What is 5 1/3 minus 1 1/3 equal to?

Answer:

Step-by-step explanation:

We are given that IE bisects <KID

Using this, we can say that <EID is congruent to <EIK by the definition of an angle bisector.

We are also given that <IED is congruent to <IEK.

Since these two angles are congruent, we can say that <IDE is congruent to <IKE. This is proven with the 3rd angle theorem.

Since the two base angles are congruent, the triangle is isosceles by the definition of an isosceles triangle.

Answer:

The system cannot be solved by a unique cost for each soldier

Step-by-step explanation:

The correct question is

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3 archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables.

Can we solve for a unique cost for each soldier?

Let

x-------> the cost of a legionary per day

y-------> the cost of an archer per day

we know that

[tex]3x+3y=10[/tex]

isolate the variable y

subtract 3x both sides

[tex]3y=10-3x[/tex]

Divide by 3 both sides

[tex]y=-x+\frac{10}{3}[/tex] ------> equation A

[tex]x+y=3[/tex]

isolate the variable y

subtract x both sides

[tex]y=-x+3[/tex] ------> equation B

Remember , If two lines are parallel, then their slopes are equal

In this problem Line A and Line B are parallel lines, because their slopes are equal.

we know that that the solution of the system of equations is the intersection point both graphs

If the lines are parallel, then the lines don't intersect

see the attached figure to better understand the problem

therefore

The system has no solutions (Is a inconsistent system)

Answer:

Therefore the missing length is AC = 24.46 units

Step-by-step explanation:

Consider a Δ ABC with

∠ B = 43°

AB = c = 18

BC = a = 8

To Find:

AC = c = ?

Solution:

We know in a Triangle Cosine Rule Says that,

[tex]b^{2} =c^{2}+ a^{2}-2\times a\times c\times \cos B[/tex]

Substituting the given values in above formula we get

[tex]b^{2} =18^{2}+ 8^{2}-2\times 8\times 18\times \cos 43\\\\b^{2} =324+64+288\times 0.7313\\\\b^{2} =598.6144\\\\Squaare\ Rooting\\\therefore b = 24.46\ units[/tex]

Therefore the missing length is AC = 24.46 units

Answer:

13.32

Step-by-step explanation:

if the missing side length is b,

1.)  b^2 = 18^2 + 8^2 - 2(8)(18)(cos43)

2.)  b^2 = 177.3701

then take square root of 177.3701

3.)  √(b^2) = √(177.3701)

4.)  b = 13.32

see ya have a good day

Answer:

$650

Step-by-step explanation:

the child stole $500 then the shopkeeper gave him change of $150 that equals to the amount of money the shopkeeper lost.

working....

$500+$150=$600

Final answer:

The shopkeeper lost a total of $500 due to the child stealing $500, buying items worth $350, and receiving $150 in change.

Explanation:

The question involves determining the total amount of money the shopkeeper lost due to a theft. When the child stole $500 from the cash register and then used some of this money to buy items worth $350, the shopkeeper effectively lost that amount due to the child not legitimately paying for the goods. Furthermore, the child received $150 in change when they used the stolen money to pay for the items. Therefore, the total money lost by the shopkeeper is the sum of the cost of the goods taken and the change given out, which amounts to $350 + $150, equating to a total loss of $500.

Answer:

[tex]A(s)=s^2[/tex]

Step-by-step explanation:

we know that

The square  is a regular polygon that has four right angles and four parallel and congruent sides.

The area of a square is equal to the length side squared

Let

s ----> the length side of the square

we have that

[tex]A(s)=s^2[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

Yes. This is called a solution of the equations and is the intersection point.

The parallel lines are:

Know more:-

Answer: 16

Step-by-step explanation: 80x20=1600

Put the decimal place where it belongs

80% of 20=16

Hope this helps!

To find the number of red skittles in the bag, multiply the total number of skittles by the percentage of red skittles (in decimal form). In this case, there are 16 red skittles in the bag. So, there are 16 red skittles in the bag.

To find the number of red skittles in the bag, we can use the concept of percentages. We know that 20% of the skittles are red, and there are 80 skittles in total. To find the number of red skittles, we multiply 80 by 20% (or 0.20).

80 * 0.20 = 16

So, there are 16 red skittles in the bag.

