A:what are the solutions to the Quadratic equation
x^2 +4=0?

B:what is the factored form of the quadratic equation x^2+4?

Answer: Hello there!

here we have two equations:

1) x + 3y = 7

2) 2x + 4y = 8

a) first we want to isolate x in the first equation:

x + 3y = 7

x = 7 -3y

done!

b) now we want to replace it in the second equation, and in this way get a equation that depends only on the variable y.

2x + 4y = 8

2(7 - 3y) + 4y = 8

c) now we sole this equation and obtain the value of y.

14 - 6y + 4y = 8

14 - 2y = 8

-2y = 8 - 14 = -6

y = 6/2 = 3

d) now we have the value of y, and we can substitute it on the equation that we got in the part a)

x = 7 - 3y

x = 7 - 3*3 = 7 - 9 = -2

e) now we knowt that x = -2 and y = 3, then the pair (x,y) can be written as:

(-2,3).

The solution to the system of equations, as an ordered pair, is (-2,3).

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives step by step of the solution for the system of linear equations. The exercise found the value of y, then you should find the value of x.

The step 4 of the question shows: x = 7 − 3(3). Therefore:

x = 7 − 3(3)

x = 7 − 9

x= -2

You can check the values found for x and y from equation 2x + 4y = 8. Therefore:

2*(-2)+4*(3)

-4+12=8

Thus, the values found for x and y are correct.

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The indicated z score is -1.08

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1 and it is given by the probability density function and distribution function

. Areas of the normal distribution are often represented by tables of the standard normal distribution.

Shaded area is 0.8599 according to the attachment. Then the lookup area is

Find the indicated z score.

[tex]Z = \frac{ (X - \mu)}{\sigma}[/tex]

where Z is the value on the standard normal distribution, X is the value on the original distribution, μ is the mean of the original distribution, and σ is the standard deviation of the original distribution.

According to the picture below z is

[tex]Z = \frac{ (0.8599 - 0.5)}{1} = 0.3599[/tex]

Then if we look at the table, the z score is -(1.0 + 0.08) = -1.08 (C)

The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. It learns about heights, blood pressure, measurement error, and IQ scores. The normal distribution is also known as the Gaussian distribution and the bell curve.

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To find the indicated z-score, we use the z-score formula and refer to the z-table. The z-score that corresponds to a shaded area of 0.8599 is approximately 1.28.

The z-score formula is used to find the indicated z-score. In this case, since the shaded area is 0.8599, we need to find the z-score that corresponds to this area. Referring to the z-table, we find that a z-score of approximately 1.28 corresponds to an area of 0.9. Therefore, the indicated z-score is 1.28.

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Answer:

-x < 8

Step-by-step explanation:

-x/4 < 2

-x/4 (x4) < 2 (4)

-x < 8

The restriction on the domain of the function [tex]f(x) = {x + 5}/{x - 2}.[/tex] is that x cannot be equal to 2, since it would make the denominator zero, which is undefined in real numbers.

The student is asking to identify the restrictions on the domain of the function [tex]f(x) = {x + 5}/{x - 2}.[/tex] The domain of a function includes all the values that x can take for which the function is defined. In the case of a rational function, any values that make the denominator zero must be excluded from the domain since division by zero is undefined.

In this function, the denominator is x - 2. Therefore, the value that makes the denominator zero is x = 2. To identify the restrictions on the domain of [tex]f(x) = {x + 5}/{x - 2}.[/tex] we set the denominator equal to zero and solve for x:

Hence, the only restriction on the domain of this function is that x cannot be 2. So the domain of f(x) is all real numbers except x = 2.

For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It is the slope of the line

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes

We have as data that:

[tex](x_ {0}, y_ {0}) = (1, -4)[/tex]

Substituting:

[tex]y - (- 4) = m (x-1)\\y + 4 = m (x-1)[/tex]

All that remains is to replace the value of the slope.

Answer:

[tex]y + 4 = m (x-1)[/tex]

Answer:

45.55 m to the nearest hundredth.

Step-by-step explanation:

tan 26 = opposite / adjacent side = h / 90   where h = height of the dam - Scarlett's height.

The height of the dam =

y = 90 tan 26

= 43.895 m

Now we need to add Scarlett's height  

= 45.55 m.

Answer:

grg

Step-by-step explanation:

rgg

Answer:

29.1 cm

Step-by-step explanation:

Circumference of a circle is:

C = 2πr

Given that C = 183 cm:

183 = 2πr

r = 183 / (2π)

r ≈ 29.1 cm

Answer:

270

Step-by-step explanation:

base area=18

18*15=270

The volume of the triangular prism is equal to [tex]270[/tex] cu. units.

