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The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3

Given,

x - intercepts = (−3,0) and (1,0).

The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

Quadratic equations;-

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

Here,

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

y = x² + 2·x - 3 and y = -x² - 2·x + 3

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Answer:

i) Mean = 1933.1817

ii) Range = 5684

iii) Third quartile = 6054

Step-by-step explanation:

Given data :

currency exchange rate : 1 AUD = 5.8 HKD

cost of each ounce = 2 AUD

Fixed shipping cost for each carton = 80 HKD

number of cartons = 20

next determine the total cost of the 20 cartons in HKD

= ∑(weight in ounce * cost of each ounce *exchange rate) +fixed shipping cost

= ∑ ( 160*2*5.8 + 80 )  + -------------- + (650 *2*5.8 + 80 ) ----------------- ( 1 )

= 81756 HKD

i) find the mean value ( X )

= Total cost / number of cartons

= 81756 / 20 = 4087.8

ii) Find the standard deviation

= \(\sqrt{\frac{(1936-4087.8)^2+-----+(7620-4087.8)^2}{20-1} }\)      note: std =  √∑(xi-X )^2 / (n-1)

= 1933.1817

iii) Find the range

Range = highest cost - lowest cost   ( values gotten from equation 1 )

           = 7650 - 1936

           = 5684

iv) Determine the third quartile

third quartile = 6054

attached below is the detailed solution

The ordered list is:

Answer:

Step-by-step explanation:

4/mx

Answer:

(A) on edge

He did not distribute the 2 to both components of vector u.

Step-by-step explanation:

The -8 in his work did not change to -16 as it should if it was multiplied by 2

Correct on edge

Answer:

it's a

Step-by-step explanation:

Answer:

3a + 2b + 4c = D

D = Amount Spent

Step-by-step explanation:

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

2x+4=18

2x=14

x=7

.........

Answer:

20

Step-by-step explanation:

(25-5)/(1-0)

20/1

20

Answer:

20

Step-by-step explanation:

use y2-y1/x2-x1 by finding 2 points on the graph

(0,5) and (2,45)

45-5/2-0

40/2

20

Hopes this helps please mark brainliest

The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

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Answer:

10 to the third power is 10x10x10 which is 1000. So you do 0.15 x 1000 which equals 150. So the answer is 150

Step-by-step explanation:

Jordan's canonical form can be written in a matrix as follow:

Calculate the eigenvalues of the given polynomial which are 0, 3, 5.

Calculate the algebraic multiplicity of the eigenvalues which are 1, 2, 2 respectively. Create a matrix B in Jordan canonical form with dimensions of 5x5.

Fill the diagonal elements of the matrix with eigenvalues.

Fill the upper off-diagonal elements with ones and lower off-diagonal elements with zeros.

The final matrix B in Jordan canonical form is as follows:

B =

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 3 1 0]

[0 0 0 3 0]

[0 0 0 0 5]

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Once the apartment complex have been turned to a parking area, the total parking area will be 1620 square units

From the complete question, the parking area consists of the following shapes and dimensions

The area of a rectangle is the product of its dimensions.

So, the area of the parking area is:

Area = 28x40 + 20x25

Evaluate the products

Area = 1120 + 500

Evaluate the sum

Area = 1620

Hence, the total area of the parking area is 1620 square units

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Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

Answer:

1. W=19, L=12

2. Next year Stephanie will be 14 and her Brother will be 6

3. 8, 9, 10

Step-by-step explanation:

1.

(a) W = 2L -5 => W - 2L = -5

(b) 2W + 2L = 62

Making (a)+(b):

3W = 57 => W = 19

from (a): L = (W+5)/2 = 12

2.

Today: S = 2B + 3 => S - 2B = 3 (a),

where S and B are Stephanie and Brother current age

2 years ago: (S-2) + (B-2) = 14,

so S + B = 14 + 4

S + B = 18 (b)

(a) - (b):

-3B = -15 => B = 5

from (a) S = 13

Verification:

2 years ago Stephanie was 11 and Brother was 3, the sum was 14, ok.

