f(x)=(x+3)^2 -8 how many real solutions?

Answers

Answer 1

Answer:

2 real solutions

Step-by-step explanation:

[tex]f(x)=(x+3)^2-8\\\\0=(x+3)^2-8\\\\8=(x+3)^2\\\\\pm\sqrt{8}=x+3\\\\x=-3\pm\sqrt{8}[/tex]

Therefore, the function set at [tex]f(x)=0[/tex] has two real solutions (x-intercepts).

You can also check the discriminant of the function by expanding it:

[tex](x+3)^2-8=x^2+6x+9-8=x^2+6x+1\\\\b^2-4ac=6^2-4(1)(1)=36-4=32 > 0[/tex]

Since it's greater than 0, there's two real solutions


Related Questions

Hey can someone please help me with this question. Im having a hard time with them.

Answers

Answer:

B

Step-by-step explanation:

The event of a baby boom would cause a huge growth in the population whilst the other options would create ethical and financial issues with having many children.

Will give brainliest look at pitcure

Answers

Answer:

x = 15

Step-by-step explanation:

angle FoH = 360° - 90° - 90° - angle G

= 180° - 75°

= 105°

17x° = 360° - angle FoH

17x° = 360° - 105°

17x° = 255°

x = 255 ÷ 17

x = 15

HOPE THIS HELPS AND HAVE A NICE DAY <3

.
6) The function of f(x) = x2 – 3 is given.
Find f(-2)

Answers

Answer: 4

Step-by-step explanation:

The given function :

The average rate of change in a function g(x) from x=a to x=b is given by :-

Then, the average rate of change of the given function from x = 1 to x = 3 will be :-

x = 1 to x = 3 is 4

What does it mean when someone states "she gave it 110" how can this comment be explained using math?

Answers

Answer:

It means you put full effort into what you're doing, because in math, 100% is perfect, but 110% is more than perfect, so they are saying she put extreme effort into the problem.

What is the exact volume of the cylinder?
Cylinder with radius labeled 4 inches and height labeled 8 inches

32π in³

64π in³

128π in³

512π in³

Answers

128pi in^3

because:
Volume = Area of the base * height
Volume= pi*r^2*height
= pi4^2 * 8
= 128pi

Consider the diagram below.
Find the value of x
Enter each line of work as an equation.

Answers

5x-16=45x=4+165x=20x=20/5x=4

Answer:

x = 4

Step-by-step explanation:

We know that,

A parallelogram is a quadrilateral whose opposite sides are parallel.

Then the value of x will be,

→ 5x - 16 = 4

→ 5x = 4 + 16

→ 5x = 20

→ x = 20/5

→ [ x = 4 ]

Verification of the value of x,

→ 5x - 16 = 4

→ 5(4) - 16 = 4

→ 20 - 16 = 4

→ 4 = 4

→ [ LHS = RHS ]

Hence, the value of x is 4.

please explain Algebraic Equation​

Answers

Detailed Answer:

An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other.

Example of Algebraic Equations:

Eg. 1) x + 10 = 20
Eg. 2) 5x + 10 = 20
Eg. 3) 2x + 2 = 4

The diagram shows inner perimeter of a running track.
a. The total length must be 400m. Fund the length of the straight sides.
b. The track has 6 lanes, each 1.5m wide. Find the difference in the length between the outer and inner perimetres.

Answers

Answer:

Complete the sentence.

is 8 times as much as 10.

Step-by-step explanation:

you have to divide it by the length

If 3 pens cost 6 dollars how much is each pen?




Please help I need this asap

Answers

Answer: $2

Step-by-step explanation:

Amanda deposits $500 into a savings account
arning simple interest at an annual rate of 8%. tori deposits $1,000 into a
vings account earning simple interest at an annual rate of 2.5%. neithe
i makes any additional deposits or withdrawals. which girl's account
i reach a balance of $1,500 first? justify your answer.

Answers

[tex]~~~~~~ \stackrel{\textit{\LARGE Amanda}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 1500=500[1+(0.08)(t)]\implies \cfrac{1500}{500}=1+0.08t\implies 3= 1 + 0.08t \\\\\\ 2 = 0.08t\implies \cfrac{2}{0.08}=t\implies \boxed{25=t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Tori}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years \end{cases}[/tex]

[tex]1500=1000[1+(0.025)(t)]\implies \cfrac{1500}{1000}=1+0.025t\implies \cfrac{3}{2}=1 + 0.025t \\\\\\ \cfrac{3}{2}-1= 0.025t\implies \cfrac{1}{2}=0.025t\implies \cfrac{ ~~ \frac{1}{2} ~~ }{0.025}=t\implies \boxed{20=t}[/tex]

well, clearly Tori is Da Bomb!.



