A contractor is building a set of stairs out of concrete. Each step is exactly the same length and width is the same and height from the last step.

A) Which solid figures can the staircase be broken into?
B) What are the dimensions of each solid figure?
C) How much concrete will be needed to form the staircase?
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The value of x is 7.63

The formula of the determinant is

x = -b ± √(b² - 4ac) / 2a

Where the equation is in the form of ax² + bx + c = 0

The error made by Peta is to use the determinant formula to find the root of the equation x (x - 5) = 20.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

x (x - 5) = 20

Removing the parenthesis.

x² - 5x = 20

x² - 5x - 20 = 0

This is in the form of ax² + bx + c = 0

Now,

a = 1

b = -5

c = -20

Using the determinant formula.

x = -b ± √(b² - 4ac) / 2a

x = 5 ± √(25 + 80) / 2

x = 5 ± √105 / 2

x = (5 + √105) / 2

x = (5 + 10.25) / 2

x = 15.25/2

x = 7.63

x = (5 - √105) / 2

x = (5 - 10.25) / 2

x = -5.25/2

x = -2.63 (neglected)

Thus,

The value of x is 7.63

The error made by Peta is to use the determinant formula to find the root of the equation x (x - 5) = 20.

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Answer:

3.2

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (A(2,2) and (x₂, y₂ ) = B(5, 1)

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

  = [tex]\sqrt{3^2+(-1)^2}[/tex]

  = [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex] ≈ 3.2 ( nearest tenth )

Answer:

3.2

Step-by-step explanation:

Distance formula = √ (x₂ - x₁ )² + (y₂ - y₁ )²

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

Distance = [tex]\sqrt{ {3}^{2}  + ( - 1 )^{2}[/tex]

Distance = 3.16227766

Answer:

The value of the expression is 100

Step-by-step explanation:

we have

5,200-[40%(300*42.5)]

we know that

(300*42.5)=3*100*42.5=3*4,250=12,750

40%=40/100=0.40

substitute

5,200-[0.40*12,750]

5,200-5,100=100

A line parallel to 2x - 3y = 9 would have the same slope, 2/3, and a different y-intercept, represented as y = (2/3)x + b, where 'b' is any real number.

The equation 2x - 3y = 9 represents a line in a standard form. To find a line that is parallel to it, we need another line with the same slope. The slope-intercept form of the given equation, by isolating y, is y = (2/3)x - 3. A parallel line must have the same slope, which is 2/3 in this case. Therefore, a line parallel to 2x - 3y = 9 could be represented as y = (2/3)x + b, where 'b' is any y-intercept. For example, if b = 5, a parallel line would be given by y = (2/3)x + 5.

Answer:

160

Step-by-step explanation:

The top right quadrant is 90 and the given is 70, adding them equal 160. It is the only option that is greater than 90 degrees anyway.

Answer:

$ 5674.076

Step-by-step explanation:

The question is on compound interest

The formulae = A= P(1+ r/n) ^nt .......where P is the principal amount, r is the rate of interest in decimal, n is number of compoundings per year and t is the total number of years.

Given; P= $4,000.00 , r=12/100=0.12, n=2 and t=3

Substituting values in the equation  A= P(1+ r/n) ^nt

A= 4000 ( 1+0.12/2)^2×3

A=4000(1.06)^6

A=$ 5674.08

Answer:

15.597 mm^2

Step-by-step explanation:

The formula for circumference of a circle 2πr, in which r is the circle's radius.

The formula for area of a circle π[tex]r^{2}[/tex]. This means that we can find the radius from the circle's circumference and use it to find the area.

First we have to equal 14 to 2πr because both are representations of circumference and we need to find r.

14 = 2πr

Solve:

14/2 = 2πr/2

7 = πr

7/π = πr/π

2.23 = r

Plug 2.23 into the formula for area as r and solve:

π(2.23)^2

π4.96

15.597

For this case we have by definition, that if two lines are parallel then their slopes are equal.

