Solve the equation using the method of factorisation-
x2 - 4x - 45 = 0

x² + 4x -9= (x + a)^2 + b
Find the value of a and the value of b.

Answers

Answer 1

Answer:

X = 9,X= -5, a =  2, b = -13

Step-by-step explanation:

For (1),

Using Cross-factorization,

it can be reduced to (X - 9)(X + 5) = 0

Equate each factor to 0:

we have X = 9 and X = -5

For (2),

It is the case of completing the Square,

add 4 so we get the completed square ( we want the form X^2 + 2a + a^2)

(X^2 + 4X + 4) - 9

can be simplified to (X+2)^2 -9

However since we added 4 it means we have to subtract 4

So it becomes (X+2)^2 -9 -4

= (X+2)^2 -13


Related Questions

what property of equality is used to isolate the term with variable in the equation 2 x + 2 = 4?
A. Addition property
B. Reflexive property
C. Multiplication property
D. Transitive property
(it will help me a lot)​

Answers

Answer:

I think it is addition property

Addition property (A)

I need help please!!

Answers

Answer:

3 1/4 + 4 2/5 + 6 1/2 = 14.15 hours

Step-by-step explanation:

If the graph of the second equation in the system passes through the points (-12, 20) and
(4, 12), which statement is true?

Answers

answer: the system had no solution

For rhombus GHJK, find m21.

Answers

half angle K is 30 and the center is 90 so that half angle J is 60 and angle H is equal to angle K so half of H is 30 so that half of G is 60

m<1 =60

Which rational number is NOT greater than point A?
Answers:
2 1/4
1.95
2.05
1 6/24

Answers

The answer is 21/4 u think

PLS HELP ME!! :((

Find the volume, given that the apothem is 11.3 in. (hint: remember for regular polygons, A = 2 (apothem) (Perimeter) Round your answer to the nearest - tenth.

Answers

Answer:

V = 3085 in³

Step-by-step explanation:

The volume is given by:

[tex] V = A*h [/tex]

Where:

A: is the area

h: is the height = 7 in

The area of the polygon can be found by using the given equation:

[tex] A = \frac{1}{2}a*p [/tex]

Where:  

a: is the apothem = 11.3 in

p: is the perimeter

The perimeter is:

[tex] p = 13*6 = 78 in [/tex]      

Hence, the volume is:

[tex] V = A*h = \frac{1}{2}a*p*h = \frac{1}{2}11.3 in*78 in*7 in = 3085 in^{3} [/tex]  

     

I hope it helps you!                      

y∝1√x
If
y=7 when x=64
find,
x when y=8

Answers

Answer:

uhm im really sorry about this but i really need points i would help but id get it wrong im bad aat math

Step-by-step explanation:

Please Help me!!! with this problem

Answers

9514 1404 393

Answer:

  D  120

Step-by-step explanation:

We are given the relation ...

  48 = 0.40 × sales

Dividing by 0.40 gives the sales for the day.

  sales = 48/0.40 = 120

120 milkshakes were sold that day.

Find the slope of the line passing through the points (6, 7) and (6, -5).

Answers

Answer:

undefined

It is undefined because if you put it on a graph you get a line going straight down.

How many pints are in 6.5 gallons?

Answers

Answer:

52 pints in 6.5 gallons.

Step-by-step explanation:

6.5 *8= 52

Answer:

52 pints

Step-by-step explanation:

6.5 * 8 = 52

(*8 because there are 8 pints in a gallon)

in Enter a number into each box to create
an equation that has exactly no real solution.
3(2x+5)-X =

2) Enter a number into
each box to create an
equation that has exactly one real solution.
19x -(5x+9)+7=

Answers

Answer: 5X+15

The first one is

The second one is 2(7X+8)

Plssss helppppppl:((((

Answers

Answer:

I think it's 1.5 I'm not sure ._.

