The original price of a mountain bike was reduced $125 if p = the mountain bike's original price in dollars, which algebraic expression represents the reduce price?

Answer:

Option D (20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70).

Step-by-step explanation:

The given inequality is 30 ≤ x + 10 ≤ 80 . There are basically two inequalities. One is 30 ≤ x + 10 and x + 10 ≤ 80. x is the number of hamburgers that are to be made, 10 is the number of hamburgers already made, 30 is the lower limit of the hamburgers required, and 80 is the upper limit of the hamburgers required. The question requires to solve the inequality. To solve this, the inequality will be separated as done above.

1)

30 ≤ x + 10.

20 ≤ x.

2)

x + 10 ≤ 80.

x ≤ 70.

Now combining the two inequality gives:

20 ≤ x ≤ 70. So Rodney needs to make at least 20 more hamburgers but no more than 70. Therefore, Option D is the correct answer!!!

Answer:

20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70

Step-by-step explanation:

Let

x ----> the numbers of hamburgers that Rodney needs to make

we know that

[tex]x+10\geq 30[/tex] ----> inequality A

[tex]x+10\leq 80[/tex] -----> inequality B

Solve the inequality A

[tex]x\geq 30-10[/tex]

[tex]x\geq 20\ hamburgers[/tex]

Solve the inequality B

[tex]x\leq 80-10[/tex]

[tex]x\leq 70\ hamburgers[/tex]

so

The solution of the system of inequalities is the interval

[20,70]

[tex]20 \leq x \leq 70[/tex]

All whole numbers greater than or equal to 20 hamburgers and less than or equal to 70 hamburgers

therefore

Rodney needs to make at least 20 more hamburgers but no more than 70.

Answer:

m + 15

Step-by-step explanation:

Start at the end and work backwards to the beginning of the sentence.  Most times these work like that.  I'll start with "m", then I know that 15 more than "m" is m + 15.  It would be the same thing to express that particular problem as 15 + m because addition is commutative.  But subtraction is not.

"15 less than m" is m - 15, wheras

"m less than 15" is 15 - m.  

This matters because if m = 10, for example, 10 - 15 = -5 where 15 - 10 = 5

5 and -5 are not the same answer.

Answer:

Step-by-step explanation:

C

The equivalent expression is option (B) x^2/3 is the correct answer.

An equivalent expression is an expression that has the same value but does not look the same. When you simplify an expression, you're basically trying to write it in the simplest way possible.

For the given situation,

The expression is [tex](x^{\frac{4}{3} }x^{\frac{2}{3} } )^{\frac{1}{3} }[/tex]

The equivalent expression can be obtained as

⇒ [tex](x^{\frac{4}{3}+\frac{2}{3} } )^{\frac{1}{3} }[/tex]                       [ ∵ [tex]x^{a} x^{b}=x^{a+b}[/tex]]

⇒ [tex](x^{\frac{6}{3}} )^{\frac{1}{3} }[/tex]

⇒ [tex]x^{(\frac{6}{3}) (\frac{1}{3}) }[/tex]                         [∵ [tex]x^{(a)(b)}=x^{ab}[/tex]]

⇒ [tex]x^{\frac{6}{9} }[/tex]

⇒ [tex]x^{\frac{2}{3} }[/tex]

Hence we can conclude that the equivalent expression is option (B) x^2/3 is the correct answer.

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Answer:

C. SAS

Step-by-step explanation:

Proof:

AB ≅ DC - Given (Side)

∠BAC ≅ ∠DCA - Given (Angle)

AC ≅ AC -  Reflexive Property (Side)

~

Answer:

  A.  ASA

Step-by-step explanation:

Two angles and the side between them are marked congruent. In the congruence theorem designators, A stands for Angle, and S stands for side. When there is a congruent side between two corresponding congruent angles, the ordering of the designators is A - S - A.

The ASA postulate applies.

