the original price of a video game was 49.95 .The price was dropped to 45.50 .What was the percent of decrease from the original price

X^2+4x+4+12x+24-14=0

x^2+16x+14=0

x= -16 ± √(16)^2-4(1)(14) /2(1)

=-16± √200   /2

-16 ± 2√50    /2

-16 ± 10√2   /2

-8 ± 5√2  

Answer: A) x=-8±5[tex]\sqrt{2}[/tex]

Step-by-step explanation: to find the solutions of the given equation, we need to use the substitution u=x+2, so the equation would now be:

[tex]u^{2} +12u-14=0[/tex]

the quadratic formula is:

u=(-b±[tex]\sqrt{b^{2}-4ac }[/tex])/2a

in this case a=1;  b=12;  and c=-14

so replacing the values it remains:

u=(-12±[tex]\sqrt{12^{2}-4*1*(-14) }[/tex])/2*1

u=(-12±[tex]\sqrt{144+56}[/tex])/2

u=(-12±[tex]\sqrt{200}[/tex])/2              

we can write 200 as 100*2 and the square root of 100 is 10:

u=(-12±10[tex]\sqrt{2}[/tex])/2

u=-6±5[tex]\sqrt{2}[/tex]

and finally:

x=u-2

x=-6±5[tex]\sqrt{2}[/tex]-2

x=-8±5[tex]\sqrt{2}[/tex]

The area of the pentagon is 130.5 sq.inches

Apothem is the line that extends from the pentagon's center to a side and makes a 90° right angle with the side.

The basic formula for calculating the area of a regular pentagon is Area of pentagon = 1/2 p a, where p denotes the pentagon's perimeter and a denotes its apothem.

perimeter = 5 * 8.7 = 43.5

a = 6

area = 1/2 * 43.5 * 6 = 130.5

Therefore, The area of the pentagon is 130.5 sq.inches

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Your answer would be 64. To find this, you would follow PEMDAS, and multiply 6*5. You would then get 30. From there, you would add 30 to 34, getting 65. Hope this helped! Please mark brainliest! Thank you v much! :)

Answer:

64

Step-by-step explanation:

34+6.5=30+34=64:)

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]2x-5 < 15[/tex]

Solve for the inequality

Adds 5 both sides

[tex]2x < 15+5[/tex]

[tex]2x < 20[/tex]

Divide by 2 both sides

[tex]x < 20/2[/tex]

[tex]x < 10[/tex]

The solution is the interval ------> (-∞,10)

All real numbers less than 10

In a number line , the solution is the shaded area at left of x=10 (open circle)

The graph in the attached figure

Answer:

Income tax

Step-by-step explanation:

The more money someone earns, the higher their income, and the more government expects them to pay in taxes.

Answer:

[tex]cos(A) =\frac{3}{5}=0.6[/tex]

Step-by-step explanation:

By definition the cosine of an angle is the quotient between the side adjacent to the angle and the hypotenuse.

In other words:

[tex]cos (A) = \frac{adjacent}{hypotenuse}[/tex]

In this triangle the length of the side adjacent to the angle A is 30, and the length of the hypotenuse is 50

So:

[tex]cos(A) = \frac{30}{50}[/tex]

Simplifying we have that:

[tex]cos(A) = \frac{3}{5}=0.6[/tex]

Answer:

Final answer is [tex]\cos\left(A\right)=\frac{3}{5}[/tex].

Step-by-step explanation:

Using given information in the picture, we need ot find the missing value of Cos(A).

Apply formula of cosine function which is :

[tex]\cos\left(A\right)=\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos\left(A\right)=\frac{30}{50}[/tex]

[tex]\cos\left(A\right)=\frac{3}{5}[/tex]

Hence final answer is [tex]\cos\left(A\right)=\frac{3}{5}[/tex].

Answer:

See below

Step-by-step explanation:

(1) Create a table containing a few values of x and y

I chose x = -5, 0, and 5.

