The flower garden has the shape of a right triangle. 68 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 28 ft longer than other leg. find the lengths of the legs.

Answers

Answer 1

The shorter leg of the triangle is 32 feet long.

The longer leg of the triangle is 60 feet long.

In this case, we are given that the hypotenuse of the triangle is 68 feet, and one leg is 28 feet longer than the other leg. Let's call the length of the shorter leg "x". Then, the length of the longer leg is "x + 28".

Using the Pythagorean theorem, we can write the following equation:

68^2 = x² + (x + 28)²

Simplifying this equation, we get:

4624 = 2x² + 56x + 784

Solving for x, we find that:

x = 32 or x = -60

Since the length of a side of a triangle cannot be negative, we reject the solution x = -60. Therefore, the length of the shorter leg is 32 feet, and the length of the longer leg is 32 + 28 = 60 feet.

Related Questions

Will give brainliest! Which are simplified forms of the expression sec^2theta sin2theta
Which is the second answer? I already got the first one

Answers

[tex]\bf \cfrac{sin(2\theta )}{cos^2(\theta )}\implies \cfrac{1}{cos^2(\theta )}\cdot sin(2\theta )\implies sec^2(\theta )sin(2\theta )\\\\ -------------------------------\\\\ 2tan(\theta )\implies \cfrac{2sin(\theta )}{cos(\theta )}\implies \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )cos(\theta )}\implies \cfrac{2sin(2\theta )}{cos^2(\theta )} \\\\\\ \cfrac{1}{cos^2(\theta )}\cdot sin(2\theta )\implies sec^2(\theta )sin(2\theta )[/tex]

Answer:

C) 2 tan θ

E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)

Step-by-step explanation:

This is essentially what the other person said, but in a better format.

HELP!! Drag values to complete each equation.

Answers

(12²)³ x 12^-4 = 144 which means it is 12² = 144.

12^7 x 12^-5 / 12² which equals 1.

Hope this Helps!!

Answer:

a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

Step-by-step explanation:

We have to complete each equation

We are given that

[tex]((12)^2)^3\cdot (12)^{-4}[/tex]

[tex](12)^6\cdot (12)^{-4}[/tex]

Using identity

[tex](a^x)^y=a^{xy}[/tex]

[tex](12)^{6-4}=(12)^2[/tex]

Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]

[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]

[tex]\frac{(12)^2}{(12)^2}[/tex]

[tex](12)^{2-2}=(12)^0=1[/tex]

Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]

[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

what is 3√27x^9

3x^6
3x^3
9x^3
9x^6

Answers

The first step for solving this expression is to know that the root of a product is equal to the product of the roots of each factor. Knowing this,, the expression becomes the following:
[tex] \sqrt[3]{27} \sqrt[3]{ x^{9} } [/tex]
Write the number in the first square root in exponential form with a base of 3.
[tex] \sqrt[3]{ 3^{3} } \sqrt[3]{ x^{9} } [/tex]
Now reduce the index of the radical and exponent in the second square root with 3.
[tex] \sqrt[3]{ 3^{3} } [/tex] x³
Lastly,, reduce the index of the radical and exponent with 3 to get your final answer.
3x³
This means that the correct answer to your question will be option B.
Let me know if you have any further questions.
:)

The value of the expression ∛27x⁹ is 9x³.

The given expression is ∛27x⁹.

Cube root of twenty seven times of x power nine.

We can split the terms inside the cube root.

27=3×3×3

∛x⁹ = x³

Now let us plug in the above expression.

= 3√3³ × x⁹

= 3√3³ × √ x⁹

= 3 × 3 × x³

= 9x³.

Hence, the value of the expression ∛27x⁹ is 9x³.

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What is grater 9km or 145cm

Answers

First, you want to convert centimeters into kilometers to figure it out. 145cm = 0.00145 km. So then you need to compare 0.00145km to 9km. As you can see, 9km is greater. So your answer is 9km.

9km is greater than 145cm due to the conversion factor between kilometers and centimeters.

9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.

help! I will give thanks!

Answers

Mode = 60

Reason: 60 appeared 4 times.

