Use point-slope form to write the equation of a line that passes through the point (1,-3)(1,−3) with slope -\frac{5}{3}−
3
5
​
.

The solution to the quadratic equation using quadratic formula is X has a negative value x is undefined with no real solution.

    x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Using quadratic formula to solve the equation

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

2x^2-4x +3 = 0

All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula:  

The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

we need to identify a, b and c

from the quadratic equation a = 2, b= -4 and c=3

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the value of a, b and c into the equation

[tex]x = \frac{-(-4) ± \sqrt{(-4^{2} - 4(2)(3)} }{2(2)}[/tex]

[tex]x=\frac{ 4 ± \sqrt{16 -28} }{4}[/tex]

x= [tex]\frac{4+\sqrt{-12} }{4}[/tex] or  x= [tex]\frac{4-\sqrt{-12} }{4}[/tex]

x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Since X has a negative value x is undefined with no real solution.

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Answer:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]2x^2-4x+3=0[/tex]

When completing the square for a quadratic equation in the form ax²+bx+c=0, first move the constant to the right side of the equation:

[tex]2x^2-4x=-3[/tex]

Divide both sides of the equation by the coefficient of x²:

[tex]x^2-2x=-\dfrac{3}{2}[/tex]

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]x^2-2x+\left(\dfrac{-2}{2}\right)^2=-\dfrac{3}{2}+\left(\dfrac{-2}{2}\right)^2[/tex]

Simplify:

[tex]x^2-2x+1=-\dfrac{3}{2}+1[/tex]

[tex]x^2-2x+1=-\dfrac{1}{2}[/tex]

Factor the perfect square trinomial on the left side:

[tex](x-1)^2=-\dfrac{1}{2}[/tex]

Square root both sides:

[tex]\sqrt{(x-1)^2}=\sqrt{-\dfrac{1}{2}}[/tex]

[tex]x-1=\pm\sqrt{-\dfrac{1}{2}}[/tex]

Simplify:

[tex]x-1=\pm\sqrt{\dfrac{1}{2} \cdot -1}[/tex]

[tex]x-1=\pm\sqrt{\dfrac{1}{2}} \sqrt{-1}[/tex]

[tex]x-1=\pm\dfrac{1}{\sqrt{2}} i[/tex]

[tex]x-1=\pm\dfrac{\sqrt{2}}{2} i[/tex]

Add 1 to both sides:

[tex]x=1\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2}{2}\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2\pm\sqrt{2}\: i}{2}[/tex]

Therefore, the solutions of the given quadratic equation using the method of completing the square are:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

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The system of equations that models the situation are:

g + 3b = $26

g + 5b = $38

The price of one miniature golf game is $8 and the price of one bracelet price is $6

g + 3b = $26 equation 1

g + 5b = $38 equation 2

Where:

The elimination method would be used to solve the equations.

in order to determine the value of b, subtract equation 1 from equation 2

2b = 12

Divide both sides of the equation by 2

b = 12 /2

b = 6

In order to determine the value of g, substitute for b in equation 1:

g + 3(6) = $26

g + 18 = $26

g = $26 - $18

g = $8

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The predicted amount of an unstable element that is left after 6 years is 5.46 grams.

For the stated question-

The equation for the least-squares regression line, is;

In(Element) = 2.305 -0.101(Time)

Amount of unstable element left after time t = 6 years.

In (Element) = 2.305 -0.101(6)

ln (Element) = 1.699

(Element) = e¹°⁶⁹⁹

(Element) = 5.46

Thus, the predicted amount of an unstable element that is left after 6 years is 5.46 grams.

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The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

[tex]\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}[/tex]

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

[tex]\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}[/tex]

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

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The account balance after 3 years will be $218.

The crediting of cash flows connected with an investment or deposit is referred to as "simple" interest.

Given that you deposit $200 in an account that earns simple interest at an annual rate of 3%.

The formula to calculate the simple interest is given below,

SI = ( P x R x T ) / 100

SI = ( 200 x 3 x 3 ) / 100

SI = 2 x 3 x 3

SI = $18

Total account balance = 200 + 18 = $218

Therefore, the account balance after 3 years will be $218.

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The degrees of freedom here is 5.

Given,

A grocery store company wanted to know how well some of their local stores were doing.

The number of sample reviewers they hired to rate 15 local stores = 6

We have to find the degrees of freedom;

Degrees of freedom;-

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the number of items in the data sample.

Here,

Degrees of freedom = n - 1

n = 6

Then,

Degrees of freedom = 6 - 1 = 5

That is,

5 is the degrees of freedom in this case.

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The average speed is 54 miles per hour.

What is average ?

In plain English, an average is one number chosen to represent a list of numbers. It is often calculated by dividing the total number of numbers in the list by the number of numbers in the list. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

The definition of the average is the mean value, which is the ratio of the sum of the values in a given set to the total number of values in the set.

