Will the graph of the equation above intersect the x-axis in zero, one, or two points?

Will The Graph Of The Equation Above Intersect The X-axis In Zero, One, Or Two Points?

Answers

Answer 1

Answer: Option D

Step-by-step explanation:

Add 4x² to both sides  of the equation:

[tex]16x+8+4x^2=-4x^2+4x^2\\4x^2+16x+8=0[/tex]

The Quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

You can identify that in this case:

[tex]a=4\\b=16\\c=8[/tex]

Substitute into the Quadratic formula:

[tex]x=\frac{-16\±\sqrt{(16)^2-4(4)(8)}}{2(4)}[/tex]

 [tex]x_1=-0.58\\x_2=-3.41[/tex]

Therefore, the graph of the equation above intersect the x-axis in two points.

Answer 2
Hello!

The answer is:

D. The parabola intercepts the x-axis in two points.

[tex]x_{1}=-0.59\\\\x_{2}=-3.41[/tex]

Why?

To find the parabola intercepts, we need to use the quadratic formula. The parabola intercepts with the x-axis, are also called roots or zeroes.

The quadratic formula states that:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

We are given the parabola:

[tex]16x+8=-4x^{2} \\[/tex]

Which is also equal to:

[tex]4x^{2}+16x+8=0[/tex]

Where,

[tex]a=4\\b=16\\c=8\\[/tex]

Then, substituting into the quadratic formula to find the roots of the parabola, we have:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\\\\x=\frac{-16+-\sqrt{(16)^{2}-4*4*8 } }{2*4}=\frac{-16+-\sqrt{(256-128) } }{8}\\\\x==\frac{-16+-\sqrt{(256-128) } }{8}=\frac{-16+-\sqrt{(28 } }{8}\\\\x=\frac{-16+-\sqrt{128 } }{8}=\frac{-16+-(11.31) }{8}\\\\\\x_{1}=\frac{-16+(11.31) }{8}=-0.59\\\\x_{1}=\frac{-16-(11.31) }{8}=-3.41[/tex]

Hence,the parabola intercepts the x-axis in two points.

[tex]x_{1}=-0.59\\\\x_{2}=-3.41[/tex]

Have a nice day!


Related Questions

Plz help me with this

Answers

Answer:  [tex]A)\quad \dfrac{x^6\ z}{y^{10}}[/tex]

Step-by-step explanation:

[tex].\quad \dfrac{(x^{2}\cdot y^{-3}\cdot z^{4})^2}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\= \dfrac{x^{2\cdot 2}\cdot y^{-3\cdot 2}\cdot z^{4\cdot 2}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4}\cdot y^{-6}\cdot z^{8}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4+2}\cdot y^{-6+6}\cdot z^{8-7}}{x^{-2+2}\cdot y^{4+6}\cdot z^{7-7}}\\\\\\=\large\boxed{\dfrac{x^6\ z}{y^{10}}}[/tex]

The radius of the circle whose equation is (x-3)^2 + (y+1)^2 = 16 is

Answers

Answer:

4

Step-by-step explanation:

The general equation of a circle with center (a, b) and radius r is given by the equation;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]

The constant in the right hand side of the equation is simply the square of the radius;

We have been given the following equation;

(x-3)^2 + (y+1)^2 = 16

Comparing this with the general equation above;

[tex]r^{2}=16\\\\r=\sqrt{16}=4[/tex]

if x is 5, then what does 6x =

Answers

Answer:

x=30

Step-by-step explanation:

You'll find lots of clouds over _____________ climates and practically no clouds over ___________ climates.

these are your answers : tropical, desert, polar, maritime. ( they will work for both)





(this is science)

Answers

Answer:

you'll find lots of clouds over tropical climates and practically no clouds over desert clmates.

Answer:

encontrará muchas nubes sobre climas tropicales y prácticamente ninguna nube sobre climas desérticos.