We manipulate the equations algebraically to take them to the form y = mx + b.

Equation 1:

[tex]2y = -3x + 8\\y = - \frac {3} {2} x + 4[/tex]

Thus, the slope of this line is [tex]- \frac {3} {2}.[/tex]

Equation 2:

[tex]6x + 2y = 9\\2y = 9-6x\\2y = -6x + 9\\y = \frac {-6x + 9} {2}\\y = -3x + \frac {9} {2}[/tex]

The slope of this line is -3.

As the slopes are not equal, then the lines are not parallel.

Answer:

False

Answer:

125a^3 + 300a^2b + 240ab^2 + 64b^3

Step-by-step explanation:

The volume of a cube is the cube of the side length.

V = s^3

Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.

V = (5a + 4b)^3

V = (5a + 4b)(5a + 4b)(5a + 4b)

V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)

V = (25a^2 + 40ab + 16b^2)(5a + 4b)

V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3

V = 125a^3 + 300a^2b + 240ab^2 + 64b^3

Answer:

The 51 and 62 triangle is 67°

The 43 triangle is 47°

Step-by-step explanation:

Angles in a triangle add to 180°

180 - ( 51 + 62 ) = 180 - ( 113 ) = 67°

180 - ( 43 + 90 ) = 180 - 133 = 47°

Answer:

f(w) = 120 + 5(30-h)

Step-by-step explanation:

It is given that, Andrew gets paid $4 for first 30 hours of the week

So,

For first 30 hours, his wage will be:

4(30) = $120

Now, let w denote wages and h denote total number or hours he works in the week

So he will be paid $5 for h-30 hours

So the function will be

f(w) = 120 + 5(30-h)

Where $120 is the fixed income for first 30 hours and the second term is the wage of hours more than 30 at the rate of $5 per hour..

Answer:

x-intercept: 4  This means that only 4 adults can come under the budjet of $20

y-intercept: 10 This means that only 10 children can come under the budjet of $20

Step-by-step explanation:

for y:

5(0) + 2y = 20

2y = 20

2y/2 = 20/2

y = 10

for x:

5x + 2(0) = 20

5x = 20

5x/5 = 20/5

x = 4

Answer: 36ft

Step-by-step explanation: 180*.2=36

Answer:

36 ft

Step-by-step explanation:

to find 20% of 180 ft, multiply 180 ft by 0.20:  0.20(180 ft) = 36 ft

Answer:

The Answer is A

Step-by-step explanation:

The mean or average is highly sensitive to outliers - and is one reason why the median is a more reliable statistic.

Answer:

Part 1) The new distance from the water to the top of the tank is [tex]1.979\ in[/tex]

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

[tex]V=20*10*15=3,000\ in^{3}[/tex]

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

[tex]V=20*10*(15-2)=2,600\ in^{3}[/tex]

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=1\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(1)^{3}[/tex]

[tex]V=4.2\ in^{3}[/tex]

step 4

What is the new distance from the water to the top of the tank?

we know that

[tex]2 in -----> represent (3,000-2,600)=400\ in^{3}[/tex]

so

using proportion

Find how many inches correspond a volume of [tex]4.2\ in^{3}[/tex]

[tex]\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in[/tex]

The new distance from the water to the top of the tank is

[tex]2-0.021=1.979\ in[/tex]

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to  [tex]4.2\ in^{3}[/tex]

using proportion

[tex]\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls[/tex]

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Answer:

3x + 5y = 105

3x + y = 57

------------------

4y = 48

y = 12, x = 15

{(15, 12)}

Answer:

-5/3, -0.1, 0.7, √2 and √5

Step-by-step explanation:

To start ordering these items, we first need to have a common point of comparison... so we'll get an approximation of their decimal value.  No need to be very precise, just have a rough estimate:

