/tex]   .. (ii)

From equation (i);

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]

[tex]x = \dfrac{2y}{3}[/tex]

Substitute the above value of x in (ii);

[tex]x + y = 535[/tex]

[tex]\dfrac{2y}{3} + y = 535[/tex]

[tex]2y + 3y = 535 \times 3[/tex]

[tex]5y = 1605[/tex]

[tex]y = 321[/tex]

From equation (i);

[tex]x = \dfrac{2y}{3}[/tex]

[tex]x = \dfrac{2\times 321}{3}[/tex]

[tex]x = 214[/tex]

Therefore, the number is 321. So option B is true.

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Answer:

∠α = 5.001°

a easy calculator for this is:

https://www.calculator.net/right-triangle-calculator.html?av=3.5&alphav=&alphaunit=d&bv=40&betav=&betaunit=d&cv=&hv=&areav=&perimeterv=&x=57&y=16

The size of the angle subtended at the center of the circle is θ = 80.5397°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

The area of a sector of a circle of radius 8cm is 45cm²

On simplifying , we get

A = θ/360 x πr²

45 = θ/360 ( 22/7 ) ( 8 )²

45 = ( θ/360 ) ( 201.1428 )

Divide by 201.1428 on both sides , we get

( θ/360 ) = 0.22372159

Multiply by 360 on both sides , we get

θ = 80.5397

Hence , the angle is θ = 80.5397°

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Step-by-step explanation:

[tex] - 32 + 45 = 13 \\ t_{n} = ( a_{1} + (n - 1)d) \\ \\ d = 13 \: \: a_{1} = - 45[/tex]

[tex] t_{n} = - 45 + (n - 1)13 = = = > \\ - 45 + 13n - 13 = = = > \\ t_{n} = 13n - 58[/tex]

and now

[tex]124 = 13n - 58 = = = > \\ 182 = 13n = = = > n = 14[/tex]

The number of terms in the sequence: –45, –32, –19, –6, ..., 124 = 9.

The common difference is -45 - (-32)= 13

                                                  d = 13.

AP is a sequence of numbers in order, in which the difference among any two consecutive numbers is a constant cost. it's also referred to as mathematics series.

using arithmetic progress:-

last term = (n-1)d

first term(a) = –45

    term = a + (n-1)d

there is a difference of 13, so the sequence will be

–45, –32, –19, –6,7, 20, 33, 46, 59, 72, 85, 98, 111, 124.

∴ number of terms = 9

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Answer:

sin(x - y) = 0.21

Step-by-step explanation:

we have the sin values which we need to get cos values

sin (A-B) = sin A cos B - sin B cos A

sin² A + cos² A = 1

sin x = 4/9

cos² x = 1 - sin² x = 1 - 16/81 = 65/81

cos² x = 65/81

cos x = √65/9

sin y = 1/4

cos² y = 1 - sin² y = 1 - 1/16 = 15/16

cos² y = 15/16

cos y = √15/4

sin(x − y) = sin x cos y - sin y cos x

sin(x - y) = 4/9 √15/4 - 1/4 √65/9

sin(x - y) = (4√15-√65)/36

sin(x - y) = 0.21

socratic Narad T

Answer: C

Step-by-step explanation:

on edg

Answer:

C.  b^8.

Step-by-step explanation:

b^10/b^2     We subtract the exponents:-

= b^(10-2)

= b^8.

b^8

Step-by-step explanation:

b^10/b^2 ,. b^10-2 ;. b^8

We kindly invite to check the image attached below to see the representation of the exponential function. This function shows exponential growth.

In this occasion we must plot the graph of exponential functions of the form:

y = a · bˣ     (1)

Where:

First, we need to follow this procedure to create the graph of the curve on Cartesian plane:

Therefore, we build the exponential curve with the help of a graphing tool (i.e. Desmos), whose result is shown in the image attached below.

