Tiara earned 12 dollars on her
first day selling lemonade, and she
was determined to earn 3 more
dollars each day than she had
made the day before. If she met
this goal exactly, how much
money did she earn, in total, for
her first 20 days selling lemonade?
A. 610 B. 810 C.72 D. 69

The length of AD is 1 unit.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let us solve the question

In Δ ABC

∠B is a right angle

BD is perpendicular to the hypotenuse AC

(AB)² = AD × AC ⇒ rule

AB = 3 units

AC = 9 units

Let AD = x

Substitute them in the rule above

(3)² = x × 9

9 = 9x

Divide both sides by 9

x=1

Hence, the length of AD is 1 unit.

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Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

Answer:

You have the right answer selected, Mohamed is correct.

Answer:

x > 4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Answer:

0.435 pounds

Step-by-step explanation:

There are 16 ounces in one pound. Use that conversion to find your answer.

Answer:

7oz=0.4375lb

Step-by-step explanation:

i hope this helps

have a nice night

mark brainliest please :)

Total gallons of water used in the park after the ride is installed

 = 9.51 * 10^5 GALLONS.

Exponent addition is the process of multiplying a number by its exponents or powers, whether or not the base is the same. Exponents, which show how many times a number can be multiplied by itself, are also known as the power of numbers. As an illustration, 3^2 = 3*3, where 3 is the base and 2 the exponent.

When the base and exponents are the same, exponents can be added. Sometimes the base and exponent will differ, but adding can still be done for certain formulas. Let's examine the procedures for adding exponents.

Step 1: Verify that the expression's terms all have the same base and exponents. 22 + 22, as an illustration. As can be seen, the exponent and base are both 2.

Step 2: Calculate the expression using individual terms if the base and exponent are different. for instance, 53 plus 42. Exponents and bases are different.

Step 3: Add the results together.

water used in the park initially                  = 8.6*10^5 gallons

water used by the additional ride added = 9.1 *10^4 gallons

                                                                    =0.91*10^5 gallons

Total gallons of water used in the park after the new ride is installed

                                                                   = (8.6*10^5 + 0.91*10^5) gallons

                                                                   = (8.6+0.91) *10^5 gallons

                                                                   = 9.51* 10^5 gallons

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Answer:

h = 61.25 m

Step-by-step explanation:

It is given that,

The initial velocity of the ball, v = 60 m/s

It is thrown from a height of 5 feet, \(h_o=5\ ft\)

We need to find the maximum height it reaches. The height reached by the projectile as a function of time t is given by :

\(h=-16t^2+vt+h_0\)

Putting all the values,

\(h=-16t^2+60t+5\) .....(1)

For maximum height, put

\(\dfrac{dh}{dt}=0\\\\\dfrac{-16t^2+60t+5}{dt}=0\\\\-32t+60=0\\\\t=\dfrac{-60}{-32}\\\\t=1.875\ s\)

Put t = 1.875 in equation (1)

\(h=-16(1.875)^2+60(1.875)+5\\\\h=61.25\ m\)

So, the maximum height reached by the ball is 61.25 m.

Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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The answer is b. none. This is because the lines are parallel and therefore do not intersect at a point, meaning that there are no solutions.

Answer:

-1.5

Step-by-step explanation:

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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The exact value of the specified trigonometric identity found using the the trigonometric identity for tan(A - B) and tan(arccos(x)) and tanarcsin(x)) is presented as follows;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

A trigonometric identity is an equality that involves trigonometric functions that is valid for all values of the arguments of the equation

The required trigonometric identities are;

\(tan (A - B) = \dfrac{tan(A) -tan(B)}{1-tan(A)\cdot tan(B)}\)

\(tan(sin^{-1}(x)) = \dfrac{x}{\sqrt{1-x^2} }\)

\(tan(cos^{-1}(x)) = \dfrac{\sqrt{1-x^2}}{x }\)

Therefore;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) = \dfrac{tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)-tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}{1-tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)\times tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}\)

Which gives;

\(\dfrac{\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } -\dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} } }{1+\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } \times \dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} }}=\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }\)

\(\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }=\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Which indicates that we have;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

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A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation

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A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.

The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.

Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

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A) 4.127

Explanation:

With your calculator search for the ln function and it will give you the direct answer

For the given monthly salaries of the 7 employees of the firm , then the true statement is : (a) mean = median .

In statistics the Mean is defined as sum of a collection of numbers divided by count of numbers .

the given monthly salaries is 9, 7, 8, 7, 10, 11 and 11.  

arranging the data in ascending order ,

we get ; 7 , 7 , 8 , 9 , 10 , 11 , 11 .

the sum of the salaries is = 63 ;

So , the mean is  = 63/7 = 9 .

median is the middle term of the given data that is = 9 ;

the mode is the most times occurred frequency that is 7 and 11 .

On comparing the mean , mode and median ,

we get ; mean = median .

Therefore , the correct statement is (a) mean = median .

The given question is incomplete , the complete question is

The monthly salaries (in thousands of dollars) for a sample of 7 employees of a firm are: 9, 7, 8, 7, 10, 11 and 11.

Which of the following statements is true about the mean, median and mode ?

(a) mean = median

(b) mode < median < mean

(c) mode < mean < median

(d) mode = median = mode .

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The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer: \(x\in (0,1)\cup (4,\infty)\)

Step-by-step explanation:

Given

In equality is \(x^3+4x>5x^2\)

Taking terms one side

\(\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0\)

Using wavy curve method

\(x\in (0,1)\cup (4,\infty)\)

Answer:

21.875 percent decrease

Step-by-step explanation:

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.

Given the amount of money that is the principal = $6000

Rate = 4% compounded quarterly.

Time = t

Amount = $8670

Now we know that the amount is calculated by the formula:

A = P(1+r/4)ⁿ

8670 = 6000(1+0.01)ⁿ

Hence

log 1.445 = n log 1.01

or, n = 36.99

Number of years = 36.99 / 4 = 9.24 years.

The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.

If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.

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The calculated measure of m∠PNM is 87 degrees

from the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

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Answer:

2 1/5 x 1 1/4 is greater than 1 1/4

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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