A cuboid with a volume of 924cm^3 has dimensions
4cm,(x+1)cm and (x+11)cm
Clearly show that x^2+12x-220=0
Solve the equation by factorising,make sure you show your factorisation.
State both values of x on the same line
Finally,find the dimensions of the cuboid,writing all three on one line

Answer:

Therefore

m∠ DAB is 105°

Step-by-step explanation:

Given:

ABCD is a parallelogram. The diagram is not drawn to scale.

m∠CDA = 75°,

To FInd

m∠DAB  = ?

Solution:

ABCD is a parallelogram.

AB || CD .......{opposite sides of a parallelogram are parallel}

∴∠CDA+∠DAB = 180°{SUM of the interior angles between parallel are supplementary}

substituting the values we get

[tex]75+m\angle DAB=180\\\\m\angle DAB =180-75=105\\\\m\angle DAB =105\°[/tex]

Therefore

m∠ DAB is 105°

Answer:

y = - 7

Step-by-step explanation:

line pass (8, - 7) (- 6, -7)

y = mx + b   m: slope        b: y intercept

m = difference of y / difference of x

m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0  ...  line parallel to x axis

b = y - mx = - 7 - 0*8 = -7

equation : y = -7

Answer:

y = - 7

Step-by-step explanation:

line pass (8, - 7) (- 6, -7)

y = mx + b   m: slope        b: y intercept

m = difference of y / difference of x

m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0  ...  line parallel to x axis

b = y - mx = - 7 - 0*8 = -7

equation : y = -7

Answer:

The solution of the inequality is:

[tex]x>2[/tex]

Step-by-step explanation:

Given inequality:

[tex]-1 >-2(x - 4)-5(4x-7)[/tex]

Solving the inequality.

Using distribution.

⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]

⇒ [tex]-1 >-2x +8-20x+35[/tex]

Combining like terms

⇒ [tex]-1 >-2x-20x+35+8[/tex]

⇒ [tex]-1 >-22x +43[/tex]

Adding [tex]22x[/tex] both sides.

⇒ [tex]-1+22x >-22x +43+22x[/tex]

⇒ [tex]-1 +22x> 43[/tex]

Adding 1 both sides.

⇒ [tex]-1+1 +22x> 43+1[/tex]

⇒ [tex]22x>44[/tex]

Dividing both sides by 22.

⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]

⇒ [tex]x>2[/tex]

Thus, the solution of the inequality is:

[tex]x>2[/tex]

Answer:

(42.26/100)*120 = $50.712

Step-by-step explanation:

Answer: tip = 8.452

Step-by-step explanation:

The relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

In a dilation, lines that pass through the center of dilation (the point about which the dilation occurs) remain unchanged.

This means that the line WX and its corresponding line W'X' would be collinear and have the same length if they pass through the center of dilation.

If the larger figure was dilated using a scale factor of 4, it means that every point in the larger figure is four times farther from the center of dilation than its corresponding point in the smaller figure. In this case, line WX would be four times longer than line W'X', and they would be parallel since they maintain the same direction.

So, the relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

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Just multiply the total length by the fraction:

14.3 * 1/10 = 1.43 miles

Answer:

1.43

Step-by-step explanation:

NOTE: This is the way I do it , other people may have a other/faster way to do it.

For this question you simpily have to divide 14.3 by 10:

1. Convert 14.3 into a mixed number - 14 3/10

2. Divide 14 by 10 - 1.4

3. Divide 3/10 by 10 - 3/100

4. Convert 3/100 into a decimal- 0.03

5. Add the two decimals - 0.03 + 1.4 = 1.43

Answer:

D

Step-by-step explanation:

= −8x − 2y - (−9x + 8y)

Open bracket

= -8x -2y + 9x - 8y

= x - 10y

Final answer:

Subtracting Expression 1 from Expression 2 term by term results in x - 10y, which corresponds to option D).

Explanation:

To subtract Expression 1 from Expression 2, we perform the subtraction operation term by term.

For the x-terms: (-8x) - (-9x) simplifies to x.

For the y-terms: (-2y) - (8y) simplifies to -10y.