The ASA, AAS, and SAA postulates can all be used to prove that triangles are congruent, depending on the given congruent parts. ASA stands for Angle-Side-Angle, AAS is Angle-Angle-Side, and SAA is Side-Angle-Angle (similar to ASA). If none of these postulates apply, the triangles might not be congruent.

In Mathematics, to determine whether two triangles are congruent, various postulates are employed. The options given, ASA, AAS, and SAA, are all valid postulates in which to demonstrate congruence.

The ASA postulate (Angle-Side-Angle) proves that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

The AAS postulate (Angle-Angle-Side) proves that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.

The SAA postulate, also known as the ASA postulate, stands for Side-Angle-Angle. If the two angles and the side opposite one of them in a triangle are congruent to the corresponding parts in another triangle, the triangles are congruent.

If none of the above postulates apply, the triangles may be not congruent.

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Answer:

2.16

Step-by-step explanation:

The question is on mean absolute deviation

The general formula ,

Mean deviation = sum║x-μ║/N where  x is the each individual value, μ is the mean and N is number of values

Team 1

Finding the mean ;

[tex]mean= \frac{51+47+35+48+64}{5}  =49[/tex]

Points     Absolute Deviation from mean

51                          2

47                         2

35                        14

48                         1

64                         15

Sum                    34          

Absolute mean deviation = 34/5= 6.8

Team 2

Finding the mean

[tex]mean=\frac{27+55+53+38+41}{5} = 42.8[/tex]

Points                      Absolute deviation from the mean

27                                    15.8

55                                    12.2

53                                     10.2

38                                      4.8

41                                       1.8

Sum                                 44.8        

Absolute deviation from the mean = 44.8/5 =8.96

Solution

Difference in mean absolute deviation of the two teams = 8.96-6.8 = 2.16

Answer:

A. right angle

B. complementary angles

Step-by-step explanation:

<EFH is right angle

<EFG + <GFH = 90 (complementary angles, sum = 90)

Answers

A. right angle

B. complementary angles

There are multiple types of angles which can be found in geometry such as right angles (90°), acute angles (less than 90°), obtuse angles (greater than 90° but less than 180°), and straight angles (180°). Other structures like Trigonal Bipyramidal also exhibit specific angles of 90° or 120°. Trigonometry and the concept of reflection also involve dealing with angles.

In attempting to understand the types of angles that you may be referencing in your query, I am basing this response on the idea that you're asking about geometrical angles, or those about the incline referenced. In simple geometrical terms, there are a few principal types of angles we can name:

Based on the provided information, we might also be looking at the angles in a Trigonal Bipyramidal formation. Here the angles can be of 90° or 120°. The atoms attached to this structure can either be equatorial (in the plane of the triangle) or axial (above or below the plane of the triangle). Determining these from reason might require some knowledge of trigonometry. Additionally, the concept of angle of incidence and angle of reflection in the law of reflection also comes into play when dealing with angles and their measures.

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Answer:

$532.50 / (number of members)

Step-by-step explanation:

Let m represent the number of members.

The net income (after subtracting the cost of the popcorn) was $532.50.

Thus, the amount of $ raised per member of the club was $532.50/m

Answer

(627.50-95)/m

Step-by-step explanation:

got 100%

Answer: A

Step-by-step explanation: Complementary angles must add up to 90 degrees.

Answer:

Step-by-step explanation:

| x - y | = 5

x * y = 126

x = -9; y = -14

x + y = -23

I'm not sure this may help you since I don't know how well you are at mental math so I just used guess and check by checking which pair of numbers would work.

Since the numbers are 5 apart, and they're both negative, I check which pair is equal to 126.

-6 * -11 = 66

...

-9 * -14 = 126

Remember to start from a reasonable area.  

Also, I just realized that you can use the process of elimination for this question last minute.  Since both numbers are negative, they add up to a negative number so you can cross off C and D.  You can cross of B since the only way to end up with a sum of -5 is if you end up having 0 and -5, and 0 * (-5) = 0.

