complete the square to rewrite the following equation in standard form

The solutions to the equation −11x − 7 = \(-3x^2\), rounded to the nearest tenth, are x ≈ -1.1 and x ≈ 6.1.

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = \(3x^2\) - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

We are given the equation \(-11x - 7 = -3x^2\).

To solve for x, we can rearrange the equation into a quadratic form by bringing all terms to one side:

\(-3x^2 + 11x + 7\) = 0

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± sqrt(\(b^2\) - 4ac)) / 2a

where a = -3, b = 11, and c = 7.

Substituting these values, we get:

x = (-11 ± sqrt(\(11^2\) - 4(-3)(7))) / 2(-3)

Simplifying inside the square root:

x = (-11 ± sqrt(121 + 84)) / (-6)

x = (-11 ± sqrt(205)) / (-6)

Using a calculator, we can approximate this to:

x ≈ -1.1 or x ≈ 6.1

Therefore, the solutions to the equation \(-11x - 7 = -3x^2\), rounded to the nearest tenth, are x ≈ -1.1 and x ≈ 6.1.

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The first-order Adams-Moulton formula derived as: y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))].

The first-order Adams-Moulton formula is equivalent to the trapezoid rule for approximating the integral in ordinary differential equations.

The first-order Adams-Moulton formula is derived by approximating the integral in the ordinary differential equation (ODE) using the trapezoid rule.

To derive the formula, we start with the integral form of the ODE:

∫[t, t+h] y'(t) dt = ∫[t, t+h] f(t, y(t)) dt

Approximating the integral using the trapezoid rule, we have:

h/2 * [f(t, y(t)) + f(t+h, y(t+h))] ≈ ∫[t, t+h] f(t, y(t)) dt

Rearranging the equation, we get:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is the first-order Adams-Moulton formula.

To verify its equivalence to the trapezoid rule, we can substitute the derivative approximation from the trapezoid rule into the Adams-Moulton formula. Doing so yields:

y(t+h) ≈ y(t) + h/2 * [y'(t) + y'(t+h)]

Since y'(t) = f(t, y(t)), we can replace it in the equation:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is equivalent to the trapezoid rule for approximating the integral. Therefore, the first-order Adams-Moulton formula is indeed equivalent to the trapezoid rule.

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In the equation 4y-12x=36 the solution of y is 9+3x

The given equation is 4y-12x=36

Four times of y minus twelve times of x equal to thirty six

We have to solve for y

Add 12x on both sides

4y=36+12x

Four times of y equal to thirty six plus twelve times of x

Divide both sides by four

y=36/4 +12x/4

y=9+3x

Hence, the solution of y is 9+3x in the equation 4y-12x=36

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Answer:

There will be no change

Step-by-step explanation:

The correlation Coefficient is a measure used in regression studies to examine the strength and type of relationship which exists between two variables (dependent and independent). The Coefficient gives a negative and positive values for negative and positive relationships respectively. The correlation Coefficient has no units and hence does not depend on the unit if measurement. Therefore. Changing the unit if measurement of a certain variable, will have no effect on the correlation Coefficient.

Hey there! :)

Answer:

C. x = 6.

Step-by-step explanation:

Given:

4(8 - x) = 8

Solve for x. Distribute:

32 - 4x = 8

Subtract 32 from both sides:

-4x = -24

Divide both sides by -4:

-4x/(-4) = -24/(-4)

x = 6.

Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.

Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.

Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.

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The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Hi!

y = m x + c is the slope intercept form of a line whose slope is m and

y intercept is c. Hence

y=x/2+5

LCM

y=x+10/2

2y=x+10

x-2y+10=o

Required equation of the line is x - 2 y +10 = 0

Answer:

15

Step-by-step explanation:

2 + 13 = 15

15( 3 ) = 45

45-35= 15

The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations.

As per the given data:

Cost of one trail mix = $3.00 per pound

Cost of another trail mix = $1. 50 per pound

The grocer makes 15 lb of trail mix that costs $2.50 per pound.

Let's assume the grocer used 'A' pounds of $3.00 per pound trail mix and 'B' pounds of  $1. 50 per pound trail mix.