Subtracting expression 1 from expression 2:

Expression 2 - Expression 1 = (-8x - 2y) - (-9x + 8y)

Simplify to get: (-8x - 2y) + (9x - 8y)

Combining like terms, the result is x - 10y.

Therefore, subtracting Expression 1 from Expression 2 gives us x - 10y, which matches option D).

Answer:

wouldn't it just be [tex]\frac{10}{11} x[/tex]

Step-by-step explanation:

this is also: [tex]\frac{-10*x}{-11}[/tex]

which is why it simplifies to the answer

Answer:

5

Step-by-step explanation:

1.24 times 3 = 3.72

.95 (the value of pence to a pound in decimal form) = 2.85

6.18 for the teapot

2.72+2.85+6.18=11.75

She now has £8.25 left (20-11.75).

8.25/1.57=the amount of plates she can buy: 5.25477707006, so 5 with some money left

Answer:

x^3 - 3x^2 - 3x + 9 + (-36/(x+3))

OR

x^3 - 3x^2 - 3x + 9 - (36/(x+3))

Step-by-step explanation:

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

x^4 + 0x^3 - 12x^2 + 0x -9

Coefficents: 1. 0.  -12. 0 -9.

Please see the image for the next steps.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)

-36/(x+3)

Divide using synthetic division the remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

[tex]x^4 + 0x^3 - 12x^2 + 0x -9[/tex]

Coefficents: 1. 0.  -12. 0 -9.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

Answer:

y = 2 + ((-)6/5)x

Step-by-step explanation:

-6x-5y=-10

add 6x to both sides.

-5y = -10 +6x

divide both sides by -5

y = 2 - (6/5)x

Plug in 0 for x to get the y intercept:

f(0) = 2 - (6/5) (0)

y = 2

(0, 2) is the y intercept.

Do the same for values such as -1, -2, 1, and 2, etc.

Then graph it.

To find the correct graph for -6x - 5y = -10, transform it to the slope-intercept form y = 6/5x - 2, which reveals a slope of 6/5 and a y-intercept at -2. Seek a graph with a line that increases 6 units vertically for every 5 units horizontally and intersects the y-axis at -2.

To find the graph that represents the equation -6x - 5y = -10,

we first need to manipulate the equation into slope-intercept form,

which is y = mx + b where m is the slope and b is the y-intercept. Starting with the given equation:

-6x - 5y = -10

Let's isolate y by adding 6x to both sides:

-5y = 6x - 10

Now, divide each term by -5 to solve for y:

y = -6x / -5 + 10 / -5

y = 6/5x - 2

The slope-intercept form of the equation is now y = 6/5x - 2. This tells us that the slope (m) of the line is 6/5 and the y-intercept (b) is -2. You will look for the graph with a line that rises 6 units for every 5 units it moves to the right (since the slope is positive) and crosses the y-axis at -2.

Answer:

The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.

The vertex of the function is (-2,-1)

Domain of the function is (-∞, +∞)

Range of the function is [-1, +∞).

Step-by-step explanation:

The function has a graph in two parts.

The right side part passes through the points (-2,-1) and (0,3).

So, the equation of this part will be  

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

⇒ y - 3 = 2x

⇒ y = 2x + 3

Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).

Therefore, the equation of this part will be  

[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]

⇒ y - 3 = - 2(x + 4)

⇒ y - 3 = - 2x - 8

⇒ y = - 2x - 5

Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)

The vertex of the function is (-2,-1) (Answer)

Domain of the function is (-∞, +∞) (Answer)

Range of the function is [-1, +∞). (Answer)

Answer:

y=-1/5x+1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-2)/(10-(-5))

m=-3/(10+5)

m=-3/15

m=-1/5

y-y1=m(x-x1)

y-2=-1/5(x-(-5))

y-2=-1/5(x+5)

y=-1/5x-5/5+2

y=-1/5x-1+2

y=-1/5x+1

You got the equations correct, great job on that!

Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.

Equation for the store at Town Center mall:

p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)

Equation for the store in Arlington:

p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)

We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.

p = 80 + 3.5s

p = 120 + 2.5s

We know that variable "p" is equal for both equations; thus, we can combine both equations into:

80 + 3.5s = 120 + 2.5s

Subtract both sides by 2.5s

80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s

80 + s = 120

Subtract both sides by 80

s = 40

Thus, both equations are equal when 40 shirts are bought.

