Two different ways to solve 1/4x-5=3/4x-12

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:

$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.

The parallel lines are:

Know more:-

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:

Step-by-step explanation:

Incomplete question.

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

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]

Answer:

x=14.5

Step-by-step explanation:

50.48=-22.02+5x

5x=50.48-(-22.02)

5x=50.48+22.02

5x=72.5

x=72.5/5

x=14.5

Answer:

Looking at the example Alana will walk. 15.23 miles in two days

step-by-step explanation:

Looking at the example and using place value system

8.63 + 6.60= 15.23 miles

Sum = 14 ones + 8 tenths + 6 hundredths

= 4 ones + 2 tenths + 3 hundredths

= 1 ten + 4 ones + 2 tenths + 3 hundredths

Alana walks 12.3 miles in two days.

In the given problem, Alana walks 6.6 miles on the first day.

To find the total distance she walks in two days, we perform a multi-digit addition.

We start by adding the ones place, which gives us 14 ones. Moving to the tenths place, we add 8 tenths to the existing sum.

In the hundredths place, we have 6 hundredths. This gives us a total of 14 ones, 8 tenths, and 6 hundredths.

Next, we simplify this into a mixed decimal, resulting in 4 ones, 2 tenths, and 3 hundredths.

Converting to place value, this becomes 1 ten, 4 ones, 2 tenths, and 3 hundredths.

Therefore, Alana walks a total of 12.3 miles in two days.

This process involves careful consideration of place value and addition to accurately determine the distance covered over the two-day period.

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complete question should be:

Look at the example problem. Suppose Alana walks 6.6 miles the next day. Complete the steps below to find the number of miles she walks in two days.                                                                                                  

Alana walks ____ miles in 2 days.

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:

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:

[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:

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:

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: Total cost = Cost of each bottle × Number of bottles

Step-by-step explanation: If each bottle of water Marissa bought cost 0.95cents. This means four bottles will cost = 0.95 + 0.95 + 0.95 + 0.95 = 3.80 cents

This can be written simply as 0.95 × 4 = 3.80 cents

Therefore, a general equation for calculating the total cost of bottle water will be;

Total cost = Cost of each bottle × Number of bottles.

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:

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 :)

Answer:

yes

Step-by-step explanation:

Answer:

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

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.

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:

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].

Buckets of cement needed is 5 and sand needed is 20

Solution:

Given that Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1 : 4 : 6

cement : sand : gravel = 1 : 4 : 6

Let the cement needed be "1x"

Let the sand needed be "4x"

Let the gravel needed be "6x"

Given that 20 buckets of sand used

4x = 20

x = 5

Thus buckets of cement needed = 1x = 1(5) = 5

Buckets of sand needed = 4x = 4(5) = 20

5 buckets of cement and 20 buckets of sand are needed

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:

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:

perpendicular

Step-by-step explanation:

Convert into y = mx + b form

5y = 6x + 1

y = 6/5x + 1/5

6y = -5x - 4

y = -5/6x - 2/3

Since the y int are different, and the slopes are perpendicular (neg reciprocal), the 2 lines are perpendicular

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:

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:

6y^4 + 3y^4

1296y + 81y

1377y

Step-by-step explanation: