A sale at a furniture store advertised that all furniture was being sold at 40% off the
original selling price.
a) Write a function that gives the sale price as a function of original selling price.
b) Find the inverse of this function.
c) What does the inverse represents?

Answer:

The money earned by Drea was [tex]\$225[/tex]

The money earned by Sajini was [tex]\$200[/tex]

Step-by-step explanation:

Let

x------> money earned by Drea

y------> money earned by Sajini

we know that

[tex]x+y=425[/tex] -----> equation A

[tex]x=y+25[/tex] ----> equation B

substitute equation B in equation A

[tex](y+25)+y=425[/tex]

solve for y

[tex]2y=425-25[/tex]

[tex]y=400/2=\$200[/tex]

Find the value of x

[tex]x=y+25[/tex] ----> [tex]x=200+25=\$225[/tex]

using a graphing tool

solve the system of equations

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is [tex](225,200)[/tex]

see the attached figure

Answer:

Drea: $225

Sajini: $200

Step-by-step explanation:

D + S = 425

D = S + 25

S + 25 + S = 425

2S = 400

S = 200

D = 200 + 25 = 225

Answerenise's rock sample has  

38

,

890

centigrams more mass than that of Pauline

:

Step-by-step explanation:

Answer:

y = (x + 9)² + 9

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

given a parabola in standard form : ax² + bx + c : a ≠ 0

the the x-coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = x² + 18x + 90 is in standard form

with a = 1, b= 18 and c = 90

[tex]x_{vertex}[/tex] = - [tex]\frac{18}{2}[/tex] = - 9

to find the corresponding y-coordinate substitute x = - 9 into the equation

y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9

⇒ y = (x + 9)² + 9 ← in vertex form

Option B. 12/ 125  is the answer.

Explanation

Total umber of sour ball candies = 50

Number of lemon candies = 12

Hence the probability to get a lemon candy is = 12/50

Number of cherry sour balls = 20

So, the probability to get a cherry sour ball = 20/50

So, to get the joint probability for a random selection to either get a lemon or cherry candy, we will multiply both the probabilities.

[tex]\frac{12}{50}*\frac{20}{50}[/tex]

= [tex]\frac{12}{125}[/tex]

Answer:

Step-by-step explanation:

It is given that the perimeter of the regular hexagon is 48 inch. Thus,

Perimeter of the regular hexagon = 48

⇒[tex]Sum of all the sides=48[/tex]

⇒[tex]6x=48[/tex]

⇒[tex]x=8inch[/tex]

Thus, the side of the regular hexagon is 8 inch.

Now, [tex]area of the regular hexagon=\frac{3\sqrt{3}}{2}(x)^2[/tex]

⇒[tex]A=\frac{3\sqrt{3}}{2}(8)^2[/tex]

⇒[tex]A=\frac{3\sqrt{3}}{2}(64)[/tex]

⇒[tex]A=96\sqrt{3}[/tex]

⇒[tex]A=166.03 sq inches[/tex]

Thus, the area of the regular hexagon is 166.03 sq inches.

The area of the regular hexagon that's given will be 166.03 inches².

From the information, it was stated that the regular hexagon has a perimeter of 48 inches.

Therefore, the length of each side will be:

= 48/6

= 8 inches

The area of a regular hexagon calculated as:

= 3✓3/2 × x²

= 3✓3/2 × 8²

= 96✓3

= 166.03

In conclusion, the area is 166.03 inches².

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The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given

Angle bisector of the triangle.

To find

The angle bisector of a triangle divides the triangle into two similar triangles always, sometimes, or never.

The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.

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The angle bisector divides a triangle into two similar triangles Option B) sometimes, specifically when the triangle is isosceles.

1. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. When the angle bisector of the vertex angle is drawn, it also bisects the base, creating two congruent triangles (by the Angle Bisector Theorem). Congruent triangles are always similar, so in this case, the statement holds true.

2. Scalene Triangle: In a scalene triangle, none of the sides are equal. When you draw the angle bisector of one of the angles, it won't necessarily bisect any other side into two equal lengths. Hence, the resulting triangles formed by the angle bisector won't necessarily be similar.

So, the angle bisector divides the triangle into two similar triangles sometimes (when it's an isosceles triangle) but not always (when it's a scalene triangle).

Answer: A swimming pool that is 5/10 full.

Answer:

The second dealer is better.

Step-by-step explanation:

To figure this out we need to divide the price by the amount of milk. Lets do both at the same time.

3.8/2=   2.7/1.5=

3.8/2=1.9   2.7/1.5=1.8

The second dealer is better.

Price per unit is the cost of the sing unit or measure of goods or the service provided.The second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.

Given information-

First vendor sells 2 liters for $3.80.

Second vendor sells 1.5 liters for $2.70.

Price per unit is the cost of the sing unit or measure of goods or the service provided.

Price per unit helps to compare the two product with there cost. The less will be the price per unit of a product the product will be more cheaper.

Price per unit is the ratio of the total cost to the number of units.

The vendor which provide more milk in less rate will be the better deal.

As first vendor sells 2 liters for $3.80. Thus the price of milk per liter is,

[tex]P_1=\dfrac{3.80}{2} \\P_1=1.90[/tex]

Hence the first vendor sells the 1 liter milk in $1.90.

As Second vendor sells 1.5 liters for $2.70. Thus the price of milk per liter is,

[tex]P_2=\dfrac{2.70}{1.5} \\P_2=1.80[/tex]

Hence the second vendor sells the 1 liter milk in $1.80.

Hence the second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.

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Answer:

the answer is 16

Step-by-step explanation:

25-9=16 pens

Answer:25-9= 16 pens

Step-by-step explanation:

Answer:

The correct answer is for the given expression is -43.

Step-by-step explanation:

We are given the following expression and we are supposed to evaluate it:

[tex](-2)^2 + (-42) + (18 - 23)[/tex]

Solving the terms inside the brackets first, following the order of operations to solve a mathematical expression to get:

= 4 + (-42) + (-5)

Further adding and subtracting the terms to get:

= 4 - 42 - 5

= -38 - 5

= -43

Answer:

-17

Step-by-step explanation:

Evaluate the expression: (–2)^2 + (–4^2) + (18 – 23) = -17

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]4x+y>1[/tex] -----> inequality A

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is [tex]4x+y=1[/tex]

The slope of the dashed line is negative

The y-intercept of the dashed line is the point [tex](0,1)[/tex]

The x-intercept of the dashed line is the point [tex](0.25,0)[/tex]

[tex]y\leq \frac{3}{2}x+2[/tex] -----> inequality B  

The solution of the inequality B is the shaded area below the solid line

The equation of the solid line is [tex]y=\frac{3}{2}x+2[/tex]

The slope of the solid line is positive

The y-intercept of the solid line is the point [tex](0,2)[/tex]

The x-intercept of the solid line is the point [tex](-1.33,0)[/tex]

using a graphing tool

The graph in the attached figure

Answer:

18 = diameter

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x-7\\-6x-4y=-24&\text{divide both sides by (-2)}\end{array}\right\\\left\{\begin{array}{ccc}y=5x-7&(*)\\3x+2y=12&(**)\end{array}\right\\\\\text{substitute }\ (*)\ \text{to}\ (**):\\\\3x+2(5x-7)=12\qquad\text{use distributive property}\\\\3x+(2)(5x)+(2)(-7)=12\\\\3x+10x-14=12\qquad\text{add 14 to both sides}\\\\13x=26\qquad\text{divide oth sides by 13}\\\\\boxed{x=2}\\\\\text{Put the vaalue of x to}\ (*):\\\\y=5(2)-7\\\\y=10-7\\\\\boxed{y=3}\\\\Answer:\ \boxed{x=2\ and\ y=3\to(2,\ 3)}[/tex]

Answer:

ax²+ bx + c = 0

Step-by-step explanation

Multiplying (x+4) and (x−1) together (called Expanding) gets x2 + 3x − 4 :

expand vs factor quadratic

So (x+4) and (x−1) are factors of x2 + 3x − 4

Just to be sure, let us check:

(x+4)(x−1)  = x(x−1) + 4(x−1)

 = x2 − x + 4x − 4

 = x2 + 3x − 4 yes

Yes, (x+4) and (x−1) are definitely factors of x2 + 3x − 4

To factorise a quadratic equation, express it in the standard form ax² + bx + c = 0, identify coefficients a, b, and c, and then apply the quadratic formula.

To factorise quadratics in their simplest form, you need to express them in the standard quadratic form, which is ax² + bx + c = 0. For example, if you are given the equation x² + 4x - 21 = 0, you should identify a = 1, b = 4, and c = -21. Then you can apply the quadratic formula:

'x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c’, all over two 'a' (x = [tex]\frac{-b \pm \sqrt{b^2- 4ac} }{2a}[/tex])

If you are given an equation like 3x +3 + x² + x = 24, first rearrange it into the standard quadratic form by combining like terms. Use the quadratic formula if you cannot factor the quadratic easily.

Keep in mind that the quadratic formula can only be used if the equation is a true quadratic with powers confined to the second, first, and zeroth (constant term). If other powers or roots are present, then alternative methods must be used.

Answer:

2 hours

Step-by-step explanation:

To find out how much she has read, we multiply the number of nights by how much read per night

time read = 8 nights * 1/4 hours per night

time read = 8/4 hours

time read = 2 hours

Answer: 2 weeks?

Step-by-step explanation: 1/4 x 8= 2

If ΔGJI and ΔPKH are similar, then ∡G≅∡P, ∡J≅∡K and ∡I≅∡H.

We have m∡G + m∡P = 50°, therefore m∡G = m∡P = 50° : 2 = 25°.

m∡I = 48° therefore m∡H = 48°.

We know, the sum of the measures of the angles of a triangle is equal 180°.

Therefore we have the equation:

m∡G + m∡J + m∡I = 180°

25° + m∡J + 48° =180°

73° + m∡J = 180°      subtract 73° from both sides

m∡J = 107° → m∡K = 107°.

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex] and this can be determined by using the properties of the triangle.

Given :

Given that triangle GJI and triangle PKH are similar therefore:

[tex]\rm \angle G = \angle P[/tex]

[tex]\rm \angle J = \angle K[/tex]

[tex]\rm \angle I = \angle H[/tex]

The sum of the interior angles of the triangle is [tex]180^\circ[/tex].

[tex]\rm \angle G + \angle I + \angle J = 180^\circ[/tex]

[tex]\rm 25^\circ + 48^\circ + \angle J = 180^\circ[/tex]

[tex]\rm 73^\circ + \angle J = 180^\circ[/tex]

[tex]\rm \angle J = 107^\circ = \angle K[/tex]

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex].

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To find the diagonal of a door frame, use the Pythagorean theorem. Substitute the door's height and width into the formula, then find the square root of the sum. Round your answer to the nearest tenth.

To find the length of the diagonal of the door frame, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the long side, or in this case, the diagonal) is equal to the sum of the squares of the other two sides (height and width of the door).

So, the formula becomes: Diagonal = √((Height)^2 + (Width)^2)

Substitute the given values of the height and width into the equation: Diagonal = √((80 inches)^2 + (36 inches)^2) = √(6400 + 1296) = √7696

The square root of 7696 is about 87.7 inches. So, the length of the diagonal of the door frame, rounded to the nearest tenth, is 87.7 inches.

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To calculate the length of the diagonal of the door frame, use the Pythagorean theorem by squaring the width and height, adding the squared values, and then taking the square root. The length of the diagonal is approximately 87.9 inches.

To calculate the length of the diagonal of the door frame, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the width and the height of the door frame form the legs of the right triangle, and the diagonal is the hypotenuse. Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:

Therefore, the length of the diagonal of the door frame is approximately 87.9 inches, rounded to the nearest 10th.

