given the quadratic function y=x^2+ax+b, the minimum value is -3, and the graph passes through point (1,1). find the values of the consists a and b.​

The linear equation of line will be y=4/7x-6/7.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

From graph take two point on line

(x1,y1),(x2,y2)=(5,2)(-2,-2)

As standard equation of a line is y=mx+c

where m=slope and c=constant

m=(y2-y1)/(x2-x1)

m=(-2-2)/(-2-5)=4/7

then equation of line will be

y-y1=4/7(x-x1)

y-2=4/7(x-5)

y=4/7x-20/7

Hence,

           The linear equation of line will be y=4/7x-6/7 in form of y=mx+c.

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The linear equation for this scenario could be: y = 5x + 77, where y represents the total amount of money Finn has after cooking x number of meals and 77 is the initial amount owed to his mom.

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to get both intercepts when an equation is stated in this way (x and y).

As per the data given,

The total amount Finn has = $ 77.

Amount spent on meal = $5 per meal.

Total number of meal = x

So, the amount spent on taking x meal will be = 5*x = 5x

Hence, the required linear equation will be: y = 5x + 77

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Answer:

If angle B is 60 and angle C is 70, We can make an equation by:

180 - (60+70)

The answer for this equation will be 50.

According to the upper equation, angle A is 50, angle B is 60, and angle C is 70.

The Transformation of the function f(x) = log₅(x) to g(x) = 3 - log₅(x) is a vertical reflection followed by a vertical translation.

(i) The original function f(x) = log₅(x) is first reflected over the x-axis, which changes the sign of the function. The result is a graph that is upside-down compared to the original. the function becomes -log₅(x)  .

(ii) Next, the transformed function g(x) is shifted up by 3 units, which results in the vertical translation of the graph. This transformation changes the range of the original function, but the shape of the graph remains unchanged.

So , the function becomes g(x) = 3 - log₅(x).

Therefore , The transformation of f(x) to g(x) changes the orientation of the graph and shifts it vertically, but does not affect its shape.

The given question is incomplete , the complete question is

The function f(x) = log₅(x) , is transformed to g(x) = 3 - log₅(x).

Describe the transformation.

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The stopping distance of regular tires on glare ice is estimated by the function D(F) = 2F+115, where D(F) is the stopping distance in feet and F is the air temperature in degrees Fahrenheit.

(a) D(0°) = 115 feet, D(-20°) = 95 feet, D(32°) = 147 feet

(b) The domain should be restricted to [-57.5°,32°] because the function D(F) gives a negative value when F is less than -57.5°, which is not physically possible. The function is also not defined for temperatures greater than 32° because the stopping distance is not a linear function of the temperature at higher temperatures.

The stopping distance of regular tires on glare ice is estimated by the function D(F) = 2F+115, where D(F) is the stopping distance in feet and F is the air temperature in degrees Fahrenheit. For specific temperatures, D(0°) = 115 feet, D(-20°) = 95 feet, and D(32°) = 147 feet. The domain should be restricted to [-57.5°,32°] because the function is not physically possible for temperatures less than -57.5° and is not a linear function of temperature at higher temperatures.

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As per the initial-value problem, the formula for the solution is dy/dt = y³

An initial-value problem, which involves finding a formula for a solution based on an initial value and a differential equation.

In this specific problem, the differential equation is

=> dy/dt = y³

and the initial value is

=> y(0) = 1.

To solve for the formula, we will use mathematical techniques to find the solution for y based on the given conditions.

The domain of the definition of the solution refers to the set of all possible values for the independent variable (t in this case) for which the solution is valid. In this problem, the domain of the solution is determined by the conditions that ensure the solution is well-defined.

As the solution approaches the limits of its domain, certain properties of the solution may change.

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Number of Excavation                                  Height of Soils(inches)

0                                                                       3 ins

1                                                                        5 ins

5                                                                       13 ins

10                                                                      23 ins

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

It is already noted that when Levi starts digging the hole is already 3 inches dip with soil

In each excavation he digs 2 inches of soil each

So, when number of Excavation is :

Zero :  the inches of soil is 3 inches

One : the inches of soil is 3+2 = 5 inches

Five : the inches of soil is 3+2*5 = 13 inches

Ten :the inches of soil is 3 + 2*10 = 23 inches

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The set of side measurement that will form a triangle is 8, 9 and 15.

A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.

Therefore, the triangle inequality theorem can be used to know the length of sides that can form a triangle.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If the length are a, b and c. Therefore,

a + b > c

a + c > b

b + c > a

Therefore, applying this principle the measurement that will form a triangle is  8, 9 and 15.

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In this study, the group of students who take the exam in a regularly lit room can be considered the control group.

The control group provides a baseline or comparison for the experimental group (the group of students who take the exam in a dimly lit room). The control group helps to establish a cause-and-effect relationship between the independent variable (room lighting) and the dependent variable (test performance), as any observed differences in test performance between the two groups can be attributed to the difference in lighting conditions.

By having a control group, the researcher can ensure that any observed effects are due to the independent variable and not due to extraneous variables.

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Statements i. and ii. are true while statement iii. is incorrect because, in an experiment, the control group is usually selected and assigned by the researchers, not self-selected by the participants.

i. True. In an experiment, the researchers have control over how participants are placed into different groups, usually through random assignment.

ii. True. In an observational study, participants are usually not manipulated by the researchers and are free to choose which group they belong to.

iii. False. A control group in an experiment is usually not self-selected. The control group is typically determined by the researchers through random assignment. The purpose of the control group is to provide a comparison to the experimental group in order to determine if the treatment has a significant effect.

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The possible additional amount he will spend more than 15.

An inequality is a relationship that denotes a non-equal comparison between two numbers or mathematical expressions.

According to  the question,

Let Amy, will spend $c additional amount.

Amy will spend more than $32 on gifts.

He spent $17.

We solved this question by using inequality.

The inequality equation is:

  c + 1 7 > 32

    c > 32 -17  ( by changing the sign)

     C > 15

So, the possible additional amount he will spend more than 15.

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There are 13 elements of the sample space that will have a green ball.

The various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Since, when a green ball is drawn, three coins are tossed. So, sample points are  OHHH, OHHT, OHTH, and OHTT. OTHH, 0THT, OTTH, OTTT

So, clearly, 9 sample points will have an orange ball.

When a blue ball is drawn, two coins are tossed. So, sample points are BHH, BHT, BTH, and BTT.

So, clearly, 4 sample points will be when a blue ball is drawn.

Total samples points=4+9=13

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Answer:

18.84 inches

Step-by-step explanation:

circumference of a circle = diameter x pi

diameter = radius x 2

==> circumference = radius x 2 x pi = 3 in x 2 x 3.14 = 18.84 in

Answer:

True

Step-by-step explanation:

the function is y = x/5

Josh washed a total of 5 plates if he want to do the dishes after work.

To find the total number of plates washed by Josh:

The scenario describes a person named Josh who had to wash dishes after work.

The method used to find the total number of plates washed by Josh was simple addition. The number of small plates (1) and the number of large plates (4) were added together to find the total number of plates (1 + 4 = 5). This type of problem is usually taught in grade 1 or grade 2, as part of early mathematics education that focuses on basic addition and counting skills.

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Logarithm ln3 is approximately 1.682.

Logarithm, the exponent or power to which a base must be raised in order to produce a specific number.

The linear approximation of the natural logarithm function near x=e is given by y ≈ ln(e) + (y'(e))(x-e), where y'(e) is the derivative of the logarithm function at x=e.

Since ln'(x) = 1/x, we have y'(e) = 1/e.

Substituting x=3 and e=2.71828... into the approximation, we get:

ln(3) ≈ ln(e) + (1/e)(3-e) = ln(e) + (3-e)/e

ln(e) = 1, so the result is:

ln(3) ≈ 1 + (3-e)/e ≈ 1 + 0.682 ≈ 1.682.

Hence, ln3 = 1.682.

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Answer:

The slope of the line that is perpendicular to y = 4x + 6 is the negative reciprocal of the slope of y = 4x + 6, which is -1/4.

We can use the point-slope form of a line, y - y1 = m(x - x1), to find the equation of the line that passes through the point (8, -4) and has a slope of -1/4, where m = -1/4 and (x1, y1) = (8, -4).

Plugging in the values, we get:

y - (-4) = -1/4 (x - 8)

y + 4 = -1/4 x + 2

Multiplying both sides by 4, we get:

4y + 16 = -x + 8

Adding x to both sides, we get:

4y + 16 + x = 8

y = -x/4 - 2

So the equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2.

The required simplified solution of the given radical expression is  [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a radical expression,
[tex]= \sqrt{15xy} / \sqrt[3]{10xy^3}[/tex]

Now, [tex]\sqrt{15xy} = [15xy]^{1/2}[/tex] and [tex]\sqrt[3]{10xy^3} = [10xy^3]^{1/3}[/tex]
[tex]= [15xy]^{1/2}/ [10xy^3]^{1/3}\\[/tex]

After simplifying the above expression,
= [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex]

Thus, the required simplified solution of the given radical expression is  [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex].

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A quadratic function can have two irrational roots.

but A quadratic equation can have no real number solutions.

What is quadratic function?

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree. It is an algebraic function.

The parent quadratic function is of the form f(x) = x^2 and it connects the points whose coordinates are of the form (number, number^2). Transformations can be applied on this function on which it typically looks of the form f(x) = a (x - h)^2 + k and further it can be converted into the form f(x) = ax^2 + bx + c.

Now,

According to the question,

A quadratic function can have two irrational roots. we can understand this by taking a example.

example:

x^2-x-2=0

This equation have two irrational roots  1+√3 and 1 - √3.

A quadratic function can have no real number solutions.

Hence,

             A quadratic function can have two irrational roots.

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By taking a quotient we will see that he has saved $450.

On the first month Lance earnesd $546, and on the second month he earned $354.

