How many x-intercepts does the graph of y = 2x2 + 5x + 9 have?

Answer:

The real zeroes are -√5 , 0 , √5

Step-by-step explanation:

* Lets explain how to solve the problem

- The function is y = x^5 + x³ - 30x

- Zeros of any equation is the values of x when y = 0

- To find the zeroes of the function equate y by zero

∴ x^5 + x³ - 30x = 0

- To solve this equation factorize it

∵ x^5 + x³ - 30x = 0

- There is a common factor x in all the terms of the equation

- Take x as a common factor from each term and divide the terms by x

∴ x(x^5/x + x³/x - 30x/x) = 0

∴ x(x^4 + x² - 30) = 0

- Equate x by 0 and (x^4 + x² - 30) by 0

∴ x = 0

∴ (x^4 + x² - 30) = 0

* Now lets factorize (x^4 + x² - 30)

- Let x² = h and x^4 = h² and replace x by h in the equation

∴ (x^4 + x² - 30) = (h² + h - 30)

∵ (x^4 + x² - 30) = 0

∴ (h² + h - 30) = 0

- Factorize the trinomial into two brackets

- In trinomial h² + h - 30, the last term is negative then the brackets

 have different signs (     +     )(     -     )

∵ h² = h × h ⇒ the 1st terms in the two brackets

∵ 30 = 5 × 6 ⇒ the second terms of the brackets

∵ h × 6 = 6h

∵ h × 5 = 5h

∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with

  (+ ve) and 5 will be with (- ve)

∴ h² + h - 30 = (h + 6)(h - 5)

- Lets find the values of h

∵ h² + h - 30 = 0

∴ (h + 6)(h - 5) = 0

∵ h + 6 = 0 ⇒ subtract 6 from both sides

∴ h = -6

∵ h - 5 = 0 ⇒ add 5 to both sides

∴ h = 5

* Lets replace h by x

∵ h = x²

∴ x² = -6 and x² = 5

∵ x² = -6 has no value (no square root for negative values)

∵ x² = 5 ⇒ take √ for both sides

∴ x = ± √5

- There are three values of x ⇒ x = 0 , x = √5 , x = -√5

∴ The real zeroes are -√5 , 0 , √5

Answer:

The coefficient of xy^4 is 10

Step-by-step explanation:

to solve the questions we proceed as follows:

(2x+y)^5

=(2x+y)²(2x+y)²(2x+y)

We will solve the brackets by whole square formula:

=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)

By multiplying the brackets we get:

=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+

16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5

=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5

Therefore the coefficient of xy^4 is 10

The answer is 10....

Answer: 10

Step-by-step explanation: a p e x

This statement would be true: if the vertex of an angle is at the center of the circle, then it would be the central angle.

Answer:

The answer is C

Step-by-step explanation:

Answer:

Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.

Step-by-step explanation:

Both linear and nonlinear associations could increase along the whole data set. That's why Joseph and the fourth option are incorrect.

Answer:

x ≥ 0

Step-by-step explanation:

The domain of the function is the inputs, or in this case, the x values.

The inputs are  x greater than or equal to zero all the way to infinity.

Answer:

Step-by-step explanation:

The domain includes 0 and all real numbers greater than 0:  x ≥ 0

The length and width of the rectangular field are determined using algebra by setting up and solving two equations which represent the relationships between the length, width, and perimeter of the field. The dimensions are found to be 46 yards for the width and 137 yards for the length.

The dimensions of the rectangular playing field can be found using algebra, specifically the formulas for the dimensions and perimeter of a rectangle. The problem can be translated into two equations reflecting the relationships of the field's width and length to the perimeter.

The first equation is: L = 3W + 5, which represents the relationship that the length is 5 yards longer than triple the width.

The second equation is derived from the formula for the perimeter of a rectangle (P = 2L + 2W), which given the problem's perimeter of 346 yards gets us: 2L + 2W = 346.