[tex]\begin{array}{rcc}& \mathbf{y = x + 6} & \mathbf{y = 3x - 2}\\\mathbf{x} & \mathbf{y} & \mathbf{y}\\-5 & 1 & -17\\0 & 6 & -2\\5 & 11 & 13\\\end{array}[/tex]

(2) Plot your points

Draw dots at the coordinates of each point ( Fig. 1).

(3) Draw the graph

Draw smooth lines through the points for each function.

Extend the lines in both directions to the edges of the plot area.

Your graphs should look like Fig. 2.

(4) Plot the solution

Note where the lines cross.

They appear to intersect at (4, 10).

Plot the point, and the finished graph should look like Fig. 3.

Answer:

(2, 4)

Step-by-step explanation:

Both equations have been solved for y, so to find x we need only set the equations = to each other:    y=-x+6   =  y=3x-2

Combining like terms, we get 4x = 8, and x = 2.  Substituting 2 for x in y = 3x -2, we get y = 3(2) - 2 = 4.

The solution is (2, 4).  If you were to graph these two lines, you'd find that they intersect at (2, 4).

Answer:

9

Step-by-step explanation:

The coefficient is the number directly next to the variable, in this case, the variable being y, and the number being 9.

In the question:

9y + 5,

9 is the coefficient

y is the variable

5 is a constant (does not change).

Note that the coefficient and constant cannot change, but the value of the variable (y) can vary (hence the name).

~

The coefficient in the expression is 9.

The coefficient of a term in an algebraic expression is the number that is multiplied by the variable in the term.

To find the coefficient of a term, you can follow these steps:

1. Identify the variable in the term.

2. Look for the number that is multiplied by the variable.

3. That number is the coefficient of the term.

In the expression 5+ 9y, the variable is y. The number that is multiplied by y is 9.

Therefore, the coefficient in the expression is 9.

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The correct answers are:

A. P = 58 and Q = 78

C. P = -78 and Q = -52

D. P = 58 and Q = -78

To determine which values of P and Q result in the equation Px + 52 = Qx - 78 having exactly one solution, we need to ensure that the coefficients of x on both sides are not equal. This means P should not be equal to Q.

The given equation is:

Px + 52 = Qx - 78

First, let's rearrange the terms to isolate x:

Px - Qx = -78 - 52

(P - Q)x = -130

For this equation to have exactly one solution, P - Q must be non-zero. Therefore, P - Q.

Let's evaluate each option:

A. P = 58 and Q = 78

- P - Q = 58 - 78 = -20

- Since -20 is not zero, this pair results in exactly one solution.

B. P = 52 and Q = 52

- P - Q = 52 - 52 = 0

- Since 0 is zero, this pair does not result in exactly one solution.

C. P = -78 and Q = -52

- P - Q = -78 - (-52) = -78 + 52 = -26

- Since -26 is not zero, this pair results in exactly one solution.

D. P = 58 and Q = -78

- P - Q = 58 - (-78) = 58 + 78 = 136

- Since 136 is not zero, this pair results in exactly one solution.

Answer:

A- y=0.5x+3

Step-by-step explanation:

ANSWER

10.9

EXPLANATION

We use the Altitude Theorem to determine the value of h.

According to the Altitude Theorem, the height, h is equal to the geometric mean of the two segment created by the leg of the altitude on the hypotenuse.

This implies that:

[tex] h= \sqrt{MP \times PO} [/tex]

That's,

[tex]h= \sqrt{(24- 7)7} [/tex]

[tex]h= \sqrt{17 \times 7} [/tex]

[tex]h= \sqrt{119} [/tex]

[tex]h= 10.9[/tex]

to the nearest tenth.

Answer:

The second one.

Step-by-step explanation:

The slope of the graph, -1/3, is going down from left to right because it is negative, so it is decreasing. Slope is the rise over run, so because the slope is -1/3 look for lines that go down 1 unit and across 3 at the same time (from one corner of a square to the other). Then, because your y-intercept is a 5, just look for your line to cross the y-axis at 5. And that's it.