6\000= 60 7/00=70 8/00 =80 9/0=90

My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin?
PLEASE SHOW WORK

Answers

ask if you want me to explain

Mary is walking 3 miles per hour jerry starts jogging at a rate of 4 miles per hour after marry has been walking for 15 minuets jerry jogs 2 miles as Mary continues walking and they both stop at the same time

Answers

Missing question: Determine the distanced covered by Mary.

Solution:
Mary: 3 mph
Jerry: 4 mph
Jerry starts jogging after Mary had been walking for 15 minutes.

Distance Mary had walked before Jerry starts jogging = Speed * Time = 3*15/60 = 0.75 miles.

Time taken by Jerry to jog for 2 miles = Distance/Speed = 2/4 =1/2 = 0.5 hrs.
Since they stopped at the same time,
Distance Mary walked while Jerry jogged = Speed* Time = 3*0.5 = 1.5 miles

Therefore,
Total distance Mary walked = 0.75+1.5 = 2.25 miles.

simplify the problem sqrt 245c^5

Answers

we have that
√[245c^5]-------> √245*√c^5

we know that
245-----> 5*7²
c^5---- c²*c²*c
so
√245-----> √[5*7²]----> 7√5
√c^5----> √[c²*c²*c]---> c²√c

√245*√c^5-----> [7√5]*[c²√c]----> 7c²√(5c)

the answer is
7c²√(5c)

Answer: the answer above is pretty much right, the answe is B

An equiangular triangle can be scalene. A. True B. False

Answers

False is correct answer.

Because equiangular triangle is not to be scalene.

Hope it helped you.

-Charlie

:)

False, Scalene triangles have three unequal sides and equilateral have three equal sides

A fair dice is rolled 5 times in sequence. what is the probability that you will get exactly the same number for all 5 rollings

Answers

1/7776. The probability of you getting any one number when rolling a dice is 1/6. Since you are rolling the dice 5 times and you are trying to get the same number each time. You would multiply 1/6 5-times. 1/6*1/6*1/6*1/6*1/6=1/7776.

how do you do 27?????

Answers

Hey there!

To start, the equation needed to represent this problem would be an equation:
y= ab^x

a represents the initial amount. In this case, the initial amount would be 4 billion. It would be represented as 4 since each 1= one billion.

b represents the rate. Because the problem discusses a growth, convert the rate, 1.9% to a decimal and add 1 to it (add one if it is a growth, subtract one if it is a decay). b would be 1.019.

x represents the time in which the population grows or t.

When you piece this together, your equation should look like:
y=4(1.019)^t

or

Choice A.

Hope this helps and have a nice day! Feel free to ask any questions about my work. :)

The correct answer is: [A]: " P(t) = 4 * (1 .019)^t " .
_______________________________________________________
Explanation:
______________________________________________________
Use the formula for "exponential growth" :
______________________________________________________
→ " y = A * (1 + r)^t " ;
______________________________________________________
in which:
______________________________________________________
A = the "beginning population" ;

→ (in number representing "billions of people") ;

→ given the "beginning population" is "4 billion" ;

→ " A = 4 " ;
______________________________________________________
r = rate (of change) = 1.9% ; expressed as a decimal:

→ "r = rate = 1.9% = { 1.9 ÷ 100 } ;

→ {Take the "1.9" ; & move the decimal point 2 (two) spaces backward }:

→ 1.9% = 1.9 ÷ 100 = 0.019 ;

→ " r = 0.019 " ;

→ " t = time" ; (usually in "years" ; however, all the answer choices provided leave the "t" as it is; so we shall do so, too.
________________________________________________________

→ Replace "y" with: " P(t) " ;

→ And rewrite the equation of the function with our known values:

→ " y = A * (1 + r)^t " ;
____________________________________________________
→ becomes:

→ " P(t) = 4* (1 + 0.019)^t " ;

→ " P(t) = 4 * (1 .019)^t " ;
____________________________________________________
→ which is: Answer choice: [A]: " P(t) = 4 * (1 .019)^t " .
____________________________________________________

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Which angles are alternate exterior angles with angle 11?

Answers

Answer:

The alternate exterior angles with angle 11 are angle 13 and angle 5.

