Solve the Percent Discount Application.

The local grocery store has just marked down a patio set by 20%. If the patio set costs $79.90, what is the discounted price?

$63.92
$94.80
$15.80
$70.00

Step-by-step explanation:

the area is

(x² + 17x + 72) m²

it is the result of the usual

length × width

calculation.

length = x + g

width = x + h

length × width = x² + gx + hx + ab = x² + (g+h)x + gh =

= x² + 17x + 72

g + h = 17

gh = 72

just by looking at it that gives us 9 and 8 as g and h.

FYI - formally to calculate them we can say

g = 17 - h

(17 - h)h = 72

17h - h² = 72

h² - 17h + 72 = 0

the solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = h

a = 1

b = -17

c = 72

h = (17 ± sqrt(17² - 4×1×72))/(2×1) =

= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2

h1 = (17 + 1)/2 = 18/2 = 9

h2 = (17 - 1)/2 = 16/2 = 8

as we can see

g = 17 - h

if we say h = 9, then g = 8.

if we say h = 8, then g = 9.

so, these are our solutions.

we simply pick that length is longer than width, so, g = 9, h = 8.

the area including the walkway is then

(length + 3)(width + 3) =

= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²

and the dimensions incl. the walkway are

length = x + 9 + 3 = x + 12

width = x + 8 + 3 = x + 11

Answer:

22

Step-by-step explanation:

BD bisects <ABC, this means the half-line divided the angle into two equal parts.

If m<ABC is equal to 44 then m<ABD is

44/2 = 22

Answer:

Step-by-step explanation:

Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.

1.

 a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.

 b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].

2.

 a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]

 b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]

 c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n

 d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.

Answer:

The inverse is  -1/7(x+4)

Step-by-step explanation:

We have the function

y = -7x-4

To find the inverse, exchange x and y

x = -7y -4

Solve for y

Add 4 to each side

x+4 = -7y -4+4

x+4 = -7y

Divide each side by -7

-1/7(x+4) = -7y/-7

-1/7(x+4) = y

The inverse is  -1/7(x+4)

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

Read more on sine trigonometry here: https://brainly.com/question/20367642

#SJP1

Answer:

Step-by-step explanation:

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

How to apply basic trigonometry?

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

Angle (θ) = 45°.

Opposite (Opp) side = a.

Hypotenuse (Hyp) = c.

Adjacent (Adj) side = b.

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

Read more on sine trigonometry here: brainly.com/question/20367642

#SJP1

The roots are (x + 1), (x - 4), (2 + 5i), and (2 - 5i).

g(x) = (x2 - 3x - 4)(x2 - 4x + 29)

Let us first consider x^2 - 3x - 4

By splitting the middle term

= x^2 + 1x - 4x - 4

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

= (x + 1)(x - 4)

Now let us consider x^2 - 4x + 29

First group the terms with variable on LHS and move the constant on the other side

x^2 - 4x = -29

Add 4 on both sides

x^2 - 4x + 4 = -29 + 4

x^2 - 4x + 4 = -25

It can be written as perfect squares

(x - 2)^2 = -25

We know that

i =√1

Take square root on both sides

x - 2 = ± 5i

x = 2 ± 5i

So we get,

x = 2 + 5i and x = 2 - 5i

g(x) = (x + 1)(x - 4)(2 + 5i)(2 - 5i)

A square root of a number is a price that, whilst extended by means of itself, offers variety. instance: four × four = 16, so a square root of 16 is four. The word that (−four) × (−four) = 16 too, so −four is likewise a square root of sixteen. The symbol is √ usually way the wonderful rectangular root. example: √36 = 6 (because 6 x 6 = 36).

Learn more about the square roots here https://brainly.com/question/3617398

#SPJ4

The linear function which represents the line given by the point slope equation y+1=-3(x-5) is f(x) =-3x+14 which is option D.

Given the equation y+1=-3(x-5) and we have to find the equation of line that represents this equation.

An equation is a relationship between two or more variables which are expressed in equal to form. Equation of two variables looks like ax+ by=c. It is solved in order to get the values of variables. Linear function is like equation whose graph shows a straight line.

We have to just find out the value of y in terms of x to find the linear function which can be done as under:

y+1=-3x(x-5)

y+1=-3x+15

y=-3x-1+15

y=-3x+14

Hence y=-3x+14 is the linear equation which represents the point slope equation y+1=-3(x-5).

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

Answer:

So the shorter version of what the guy above me is saying is that it is:

[tex]f(x) = -3x + 14[/tex]  or

D

Step-by-step explanation:

I got it right on the test.

Answer:

The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.

Step-by-step explanation:

A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(a, b),(c, d),(e, d)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {a, c, e}.

The set of the second components of each ordered the range.

From the relation, the range is {b, d, d}.

The given relation is a function. But it is not a one-to-one function.

When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

     Distances                     Time

            0                              0

            1                               3

            2                              6

            3                               9

            4                               12

            5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

Learn more about graph at brainly.com/question/4025726

#SPJ10

The perimeter of the shaded part is: 25.1 cm.

The area of the shaded part is: 36.6 cm².

Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).

Parameters given are:

Plug in the values into the equation

Area = 8² - 2(8² - 1/4π(8²)).

Area = 64 - 2(64 - 50.3)

Area = 36.6 cm²

Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm

Learn more about perimeter and area on:

https://brainly.com/question/443376

#SPJ1

Step-by-step explanation:

so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.

Answer:

The length of one side is 12ft

Step-by-step explanation:

The triangle is equilateral so all the sides are the same length.

So you are simply going to divide 36ft by the 3 sides.

36ft/3 = 12ft

Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The total number of legs in the room would be 10.

From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.

It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.

The legs of the bed and the chair do.

So we can say that the chair and the bed each have four legs.

so that would be two more legs.

In total we have:

4 + 4 + 2 = 10.

Learn more about riddles here:

brainly.com/question/20140875

#SPJ2

The domain and the range of the function are all set of real numbers

The function is given as:

f(x) = 4x + 3

The above function is a linear function

Linear functions have a domain and a range of all set of real numbers

Hence, the domain and the range of the function are all set of real numbers

Read more about domain and range at:

https://brainly.com/question/1632425

#SPJ1

Answer:

C

Step-by-step explanation:

first you need to memorize

SOH CAH TOA

IT means

Sine =opposite/hipotenuse

Cosine = adjecent/hipotenuse

tangent = opposite/adjecent

in this case, we need to find sine

so it's SOH

opposite of theta Θ is 15

and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem

let it be x

x =√ 15²+ 8²

=√ 225+ 64

=√289

= 17

so the answer is 15/17

The number line that shows that x ≥ -4 is; Option B

We want to find the number line that represents x ≥ -4

Now, for greater than sign, the number line would point to the right while  for less than sign the number line would point to the left.

Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.

Read more about Number Lines at; https://brainly.com/question/4727909

#SPJ1

The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a

JK = KL = √17

We know the following:

J = (4,5)

K = (5,1)

L = (1,2)

M = (1, 5)

We must commence by computing the length of the sides of the quadrilateral using:

D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]

JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

From the above, it is clear that

LM = MJ = 3; and

JK = KL = [tex]\sqrt{17}[/tex]

QED

Learn more about Proof and Kites at;
https://brainly.com/question/12160818
#SPJ1

Answer: B

Step-by-step explanation:

The sample space is a combination of these two dice as we have shown in the attachment

This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.

The question has two dice. These dice are made up of numbers from 1 to 6  each.

Die A = {1,2,3,4,5,6}

Die b = {1,2,3,4,5,6}

The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.