" Volume is defined as the total space occupied by a three-dimensional object."

Formula used

Volume of a triangular prism = Area of the base × height

Area of the base [tex]= \frac{1}{2} \times base \times height[/tex]

According to the question,

Given dimensions,

Base of triangle [tex]= 9 units[/tex]

Height of the triangle [tex]=4 units[/tex]

Height of the triangular prism [tex]= 15 units[/tex]

Substitute the value in the formula to get the area of the base we have,

Area of the base [tex]= \frac{1}{2}\times 9\times 4[/tex]

                             [tex]= 18 square units[/tex]

Volume of a triangular prism [tex]= 18 \times 15[/tex]

                                                  [tex]= 270 cu.units[/tex]

Hence, the volume of the triangular prism is equal to [tex]270[/tex] cu. units.

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Answer:

This is the definition of rational number.

These include: Integers, Terminating Decimals, Repeating Decimals, or Proper, Improper, and Mixed Fractions where each part is an integer.  

Step-by-step explanation:

This is the definition of rational number.

Here are some examples of rational number:

-3  (negative integers are included because they can be rewritten; here -3=-3/1)

5 (positive integers are included because they can be rewritten; here 5=5/1)

0 (neutral integers are included also because 0/4 or 0/1 are still 0)

5/3 (impropert fractions where top and bottom are integers; this is already written in the form required)

1   2/3  (mixed fractions because they can rewritten as improper fractions with top and bottom as integers; example here this 5/3)

2/5  (proper fractions where top and bottom are integers; this is already written in the form required)

.55555555555...=[tex]. \overline{5}[/tex] (repeating decimals; example this one can be written as 5/9)

.23 (terminating decimals; example this can be written as 23/100 )

Answer:

The rate is 13 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- Jim lives three miles east of State College

- At noon, he leaves his house and begins to walk due east at a

 constant speed of 2 miles per hour

- Annie lives four miles north of State College

- At noon, she leaves her house and begins to bicycle due north at a

 constant speed of 8 miles per hour

- The east is perpendicular to the north

* Lets solve the problem

∵ At noon means 12 p.m

∵ They moved till 1 p.m

∵ Jim walked for 1 hour and Annie bicycled for 1 hour

∵ The rate of Jim is 2 miles per hour

∵ The rate of Annie is 8 miles per hour

- The distance = rate × time

∴ Jim walked = 2 × 1 = 2 miles

∴ Annie bicycled = 8 × 1 = 8 miles

- Lets calculate the distance of Jim from the State College till his

 position at 1 p.m

∵ Jim lives three miles east of State College

∴ His distance at 1 p.m = 3 + 2 = 5 miles east

- Lats calculate the distance of Annie from the State College till her

 position at 1 p.m

∵ Annie lives four miles north of State College

∴ Her distance at 1 p.m = 4 + 8 = 12 miles North

- Lets find the distance between them at 1 p.m

∵ The north ⊥ east

- Use Pythagoras Theorem to find the distance

∴ The distance = √(5² + 12)² = √(25 + 144) = √169 = 13 miles

- The rate = distance/time

∵ The distance between them is 13 miles in 1 hour

∴ The rate = 13/1 = 13 miles per hour

* The rate is 13 miles per hour

To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.

Original equation:

y = 2x + 17

Switched:

x = 2y + 17

Solve for y by isolating it:

x - 17 = 2y + 17 - 17

x - 17 = 2y

(x - 17)/2 = 2y/2

[tex]\frac{1}{2}x-\frac{17}{2}= y[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y = - 6x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{6}[/tex] x + 3 ← is in slope- intercept form

with slope m = [tex]\frac{1}{6}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6, hence

y = - 6x + c ← is the partial equation of the perpendicular line.

To find c substitute (- 3, 23) into the partial equation

23 = 18 + c ⇒ c = 23 - 18 = 5

y = - 6x + 5 ← equation of perpendicular line

Answer:

800 milliliters

Step-by-step explanation:

we know that

To find out the total amount Kelly drank, add the amount of coffee and the amount of yogurt and convert the result to milliliters.

so

0.5+0.3=0.8 liters

Remember that

1 liter= 1,000 milliliters

so

0.8 liters=0.8*1,000=800 milliliters

Answer:

800 mL

Step-by-step explanation:

Because we know that

1 liter equals 1000 milliliters

So 0.5+0.3=0.8

0.8 Liters=0.8*1,000 ML

Answer:

it must be 9

Step-by-step explanation:

it is a simple division.