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Answer:

A

- 23

Step-by-step explanation:

Two negative numbers differ by 5

Let the smaller one be x

Let the larger one be y

y - x = 5                    this will give you a plus. Let us suppose the numbers are -20 and -25.  - 25 is smaller than - 20. Which would you rather be, 20 dollars in debt or 25 dollars in debt?

So using -20 - - 25 = 5

y = x + 5                   Obtained by adding x to both sides.

xy = 126

You can eliminate C and D. Both are positive. That's not what the question says.

xy = 126                          Put  y = x + 5 in for y.

x(x + 5) = 126                  Remove the brackets

x^2 + 5x = 126                Subtract 126 from both sides.

x^2 + 5x - 126 = 0           Factor

(x + 14)(x - 9) = 0

You cannot use x - 9 = 0 because 9 is not a negative number.

x + 14 = 0

x = - 14

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

y = x + 5

y = -14 + 5

y = - 9

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

The sum of the two numbers is

- 14 + -9 = - 23

Answer:

So the three new vertices are (0,0)  , (-1,-0) , and (-1,3)

Step-by-step explanation:

So let's pick a point on the triangle like (-3,-1).

The center point of dilation is (3,1).  The horizontal distance that (3,1) is from (-3,-1) is 3-(-3)=6. The scale factor is 0.5 so multiply 0.5 to the horizontal distance which is 3. The vertical distance that (-3,-1) is from (3,1) is 1-(-1)=2. The scale factor is 0.5 so multiply 2 and 0.5 giving you 1.

So this means the image of the point (-3,-1) is going to be at: starting from center (3,1) move left 3 and down 1 and you are at (0,0).

Or if you prefer just use a formula

(k(x-a)+a,k(y-b)+b)

(x,y) is a point on the triangle

(a,b) is the center=(3,1)

k is the scale factor=.5

So let's do this formula to the other two points...

(x,y)=(-5,-1)

(.5(-5-3)+3,.5(-1-1)+1)

(.5(-8)+3,.5(-2)+1)

(-4+3,-1+1)

(-1,0)

Last point (x,y)=(-5,5)

(.5(-5-3)+3,.5(5-1)+1)

(.5(-8)+3,.5(4)+1)

(-1,3)

So the three new vertices are (0,0)  , (-1,-0) , and (-1,3)

Answer:

Step-by-step explanation:

The cubic equation ...

  (x -3)(x -1)(x +5) = 80

has one real root: x = 5. Using that value for x, the dimensions become ...

  length = 5 - 3 = 2

  width = 5 - 1 = 4

  height = 5 + 5 = 10

The dimensions are (length, width, height) = (2, 4, 10).

_____

We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the Rational Root theorem to find possible values of x. That form can be found to be ...

  (x -3)(x -1)(x +5) -80 = 0

  x³ +x² -17x -65 = 0

Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:

  1, 5, 13, 65

We know that x must be greater than 3 (so all dimensions are positive). Thus possible values of x are 5, 13, 65, and we're pretty sure that 65 is way too large.

Answer:

  17

Step-by-step explanation:

If 3 times the quantity is 57, then the quantity is 57/3 = 19.

If 2 more than the number is 19, then the number is 17.

Answer:

The image of [tex](7,2)[/tex] is [tex](2,12)[/tex]

Step-by-step explanation:

First you need to find the translation vector.

Let the translation vector be [tex]u=(a,b)[/tex]. Then the translation rule is

[tex](x,y)\to (x+a,y+b)[/tex].

