Find the length of the short leg of a 30 - 60 - 90 triangle If the long side is 4/3 units.

Using the inequality concept, the expression models the number of days Samuel can afford to rent while staying within his budget is 11x + 18 ≤  40

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

A rental car company charges $22 per day to rent a car and $0.08 for every mile driven

The maximum amount to spend = $80

Fixed charge per day $22

Charge per mile = $0.08

The inequality which represents the number of days Can be expressed thus :

(Charge per day × number of days) + (charge per mile × number of miles) ≤  80

22x + 0.08× 450 ≤ 80

22x + 36 ≤  80

Divided by 2 both sides of an inequality,

11x + 18 ≤  40

Hence, the required inequality expression is 11x + 18 ≤  40

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The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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Answer:

the answer is 1/3 because dividing two negatives equals a positive and then rewrite the division to a fraction and get 15/45 and reduce the fraction by 15 and you get 1/3

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

Answer:

1. 17.8 cm

2. 32.0 cm

3. 15.9 m

Step-by-step explanation:

1. Determination of the length of the arc.

Radius (r) = 6 cm

Angle at the centre (θ) = 170°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 170/360 × 2 × 3.14 × 6

L = 17/36 × 37.68

L = 17.8 cm

2. Determination of the length of the arc.

Diameter (d) = 13 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

Next, we shall determine the radius. This can be obtained as follow:

Diameter (d) = 13 cm

Radius (r) =?

r = d/2

r = 13/2

r = 6.5 cm

Finally, we shall determine the length of the arc. This can be obtained as follow:

Radius (r) = 6.5 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 282/360 × 2 × 3.14 × 6.5

L = 282/360 × 40.82

L = 32.0 cm

3. Determination of the length of the arc.

Radius (r) = 11 m

Angle at the centre (θ) = 83°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 83/360 × 2 × 3.14 × 11

L = 83/360 × 69.08

L = 15.9 m

For the given figure of intersecting lines the expression holds is m∠1 + m∠3 + m∠5 = 180°. Option D is correct.

Given that, A figure of the intersecting lines is given where 3 lines intersect at the same point.

The angle can be defined as one line inclined over another line.

A line can be defined by the shortest distance between two points is called a line.

Here,
From the figure
∠1 = ∠4
∠2 = ∠5
So,
∠6 = ∠3
Now, from the option, the property hold is m∠1 + m∠3 + m∠5 = 180°. because m∠1 + m∠6 + m∠5 = 180°, or ∠6 = ∠3.

Thus, for the given figure of intersecting lines the expression holds is m∠1 + m∠3 + m∠5 = 180°. Option D is correct.

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Answer:

\(\cos(J) = 0.67\)

Step-by-step explanation:

Given

\(\angle K = 90^o\)

\(KJ = 65\)

\(IK = 72\)

\(JI = 97\)

Required

\(\cos(J)\)

The question is illustrated with the attached image.

From the image, we have:

\(\cos(J) = \frac{KJ}{JI}\)

This gives:

\(\cos(J) = \frac{65}{97}\)

\(\cos(J) = 0.67010309278\)

\(\cos(J) = 0.67\) --- approximated

Answer:

A) 5

Step-by-step explanation:

...................................

The answer is A)5

Answer:

-2

Step-by-step explanation:

Let's flip it.

1-3/x=1

1-3= -2

-2/x=1

What can get us to 1 from -2 from dividing?

Try doing it from multiplying. -2x1= your answer!

I really hope this helped, im sorry if it didn't!

Answer:

x=65 degrees

Step-by-step explanation:

It's a right angle because a line is equal to 180* and one side is a right angle so the other is one as well so 90*-25*=65*

Answer:

4y

Step-by-step explanation:

y - (-3y)

y + 3y

4y

When you see two negatives they basically become an addition symbol. In this case you then add the like terms which are y and 3y to get 4y. Hope this helps!!