From (1) we must understand that exponential functions report growth for b > 1 and decay for 0 < b < 1. Thus, the exponential function y = 3ˣ shows exponential growth according to graphical and analytical findings.

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Answer:

13

Step-by-step explanation:

Given x = 2, y = 3 and z = 4. We'll evaluate the value of x² + y² with given condition.

First, remind that we are only given the expression of x-term and y-term only and therefore, z-term is not included - it's not to be considered.

Substitute x = 2 and y = 3 in the expression:

[tex]\displaystyle{2^2+3^2 = 4+9}\\\\\displaystyle{4+9 = 13}[/tex]

Hence, the value of x² + y² when x = 2 and y = 3 is 13.

Please let me know if you have any questions!

The steps in evaluating each of the following expressions is shown below.

An expression is a mathematical equation which shows the relationship that exist between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 -2 + 3 -4

B. 10 + 2(9 - 5) - 16/18

Answer:

  h(x) = 2x² -8x -10

Step-by-step explanation:

In the US, a quadratic is in standard form when the terms are listed in order of decreasing degree.

In the UK, a quadratic is in standard form when it is written in vertex form.

__

The only function with terms in order of decreasing degree is ...

  h(x) = 2x² -8x -10

All of the functions except the last are written in vertex form:

__

Additional comment

Since the question asks about one function, we assume it is from the perspective of the US understanding of standard form. The point here is that "standard form" may vary from one tradition to another. (The "standard form" for numerical values varies by tradition, as well.)

Answer:

  the graph of f has 3 turning points

Step-by-step explanation:

The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.

The derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.

Where the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.

The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.

If the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.

__

Additional comment

In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.

Answer: B

Step-by-step explanation:

A) False. Rotations do not preserve parallelism.

B) True. Rotations are rigid motions and thus preserve angle measure.

C) False. A rotation that changes the location of every point except for the center of rotation.

Answer:

Step-by-step explanation:

The function that has a domain of all real numbers is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

The domain of a function is the set that contains all possible input values for the function.

If a function has an even root, equivalent to an exponent of [tex]\frac{1}{n}[/tex] with n even, the domain is only positive values, while if the exponent is odd, the domain is all real values.

Researching the problem on the internet, the function with odd exponent is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

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Answer:  C) Sometimes positive; sometimes negative

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

Explanation:

Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5

Plug this into f(x)

f(x) = x(x+3)(x+1)(x-4)

f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)

f(-0.5) = -0.5(2.5)(0.5)(-4.5)

f(-0.5) = 2.8125

We get a positive value.

This shows that f(x) is positive on the region of -1 < x < 0

----------------

Now pick a value between x = 0 and x = 4. I'll use x = 1

f(x) = x(x+3)(x+1)(x-4)

f(1) = 1(1+3)(1+1)(1-4)

f(1) = 1(4)(2)(-3)

f(1) = -24

Therefore, f(x) is negative on the interval 0 < x < 4

----------------

In short, f(x) is both positive and negative on the interval -1 < x < 4

It's positive when -1 < x < 0

And it's negative when 0 < x < 4

Answer:

sometimes positive sometimes negative

Step-by-step explanation:

I did it on Khan Academy

Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of [tex]R = 10^{12}[/tex].

The equation is:

[tex]L = 10\log{R}[/tex]

In which:

For this problem, we have that L = 120, hence the relative intensity is found as follows:

[tex]120 = 10\log{R}[/tex]

[tex]\log{R} = 12[/tex]

[tex]R = 10^{12}[/tex]

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Step-by-step explanation:

is there something missing in the question ?

or is this meant to be a trick question ?

let me repeat :

pot1 contains 5 black and 7 white beads

pot2 contains 6 white beads (and nothing else, right ?)

then one bead is drawn from each pot.

so, 1 bead from pot1, and 1 bead from pot2.

the bead from pot1 is either white or black.

the bead from pot2 is white for sure.

so, the probability to get at least 1 white bead is 100% or 1, as there will be always the white bead taken from pot2.