Answer:

1/3

Step-by-step explanation:

Total students = 36

No of boys = 24

No of girls = 36 - 24 = 12

Probability of selecting a girl = 12/36 = 1/3

Please try, I’ll give Brainliest, and 70 points to the one who answers this
It’s due tomorrow so answers ASAP

Answers

What’s the question?

Please help me with number 6

Answers

x-4=y so when x is 40 then y will be 36
It’s gonna be 36 I think

x:y=5:3 and x+y=56 work ouy the value of x and y​

Answers

Answer:

x=35, y=21

Step-by-step explanation:

A way to rewrite the first equation is  [tex]\frac{x}{y} =\frac{5}{3}[/tex]

after cross-multiplying, we get 3x=5y.

If we solve for one variable, we can substitute it into the other equation.

Let's solve for x.

3x=5y

x=(5/3)y

Now, we can substitute x=(5/3)y in the equation x+y=56.

(5/3)y+y=56

(8/3)y=56

y=21

Going back to x+y=56, we can now plug back in y, knowing that it is 21.

x+21=56

x=35.

jim began to bike a 173 mile bicycle trip to build up stamina for a for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 5 hours. If Jim walks at a rate of 4 miles per hour and rides at the rate of 38 miles per hour , find the amount of time he spent on the bicycle

Answers

Answer

3.5 hours

Step-by-step explanation:

Let us represent

The time spent walking as x

The time spent riding as y

Jim began a 146​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 5 hours.

Hence:

x + y = 5.... Equation 1

x = 5 - y

If Jim walks at a rate of 4 miles per hour and rides at 40 miles per​ hour,

The formula for Distance = Speed × time. Hence,

4 × x + 40 × y = 146 miles

4x + 40y = 146.... Equation 2

We substitute 5 - y for x in Equation 2

4(5 - y) + 40y = 146

20 - 4y + 40y = 146

Subtract 20 from both sides

20 - 20 - 4y + 40y = 146 - 20

- 4y + 40y = 146 - 20

36y = 126

y = 126/36

y = 3.5 hours

Since the time he spent raiding his bicycle is represented by "y", the amount of time he spent on the bicycle is 3.5 hours      

I think this is right I had this question I think it was the same one I dont know tho

Which of the following could not be a cross section of a rectangular prism?

A. Rectangle
B. Circle
C. Parallelogram
D. Triangle

Answers

B cause it has not vertexes

Answer:

B

Step-by-step explanation:

Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?"

Answers

Answer:

$3.25

Step-by-step explanation:

Given that:

Mean, λ = 1.4

Strike within next minute = $3 won

Strike between one and 2 minutes = $5

Strike more than 2 minutes = $1

Probability that next strike occurs within the next minute :

Using poisson :

P(x < 1) = 1 - e^-(λx) ;

P(x < 1) = 1 - e^-(1.4*1) = 1 - e^-1.4

P(x < 1) = 1 - 0.2465969

P(x < 1) = 0.7534030

Next strike occurs between 1 and 2 minutes :

(1 < x < 2) :

P(x < 2) - P(x < 1)

P(x < 2) = 1 - e^-(λx) ;

P(x < 2) = 1 - e^-(1.4*2) = 1 - e^-2.8

P(x < 2) = 1 - 0.0608100

P(x < 2) = 0.9391899

P(x < 2) - P(x < 1)

0.9391899 - 0.7534030 = 0.1857869

P(striking after 2 minutes)

P(x > 2) = e^-(λx) ;

P(x > 2) = e^-(1.4*2) = e^-2.8

P(x > 2) = 0.0608100

Amount charged :

(0.7534030 * 3) + (0.1857869 * 5) + (0.06081 * 1)

= 3.2499

= $3.25

Trying to help my daughter can't figure this out.

