Which statement best describes what happened when h is changed from 4 to - 2.

The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

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Answer:

The price of each latte was $4.5.

Step-by-step explanation:

6x + 18 = 45

6x = 45 - 18

6x = 27

x = 27/6

x = 4.5

The variable represents the cost of each latte.

SOLUTION

Given the question in the question tab, the following are the solution step to get the number of books they have altogether.

Step 1: Write the notations for Joseph's and Mike's books

Step 2: Write the statements in a mathematical form

Step 3: Solve to get the value of j by using substitution method

Therefore, Joseph had 84 books initially.

Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially

Hence, they both had 112 books altogether.

The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. \(f(x)=a(x-h)^2+k, where (h,k)\) is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a\(x^2\) is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

\(a(x+\frac{b}{2a} )^2\) This is a horizontal shift of magnitude |\(\frac{b}{2a}\)| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |\(\frac{D}{4a}\)| units. The direction of the shift will be decided by the sign of \(\frac{D}{4a}\). The final vertex of the parabola will be at (\(\frac{-b}{2a} ,\frac{-D}{4a}\)).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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The result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

To subtract the expression 7x - 9 from 2x² - 11, we need to distribute the negative sign to every term within the expression 7x - 9, and then combine like terms.

First, let's distribute the negative sign:

2x² - 11 - (7x - 9)

Now, distribute the negative sign to each term within the parentheses:

2x² - 11 - 7x + 9

Next, let's combine like terms:

2x² - 7x - 2

Therefore, the result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

In this expression, the highest power of x is 2, which means it is a quadratic expression. The coefficient of x² is 2, and the coefficient of x is -7. The constant term is -2.

This quadratic expression can be further simplified or factored if needed, but the subtraction process is complete with the result 2x² - 7x - 2.

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By simplifying the given expression:

(-5a-3)+(2a+7)

We will find the equivalent one:

-3a + 4

Here we have the following expression:

(-5a-3)+(2a+7)

And we want to find an equivalent expression to this one. To find it, we need to simplify the given expression.

If we break the parenthesis, we will get:

-5a - 3 + 2a + 7

Now we should group like terms, then we will get:

(-5a + 2a) + (-3 + 7)

And now we can simplify this so we get:

(-5 + 2)*a + 4

-3a + 4

That is the equivalent expression we wanted to find.

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Answer:

3 3/4

Step-by-step explanation:

(4x+3)(x-8)+(x-1)(4x+3)=0

Factor out 4x+3

(4x+3)( x-8+x-1) =0

Combine terms

(4x+3) ( 2x-9) =0

Using the zero product property

4x+3 = 0    2x-9 =0

4x=-3         2x = 9

x = -3/4       x = 9/2

Sum the solutions

-3/4 + 9/2

-3/4 + 18/4

15/4

3 3/4

Answer:

2/7 I hope this helps

Answer:

\(\frac{16}{49}\)

Step-by-step explanation:

Given

(\(\frac{4}{7}\) )² = \(\frac{4^2}{7^2}\) = \(\frac{16}{49}\)

The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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Answer:

$ 20,043.46

Step-by-step explanation:

Answer:

A = $ 20,043.46

A = P + I where

P (principal) = $ 8,300.00

I (interest) = $ 11,743.46

Calculation Steps:

First, convert R percent to r a decimal

r = R/100

r = 6.5%/100

r = 0.065 per year,

Then, solve our equation for A

A = P(1 + r/n)nt

A = 8,300.00(1 + 0.065/1)(1)(14)

A = $ 20,043.46

Summary:

The total amount accrued, principal plus interest,

from compound interest on an original principal of

$ 8,300.00 at a rate of 6.5% per year

compounded 1 times per year

over 14 years is $ 20,043.46.

1) The sequence S is: 9, 12, 15, 18.

2) The types of sequences are:

a) Sequence a is increasing.

b) Sequence 200, 130, 130, 90, 90, 43, 43, 20 is non-decreasing.

1) The sequence S is defined as sn = 3n + 3 * 2. To find the values of S, we can substitute different values of n into the equation:

S1 = 3(1) + 3 * 2 = 3 + 6 = 9

S2 = 3(2) + 3 * 2 = 6 + 6 = 12

S3 = 3(3) + 3 * 2 = 9 + 6 = 15

S4 = 3(4) + 3 * 2 = 12 + 6 = 18

So, the sequence S is: 9, 12, 15, 18.

2) Let's determine the type of the sequences:

a) Sequence a = 2/1, 131.

- This sequence is increasing since the terms are getting larger.

b) Sequence 200, 130, 130, 90, 90, 43, 43, 20.

- This sequence is non-decreasing since the terms are either increasing or staying the same (repeated).

To summarize:

a) Sequence a is increasing.

b) Sequence 200, 130, 130, 90, 90, 43, 43, 20 is non-decreasing.

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Value of x is 156 in inequality.

What is a mathematical inequality?

The equation-like shape of the formula 5x 4 > 2x + 3 is maintained despite the arrowhead in place of the equals sign. It serves as a symbol of unfairness. According to the equation, this demonstrates that the left component, 5x 4, is larger than the right component, 2x + 3.

                            An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is done in an unfair manner. It is typically used to contrast the dimensions of two numbers on a number line.

X = -13 * -12

X = 156

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It will take approximately 6.2 years for the account to grow to $14500 when $9000 is invested at 8% interest compounded annually.

The compound interest formula is expressed as:

\(A = P( 1 + \frac{r}{t})^{nt}\)

\(t = \frac{In(\frac{A}{P} )}{n[In(1 + \frac{r}{n} )]}\)

Where A is accrued amount, P is the principal, r is the interest rate and t is time.

Given that:

Principal P = $9,000, compounded annually n = 1, interest rate r = 8%, Accrued amount A = $14500.

Plug these values into the above formula and solve for time t.

\(t = \frac{In(\frac{A}{P} )}{n[In(1 + \frac{r}{n} )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{1*[In(1 + \frac{0.08}{1} )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{[In(1 + 0.8 )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{[In(1.8 )]}\\\\t = 6.197 \ years\)

Therefore, the time required is 6.197 years.

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If Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. If the second cylinder has the same ratio of diameter to height,  its height is: 7 inches.

Since the first cylinder has a diameter of 6 inches and a height of 14 inches the ratio for the first cylinder is 14 : 6

The ratio for the second cylinder is h : 3.

Where:

h= height

Hence

h/14 = 3/6

h= 14 × 3/6

h = 7 inches

Therefore If Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. If the second cylinder has the same ratio of diameter to height,  its height is: 7 inches.

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The complete question is:

Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. The second cylinder has a diameter of 3 inches.

If the second cylinder has the same ratio of diameter to height, what is its height?

Answer:

Can you construct the question better.Maybe then I would be able to answer it.

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

Analytics is often described as the study of historical data to extract insights and make informed decisions. It involves the collection, processing, and analysis of data to discover patterns, identify trends, and gain insights into business operations. By examining data sets, analytics can help businesses identify areas of improvement, optimize performance, and increase efficiency. Analytics tools and techniques can be used across many different fields, including finance, marketing, healthcare, and sports. In finance, analytics can be used to analyze market trends and predict future outcomes. In marketing, analytics can help businesses identify customer behavior patterns and optimize marketing campaigns. In healthcare, analytics can help identify patterns in patient data and improve healthcare outcomes. In sports, analytics can be used to analyze player performance and predict game outcomes.

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The probability that either 19 or 20 of the randomly selected batteries have acceptable voltages is 0.4399.

First, we have to understand that there are 2 batteries required for the flashlight to work. And for the flashlight to work, both batteries must have acceptable voltages.

To solve this, you can use the binomial probability formula:

P(x) = nCx * p^x * (1 - p)^(n-x)

Where n is the number of trials, x is the number of successes, and p is the probability of success.

For this problem, n = 20, p = 0.88, and x is either 19 or 20.

P(19) = 20C19 * 0.88^19 * (1 - 0.88)^(20 - 19) = 0.0239
P(20) = 20C20 * 0.88^20 * (1 - 0.88)^(20 - 20) = 0.4160

P(19) + P(20) = 0.0239 + 0.4160 = 0.4399

Therefore, the probability that either 19 or 20 of the batteries have acceptable voltages is 0.4399.

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Answer:

e. y = sin(x) + π

Step-by-step explanation:

We can see that the graph of y = sin(x) has been shifted vertically. This means that the added π should be outside the trigonometric function.

Therefore, e. y = sin(x) + π is the correct answer.

See the attached image for how a, b, c, and d values change the graphs of sine and cosine.

\(r =\frac{3t}{(t-1)}\)  is the r subject of the formula  t=r/r-3

How is r made the subject of t=r/r-3?

\(t =\frac{r}{r-3} \\\\t(r-3) =r\\\\tr - 3t = r\\\\tr- r = 3t\\\\r(t-1)=3t\\\\r = \frac{3t}{(t-1)}\)

What does making r the subject mean?

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The 98% confidence interval for the difference in the proportion of people that live in a city who identify as a republican and the proportion of people that live in a rural area who identify as a republican is (-0.3605, -0.0506).

Here, we need to find a 98% confidence interval for the difference in the proportion of people that live in a city who identify as a republican and the proportion of people that live in a rural area who identify as a republican.