Step-by-step explanation:

what is 26.553 rounded to the nearest hundred?​

Answers

Answer:

26.55

Step-by-step explanation:

When rounding to the nearest whatever, you always look at the digit to the right of it. In this case, you look at the thousandth digit. 3 is not equal to or less than five, so you round 3 to 0 and you get 26.55

Simplify the following expression
7x^2 - 15x + 5 - 2x - 8x^2

Answers

Answer:

[tex]\large\boxed{7x^2-15x+5-2x-8x^2=-x^2-17x+5}[/tex]

Step-by-step explanation:

[tex]7x^2-15x+5-2x-8x^2\qquad\text{combine like terms}\\\\=(7x^2-8x^2)+(-15x-2x)+5\\\\=-x^2-17x+5[/tex]

The students in Mr. Taylor's class are part of different clubs. 8 boys in reading club 4 girls in reading club 2 boys in drama club 12 girls in drama club Which of the following statements is correct? A. For every boy in the drama club, there are two boys in the reading club. B. For every boy in the drama club, there are six boys in the reading club. C. For every girl in the reading club, there are three girls in the drama club. D. For every girl in the reading club, there are four girls in the drama club.

Answers

Answer:

The answer is D. For every girl in the reading club, there are four girls in the drama club. It is not B. For every boy in the drama club, there are six boys in the reading club.

Pls make me brinlyest .

Hope this helped

The correct statement is, C. For every girl in the reading club, there are three girls in the drama club.  

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given,  8 boys in reading club 4 girls in reading club 2 boys in drama club 12 girls in drama club.

Going through the given options (given statements so multiple options would be correct).

For every girl in the reading club, there are three girls in the drama club,

As 12 is a multiple of 4 and 3.

learn more about proportion here :

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ANSWER NEEDED ASAP!!!!!!!!

Answers

1. 428 pages: There are a total of 428 pages that you can flip to.

2. 1/428: Page 45 is only one page out of the total sample space.

3. 1/2: Since the last page is 428, there is an even number of pages. That means that there are 214 page numbers that are even. 214/428 = 1/2.

Answer:

1. What is the sample space for this experiment?

A: 1 to 428

2. What is the probability that you will turn to page 45?

A: There is a 1 out of 428 chance you will turn to page 45.

3. What is the probability that you turn to an even numbered page?

A: There is a 1 out of 2 chance you will turn to an even numbered page.

If M = N, the diameter of M = 148, and AB = 140, what is the length of NQ?

Answers

Answer:

[tex]NQ=24\ units[/tex]

Step-by-step explanation:

we know that

Triangles ABM and CDN are congruent

so

CD=AB

AB=2AL ----> because the diameter divide the circle into two equal parts

CQ=AL=140/2=70 units

NC----> is the radius

NC=148/2=74 units ----> the radius is half the diameter

Applying Pythagoras Theorem find the value of NQ

[tex]NC^{2}=NQ^{2}+CQ^{2}[/tex]

substitute the values

[tex]74^{2}=NQ^{2}+70^{2}[/tex]

[tex]NQ^{2}=74^{2}-70^{2}[/tex]

[tex]NQ^{2}=576[/tex]

[tex]NQ=24\ units[/tex]

The vertices of ABC are A(-2,2), B(6,2), and C(0,8). The perimeter of ABC

Answers

Answer:

The perimeter of the triangle ABC is 22.8 units

Step-by-step explanation:

* Lets study the information in the problem

- There is Δ ABC with vertices:

  A (-2 , 2) , B (6 , 2) , C (0 , 8)

- The perimeter of the triangle is the sum of the length of its

  three sides

* We must to find the lengths of AB , BC and CD

- The rule to find the distance between 2 points (x1 , y1) and (x2 , y2) is

  √[(x2 - x1)² + (y2 - y1)²]

* Lets find the lengths of the three sides

- Length of AB

∵ A = (-2 , 2) and B = (6 , 2)

AB = √[(6 - -2)² + (2 - 2)²] = √8² = 8 units

- Length of BC

∵ B = (6 , 2) and C = (0 , 8)

BC = √[(0 - 6)² + (8 - 2)²] = √[6² + 6²] = √72 = 6√2 units

- Length of AC

∵ A = (-2 , 2) and C = (0 , 8)

AC = √[(0 - -2)² + (8 - 2)²] = √[2² + 6²] = √40 = 2√10 units

* Now lets find the perimeter of the triangle

∵ The perimeter = AB + BD + AC

The perimeter = 8 + 6√2 + 2√10 = 22.8 units

* The perimeter of the triangle ABC is 22.8 units

Answer:

The perimeter of triangle ABC = 22.78 units

Step-by-step explanation:

Formula:-

The length of line segment with end points (x₁, y₁) and (x₂, y₂) is given by,

Length = √ [(x₂ - x₁)² + (y₂ - y₁)²]

To find the each side of triangle

We have  A(-2,2), B(6,2), and C(0,8).