Substitute the first equation into the second to solve for the width, then use that result to find the length. The solution indicates that the width of the rectangular playing field is 46 yards, and the length is 137 yards.

https://brainly.com/question/35474401

#SPJ2

Answer:

A - 48,96, -192

Step-by-step explanation:

Given:

geometric sequence:

-3, 6, -12, 24,

geometric sequence has a constant ratio r and is given by

an=a1(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=-3

r= a(n+1)/an

r=6/-3

r=-2

Now computing next term a5

a5=a1(r)^(n-1)

    = -3(-2)^(4)

   = -48

a6=a1(r)^(n-1)

    = -3(-2)^(5)

   = 96

a7=a1(r)^(n-1)

    = -3(-2)^(9)

   = -192

So the sequence now is -3, 6, -12, 24,-48,96,-192

correct option is A!

the assumption being, that there's a 7% sales tax on any item in the store.

so if you buy the jacket, you pay 25.5 plust 7% of 25.5.

and if you buy the shoes for price say "s", then you pay "s" plus 7% of "s".

whatever those two amounts are, they must be $60, because that's all you have in your pocket anyway.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 25.5}}{\left( \cfrac{7}{100} \right)25.5}\implies 0.07(25.5)~\hfill \stackrel{\textit{7\% of "s"}}{\left( \cfrac{7}{100} \right)s}\implies 0.07s \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{jacket}}{25.5}+\stackrel{\textit{jacket's tax}}{0.07(25.5)}+\stackrel{\textit{shoes}}{s}+\stackrel{\textit{shoe's tax}}{0.07s}~~=~~\stackrel{\textit{in your pocket}}{60} \\\\\\ 25.5+1.785+s+0.07s=60\implies 27.285+1.07s=60 \\\\\\ 1.07s=60-27.285\implies 1.07s=32.715\implies s=\cfrac{32.715}{1.07}\implies s\approx 30.57[/tex]

Answer:

82.8 degrees

Step-by-step explanation:

The information given here SSS.  That means side-side-side.

So we get to use law of cosines.

[tex](\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})[/tex]

Let's enter are values in.

[tex]12^2=10^2+8^2-2(10)(8) \cos(B)[/tex]

I'm going to a little simplification like multiplication and exponents.

[tex]144=100+64-160 \cos(B)[/tex]

I'm going to some more simplification like addition.

[tex]144=164-160\cos(B)[/tex]

Now time for the solving part.

I'm going to subtract 164 on both sides:

[tex]-20=-160\cos(B)[/tex]

I'm going to divide both sides by -160:

[tex]\frac{-20}{-160}=\cos(B)[/tex]

Simplifying left hand side fraction a little:

[tex]\frac{1}{8}=\cos(B)[/tex]

Now to find B since it is inside the cosine, we just have to do the inverse of cosine.

That looks like one of these:

[tex]\cos^{-1}( )[/tex] or [tex]\arccos( )[/tex]

Pick your favorite notation there.  They are the same.

[tex]\cos^{-1}(\frac{1}{8})=B[/tex]

To the calculator now:

[tex]82.81924422=B[/tex]

Round answer to nearest tenths:

[tex]82.8[/tex]

Answer:

2c

Step-by-step explanation:

c is a common factor of both terms

Consider the factors of the coefficients 4 and 18

factors of 4 : 1, 2, 4

factors of 18 : 1, 2, 3, 6, 9, 18

The common factors are 1, 2

The greatest common factor is 2

Combining with c gives

Greatest common factor of 2c

To find the greatest common factor of 4c and 18c, the common factor is 2c.

To find the greatest common factor of 4c and 18c, you need to identify the largest factor that both numbers share. In this case, the common factor is 2c. Here's how you can determine it:

Write the numbers as a product of their prime factors: 4c = 2 * 2 * c and 18c = 2 * 3 * 3 * c.

Identify the common factors: The common factors are 2 and c.

Multiply the common factors together: 2 * c = 2c.

Answer:

x = -1223, y = -629, and z = -31.

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  1    -2    1       |  4

•  3   -5   -17     |  3

•  2   -6   43     |  -5

Step 2: Multiply row 1 with -3 and add it in row 2:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  2   -6   43     |  -5

Step 3: Multiply row 1 with -2 and add it in row 3:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0   -2   41      |  -13

Step 4: Multiply row 2 with 2 and add it in row 3:

0 2 -40 -18

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0    0     1      |  -31

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x - 2y + z = 4

• y - 20z = -9

• z = -31

Step 6: Since we have calculated z = -31, put this value in equation 2:

• y - 20(-31) = -9

• y = -9 - 620

• y = -629.

Step 8: Put z = -31 and y = -629 in equation 1:

• x - 2(-629) - 31 = 4

• x + 1258 - 31 = 4

• x = 35 - 1258.

• x = -1223

So final answer is x = -1223, y = -629, and z = -31!!!

Answer:

Total cost spent on supplies = 5 dollars

Lemonade will be sold at 0.5 dollars.