To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.

p = 80 + 3.5(40) = 220

p = 120 + 2.5(40) = 220

Thus, the total price/cost at both stores is $220.

Let me know if you need any clarifications, thanks!

                                               Question # 1

Use the points in the diagram to name the figure?

Answer:

Option B is correct. The figure is named as a line 'CD'. The symbol '⟷' is placed UPPER on a line 'CD'.

Explanation:

Note: The symbol '⟷' is placed UPPER on a line 'CD'. Also remember, that the a line is named in alphabetical order.

                                           Question # 2

Which of the following correctly names a line shown in the figure?

Answer:

The option A is correct as the line AP carries the points A and P  and extends infinitely in two directions, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.

Explanation:

Let us look at some definitions.

As we have to determine the correct name of a line shown in figure in question 2. So, we need to recall that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions.

In question 2, the figure shows that:

So, option A is correct.

                                              Question 3.

Which of the following correctly names a ray shown in the figure?

Answer:

Explanation:

Keywords: ray, segment, line

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Answer:

C

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Here linear ratio = 42 : 56 ← divide both parts by 14

linear ratio = 3 : 4 ← in simplest form, thus

ratio of areas = 3² : 4² = 9 : 16

ratio of volumes = 3³ : 4³ = 27 : 64

25 cakes can be completely decorated using 4 gallons of icing.

Step-by-step explanation:

Given:

4 gallons of icing

16 cups =1 gallon

No. of icing cups = [tex]4\times16[/tex] cups

       =64 cups

No. of cups required to decorate and frost a cake= 4% of total no. of icing cups

          = [tex]\frac{(4\times64)}{100}[/tex]

          = 2.56

2.56 cups of icing is required to decorate each cake.

Maximum no. of cakes decorated = [tex]\frac{ (64\times1)}{2.56}[/tex]

                    = 25

25 cakes can be completely decorated using 4 gallons of icing.

Answer: D

Step-by-step explanation: I just did the quiz

Answer: D

Step-by-step explanation:

Yeah the quiz was like, dud the answers D, so I was like okay it's D

Explanation:

When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.

The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.

When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.

Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:

Otherwise, the shaded solution space will be below or to the left of the boundary line.

_____

Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.

_____

The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.

Answer:

The coordinates of point Q will be given by (11,-2)

Step-by-step explanation:

See the attached diagram.

Given that R is the midpoint of PS and Q is the midpoint of RS.

Therefore, the point Q divides the line PS in the ratio 3 : 1.

Now, coordinates of P are (8,10) and that of point S is (12,-6).

Therefore, the coordinates of point Q will be given by  

[tex](\frac{3\times 12 + 1 \times 8}{3 + 1}, \frac{3 \times (- 6) + 1 \times 10}{3 + 1})[/tex]  

= (11,-2) (Answer)

Answer:

25

Step-by-step explanation:

60 per day 25 in sales 63.75-60=3.75

3.75÷.15=25

If Nicole's earns 15% commission of her total sales, then Nicole's total sale of Monday is 25.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

Total salary of Nicole's = $60.

Also,

Nicole gets 15% commission of her total sales,

Total earning on Monday = $63.75

The commission earned on Monday = 63.75 - 60 = 3.75

According to given condition,

15 % = 3.75

1 % = 3.75 / 15

100 % = 3.75 / 15 x 100

100 % = 25

Total sale of Nicole's on Monday is 25.

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Answer: D. 9

Step-by-step explanation: If BD is 18 then BE is 9

Answer:

can confirm that it is 9

Step-by-step explanation:

slay have a nice day!