Answer:

There are 97920 ways to formed the committee

Step-by-step explanation:

* Lets solve explain the combination

- combination is a collection of the objects where the order doesn't

 matter

- Combinations is nCr, where n is the total number and r is the number  

 of the choices

# Example: chose a group of three students from the group of 10

  students  n = 10 and r = 3,then 10C3 is 120

* Lets solve the problem

- The club has 30 members

- There are 3 lawyers, 4 teachers , 5 doctors in the group

- We want to formed a committee of 8 contains 1 teacher, 2 lawyers,

  2 doctors

∵ There are 4 teachers, we want to chose 1 of them

∴ 4C1 = 4

∵ There are 3 lawyers, we want to chose 2 of them

∴ 3C2 = 3

∵ There are 5 doctors, we want to chose 2 of them

∴ 5C2 = 10

- To find how many ways multiply 4C1 by 3C2 by 5C2

∵ 4C1 × 3C2 × 5C2 = 4 × 3 × 10 = 120

∵ The total numbers of the teachers, the lawyers and the doctors is

   4 + 3 + 5 = 12 members from the 30 members

∴ There are 120 ways to chose 5 members from 12 members

∵ The committee has 8 members

∴ We want to chose another 3 from the rest of the members

∵ The rest of the members = 30 - 12 = 18

∴ We must to find 18C3

∵ 18C3 = 816

- To find the total ways of the 8 members multiply the ways of the 5

  members and the 3 members

∴ The total number of ways = 120 × 816 = 97920

∴ There are 97920 ways to formed the committee

Answer:

D. Negative slope

Step-by-step explanation:

Since it is a proportional relation, it must be linear. A line has a slope. Since it is decreasing, it is a negative slope.

Answer:

4 units

Step-by-step explanation:

just took a quiz and got it right

Answer: 4

Step-by-step explanation:

took the test

Answer:

B. 43.3 cm

Step-by-step explanation:

The formula for the circumference of a circle is [tex]2 \pi r[/tex] if you want it in terms of the radius but you can also say the circumference is [tex]d \pi[/tex] if you want it in terms of the diameter since you know the radius is twice the diameter.

So we are actually given the diameter which is 13.8 cm.

So the Circumference is just pi times that.

So I'm going to put pi times 13.8 in my calculator and select the closest answer.

13.8*pi=43.35 cm.

Answer:

the answer is B

Step-by-step explanation:

Answer:  The expressions for the length and width of the new patio are

[tex]\ell=x+4,~~w=x-4.[/tex]

And the area of the new patio is 384 sq. feet.

Step-by-step explanation:  Given that Stephen has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.

The length of one side of the square patio is represented by x.

We are to write the expressions for the length and width of the new patio and then to find the area of the new patio if the original patio measures 20 feet by 20 feet.

Since Stephen wants to reduce width of the patio by 4 feet, so the width of the new patio will be

[tex]w=(x-4)~\textup{feet}.[/tex]

The length of the patio is increased by 4 feet, so the length of the new patio will be

[tex]\ell=(x+4)~\textup{feet}.[/tex]

Now, if the original patio measures 20 feet by 20 feet, then we must have

[tex]w=x-4=20-4=16~\textup{feet}[/tex]

and

[tex]\ell=x+4=20+4=24~\textup{feet}.[/tex]

Therefore, the area of the new patio is given by

[tex]A_n=\ell \times w=24\times16=384~\textup{sq. feet}.[/tex]

Thus, the expressions for the length and width of the new patio are

[tex]\ell=x+4,~~w=x-4.[/tex]

And the area of the new patio is 384 sq. feet.

Final answer:

Stephon is altering his square patio's dimensions by reducing the width by 4 feet and increasing the length by 4 feet. For an original side length of 20 feet, the new dimensions are 24 feet by 16 feet, resulting in an area of 384 square feet.

Explanation:

Stephon has a square brick patio and is planning on changing its dimensions. Initially, the patio is a square with each side measuring x feet. To find the expressions for the new length and width of the patio after the alterations:

Given that the original side length of the patio is 20 feet, we can substitute this value into the expressions:

To find the area of the new patio, multiply the new length by the new width:

Area = Length × Width = 24 feet × 16 feet = 384 square feet.