The formula for distance is

Distance = Rate × Time

Total distance = 50 × 3 + 60 × 2 = 270

Total time = 3 + 2 = 5

Using the formula:

[tex]Speed = \frac{Distance}{Time}[/tex]

       = 270 / 5

       = 54

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The equivalent form of the function is [tex]Q(t)=4000(64)^t[/tex]

The equation of the function, according to the question is given as

Q(t)=4000(4)3t

This equation can be properly rewritten as

Q(t)=4000(4)³⁺

Express 4 as a radical expression

So, we have the following representation

Q(t)=4000(4³)⁺

Evaluate the exponent in the above expression

Q(t)=4000(64)⁺

The above expression cannot be further simplified

Hence, the solution to the exponential expression is Q(t)=4000(64)⁺

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Complete question

Q(t)=4000(4)3t.

Write an equivalent function of the form Q(t)=ab^t.

To find the distance between the high school and the stadium, we need to use the distance formula. The distance formula is given by the following equation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the starting point, and (x2, y2) is the coordinates of the ending point.

In this case, the starting point is the high school, which is located at the coordinates (2, 5), and the ending point is the stadium in Columbus, which is located at the coordinates (8, 13). Plugging these values into the distance formula, we get:

d = sqrt((8 - 2)^2 + (13 - 5)^2)

d = sqrt(6^2 + 8^2)

d = sqrt(36 + 64)

d = sqrt(100)

d = 10

Therefore, the distance between the high school and the stadium is 10 units. Since 1 unit is equal to 8.6 miles, the distance between the high school and the stadium is 86 miles.

It's worth noting that the rest stop is located halfway between the high school and the stadium. This means that the distance from the high school to the rest stop is 86/2 = 43 miles, and the distance from the rest stop to the stadium is also 43 miles. This can be verified by using the distance formula to find the distance between the rest stop and the high school, and then between the rest stop and the stadium.

The total proportion of shirts between two prices is 0.9431, which is obtained using the knowledge of proportion and statistics.

What is proportion?

In mathematics, a proportion is defined as the comparison between two numerical quantities. If both possess the same nature, they are called directly proportional, or else called inversely proportional.

Calculation of the proportion based on the problem

The mean and standard deviation are given to be 45 and 5 respectively

Calculate standard normal variate using the formula, z = (x - 45) / 5

Taking x = 37, we get,

z1 = (37 - 45) / 5

= -1.6

Using the z table, we get the value, z1 = 0.0548

Now, taking x = 59.35, we get,

z2 = (59.35 - 45) / 5

= 2.87

Using the z table, we get the value, z2 = 0.9979

The proportion between two prices is given by z = z2 - z1

z = 0.9979 - 0.0548

= 0.9431

Hence, the proportion of shirts between the two prices is 0.9431.

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Answer:85%

Step-by-step explanation:

51 is what percent of 60 is equal to (51 / 60) x 100 = 85%. So if you buy an item at $60 with $51 discounts, you will pay $9 and get 85% discount cashback rewards. So 51 out of 60 as a percentage is 85%

Can you help me too???????

 This is an example of discrete data because this data cannot be broken into decimals.

Among the following, the population mean u = (upper confidence limit) + (lower confidence limit) is not derived from the confidence interval.

A confidence interval is defined as the range of values that we observe in our samples and for which  we expect to find the value that accurately reflects the population.

In frequentist statistic, a confidence interval is a range of estimates for an unknown parameter.    

To find a confidence level for a data set by taking half of the size of the confidence interval, multiplying it by the square root of the sample size and then dividing by the sample standard deviation.

Confidence level refers to the percentage of probability,or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times. The most common confidence levels are 90%, 95% and 99%.

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The sandwich and soup combos that can be served is 48.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 1/3 liter of soup is served with each sandwich and soup combo.

Since the cook made 16 liters of soup to serve with sandwiches as part of the combo. The sandwich and soup combination will be:

= 16 ÷ 1/3.

= 16 × 3

= 48

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Step-by-step explanation:

y=Mx+b

M- slope

B- y intercept

1. find slope by choosing 2 point(any 2)

Once you’ve picked 2 point- (X1, y1) (x2, y2) set up the equation to calculate slope

y2-y1 / x2-x1 = m

2. Solve for b

Take any point and plug in the x and y value

Plug in y= (the slope you solved for)(x intercept) + b

3. then write the equation

Y= (slope)x + b

The value of z after solving the equation z³ = 8 is 2.

The result of a number (x) being multiplied three times is referred to as the cube of that number. The phrase "cube root" in mathematics means "the number that needs to be multiplied three times in order to acquire the original number." Let's now examine the cube root formula, in which y is equal to the cube root of x. ∛x = y. Any integer can be represented as the cube root by the radical sign ∛, which has a little 3 written on the top left of the sign. Writing 1/3 as a number's exponent is another method to represent a cube root.

The given equation

z³ = 8

The number 8 can be written as

8 = 2 × 2 × 2

= 2³

So,

z³ = 2³

So, comparing both sides, we get

z = 2

This is the solution to the equation.

