Griffin and three friends go golfing. Two of the friends spend $6 each to rent clubs. The total cost for the rented clubs and green fees was $76. Define a variable, and write and solve an equation to find the cost of the green fees for each person.

Answer: Option A.

Step-by-step explanation:

By definition, the equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope of the line and b is the y-intercept.

Let's solve for y from the equation A, as following:

[tex]5x-y=7\\-y=-5x+7\\(-1)(-y)=(-5x+7)(-1)\\y=5x-7[/tex]

As you can see in the equation:

[tex]m=5\\b=7[/tex]

Therefore, the option A is the answer.

In Mathematics, the slope of a line is represented by 'm' in the equation y=mx+b. By comparing the provided options with this format, we find option A has the equation of a line with a slope of 5.

In the subject of

Mathematics

, particularly

Algebra

, the equation of a line in the form y=mx+b represents a straight line on the xy-plane, where 'm' is the slope and 'b' is the y-intercept. With this in mind, we analyze the given options.

Therefore, option A has a line with a slope of 5.

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Answer:

A. (x - 5)(x - 5)

Step-by-step explanation:

We will do this the old fashioned way...just plain old factoring.  

This polynomial is of the form

[tex]y=ax^2+bx+c[/tex]

The product of a and c have to add up to equal the "middle" term, -10.  

a = 1, b = -10, c = 25

a * c = 1 * 25 = 25

Now we need the factors of 25 to find the combination of factors that will result in a -10.  The factors of 25 are: 1, 25 and 5, 5

5 and 5 add up to be 10, but since we need a -10, we will use -5 and -5.  The product of -5 * -5 = 25, so we are not messing anything up by using the negative 5.

Putting them in order in standard form we have

[tex]x^2-5x-5x+25[/tex]

Factor by grouping:

[tex](x^2-5x)-(5x+25)[/tex]

There is an x common to both terms in the first set of parenthesis, so we will factor that out; there is a 5 common to both terms in the second set of parenthesis, so we will factor that out:

x(x - 5) - 5(x - 5)

NOW what's common in both terms is the (x - 5) so we factor THAT out, and what's left gets grouped together:

(x - 5)(x - 5)

Answer: There are 208 shots she make if she shot 125 foul shots.

Step-by-step explanation:

Since we have given that

Number of foul shots = 12

Number of shots she misses = 8

Total number of shots = 12+8=20

So, if the number of foul shots = 125

We need to find the number of shots she make.

According to question, we get that

[tex]\dfrac{12}{20}=\dfrac{125}{x}\\\\12x=125\times 20\\\\12x=2500\\\\x=\dfrac{2500}{12}\\\\x=208.33\\\\x\approx 208[/tex]

Hence, there are 208 shots she make if she shot 125 foul shots.

your fraction would be 3 12/15

Answer:

with wind velocity = 3156/4 = 789 mph

against wind velocity = 2836/4 = 709 mph

(789/709) / 2 = 40 mph

wind velocity = 40 mph

plane velocity = 789 - 40 = 749 mph

Step-by-step explanation:

Answer: a loss of 4 cents

Step-by-step explanation:

The probability of rolling a sum of 2, 3, 4, 5, or 6 is [tex]\dfrac{15}{36}[/tex] which earns $2.00

The probability of rolling a sum of 28, 9, 10, 11, or 12 is [tex]\dfrac{15}{36}[/tex] which loses $2.00

The probability of rolling a sum of 7 is [tex]\dfrac{6}{36}[/tex] which loses $0.25

[tex]\bigg(\dfrac{15}{36}\times \$2.00\bigg)+\bigg(\dfrac{15}{36}\times -\$2.00\bigg)+\bigg(\dfrac{6}{36}\times -\$0.25\bigg)=\boxed{-\$0.04}[/tex]

The expected value of playing the game once is -$0.62, indicating an expected average loss of 62 cents per game.

The expected value of playing the game once is -$0.62, rounded to the nearest cent. This means that if you play the game repeatedly over a long string of games, you would expect to lose 62 cents per game, on average. The expected value indicates an expected average loss, so it is not recommended to play this game to win money.

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ANSWER

[tex]b = \frac{1}{3} [/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

EXPLANATION

The given expression is

[tex](b - 5) {x}^{2} - (b - 2)x + b = 0[/tex]

If

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

is a root, then it must satisfy the given equation.

