A cube with 2-inch sides is placed on a cube with 3-inch sides. Then a cube with 1-inch sides is placed on the 2-inch cube. What is the surface area of the three cube tower? Show your work.

Answer: [tex]a_{25} = 128[/tex]

Step-by-step explanation:

You need to use this formula:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where [tex]a_n[/tex] is the nth] term,  [tex]a_1[/tex] is the first term,"n" is the term position and  "d" is the common diference.

You must find the value of "d". Substitute [tex]a_1=8[/tex], [tex]a_9=48[/tex] and [tex]n=9[/tex] into the formula and solve for "d":

[tex]48 = 8 + (9 - 1)d\\48=8+8d\\48-8=8d\\40=8d\\d=5[/tex]

Now, you can calculate the 25th term substituting into the formula these values:

[tex]a_1=8[/tex]

[tex]d=5[/tex] and [tex]n=25[/tex]

Then you get:

[tex]a_{25} = 8 + (25 - 1)5[/tex]

[tex]a_{25} = 8 + 120[/tex]

[tex]a_{25} = 128[/tex]

Answer:

A right triangle

Step-by-step explanation:

Suppose a, b, c are the sides of a triangle,

If a² = b² + c² or b² = a² + c² or c² = a² + b²

Then the triangle is called a right angled triangle,

If a² + b² > c², a² + c² > b², b² + c² > a²

Then the triangle is called an acute triangle,

If a = b = c

Then the triangle is called an equilateral triangle,

If a² + b² < c², where c is the largest side of the triangle,

Then the triangle is called an obtuse triangle,

Now, In triangle RST,

By the distance formula,

[tex]RS=\sqrt{(3-1)^2+(-1-(-3))^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}\text{ unit }[/tex]

Similarly,

ST = √40 unit,

TR = √32 units,

Since, ST² = RS² + TR²

Hence, by the above explanation it is clear that,

Triangle RST is a right angled triangle,

First option is correct.

Answer:

this isa right triangle!!!

Step-by-step explanation:

this isa right triangle!!!

Answer:

the answer is C

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

Answer:

Exactly one solution.

Step-by-step explanation:

We have been given a system of equations. We are asked to find the number of solutions for our given system.

[tex]y=x+2...(1)[/tex]

[tex]6x-4y=-10...(2)[/tex]

We can see that equation (1) in slope-intercept form of equation.

We will convert equation (2) in slope-intercept form of equation as shown below:

[tex]6x-6x-4y=-10-6x[/tex]

[tex]-4y=-6x-10[/tex]

Divide both sides by [tex]-4[/tex].

[tex]\frac{-4y}{-4}=\frac{-6x}{-4}+\frac{-10}{-4}[/tex]

[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]

We can see that slopes of both lines are different, therefore, our given lines will intersect exactly at one point and our given system of equations has exactly one solution.

Answer:

Car B

Step-by-step explanation:

Car B's price changes by the greatest amount (£40) when rounded to the nearest £100 among the three cars.

To determine which price changes by the greatest amount when rounded to the nearest £100, let's first calculate the rounded prices for each car:

Car A: £12380 rounds to £12400

Car B: £16760 rounds to £16800

Car C: £14580 rounds to £14600

Now, let's compare the differences between the original prices and the rounded prices:

- For Car A: £12400 - £12380 = £20

- For Car B: £16800 - £16760 = £40

- For Car C: £14600 - £14580 = £20

The greatest difference is £40, which occurs for Car B. Therefore, the price of Car B changes by the greatest amount when rounded to the nearest £100.

Answer

2/5

Hoped this helped

Answer:

2/5

Step-by-step explanation:

3

____

7 1/2

3

____

15/2

= 2/5

ANSWER

[tex]c. \ln( \frac{2 {x}^{3} }{3y}) [/tex]

EXPLANATION

We want to write

[tex] ln(2x) + 2 ln(x) - ln(3y) [/tex]

as a single logarithm.