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Answer:

35

Step-by-step explanation:

[tex]d=-2\\n=4\\a_4=a_1+3d\\if\; a_1=41\; then\; a_4=41+3\times(-2)=41-6=35[/tex]

Answer:

Step-by-step explanation:

22

Answer:

Factored :

2 (5x-3)(x^2+5)

Roots :

[tex]x=\frac{3}{5}  , i\sqrt{5} , -i\sqrt{5} \\[/tex]

Step-by-step explanation:

Answer:

Option C. [tex]64\ cm^2[/tex]

Step-by-step explanation:

see the attached figure N 1 to better understand the problem

we know that

The trapezoid can be decomposed into two right triangles and a rectangle

see the attached figure N 2

so

The area of the trapezoid is equal to the area of two right triangles and one rectangle

The area of trapezoid is equal to

[tex]A=\frac{1}{2}(5)(4)+(12)(4)+\frac{1}{2}(3)(4)[/tex]

[tex]A=10+48+6[/tex]

[tex]A=64\ cm^2[/tex]

Answer:

C) y=0

Step-by-step explanation:

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

m=(-2-0)/(5-5)

m=-2/0

m=0

y-y1=m(x-x1)

y-0=0(x-5)

y-0=0

y=0+0

y=0

Answer:

x=5

Step-by-step explanation:

a

Answer:

Step-by-step explanation:

You are expected to know and make use of the following relations:

__

For this problem, it isn't always easiest to work the questions in order. It is best to start with the angles easiest to find from those given.

  b and 144° are a linear pair, so b = 180° -144° = 36°

  a and b are alternate interior angles, so a = b = 36°

  2d and 144° are corresponding angles, so d = 144°/2 = 72°

  e is the apex angle of an isosceles triangle with base angles 36°, so is 180° -2(36°) = 108° = e

  f and 164° are a linear pair, so f = 180° -164° = 16°

  g and f are complementary, so g = 90° -16° = 74°

  g+h is a vertical angle with 144°, so is congruent to that. h = 144° -74° = 70°

  c is the base angle of an isosceles triangle with b as the vertex angle. That means c = (180° -36°)/2 = 72°

Answer:

Maya = $1260

Emily = $5040

Step-by-step explanation:

2740+3560 =6300

M + (4M) = 6300

5M=6300

M=6300/5

M=1260

E=5040

Maya has $1260, and Emily has $5040 in the end. Maya gives $1480 to Emily.

Maya has $2740, and Emily has $3560.

We're looking for the amount Maya gives to Emily so that Emily ends up with 4 times as much as Maya.

Let M be the amount Maya gives to Emily.

Emily ends up with 4 times Maya's amount:

Emily's amount = 4 * Maya's amount

$3560 + M = 4 * ($2740 - 4M

Simplify:

$3560 + M = $10960 - 4M

$3560 + M + 4M = $10960

5M = $10960 - $3560

5M = $7400

Divide by 5 to solve for M:

M = $7400 / 5

M = $1480

So, Maya gives $1480 to Emily.

To find how much each girl has in the end:

Maya: $2740 - $1480 = $1260

Emily: $3560 + $1480 = $5040

Maya has $1260, and Emily has $5040 in the end.

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Answer:

The radius of Astrodome is 355.09 foot,

The Area of Astrodome is 395919.146 square foot .

Step-by-step explanation:

Given as :

The circumference of Astrodome = 2230 foot

∵ The circumference of circular shape = 2 × [tex]\pi[/tex] × radius

where  [tex]\pi[/tex] = 3.14

So, The circumference of Astrodome = 2 × [tex]\pi[/tex] × radius

Or, 2230 foot = 2 × 3.14 × radius

Or, 2230 foot = 6.28 × radius

∴ radius = [tex]\dfrac{2230}{6.28}[/tex]

I.e radius = 355.09 foot

Now,

∵The area of circular shape = [tex]\pi[/tex] × radius²

So, The area of Astrodome = [tex]\pi[/tex] × radius²

Or, The area of Astrodome = 3.14 × radius²

Put the value of radius = 355.09 foot

So , The area of Astrodome = 3.14 × (355.09)²

or, The area of Astrodome = 3.14 × 126088.9

∴  The area of Astrodome = 395919.146 square foot

Hence , The radius of Astrodome is 355.09 foot, and The Area of Astrodome is 395919.146 square foot . Answer

Answer

[tex]AP=14[/tex]

Step by Step Explanation

1) Due to the Centroids Theorem we can say that:

AP=2/3AE

AP=2/3*21

∴AP=14

2) Finally, AE =AP+AE

21=14+7 ⇒21=21 True

AP =2PE verifies the Theorem too.

So, the size is 14 .

[tex]AP=14\:u[/tex]

The computer costs $304 now.

Step-by-step explanation:

Given,

Cost of computer = $400

First discount = 20%

Amount of discount = 20% of $400

Amount of discount = [tex]\frac{20}{100}*400=\frac{8000}{100}[/tex]

Amount of discount = $80

Price after first discount = 400-80 = $320

Additional discount = 5%

Amount of additional discount = 5% of price after first discount

Amount of additional discount = [tex]\frac{5}{100}*320=\frac{1600}{100}[/tex]

Amount of additional discount = $16

Final cost = 320-16 = $304

The computer costs $304 now.

Keywords: discount, subtraction

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Answer:

8 CD's for $56.99 is better value than 3 CD's for $22.99.

Step-by-step explanation:

We are given that,

Cost of 8 CD's is $56.99 and cost of 3 CD's is $22.99.

Now, to determine which is the better value, we will find the cost of 1 CD in both the cases. The case which will give cost per CD less will represent the better value.

CASE 1 :

Cost of 8 CD's = $ 56.99

So, cost of 1 CD = $ 56.99 ÷ 8 = $ 7.12  (approx.)

CASE 2 :

Cost of 3 CD's = $ 22.99

∴ Cost of 1 CD = $ 22.99 ÷ 3 = $ 7.66 (Approx.)

So, the CD's are available in cheaper rates in the first case in comparison to second case.

So, 8 CD's for $56.99 is better value than 3 CD's for $22.99.

Answer:

The unit cost of 8 CDs for $56.99 is $7.12 and the unit cost of 3 CDs for $22.99 is $7.66.

And the better value is of 8 CDs for $56.99.

Step-by-step explanation:

Given:

8 CDs for $56.99 or 3 CDs for $22.99.

Now, to find the unit cost to determine which is better value.

By using unitary method we find it:

So, to get the unit cost of 8 CDs for $56.99:

If 8 CDs cost $56.99.

Then, 1 CD cost = [tex]56.99\div 8=\$7.12.[/tex]

Thus, the unit cost = $7.12.

Now, to get the unit cost of 3 CDs for $22.99:

If 3 CDs cost $22.99.

Then, 1 CD cost = [tex]22.99\div 3=\$7.66.[/tex]

Thus, the unit cost = $7.66.

Now, on comparing we determine the better value is of 8 CDs for $56.99.

Therefore, the unit cost of 8 CDs for $56.99 is $7.12 and the unit cost of 3 CDs for $22.99 is $7.66.

And the better value is of 8 CDs for $56.99.

Final answer:

To complete the square for f(x) = x^2 - 6x + 19, we create a perfect square trinomial to rewrite the function as f(x) = (x - 3)^2 + 10, which has a minimum value at the vertex (3, 10).

Explanation:

To complete the square for the quadratic function f(x) = x2 - 6x + 19, we need to form a perfect square trinomial from the x2 and the -6x terms and then adjust the constant term accordingly.

First, we divide the coefficient of the x term, which is -6, by 2, getting -3, and then square it to get 9. We add and subtract this number inside the function to maintain the equality:

f(x) = (x2 - 6x + 9) - 9 + 19

Now, f(x) becomes:

f(x) = (x - 3)2 + 10

Since the coefficient of the x2 term is positive, the parabola opens upward, and the vertex represents the minimum value of the function.

The vertex of the parabola is at (3, 10), so f(3) = 10 is the minimum value of f(x). Therefore, the correct answer is:

D) f(x) = (x - 3)2 + 10 and f(x) has a minimum value f(3) = 10.

Answer:

2:5

Step-by-step explanation:

The ratio of pair of flip flop to pair of sneakers is 4:10 we simplify it to 2:5 by dividing both sides by 2

Answer:

The area \(A\) of a trapezoid can be calculated using the formula:

\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \(b_1\) and \(b_2\) are the lengths of the parallel bases, and \(h\) is the height.

For this trapezoid:

- \(b_1 = 3\) inches

- \(b_2 = 5\) inches

- \(h = 8\) inches

Plugging in the values:

\[ A = \frac{1}{2} \times (3 + 5) \times 8 \]

\[ A = \frac{1}{2} \times 8 \times 8 \]

\[ A = \frac{1}{2} \times 64 \]

\[ A = 32 \]

The area of the trapezoid is 32.

Answer:

6y^4 + 3y^4

1296y + 81y

1377y

Step-by-step explanation:

Answer:

The number of years in which house value goes up is 145 years .