To solve this, we need to compute the difference in sample proportions and its standard error. Then we construct a confidence interval using the difference and standard error.

Let P1 and P2 denote the population proportions of people living in the city and rural areas that identify as Republicans. Then we have the sample proportions as 115/206 and 62/107, respectively.

The difference in sample proportions is computed as

0.3738 - 0.5794 = -0.2056.

Using the formula for standard error, the standard error is given by

√((p1(1-p1))/n1 + (p2(1-p2))/n2)

= √((0.3738(1-0.3738))/206 + (0.5794(1-0.5794))/107)

= 0.0808.

The 98% confidence interval is given by (-0.3605, -0.0506). Therefore, we can conclude that the difference between the proportion of people living in a city who identify as a republican and the proportion of people living in a rural area who identify as a republican is statistically significant and lies within this interval.



Thus, the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a republican and the proportion of people that live in a rural area who identify as a republican is (-0.3605, -0.0506).

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Answer:

r = \(\frac{29x}{2\pi }\)

x = \(\frac{2\pi r}{29}\)

Step-by-step explanation:

C = 2\(\pi\)r

29x = 2\(\pi\)r  --------- (i)

divide both sides of (i) by 2\(\pi\)

r =  \(\frac{29x}{2\pi }\)

but when you divide both sides of (i) by 29, you get

x = \(\frac{2\pi r}{29}\)

Answer:

answer : x = 3±√ 119 / 16

is correct answer ...plz mark my answer as brainlist ... plzzzz and plz vote me as brainlist

Answer:

x= 1 /3 + −1 /3 √7

or

x= 1/ 3 + 1 /3  √7

Step-by-step explanation:

−12x2+8x+8=0

a=-12, b=8, c=8

−12x2+8x+8=0

x= −b±√b2−4ac /2a

=

x=−(8)±√(8)2−4(−12)(8) /2(−12)

x= −8±√448 −/24

x= 1/ 3 + 1 /3  √7 or x= 1 /3 + −1 /3 √7

(btw not sure)

Answer:

a) growth

b) 3%

c) 6 years (since the beginning of the decade)

Step-by-step explanation:

Given:

The population P (in thousands) of Austin, Texas during a recent decade can be approximated by \(y=494.29(1.03)^t\) when t is the number of years since the beginning of the decade.

General form of an exponential function: \(y=ab^x\)

where:

If \(b > 1\) then it is an increasing function

If \(0 < b < 1\) then it is a decreasing function

a) The model represents exponential growth as 1.03 > 1

b) The annual percent increase of the population is 3%

1.03 - 1 = 0.03

0.03 x 100 = 3%

c) To estimate when was population about 590,000 set y = 590 and solve for t:

\(\implies 590=494.29(1.03)^t\)

\(\implies \dfrac{590}{494.29}=(1.03)^t\)

Take natural logs of both sides:

\(\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t\)

\(\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)\)

\(\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}\)

\(\implies t=5.988069001...\)

Therefore the population was about 590,000 6 years since the beginning of the decade.

Answer:

The answer 11:3 leve; is the maple trees and the three is the oak trees.

Step-by-step explanation:

So the ratio is 5:3 right. So its says There are 6 more maple trees than oak trees.

What is the total number of trees at the park?​

if u do the math 5:3

             6+5+11:3. So the finally answer is 11;3

Total number of trees at the park is 24 trees

Ratio of maple trees to oak trees = 5:3

6 more maple trees than oak trees

Total number of trees at the park

Assume;

Number of oak trees = x

So,

Number of maple trees = x + 6

So,

[x + 6] / x = 5 / 3

3x + 18 = 5x

2x = 18

x = 9

Number of oak trees = 9

Number of maple trees = x + 6

Number of maple trees = 9 + 6

Number of maple trees = 15

Total number of trees at the park = 9 + 15

Total number of trees at the park = 24 trees

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Basically we need to find the distance between A and B, so:

Let P be a number. We have to check whether it is a prime number or not.

Let us consider that P is not a prime number.

Hence, P can be represented as a product of two of its factors other than itself and 1.

Let those two numbers be x and y.

Hence, we can write,

P = x*y

Without the loss of generality, we can write,

x < y

Multiplying both the sides of the inequality by x, we can write,

\(x^2\) < x*y = P

Square rooting on both the sides of inequality, we get,

x < \(\sqrt{P}\)

Hence, if there is a number which is a factor of P, that will be less than \(\sqrt{P}\).

That's why we check for prime number only up to square root of number rather than half the number.

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Answer:

Step-by-step explanation:

To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.

So, 20 cm = 20/100 m = 0.2 m

To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.

So, 0.2 m = 0.2/15 m = 0.013 m

So the final answer is 0.013 m.