Use the power rule to rewrite the middle term:

[tex]n \: ln(a) = ln( {a}^{n} ) [/tex]

[tex]ln(2x) + ln( {x}^{2} ) - ln(3y) [/tex]

Use the product rule to obtain:

[tex]ln(a) + ln(b) = ln(ab) [/tex]

[tex]ln(2x \times {x}^{2} )- ln(3y) [/tex]

[tex]ln(2{x}^{3} )- ln(3y)[/tex]

Apply the quotient rule:

[tex] ln(a) - ln(b) = ln( \frac{a}{b})[/tex]

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

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{12}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-12^2}=b\implies \sqrt{25}=b\implies 5=b[/tex]

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

13 is the hypotenuse because it is the longest side.

12^2 + b^2 = 13^2

144 + b^2 = 169

subtract the 144 from both sides to isolate the variable you are solving for

b^2 = 25

Square root both sides to solve

b = 5

Answer:

2110 dollars / month

Step-by-step explanation:

Formula

New Salary = Old Salary * (1 + 5.5/100)

Solution

New Salary = 2000 * (1 + 0.055)

New Salary = 2000 * 1.055

New Salary = 2110 dollars / month

Answer:

see explanation

Step-by-step explanation:

Either both equations are equal or are multiples of each other

As an example consider the 2 equations

4x - y = 2 → (1)

- 12x + 3y = - 6 → (2)

Multiply (1) by - 3

- 12x + 3y = - 6 → (3)

Subtract (3) from (2) term by term

(- 12x - (- 12)x) + (3y - 3y) = (- 6 - (- 6)), that is

(- 12x + 12x) + 0 = - 6 + 6

0 = 0

This indicates the solution has infinite solutions

let x = k, k is a real number then from (1) y = 4x - 2 ⇒ y = 4k - 2

Thus (k, 4k - 2) will generate solutions to the system of equations

B. y=2.25x+4.00 (eg. 2020)

Answer:

$930

Step-by-step explanation:

The amount payable at maturity of the loan is simply the sum of the loan amount and the fee charged on the loan.

The loan amount is 890 while the fee charged on the loan is 40. The amount repayable at maturity is thus;

890 + 40 = 930.

Therefore, he has to pay $930 by the time the loan reaches maturity.

Answer:

$930

Step-by-step explanation:

Daryl took out a single payment loan for $890.

That charged a $40 fee.

He takes loan of $890 that charged a $40 fee for a single time, so his maturity amount = loan amount + fees of $40

He have to pay by the time the loan reaches maturity = 890 + 40

                                                                                         = $930

He have to pay $930 by the time of maturity.

bearing in mind that perpendicular lines have negative reciprocal slopes hmmmmm wait a second, what's the slope of that line above anyway?

[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}} x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

therefore any perpendicular line to that

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{1}\implies 3}}[/tex]

so, we're really looking for the equation of a line whose slope is 3 and runs through (1, -10)

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-10})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-10)=3(x-1) \\\\\\ y+10=3x-3\implies y=3x-13[/tex]

Answer:

use M=(Y-Y)/(X-X)format and see what you get

Step-by-step explanation:

so it should be

-10-3/1-1

Im not sure how to explain this without having the proper set up

(2,2) = (x,y)

(1,1) = (x,y)

so if we set this up right

-13/0....

Answer:

9

Step-by-step explanation:

if every container needs 1/3 of one cup and you have 3 cups then multiply 3 by 3 and you have your answer

Miss Diego will be able to fill 9 containers.

We must divide the quantity of sugar by the quantity of sugar each container can hold to find the total number of containers.

It is given that Miss Diego has three cups of sugar.

It is also given that the containers can hold 1/3 of a cup.

We are asked to find the total number of containers she can fill.

This can be done as shown below:

Total number of cups = Total cups of sugar/quantity of sugar each container can hold

= 3 / (1/3)

= 3 * 3

= 9

The number of containers that can be filled is found. The total number of containers that can be filled is equal to 9 containers.