Total quantity of $2.50 per pound trail mix = 15 lb

Now, from the given data,

A + B = 15 ...(i)

Also, the total cost is going to remain the same.

3A + 1.5B = 15 × 2.50

3A + 1.5B = 37.5 ...(ii)

Using eq(i) A = 15 - B

Substituting in (ii):

3(15 - B) + 1.5B = 37.5

45 - 3B + 1.5B = 37.5

B = 7.5/1.5

B = 5

and A = 10

The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

Hence, The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

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Answer:

3x+y = 8

yes, its parallel

Step-by-step explanation:

Choices:

a. 3x+y=18

b. 3x+y=-8

c. 3x+y=8

d. 3x+y=-10

1. if we plug in (6, -10) to 3x+y=8 we get:

3(6) + (-10) = 8

18 - 10 = 8

8 = 8, this is true

2. if we simplify 6x+2y=12 we get:

2y = -6x + 12

y = -3x + 6

if we simplify 3x+y = 8 we get

y = -3x + 8

the slopes of the equations are the same, therefore they are parallel.

The minimum value and median are used in the five-number summary.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

A five-number summary.

That means minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value.

From the given choices:

The minimum value and median are the required measures.

Therefore, the minimum value and median are the required measures.

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A scatter diagram with Admit Rate (independent variable) and -yr Grad. Rate (dependent variable) would plot the data points with Admit Rate on the x-axis and -yr Grad. Rate on the y-axis.

The scatter diagram would show the relationship between these two variables for the sampled colleges. b. To compute the sample correlation coefficient, you would need to use a statistical software or spreadsheet program. The sample correlation coefficient measures the strength and direction of the linear relationship between two variables. If the sample correlation coefficient is close to +1, it indicates a strong positive linear relationship. If it is close to -1, it indicates a strong negative linear relationship. If it is close to 0, it indicates a weak or no linear relationship.

Without the specific data, I cannot provide the computed correlation coefficient or interpret its value for the relationship between Admit Rate and -yr Grad. Rate.

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Answer:

Step-by-step explanation:

Use the proportion we have to find the horizontal length:

When y = 10, the value of x is:

\(\\ \sf\longmapsto y=2x\)

Put y=10 in equation

\(\\ \sf\longmapsto 10=2x{/tex]

\(\\ \sf\longmapsto x=\dfrac{10}{2}\)

\(\\ \sf\longmapsto x=5units\)

Answer:

B)

Step-by-step explanation:

The answer is B) you have to devide the terms

In the coordinate axis the point D is located at the position of (5,-2) .

In the given graph of the coordinate axis , we can see that the four points A,B,C and D are located

The coordinates of each point are :

A (-5,-2)

B (-2,5)

C (2,-5)

D (5,-2)

Therefore using the given abscissae and ordinate of the points the point that is located at (5,-2) is D.

A coordinate system in geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points or other geometrical objects on a manifold, such Euclidean space.

The order of the coordinates is crucial, and they are frequently identified by their position in an ordered tuple or by a letter, such as "the x-coordinate." The coordinates are often real values in elementary mathematics, but they could also be complex numbers or parts of a more abstract system, such a commutative ring.

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Answer:

13

Step-by-step explanation:

x^2=5^2+12^2

x^2=25+144

x^2=169

x=13

Answer:

5 kilometers per hour

Step-by-step explanation:

25 (kilometers) divided by 5 (hours) = 5 kilometers per hour

The distance between your house and school is 4.1 miles.

According to the given question.

Point c represents your house.

Point d represents post office which is directly west to the point c i.e from house.

And point e represents school which is west of the post office.

Also, it is given that the distance between house and post office, cd is 1.7 miles.

And the distance between the post office and school,de is 2.4 miles.

Now, if we see the attached figure we can say that

cd + de = ce

⇒ 1.7miles  + 2.4miles  = 4.1 miles

Hence, the distance between your house and school is 4.1 miles.

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The probability that Venus picks three new (unused) balls from the box is 0.1296.Given that a box contains 18 tennis balls of which 8 are new (unused).