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The correct answer is option (D).

Inequality shows relation between two expression which are not equal to each others.

The graph shows an open circle at -6,

which implies that -6 is not a solution to the inequality.

The shaded arrow on all values shows that values are smaller than -6 and  x < -6 is the inequality that represented on the line graph.

The required inequality is x < -6.

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Answer: [tex]F=15N[/tex]

Step-by-step explanation:

1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:

[tex]F=ka[/tex]

Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.

2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=18[/tex] and [tex]a=6[/tex] into the equation and solving for [tex]k[/tex]:

[tex]18=k6\\k=\frac{18}{6}\\k=3[/tex]

3. Now, you can calculate the force when the acceleration of the object becomes 5 m/s², as following:

[tex]F=3(5)\\F=15[/tex]

3. The result is:

[tex]F=15N[/tex]

The acceleration that an objects gains is given by the mass of the object.

Reason:

The given parameters are;

The acting force ∝ The acceleration of the object.

The acceleration given by an amount of force, F, of 18 N = 6 m/s²

Required:

The force acting on the object acceleration, a, is 5 m/s².

Solution:

According to Newton's Second Law of motion, we have;

F = m·a

Where;

m = The mass of the object

Therefore, we have;

[tex]Mass, \, m = \dfrac{F}{a}[/tex]

From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the

given object is given as follows;

[tex]Mass \ of \ the \ object, \, m = \dfrac{18 \, N}{6 \ m/s^2} = 3 \, kg[/tex]

The force acting when the the acceleration, a = 5 m/s², is therefore;

F = 3 kg × 5 m/s² = 15 N

If the acceleration of the object becomes 5 m/s² the force is 15 N.

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Answer:

The total cost is D) $141

Step-by-step explanation:

To solve we can use the equation: [tex]y=25d+0.10m[/tex]

d= number of days  m= number of miles

We know both of these values so we can plug them in and solve.

y= 25(3) + 0.10(660)

y= 75 + 66

y = 141

Answer:

[tex]S_{10}[/tex] = - 30

Step-by-step explanation:

For a given arithmetic sequence the n th term formula is

[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d

where d is the common difference and [tex]t_{1}[/tex] the first term

We have to find d and [tex]t_{1}[/tex]

from the given information we can write 2 equations and solve for d and [tex]t_{1}[/tex]

[tex]t_{6}[/tex] = [tex]t_{1}[/tex] + 5d = - 4 → (1)

[tex]t_{10}[/tex] = [tex]t_{1}[/tex] + 9d = - 12 → (2)

subtract (1) from (2) term by term

4d = - 8 ⇒ d = - 2

substitute d = - 2 in (1)

[tex]t_{1}[/tex] - 10 = - 4 ⇒ [tex]t_{1}[/tex] = - 4 + 10 = 6

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ], hence

[tex]S_{10}[/tex] = 5[(2 × 6) + (9 × - 2) ] = 5(12 - 18) = 5 × - 6 = - 30

Answer:

3 weeks, $45

Step-by-step explanation:

So we can make an equation!

55+5x=100-10x

So solving for x,

X=3

Final answer:

After solving the equations, Mindy and Sean will have the same amount of money, which is $70, after 3 weeks.

Explanation:

The question is about finding after how many weeks Mindy and Sean would have the same amount of money and how much that amount would be. Let's denote the number of weeks as w. For Mindy, who starts with $55 and saves $5 per week, her amount of money as a function of weeks is 55 + 5w. For Sean, who starts with $100 and spends $10 every week, his amount of money as a function of weeks is 100 - 10w.