[tex](b - 5) {( \frac{1}{2} )}^{2} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

[tex](b - 5) {( \frac{1}{4} )} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

Multiply through by 4,

[tex](b - 5)- 2(b - 2)+4 b = 0[/tex]

Expand:

[tex]b - 5- 2b + 4+4 b = 0[/tex]

Group similar terms;

[tex]b - 2b + 4b = 5 - 4[/tex]

[tex]3b = 1[/tex]

[tex]b = \frac{1}{3} [/tex]

Our equation then becomes:

[tex]( \frac{1}{3} - 5) {x}^{2} - ( \frac{1}{3} - 2)x + \frac{1}{3} = 0[/tex]

[tex]( - \frac{14}{3} ) {x}^{2} - ( - \frac{5}{3} )x + \frac{1}{3} = 0[/tex]

[tex] - 14{x}^{2} + 5x + 1= 0[/tex]

Factor:

[tex](2x - 1)(7x + 1) = 0[/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

Answer:

vertical intercepts: (7, pi/2) and (-7, pi/2)

horizontal intercepts: (10,0) and (-4,0)

Step-by-step explanation:

The horizontal and vertical intercepts are respectively; [(10,0) and (-4,0)] and [(7, π/2) and (-7, π/2)]

We are given the parametric equation;

r = 7 + 3 cos θ

Now, the vertical intercept will be when cos θ = 0 and that is at θ = π/2

Thus;

At θ = π/2, we have;

r = 7 + (3 * 0)

r = 7

But this will also give the same value of θ when r = -7

Thus; vertical intercepts are; (7, π/2) and (-7, π/2)

Horizontal intercept will occur when cos θ = 1. Thus;

At θ = 0, we have;

r = 7 + (3 * 1)

r = 10

Also, the lower interval will be when cos θ = -1. Which is 0 on the negative side. Thus

r = 7 + (3 * -1)

r = 4

Thus; horizontal intercepts are; (10,0) and (-4,0)

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Answer:

44%

Why? Because there is only 4 of each and you have so many more chances to pull a different card.

Answer:

2160 BTU

Step-by-step explanation:

Ben looks at his plan and realizes that his building can be viewed as a triangular prism sitting on a cube.

Calculating the volume of a cube is easy… Length x Width x Height (LWH)… so 12 x 10 x 8 = 120 x 8 = 960 cubic feet for the cube part.

For the prism, it’s almost the same… but divided by 2 : (LWH)/2, so… (12 x 10 x 2) / 2 = (120 x 2) / 2 = 240 / 2 = 120 cubic feet for the prism part.

Total for the building : 960 + 120 = 1080 cubic feet

Since 2 BTU per cubic foot, the power of the unit needs to be at least  1080 x 2 = 2160 BTU.

Answer: third option

Step-by-step explanation:

As you can see in the figure attached, the triangle is a right triangle.

Then, you can calculate cosA as it is shown below:

- You need to remember the following:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

- Now, you must substitute values. Based on the figure:

[tex]adjacent=3\\ hyppotenuse=5[/tex]

[tex]\alpha=A[/tex]

Therefore, you obtain that cosA is:

[tex]cosA=\frac{3}{5}[/tex]

Answer:

Cos A = 3/5

Step-by-step explanation:

We are given a right angled triangle, ΔBCD,  with all three side lengths known and we are to find the value of Cos A.

We Cos is the ratio of the base of the triangle to its hypotenuse, with respect to the angle (here angle A).

Considering the angle A, our perpendicular is CD, base is BC and hypotenuse BD.

Therefore, Cos A = BC/BD = 3/5

Answer:The domain: x > -2\to x\in(-2;\ \infty)

Step-by-step explanation:

y = ln(x + 2)

D:

x + 2 > 0    |subtract 2 from both sides

x > -2

Answer: The domain: x > -2\to x\in(-2;\ \infty)

Answer:

[tex]\large\boxed{x>-2\to x\in(-2,\ \infty)}[/tex]

Step-by-step explanation:

[tex]\text{The domain of}\ \log_ax:\\\\a>0\ \wedge\ a\neq1\ \vedge\ x>0\\=========================\\\\y=\ln(x+2)\\\\\text{The domain:}\\\\x+2>0\qquad\text{subtract 2 from both sides}\\\\x+2-2>0-2\\\\x>-2\to x\in(-2,\ \infty)[/tex]

Answer:

Final answer is approx x=0.16.