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) [tex]\$68.76[/tex]

Part 4) [tex]\$12\ per\ hour[/tex]

Part 5) The equation that can be used is [tex]27x=242.73[/tex]  and the cost of one print is [tex]\$8.99[/tex]

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$10\ per\ class[/tex]

The y-intercept is [tex]b=\$100[/tex]

so

[tex]y=10x+100[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$15\ per\ class[/tex]

so

[tex]y=15x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]10x+100 < 15x[/tex]

Solve for x

subtract 10 x both sides

[tex]100 < 15x-10x[/tex]

[tex]100 < 5x[/tex]

Divide by 5 both sides

[tex]20 < x[/tex]

Rewrite

[tex]x > 20[/tex]

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

[tex]8+3x=23[/tex]

solve for x

subtract 8 both sides

[tex]3x=23-8[/tex]

[tex]3x=15[/tex]

Divide by 3 both sides

[tex]x=5[/tex]

Part 3) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is [tex]m=\$0.42\ per\ mile[/tex]

The y-intercept is [tex]b=\$36[/tex]

so

[tex]y=0.42x+36[/tex]

For x=78 miles

substitute in the linear equation and solve for y

[tex]y=0.42(78)+36[/tex]

[tex]y=\$68.76[/tex]

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

[tex]40x+10(1.5x)=660[/tex]

solve for x

[tex]40x+15x=660[/tex]

[tex]55x=660[/tex]

Divide by 55 both sides

[tex]x=\$12\ per\ hour[/tex]

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

[tex]27x=242.73[/tex]

solve for x

Divide by 27 both sides

[tex]x=\$8.99[/tex]

Part 6) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$7\ per\ class[/tex]

The y-intercept is [tex]b=\$120[/tex]

so

[tex]y=7x+120[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$11\ per\ class[/tex]

so

[tex]y=11x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]7x+120 < 11x[/tex]

Solve for x

subtract 7x both sides

[tex]120 < 11x-7x[/tex]

[tex]120 < 4x[/tex]

Divide by 4 both sides

[tex]30 < x[/tex]

Rewrite

[tex]x > 30[/tex]

therefore

The number of classes must be greater than 30

Answer:

[tex]\displaystyle x=-15[/tex]

Step-by-step explanation:

Solution Of A System Of Equations

A system of linear equations is given as

[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]

There are many methods to solve them. We will use the method of reduction

The given system is

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.[/tex]

Multiplying the second equation by -3

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.[/tex]

Adding the resulting equations

[tex]\displaystyle -x=15[/tex]

[tex]\displaystyle x=-15[/tex]

Answer:

1036 students

Step-by-step explanation:

Let the number of students at West High be "w" and the number of students at East High be "e"

West High population is 250 FEWER than TWICE of East High, we can write:

w = 2e - 250

Total students in both schools is 2858, so we can write 2nd equation as:

e + w = 2858

We can replace 1st equation in 2nd to get an equation in e, and find "e":

e + w = 2858

e + (2e - 250) = 2858

3e - 250 = 2858

3e = 2858 + 250

3e = 3108

e = 3108/3

e = 1036

Hence,

number of students attending East High School = 1036 students

8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)

Step-by-step explanation:

Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,

                         20% in x + 50% in (15 – x) = 15 litres of 34%

Convert percentage values, we get

                              0.20(x) + 0.50 (15 – x) = 15 (0.34)

                              0.20 x + 7.5 – 0.50 x = 5.1

                              -0.3 x + 7.5 = 5.1

                              0.3 x = 7.5 – 5.1

                              0.3 x = 2.4

[tex]x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)[/tex]

Apply ‘x = 8’ value in (15 – x) we get,

                         15 – 8 = 7 litres

The value of 7 litres for (amount of 50% solution needed)

Answer:

1/20

Step-by-step explanation:

Answer:

The cost of the sofa is $216

Step-by-step explanation:

The sofa was sold at cost plus 25% profit

let the cost of the sofa be                               = x

therefore                                     x + 25% of x = 270

                                                    x + .25x        =  270

                                                    1.25x            =   270

                                                    1.25x/1.25    =   270/1.25

                                                     x                  =   $216

Answer:

Step-by-step explanation:

-3w+9-8

=-3w+1

Answer:

The distance of the park from the Gary's house is 125 miles.

Step-by-step explanation:

Speed of Gary = 50 miles/hour

Time taken by Gary to reach the park from his house = 2.5 hours

Now, we know that,

Distance travelled = speed × time

So,  distance between park and Gary's house = speed × time

= 50 × 2.5

= 125 miles

So, the park is 125 miles away from the Gary's house.