Step-by-step explanation:

Two angles are called Alternate exterior angles if

1. They are on the exterior side of parallel lines and

2. Lie on the opposite sides of the transversal line.

It is given that

[tex]r\parallel s[/tex] and [tex]t\parallel u[/tex]

From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.

Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.

Answer:

The alternate exterior angles with angle 11 are angle 13 and angle 5.

Step-by-step explanation:

which of the points satisfy the linear inequality graphed here?

a) (0,0)
b) (10,0)
c) (-10,0)
d) (10,10)

Answers

only
c) (-10,0)
because that is the only point in the shaded region.

The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?

Answers

the complete question in the attached figure

we know that
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so

the answer is the option
A. the remote interior angles

The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.

the answer is the option

A. the remote interior angles

fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?

Answers

we know that
1+cot ²∅=csc² ∅
cot ∅=4/7
so
1+(4/7)²=csc² ∅
csc² ∅=1+(16/49)
csc² ∅=(65/49)
csc ∅=(√65)/7

remember that
csc ∅=1/sin ∅
sin ∅=1/csc ∅------> sin ∅=7/√65-----> sin ∅=(7√65)/65

the answer is
the best identity to find sin ∅ is
1+cot ²∅=csc² ∅

Answer:

D edge

Step-by-step explanation:

The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?

A)
v + 2b = 180; 2b - 20 = v

B)
v + 2b = 180; 2b + 20 = v

C)
v - 2b = 180; v + 2b = -20

D)
v - 2b = 180; -2b - 20 = v

Answers

The answer to the above question can be explained as under -

We know that, the sum of angles of triangle is 180°.

So, vertex angle plus base angles are equal are equal to 180°.

Let the vertex angle be represented by "v" and base angles be represented by "b".

Thus, v + b + b = 180°

So, v + 2b = 180°

Next, the question says, the vertex angle is 20° less than the sum of base angles.

Thus, 2b - 20° = v

Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v

The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.

The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:

The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.

To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.

Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?

Answers

The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

How to calculate EMI?

The EMI formula is :

[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]

Where r = 5.5/12/100 = 0.00425

p = 37,796.89

and n = 20 x 12 = 240

Putting the values in formula we get'

= (37,796.89x 0.00425 x 2.767)/1.767

= $350

Hence,

The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

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Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.

Step-by-step explanation:

Which equation in point-slope form contains the point (4, –1) and has slope 3? y – 1 = 3(x + 4) y – 4 = 3(x + 1) y + 1 = 3(x – 4)

Answers

Hello!

The equation for point-slope form is

y - b = m(x - a)

m is the slope
(a, b) is a point the line goes through

Put in the values into the equation

y - -1 = 3(x - 4)

Simplify

y + 1 = 3(x - 4)

The answer is C) y + 1 = 3(x - 4)

Hope this helps!

Answer:

the answer is option d y+1 =3 (x-4)

Add (13a + 5b) + (a + 5b - 3)

Answers

(13a + 5b) + (a + 5b - 3)

= 13a + 5b + a + 5b - 3

= 14a + 10b - 3

Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.

Answers

The given number arranged in order are:
9, 9, 10, 10, 12, 12, 14, 15, 15, 15, 17
1. To find the mean, add all the number together and divide the summation by 11[ which is the total number of the figures given]
Mean = [9 + 9 + 10 + 10 + 12 + 12 + 14+ 15 + 15 + 15 + 17] / 11 = 138 / 11
Mean = 12.5
Therefore, the mean is approximately equal to 13.

2. The median of a number refers to the number in the middle of a sorted set of number.
To find the median of a set of numbers, the numbers have to be arranged first in the correct increasing order and the number that falls in the middle will be the median. If two numbers fall in the middle, add the two together and find the average. For the set of number given above, the number that falls in the middle is 12.
Therefore, the median = 12.

3. The mode of a set of number refers to the number in the set, which has the highest frequency of occurrence, that is, it is the number that occur most. Looking at the set of number given above, 15 occurred three different times. Therefore, the mode of the set of number given above is 15.
Mode = 15.

4. The range of a set of number refers to the difference between the highest and the lowest numbers in the set of a given number. It represents the spread of the data. In the set of numbers given above the range is determined thus:
Range = 17 - 9 = 8.
Therefore, Range = 8.