Read more on sample space here:

https://brainly.com/question/10558496

#SPJ1

Answer:

y-intercept: (0,2)

x-intercepts: (-4,0), (2,0)

Step-by-step explanation:

y-intercepts are found where the graph intersects the y-axis

same with x-intercepts, are found where the graph intersects the x-axis

The y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Where the line segment crosses the y-axis is the y-intercept,

And where the line segment crosses the x-axis is the x-intercept,

From the graph,

y-intercept is at (0,2)

x-intercepts is at (-4,0), (2,0)

Thus, the y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ1

Answer:

E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.

E must be 6.

E = 6

Step-by-step explanation:

16 * 6 = 96

The solution to the inequality: [tex]1.29m\leq 25[/tex]  is m=19.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Value of gift card=$25

Cost of each song=$1.29

Let m be the number of songs purchased.

Then, the required inequality is as follows:

[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]

The value of m rounded to the nearest whole number is 19.

Learn more about inequality here:

https://brainly.com/question/24372553

#SPJ4

The mean score of class B is 82. 92

Class A = 30 pupils

Class B = 26 pupils

Mean score for class A = 70

Mean score of class B = unknown

Total mean score = 76

We have, [tex]\frac{(76 *( 30 + 26) - 70 *30) }{26}[/tex]

Then simply,

Calculate the sum or difference between the classes = [tex]\frac{76 * 56 - 70 * 30}{26}[/tex]

Calculate the product or quotient of the classes = [tex]\frac{4256 - 70 * 30}{26}[/tex]

= [tex]\frac{4256 - 2100}{26}[/tex]

= [tex]\frac{2156}{26}[/tex]

= [tex]\frac{1078}{13}[/tex]

= [tex]82. 92[/tex]

Thus, the mean score of class B is 82. 92

Learn more about mean score here:

https://brainly.com/question/17203075

#SPJ1

[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]

[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]

[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]

[tex]10y {}^{2} + 90y + 200 = 0[/tex]

[tex]y {}^{2} + 9y + 20 = 0[/tex]

[tex](y + 4)(y + 5) = 0[/tex]

[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]

[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]

[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]

Hello!

The mean is the average of the terms.

⇒ Mean = Sum of terms / Number of terms

⇒ 130 = 104 + 137 + 154 + 131 + x / 5

⇒ x + 526 = 650

⇒ x = 124

∴ The missing number is 124.

The closest surface area of the container is: 1,696 ft².

Curved surface area of a cone = πrl

Surface of a cylinder = 2πr(h + r)

Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base

= πrl + 2πr(h + r) - πr²

r = 24/2 = 12 ft

l = 13 ft

h = 10 ft

Plug in the values

Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².

Learn more about surface area on:

https://brainly.com/question/76387

#SPJ1

Answer:

Find the derivative using the chain and power rules.

-6csc^(2 )(x^(3)-2x^(2))(3x^(2)-4x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the first number be x.

Then, given:

Since their sum is 131, we get the following equation:

or

This is matching the answer choice C.

Answer:

[tex]\left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]

Step-by-step explanation:

[tex]2*cos^2\theta-1=0\ \ \ \ (0^0\leq \theta\leq 360^0)\ \ \ \ \ \theta=?\\2*cos^2\theta-(sin^2\theta+cos^2\theta)=0\\2*cos^2\theta-sin^2\theta-cos^2\theta=0\\cos^2\theta-sin^2\theta=0\\cos2\theta=0\\0^0\leq \theta\leq 360^0\ \ \ \ \Rightarrow\\\left \{ {{2\theta=\frac{\pi }{2}\ |:2 } \atop {2\theta=\frac{3\pi }{2}\ |:2 }} \right. \ \ \ \ \left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]

Good luck and have a nice day!

A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sum of all three angles can be written as,

118° + 22° + x = 180°

x = 40°

For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.

For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.

Hence, Only the law of Sine can be applied to solve the triangle.

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ1

Equation: x² + 10x + 21

Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21

Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)

Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).

Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)

(x+3) (x+7)

Answer:

A. (x + 3)(x + 7)

Step-by-step explanation:

Got it correct… You’re welcome