Differentiate each of the following expressions with respect
to x
(a) (x^2+ 1)(x - 3)^4

Answers

Answer: (A(x2+1)x-3)^=134

Step-by-step explanation: what me  my brother did was just look it up

Danielle has the following averages in her math class: Homework Avg.: 80, Quiz Avg.: 84, Test Avg.: 74, Final Exam: 60. The teacher weights Homework at 10%, Quizzes at 30%, Tests at 40%, and the Final Exam at 20%. How many points did Danielle earn in the HOMEWORK category?

Answers

Answer:

75

Step-by-step explanation:

-given averages-

-Homework Avg : 80

-Quiz Avg.: 84-

-Test Ayg: 74

-Final Exam: 60

-weights

-Homework at 10%,

-Quizzes at 30%,

-Tests at 40%

-Final  Exam at 20%

Homework points:

16. Tahlia has 12 cups of flour in her pantry. Each time she bakes cookies, she uses 2 cups of
Flour.
a. Write an expression that gives the cups of flour Tahlia has left in terms of n, the
number of times she has baked cookies.
FLOUR
b. Use factoring to write an equivalent expression to the expression in part a.
1
TI 2015

Answers

Answer:

a. 12 cups - 2 * n cups b. 2 * (6-n) cups

Step-by-step explanation:

a.

we start with 12 cups of flour

we subtract 2 cups of flour for each baking cycle

thus, cups of flour = 12 cups - 2 cups for each cycle

2 cups for each cycle = 2 cups * number of cycles = 2 cups * n

cups of flour = 12 cups - 2 * n cups

b.

note that 12 is a multiple of 2 -- 2 * 6 = 12

thus, 12 cups = 2* 6 cups

cups of flour = 12 cups - 2 * n cups = 2 * 6 cups - 2 * n cups

factor out the 2

cups of flour = 2 * (6-n) cups

√3x2+2x-√3
how can we solve ​

Answers

Answer:

[tex]x = \sqrt{3 \frac{ - 1}{3} } [/tex]

Need the answer for this

Answers

Answer:

Just B and C

Step-by-step explanation:

Not A as cost is always increasing with x.

Yes B as is x squared relationship

Yes C as 15*9 = 135

No D as it is a squared relationship so much more than double

Not E as the the cost increases by a different amount for each increase in x.

help me pls reallly fast pls

Answers

Answer:

180 degrees.

Step-by-step explanation:

A supplementary angle is an angle which either of two angles whose sum is 180°.

No matter how big the triangle grows, the angles will stay the same degrees all throughout.

Pretty sure this is what you needed, hope this helps!

Thomas wants to double the volume of his original box. what could be the new dimensions of the box? recorded in length, width, height.






14 x 8 x 4 inches


16 x 10 x 4 inches


14 x 10 x 2 inches


28 x 10 x 2 inches

Answers

The possible dimension of the new box is 16 x 10 x 4 inches

The complete question

Thomas buys a box that is 8 by 10 by 4 inches. Thomas wants to double the volume of his original box. what could be the new dimensions of the box? recorded in length, width, height.

How to determine the possible dimensions?

The dimension of the box is given as:

Dimension: 8 by 10 by 4

So, the volume of the box is:

Volume = 8 * 10 * 4

When the volume is doubled, we have:

Volume = 2 * 8 * 10 * 4

Evaluate the product

Volume = 16 * 10 * 4

This means that the possible dimension of the new box is 16 x 10 x 4 inches

Read more about volumes at:

https://brainly.com/question/1972490

#SPJ4

The perimeter of ΔABC is 13 cm. It was dilated to create ΔA'B'C'.

What is the perimeter of ΔA'B'C'?
1. 13 cm
2. 26 cm
3. 39 cm
4. 52 cm

Answers

Perimeter of ΔA'B'C' is 52 cm.

The perimeter of ΔABC is =13 cm

Length of OB = 5 cm

Length of OB' = 15 + 5 = 20 cm

The Dilation factor can be found out b

ΔOCB and ΔOC'B' are similar as BC|| B'C'

From triangles ΔOCB & ΔOC'B' the dilation factor can be found out

by the formula below

[tex]\frac{BC}{B'C'} =\frac{5}{20}[/tex]

B'C'= 4BC

so the dilation factor = 4

hence the new perimeter of the triangle = 13  4 = 52 cm

for more information please refer the link below

https://brainly.com/question/20502441

Answer:D

Step-by-step explanation:

I need the answer asap!!!!

Which expression is equivalent to 6x+ 8?
2(3x-4)
2(3x+4)
2(4x+6)
2(3x+8)

Answers

2(3x+4). We need to multiply the outside by the inside because of the variable. 2 times 3x is 6x. 2 times 4 is 8. This gives us 2(3x+4).