AB =  √[(6 - -2)² + (2 - 2)²] =  √64 = 8

BC = √[(0 - 6)² + (8 - 2)²] = √(36 + 36) = 8.48

AC = √[(0 - -2)² + (8 - 2)²] = √(4 + 36) = 6.3

To find the perimeter of triangle ABC

Perimeter = AB + BC + AC

 = 8 + 8.48 + 6.3 = 22.78 units

Which expression is equivalent to this one? 1/6(x - 18)

A)1/6x - 18
B)1/6x • (-18)
C)1/6x - 3
D)1/6 + x - 18

Answers

C, because you distribute the 1/6 to x and 18 which ends up being 1/6x - 3

[tex]\frac{1}{6}(x-18)[/tex]   Distribute 1/6(multiple 1/6 to x and -18)

[tex]\frac{1}{6}(x) -\frac{1}{6} (18)[/tex]     Simplify

[tex]\frac{1}{6}x -3[/tex]       Your answer is C

Steve can train 48 dogs in 6 hours. How many dogs can Steve train in 10 hours?

Answers

Answer:

80

Step-by-step explanation:

Steval train 80 dogs in 10 hours because 48÷6 = 8 so if you do 10 times a day you get 80 so you will get a total of 80 dogs in 10 hours

The function H(t) = −16t^2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

Answers

Answer:

see the attachment for a table

Step-by-step explanation:

A. The table is shown in the attachment. The solution to h(t) = g(t) is at a value of t that lies between 6 and 7. At t=6, h(t) > g(t). At t=7, h(t) < g(t). Since both functions are continuous, they must have equal values somewhere between t=6 and t=7. (Intermediate value theorem.)

__

B. The solution means the cannon balls will have the same height at a value of t between 6 and 7.

Answer:

b

Step-by-step explanation:

Which side lengths form a right triangle 30 POINTS!!

Answers

Answer:

A. 3, 4, 5

Step-by-step explanation:

Option A:

LHS = 3² + 4² = 9 + 16 = 25

RHS = 5² = 25

(3, 4, 5) is a right triangle.

Option B:

LHS = 7² + 8² = 49 + 64 = 113

RHS = 9² = 81

(7, 8, 9) is NOT a right triangle.

Option C:

LHS = 3² + 9² = 9 + 81 = 90

RHS = √95² = 95

(3, 9, √95)  is NOT a right triangle.

Hope this help!!!

Have a nice day!!!

An important postulate in geometry states: "Through Point P, there is only one line parallel to ". What is the equation of line l, parallel to AB that passes through Point X?

Answers

Answer:

y=(-5/12)x+(95/12)

Step-by-step explanation:

step 1

Find the slope of the line AB

m=(3-8)/(2+10)=-5/12

step 2

Find the slope of the line parallel to AB

we know that

If two lines are parallel then their slopes are the same

so

the slope is m=-5/12

step 3

Find the equation of the line l parallel to AB that passes through Point X

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

substitute

y-10=(-5/12)(x+5)

y=(-5/12)x-(25/12)+10

y=(-5/12)x+(95/12)

Solve for 3/4u = 12
.
Simplify your answer as much as possible.

Answers

Answer:

u = 16

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] u = 12

Multiply both sides by 4 to eliminate the fraction

3u = 48 ( divide both sides by 3 )

u = 16

If f(x) = 5x + 40, what is f(x) when x = -5?

Answers

the answer to this problem is 15

I believe 15 is correct ^^

very confused please help asap ( 13 points)

Answers

Answer:

2 and a half

Step-by-step explanation:

To solve this, divide the total amount of free time [5/6] by the time it takes to play one video game [1/3]

Remember that dividing 5/6 by 1/3 is the same as multiplying 5/6 by 3/1.