Mean: 12.545454545455

Median: 12

Range: 8

Mode: 15, appeared 3 times

Largest: 17

Smallest: 9

Sum: 138

Count: 11

The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.

A.26.5cm3
B.44.2cm3
C.79.5cm3
D.132.5cm3

Answers

Para resolver este problema, debe aplicar el procedimiento que se muestra a continuación:

1of the first figure in the image attached, is:

a ^ 2 = b ^ 2 + c ^ 2
c =
c=√(6 cm)^2-(4.8 cm)^2
c=3.6 cm

2. The area of the base of the first figure is:

A=BxH/2
A=3.6x4.8/2
A=8.64 cm^2

3. Therefore, the volume of the cone is:

V=(8.64 cm^2)(9.2 cm)
V=79.5 cm^3

Therefore, the answer is: C. 79.5 cm^3

Find the variable of each pair

Answers

A. X=4
B. Y= 24, X= 6

the probability of winning the game is 7/10. What is the probability that they will lose?

Answers

3/10 is the probability of them losing.

The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.

If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.

Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?

Answers

500 x(1.04)^3=562.432
562.432-500= 62.432
62.432 / 3= 20.8106

Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. What is the speed of the train, if it is 5 km/h greater than the speed of the car?

Answers

Speed of the car = 255 ÷ 4 = 63.75 km/h

Speed of the train = 63.75 + 5 = 68.75 km/h

Answer: 68.75 km/h

[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]

The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.

The speed of the train is given by 25 km/hr.

If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch

Answers

A 5 by 5 square would have a diagonal equal to

square root (25 + 25) =
square root (50) =
7.07106781 =
7.1 (rounded to nearest 10th of an inch.

Find the surface area 4cm 5cm 6cm 13cm

Answers

[tex]A_\Delta=\dfrac{1}{2}\cdot6\cdot4=12\ cm^2\\\\A_{[]_1}=6\cdot13=78\ cm^2\\\\A_{[]_2}=5\cdot13=65\ cm^2\\\\A=2A_\Delta+A_{[]_1}+2A_{[]_2}\\\\A=2\cdot12+78+2\cdot65=24+78+130=232\ cm^2[/tex]

If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?

Answers

Final answer:

The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.

Explanation:

To calculate the monthly payments, you can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^-n)

Where:

P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of payments

Using the given values, we can calculate:

P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)

P ≈ $61.02

Therefore, the monthly payments would be approximately $61.02.

To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:

Total Interest = (P * n) - PV

Total Interest ≈ ($61.02 * 48) - $2469

Total Interest ≈ $1704.96 - $2469

Total Interest ≈ -$764.04

Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.

what is 3 ^9? how to solve?

Answers

3⁹ is the same as doing:

3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3

What I would do it is narrow it down piece by piece.

3 * 3 * 3 = 27. Do that 3 times, now you are left with:

27 * 27 * 27

27 * 27 or 27² = 729.

That leaves you with:

729 * 27

You can multiply by hand or use a calculator to get your answer of 19683.

To check your answer, plug 3⁹ into a calculator. Your answer should match this.

Which graph would help solve the equation 5log(x+3)=5

Answers

5log(x+3)=55log(x+3)=5Simplify 5log(x+3)5log(x+3) by moving 55 inside the logarithm.log((x+3)5)log((x+3)5)Simplify the right side of the equation.55Graph each side of the equation. The solution is the x-value of the point of intersection.x=7

The value of x is 7 for the given equation.

What is logarithm?

Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.

For the given situation,

The equation is 5log(x+3)=5.

On solving this equation, we can get value of x.

⇒ [tex]5log(x+3)=5[/tex]

⇒ [tex]log(x+3)=1[/tex]

We know that, log 10 = 1

Then,

⇒ [tex]log(x+3)=log10[/tex]

⇒ [tex]x+3=10[/tex]

⇒ [tex]x=7[/tex]

Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.

Learn more about the logarithm here

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The flower garden has the shape of a right triangle. 68 ft of a perennial border forms the hypotenuse of the​ triangle, and one leg is 28 ft longer than other leg. find the lengths of the legs.

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The flower garden has the shape of a right triangle. 68 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 28 ft longer than other leg. find the lengths of the legs.