√5: roughly 2.2

-0.1:  -0.1

-5/3: -1.66

0.7: 0.7

√2: roughly  1.4

Now that we have the same comparing point (a decimal value), it's easy to sort them from the smallest value to the greatest value:

-5/3, -0.1, 0.7, √2 and √5

Of course, √2 is smaller than √5

Answer:

[tex]\large\boxed{-\dfrac{5}{3},\ -0.1,\ 0.7,\ \sqrt2,\ \sqrt5}[/tex]

Step-by-step explanation:

[tex]\sqrt5\\\\-0.1=-\sqrt{0.1^2}=-\sqrt{0.01}\\\\-\dfrac{5}{3}=-\sqrt{\left(\dfrac{5}{3}\right)^2}=-\sqrt{\dfrac{25}{9}}=-\sqrt{2\dfrac{7}{9}}\\\\0.7=\sqrt{0.7^2}=\sqrt{0.49}\\\\\sqrt2\\\\-\sqrt{2\dfrac{7}{9}}<-\sqrt{0.01}<\sqrt{0.49}<\sqrt2<\sqrt5[/tex]

Answer:

Option C

Step-by-step explanation:

we know that

Two angles are complements if their sum is equal to 90 degrees

we have that

∠SWT=50°

so

Its complement must be equal to 40 degrees

we know that

∠USP=40°

∠TSV=40°

therefore

∠USP and ∠TSV are complements to ∠ SWT

Answer:

240 units^3

Step-by-step explanation:

To find the volume of a rectangular prism you just multiply length times width times height. So, 8*6*5 which equals 240 units^3.

The dimensions of the prism is given as Length = 8 units, width = 6, Height = 5. Therefore, the volume of the prism is 240 units^3.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,

then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

The dimensions of the prism is given as

Length = 8 units

width = 6

Height = 5

To find the volume of a rectangular prism

[tex]V = a\times b \times c \: \: unit^3[/tex]

V = 8 x 6 x 5

V = 240 units^3.

Therefore, the volume of the prism is 240 units^3.

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Answer:

910 yards

Step-by-step explanation:

The total is the yards dyed teal plus the yards dyed indigo:

851 + 59 = 910

Total 910 yards of silk was dyed by the factory for that order.

The addition is defined as a mathematical operation i.e. a method of adding numbers to get total.

We have,

Factory dyed silk teal = 851 yards,

Factory dyed silk indigo = 59 yards,

So,

To get the total we will add the given data,

i.e.

Total silk dyed = dyed silk teal + dyed silk indigo

                        = 851 + 59

                        = 910 yards,

So,

In total 910 yards of silk was dyed by the factory.

Hence, we can say that total 910 yards of silk was dyed by the factory for that order.

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Answer:

7/9

Step-by-step explanation:

6x^3-8y^3-12x^2y^2+4xy       x=2/3 y=1/2

=6(2/3)^3-8(1/2)^3-12(2/3)^2(1/2)^2+4(2/3)(1/2)

=6(8/27)-8(1/8)-12(4/9)(1/4)+4(1/3)

=(16/9)-1-(4/3)+(4/3)

=(1 7/9)-1

=7/9

Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

12-5x= 7x+3

12-7x-5x= 7x-7x+3

12-12x= 3

12-12-12x= 3-12

-12x= -9

Divide by -12 for -12x and -9

-12x/-12= -9/-12

x= 9/12

Divide by 3 for 9/12

x= 3/4

Answer is x= 3/4

Step-by-step explanation:

12 - 5x = 7x + 3

Add 5x on the both sides so there would only be 12 on the right side.

So...... 12 = 12x + 3

Then minus 3 from both sides

9 = 12x

0.75 = x

:0 ITS MAGIC

:)))

Answer:

Step-by-step explanation:

The slope is  1.5 miles / day

Final answer:

The slope of the equation that represents Ashley's walking distance over the number of trips is 1.5, which indicates that she walks 1.5 miles for each trip to school.

