find the values of a and b such that x squared-4x+9= (x+a) squared+b

Answers

Answer 1

Answer:

a = - 2, b = 5

Step-by-step explanation:

expand the right side using FOIL and compare the coefficients of like terms on both sides.

(x + a)² + b

= x² + 2ax + a² + b

compare terms with x² - 4x + 9

coefficients of x- term

- 2a = 4 ( divide both sides by - 2 )

a = - 2

compare constant terms

a² + b = 9

(- 2)² + b = 9

4 + b = 9 ( subtract 4 from both sides )

b = 5


Related Questions

Dumpster #1 contains 45 fewer molded vegetables than dumpster #2. Dumpster #2 contains 80 fewer molded vegetables than dumpster #3. If there are 236 molded vegetables in all the dumpsters combined, how many vegetables are in dumpster #1?

Answers

Answer:

22 vegetables

Step-by-step explanation:

Set the #number of molded vegatables in dumpster 1 as X

The number of molded vegetables in 2 is x + 45 and the number of molded vegies in 3 is x + 45 + 80

x + x + 45 + x + 45 + 80 = 236 (combine similar terms)

         Thats 3x = 66

Which equas 22

Calculate the area of the trapezoid. Use paper to show your work. The figure is not drawn to scale.
12 cm
12 cm
21 cm
The area of the trapezoid is how many cm?

Answers

The area of a trapezium with the given dimensions is: 198 cm²

What is the Area of a Trapezium?

Area of a trapezium = 1/2(a + b)h, where h is the heght of the trapezium and a and b are the length of its bases.

Given the following:

a = 12 cmb = 21 cmh = 12 cm

Area of a trapezium = 1/2(12 + 21)12

Area of a trapezium = 198 cm²

Learn more about the area of trapezium on:

https://brainly.com/question/1463152

Find the Circumference.​

Answers

Answer:

1.

r = 12 m.

d = 24 m.

circumference: 75.36 m² or 24π m²

2.

r = 10 cm.

d = 20 cm.

circumference: 62.8 cm² or 20π cm²

3.

r = 4 dm.

d = 24 dm.

circumference: 25.12 dm² or 8π dm²

Step-by-step explanation:

Circumference of a circle: 2πrπ (pi) = 3.14r (radius) = d/2d (diamater) = 2r

Substitute the the values of the table into the formula:

1.

r = 12 m.

d = 24 m.

circumference: 75.36 m² or 24π m²

2πr

2 * 3.14 * 12

3.14 * 24

75.36 m² or 24π m² <== circumference

12 * 2 = 24 m <== diameter

2.

r = 10 cm.

d = 20 cm.

circumference: 62.8 cm² or 20π cm²

r = 20/2 = 10 cm <== radius

2πr

2 * 3.14 * 10

3.14 * 20

62.8 cm² or 20π cm² <== circumference

3.

r = 4 dm.

d = 24 dm.

circumference: 25.12 dm² or 8π dm²

2πr

2 * 3.14 * 4

3.14 * 8

25.12 dm² or 8π dm² <== circumference

4 * 2 = 8 dm <== diameter

Hope this helps!

7,14,21,28,35, __
Which sentence about the missing number in the Pattern is true?
The missing number ends with a 5.
The missing number is a Multiple of 10.
The missing number is a odd number.
The missing number is a even number.

Answers

Answer:

the patters is that they are multiple of 7.. so next number is 42.

which means option D The missing number is even is correct..

Find the inverse of function f.
1
fir)
-
COIH
r – 2
2
OA. fhr) = 3.5 + 6
3r
OB. 8) = 5x +
5115 1 2 3
OC. 1x) = 3x -
5-1(
OD. 1115) = 3r + 2
.
= 3r
2
3

Answers

Answer:

Step-by-step explanation:

Let's solve for f.

fx=

1

3

x−2

Step 1: Divide both sides by x.

fx

x

=

1

3

x−2

x

f=

x−6

3x

Answer:

f=

x−6

3x

Answer number 1 please thank you

Answers

Answer:

$52.5

Step-by-step explanation:

Since 25% is the sale, we subtract 100% (the whole) by the discount, 25%. That leads us to say that we are paying for 75% of the product's price.

