p = awb
solve for a
Please help someone

Given that g(9) = 2 and limₓ→9 [3f(x)²g(x)] = 25, f(9) = ±√(25/6).

Since limₓ→9 [3f(x)²g(x)] = 25, we know that limₓ→9 [f(x)²g(x)] = 25/3. As g(x) is continuous, we have g(9) = 2. Therefore, limₓ→9 [f(x)²] = 25/6.

Since f(x) is continuous, we can write:

limₓ→9 [f(x)²] = (limₓ→9 f(x))² = (f(9))².

Thus, we have:

(f(9))² = 25/6.

Taking the square root of both sides, we get:

f(9) = ±√(25/6).

However, since we know nothing about the sign of f(9), we can't determine its value exactly. Therefore, the answer is:

f(9) = ±√(25/6).

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Answer:

32 quarters and 3 dimes

Step-by-step explanation:

you could do 4 x 8 to get to the 8 dollars so 4 x 8 = 32 so that would be 32 quarters now you got 30 cents left that will be the dimes so 3 dimes

\( \frac{y}{4} = - 3\)

\(y = - 3 \times 4\)

\(y = - 12\)

Multiplication would be used.

Answer:

Let the base of the 15ft long ladder be placed x ft away from the wall so that it exactly reaches the top of a 12- foot tall wall.

By Pythagorean theorem

12

2

+

x

2

=

15

2

⇒

x

2

=

15

2

−

12

2

=

81

⇒

x

=

√

81

=

9

ft

The base of the 15-foot ladder should be set back from the wall by x feet in order for it to precisely reach the top of a 12-foot wall.

The decimal number can also be rounded to the nearest tenths place value. The first number that appears after the decimal point is the tenth place value. Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value.

The tenths digit stays the same if it is 4 or less. The hundredths place digit, 8, is greater than or equal to 5, so 3.58 can be rounded to 3.6. Due to the fact that the digit in the hundredths place, 2, is less than 5, 3.32 would be rounded to 3.3.

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Step-by-step explanation:

I have to assume the equations are

4x + y = 13

(1/2)y = -2x + 5

let's bring both of them into a "y = ..." form :

y = -4x + 13

y = -4x + 10

now we see that both equations are lines with the same slope but different y-intersect.

so, they are parallel but not identical.

therefore, there are 0 solutions. the lines will never intersect and have no point in common.

Answer:

y = 35x - 517.

Step-by-step explanation:

y=35x−7

This line has a slope of 35so we can write a line parallel to it as

y - y1 = 35(x - x1) where (x1, y1) is a point on the line.

We are given this point (15, 8), so:

y - 8 = 35(x - 15)

y = 35x - 525 + 8

y = 35x - 517  is the required equation.

Answer: 4c+32

Step-by-step explanation:

The intersection of two events A and B contains only those outcomes that are in both A and B.

The intersection of two events A and B, denoted by A ∩ B, is the set of all outcomes that are common to both A and B. In other words, it contains only those outcomes that are in both A and B.

For example, if event A is "rolling an even number on a fair six-sided die" and event B is "rolling a number greater than 3 on a fair six-sided die", then the intersection of A and B is the event "rolling an even number greater than 3 on a fair six-sided die", which contains the outcome 4 and has probability \(\frac{1}{6}\).

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Answer:

(i)  2² · 3 · 7

(ii)  3024

(iii) k = 16

(iv) 12 cm

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:

⇒ 84 ÷ 2 = 42

As 42 is not a prime number, we need to divide again:

⇒ 42 ÷ 2 = 21

As 21 is not a prime number, we need to divide again.  

21 is not divisible by 2, so let's try dividing by the next prime number, 3:

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 84 is the product of:

⇒ 84 = 2 · 2 · 3 · 7

As 2 appears two times, we can write this using exponents:

⇒ 84 = 2² · 3 · 7

Lowest Common Multiple (LCM):  The lowest multiple shared by two or more numbers.

Prime Factors Method of finding LCM

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

\(\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}\)

Step 3

Bring down the primes in each column then multiply the factors to get the LCM:

⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7

⇒ LCM = 2⁴ · 3³ · 7

⇒ LCM = 3024

From part (ii) we know that the prime factorization of 432 is:

432 = 2⁴ · 3³

A perfect cube is a number multiplied by itself three times.

One of the factors of 432 is a perfect cube → 3³.

Therefore,

\(\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}\)

So we need to divide 432 by 2⁴ to get the perfect cube 3³.

Therefore,

⇒ k = 2⁴

⇒ k = 2 · 2 · 2 · 2

⇒ k = 16

To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.

Prime Factors Method of finding GCF

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

\(\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}\)

Step 3

Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:

⇒ GCF = 2 · 2 · 3

⇒ GCF = 12

Therefore, the largest possible length of the side of the square is 12 cm.

Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

The area of square abcd is  be parallel lines passing through $a$, $b$, $c$, respectively is the 433.

Squares are quadrilaterals with four congruent aspects and four proper angles, and additionally they have units of parallel aspects. Parallelograms are quadrilaterals with units of parallel aspects. Since squares have to be quadrilaterals with units of parallel aspects, then all squares are parallelograms.

Here we have the values the distance between lines a and b is 12, and the distance between lines b and c is 17.

The distance is 12 and 17

x^2 = 12^2 + 17^2 = 144 +289 = 433

433 is the total that is the area of square of abcd.

Thus the area = 433.

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Answer/Step-by-step explanation:

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

Answer:

A) 8+2.50x=28

B) 8 rides

C) Jada can go on 8 rides before she has spent all of her money

Step-by-step explanation:

subtract the $8 fee from 28 and get 20, then divide 20 by how much each ride costs (2.50) and get 8 :)

Answer:

She went on 8 rides

Step-by-step explanation:

28-8=20÷2.50=8

Answer:

The sequence is geometric

The common ratio is 0.5

Step-by-step explanation:

In the arithmetic sequence, there is a common difference between each two consecutive terms

In the geometric sequence, there is a common ratio between each two consecutive terms

Let us check the given sequence

∵ The first 3 terms are 12, 6, 3

∵ 6 - 12 = -6

∵ 3 - 6 = -3

∵ There is no common difference between the consecutive terms

∴ The sequence is not an arithmetic sequence

∵ 6 ÷ 12 = 0.5

∵ 3 ÷ 6 = 0.5

∴ There is a common ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∴ The common ratio is 0.5

Step-by-step explanation:

as this is total 90°angle

68°+x = 90 °

x = 90°-68°

x = 22 °

also

68° + 22 ° = 90 °

Answer:

90 - 68 = 22

the whole angle is 90

if we substract 68 from 90 , we will get the answer.

Answer:

The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.

Step-by-step explanation:

The volume of a cylinder is given by:

\(V = \pi*r^2*h\)

If we increase the diameter by 15%, then the radius is increased by 7.5% and the new radius is:

\(r_{new} = 1.075*r\)

If we decrease the height by 30%, then the new height is 70% of the prior and is given by:

\(h_{new} = 0.7*h\)

Applying to the volume formula we have:

\(V_{new} = pi*(r_{new})^2*h_{new}\)

\(V_{new} = \pi*(1.075*r)^2*0.7*h\\V_{new} = 1.16*0.7*\pi*r^2*h\\V_{new} = 0.812*\pi*r^2*h\\V_{new} = 0.812*V\)

The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.

Answer:

The point where f(x), g(x), and h(x) have the same value is (8, 11)

Step-by-step explanation:

The points where g(x) and h(x) have the same value is given as follows;

2x - 5 = 8/x + 10

2x² - 15x - 8 = 0

Using an online tool, we have;

(x - 8)(2x + 1) = 0

x = 8 or x = -1/2

∴ g(x) and h(x) = 11 or y = -6

For x = 8, we have;

f(x) = 2^(x - 5) + 3 = 2^(8 - 5) + 3 = 2^3 + 3 = 11

For x = -1/2, we have;

f(x) = 2^(-1/2 - 5) + 3 = 3.022

Therefore, the point where f(x), g(x), and h(x) have the same value is (8, 11), therefore, for x = 8, f(x) = g(x) = h(x) = 11.

To find the general solution of the system x' = 10 −5 8 −12 x, we first need to find the eigenvalues and eigenvectors of the coefficient matrix.

The characteristic equation is det(A - λI) = 0, where A is the coefficient matrix, λ is the eigenvalue, and I is the identity matrix. So, we have:

det(10-λ -5 8 -12-λ) = 0
(10-λ)(-12-λ) - (-5)(8) = 0
λ\(^2\) - 2λ - 64 = 0
(λ - 8)(λ + 8) = 0
λ1 = 8, λ2 = -8

Next, we need to find the eigenvectors corresponding to each eigenvalue. For λ1 = 8, we have:

(10-8)x1 - 5y1 + 8z1 = 0
-5x1 + (8-8)y1 + 8z1 = 0
8x1 + 8y1 + (-12-8)z1 = 0

Simplifying the system, we get:

2x1 - y1 + 4z1 = 0
-5x1 = 0
8x1 + 8y1 - 20z1 = 0

Solving for x1, y1, and z1, we get:

x1 = 0
y1 = 0
z1 = t

So, the eigenvector corresponding to λ1 = 8 is [0, 0, t].

For λ2 = -8, we have:

(10+8)x2 - 5y2 + 8z2 = 0
-5x2 + (8+8)y2 + 8z2 = 0
8x2 + 8y2 + (-12+8)z2 = 0

Simplifying the system, we get:

18x2 - 5y2 + 8z2 = 0
-5x2 + 16y2 + 8z2 = 0
8x2 + 8y2 - 4z2 = 0

Solving for x2, y2, and z2, we get:

x2 = 2t
y2 = 5t
z2 = -2t

So, the eigenvector corresponding to λ2 = -8 is [2t, 5t, -2t].

Now that we have the eigenvalues and eigenvectors, we can write the general solution as:

\(x(t) = c1[0, 0, t]e^{(8t)} + c2[2t, 5t, -2t]e^{(-8t)}\)
where c1 and c2 are constants determined by initial conditions.

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After scoring 77, 87, and 74 on her previous three tests, Amy needs to score 66 on her next test in order to have an average of 76.

To find the score that Amy needs on her next test to have an average of 76, we need to use the formula for the mean of a set of numbers:
Mean = (Sum of all numbers) / (Total number of numbers)

We know that Amy's current scores are 77, 87, and 74, and we want her average to be 76. Let's call the score she needs on her next test "x".
So, we can plug these values into the formula:
76 = (77 + 87 + 74 + x) / 4

Now, we just need to solve for x:
76 * 4 = 77 + 87 + 74 + x
304 = 238 + x
x = 304 - 238
x = 66

So, Amy needs to score a 66 on her next test in order to have an average of 76.

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The choice of which statement is true depends on the specific relationship being described.

A variable is a sum that can change based on the underlying mathematical problem. The generic letters x, y, and z are used in many mathematical statements and equations. In other words, a variable is a symbol that designates a numeric value that is unknown. Let's say that x + 5 = 10. "X" is a variable here.

The dependent variable's values rise when a constant is added in a linear relationship. This relates to choice A.

In an exponential connection, the values of the dependent variable increase by multiplication by some constant. This relates to choice B.

The dependent variable's and independent variable's product is constant in an inverted connection. This relates to choice C.

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Answer:

-15

Step-by-step explanation:

Step 1: Multiply 3 by both sides

3(2/3x)=3(-10)

Step 2: Simplify

2x=-30

Step 3: Divide both sides by 2

2x/2=-30/2

Step 4: Simplify

x=-15

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Thus, a decision to not reject the null hypothesis should be interpreted with caution and further investigation may be needed to fully understand the underlying factors affecting student study habits at the university.

The null hypothesis in this scenario would be that the mean number of hours students study at the university (per day) is equal to or greater than 4.4 hours.

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s c

\(2(4x+1)<3(2x-3)\\\\\implies 8x +2 < 6x -9\\\\\implies 8x <6x -9 -2\\\\\implies 8x -6x < -11\\\\\implies 2x<-11\\\\\implies x< -\dfrac{11}2\\\\\\\text{Interval,} ~ \left(-\infty, -\dfrac{11}2 \right)\)

Answer:

x<3.5

Step-by-step explanation:

multiply 2 with 4x and 1 to get 8x + 2 < 3(2x-3). Then multiply 3 by 2x and -3 to get 8x + 2 < 6x- 9. Then subtract -6x on both sides to get 2x + 2< -9. Next subtract 2 from -9 so x is by itself and then you get 2x < 7. Finally divide 2 on each side so you leave x byitself completely. You get x > 3.5

I hope u get it right!

Theoretical flow time = 58 minutes

The complete question is

Mamossa Assaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (15 minutes per roof) and then formed in a roof forming press (8 minutes per roof). Bases are punched in a base punching press (3 minutes per base) and then formed in a base forming press (10 minutes per base), and the formed base is welded in a base welding machine (12 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per https://brainly.com/question/27786618garage) on an assembly welding machine to complete the garage. Assume one operator at each station.

Roof → Roof - punch(15 min) → Roof-form(8 min) →→→→→→→→↓

                                                                                      (10)Assembly→ Door

Base → Base - punch(3 min) → Base - form(10 min) → weld(12 min)↑

Roof path = 15 + 8 = 23

Base path = 3 + 10 + 12 =25

Theoretical flow time = Roof path + base path + assembly = 23 + 25 +10 = 58 mins

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Step-by-step explanation:

first pool :

in 4 hours the pool gets 5200 gallons.

that means in 1 hour it gets 5200/4 = 1300 gallons.

so, the filing rate is 1300 gallons / hour.

second pool :

we seen on the graph that

in 3 hours the pool gets 10800 gallons.

that means in 1 hour it gets 10800/3 = 3600 gallons.

so, the filing rate is 3600 gallons / hour.

therefore, the second pool fills at a much faster rate than the first pool (3600 gallons vs. 1300 gallons / hour).

Answer:

72

Step-by-step explanation:

First of all, we need the numbers as a product of its prime numbers.

8 = 2×2×2

12 = 2×2×3

18 = 2×3×3

Now we can see that there is one 2 in all three numbers. And also two twos in 8,12 and two threes in 12,18. We need to group it and take it as one. The rest we take it individually each

So 2×2×2×3×3 = 8×9 = 72