Let the total glasses of lemonade sold be x

So, revenue generated will be = 0.5x

To get the break even we will equal both.

[tex]0.5x=5[/tex]

[tex]x=5/0.5[/tex]

x = 10

Hence, number of glasses to be sold are 10.

The profit or y can be found as;

[tex]y=0.5x-5[/tex]

So, putting x = 11

[tex]y=0.5(11)-5[/tex]

y = 0.5

Putting x = 12

[tex]y=0.5(12)-5[/tex]

y = 1

Putting x = 13

[tex]y=0.5(13)-5[/tex]

y = 1.5

The slope is 0.5.

The y-intercept is -5. This means if 0 glasses of lemonade are sold then there is a loss of $5.

The y intercept is obtained when x=0.

[tex]y=0.5(0)-5[/tex]

y = -5

The x-intercept is 10 or the number of glasses I must sell to break even.

Answer:

3x yrs old

Step-by-step explanation:

Answer:

A=10753.5715 m^2.

Step-by-step explanation:

The area of a triangle with the information SAS given is:

A=1/2 * (side) * (other side) * sin(angle between)

A=1/2 * (204.61)*(120.32) * sin(60.881)

A=10753.5715 m^2.

SAS means two sides with angle between.

Answer: [tex]10,753.57\ m^2[/tex]

Step-by-step explanation:

You need to use the SAS area formula. This is:

[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]

You know that the  triangular field has sides of 120.32 meters and 204.61 meters and the angle between them measures 60.881°. Then:

[tex]a=120.32\ m\\b=204.61\ m\\\alpha =60.881\°[/tex]

Substituting these values into the formula, you get that the area of this triangle is:

[tex]A=\frac{(120.32\ m)(204.61\ m)*sin(60.881\°)}{2}\\\\A=10,753.57\ m^2[/tex]

Answer:

probably sas

Step-by-step explanation:

sas because the 2 sides are congruent, but i don't have enough information to know for sure

Answer:

[tex]2\ miles[/tex]

Step-by-step explanation:

we know that

The distance around the park is equal to the perimeter of the rectangular park

The perimeter is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=\frac{3}{4}\ mi[/tex]

[tex]W=\frac{1}{4}\ mi[/tex]

substitute the values

[tex]P=2(\frac{3}{4}+\frac{1}{4})[/tex]

[tex]P=2(\frac{4}{4})[/tex]

[tex]P=2\ mi[/tex]

Answer:

3 219⁄1000 km. [2 mi.]

Step-by-step explanation:

P = 2l + 2w

P = 2[¾] + 2[¼]

P = 1½ + ½

P = 2

I am joyous to assist you anytime.

Answer:

Option C 89

Step-by-step explanation:

In this problem we  know that

KJ=KR+RJ

we have

KJ=95 units

KR=6 units

substitute and solve for RJ

95=6+RJ

subtract 6 both sides

RJ=95-6=89 units

Answer:

The correct option is C.

Step-by-step explanation:

We need to find the length of line segment  RJ.

From the given figure it is clear that line segment KJ is the sum of line segments KR and RJ.

[tex]KJ=KR+RJ[/tex]

The length of line segment KJ is 95 units and the length of KR is 6 units.

Substitute KJ=95 and KR=6 in the above equation.

[tex]95=6+RJ[/tex]

Subtract 6 from both the sides.

[tex]95-6=6+RJ-6[/tex]

[tex]89=RJ[/tex]

The length of segment RJ is 89 units. Therefore the correct option is C.

Answer:

4/3

Step-by-step explanation:

I drew a picture in the attachment to show what we are looking at.

I found the point (-3,-4).  I drew my angle my triangle from the x-axis and the origin to the point.

The angle that is theta is the one formed by the x-axis and the hypotenuse of the triangle where this hypotenuse was formed from the line segment from the origin to the given point.

[tex]\tan(\theta)=\frac{\text{opposite to }\theta}{\text{adjacent to }\theta}=\frac{-4}{-3}=\frac{4}{3}[/tex]

So we could have said [tex]\tan(\theta)=\frac{y}{x}[/tex].

Answer:

A. f and h

Step-by-step explanation:

For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.

For function f:

The values of f(x) are: 5,8,11,14

We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.

For function g:

The values of g(x) are: 8,4,16,32

We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.

For function h:

The values of h(x) are: 28, 64, 100, 136

We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.

To identify the linear relationships in the tables, we need to look for constant rates of change. Functions f and g have this property, while h does not.