Next year Stephanie will be 14 and her Brother will be 6

3. We will find integers: s, m and b:

they are consecutive, so:

m = s+1

b = m+1 = s+2

and:::

s + 2m = b + 16 (a)

In (a) let's express all in terms of s:

s + 2(s+1) = s+2 + 16 =>

2s + 2 = 2 + 16 => s = 8, m=9, b=10

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

We can simplify the expression as follows:

4^3 * 4^4 / 4^9

First, we can simplify the terms in the numerator by adding the exponents of 4:

4^3 * 4^4 = 4^(3+4) = 4^7

Now, we can substitute this value in the expression:

4^7 / 4^9

To divide powers with the same base, we can subtract their exponents:

4^(7-9) = 4^(-2)

Therefore, the simplified expression is:

4^3 * 4^4 / 4^9 = 4^(-2)

So, the final answer is 1/16 or 0.0625.

The correct way of writing the equation of the line that passes through the points are y = -3x - 5.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

The slope-intercept form, point-slope form, and standard form are the three primary types of equations. These equations provide sufficient details about the line to make graphing them simple.

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Answer:4 hours

Step-by-step explanation:

7 divided by 5= 1.4

1.4x4=5.6

Answer:

Step-by-step explanation:

y=3√x

domain : all real values≥0

Answer:

Step-by-step explanation:

you want to use the slope intercept formula,  and you may as well remember this,  you'll need it often  

y = mb + b

where m = the slope of the line. and is , for later math , the derivative :) any way

perpendicular means going perfectly across, and also the slope is a reciprocal of the line we are going orthogonal to  ( another way of saying perpendicular, but more for 3D things. )

y = 1/3 x - 3

we want the 1/3  and then the reciprocal  so  3/1 or just 3  and then the negative of that so -3   :)  

now use the point given (3,2) to choose where the ling passes thur the y axis. so when x=3 , then y = 2, use the point slope formula

y - y1 = m(x-x1)

now plug in the given point and the slope that was figured out

y-2 =-3(x-3)    (distribute the 3 and move the 2 over )

y = -3x +9 +2

y = -3x +11  

that's a perfectly fine perpendicular line to the given line.

Answer: 0.16

Step-by-step explanation:

Let X be a random variable that represents the heights of women at a large university are approximately bell-shaped, with a mean of 66 inches and standard deviation of 3 inches.

According to the Empirical Rule, for bell-shaped distributions, about 68% of the values fall within 1 standard deviation of the mean.

About 68% woman have height between ( 66-3) inches and (66+3) inches.

i.e. About 68% woman have height between 63 inches and 69 inches.

The percentage of woman have height either less than 69 inches or greater than 69 inches =100% - 68%= 32% [both share equal area on curve.]

The percentage of woman have height  is 69 inches or taller = 32%÷2

= 16%

Hence, the probability that a randomly selected woman from this university is 69 inches or taller =16%=0.16

Answer: 7.5

Step-by-step explanation:

5x3 = 15 A = 1 half L x H

A = (3)(5)

A = 15

A =  15 x 1 half = 7.5

correct me if i am wrong.

Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

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The line segment FG represent the volume of water decreases in Katherine's water bottle.

From the given graph, x-axis represents the distance from home (km) and the y-axis represents the volume (L).

The line segment FG represent the volume of water decreases in Katherine's water bottle, the line segment HI represent the volume of water increases in Katherine's water bottle and the line segment KL represents there is no change in water level.

Therefore, the line segment FG represent the volume of water decreases in Katherine's water bottle.

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Answer:

D on edge 2022
all real numbers except -1 and 1

Step-by-step explanation:

The outlier in this data set is the sweatshirt priced at $18 since it is significantly higher than the rest of the prices.

The mean is affected more by outliers than the median.

In the provided data, the mean is higher than the median, which suggests that there may be an outlier pulling the average up. The outlier value of $18 is causing the mean to be higher.

If we remove the outlier value of $18, the mean price would be (6+12+11+15)/4 = $11, which is lower than the original mean of $12.40.

On the other hand, the median would remain the same since it is not affected by extreme values.

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x = 20

Hi there !

we have opposite angles =>

2 + 3x = 62

3x = 62 - 2

3x = 60

x = 60 : 3

x = 20

Good luck !