We multiply $70 by 0.75 and you get $52.5!

Please mark brainiest if this helped you!

I need help please!!!

Answers

Answer:

Step-by-step explanation:

Which value of b will cause the quadratic equation x2 bx 5 = 0 to have two real number solutions? –5 –3 3 4

Answers

The value of b for the quadratic equation x2 bx 5 = 0 to have two real number solutions is -5.

When a quadratic equation has two real number solutions?

The standard form of the quadratic equation is,

[tex]ax^2+bx+c=0[/tex]

The quadratic equation has two real number solutions when the value of the following equation is positive.

[tex]b^2-4ac[/tex]

The quadratic equation given in the problem is,

[tex]x^2 +bx+ 5 = 0[/tex]

The value of b has to be found out such that the equation have two real number solutions. For this equation,

[tex]a=1\\c=5[/tex]

Put this value in the above equation as,

[tex]b^2-4\times1\times5\\b^2-20[/tex]

The value of the above expression to be positive, the value of b should be at least 5 or -5.

[tex](-5)^2-20\\25-20\\5[/tex]

Thus, the value of b for the quadratic equation x2 bx 5 = 0 to have two real number solutions is -5.

Learn more about the quadratic equation here;

https://brainly.com/question/1214333

Answer:

Which value of [tex]b[/tex] will cause the quadratic equation [tex]x^2 + bx + 5 = 0[/tex] to have two real number solutions?

✔ A) -5

B) -3

C) 3

D) 4

There one Thing That would got to 0 so it A) -5

Have a Nice Day .

15. If a=3 and b= -2, find the values of:
(i) a^a + b^b
ii) a^b + b^a

Answers

Answer:

Step-by-step explanation:

(i) a^a + b^b

for a=3 and b= -2

3^3 + -2^(-2)

          -2^(-2) = -(1/2^2)

3^3  -(1/2^2)

27 - (1/4)

26 3/4

ii) a^b + b^a

a^b + b^a

for a=3 and b= -2

3^(-2) + (-2)^3

1/3^2 + (-2)(-2)(-2)

1/9 - 8

-7 8/9

In future just substitute the number in

NEED HELP!! WILL GIVE BRAINLIEST!! PLEASE COMPLETE BOTH!

Answers

Answer:

[tex]10 \frac{5}{6}\\\\5 \frac{5}{6}[/tex]

Step-by-step explanation:

[tex]5 \times 2 \frac{1}{6} \\ \\ = 5 \times \frac{13}{6} \\ \\ = \frac{65}{6} \\ \\ = 10 \frac{5}{6} \\ \\ \\ 3 \frac{1}{2} \times 1 \frac{2}{3} \\ \\ = \frac{7}{2} \times \frac{5}{3} \\ \\ = \frac{35}{6} \\ \\ = 5 \frac{5}{6} [/tex]

Consider the first radical :

[tex]{:\implies \quad \sf 5\times 2\dfrac16}[/tex]

Using the properties of mixed fraction, writing the mixed fraction as an improper fraction, we will be having

[tex]{:\implies \quad \sf 5\times \bigg(\dfrac{6\times 2+1}{6}\bigg)}[/tex]

[tex]{:\implies \quad \sf 5\times \bigg(\dfrac{12+1}{6}\bigg)}[/tex]

[tex]{:\implies \quad \sf 5\times \dfrac{13}{6}}[/tex]

[tex]{:\implies \quad \sf \dfrac{65}{6}}[/tex]

[tex]{:\implies \quad \boxed{\bf{10\dfrac56}}}[/tex]

Hence, Option D) is correct

Now, coming to the 2nd question :

[tex]{:\implies \quad \sf 3\dfrac{1}{2}\times 1\dfrac{2}{3}}[/tex]