Adding these we get:

$546 + $354 = $900

So he earned a total of 900 dollars between April and June. And we know that he saves half of that, then the amount saved is equal to that divided by 2:

$90/2 = $450

He has saved 450 dollars.

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The Department of Energy was also eager to sign on, in part because it wanted to learn about how radiation causes genetic mutations.

An modification in the nucleic acid sequence of an organism's, virus's, or extrachromosomal DNA is referred to as a mutation. DNA or RNA can be found in the viral genome.

Any alteration to a cell's DNA sequence. Mistakes in cell division can result in mutations, as can exposure to environmental DNA-damaging substances.

Ionizing radiation may harm genetic material (mutations) in gonads or germ cells, which can result in disorders with a genetic component (hereditary defects). Malformations, metabolic issues, immune system deficits, etc. might occur from them.

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Equations and inequalities are both mathematical constructions made by joining two expressions.

A connection in mathematics that compares two numbers variables  or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. Less than or equal to, larger than, less than, and more than or equal to are the four fundamental inequalities.

Here,

Given :

-1 to 2 in the graph ,

To find the solution for the inequality ,

We get option -1 as the inequality

=> -1 ,0 ,1,2

=> -1 is the solution for this

These symbols for inequality are not equal (≠), less than (<), greater than (>), less than or equal (≤), and more than or equal (≥). Comparing numbers and identifying the range or ranges of values that satisfy the requirements of a given variable are both done using inequalities.

Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >, <, ≤ or ≥ indicate that the two expressions in an inequality are not always equal.

Therefore, the correct answer is option b.

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The third table shows a proportional relationship. Its graph is shown below.

A table of a proportional relationship is a set of pairs of values of the two variables involved in the relationship, where one variable is proportional to the other.

If the relationship between the variables on a table is proportional, the values in the table will form a straight line when plotted on a graph.

The constant of proportionality (k) for the third table = y/x = 2. Therefore it represents a proportional relationship.

The graph of the table is shown below.

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She need to contribute to the account every month, to the nearest dollar is  $26,195.00.

An annual interest rate of 3% compounded monthly. If Gianna would like to end up with $26, 000 after 3 years,

A = $26,195.00

I = A - P = $195.00

A is equal to P(1 + rt).

Calculation:

To start, multiplying R percent by 100 gives us 3%/100, or 0.03 each year.

For ease of calculation, let's convert time to years: 3 months / 12 months / year = 0.25 years.

How to resolve our equation

A = 26000(1 + (0.03 × 0.25)) = 26195\sA = $26,195.00

The total amount accrued, principal plus interest, from simple interest on a principal of $26,000.00 at a rate of 3% per year for 0.25 years (3 months) is $26,195.00.

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Answer: 98

Step-by-step explanation:

63 + 35

= 63 + 30 + 5

= 93 + 5

= 98

Answer:

63+35=98

Step-by-step explanation:

Step-by-step explanation:

this means a triangle with one angle 30°, a second angle 60°, and the third angle 90°.

the sides of such a 30-60-90 triangle are always in the ratio of 1 : √3 : 2

that means the Hypotenuse is twice the length of the shorter leg. and the longer leg is square root of 3 times longer than the shorter leg.

30-60-90 Theorem: If a triangle has sides in the ratio x: x 3: 2 x and angles of 30, 60, and, then it is a triangle. The longer leg, the hypotenuse, and the shorter leg are always the same. The Pythagorean Theorem can be used in their place if you ever forget these theorems.

Triangle with sides of 30-60-90

Sides of a triangle with angles of 30–60–90:

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According to the information, on the 11th day, half of the substance should remain.

To calculate what day half of the substance will remain, we must carry out the following mathematical procedure.

First of all we must find the range of decrease from one value to another.

4, 4.5, 5.5, 4 and 3

We average these values and it gives us 4.4.

We then subtract 78 - 50 to identify the difference between these two mass values. and then we divide the result in the decreasing range (4.4).

According to the above, it would take another 6.3 days to reach 50%, so more or less on day 11 half of the substance would remain.

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X1+X2 have distribution Bi(n1+n2, p) then the probability is P(X1+X2 = 1 | X2 = 0) =  np(1-p)ⁿ¹⁻¹ ,P(X1+X2 = 1| X2 = 1) = (1-p)ⁿ¹and P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹

Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).

Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).

If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹

If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹

Thus,

P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹

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The value of the composition function f ( g ( 4 ) ) = 31

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) = 3x + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) = x² - 6

And , the composition function f ( g ( x ) ) is calculated as

when x = 4

Substitute the value of x = 4 in the equation , we get

g ( x ) = x² - 6

g ( 4 ) = 4² - 6

g ( 4 ) = 10

f ( g ( 4 ) ) = f ( 10 )

Substitute the value of x = 10 in the equation , we get

f ( x ) = 3x + 1

f ( 10 ) = 3 ( 10 ) + 1

f ( 10 ) = 31

Hence , the equation is f ( g ( 4 ) ) = 31

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