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The number of bacteria in the petri dish after 24 hours will be y = 125 + 24x

Given is Gina was working in the laboratory on an experiment involving the population of bacteria. Her initial starting amount in a petri dish was 125 bacteria.

Assume that each hour the bacteria rises by [x] bacteria per hour. Then,

the number of bacteria in the petri dish after 24 hours will be -

y = 125 + 24x

Therefore, the number of bacteria in the petri dish after 24 hours will be y = 125 + 24x.

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Check the picture below.

bearing in mind that the ratio of the sides of similar figures is the same as the ratio of their perimeters

[tex]\stackrel{\textit{\Large perimeters}}{21.3\hspace{5em}p}\hspace{5em}\stackrel{\textit{\Large areas}}{16\hspace{5em}25} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(21.3)^2}{(p)^2}~~ = ~~\cfrac{16}{25}\implies \left( \cfrac{21.3}{p} \right)^2=\cfrac{16}{25}\implies \cfrac{21.3}{p}=\sqrt{\cfrac{16}{25}}\implies \cfrac{21.3}{p}=\cfrac{\sqrt{16}}{\sqrt{25}} \\\\\\ \cfrac{21.3}{p}=\cfrac{4}{5}\implies 106.5=4p\implies \cfrac{106.5}{4}=p\implies {\Large \begin{array}{llll} 26.625=p \end{array}}[/tex]

Since pp-value is greater than all considerable significance levels (alpha = 0.05, 0.01α=0.05,0.01), we fail to reject the null hypothesis. In order words, we do not have enough evidence to disapprove hatchery's claims.

A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A straightforward hypothesis is a claim that expresses the relationship between precisely two variables. a dependent and a single independent. Take the statement "Smoking is a significant cause of lung cancer" as an example. Smoking is an independent variable that influences the dependent variable, lung cancer.

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Answer: -9

Step-by-step explanation: To find the value of u, we can use the slope formula to calculate the slope of the line that goes through the points (9, u) and (10, -1). The slope formula is: slope = (y2 - y1)/(x2 - x1). In this case, we have: slope = (-1 - u)/(10 - 9) = (-1 - u)/1. Since the slope of the line is given as 8, we can set this equal to the value we calculated above and solve for u. This gives us: 8 = (-1 - u)/1. Multiplying both sides by 1 gives us: 8 = -1 - u. Adding 1 to both sides gives us: 9 = -u. Finally, negating both sides gives us: u = -9. Therefore, the value of u is -9.

Answer:

h = -3y + 2x

Step-by-step explanation:

Add 4x to both sides of the equation.

2h = −6y + 4x

Divide each term in 2h = −6y + 4x by 2 and simplify.

Divide each term in 2h = −6y + 4x by 2.

2h/2 = -6y/2 + 4x/2

Simplify the left side.

h = −6y/2 + 4x/2

Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.

h = -3y+2(2x)/2

Cancel the common factors.
Factor 2 out of 2.

h = -3y+2(2x)/2(1)
Cancel the common factor

h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1

Divide 2x by 1.
h = -3y + 2x

hopefully its right LOLZ

The correct option is . D) Her IQ score is above the majority of the population types of intelligence.

IQ is an abbreviation for intelligence quotient. IQ tests are used to assess people's intellectual abilities and potential. They are intended to test a wide range of cognitive abilities, including reasoning, logic, and problem-solving.

It's a test of intelligence, which you're born with. It is not a test of knowledge that represents what you learn in school or through life experience.

Amber's mental age = 14

Amer's age = 10

Then her IQ can be calculated by

[tex]IQ=\frac{mental\ age}{chronological\ age}*100=\frac{14}{10}*100=140[/tex]

Average IQ of majority of population is between 85 to 115.

Only small percentage of population has IQ score higher than 130.

It means Amber's IQ score is above the majority of the population.

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Answer:

5 1/5

Step-by-step explanation:

you set up the fraction in the division bracket with the denominator staying the same in the final answer. The denominator will go on the inside, and the 5 on the outside.

5 1/5 :)))))))))))))))))))))))))))))))))))))))))))

The required answer are according to the following order,

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

What do you mean by sum of angles?

We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:

The angle subtended is obtained from number of people that chose a particular location.

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

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The polygon ABCD and polygon EFGH are congruent polygons.

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons, etc

Here,
Consider two polygons,
ABCD and EFGH,
As given in the figure,
AB = EF,
AD = EH
∠A = ∠E
∠D = ∠H
ABCD ≅ EFGH,

Thus, Congruent polygons are polygons ABCD and EFGH.

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Blank 1: Corresponding because All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Blank 2:

Blank 3: x= 46 as 180-134 = 46

The equation that represents the proportional relationship in this graph is y = 2 / 7 x.

Two variables have a proportional relationship if all the ratios of the variables are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

for some constant k , called the constant of proportionality .

Therefore, the variables in this case are y and x.

Hence, let's find k using the coordinates on the graph

(0.7, 0.2)

0.2 = k (0.7)

k = 0.2 / 0.7

k = 2 / 7

Hence,

y = 2 / 7 x

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