[tex]{:\implies \quad \sf \bigg(\dfrac{3\times 2+1}{2}\bigg)\times \bigg(\dfrac{3\times 1+2}{3}\bigg)}[/tex]

[tex]{:\implies \quad \sf \bigg(\dfrac{6+1}{2}\bigg)\times \bigg(\dfrac{3+2}{3}\bigg)}[/tex]

[tex]{:\implies \quad \sf \dfrac{7}{2}\times \dfrac{5}{3}}[/tex]

[tex]{:\implies \quad \sf \dfrac{35}{6}}[/tex]

Now, Rewriting this improper fraction as mixed fraction, we will be having :

[tex]{:\implies \quad \boxed{\bf{5\dfrac56}}}[/tex]

Hence, Option C) is correct

what is the interest rate (as a percent)

Answers

Answer:

I didn't understood your question. But,

Formula to find rate of interest=

100/T

Can someone help me with this problem? It’s rlly hard

Answers

Answer:

4(5+8)

Step-by-step explanation:

The GCF of 20 and 32 is 4. Then you divide 20 and 34 by 4.

Part E

Using the dimensions from part D, find the area of each simple shape. Do this for all your decompositions (sets of shapes).

Answers

Answer:

What type of question is this

Answer:

The area of a rectangle is given by A = l × w, where l is the length and w is the width.

The length (l) and width (w) of the small rectangle are 14 feet and 6 feet, respectively, so the area of the small rectangle (As) is:

AS  =  14 ft. × 6 ft.

= 84 sq. ft.

The length (l) and width (w) of the large rectangle are 20 feet and 7 feet, respectively, so the area of the large rectangle (Al) is:

Al  =  20 ft. × 7 ft.

= 140 sq. ft.

The area of a triangle is given by , where b is the base and h is the height of the triangle.

The base and height of the triangle both measure 6 feet, so the area of the triangle (At) is:

   ft.  ft.

  sq. ft.

  sq. ft.

Step-by-step explanation:



10. Ken has 22 coins, some of which are dimes and the rest are quarters. Alto-

gether, the coins are worth more than $3. 40. At least how many of the

coins are quarters? At most how many are dimes?

Answers

Answer: Ken has 22 coins, some of which are dimes and the rest are quarters

Step-by-step explanation:Step 1. Let x be the number of dimes and let 25-x be the number of quarters.

Step 2. Let 0.10x be the total cost for x number of dimes

Step 3. Let 0.25(25-x) be the total cost for 25-x number of quarters.

Step 4. Since the man has $4.60, then 4.60=0.10x+0.25(25-x). Solving for x yields the following steps

Find the area (please hurry if you are answering, due soon)

Answers

Area of the figure is 171 cm²

See the attachment......

Area of triangle:-

1/2(12)(19)6(19)114cm²

Area of square:-

7²49cm²

Area of rectangle:

5(3)15cm²

Total:-

15+49+114178cm²

Pls help i will give brainliest

Answers

Answer:

i think 31

Step-by-step explanation:

What is the question asking here ?

GUYS PLEASE HELP ME I NEED TO FINISH THIS

Answers

The answer is B you’re welcome

PLEASE ANSWER the altitude y in feet of a hawk that is descending can be represented by the equation y=-20x+350, where x represents the time in minutes. The equation y=-10x+400 represents the altitude y in feet of an eagle after descending x minutes. Which bird is closer to the ground after 8 minutes? How much closer?

Answers

Answer:

The eagle by 130 feet

Step-by-step explanation:

you plug it in and then find the difference

Please help!!!

Let f be the function given by f(x) = x2.

Write an equation for the function g whose graph is the graph of f translated 3 units left and up 5 units.

Answers

Answer:

If it is x squrared the answer would be (x+3)²+5. If it is 2 times x then it would be (2x+3)+5

Step-by-step explanation:

how can i write this in a calculator?