From the equation, the image of [tex]P(2,-4)[/tex] is  [tex]P'(-3,6)[/tex].When we apply this rule using the translation vector, we get

[tex]P(2,-4)\to P'(2+a,-4+b)[/tex]

Now we have

[tex]P'(2+a,-4+b)=P'(-3,6)[/tex]

We can therefore equate corresponding coordinates

[tex]2+a=-3[/tex] and [tex]-4+b=6[/tex]

This implies that:

[tex]a=-3-2[/tex] and [tex]b=6+4[/tex]

[tex]a=-5[/tex] and [tex]b=10[/tex]

Hence our translation vector is [tex]u=(-5,10)[/tex]

The translation rule now becomes:

[tex](x,y)\to (x-5,y+10)[/tex].

To find the image of (7,2), we plug it into the translation rule.

[tex](7,2)\to (7-5,2+10)[/tex].

[tex](7,2)\to (2,12)[/tex].

Answer:

  9840

Step-by-step explanation:

1 - 18% = 82% survive, so the number available for sale is ...

  0.82 × 12,000 = 9,840

Answer:

9,840 apples.

Step-by-step explanation:

We have been given that in an apple farm each year, about eighteen percent of the collected apples must be thrown out because of rot.

To find the number of apples that survive for the farmer to sell, we need to find 82% of 12,000. As 18% apples must be thrown each year, so left apples (100-18=82) will be available to sell.

[tex]\text{Apples survive for the farmer to sell}=12000\times \frac{82}{100}[/tex]

[tex]\text{Apples survive for the farmer to sell}=120\times 82[/tex]

[tex]\text{Apples survive for the farmer to sell}=9840[/tex]

Therefore, 9,840 apples survive for the farmer to sell.

Answer:

C.

Step-by-step explanation:

To solve for x you have to move the -5y to the other side of the equals sign.  Since the opposite of subtracting is adding, we will add 5y to both sides to get

x = 5y + 6

Choice C

The value of x − 5y = 6 is x = 5y + 6.

Given:

x − 5y = 6

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Solve the value of x, then

x - 5y = 6

Simplifying the above equation, we get

x = 6 + 5y

Therefore, the correct answer is option C) x = 5y + 6.

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Answer:

5

Step-by-step explanation:

Distance from B to B' is equal to the distance from A to A', AA'=5 so BB'=5

Answer:

y=2x-3

when two lines are parallel, they have the same slope.

in the formula y=mx+b, m=slope of the line

we know 2 will be the slope for the line passing through (4,5)

next plug in (4,5) into the formula with 2 as the slope

4=x 5=y

next 5=2(4)+b

and you end up with

y=2x-3 when you simplify

Answer: (4.25,-2)

Step-by-step explanation:

Answer:

(4.25, -2) is the focus point

Step-by-step explanation:

Answer:

Option C is correct

Step-by-step explanation:

We need to simplify the radical

[tex]\sqrt{\frac{20x^{13}y^5}{5xy^7}}[/tex]

We know that a^m/a^n = a^m-n and 20/5 = 4

Solving

[tex]\sqrt{4x^{13-1}y^{5-7}}\\\sqrt{4x^{12}y^{-2}}\\[/tex]

Now, √4 = 2 and a^-m = 1/a^m

Applying,

[tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex]

So, Option C [tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex] is correct.

Answer:

Prakhar is 13 years older than his youngest sister.

Step-by-step explanation:

if we let his younger sisters age be x, and prakar is 13 years older,

then prakar's age is (13 + x)

The statement that represents the expression 13 + x is " Prakhar is 13 years older than his youngest sister".

The expression consists of at least one variable and constants with basic arithmetic operators.

Statement 1: Andrea has 13 eggs and bought 13 more

Here there is no use of variables. So, Andrea has a total of 26 eggs. "false"

Statement 2: Victoria has 13 flowers. This is greater than the number of flowers Elisa has.

The expression that represents this statement is V > E (the number of flowers that Victoria and Elisa have are denoted by V and E)

So, this also does not represent the given equation. "false"

Statement 3: Prakhar is 13 years older than his youngest sister.