The perimeter of a rectangle is 72 meters. The width of the rectangle is 4meters less than the length. Find the length and width of the rectangle. (use l for the length)​

Answers

Answer:

width equals 16

length = 20

Step-by-step explanation:

Hello there!

we know that the perimeter is 72 m

and the width is 4 m less then the length

perimeter is 2w+2l

w=width and l = length

72 + (2x-4) = 72+8 = 80

80 / 4 (because there are 4 values, w, w, l, l ) = 20

so now...

20 - 4 = w

16 = w

and 20 = l

16+16 = 32

20+20 = 40

32+40 = 72

solve (x+5)/3 = 4 for x

please help asap

Answers

Answer:

x=7, because 7 plus 5 is 12 and 12 divided by 3 is 4

Step-by-step explanation:

7+5=12/3=4

i will love you if u please answer this question PLSS

Answers

Answer:

On the dive boat deck

Step-by-step explanation:

This is above the water level and water level is considered to be 0

pls love me <3

There are 40 people in a choir.
Half of the people in the choir are women.
The number of women in the choir is 5 times the number of
men in the choir.
The rest of the people in the choir are children.
the number of
children in the
choir
:
the number of
men in the choir
n : 1
Work out the value of n.
You must show how you get your answer.
n =

Answers

9514 1404 393

Answer:

  n = 4

Step-by-step explanation:

Of the 40 people, half are women, so there are 20 women.

There are 5 times as many women as men, so 20/5 = 4 are men.

The remainder are children, so there are 20-4 = 16 children.

The ratio of children to men is ...

  children : men = 16 : 4 = 4 : 1 = n : 1 . . . . . . . . remove a factor of 4 from 16:4

The value of n is 4.

Kai can wrap 42 gifts in 3 hours. Answer the following questions, assuming that Kai can continue wrapping gifts at that same rate. How many gifts can Kai wrap in 24 hours? _______________ How many hours would it take him to wrap 126 gifts? _______________ How many gifts does Kai wrap per hour? _______________

Answers

Answer:

1. 336

2. 9

3. 14

Step-by-step explanation:

He wraps 42 gifts/3hours

24 hours is 8 "3 hours"

42 hours per 3 gifts * 8 "3 hours" = 336 gifts

126 gifts is 3 "42 gifts"

3 hours per 42 gifts * 3 "42 gifts" = 9 hours

He wraps 42 gifts/3hours

divide these values by 3 and you get  14 gifts/one hour

14 gifts every one hour

Leon older brother is 4 and 3/4 feet tall Leon is 1/3 foot shorter than his brother how tall is Leon

Answers

Answer:

4 5/12 feet tall

Step-by-step explanation:

All you have to do is subtract 1/3 from 4 and 3/4 in order to get this answer.

Answer:

Leon is 53/12 feet or 4 & 5/12 or 4.4167 (same answer different forms)

Step-by-step explanation:

Leon older brother is 19/4 feet tall or 57/12.

Leon is 1/3 or 4/12 foot shorter than his brother.

57/12-4/12= 53/12

HURRY!!!!
What is the volume, in cubic inches, of the right rectangular prism with a length of 5 inches, a width of 8 inches, and a height of 20 inches

Answers

Answer:

800 cubic inches

Step-by-step explanation:

We will use the formula= V=lwh or Volume= length times width times height

so, Volume=5inches times 8 inches times 20 inches

so, volume= 5 times 8 times 20

=40 times 20

=800 cubic inches

Please mark me as a brainliest

Answer:

800

Step-by-step explanation:

Following are weights, in pounds, of two-month-old baby girls. It is reasonable to assume that the population is approximately normal.

12.32 11.87 12.34 11.48 12.66
8.51 14.13 12.95 9.34 8.63

Required:
a. Construct a interval for the mean weight of two-month-old baby girls.
b. According to the National Health Statistics Reports, the mean weight of two—month-old baby boys is 13.9 pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two-month—old baby girls may be the same as that of two-month-old baby boys? Explain.