The second graph is the graph of the linear equation y = - 1/3x + 5.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given linear equation is  y = - 1/3x + 5

We need to select the graph of the equation.

The slope of the line is -1/3

y intercept is 5.

Let us find few points to determine the graph.

if x=0, then y=-1/3(0)+5=5

So (0, 5) is one of the point

if x=1, then y=-1/3(1)+5

=14/3

(1, 14/3)

if x=2, then y=-1/3(2)+5

=13/3

(2, 13/3)

if x=3, then y=-1/3(3)+5

(3, 4) is point.

Now let us check these points which satisfy the graph.

Hence, the second graph is the graph of the linear equation y = - 1/3x + 5.

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Answer:

135 square ft.

Step-by-step explanation:

To solve this equation, you need to find the area of this rectangle. Area is always base x height, or in this case, length x width. Now you multply your length, 15', by your width, 9', to get your answer, 135 square feet. When you multiply two measurments of the same unit together, you get square (units), which simply means that you multiplied two of the same unit of measurment together.

Answer:

3.28084

hope this helps

Answer:

3.28

Step-by-step explanation:

1 cm = 0.0109361 yards

Multiply by 300

300 cm = 3.28083 yards

Answer: The answer is A

Step-by-step explanation: When you add 1/2+1/5+1/3 it equals 31/30 which when converted is equal to 1.033 which is less than 1 1/2.

Answer:

[tex]r=\frac{9\cos \theta}{\sin^2 \theta}[/tex]

Step-by-step explanation:

The given equation in rectangular coordinates is;

[tex]y^2=9x[/tex]

We use the relation;

[tex]x=r\cos \theta[/tex]

and

[tex]y=r \sin \theta[/tex]

This implies that;

[tex](r \sin \theta)^2=9(r \cos \theta)[/tex]

[tex]r^2 \sin^2 \theta=9r \cos \theta[/tex]

Divide through by r to get;

[tex]r \sin^2 \theta=9\cos \theta[/tex]

Divide both sides by [tex]\sin^2 \theta[/tex]

[tex]r=\frac{9\cos \theta}{\sin^2 \theta}[/tex]

The line perp. With this equation is y=-5/3+4x

Answer:

x=2π/3+π n

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

The solution to tan X + √(3) = 0 is option D)300°.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Given function;

tan X + √(3) = 0

Solving;

tan X = -√(3)

tan X = -(tan 60) = 300 degrees (beacuse of negative)

Here, the tangent function is posittive in the first and the third quadrants.

The solution to tan X + √(3) = 0 is option D)300°.

The remaining question is

'Which of the following is a solution to tanx+sqrt3=0?

A)60°

B)150°

C)240°

D)300°'

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It is -1, you first make the -1 positive but then the negative sign outside makes that 1 turn -1

The value of the absolute numerical expression will be negative 1.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The expression is given below.

⇒ - |- 1|

If the mode is removed, then the value inside the mode comes out to be positive. Then the value of the expression will be calculated as,

⇒ - |- 1|

⇒ - (1)

⇒ - 1

The value of the absolute numerical expression will be negative 1.

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Answer:

8:20

Step-by-step explanation:

It says brown tiles to total tiles.

12+8=20

Final answer:

The ratio of 12 brown tiles to 20 total tiles is 3:5, indicating that for every 3 brown tiles, there are 5 total tiles in that section.

Explanation:

To compare the number of brown tiles to the total number of tiles in one section, use the ratio:

12 brown tiles : 20 total tiles = 12 : 20 = 3 : 5

This ratio simplifies to 3:5, showing that for every 3 brown tiles, there are 5 total tiles in that section. The ratio of 12 brown tiles to 20 total tiles is 3:5, indicating that for every 3 brown tiles, there are 5 total tiles in that section.

- This is what it is in vertex form, (-1/4,-1/2).

Answer:

4/10= 0.4

3 1/10= 3.1

7/10= 0.7

6 5/10= 6.5

9/10= 0.9

Step-by-step explanation:

Answer:

The answer is 9/11.