Explanation:

Ashley has already walked 0.5 miles this week and plans to walk 1.5 miles each trip to school for a total of 3 trips. To find the slope of the equation that represents her walking distance as a function of the number of trips, we use the slope formula, which is rise over run, or in this context, the change in distance over the number of trips.

Let's calculate her total planned distance. Since she plans on walking 1.5 miles for each trip and takes 3 trips, that's 1.5 miles/trip × 3 trips = 4.5 miles. Including the 0.5 miles she has already walked, her total distance for the week would be 0.5 miles + 4.5 miles = 5 miles, which matches with her goal.

Now, the slope is the distance she covers per trip, which is consistent and equal to 1.5 miles per trip. Therefore, the slope of the line that represents her distance over the week as a function of each trip is 1.5.

The answer is:

[tex](g\circ f)(0)=-216[/tex]

To composite functions, we need to evaluate functions in another function(s), for example:

Given f(x) and g(x), if we want to calculate f(x) composite g(x), we need to evaluate g(x) into f(x).

So, we are given the functions:

[tex]f(x)=2x-6\\g(x)=x^{3}[/tex]

And we are asked to calculate g(x) composite f(x), and then evaluate "x" to 0, so, calculating we have:

[tex](g\circ f)(x)=g(f(x))\\\\(g\circ f)(x)=(2x-6)^{3}[/tex]

Now that we have the composite function, we need to evaluate "x" equal to 0, so:

[tex](g\circ f)(0)=(2x-6)^{3}\\\\(g\circ f)(0)=(2*(0)-6)^{3}=(0-6)^{3}=-6*-6*-6=-216[/tex]

Hence, we have that:

[tex](g\circ f)(0)=-216[/tex]

Have a nice day!

Answer:

Step-by-step explanation:216

Answer:

Step-by-step explanation:

The total number of marbles is 24 + 36 + 60 = 120

Red: 24/120 = 1/5

Blue: 36/120 = 6/20 = 3/10

Yellow: 60 / 120 = 1/2

Answer:

I think it is A.

Step-by-step explanation:

Hope my answer has helped you!

The true statement is:

Hence, such points could never form a triangle.

Because a triangle is formed with the help of three non-collinear points.

Hence, the points will be coplanar (i.e. they lie in the same plane)

Answer:

222- 50+1=0? 225 - 50 = 175 175+1 = 176 176+0 = 176

Answer:

[tex]-11b^2+8b-4[/tex]

Step-by-step explanation:

We can substitute in our expressions for P and Q to get

[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\(-4b^2+6b-9)-(7b^2-2b-5)[/tex]

Next, we need to distribute the negative to the values within the parenthesis. Then we can combine like terms in order to get our answer

[tex](-4b^2+6b-9)-(7b^2-2b-5)\\\\-4b^2+6b-9-7b^2+2b+5\\\\-11b^2+8b-4[/tex]

Answer:

-11b^2 + 8b - 4

Step-by-step explanation:

(-4b^2 + 6b - 9) - (7b^2 - 2b - 5) =

Drop the first set of parentheses because it is unnecessary. To drop the second set of parentheses, you must distribute the negative sign. That means you must change every sign inside the second set of parentheses.

= -4b^2 + 6b - 9 - 7b^2 + 2b + 5

Now, group like terms.

= -4b^2 - 7b^2 + 6b + 2b - 9 + 5

Finally, combine like terms.

= -11b^2 + 8b - 4

ANSWER

The solution is

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

EXPLANATION

The equations are:

1st equation: 6x +5y=-19

2nd equation: 12x-8y=52

Multiply the first equation by 2:

3rd equation: 12x +10y=-38

Subtracy the 2nd equation from the 3rd equations.

12x-12x+10y--8y=-38-52

18y=-90

Divide both sides by 18.

y=-5

Put y=-5 into any of the equations and solve for x.

Preferably, the first equation will do.

6x +5(-5)=-19

6x -25=-19

6x=25-19

6x=6

x=1

The solution is

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