Answer:x=- 17-root 217/12

Step-by-step explanation:

the answer is x=17

Step-by-step explanation:

I just did it

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

Answer:

D

Step-by-step explanation:

Answer: l=-3+square root of 29

Step-by-step explanation:

I got this on my math homework

Answer:

1. x≥−33

2. x<−9

3. m≤−475

4. f<−18

5. q<5

6. x<15

Step-by-step explanation:

Hope this helps.

Answer:

Length = 24 yards

Width = 3 yards

Step-by-step explanation:

First you find the perimeter of the rectangle assuming It's length is 8 and its width is 1. The perimeter is then 18. Lets call this rectangle A

Now you divide 54 by 18 which gives you 3. That means the rectangle is 3 times the size of the rectangle  A.

So to find the length and width you do this:

Length: 8 X 3 = 24 yards

Width: 1 X 3 = 3 yards

see the attached sheet.

I hope it helps you .

Answer: $1.6

Step-by-step explanation:

price × percentage of tax=amount of tax

$20 × 8%=20 × 0.08= $1.6

Hope this helps!! :)

$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

where:

PV is the present value of the annuity

PMT is the payment amount per period

r is the interest rate per period

n is the total number of periods

In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.

The interest rate per period is 7% / 12 = 0.5833%.

Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833

Solving for PMT, we get:

PMT = PV × r / [1 - (1 + r)⁻ⁿ]

PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]

PMT = $3,244.21

Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

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Answer:

820,000

Step-by-step explanation:

2 is lower than 5 so round down to 20

Pls Brainliest If Helps

Answer:

820,000

Step-by-step explanation:

The 10,000 digit is the 2 on the left.

All digits to the right of the left 2 become zero.

820,000

The first digit that is dropped is the right 2.

Since it is not 5 or more, the 2 that is kept does not go up to 3.

Answer: 820,000

Answer:

m=0

Step-by-step explanation:

A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

Step-by-step explanation:

if the first equation is y=-23x-1 than the answer is A

Answer:

\(60%\)%

Step-by-step explanation:

\(17+23=40\)\(, 40\) in total.

\(10+14=24\), 24 students trying out.

24 of 40 as a percent\(=60\)

Answer:

60%

Step-by-step explanation:

According to formula if finding percent, given number(10+14)divide by total number(17+23) multiply 100% which is 24/40*100= 60%

Answer:

The proportion of number of weeks (x) to the number of years aged in that week (y) would be 1:7. I'm not very good at explaining things but I hope this helped...

Answer: haha

Step-by-step explanation:

j kkkkkkkkkknk  

By applying the unitary method, counting 67 colonies on a plate with 1ml of the 1:1,000,000 dilution indicates that 67,000,000 bacteria were present in 1ml of the original sample.

The unitary method is a mathematical technique that involves finding a unit value and using it to solve problems. In this case, we need to determine the number of bacteria present in 1ml of the original sample.

The dilution factor represents the ratio of the volume of the original sample to the volume of the diluted sample. In this case, the dilution factor is 1:1,000,000, which means that 1ml of the original sample was diluted with 1,000,000ml of a diluent solution to obtain 1ml of the diluted sample. Therefore, the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample.

Now, let's use the colony count to determine the number of bacteria in the diluted sample. We are told that 67 colonies were counted on the plate with 1ml of the 1:1,000,000 dilution. This means that each colony represents the growth of a single bacterium in the diluted sample. Therefore, the number of bacteria in the diluted sample is 67.

Using the unitary method, we can now determine the number of bacteria in 1ml of the original sample. We know that the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample. Therefore:

Number of bacteria in original sample = Dilution factor x Number of bacteria in diluted sample

Number of bacteria in original sample = 1,000,000 x 67

Number of bacteria in original sample = 67,000,000

So, the answer is that 67,000,000 bacteria were present in 1ml of the original sample.

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Answer:

102 tickets

Step-by-step explanation:

start by adding

Mon 198

Tues 96

We'd 204

then you would get 498 and max people that can fit in the gym is 600 so then you would subtract 600-498 and get 102 so the maximum amount of tickets they can sell on Thursday is 102 tickets