Answers

Answer:

10.224 < μ < 12.622 ;

Since the mean weight of 2-montj old baby boys (13.9) falls outside the confidence interval, we can conclude that it is not reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys.

Step-by-step explanation:

The confidence interval is given as :

Mean ± Margin of Error

margin of error = Zcritical * standard deviation /sqrt(n)

n = sample size

From the data:

12.32, 11.87, 12.34, 11.48, 12.66, 8.51, 14.13, 12.95, 9.34, 8.63

From the data:

Using calculator :

Mean, = 11.423

Standard deviation, s = 1.934

Zcritical at 95% confidence interval = 1.96

Sample size, n = 10

Margin of Error = 1.96* 1.934/sqrt(10) = 1.199

Lower boundary = 11.423 - 1.199 = 10.224

Upper boundary = 11.423 + 1.199 = 12.622

10.224 < μ < 12.622

Since the mean weight of 2-montj old baby boys (13.9) falls outside the confidence interval, we can conclude that it is not reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys.

Find the area inside the square and outside the circle. ​(Simplify your answer. Type an exact answer in terms of pi​.)

Answers

9514 1404 393

Answer:

  (676 -169π) ft²

Step-by-step explanation:

The area of the square is ...

  A = s² = (26 ft)² = 676 ft²

The area of the circle is ...

  A = πr² = π(13 ft)² = 169π ft²

Then the shaded area is ...

  (676 -169π) ft²

round 38.68 to the nearest hundred​

Answers

38.68 is rounded to the nearest hundredth

(15x-7)-(23x-2)
use foil​

Answers

Answer:

=15x-7-23+2

=-8x-7+2

=-8x-5

Step-by-step explanation:

Evaluate the expression x (3) – (3 + x)2 for x = 4.

Answers

Answer:

if x=4, the answer is -2.

Step-by-step explanation:

4x3-(3+4)2

12-7x2

12-14

= -2

i hope this helps :)

Other Questions
Convert 678.92 cm into meters 2x + 3y = 16 3x + 4y = 22System of Equations Which of the following is a good example of a verbal cue?A.) a repeated imageB.) a numbered listC.) a bolded headingD.) a highlighted word LMN is a right-angle triangle. Angle NLM=90. PQ is parallel to LM. The area of triangle PNQ is 8cm^2. The area of triangle LPQ is 16cm^2. Work out the area of triangle Help with homework pls Why did some colonists support England and oppose independencepls help Please help me with the questions please ASAP The following extract is missing four commas. Insert them in the appropriate places.The meadow which was covered with yellow, blue and white flowers was a beautiful sight. The native grasses were thriving because the whole area, barring only the pasture had become a registered nature reserve. In fact, it was so pretty that I tried to take a picture, but then I saw that my phone battery had died. Disappointed I walked back to the hotel to recharge it. A set of 25 cards are shown.what is the probability of choosing a card with a sheep on it? what is the area of this trapezoid? simplify it the following:X u ( X n Y ) Write an expression for the area of the gym.Write an expression for the area of the cafeteria Explain how the crash of 1929 brought the roaring 20's to an end 5 1/3 is what percent Tarzan is making his mom a card for her birthday. He drew a model of the card before he created it. The model is shown below.The front of the card is shown. If Tarzan covers the whole front side of the actual card with decorative paper, how much paper would he need? you may use exact answers or round to the nearest hundredth. que se selebra en semana santa What is the area?6 cm4 cm4 cm:) assign an oxidation number to each element in the following species. H2O According to the author of "The Case of the Missing Bees," why are bees important to the environment? A. Bees will only sting if they feel threatened. B. Many plants, including those that produce our food, rely on the bees. C. Some pesticides are poisonous to bees. D. When forced, the bees will leave their homes and their queen, and sometimes they will not return. Which expression could help you find the distancebetween (10, 4) and (-6,4)?O |10+ |-41O |10| + 141O |-6] + 141O |10| + |-61