Which operation should be used to solve x + 7 = 19?

The roots of the quadratic equation 3x² + 4x = 0 are -4/3 and 0, respectively.

Amber is trying to solve 3x² + 4x and she wants to know how to solve it. To solve this quadratic equation, we need to follow the steps mentioned below:

Step 1: Write the quadratic equation in standard form i.e ax² + bx + c = 0, where a, b and c are real numbers.

Step 2: Identify the values of a, b and c.

Step 3: Calculate the discriminant, D = b² - 4ac

Step 4: If D > 0, then the quadratic equation has two real roots, D = 0, then it has one real root, D < 0, then it has two complex roots.

Step 5: Use the quadratic formula, x = (-b ± √D)/2a to solve for x, where x represents the roots of the quadratic equation.

So, let us solve the given quadratic equation, 3x² + 4x.

Step 1: Write the given equation in standard form.3x² + 4x = 0

Step 2: Identify the values of a, b and c.In the given equation, a = 3, b = 4, and c = 0

Step 3: Calculate the discriminantD = b² - 4acD = (4)² - 4(3)(0)D = 16

Step 4: Determine the nature of the rootsSince D > 0, the quadratic equation has two real roots.

Step 5: Use the quadratic formula to solve for x. x = (-b ± √D)/2a We have x = (-4 ± √16)/2(3)We have x = (-4 ± 4)/6Or x = (-8/6) or x = (0/6)Simplifying, x = -4/3 or x = 0.

Therefore, the roots of the quadratic equation 3x² + 4x = 0 are -4/3 and 0, respectively.

For more such questions on quadratic equation

https://brainly.com/question/30164833

#SPJ8

When the value of the independent variable is increased by one unit from 5 to 6, the change in the dependent variable, y-hat, is an increase of 15 - the initial value of y-hat.

To find the change in the dependent variable, y-hat, when the independent variable is increased by one unit, you will need to substitute the values you found in steps 1 and 2 into the equation for the regression line. The equation for the regression line is in the form of y-hat = mx + b, where m is the slope and b is the y-intercept.

Let's say you found the slope, m, to be 2 and the y-intercept, b, to be 3.

Substituting these values into the equation, we have:

y-hat = 2x + 3

Now, if we increase the value of the independent variable, x, by one unit, we can substitute the new value into the equation and calculate the change in y-hat.

For example, if the initial value of x is 5, and we increase it by one unit to 6, we substitute x = 6 into the equation:

y-hat = 2(6) + 3
y-hat = 12 + 3
y-hat = 15

Therefore, when the value of the independent variable is increased by one unit from 5 to 6, the change in the dependent variable, y-hat, is an increase of 15 - the initial value of y-hat.

Remember to use the specific values you obtained in steps 1 and 2 to substitute into the equation for the regression line and calculate the change in y-hat accurately.

To know more about independent variable refer here:

https://brainly.com/question/33270051

#SPJ11

The length of three sides will be 35 feet, 70 feet and 51 feet

Define Perimeter of triangle

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Perimeter of Triangle = side1 + base + side2

Let, the shortest side of the triangle = x

The other side length is = 2x

and, the length of third side is = x + 16

given perimeter = 156 feet

We know, perimeter of triangle = a + b +c

where, 'a' and 'c' stands for sides of triangle

and, b stands for base

hence, the expression will be according to formula,

x + 2x + x + 16 = 156

solve for 'x'

4x + 16 = 156

4x = 156 - 16

x = 140/4

x = 35

2x = 2 * 35 = 70

x + 16 = 35 + 16 = 51

Therefore, the length of three sides will be 35 feet, 70 feet and 51 feet.

To read more about perimeter of triangle

https://brainly.com/question/24382052

#SPJ9

The number of bicycle  store needs to sell each month to break even is, 55

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

A bicycle store costs ​$3850 per month to operate

The store pays an average of ​$75 per bike

The average selling price of each bicycle is ​$145

The number of sells to break even = ?

Suppose, the number of sales is x

So, it can be written as,

For break even condition

75x + 3850 = 145x

145x - 75x  = 3850

70x = 3850

    x = 3850/70

    x =  55

Hence, the number of sales is 55

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

The approximate measure, in radians, of the central angle corresponding to a ⢠b is 3.77 rad.

What is central angle?

A central angle is an angle having endpoints on the perimeter of a circle and a vertex in the circle's center. An arc is defined by the centre angle of a circle.

What is area of sector?

The size of a circle's sector is the amount of space encompassed inside the sector's boundary. A sector always begins at the circle's center.

The area of a sector is given by the formula,

Area of sector =  / 360 ✕r2

Where,

θ is the central angle

r is the radius of the circle

Area of circle = πr\(^2\)

From above equations,

\(\frac{area of sector }{area of circle} =\) Ф / 360

According to question,

\(\frac{area of sector }{area of circle} =\) \(\frac{3}{5}\)

Ф \(= \frac{3 * 360}{5}\)

Ф = 216°

Now, the measure of central angle in radians =  216° * π/180

The measure of the central angle in radians = 3.77 rad

The approximate measure, in radians, of the central angle corresponding to a ⢠b is 3.77 rad.