Step-by-step explanation:

Given as :

The initial purchased value of the house = p = $179,300,00

The value of house goes up every years at the rate = r = 4%

Let The number of years in which house value goes up = t  years

The value of the house after t years = $A = $5197,230,002

Now, According to question

The value of the house after t years = The initial purchased value of the house × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

I.e A = $p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or,$5197,230,002 = $17930000 × [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]

Or, [tex]\dfrac{5197,230,002}{179,300,00}[/tex] = [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]

Or, 289.86 = [tex](1.04)^{t}[/tex]

Now, taking Log both side

So, [tex]Log_{10}[/tex]289.86 = [tex]Log_{10}[/tex] [tex](1.04)^{t}[/tex]

or, 2.462 = t ×  [tex]Log_{10}1.04

or, 2.462 = t × 0.01703

∴ t = [tex]\dfrac{2.462}{0.01703}[/tex]

I.e t = 144.56 ≈ 145

So, Number of years = t = 145 years

Hence The number of years in which house value goes up is 145 years . Answer

To determine the number of years it will take for the value of Isaac's house to reach $5,197,230.002 with an annual appreciation rate of 4%, use the compound interest formula. Solving for the number of years, the approximate result is 84 years.

Isaac purchased a house for $179,300. Every year, the value of the house increases by 4%. To determine the number of years after purchase that the value of Isaac's house will reach $5,197,230.002, we can use the formula for compound interest:

FV = PV × (1 + r)ⁿ

We need to solve for n in the equation:  

First, isolate the exponential expression:

Next, apply the natural logarithm to both sides to solve for n:

So, the value of Isaac's house will reach $5,197,230.002 approximately 84 years after purchase.

Answer:

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

From the given graph it is clear that the graph passes through the points (0,3) and (-5,0).

It a line passes through wo points then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The equation of given line is

[tex]y-3=\dfrac{0-3}{-5-0}(x-0)[/tex]

Add 3 on both sides.

[tex]y=\dfrac{-3}{-5}x+3[/tex]

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

Therefore, the required equation is [tex]y=\dfrac{3}{5}x+3[/tex].

Answer:

The optimum price to sell the app is $2.55

Step-by-step explanation:

Modeling With Functions

The equation of the demand for the app store is given by

U=10000-2000P

Where U is the number of units sold and P is the price for each unit.

a.

The money from sales (Revenue) is U times the price of each unit, so

[tex]S=U.P[/tex]

Using the equation above

[tex]S=(10000-2000P).P=10000P-2000P^2[/tex]

b. The upfront costs function is given by

[tex]C=2000+0.1U[/tex]

Again, we use the equation for U

[tex]C=2000+0.1(10000-2000P)[/tex]

[tex]C=2000+1000-200P[/tex]

[tex]C=3000-200P[/tex]

c.

The profit is the sales minus the cost

[tex]Profic=S-C=10000P-2000P^2-(3000-200P)[/tex]

[tex]Profit=10000P-2000P^2-3000+200P[/tex]

[tex]Profit=-2000P^2+10200P-3000[/tex]

d.

The vertex of a quadratic function shown as

[tex]f(x)=ax^2+bx+c[/tex]

has an x-coordinate equal to

[tex]\displaystyle x=-\frac{b}{2a}[/tex]

The optimum price for selling the app can be found in the vertex of the above equation.

The P-coordinate of the vertex is given by

[tex]\displaystyle x=-\frac{10200}{-4000}=2.55[/tex]

The optimum price to sell the app is $2.55

25 states,  Paulo's family arrived at the reunion at

8:30 A.M. How long do they have before

the trip to Scenic Lake Park?

So the question asks how long it takes.

8:30AM to 10:15AM would be a 1:15 hour difference. This would be the answer to #25.

Let me know if you have any extra questions.

25 states,  Paulo's family arrived at the reunion at

8:30 A.M. How long do they have before

th

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

1.) subtract 3200 and 2240. Since you need to find the amount of people who were satisfied with the car.

2.) divide 960 and 3200. this is because you need to find the percent of people who were satisfied with the car.

Answer: 30%

The percentage satisfied with the purchase is 30%

The percentage who were satisfied can be calculated thus :

Difference = 3200 - 2240 = 960

Now we have :

(960 / 3200) × 100%

= 0.3 × 100%

= 30%

Hence, percentage who were satisfied is 30%

Answer:

x = 4

A

Step-by-step explanation:

2(4x - 6) = 6x - 4

8x -12 = 6x - 4

8x - 8 = 6x

8x = 6x + 8

2x = 8

x = 4

Hope this helps :)