Therefore, we have found that Miss Diego will be able to fill 9 containers.

Learn more about division here: https://brainly.com/question/1622425

#SPJ2

Answer:

D

Step-by-step explanation:

-6(2)=-12

5^-12

can't have negative power

1/5^12

Answer: OPTION D

Step-by-step explanation:

We need to remember that, according to the Negative exponents rule:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

Then, we can rewrite the expression in the following form:

[tex](5^{-6})^2=(\frac{1}{5^6})^2[/tex]

We also need to remember the Power of a power property, which states that:

[tex](a^n)^m=a^{(nm)}[/tex]

Then, applying this property, we get:

[tex]\frac{1}{5^{(6*2)}}=\frac{1}{5^{12}}[/tex]

This matches with the Option D

Answer:

108 cm²

Step-by-step explanation:

The lateral area of this pyramid is the addition of the six triangle areas formed on its lateral side.

The area of each triangle is:

Area = (1/2)*side*slant

Area = (1/2)*3*12 = 18 cm²

Then the lateral area is 6*18 = 108 cm²

Answer:

108cm2

Step-by-step explanation:

For this case we have the following expression:

[tex]3 + 2 \sqrt {2} + \frac {1} {3 + 2 \sqrt {2}} =[/tex]

We rationalize the second term multiplying by:

[tex]\frac {3-2 \sqrt {2}} {3-2 \sqrt {2}}:[/tex][tex]\frac {1} {3 + 2 \sqrt {2}} * \frac {3-2 \sqrt {2}} {3-2 \sqrt {2}} = \frac {3-2 \sqrt {2} } {9-6 \sqrt {2} +6 \sqrt {2} -4 (\sqrt {2}) ^ 2} = \frac {3-2 \sqrt {2}} {9-4 * 2} = \frac {3-2 \sqrt {2}} {1} = 3-2 \sqrt {2}[/tex]

So, we have:

[tex]3 + 2 \sqrt {2} + 3-2 \sqrt {2} = 3 + 3 = 6[/tex]

Answer:

6

these inequalities can be solved just like equations

a. x - 7 > 25

Answer:

B. {-1, 3, 7, 11, 15}

Step-by-step explanation:

The given function is [tex]f(x)=2x-1[/tex]

To find the corresponding odd numbers, we substitute the even numbers as x-values into the function.

When x=0,  [tex]f(0)=2(0)-1=-1[/tex]

When x=2,  [tex]f(2)=2(2)-1=3[/tex]

When x=4,  [tex]f(4)=2(4)-1=7[/tex]

When x=6,  [tex]f(6)=2(6)-1=11[/tex]

When x=8,  [tex]f(8)=2(8)-1=15[/tex]

Therefore the set of odd numbers corresponding to this set of even numbers are  {-1, 3, 7, 11, 15}

Answer:

B. {-1, 3, 7, 11, 15}

Step-by-step explanation:

In order to find the set of corresponding odd numbers then we have to put the even numbers one by one as we already know that x can only have even values..

So,

Putting x = 0

2(0) - 1

=0-1

= -1

Putting x=2

2(2) - 1

=4-1

=3

Putting x=4

2(4)-1

=8-1

=7

Putting x= 6

2(6) -1

=12-1

=11

Putting x=8

2(8)-1

=16-1

=15

So the corresponding set for  {0, 2, 4, 6, 8} is {-1, 3, 7, 11, 15}

Hence, option B is the correct answer ..

Answer:

x = 6

Step-by-step explanation:

(4x - 3)/3 = 7

4x - 3 = 21

4x = 24

x = 6

Answer:

6

Step-by-step explanation:

I'm going to assume you mean (4x - 3) / 3 = 7

If that is not correct, could you please correct it.

Multiply both sides by 3

3*(4x - 3) / 3 = 7*3

The 3s cancel on the left

4x - 3 = 21  

Add 3 to both sides.