To know more about area of sector, check out:

https://brainly.com/question/22972014

#SPJ4

a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

To know more about Euclidean visit :

https://brainly.com/question/3589540

#SPJ11

The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

\(\pi\) ± z\(\sqrt{\frac{\pi \p(1-\pi )}{n} }\)

z is the z-score that has a pvalue of \(1-\frac{\alpha }{2}\)

Since, the coin is fair, so \(\pi =0.5\).

The margin of error is:

\(M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}\)

99% confidence level:

So \(\alpha =0.01\) ,z is the value of Z that has a p value of 1-\(\frac{0.01}{2}\)=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=\(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

\(0.18=2.575\sqrt{\frac{0.5*0.5}{n} }\)

\(0.18\sqrt{n} =2.575*0.5\)

\(\sqrt{n}=\frac{2.575*0.5}{0.18}\)

\(\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}\)

n = 51.16

Thus, we have to flip the coin at least 52 times.

Learn more about the Probability here: https://brainly.com/question/24756209

#SPJ4

The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

To know more about smallest possible inside length, refer to the link :

https://brainly.com/question/17304098#

#SPJ11

Step-by-step explanation:

42 since 42/2=21 but 42/4=10.5 not integer

The number 42 is divisible by 2 but not divisible by 4 so it will be a counter-example so option (D) will be correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

If a number is divisible by 2 then it will also be divisible by 4 is a false statement.

For example, 6 is divisible by 2 but not 4, other examples are 10,14,16, etc.

In option (D)

42/2 = 21 + remainder 0

42/4= 10 + remainder 2 so it is not divisible by 4

Hence "The number 42 is divisible by 2 but not divisible by 4 so it will be a counter-example".

For more about the number system,

https://brainly.com/question/22046046

#SPJ6

The value will be $371.39.

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The formula to calculate the compound amount after t years is given by :-

A =P \((1 + R)^{T}\)

where the interest rate is r and P represents the principal amount.

Given: $150 is the principal sum.

Interest is charged at a rate of 12%/0.12

A = 150 will be the amount compounded after 8 years.

A = 150 \(( 1 + 12 )^{8}\)

A =371.3944

A = $371.39

Hence, the value of $150 after eight years if you earn 12 percent interest per year would be $371.39.

option a. is right

To know more about compound interest click the link:

brainly.com/question/18456266

#SPJ4

Answer:

The directional earing is N 30° E

Step-by-step explanation:

The given velocity vector is (25, 25·√3), therefor, we have;

R = 25·i + 25·√3·j

The angle of inclination of the direction of the boat with the horizontal = Arctan (y/x)

Where;

(x, y) = The coordinate of the components of the velocity of the boat

Therefore;

Arctan (y/x)  =  Arctan (25·√3/25) = Arctan (√3) = 60° North of East

The directional bearing which is the bearing relative to the northern direction is given as follows;

The directional earing = 90° - 60° = N 30° E.

Answer:

A on Egde

Step-by-step explanation:

i got it right

9514 1404 393

Answer:

  5. x° = 38°; b° = 90°

  6. m∠TSU = 110°

Step-by-step explanation:

The relationship relevant to these problems is that an inscribed angle is half the measure of the arc it intercepts. That is also true of the angle formed by a chord and a tangent.

__

5. Angle x° intercepts an arc marked 76°, so is half its measure: 76°/2 = 38°

  x° = 38°

Arc b° is intercepted by an inscribed angle of 45°, so is twice that measure.

  b° = 90°

__

6. Long arc SU is the remaining portion of the circle after short arc SVU is subtracted:

  long arc SU = 360° -140° = 220°

Angle TSU is half that measure: 220°/2 = 110°.

  m∠TSU = 110°

Answer: x=16 this is the answer without the 2 in the beginning of the equation with the 2 there's no solution

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

option A has two linear equations that intersect at one point

option B has two linear equations that are parallel and do not intersect

option C has one linear equation and an absolute value equation that intersect at two points

option D has one linear equation and a quadratic equation that intersect at two points

You should pay $13,050 for the note to earn 4% annual simple interest and be worth $13,500 in 10 months.

To calculate the amount you should pay for a note to earn 4% annual simple interest and be worth $13,500 in 10 months, follow these steps:

1. Convert the annual interest rate to a monthly rate: 4% / 12 months = 0.3333% per month.

2. Convert the investment period from 10 months to a fraction of a year: 10 months / 12 months = 0.8333 years.

3. Calculate the total interest earned during the investment period: $13,500 x 0.04 x 0.8333 = $450.

4. Subtract the interest from the final value of the note to find the initial investment amount: $13,500 - $450 = $13,050.

You can learn more about simple interest at: brainly.com/question/25845758

#SPJ11

When a parallelogram is reflected in an axis, the resulting image is also a parallelogram, with the same area and opposite angles.

To learn more about parallelograms refer to:

https://brainly.com/question/970600

#SPJ1

Which sampling method divides the population up into​ sections, randomly selects some of those​ sections, then chooses all the members from the selected sections to​ study?