Answers

Answer:

2.13

Step-by-step explanation:

cos 62⁰=10/x=0.47

x=10/0.47≈2.13

A parallelogram originally has an area of 47 square inches. Find its new area if its base
is one-fourth times as long and its height is twice as long.

PLS HELP ME!! WILL GIVE LOTS OF POINTS AND GIVE BRAINLIEST!

Answers

Answer:

23.5

Step-by-step explanation:

So this is a parallelogram so the area formlula is b*h=47? That's a no go. It is saying that if the base is 1/4th and the height is increasing by 2 so basically 1/4b*2h=1/2bh bh so it will be represented as 47 so 1/2*47=23.5

help me out please look at photo

Answers

Answer:

seek god

Step-by-step explanation:

dang maybe the 2nd one

What is the value of the one in 45.12

Answers

Answer:

Step-by-step explanation:

1 is in the tenth place

[tex]\sf 1's \ value = \dfrac{1}{10}[/tex]

What is the value of the five
digit? 315 2308

Answers

Answer:

50 000

Step-by-step explanation:

5 x 10 000

Tamora just made the last of her monthly payments on her loan. she had been making these payments for the past nine years. the loan had a principal of $10,675 and an interest rate of 4.75%, compounded monthly. in addition, tamora paid $939.25 in service charges. what was tamora’s total finance charge? round all dollar values to the nearest cent. a. $939.25 b. $11,614.25 c. $3,403.53 d. $2,464.28 please select the best answer from the choices provided a b c d

Answers

Tamora’s total finance charge was $3,403.53 if Tamora paid in addition of $939.25 in service charges option (c) is correct.

What is compound interest?

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We have:

Principal amount(Loan principal) = $10,675

Interest rate  = 4.75 %

Monthly rate = 4.75/12% ⇒0.39583% ⇒ 0.00395

Additional amount she paid in service charge = $939.25

Number of months = 9×12 = 108 months

We can find the total finance charge as follows:

Finance charge = Total amount repaid +service charge - Loan principal

The formula for the monthly payment of the loan is given by:

[tex]\rm Monthly \ payment = \frac{Loan \ principal }{\frac{(1-(1+r)^-^n)}{r} }[/tex]

[tex]\rm Monthly \ payment = \frac{10675}{\frac{(1-(1+0.00395)^-^{108})}{0.00395} }[/tex]    

After calculating, we get:

Monthly payment = $121.66

For 108 months, Tamora paid:

= 121.66×108

= $13,139.23

The finance charge will be:

= $13,139.23+$939.25-$10,675

= $3,403.53

Thus, Tamora’s total finance charge was $3,403.53 if Tamora paid in addition of $939.25 in service charges option (c) is correct.

Learn more about the compound interest here:

brainly.com/question/26457073

how many solutions do the following systems have
{0.5x-3/4y=7
:5.6-2/5x=-0.6y

Answers

Answer:

Step-by-step explanation:

I think the answer is 0-1, but i will have to see the answers to determine.

Hope it helps!

Are { 13 x (25+ 15) } and { (13x25) + (13x25) } equal?

Answers

no.

Use distributive property on the first set and you get:

{(13 x 25) + (13 x 15)}

therefore not equal to the second set of

{(13 x 25) + (13 x 25)}

the lateral surface area of cylinder R is 33π find the height of the cylinder​

Answers

Answer:

1.7507

Step-by-step explanation:

See Image

Angle K in △MKL is a right angle.

Answers

Hypotenuse= MLPerpendicular=KL=15Base= KM=8

By using Pythagoras theorem.

h²=p²+b²ML²=15²+8²ML²=225+64ML=√289

Therefore ML= 17...

Step-by-step explanation:

Hope it helps....Mark me brilliant

Help please I’m kinda stuck on these last part!

Answers

Answer:

Emmanuel will need 8 scoops to get 2 tablespoons

you need 12 1/2 tablespoons for 6 tablespoons

Step-by-step explanation:

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