Multiply the numerators

5 x 3 = 15

Multiply the denominators

6 x 1

15/6 = 2 3/6

So, Lamar can play 2 and a half video games

I hope this helps!

The answer is 2 and a half.

Big Ed’s car dealership is running a special on 2008 trucks. Big Ed offers financing at a rate of 6.71% on a loan with a term of 36 months, but he requires the customer to make a down payment of 15% of the cost of the vehicle. You are interested in a Car Crusher truck that costs $25,230. Not including the down payment, how much will you pay over the lifetime of the loan? a. $27,924.84 c. $23,735.88 b. $25,789.32 d. $21,445.50 Please select the best answer from the choices provided A B C D

Answers

Answer: C

Step-by-step explanation:

25,230 x .15= 3,784.50

25,230- 3,784.50= 21,535

21,535/36= 598.20833

598.20833 x 1.0671= 638.348109

638.348109 x 36= 22,980.5319

Answer:

Letter C $23,735.84.The result varies a few dollars, because during the solution an adjustment was made to the decimals.

Step-by-step explanation:

1. Define the price of the vehicle you are going to buy with the dealer or seller

Principal: $25230

Rate= 6.71%

N= 36 months

Down payment=15% of the cost of the vehicle= (25230*0.15)=$3784.50

25230-3784.50=21445.5

2. Apply the amortization formula to determine the monthly payments. With this taxation, you will determine the payments applied to the principal and the copper of interest.

A=P*(r(1+r)^{n})/((1+r)^{n}-1).

A= amortization or monthly payments.

P=Principal

R=interest rate

N= the total number of months

a. Calculate the monthly interest rate. The annual interest rate is 6.71% percent. Divide it by 12 to get the monthly interest rate. The monthly interest rate is 0.5592 percent (6.71/12 = 0.5592)  

A=21445.5*(0,005592 (1+0,005592)^{{36}})/(1+0,005592)^{{36}}-1.

A=21445.5*(0,00683/0,2223)

A=21445.5*0,03072=658.90

Total of the payment= 658.90*36=23720.40

What is the factored form of x^3-1

Answers

Answer:

the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]

Step-by-step explanation:

We need to find factors of x^3 -1

[tex]x^3-1 \\(x)^3 -(1)^3\\We \,\, know\,\, a^3 -b^3 = (a-b) (a^2 +ab + y^2) \\So, \,\, using\,\, the \,\, formula\,\,\\Here\,\, a= x \,\,and\,\, b= 1\\(x)^3 -(1)^3 = (x-1) (x^2 +x+1)\\[/tex]

So, the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]

And buys a pencil for $0.45 draw and label coins. Ann could use to make $0.45

Answers

Answer:

You could use one quarter and two dimes... that will equal $0.45

(I'm not sure what you are asking for)

Answer:

You could use 9 nickels

You could use 45 pennies

You could use 1 quarter and 2 dimes

You could use 4 dimes and 1 nickel

You could use 2 dimes and 5 nickels

You could use a lot more combination that equal 45...

Select "Growth" or "Decay" to classify each function.

Answers

Final answer:

Classifying functions involves identifying whether a population is experiencing growth, depicted by exponential or J-curve growth models, or decay, which is often described through logistic or S-curve models. Exponential growth shows unrestricted rapid increases, while logistic growth accounts for environmental limits and a carrying capacity. Age structure diagrams provide further context for the type of population change being observed.

Explanation:

Growth and Decay in Biological Functions

When classifying functions as growth or decay, one must consider the nature of the function in relation to the context of time and population size. For instance, when discussing bacterial growth, Curve A depicting exponential growth is characterized by a population size that increases rapidly over time, often without any constraints. This curve represents a J-curve model on a graph where population size skyrockets as time progresses. On the other hand, Curve B illustrates logistic growth, which follows an S-curve model where the population grows rapidly at first and then slows down as it reaches carrying capacity, a point where growth rate starts to decline.

Different time intervals on a growth curve represent various phases, such as the lag phase, where growth is slow or negligible; the log phase or exponential phase, where the number of cells increases dramatically; the stationary phase, where growth rate is zero due to resource depletion or waste accumulation; and the death phase, where the number of live cells declines.