4x - 3 + 3 = 21 + 3

combine

4x = 24

Divide by 4

4x/4 = 24/4

x = 6

Answer:

210.6 cm

Step-by-step explanation:

Given that a piece of ribbon is cut into two shorter pieces in the ratio 2.8:1.25.

So that means length of the first smaller piece = 2.8x

and length of the second smaller piece = 1.25x

Then difference between their lengths = 2.8x-1.25x = 1.55x

Given that difference is equal to 80.6 centimeters then we get

1.55x=80.6

or x= 80.6/1.55

or x=52

then length of the original piece = 2.8x+1.25x

= 2.8*52+1.25*52

= 145.6+65

= 210.6 cm

Answer:

1 inch : 5 yards.

Step-by-step explanation:

Paco's first scale was 2 : 5 which is 1 : 2.5.

Now as the length of the pool on the drawing was reduced from 10 in to 5 ins,  that means the scale was doubled so the answer is:

1 : 2*2.5 = 1 : 5 .

Answer:

3  5  30  32

Step-by-step explanation:

The question in English is

The age of 4 members of a family adds up to 70. Mom is 6 times bigger than her son and 10 times bigger than her daughter. Dad is 2 years older than Mom. How old are each of the family members? Write the result in ascending order and separated by spaces

Let

x----> Mon's age

y----> Son's age

z----> Daughter's age

w---> Dad's age

we know that

x+y+z+w=70 -----> equation A

x=6y ----> y=x/6 -----> equation B

x=10z ----> z=x/10 -----> equation C

w=2+x -----> equation D

substitute equation B, C and D in equation A and solve for x

x+(x/6)+(x/10)+(2+x)=70

Multiply by 60 both sides

60x+10x+6x+120+60x=4,200

136x=4,200-120

x=4,080/136

x=30 years

Find the value of y

y=x/6 -----> y=30/6=5 years

Find the value of z

z=x/10 ----> z=30/10=3 years

Find the value of w

w=2+x ----> w=2+30=32 years

Write the result in ascending order and separated by spaces

3  5  30  32

so

Daughter  Son  Mon  Dad

Answer:

[tex]c=\frac{99}{32}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]2x^2-5x+c=0[/tex].

Comparing this equation to:  [tex]ax^2+bx+c=0[/tex], we have a=2,b=-5.

Where: [tex]x_1+x_2=\frac{5}{2}[/tex] and [tex]x_1x_2=\frac{c}{2}[/tex]

The difference in roots is given by:

[tex]x_2-x_1=\sqrt{(x_1+x_2)^2-4x_1x_2}[/tex]

[tex]\implies 0.25=\sqrt{(2.5)^2-4(\frac{c}{2})}[/tex]

[tex]\implies 0.25^2=6.25-2c[/tex]

[tex]\implies 0.0625-6.25=-2c[/tex]

[tex]\implies -6.1875=-2c[/tex]

Divide both sides by -2

[tex]c=\frac{99}{32}[/tex]

Answer:

The value of c is 3.09375.

Step-by-step explanation:

Given : The difference between the roots of the equation [tex]2x^2-5x+c=0[/tex] is 0.25.

To find : The value of c?

Solution :

The general quadratic equation is [tex]ax^2+bx+c=0[/tex] with roots [tex]\alpha,\beta[/tex]

The sum of roots is [tex]\alpha+\beta=-\frac{b}{a}[/tex]

The product of roots is [tex]\alpha\beta=\frac{c}{a}[/tex]

On comparing with given equation, a=2, b=-5 and c=c

Substitute the values,

The sum of roots is [tex]\alpha+\beta=-\frac{-5}{2}[/tex]

[tex]\alpha+\beta=\frac{5}{2}[/tex] .....(1)

The product of roots is [tex]\alpha\beta=\frac{c}{2}[/tex] ....(2)

The difference between roots are [tex]\alpha-\beta=0.25[/tex] .....(3)

Using identity,

[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex]

Substitute the value in the identity,

[tex]0.25=\sqrt{(\frac{5}{2})^2-4(\frac{c}{2})}[/tex]

[tex]0.25=\sqrt{\frac{25}{4}-2c}[/tex]

[tex]0.25=\sqrt{\frac{25-8c}{4}}[/tex]

[tex]0.25\times 2=\sqrt{25-8c}[/tex]

[tex]0.5=\sqrt{25-8c}[/tex]

Squaring both side,

[tex]0.5^2=25-8c[/tex]

[tex]0.25=25-8c[/tex]

[tex]8c=25-0.25[/tex]

[tex]8c=24.75[/tex]

[tex]c=\frac{24.75}{8}[/tex]

[tex]c=3.09375[/tex]

Therefore, the value of c is 3.09375.

Answer:

(3, -7) are the coordinates

Answer:

The rate of decline is [tex]r=0.1455[/tex]  or [tex]r=14.55\%[/tex]

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]D=P(1-r)^{t}[/tex]  

where  

D is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

t  is Number of Time Periods  

in this problem we have  

[tex]P=\$19,400\\D=\$12,105\\t=3\ years[/tex]

substitute in the formula above and solve for r

[tex]\$12,105=\$19,400(1-r)^{3}[/tex]  

Simplify

[tex](12,105/19,400)=(1-r)^{3}[/tex]  

[tex](1-r)=\sqrt[3]{(12,105/19,400)}[/tex]

[tex]r=1-\sqrt[3]{(12,105/19,400)}[/tex]

[tex]r=0.1455[/tex]

Convert to percentage

[tex]r=14.55\%[/tex]

Answer:

D

Step-by-step explanation:

Given that AB and CD are parallel lines, then

∠c and ∠e are same side interior angles and are supplementary

Answer:

D. Supplementary

Step-by-step explanation:

Consecutive Interior Angles Theorem:

If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

Supplementary means the sum of the angles is 180 degrees.

Another name for consecutive interior angles is same side interior angles. The angles are on the same side of the transversal (in this case to the left) and they are in between the parallel lines which is the interior.

Answer:

x = 20; the labeled angles are 80° and 100° ⇒ the last answer

Step-by-step explanation:

* Lets revise some facts about a parallelism

- If two lines are parallel, and intersected by a line, there are 3

 pair of angles are formed

1) Alternate angles equal in measures (corners of Z letter)

2) Corresponding angles equal in measure (corners in F letter)

3) Interior supplementary angles their sum is 180° (corners of U letter)

* Now lets solve the problem

∵ There are two parallel lines intersect by another line

- The formed U letter

∴ The labeled angles are interior supplementary angles

∴ Their sum = 180°

∴ 5x + 4x = 180° ⇒ add the like terms

∴ 9x = 180° ⇒ divide both sides by 9

∴ x = 20°

* Lets find the measure of the labeled angles

∵ The measure of one of them is 4x°

∴ Its measure = 4(20) = 80°

∵ The measure of the other is 5x°

∴ Its measure = 5(20) = 100°

Answer:

4

Step-by-step explanation:

Answer:

first q is 2.75

second q is 1.5

Step-by-step explanation:

Answer:

C. [tex]y=3\cdot 5^x[/tex]

Step-by-step explanation:

First two options show linear function and last two options show exponentioal functions. From the table you can see that

[tex]\dfrac{3}{5}=5\cdot \dfrac{3}{25}\\ \\3=5\cdot \dfrac{3}{5}\\ \\15=5\cdot 3\\ \\75=5\cdot 15[/tex]

This gives you that the function is exponential. Let the expression for the function be [tex]y=ab^x.[/tex] Substitute two values:

at x=0:

[tex]y=a\cdot b^0\\ \\3=a\cdot b^0\\ \\3=a\cdot 1\\ \\a=3[/tex]

at x=1:

[tex]y=a\cdot b^1\\ \\15=a\cdot b\\ \\15=3\cdot b\\ \\b=\dfrac{15}{3}\\ \\b=5[/tex]

Hence

[tex]y=3\cdot 5^x[/tex]