What is Cluster Sampling?

Cluster sampling is a probability sampling technique where researchers divide the population into multiple groups (clusters) for research. Researchers then select random groups with a simple random or systematic random sampling technique for data collection and data analysis.

So, The above mentioned type of sampling is called cluster sampling.

Cluster sampling is a sampling technique in which the entire population of interest is divide into clusters or groups, then the investigator randomly selects some of these clusters and all the members of these randomly selected clusters are investigated.

For more learn about Cluster Sampling at:

https://brainly.com/question/20432243

#SPJ4

Answer:

2 for 25 cents is a better price

Answer:

x = 8/49

Step-by-step explanation:

Subtract 21 from both sides of the equation.

16x + 21 = 212x - 11

16x + 21-21 = 212x -11 -21

Simplify. Subtract the numbers.

16x = 212x -32

Subtract 212x from both sides of the equation.

16x = 212x - 32

16x - 212x = 212x - 32-212x

Simplify and combine like terms.

-196x = -32

Divide both sides of the equation by the same term.

-196x = -32

-196x. -32

-------- = ---------

-196. -196

Simplify.

x= 8/49

By substituting the equations the evaluated limit is 5c².

To evaluate the given limit, we need to substitute the given expressions into the function f(a) and simplify the expression (f(2 + h) - f(2))/h as h approaches 0.

First, we substitute a = 2 + h into the function f(a):

f(2 + h) = 5(2 + h)c² + 2.

Next, we substitute a = 2 into the function f(a):

f(2) = 5(2)c² + 2.

Now, we can evaluate the expression (f(2 + h) - f(2))/h:

(f(2 + h) - f(2))/h = [(5(2 + h)c² + 2) - (5(2)c² + 2)]/h.

Simplifying further:

= [(10 + 5hc² + 2) - (10c² + 2)]/h

= [5hc²]/h

= 5c².

As h approaches 0, the expression (f(2 + h) - f(2))/h simplifies to 5c².

learn more about limit here

https://brainly.com/question/8533149

#SPJ11

Answer:

its A

Step-by-step explanation:

All four angles are not congruent, only the two opposite of each other are congruent

Answer: C, y=-3x+4

Step-by-step explanation:

You're using a y=mx+b equation, where mx is the slope, and b is the y-intercept.

Your slope is -3, so we know now that

y=-3x+b

and your y-intercept is 4, so we can plug that in too

y=-3x+4

E(Y/n) = p. This result shows that Y/n is an unbiased estimator for p since its expected value is equal to the true value of the parameter p. As n gets large, the term 1/n approaches zero, and therefore, the variance V(Y/n) approaches zero as well.

a) To derive the expected value of Y/n, we can use the linearity of expectation. Since Y follows a binomial distribution with parameters n and p, we have:

E(Y/n) = E(Y) / n

The expected value of Y is given by:

E(Y) = np

Substituting this into the expression, we get:

E(Y/n) = np / n

Simplifying, we find:

E(Y/n) = p

This result shows that Y/n is an unbiased estimator for p since its expected value is equal to the true value of the parameter p.

b) To derive the variance of Y/n, we can use the properties of variance. Since Y follows a binomial distribution with parameters n and p, the variance of Y is given by:

V(Y) = np(1 - p)

Using the properties of variance, we have:

V(Y/n) = V(Y) / n²

Substituting the expression for V(Y), we get:

V(Y/n) = (np(1 - p)) / n²

Simplifying, we find:

V(Y/n) = (p(1 - p)) / n

As n gets large, the term 1/n approaches zero, and therefore, the variance V(Y/n) approaches zero as well. This means that as the sample size increases, the variability of the estimator Y/n decreases, indicating a more precise estimate of the true parameter p.

In conclusion, the expected value of Y/n is equal to the true value of the parameter p, making Y/n an unbiased estimator. Additionally, as the sample size increases, the variance of Y/n decreases, leading to a more precise estimate of the parameter p.

To know more about unbiased estimator refer here:

https://brainly.com/question/32063886#

#SPJ11

The probability associated with obtaining a particular value of z is referred to as its statistical probability or simply its probability. It represents the likelihood of observing a specific value of z in a given statistical distribution.

The probability of a specific value of z can be calculated using various statistical methods, depending on the distribution being considered. In statistics, z represents a standard score or a z-score. It is a measure of how many standard deviations a particular value is away from the mean of a distribution. The probability associated with a specific value of z is determined by the characteristics of the distribution, such as its shape, mean, and standard deviation. Different distributions, such as the normal distribution or the t-distribution, have different methods for calculating probabilities associated with specific values of z.

The probability associated with a particular value of z can be useful in hypothesis testing, confidence interval estimation, or determining the likelihood of an event occurring. By understanding the probability distribution of z-values, statisticians can make informed decisions and draw conclusions based on data analysis.

Learn more about standard deviations here: https://brainly.com/question/29115611

#SPJ11

The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).

The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.

The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).

To know more about standard error of an estimate:

https://brainly.com/question/30850106

#SPJ4