We have to find the probability that these three are all new (unused).We know that the balls Serena played with were then returned to the box, so there are 8 new balls left and a total of 19 tennis balls in the box.

Therefore, the probability of picking a new (unused) ball is `8/19`.

Thus, the probability that Venus picks three new (unused) balls from the box is `P(Three new balls) = P(New ball) × P(New ball) × P(New ball) = (4/9) × (8/19) × (8/19) = 0.1296`.Hence, the probability that Venus picks three new (unused) balls from the box is 0.1296.

Summary:A box contains 18 tennis balls of which 8 are new (unused). The probability that Venus picks three new (unused) balls from the box is `P(Three new balls) = P(New ball) × P(New ball) × P(New ball) = (4/9) × (8/19) × (8/19) = 0.1296`.

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The terms with "x" cancel out, and we're left with:

0 = 12

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.

Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:

Slices with only pepperoni: 6 slices

Slices with only mushrooms: 10 slices

Slices with both pepperoni and mushrooms: $x$ slices

Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices

We know that the total number of slices is 12, so we can write an equation:

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.

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Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

The slope at the point (x, y) = (6 cos (π/4), 6 sin (π/4)) = (3√2, 3√2) is -1.

d²y/dx² at the point (x, y) = (3√2, 3√2) is 4.

The curve is concave up at (x, y) = (3√2, 3√2).

To find the derivatives and analyze the slope and concavity at the given value of the parameter θ = π/4, we need to find the equations for x and y in terms of θ, then differentiate them with respect to θ, and finally substitute the value of θ to obtain the desired values.

Given parametric equations:

x = 6 cos θ

y = 6 sin θ

Differentiating both equations with respect to θ:

dx/dθ = -6 sin θ

dy/dθ = 6 cos θ

To find dy/dx, we need to express dy/dθ and dx/dθ in terms of dy/dx.

We can use the chain rule for differentiation:

dy/dx = (dy/dθ) / (dx/dθ)

Substituting the values of dy/dθ and dx/dθ:

dy/dx = (6 cos θ) / (-6 sin θ)

= -cos θ / sin θ

= -cot θ

Now, we can substitute θ = π/4 to find the slope and concavity at that point.

Substituting θ = π/4 into dy/dx:

dy/dx = -cot (π/4)

= -1

Therefore, the slope at the point (x, y) = (6 cos (π/4), 6 sin (π/4)) = (3√2, 3√2) is -1.

To find d²y/dx², we need to differentiate dy/dx with respect to θ:

d²y/dx² = d/dθ (-cot θ)

Differentiating -cot θ with respect to θ:

d²y/dx² = csc² θ

Substituting θ = π/4:

d²y/dx² = csc² (π/4)

= 2² / 1²

= 4

Therefore, d²y/dx² at the point (x, y) = (3√2, 3√2) is 4.

Regarding concavity, since d²y/dx² is positive (4) at the given point, the curve is concave up at (x, y) = (3√2, 3√2).

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The groups that describes 16% of the population of horse jockeys are option (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

To solve this problem, we need to use the standard normal distribution, where we can find the z-score associated with the given percentages using a z-table or calculator. The z-score tells us how many standard deviations a value is from the mean.

First, we can standardize the values using the formula

z = (x - μ) / σ

where z is the z-score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

a) To find the jockeys who are shorter than 58 in., we can standardize the value as

z = (58 - 62) / 2 = -2

Using a z-table, we can find that the percentage of values below z = -2 is approximately 0.0228, which is less than 16%. Therefore, a) is not correct.

b) To find the jockeys who are taller than 64 in., we can standardize the value as

z = (64 - 62) / 2 = 1

Using a z-table, we can find that the percentage of values above z = 1 is approximately 0.1587, which is also less than 16%. Therefore, b) is not correct.

c) To find the jockeys who are shorter than 60 in., we can standardize the value as

z = (60 - 62) / 2 = -1

Using a z-table, we can find that the percentage of values below z = -1 is approximately 0.1587, which is less than 16%. Therefore, c) is correct.

d) To find the jockeys who are between 60 in. and 64 in., we can standardize the values as

z1 = (60 - 62) / 2 = -1

z2 = (64 - 62) / 2 = 1

Using a z-table, we can find the percentage between z1 and z2, which is approximately 0.6826. Therefore, d) is also correct.