Step-by-step explanation:

To find the answer you'd first add up how many patients you have:

80+10+20 = 110.

Now find out that how many patients are taking a real drug, which is represented by 80+10 = 90.

So, the probability of a patient NOT getting a placebo is 90/110

Simplified would be 9/11

Thus the answer is 9/11....

Answer:

64

Step-by-step explanation:

115 - 51 = 64

Answer:

66

Step-by-step explanation:

put them in order from least to greatest.

51, 51, 56, 58, 68, 72, 90, 101, 101, 111, 114, 115, 117

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is...

117-51=

66

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=12\\ h=6 \end{cases}\implies V=\pi (12)^2(6)\implies \stackrel{\textit{volume of A}}{V=864\pi }[/tex]

so their difference is 864π - 648π = 216π.

if we take 864π to be the 100%, what is 216π off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 864\pi &100\\ 216\pi &x \end{array}\implies \cfrac{864\pi }{216\pi }=\cfrac{100}{x}\implies 4=\cfrac{100}{x} \\\\\\ 4x=100\implies x=\cfrac{100}{4}\implies x=25[/tex]

You can FOIL (First, Outside, Inside, Last)

(3z+1)(4z+2)

First

(3z+1)(4z+2)

3z * 4z

[tex]12z^{2}[/tex]

Outside

(3z+1)(4z+2)

3z * 2

6z

Inside

(3z+1)(4z+2)

4z * 1

4z

Last

(3z+1)(4z+2)

2*1

2

Combine all the products of FOIL together

[tex]12z^{2}[/tex] + 6z + 4z + 2

Combine like terms

[tex]12z^{2}[/tex] + 10z + 2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

I think it may be C) 5.5

Step-by-step explanation:

well the question doesn't really give us anything to work with to find the exact answer but if we look at the triangle logically then we will figure out that JZ is smaller than JS. and if JS is 8.7 then we can't have JZ being longer than JS so option D is out. and the other two options are way too short to be the length of JZ. Therefore we have option C as our winner

Hope this helps

Answer:

Step-by-step explanation:

[tex]\dfrac{2}{3}(3x+9y)+\dfrac{1}{2}(4x-2y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)(3\!\!\!\!\diagup^1x})+\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)(9\!\!\!\!\diagup^3y})+\left(\dfrac{1}{2\!\!\!\!\diagup_1}\right)(4\!\!\!\!\diagup^2x})+\left(\dfrac{1}{2\!\!\!\!\diagup_1}\right)(-2\!\!\!\!\diagup^1y})\\\\=2x+(2)(3y)+2x-y=2x+6y+2x-y\qquad\text{combine like terms}\\\\=(2x+2x)+(6y-y)=4x+5y[/tex]

The most beneficial banking service for a customer with a new debit card would be no ATM fees, as this would save money on transactions, which is especially important given that banks tend to charge for non-interest income such as ATM and overdraft fees.

For a customer who just obtained a debit card, the most beneficial banking service would be no ATM fees. Debit cards give users the ability to access their funds through an ATM. Considering banks are profit-oriented and look to maximize non-interest income through various fees as described, ATM fees can be a frequent and unnecessary expense. ATM fees average $2.97 per transaction and can quickly accumulate, especially if withdrawals are made at out-of-network ATMs, which add even more to the cost. Therefore, selecting a banking service with no ATM fees would save the cardholder potential costs associated with accessing their money.

No overdraft protection would mean the cardholder could be charged substantial overdraft fees if they were to spend more than the balance in their checking account. Given that these fees can be very high, it's better to either have overdraft protection or manage the account carefully to avoid overdrafting. On the other hand, a $25 yearly fee is a fixed cost and might be worth it if the benefits provided surpass the fee, but it is generally an additional expense that can be avoided with careful account selection. Lastly, 0% financing is typically associated with credit cards rather than debit cards and the quoted 'introductory' rates can be misleading, often coming with hidden fees and high interest rates after the introductory period ends.

Answer: 6

Step-by-step explanation:

The circumference is always x2 of the radius