Step-by-step explanation:

Given equation is [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]

Now we need to solve equation [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex] and round to the nearest hundredth.

[tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]

[tex]2.8\times 13^{4x} = 19.3-4.8 [/tex]

[tex]2.8\times 13^{4x} = 14.5 [/tex]

[tex]13^{4x} = \frac{14.5}{2.8} [/tex]

[tex]13^{4x} = 5.17857142857 [/tex]

[tex]\log(13^{4x}) = \log(5.17857142857) [/tex]

[tex]4x \log(13) = \log(5.17857142857) [/tex]

[tex]4x = \frac{\log(5.17857142857)}{\log\left(13\right)} [/tex]

[tex]4x = 0.641154659628 [/tex]

[tex]x = \frac{0.641154659628}{4} [/tex]

[tex]x = 0.160288664907 [/tex]

Round to the nearest hundredth.

Hence final answer is approx x=0.16.

Answer:

The third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].

Step-by-step explanation:

According to the binomial expansion,

[tex](a+b)^n=C(n,0)a^{n}+C(n,1)a^{n-1}b+...+C(n,n)b^n[/tex]

So, the rth term of this expansion is

[tex]C(n,r-1)a^{n-r+1}b^{(r-1)}[/tex]

We have to find the third term of the expansion [tex](a+b)^n[/tex] is

[tex]C(n,3-1)a^{n-3+1}b^{(3-1)}[/tex]

[tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex]

Therefore the third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].

The local bank charges 2%.

When the balance is $600, the local bank would charge: 600 x 0.02 = $12

This means if the balance is higher the $600, the local bank would charge more than $12.

The answer would be the second choice: The fee at the local bank will be more than the fee at the local credit union only when the account balance is more than $600.

Answer:

Option d

Step-by-step explanation:

If the ball landed 3 feet east of where it was thrown, then it moved 3 units horizontally along the x-axis.

If you moved 4 units to the north then we can say that 4 units were moved on the y axis

Therefore, the original matrix [tex]\left[\begin{array}{cc}x\\y\end{array}\right][/tex] is transformed in the matrix [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]

Therefore, the answer is [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]

Answer:

d

Step-by-step explanation:

fr ong

Answer:

2

Step-by-step explanation:

An inverse of a function is a reflection across the y=x line. This results in each (x,y) point becoming (y,x).

x         f(x)

-6          1

-3          2

2           5

5           3

8           0

So the inverse becomes:

x         Inverse

1            -6

2           -3

5            2

3            5

0            8

g(2) = -3 and f(-3) = 2.

Answer:

x = 1 and x = 2

x = 4 and x = -4

Step-by-step explanation:

Vertical asymptotes appear where the function does not have a value. This is most commonly when the denominator of a rational function is 0. Find the asymptotes by factoring the denominator and setting it equal to 0. Then solve for x.

First equation

x² - 3x + 2 factors into (x-1)(x-2)

When x-1 = 0, x = 1. When x-2=0, x = 2. The V.A. are at x = 1 and x = 2.

Second equation

x²  - 16 factors into (x+4)(x-4)

When x+4= 0, x = -4. When x-4 = 0, then x = 4. The V.A. are at x = -4 and x = 4.

Final answer:

The function f(x) = 3x/(x² - 16) is defined for x = -16, x = 0, and x = 16, but undefined for x = -4 and x = 4, where it has vertical asymptotes.

Explanation:

The question requires evaluating the function f(x) = 3x/ x²-16 for different values of x. When we evaluate this function, we must pay attention to the values at which the function is undefined, which is when the denominator x^2 - 16 equals zero. This occurs when x = -4 or x = 4, as these values make the denominator (x + 4)(x - 4) equal to zero.

Options (b) and (d) correspond to the values at which the function has vertical asymptotes, as the denominator becomes zero and the function value approaches infinity.