Consider the age of Prakhar's younger sister = x

So. Prakhar's age becomes x + 13 or 13 + x

Thus, it represents the given expression. "true"

Statement 4: Kai is 13 blocks from home. Jack is a greater distance away.

These are not connected or related to one another. So, no variable is used and it doesn't form an expression. "false"

Therefore, statement 3 is a true expression and it is represented by the expression "13 + x".

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Answer:

Infinite number of solutions

Step-by-step explanation:

Since the equations are both the same, we have an infinite number of solutions! The solutions lie on the graph y = -2x+5.

The system of equations given represents the same line with infinitely many solutions,.

The system given is y = -2x + 5 and y = -2x + 5. Both equations are identical, which means they represent the same line. Therefore, every point on the line y = -2x + 5 will satisfy both equations, indicating that the system has infinitely many solutions. The slope of the line is -2 and the y-intercept is 5. This aligns with the standard form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.

Answer:

1950 cubic units

Answer:

[tex]1040[/tex] cubic units

Step-by-step explanation:

The volume of any oblique geometric shape is equal to the product of area of its base and the height from which its top extends to its bottom base.

Mathematically, it can be represented as -

[tex]V = (Area_{base} * height)\\[/tex]

Substituting the given values in above equation, we get -

[tex]V = (10 * 13) * 8 \\V = 1040\\[/tex] cubic unit.

ANSWER

[tex]x = 71 \degree[/tex]

EXPLANATION

The sum of the exterior angles of a polygon is 360°

The angles were given in terms of x.

We add all and equate to 360° to obtain.

[tex]x + (x - 6) + (x + 4) + (x + 2) + (x + 5) = 360 \degree[/tex]

This implies that,

[tex]5x + 5 = 360[/tex]

[tex]5x = 360 - 5[/tex]

[tex]5x = 355[/tex]

[tex]x = \frac{355}{5} [/tex]

[tex]x = 71 \degree[/tex]

Answer: [tex]x=71[/tex]

Step-by-step explanation:

We need to remember that the sum of the exterior angles of a polygon is 360 degrees.

Knowing this, we can write the following expression:

[tex](x+4)+(x+2)+(x+5)+x+(x-6)=360[/tex]

Finally, we need to solve for "x" to find its value. Therefore, this is:

[tex]x+4+x+2+x+5+x+x-6=360\\\\5x+5=360\\\\5x=360-55\\\\5x=355\\\\x=\frac{355}{5}\\\\x=71[/tex]

Answer:

The image of Y is Y’. Have a good day.

Answer: first option.

Step-by-step explanation:

Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identify from the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.

You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.

Therefore, the conclusion is: The image of Y is Y'.

Answer:

Step-by-step explanation:

Fill in the given numbers and solve for k.

  y = kx²

  1000 lb = k(5 in)²

  (1000 lb)/(25 in²) = k = 40 lb/in² . . . . . . divide by the coefficient of k

__

Fill in the given numbers and solve for x.

  y = kx²

  16000 lb = (40 lb/in²)x²

  16000 lb/(40 lb/in²) = x² = 400 in² . . . . . . divide by the coefficient of x²

  20 in = x . . . . . . . . . take the square root

The depth to support 16,000 pounds should be 20 inches.

Answer:

  12.8 years

Step-by-step explanation:

Put the given numbers into the model and solve for t.

[tex]3P_0=P_0e^{.086t}\\\\3=e^{.086t} \qquad\text{divide by $P_0$}\\\\\ln{3}=.086t \qquad\text{take the natural log}\\\\\dfrac{\ln{3}}{.086}=t\approx 12.77[/tex]

It will take about 12.77 years for the population to triple at the current growth rate.

Final answer:

It will take approximately 40.1 years for a country's population to triple if it continues to grow at a rate of 0.86% per year, calculated using the exponential growth formula.