How do I solve this?

Answers

Answer:

Step-by-step explanation:

6x + 11y = 45

9x + 9y = 45

-18x - 33y = -135

18x + 18y = 90

-15y = -45

y = 3

6x + 33 = 45

6x = 12

x = 2

Write the quadratic function in vertex form: f(x) = 8x + 2x - 5

Answers

If you meant 8x^2, then it would be 8(x+1/8)^2-41/8

What are the square numbers between 73 and 186

Answers

Answer:

8^2 64 =8 X 8

9^2 81 =9 X 9

10^2 100 =10 X 10

11^2 121 =11 X 11

12^2 144 =12 X 12

13^2 169 =13 X 13

Hope it helps :))

what’s the area and the perimeter and of the triangle?

Answers

Answer:

42.9

Step-by-step explanation:

8.25x 5.2

Triange formula = b x h

2. Before the war, Kim Il-Sung informed the Soviet Union and China of his plan to invade

Answers

Before the beginning of the Korean War, Kim II-Sung had established his plans to invade South Korea and shared them with Soviet Union and China.

Why did Kim II-Sung invade South Korea?

To be able to spread communist ideologies across the neighboring countries, Kim II-Sung planned to invade South Korea for the same.

Soviet Union and China also joined hands, as they were also focused on wide-spreading the communal ideologies throughout the world.

Hence, it may be stated that the invasion of South Korea took place for spreading communism.

Learn more about South Korea invasion here:

https://brainly.com/question/451168

#SPJ1

Answer:

All answers.

1. Kim Il-Sung was the leader of

✔ North Korea.

2. Before the war, Kim Il-Sung informed the Soviet Union and China of his plan to invade

✔ South Korea.

3. The South Korean government was led by President

✔ Syngman Rhee.

4. South Korea’s leadership arrested and killed thousands of

✔ alleged North Korean agents.

Step-by-step explanation:

100%

i need the awnsers to this asap

Answers

Answer:

27.2 I believe

Step-by-step explanation:

Theren is a pattern in the numbers, the dollar is going up by 2 while the cents are going down by 2, if you follow the pattern till you get to 15 in pounds, the you'll get 27.2

a
- A glass display box has a surface area of
378 square inches. How many square
OT
inches of glass are used to create a glass
display box with dimensions that are one-
bovom
half those of the original? (Example 1)
SVRUSU

Answers

Answer:

94.5 in²

Step-by-step explanation:

Given

Area of glass display box is 378 in²The scale factor is 1/2

We know that the area is the function of two dimensions

To find the surface area of the display box we need to multiply the surface area of the original by the square of the scale factor

A = (1/2)²*378 = 378/4 = 94.5 in²

Luna measured the elementary school and made a scale drawing. The schoolyard, which is 175 meters long in real life, is 25 centimeters long in the drawing. What scale did Luna use for the drawing?

Answers

Answer:

1 cm : 7 m

Step-by-step explanation:

25 cm : 175 m simplifies to 1 cm : 7 m

Hey can someone please help me with this question. Im having a hard time with them.

Answers

Answer:

B

Step-by-step explanation:

A baby boom would cause a sudden increase of the population.

For the following graph, determine if the graph represents a polynomial function. If it is a polynomial function, then determine the number of turning points and the least degree possible.


a.Yes, this graph represents a polynomial. There are two turning points and the least degree possible is three.

b.This is not a polynomial. There are no turning points as the curve represents an odd function.

c.Yes, this graph represents a polynomial. There are two turning points and the least degree possible is two.

d.This is not a polynomial. There are no turning points as the curve is always increasing.

Answers

Using function concepts, it is found that the correct option is given by:

a.Yes, this graph represents a polynomial. There are two turning points and the least degree possible is three.

What is the least degree possible of a polynomial?

Supposing a polynomial with n turning points, the least possible degree is of n + 1.

In this problem, the polynomial has 2 turning points, hence the least possible degree is of 3 and option a is correct.

More can be learned about functions at https://brainly.com/question/25537936

#SPJ1

Classify the polynomial by the number of
terms.
5x2 + 3x – 8

Answers

[tex]\large\textsf{\textbf{Answer\::}}[/tex]

trinomial

[tex]\Large\textsf{\textbf{Calculations\::}}[/tex]

If a polynomial has one term , it's a monomial .

If a polynomial has two terms , it's a binomial .

If a polynomial has three terms , it's a trinomial .

If a polynomial has 4 or more terms , it's a polynomial .

Since the given polynomial has three terms , it's a trinomial .

[tex]\footnotesize\texttt{hope\:helpful~}[/tex]

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