Answer:

1. Dispersion: how data is distributed

2. Inter quartile range:the difference between the largest and smallest of the middle 50% of the data set

3. Lower Quartile:the median of the lower half of the data set; a value which 25% of the data set falls below

4. Outlier:a data value that is far from the others

5. Percentile: a value below which a certain percentage of the data set falls; the median is the 50th percentile.

6. Range:the difference between the largest and smallest of the numbers in a set

7. Upper Quartile:the median of the upper half of the data set; a value which 75% of the data set falls below

Final answer:

In statistics, 'dispersion' refers to the distribution of data, the 'inter-quartile range' is the spread of the middle 50% of data, 'lower quartile' (Q1) is the value below which 25% of data falls, an 'outlier' is a data point far from the others, 'percentile' is a value below a certain percentage of data, 'range' is the difference between the largest and smallest data values, and 'upper quartile' (Q3) is the value below which 75% of the data falls.

Explanation:

To correctly match the terms to their definitions from the provided options:

Dispersion is matched to 'how data is distributed.'

Inter-quartile range (IQR) is 'the difference between the largest and smallest of the middle 50% of the data set.'

Lower quartile (also known as the first quartile or Q1) is 'the median of the lower half of the data set; a value which 25% of the data set falls below.'

Outlier is 'a data value that is far from the others.'

Percentile is 'a value below which a certain percentage of the data set falls; the median is the 50th percentile.'

Range is 'the difference between the largest and smallest of the numbers in a set.'

Upper quartile (also known as the third quartile or Q3) is 'the median of the upper half of the data set; a value which 75% of the data set falls below.'

Answer:

x + 5y = 7

Step-by-step explanation:

You can find which one is correct by plugging in -3 for each x value and then solving for y.

x + 5y = 7

(-3) + 5y = 7

5y = 10

y = 2

When x = -3, y=2

(2) + 5y = 7

5y = 5

y = 1

When x=2, y=1

The equation of straight line that represents a line that passes through points (−3, 2) and (2, 1) is Option (D) x + 5y = 7.

The equation of a straight line passing through the points (x1,y1) and (x2,y2) and having slope m is given by -

y - y1 = m(x - x1) .

The slope m, can be calculated as m =  (y2 - y1)/(x2 - x1) .

Thus the equation of straight line in slope intercept form is -

[tex]y - y1 = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

Given points are (-3,2) and (2,1) .

We have x1 = -3 , x2 = 2 , y1 = 2 , y2 = 1

Slope (m) = (1 - 2)/(2 - (-3)) = -1/5

Putting the required values to find the equation of straight line in slope intercept form -

⇒ y - 2 = (-1/5)*(x - (-3))

⇒ (y - 2)*5 = -1*(x + 3)

⇒ 5y - 10  =  -x - 3

∴  x  +  5y = 7

The required equation is Option (D) x + 5y = 7.

Thus, the equation of straight line that represents a line that passes through points (−3, 2) and (2, 1) is Option(D) x + 5y = 7.

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Answer:

[tex]5 {x}^{2} + 9x - 1[/tex]

Step-by-step explanation:

A quadratic expresion is of the form

[tex]a {x}^{2} + bx + c[/tex]

where

[tex]a \ne0[/tex]

The give options are:

[tex]9x-2[/tex]

[tex]5{x}^{2}+9x - 1[/tex]

[tex]-2x^3+8 {x}^{2} -7x +1[/tex]

[tex]x^4-12x^3+8 {x}^{2} -7x +1[/tex]

From the given options, the only expression which is quadratic is

[tex]5 {x}^{2} + 9x - 1[/tex]

where a =5, b=9 and c=-1

Therefore the correct choice is the second option.

The quadratic expression is [tex]\(5x^2 + 9x - 1\),[/tex]  as it has the highest degree of 2 among the given options. :

A quadratic expression is a polynomial of degree 2, which means the highest power of [tex]\(x\)[/tex]  in the expression is  [tex]\(x^2\).[/tex]

Let's examine the given expressions:

1. [tex]\(9x - 2\)[/tex]  - This is a linear expression (degree 1).

2. [tex]\(5x^2 + 9x - 1\)[/tex]  - This is a quadratic expression (degree 2).

3. [tex]\(-2x^3 + 8x^2 - 7x + 1\)[/tex]  - This is a cubic expression (degree 3).

4. [tex]\(x^4 - 12x3 + 8x^2 - 7x + 1\)[/tex]  - This is a quartic expression (degree 4).

