40.Find the difference
41&42. Find the product

The values of  x and y in the first triangle are 60° and 5 and in the second triangle are 7 and 4

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Given are two triangles, we need to find the missing measures of them,

1) We know that, the medians bisects vertex angles and the side,

Therefore,

x = 60°

Also, the equilateral triangle have all sides equal,

8y = 40

y = 5

Therefore, the values of  x and y in the first triangle are 60° and 5

2) We know that, according to the property of a triangle, the sides opposite to equal angles are equal,

y + 12 = 3x-5

3x-5 = 5y-4

Therefore,

y+12 = 5y-4

4y = 16

y = 4

Put y = 4 in 3x-5

3(4)-5 = 7

Therefore, the values of  x and y in the second triangle are 7 and 4

Hence, the values of  x and y in the first triangle are 60° and 5 and in the second triangle are 7 and 4

Learn more about triangles, click;

https://brainly.com/question/2773823

#SPJ1

Answer: (4, 8)

Step-by-step explanation:

When you translate something to the left you need to subtract the amount you moved left from the original x input

1. Subtract 3 from the coordinates x input

4 - 3 = 1

When you translate something up you need to add the amount you moved up to the original y output

2. Add 5 to the coordinates y output

-3 + 5 = 2

When done translating to the left and up your coordinate is now (1, 2)

When dialating something you need to multiply the scale factor in which you dialated the coordinate to both the x input and y output

3. Multiply 4 to the x input and y output of your newley translated coordinate

1 × 4 = 4 (x input)

2 × 4 = 8 (y output)

So now your final coordinate for C' is (4, 8)!

Hope this helps :)

Answer:

19

Step-by-step explanation:

10 + 9 = 19

because when you add those 2 numbers together you get

19

Answer:

20 * .4 = 8 dollars off

20 - 8 = 12

original price = 20

Answer:

Step-by-step explanation:

Hello, please consider the following.

\(\begin{aligned} (2x-9)(3x+4)=\ &2(3x+4)\\&-9(3x+4)\\\\ =\ & 6x+8\\&-27x-36\\\\=\ &(6-27)x+8-36\\\\=\ &-21x-28\end{aligned}\)

Thank you.

The book value of the office building in 2004, which was worth $1 million when completed in 2000 and being depreciated linearly over 30 years, will be $866,668.

The book value of an asset is the difference between the cost and the accumulated depreciation.

The accumulated depreciation is the total depreciation over the years.

The worth of the office building on completion = $1 million

The year of completion = 2000

Depreciation period = 30 years

Depreciation method = Linear depreciation

Scrap value = $0

Annual depreciation expense = $33,333 ($1,000,000 ÷ 30)

Accumulated depreciation between 2000 and 2004 = $133,332 ($33,333 x 4)

Book value in 2004 = $866,668 ($1,000,000 - $133,332)

Thus, with an annual depreciation of $33,333, the book value is $866,668.

Learn more about the book value of an asset at https://brainly.com/question/23057744.

#SPJ1

Answer:

56.5

Step-by-step explanation:

Circumference = \(\pi d\)

C = 3.14(18) = 56.52

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

The probability of selecting 50 jars is 0%

The z score determines by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where \mu=mean,\sigma=standard\ deviation, x=raw\ score,n=sample\ size\\\\Given\ that\ \mu=17,\sigma=0.68,n=50,x=16.8\\\\z=\frac{16.8-17}{0.65/\sqrt{50} } =-5\)

The P(z < -5) = 0%

Therefore the probability of selecting 50 jars is 0%

Find out more at: https://brainly.com/question/15016913

Answer:

Step-by-step explanation:

The differential equation representing the model of the number of words memorized by the students is equal to option C. dL/dt = k(100 - L).

Let us consider function 'L' represents the number of words memorized at time 't'

Total number of words students asked to memorized = 100 words

Rate of change of number of words with time 't' is equal to ( dL/dt )

Number of words left to memorized by the students = 100 - L

Differential equation representing the situation is

= Rate of change of number of words memorized ∝ number of words left to memorized

= dL/dt ∝ ( 100 - L )

⇒ dL/dt = k( 100 - L )

Where 'k' is the constant of proportionality .

k is a positive number.

Therefore, the differential equation representing the situation of memorizing word is given by option c. dL/dt = k( 100 - L ).

Learn more about differential equation here

brainly.com/question/16358700

#SPJ4

The above question is incomplete, the complete question is:

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized.

1. Which of the following differential equations could be used to model this situation, where k is a positive constant?

A. dL/dt = kL

B. dL/dt = 100 - kL

C. dL/dt = k(100 - L)

D. dL/dt = kL - 100

The monthly Payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

The monthly payment of a 2-year loan of $1590 with 9% interest which needs to be repaid in 254 equal monthly installments, we need to use the loan repayment formula. The formula is given as:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Here,

Loan Amount = $1590

Interest Rate = 9% per annum

Time = 2 years = 24 months

number of Months = 254 (as there are 254 monthly installments)

First, we need to calculate the Monthly Interest Rate using the following formula:

Monthly Interest Rate = Annual Interest Rate / 12

The Annual Interest Rate is 9%,

so the Monthly Interest Rate is:  Monthly Interest Rate = 9 / 12 = 0.75%Putting the given values into the loan repayment formula,

we get: Monthly Payment = (1590 x 0.0075) / (1 - (1 + 0.0075)^(-254))= 11.92 (approx)

Therefore, the monthly payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

For more questions on Payment .

https://brainly.com/question/25792915

#SPJ8

Answer:

(hope this helps) He was able to build a windmill by using scraps he found in his village and he kept going back to school and reading books on how to build windmills.

Step-by-step explanation:

Answer:

The numbers that are greater than - 2 qnd less than 3 are:

-1,0,1&2

Answer: 3 kids take 3 pieces of candy each

Step-by-step explanation:

Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)

Number of children that took 5 pieces is y ( total take 5*y pieces of candy)

1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.

( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy.  So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )

So we have 2 equations or the system of 2 equations:

1).  x+y=18

2). 3*x +5*y=84

Multuply both sides of equation 1) by 3

We have   3*x+3*y=18*3

Deduct 3*y from both sides of this equation

3*x+3*y-3*y=54-3*y

3*x=54-3*y

Substitute 3*x in equation  2).  by 54-3*y

2) 54-3*y+5*y=84

2*y=30

y=15  ( kids take 5 pieces of candy each)

Using equation 1) find x

x+15=18

x=3 (kids take 3 pieces of candy each)

Answer:

Your answer

56100 per person

Mark it as Brainlist answer. Follow me to get more answer

Step-by-step explanation:

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = \(\pi* r^2 *h\)

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pounds

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

Read more about volume here:

https://brainly.com/question/27710307

#SPJ1

The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

Find out more on area at https://brainly.com/question/2129070

#SPJ1

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

\((a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}\), \(\forall\,a,b\in\mathbb{R}\)

Let prove if each option observe this:

a) \(4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}\)

1) \(4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}\) Given

2) \((2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}\) Definition of power/Distributive, associative and commutative properties.

3) \(a = 2\cdot x\), \(b = 3\cdot y\) Definition of perfect square trinomial/Result.

b) \(9\cdot a^{2}-36\cdot a + 36\)

1) \(9\cdot a^{2}-36\cdot a + 36\) Given.

2) \((3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}\) Definition of power/Distributive, associative and commutative properties.

3) \(a = 3\cdot a\), \(b = 6\) Definition of perfect square trinomial/Result.

c) \(x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}\)

1) \(x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}\) Given

2) \(x\cdot y\cdot (1-4\cdot x+4\cdot x)\) Distributive property.

3) \(x\cdot y \cdot 1\) Existence of the additive inverse/Modulative property.

4) \(x\cdot y\) Modulative property/Result.

d) \(a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}\)

1) \(a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}\) Given

2) \((a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})\) Definition of power/Distributive, associative and commutative properties.

3) \(a = a\cdot b\), \(b = 2\cdot a^{2}\) Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%

The cost and the selling price are given as:

C(x) = 24x + 103

S(x) = 33x - x^2/30

The profit is calculated using:

P(x) = S(x) - C(x)

This gives

P(x) = 33x - x^2/30 - 24x - 103

Evaluate the like terms

P(x) = -x^2/30 + 9x - 103

Hence, the expression for the profit is -x^2/30 + 9x - 103

When x = 20, we have:

Cost: C(20) = 24 * 20 + 103 = 583

Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67

The percentage profit is then calculated as:

Percentage = P(x)/C(x) * 100%

This gives

Percentage = 64.67/583 * 100%

Evaluate

Percentage = 11.1%

Hence, the percentage profit on 20 bags of rice is 11.1%

Read more about profit and cost at:

https://brainly.com/question/19104371

#SPJ1

Using the formula for calculating the area of a rhombus, the length of /AC/ is 44 units

From the question, we are to determine the length of AC

The area of a rhombus is given by

\(A = \frac{pq}{2}\)

Where A is the area

p and q are the diagonals

Then, for the given diagram,

\(A = \frac{/DB/ \times /AC/}{2}\)

From the given information,

A = 264 square units

/DB/ = 12 units

∴ \(264 = \frac{12\times /AC/}{2}\)

\(264 = 6\times /AC/\)

\(/AC/ = \frac{264}{6}\)

/AC/ = 44 units

Hence, the length of /AC/ is 44 units

Learn more on Calculating the area of a Rhombus here: https://brainly.com/question/12735921

#SPJ1

Answer:

Yes, the triangles are SIMILAR, not exact.

Step-by-step explanation:

None.

Answer:

yes

no

no

yes

Step-by-step explanation:

Answer:

3^4

Step-by-step explanation:

3^2*3^2

3*3*3*3

3^4

Answer:

  x = 50

Step-by-step explanation:

The marked angles are vertical angles, so are congruent.

  3x -3 = 147 . . . . congruent angles have equal measures

  x -1 = 49 . . . . . divide by3

  x = 50 . . . . . . add 1

Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=\(\frac{122}{3}\)≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

Learn more about regular polyhedron here:

https://brainly.com/question/29134238

#SPJ1

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

To learn more about linear equation from the given link

https://brainly.com/question/2226590

#SPJ1