Answer:

1/6

Or in decimal form,

0.16

[tex]n\cdot1\cdot\dfrac12\cdot\dfrac13\cdot\dfrac14\cdot\dfrac15=\dfrac n{5!}[/tex]

[tex]\dfrac12\cdot\dfrac14\cdot\dfrac16\cdot\dfrac18\cdot\dfrac1{10}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]

So we have

[tex]\dfrac n{5!}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]

[tex]n=\dfrac{3\cdot5\cdot7\cdot9}{6\cdot7\cdot8\cdot9\cdot10}[/tex]

[tex]n=\dfrac{3\cdot5}{6\cdot8\cdot10}[/tex]

[tex]n=\dfrac1{2\cdot8\cdot2}[/tex]

[tex]n=\dfrac1{32}[/tex]

Answer:

3

Step-by-step explanation:

trust me , it worked

The answer is true because false would mean that it’s another crazy definition. But yes it is true

A rational function is a fractional expression in the form f(x) = p(x)/q(x), where q(x) cannot be zero.

Example: f(x) = 3x/(4x - 2).

True is the answer.

Answer:

-10/3, 10/3

Step-by-step explanation:

(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)

First calculate the derivatives:

[tex]y=\cos(kt) \Rightarrow y'=-k\sin(kt) \Rightarrow y'' = -k^2\cos(kt)[/tex].

Then plug the derivtes y'' and y into the equation:

[tex]-9k^2\cos(kt) = -100\cos(kt)[/tex]

Solve the equation for k:

[tex]100\cos(kt) - 9k^2\cos(kt) = 0 \\\\\Rightarrow \cos(kt)(100-9k^2) = 0[/tex]

So then we have that [tex]y=\cos(kt)[/tex] satisfies the differential equation when [tex]\cos(kt) = 0[/tex] or when [tex]100-9k^2=0[/tex] (or both). The solutions to these equations are:

[tex]\left \{ {{\cos(kt)=0 \Rightarrow k=\frac{n\pi}{2t}} \atop {100-9k^2 = 0 \Rightarrow k= \pm \sqrt{\frac{100}{9}}=\pm \frac{10}{3}}} \right.[/tex]

I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:

k = -10/3, 10/3.

The values are [tex]k = \pm \frac{10}{3}[/tex].

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

The function is:

[tex]y = \cos{kt}[/tex]

The derivatives are:

[tex]y^{\prime}(t) = -k\sin{kt}[/tex]

[tex]y^{\prime\prime}(t) = -k^2\cos{kt}[/tex]

The equation is:

[tex]9y^{\prime\prime} = -100y[/tex]

Replacing:

[tex]-9k^2\cos{kt} = -100\cos{kt}[/tex]

[tex]9k^2 = 100[/tex]

[tex]k^2 = \frac{100}{9}[/tex]

[tex]k = \pm \sqrt{\frac{100}{9}}[/tex]

[tex]k = \pm \frac{10}{3}[/tex]

Those are the values.

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Answer:

Step-by-step explanation:

Use the cosine law:

[tex]AB^2=CB^2+CA^2-(CB)(CA)\cos(\angle C)[/tex]

We have:

[tex]AB=6,\ CB=6.5,\ CA=7.5[/tex]

Substitute:

[tex]6^2=6.5^2+7.5^2-2(6.5)(7.5)\cos(\angle C)[/tex]

[tex]36=42.25+56.25-97.5\cos(\angle C)[/tex]

[tex]36=98.5-97.5\cos(\angle C)[/tex]           subtract 98.5 from both sides

[tex]-62.5=-97.5\cos(\angle C)[/tex]           divide both sides by (-97.5)

[tex]\cos(\angle C)\approx0.641\to m\angle C\approx50^o[/tex]

Answer:

The equation after translation is x² + y² + 16x - 8y + 73 = 0 ⇒ answer (a)

Step-by-step explanation:

* Lets study the type of the equation:

∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0 ⇒ general form of conic equation

- If D and E = zero

∴ The center of the graph is the origin point (0 , 0)

- If B = 0

∴ The equation is that of a circle

* Lets study our equation:

 x² + y² = 7 ⇒ x² + y² - 7 =0

∵ B = 0 , D = 0 , E = 0

∴ It is the equation of a circle with center origin

- The equation of the circle with center origin in standard form is:

  x² + y² = r²

∴ x² + y² = 7 is the equation of a circle withe center (0 , 0)

  and its radius = √7

* We have two translation one horizontally and the other vertically

- Horizontal: x-coordinate moves right (+ve value) or left (-ve value)

- Vertical: y-coordinate moves up (+ve value) down (-ve value)

∵ The point of translation is (-8 , 4)