Therefore, the expression that represents a quadratic expression is:

[tex]\[5x^2 + 9x - 1\][/tex]

So, the correct choice is [tex]\(5x^2 + 9x - 1\).[/tex]

Answer:

A.2sinxcosx

Step-by-step explanation:

We know the trig identity

Sin (2a) = 2 sin a cos a

sin (2x) = 2 sin x cos x

Answer:

2sinxcosx

Step-by-step explanation:

A P E X

Answer:

Proof is in the explanation.

Step-by-step explanation:

I'm going to use mathematical induction.

That means we are going to show:

1) For n=3 the expression given is a multiple of 6. (We started at n=3 because it says n>2.)

2) If the base cases check out, then we are going to assume (n-2)(n-1)(2n-3) is a multiple of 6, then show ([n+1]-2)([n+1]-1)(2[n+1]-3) is also a multiple of 6.

-----------------------------------------------------------------------------------------

Proof:

Base case (n=3):

(3-2)(3-1)(2*3-3)

1(2)(6-3)

2(3)

6

6 is a multiple of 6 since 6(1)=6.

After the base case (for all natural numbers greater than 2):

Assume there is integer k such that:

6k=(n-2)(n-1)(2n-3).

We are going to show 6m=([n+1]-2)([n+1]-1)(2[n+1]-3) where m is a integer.

([n+1]-2)([n+1]-1)(2[n+1]-3)

(n-1)(n)(2n-1)

(n-2+1)(n)(2n-1)

(n-2)(n)(2n-1)+1(n)(2n-1)

(n)(n-2)(2n-1)+1(n)(2n-1)

(n-1+1)(n-2)(2n-1)+1(n)(2n-1)

(n-1)(n-2)(2n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-1)(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-3+2)(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-3)(n-2)(n-1)+2(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

6k+2(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

6k+2(n^2-3n+2)+1(2n^2-5n+2)+2n^2-n

6k+6n^2-12n+6

6(k+n^2-2n+1)

where k+n^2-2n+1 since integers are closed under addition and multiplication (referring to the n^2, the n*n part).

Since we have found an integer m, k+n^2-2n+1, such that

6m=([n+1]-2)([n+1]-1)(2[n+1]-3)

then we have shown for all integers greater than 2 we have that

(n-2)(n-1)(2n-3) is divisible by 6.

//

the answer is 63 because 63*2=126 and 126+54=180 and all triangles add up to 180

Answer:

B) 63 degrees

Step-by-step explanation:

All triangles equal up to 180 degrees so you would subtract the lengths you are given by 180.

So 180 - 54 = 126

Now you would divide 126 by 2 since this is an isosceles triangle. Isosceles triangles have two equal sides so 126 divided by 2 equals 63 degrees.

So y = 63 degrees

Answer:B 42

Step-by-step explanation:

V=pi/4 x D^2 x H

3.14/4 x 36 x 1.5 = 42 ft^3

Answer:

B) 42

Step-by-step explanation:

The area of a cylinder is pi*r^2*h where r is the radius and h is the height. Plugging in 3 for the radius(radius=diameter/2) and 1.5 for height you get area=pi*9*1.5. Assuming pi as 3.14 you get 3.14*9*1.5 which is 42.39 which is approx. 42.

Answer:

1.584

Step-by-step explanation:

1.584 = 3.96 × 0.4

Answer:

3.96*0.4 is 1.584

Answer:

[tex]\huge \boxed{y=-2}[/tex]

Step-by-step explanation:

First thing you do is switch sides.

[tex]\displaystyle 2y-3=-7[/tex]

Then add 3 from both sides of equation.

[tex]\displaystyle 2y-3+3=-7+3[/tex]

Simplify.

[tex]\displaystyle 2y=-4[/tex]

Divide by 2 from both sides of equation.

[tex]\displaystyle \frac{2y}{2}=\frac{-4}{2}[/tex]

Simplify, to find the answer.

[tex]\displaystyle -4\div2=-2[/tex]

[tex]\large \boxed{y=-2}[/tex], which is our answer.

Hope this helps!

−7=2y−3

Step 1: Flip the equation.

2y−3=−7

Step 2: Add 3 to both sides.

2y−3+3=−7+3

2y=−4

Step 3: Divide both sides by 2.

2y/2=-4/2

y=−2

Answer:

Step-by-step explanation:

note :

the area of a circle  is : A= π×r²    ....r : radius and : D=2r   ... D : diameter

47) D = 10 cm      r= 10cm/2 = 5 cm

A=π×r²  = 3.1448×5²  =78.62cm²

48) A= 3.1448×2²= 12.58cm²