Explanation:

The question asks how long it will take for a country's population to triple if it continues to grow at a continuous compound rate of 0.86% per year. Using the exponential growth formula P = P_0e^{rt}, where P is the final population, P_0 is the initial population, r is the rate of growth, and t is the time in years, we can solve for t when the population triples (P = 3P_0). Thus, the equation becomes 3 = e^{0.0086t}. Solving for t, we take the natural logarithm of both sides to get ln(3) = 0.0086t, which gives us t = ln(3) / 0.0086 years.

Calculating this, t ≈ 40.1 years. Therefore, it will take approximately 40.1 years for the country's population to triple at a continuous compound growth rate of 0.86% per year.

1. The monomial, x, a factor of  the expression x2 + 15x "represents the side length, in centimeters, of the photo." So Choice A.

2. The binomial, (x + 15), a factor  of the expression x2 + 15x is Choice D because x is the length of the photo plus the 15 cm left of the frame.

3. The first-degree term of  the expression x2 + 15x is the area of the photo since "x" is the length. So, Choice C.

4. The second-degree term of  the expression x2 + 15x is the area of the frame around the picture. That leaves us with Choice B.

Answer:

A-1

B-4

C-3

D-2.

Step-by-step explanation:

We are given that  Patricia has a square shaped photo of her soccer team that she plans to given her coach.She decided to put the photo in a rectangular frame that is 15 cm longer than the length of the picture .

Let x be the length of side of  of square shaped photo

Then length of side of rectangular shaped frame=[tex]x+5[/tex]

We are given that the area of framed picture in quadratic expression where x represents the side length in cm of photo

[tex] x^2+15x[/tex]

[tex] x(x+15)[/tex]

The area of square=[tex] side\times side [/tex]

The area of photo=[tex] side \times side[/tex]

Therefore, the area of photo =[tex] x\times x=x^2[/tex]

The area of frame =area of framed picture- area of photo=[tex]x^2+15x=x^2=15x[/tex]

A. The length of the photo

1.The monomial x a factor of the expression

B.The area of the frame around the picture

4. The second- degree term of the expression[tex]x^2+15x[/tex]

C.The are of the photo

3.The first -degree term of the expression[tex] x^2+15x[/tex]

D.The length of the frame

2.The binomial (x+15),a factor of the expression[tex]x^2+15 x[/tex]

Answer: A-1

B-4

C-3

D-2.

Answer:  f(x) and g(x) are inverses of each other

Step-by-step explanation:

To find the inverse of a function, swap the x's and y's and then solve for "y"

f(x) = 5x + 2

 y  = 5x + 2

Swap:

     x = 5y + 2

   -2        - 2

x - 2 = 5y

÷5     ÷5      

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

****************************************************************

[tex]g(x)=\dfrac{x-2}{5}\\\\y=\dfrac{x-2}{5}\\\\\text{Swap:}\\x=\dfrac{y-2}{5}\\\\\\(5)x=\dfrac{y-2}{5}(5)\\\\\\5x=y-2\\\\5x+2=y[/tex]

The function g(x) = x - 2/5 is the inverse of f(x) = 5x + 2. We can show this by switching the variables in the equation and solving for y.

Step 1: The variable in the function notation f(x) is x. So, we can write the function as an equation: y = 5x + 2.

Step 2: Now, we switch the variables. The equation becomes x = 5y + 2. Solving for y, we get y = (x - 2) / 5.

Step 3: To find the inverse of g(x), we need to switch the variables in the equation: x = (y - 2) / 5. Solving for y, we get y = 5x + 2. This is the original function f(x). Therefore, g(x) = x - 2/5 is the inverse of f(x) = 5x + 2.

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Answer:

C. 5

Step-by-step explanation:

Since Triangle ABC is congruent to EDF it mean that the sides are the same so the length of BC is congruent to the length of DF:

distance formula:

d = √(x2 - x1)^2 + (y2 - y1)^2

d = √(2 - 2)^2 + (-1 - 4)^2

d = √(0)^2 + (-5)^2

d = √0 + 25

d = √25

d = 5