∵ x = -8 (-ve value) , y = 4 (+ve value)

∴ The circle moves 8 units to the left and 4 units up

* now lets change the x- coordinate and the y-coordinate

  of the center (0 , 0)

∴ x-coordinate of the center will be -8

∵ y-coordinate of the center will be 4

* That means the center of the circle will be at point (-8 , 4)

- the standard form of the equation of the circle with center (h , k) is

 (x - h)² + (y - k)² = r²

∵ h = -8 and y = 4

∴ The equation is: (x - -8)² + (y - 4)² = 7

∴ (x + 8)² + (y - 4)² = 7

* lets change the equation to the general form by open the brackets

∴ x² + 16x + 64 + y² - 8y + 16 - 7 = 0

* Lets collect the like terms

∴ x² + y² + 16x - 8y + 73 = 0

∴ The equation after translation is x² + y² + 16x - 8y + 73 = 0

* Look at the graph the blue circle is after translation

Answer:

C

Step-by-step explanation:

a^2 + b^2 = c^2 so 6^2 + 9^2 = 36 + 81 = square root of 117

The length of the hypotenuse of right triangle ΔDEF is 10.82 units

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Here we have ,

to find hypotenuse of a right triangle:

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other legs.

Therefore,

a^2 + b^2 = c^2

so 6^2 + 9^2

= 36 + 81

= square root of 117

=10.82

learn more on Pythagoras theorem here:

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find prime factors to get the inbetween numbers for product, and choose the one that has a difference of 20, and it should be 5 and 25, both requirements are met.

Answer:

Solution 1: The numbers are 25 and 5

Solution 2: The numbers are -5 and -25

Step-by-step explanation:

We have 2 unknown numbers, then we can define them as:

x: Unknown number 1  

y: Unknown number 2

The problem states that "the difference of two numbers is 20". We can translate this to x - y = 20

We also know that "their product is 125". We can translate this to x . y = 125

Putting both equations together, we get the following system of equations

[tex]\left \{ {{x - y = 20} \atop {x y=125}} \right.[/tex]

Now, to solve this system of equations we can use the Substitution Method.

We can solve 1st equation for x, by adding y to both sides

x - y + y = 20 + y

x = 20 + y

We can substitute x by 20 + y on the 2nd equation

(20 + y) . y = 125

Applying distributive property on the left side

20y + y² = 125

Substracting 125 to both sides and rearranging the terms, we get

20y + y² - 125 = 125 -125

y² + 20y - 125 = 0

We can apply the quadratic equation attached to solve this (with a = 1, b = 20, c = -125).

( -20 ± √(20² - 4 . 1 . -125) ) / ( 2. 1 ) =

( -20 ± √(400 + 500) ) / ( 2) =

( -20 ± √900 ) / ( 2) =

( -20 ± 30 ) / ( 2) =

We get 2 results:

For each of these values of y, we can find the corresponding value of x:

Answer:

(-a, 0).

Step-by-step explanation:

The long diagonal corresponds to the y-axis. S is the same distance from the y-axis as Q.

Answer:

[tex]\large\boxed{A=112x\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

We have

b₁ = 17x m , b₂ = 11x m, h = 8 m.

Substitute:

[tex]A=\dfrac{17x+11x}{2}\cdot8=\dfrac{28x}{2}\cdot 8=14x\cdot 8=112x[/tex]

Answer:

73.2°

Step-by-step explanation:

Use Law of Sines to solve:

(Sin 50)/20 = (Sin B)/25    

Solve for Sin B

[25(Sin 50)]/20 = Sin B

Use Sin^-1 x to solve   (sine inverse)

Sin^-1 ( [25(Sin 50)]/20 ) = B

B = 73.24685774

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{RQ}{\sin(\angle P)}=\dfrac{PR}{\sin(\angle Q)}[/tex]

We have

[tex]RQ=20\ in\\\\m\angle P=50^o\to\sin50^o\approx0.766\\\\PR=25\ in[/tex]

Substitute:

[tex]\dfrac{20}{0.766}=\dfrac{25}{\sin(\angle Q)}[/tex]     cross multiply

[tex]20\sin(\angle Q)=(25)(0.766)[/tex]

[tex]20\sin(\angle Q)=19.15[/tex]            divide both sides by 20

[tex]\sin(\angle Q)=0.9575\to m\angle Q\approx73^o[/tex]