Therefore, the correct answers are (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

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The given question is incomplete, the complete question is:

Suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in.

Which group describes 16% of the population of horse jockeys?

Select each correct answer.

a) jockeys who are shorter than 58 in.

b) jockeys who are taller than 64 in.

c) jockeys who are shorter than 60 in.

d) jockeys who are between 60 in. and 64 in.

Answer:( -22•3a7b7c8)

Step-by-step explanation:

STEP1

Equation at the end of step 1

 ((0-(((4•(a3))•b)•(c2)))•(((a3)•(b2))•c))•(3ab4•c5)

STEP 2

Equation at the end of step2

 ((0 -  ((22a3 • b) • c2)) • a3b2c) • 3ab4c5

STEP 3

Multiplying exponential expressions :

3.1    a6 multiplied by a1 = a(6 + 1) = a7

Multiplying exponential expressions :

3.2    b3 multiplied by b4 = b(3 + 4) = b7

Multiplying exponential expressions :

3.3    c3 multiplied by c5 = c(3 + 5) = c8

To find where the function is increasing or decreasing, we need to take the derivative of the function and determine where it is positive or negative.

The derivative of f(x) = x/2 + cos(x) is f'(x) = 1/2 - sin(x).

To find where f'(x) is positive, we need to solve the inequality 1/2 - sin(x) > 0.

Adding sin(x) to both sides, we get 1/2 > sin(x).

This is true on the intervals (0, pi/6) and (5pi/6, 2pi).

To find where f'(x) is negative, we need to solve the inequality 1/2 - sin(x) < 0.

Subtracting 1/2 from both sides, we get -1/2 < -sin(x).

Multiplying both sides by -1 and flipping the inequality, we get sin(x) < 1/2.

This is true on the interval (pi/6, 5pi/6).

Therefore, the function is increasing on the intervals (0, pi/6) and (5pi/6, 2pi), and decreasing on the interval (pi/6, 5pi/6).

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With the given information and the results of the t-test, you can make the correct decision for this hypothesis test.

To determine the correct decision for this hypothesis test, you need to compare the observed difference in mean scores between the experimental and control groups with the critical value obtained from a t-test.

The null hypothesis for this test is that there is no difference in mean scores between the experimental and control groups. The alternative hypothesis is that the experimental group has a higher mean score than the control group.

Based on the given information, the sample mean for the experimental group is 82 and the sample mean for the control group is 74. The sample size for both groups is 60 and the standard deviations are 9 and 12, respectively.

Using these values, you can perform a t-test using statistical software or a calculator. The t-test will give you a t-statistic and a p-value, which can be used to determine the significance of the observed difference in mean scores.

If the p-value is less than the significance level of 0.05, it means that the observed difference in mean scores is statistically significant and you can reject the null hypothesis in favor of the alternative hypothesis. This means that you can conclude that the experimental group has a higher mean score than the control group.

On the other hand, if the p-value is greater than the significance level of 0.05, it means that the observed difference in mean scores is not statistically significant and you cannot reject the null hypothesis. This means that you cannot conclude that the experimental group has a higher mean score than the control group.

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If R is an odd integer, the next two consecutive odd integers are R+2 and R+4. Option D

You should understand that an odd number is a number that is not divisible by two without remember.  Examples of odd numbers are 1,3,5,7,9 etc.  The difference between two consecutive odd numbers is two.

Two numbers are consecutive if the are counted without jumping any number.  from the list of odd numbers, the difference between them starting from one is two.

So if R is odd, the numbers are in the order

R

R+2

R+2+2

Where R is the first term, R+2 is the second term and R+4 is the third term.

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Answer:

senior citizen tickets are $10 and child tickets are $8

Answer:

senior is 10 and child is 8

Step-by-step explanation: