If the fifth term in a geometric sequence is 1∕27 and the common ratio is 1∕3, find the explicit formula of the sequence.

Answer:

Step-by-step explanation:

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

Learn more about rules of exponents here : brainly.com/question/11975096

#SPJ1

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

To learn more about the quadratic equation;

https://brainly.com/question/17177510

#SPJ1

Answer:

See below.

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Transitive Property of Equality

If a=b and c=b, then a=c.

Proof that ∠1=∠2

\(\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}\)

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

Learn more about quadratic equation here:

https://brainly.com/question/30164833

#SPJ8

Answer: y=2x

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the answer is C because the 2 angles are congruent, making it the same degree

hope this helps :)

Answer:

160

Step-by-step explanation:

y is the same shape and degree is 1 60 on the other side please mark brainliest

The required 7,000 gallons of gasoline which are 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
To solve the problem, we can use the following formula:

(amount of ethanol in the final mixture) / (total amount of gasoline in the final mixture) = 7%

To find the amount of ethanol in the 2,000 gallons of gasoline with no ethanol:

ethanol in 2,000 gallons of gasoline with no ethanol = 0 × 2,000 = 0 gallons

Then, find the amount of ethanol in the final mixture:

ethanol in final mixture = (0.09x + 0 * 2,000) / (x + 2,000)

Notice that we use 0 gallons for the ethanol in the 2,000 gallons of gasoline with no ethanol, since it contains no ethanol.

Ethanol in the final mixture / total amount of gasoline in the final mixture = 7%

(0.09x + 0) / (x + 2,000) = 0.07

0.09x + 0 = 0.07(x + 2,000)

0.09x = 0.07x + 140

0.02x = 140

x = 7,000

Therefore, 7,000 gallons of gasoline which is 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ1

Answer:

2nd option

Step-by-step explanation:

x is left and right

y is up and down

just look at the y coordinate for any point and translate 5 points down.

Answer:

Step-by-step explanation:

second answer

Answer:

Assuming that we are dealing with a standard normal distribution, we can use a standard normal table or a calculator to find the value of z.

From the information given in the problem, we know that the area to the left of z is 0.02. This means that 0.98 of the area lies to the right of z.

Using a standard normal table or calculator, we can find the z-value that corresponds to an area of 0.98 to the right of the mean. This value is approximately 2.05.

However, since we are interested in the z-value that corresponds to an area of 0.02 to the left of the mean, we need to take the negative of the z-value we just found. So, our answer is:

z = -2.05 (rounded to two decimal places)

Therefore, the value of z such that 0.02 of the area lies to the left of z is -2.05.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

Answer:

2,4 3,5

Step-by-step explanation:

Answer:

the number is -15

Step-by-step explanation:

if you turn the word problem into an equation it would be

4x+19=-86-3x

with x being the unknown number

the next step is to move the -3x to the other side by adding it to the 4x

your equation should now be 7x+19=-86

next you should move the 19 to the other side by subtracting it from the -86

this leaves you with the equation

7x= -105

lastly you must divide the -105 by seven which leaves you with the answer x= -15

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

For more such questions on probability

https://brainly.com/question/1834572

#SPJ8

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

A non linear function is a function whose graph is not linear or can be represented by a straight line.

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

ANSWER and EXPLANATION

We have that the city parking garage charges a flat rate (constant rate) of $5.00 for parking and $2.00 per hour parked.

A) Let the amount of hours parked be h.

Let the total cost of parking be C.

This means that C, the total cost of parking, is equal to the sum of the flat rate and the charges for the number of hours parked.

Therefore, we have that:

C = 2 * h + 5

=> C = 2h + 5

B) To plot a graph for this equation, we have to find at least two points that satisfy the equation, i.e. (h1, C1) and (h2, C2)

Let us find the values of C when h is 2 and when h is 5, that is the total cost of parking after 2 hours and after 5 hours.

When h = 2 hours:

=> C = 2(2) + 5 = 4 + 5

C = $9

When h = 5 hours:

C = 2(5) + 5 = 10 + 5

C = $15

Now, we can plot the graph using h values on the x axis and C values on the y axis.

We will use the two points (2, 9) and (5, 15)

That is the graph of the equation.

C) There are two ways to solve this:

=> Check for the value of h when C is $20 on the graph.

=> Find the value of h when C is $20 from the equation.

Let us use the equation. We have that:

C = 2h + 5

=> 20 = 2h + 5

Collect like terms:

=> 20 - 5 = 2h

15 = 2h

Divide both sides by 2:

h = 15 / 2

h = 7.5 hours

To confirm, we can check the graph for h when C is 20, we will find that the value is the same as the solution of the equation.

The complete sentence:

If Parrish has $20, it means that he can park for 7.5 hours (or 7 and a half hours).

Answer:

here ya go

Step-by-step explanation:

zeros at x = 1 and x = 5

Answer:

pppppppppppppppppppppppppppppppppppppppppp

Answer:

Step-by-step explanation:

25% of $35 is 8.75, so the price would be $26.25. plus tax, the final price would be $27.825 or $27.83. if that doesn't work, try $27.82

(i was wrong before, this should be right now)

hope this helps!! :)

Answer:

1)   2/5

2)  -25

3)  -8 14/15

4)  4/5

5)  7

Step-by-step explanation:

\(\begin{aligned}\textsf{1)} \quad \dfrac{-22+14}{2(-10)}& =\dfrac{-8}{-20}\\\\& = \dfrac{8}{20}\\\\& = \dfrac{8 \div 4}{20 \div 4}\\\\& = \dfrac{2}{5}\end{aligned}\)

\(\begin{aligned}\textsf{2)} \quad -\dfrac{125}{5} &=-\dfrac{125 \div 5}{5 \div 5}\\\\& = -\dfrac{25}{1}\\\\& = -25\end{aligned}\)

\(\begin{aligned}\textsf{3)} \quad -2 \frac{4}{5}-6 \frac{2}{15} & = -\dfrac{2 \times 5+4}{5}-\dfrac{6 \times 15+2}{15}\\\\& = -\dfrac{14}{5}-\dfrac{92}{15}\\\\& = -\dfrac{14 \times 3}{5 \times 3}-\dfrac{92}{15}\\\\& = -\dfrac{42}{15}-\dfrac{92}{15}\\\\& = \dfrac{-42-92}{15}\\\\& = \dfrac{-134}{15}\\\\& = -8 \dfrac{14}{15}\end{aligned}\)

\(\begin{aligned}\textsf{4)} \quad 3 \frac{3}{5} \times \dfrac{2}{9} & = \dfrac{3 \times 5+3}{5} \times \dfrac{2}{9}\\\\& = \dfrac{18}{5}\times \dfrac{2}{9}\\\\& = \dfrac{18 \times 2}{5 \times 9}\\\\& = \dfrac{9 \times 2 \times 2}{5 \times 9}\\\\& = \dfrac{2 \times 2}{5}\\\\& = \dfrac{4}{5}\end{aligned}\)

\(\begin{aligned}\textsf{5)} \quad-3x-21 & =-42\\-3x-21+21 & = -42+21\\-3x & = -21\\\dfrac{-3x}{-3} & = \dfrac{-21}{-3}\\x & = 7\end{aligned}\)

Answer:

x + 3y = -15

Step-by-step explanation:

There are 2 ways to find this equation:

The first way:  We have: y = ax + b (this is the line, right?)

The line is through the point (-6, -3) so we have:

-3 = (-6)a + b      (1)

The line is also through the point (-9, -2) so we have:

-2 = (-9)a + b.       (2)

From (1) and (2) we get a equals -1/3, b equals -5. Then:

\(y=-\frac{1}{3} x - 5\)

<=> \(x + 3y=-15\)

The second way:

Let A(-6, -3) and B(-9, -2), then AB = (-3, 1).

=> The normal vector of this line is n = (1, 3).

The line that is through the points A(-6, -3) and B(-9, -2), and has the normal vector n=(1, 3) has the equation:

\(1(x+6) +3(y+3)=0\\x+3y +15=0\\x+3y=-15\)

Step-by-step explanation:

Check that attachment

Hope it helps :)

Hey! :)

________ ☆ ☆_________________________________________

Answer:

There are six trigonometric ratios, which will be under “Explanation”

Step-by-step explanation:

Trigonometric ratios are a measurements of a right triangle.

Here are the all the six trigonometric ratios.

1. cotangent (cot)

2. cosecant (csc)

3. cosine (cos)

4. secant (sec)

5. sine (sin)

6. tangent (tan)

Hope this helps! :)

_________ ☆ ☆________________________________________

By, BrainlyMember ^-^

Good luck!

Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

Learn more about  Role Strain from

https://brainly.com/question/14283116

#SPJ1

Answer:

yes there right

Step-by-step explanation:

Answer: $103.125

Step-by-step explanation:

(13.75)(2.5)(3)