In order to identify which functions represent linear relationships, we need to look for patterns in the tables. A linear relationship is characterized by a constant rate of change.

Looking at the tables, we can see that functions f and g have a constant difference between the values in the input column (x) and the output column (y). However, function h does not have a constant rate of change, so it does not represent a linear relationship.

Therefore, the correct answer is A. f and h, as these two functions represent linear relationships.

https://brainly.com/question/15070768

#SPJ3

If pressure is constant

then PV= nRT

is equivalent to V= ( nR/P) T

V= kT ( where k is constant nR/P)

As V is directly proportional to T

So V1/T1 = V2/T2

Answer:

The correct answer

Step-by-step explanation:

Answer:

The expression is (x,y) -----> (x-3,y-2)

Step-by-step explanation:

we have that

A(1,5) ----> A'(-2,3)

so

The rule of the translation is equal to

(x,y) -----> (x',y')

(x,y) -----> (x-3,y-2)

That means-----> the translation is 3 units at left and 2 units down

Answer:

y - 15000 = 12500(x-3)

Answer:

-1

Step-by-step explanation:

To find the slope of a line given two points, you can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line.

Or you could just line up the points vertically and subtract them vertically, then put 2nd difference over first.

Like so:

 (  2   ,     1   )

-(    1  ,     2   )

--------------------

    1          -1

So the slope is -1/1 or just -1.

Answer: 4

Step-by-step explanation: 4 is the answer because an integer is any whole number, but not 0.

The perimeter of the walls is  6 + 6 + 8 + 8 = 28 feet.

The perimeter of the window is 2 + 2 + 1.5 + 1.5 = 7 feet.

Total = 28 + 7 = 35 feet of tape.

I would say B.35 is the answer.

Answer:

The answer would be 14

Step-by-step explanation:

you just divide 28,00 by 200 and that gives you 14

Answer:

[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]

Step-by-step explanation:

[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=\g\bigg(f(x)\bigg)=(-x+8)^4\\\\(g\circ f)(2)\to\text{put x = 2 to the equation}\ (g\circ f)(x):\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]

[tex]\bf \begin{cases} f(x)=&-x+8\\ g(x)=&x^4\\ (g\circ f)(x) =& g(~~f(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(2)=-(2)+8\implies f(2)=\boxed{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{(g\circ f)(2)}{g(~~f(2)~~)}\implies g\left( \boxed{6} \right) = (6)^4\implies \stackrel{(g\circ f)(2)}{g(6)} = 1296[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+y+z=2&(1)\\2x+y-z=-1&(2)\\x=5-2z&(3)\end{array}\right\\\\\text{Substitute (3) to (1) and (2):}\\\\\left\{\begin{array}{ccc}(5-2z)+y+z=2\\2(5-2z)+y-z=-1&\text{use the distributive property}\end{array}\right\\\left\{\begin{array}{ccc}5-2z+y+z=2\\10-4z+y-z=-1\end{array}\right\qquad\text{combine like terms}\\\left\{\begin{array}{ccc}5+y-z=2&\text{subtract 5 from both sides}\\10+y-5z=-1&\text{subtract 10 from both sides}\end{array}\right[/tex]

[tex]\left\{\begin{array}{ccc}y-z=-3\\y-5z=-11&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y-z=-3\\-y+5z=11\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4z=8\qquad\text{divide both sides by 4}\\.\qquad\qquad \boxed{z=2}\\\\\text{Put it to the first equation:}\\\\y-2=-3\qquad\text{add 2 to both sides}\\\boxed{y=-1}\\\\\text{Put the values of}\ z\\text{to (3):}\\\\x=5-2(2)\\x=5-4\\\boxed{x=1}[/tex]

Answer:

201.143 (approx.) cm²

area of circle = (pi)x(radius)^2

= 22/7 x (8)^2

=22/7 x 64

= 1408/7

= 201.142857143

= 201.143 cm^2 (approx.)

Answer:

the approximate area of circle is 201 cm²

D is the correct option.

Step-by-step explanation:

From, the given figure, the diameter of the circle is 16 cm.

The radius is half of the diameter.

Hence, the radius of circle is 16/2 = 8 cm

The area of a circle is given by

[tex]A=\pi r^2[/tex]

Substituting the value of r and π

[tex]A=3.14(8)^2\\\\A=200.96\\\\A\approx201[/tex]

Therefore, the approximate area of circle is 201 cm²

D is the correct option.