To find out after how many weeks they would have the same amount of money, set the two expressions equal to each other:

55 + 5w = 100 - 10w

Add 10w to both sides and subtract 55 from both sides to solve for w:

15w = 45

Therefore, w = 45 / 15 = 3

To find out how much money they would have, substitute w = 3 into one of the original equations:

Mindy: 55 + 5(3) = 70

So, after 3 weeks, both Mindy and Sean will have $70

Answer:

51.544 L  in our tank

Step-by-step explanation:

We have a 13.6 gallon tank

Our conversion factor is 3.79 L = 1 gallon.  We want liters on top since that is where we want to end up

3.79 L /1 gallon is what we want to use

13.6 * 3.79L/1 gallon = 51.544 L  in our tank

Answer: The Perimeter is 90 meters

Step-by-step explanation:

Area = 126

Width = 3

Length = L

3 x L = 126

3 x L / 3 = 126/3

L = 42

Check:

3 x 42 = 126

126 = 126

Perimeter = L2 + W2

P = 42 x 2 + 3 x 2

P = 84 + 6

P = 90

Answer:

The jogging rate of Matthew is 5 mph.

Step-by-step explanation:

Let the jogging rate of Matthew be x mph.

It is given that his jogging rate was 25 mph slower than the rate when he was riding. So, the riding rate is (x+25) mph.

The distance between Matthew and his friend's house is 12 miles.

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Time=\frac{Distance}{Speed}[/tex]

The time taken by Matthew in jogging is [tex]\frac{12}{x}[/tex] and the time taken by Matthew in riding is [tex]\frac{12}{x+25}[/tex].

It took him 2 hours longer to jog there than ride back.

[tex]\frac{12}{x}=\frac{12}{x+25}+2[/tex]

[tex]\frac{12}{x}-\frac{12}{x+25}=2[/tex]

[tex]\frac{12(x+25)-12x}{x(x+25)}=2[/tex]

[tex]12x+300-12x=2x(x+25)[/tex]

[tex]300=2x^2+50x[/tex]

[tex]0=2x^2+50x-300[/tex]

[tex]0=x^2+25x-150[/tex]

[tex]0=x^2+30x-5x-150[/tex]

[tex]0=(x+30)(x-5)[/tex]

Equate each factor equal to 0.

[tex]x=5,-30[/tex]

The speed cannot be negative, therefore the jogging rate of Matthew is 5 mph.

Answer:

the answer is D

Step-by-step explanation:

Answer:

∠RQP

Step-by-step explanation:

Answer:

The number (x) is 127.1

Step-by-step explanation:

4% of a number (x) is equal to;

31% of 16.4

i.e 0.04x = 5.084

x = [tex]\frac{5.084}{0.04}[/tex] = 127.1

The number (x) is 127.1

Answer:

x = 127.1

Step-by-step explanation:

Let x be the unknown number.

It is given that 4% of the number is 31% of 16.4

4% of x  = 31% of 16.4

[tex]x\times \dfrac{4}{100}=16.4\times \dfrac{31}{100}[/tex]

[tex]\dfrac{4x}{100}=\dfrac{508.4}{100}[/tex]

Multiply both sides by 100.

[tex]\dfrac{4x}{100}\times 100=\dfrac{508.4}{100}\times 100[/tex]

[tex]4x=508.4[/tex]

Divide both sides by 4.

[tex]x=\dfrac{508.4}{4}[/tex]

[tex]x=127.1[/tex]

Therefore, the unknown number is 127.1.

Answer:

16 times the square root of 6

Step-by-step explanation:

2 radical54 simplifies:

2(radical6 x radical9), which is 6 radical6

and 5 radical24 simplifies:

5(radical6 x radical4), which is 10 radical6,

10 radical6 + 6 radical6=

16 radical6

Answer: 27-c =x

Step-by-step explanation:

We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).

We begin with 27 balloon, and take away c amount to make x.

27-c =x

The number of balloons left after c balloons have popped from an initial number of 27 balloons can be represented by the mathematical expression 27 - c.

In order to determine the number of balloons that were left after some of them had popped, we can use a simple mathematical expression. If there were initially 27 balloons and c balloons popped, then the number of balloons left would be the initial number of balloons minus the number popped.

Mathematically, this can be represented by the expression: 27 - c.

The variable c is used to represent the number of balloons that popped during the party. By subtracting this from the total number of balloons, we're left with the number of balloons that survived the party.

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