Various types of growth in organisms can be identified by their structural adaptations or ecological contexts, such as whether they are terrestrial or aquatic, or whether they are deciduous or evergreen plants. Additionally, age structure diagrams for populations can reveal if a population is rapidly growing, growing slowly, stable, or in decline.

(15 points) please help asap!!!

Answers

(4, 2) and (4, -5)

(Look at the photo. They have the same x-coordinates, but different y-coordinates; one is positive the other is negative, resuting in different quadrants)

I hope this helps!

Find the value of x for which line a is parallel to line b

Answers

Answer:

20

Step-by-step explanation:

Since we are told that line a is parallel to line b, even if it's not visible in the image, we can say that ∠5 = ∠1, since they are formed by the same line crossing parallel lines.

So, we have

∠4 = 3x

∠5 = ∠1 = 6x

Since ∠4 and ∠5 are complementary angles formed by line t, we know their sum is 180 degrees. So,

∠4 + ∠5 = 180

3x + 6x = 180

9x = 180

x = 20

Answer is 20.

does anybody know this?

Answers

Answer:

37

Step-by-step explanation:

To evaluate, substitute x = 10 into g(x) then substitute the value obtained into f(x)

g(10) = 10 - 4 = 6, then

f(6) = 6² + 1 = 36 + 1 = 37

For the direct variation such that when y = 2 then x = 3 , find the constant of variation ( k) and then find the value of y when x = - 0.5.

Answers

Answer:

k is 2/3 and y is -1/3 when x is -0.5.

Step-by-step explanation:

The direct variation relationship is y = kx, where k is the const. of var.

Subbing 3 for x and 2 for y, 2 = 3k, or k = 2/3.

Now, if x = -0.5, y = (2/3)(-1/2) = -1/3

k is 2/3 and y is -1/3 when x is -0.5.

Answer:

2/3 and y is -1/3 when x is -0.5.

Step-by-step explanation:

Hope I helped

There is a 52% chance that a player will win a certain carnival game. Which statement describes the likelihood that a player will win the game?



A. The player will definitely win the game.


B. It is unlikely that the player will win the game.


C. It is likely that the player will win the game.


D. It is neither likely nor unlikely that the player will win the game.

Answers

It’s A. Hope you already got it✨

The answer is actually D or C

the sale of a boatshaped like a right triangle with the dimensions shown below how much material is needed to make the sale​

Answers

[tex]A=\frac{ab}{2}=\frac{25\cdot12}{2}=\boxed{150}[/tex]

A certain hexagonal prism has a volume of 160 cubic meters. Its base has a perimeter of 30 meters and an area of 64 square meters. What is the surface area in square meters of the hexagonal prism??

Answers

Answer:

The surface area is equal to [tex]203\ m^{2}[/tex]

Step-by-step explanation:

step 1

Find the height of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of the prism

h is the height of the prism

we have

[tex]V=160\ m^{3}[/tex]

[tex]B=64\ m^{2}[/tex]

substitute in the formula and solve for h

[tex]160=64h[/tex]

[tex]h=160/64=2.5\ m[/tex]

step 2

Find the surface area

The surface area of the prism is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base of the prism

P is the perimeter of the base

h is the height of the prism

we have

[tex]B=64\ m^{2}[/tex]

[tex]P=30\ m[/tex]

[tex]h=2.5\ m[/tex]

substitute in the formula

[tex]SA=2(64)+(30)(2.5)=203\ m^{2}[/tex]

Dave uses the functionP(d) = 20d - 20 to calculate the net profit of his dog walking business. Where P(d) is the net profit in dollars, and "d" the number of dogs he walks. Interpret the meaning of the equation below using the context of the problem

P(3) = 40

Answers

When Dave walks three dogs he will earn a net profit of 40 dollars.

Final answer:

P(3) = 40 in the given problem context implies that Dave makes a net profit of 40 dollars from walking three dogs.

Explanation:

In the given problem context, the equation P(3) = 40 means that when Dave walks three dogs (d=3), he makes a net profit of 40 dollars. Dave's profit function is P(d) = 20d - 20. By substituting d with 3 in his profit function, we obtain P(3) = 20*3 - 20, which gives us P(3) = 60 - 20 = 40. Thus, Dave earns a net profit of 40 dollars from walking 3 dogs.

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