Choose two statements that are true for this expression.

Answer:f(x)=4x+1=9

=> 4x=9-1

=> 4x=8

=>x=2

Step-by-step explanation:

The statement "a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions" is true .

A linear equation is an algebraic equation of the form [tex]y= mx+b.[/tex]involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is , [tex]y = ax^2 + bx + c[/tex]

where a, b, and c are numbers and a cannot be 0.  

According to the question

A system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.​

This statement is true as

if we see graphically  

A quadratic equation is a parabola and a linear equation is a straight line.

There could be 3 situations of intersection of line and parabola

1. straight line never crosses the parabola

i.e line passing above or below parabola without touching

it is called zero solution

2. where the straight line is a tangent to the parabola, 'touching' it at only one point.

i.e single point lies in both line and parabola

it is called one solution

3. the line cuts across the parabola, it will cut the parabola at 2 points

it is called two solution .

Hence, The statement " a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions "is true .

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Answer:   The intersections of the graphs of a system of equation correspond to the solutions of the system. Since we saw that a line can intersect a parabola zero, one, or two times, a linear-quadratic system can have zero, one, or two solutions.

Step-by-step explanation:PLATO

9514 1404 393

Answer:

  r = 2

Step-by-step explanation:

"A varies inversely with r cubed" means the relation is of the form ...

  A = k/r³

We can find the value of k as ...

  k = Ar³ = 72·5³ = 9000 . . . . . . . multiply the above relation by r³

And we can solve this for r to get ...

  r³ = 9000/A . . . . . . divide by A

  r = ∛(9000/A) . . . . . take the cube root

So, for A = 1125, we have ...

  r = ∛(9000/1125) = ∛8

  r = 2

Answer:

option A is right answer

Answer:

C

Step-by-step explanation:

5 states per year = 5y

Already visited 10 states = +10

5y + 10 = 50

To find y

5y = 50 - 10

5y = 40

y = 40/5

y = 8 years

Answer:

f(x) = y

Step-by-step explanation:

Think of it as a input-output function machine, where you give a number as input to the machine, and the you get a number as the output from the machine. The input is x which goes inside of the ( )'s, and the output is f(x). The output 'f(x)' is sometimes called the y-value because y = f(x).

For example f(-2) = 4. The number you give to the machine is -2 since it's the x-value and the number is in ( )'s. The output number the machine gives back to you is 4, which is the y-value.

Hope this helps!

Answer:

gọi

Step-by-step explanation:

We have that the  first term of the progression is

b=4

From the Question we are told that

Third terms of a Geometric Progression is 48

Sum of third and fourth terms is 144

[tex]x_3+x_4=144[/tex]

Generally the equation for the common ratio  is mathematically given as

   [tex]\frac{br^2+br^3}{br+br^2}=\frac{144}{48}\\\\\frac{br^2+br^3}{br+br^2}=3[/tex]

  r=3

Therefore

Since

   [tex]br+br^3=48\\\\b(3)+b(3)^3=48[/tex]

  b=4

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Answer:

540

Step-by-step explanation:

Divide the rs by men. 360÷18. It's 20. Then divide by 5. Everyday each man makes 5 rs.

So use that for the other. 15x4=60 60x9=540

Step-by-step explanation:

A line perpendicular to a surface or to another line considered as a base.

Answer:

l think it's consumer spending

Answer:

true, negative, negative

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

12×4=48

mark bought twice as many pens so 48×2=96

Step-by-step explanation:

Mark bought 96 pens , 12 multiply by 8 is equal to 96

Answer:

October 30

Step-by-step explanation:

Subtract three days from November 2

Answer:

410.2 miles total

Step-by-step explanation:

58.6 miles × 7 days = 410.2 miles

[tex]\text{x}=5\\\\2\text{x}^2+\text{x}(100-15\text{x})=2\cdot5^2+5\cdot(100-15\cdot5)=\\\\=2\cdot25+5\cdot(100-75)=50+5\cdot25=\\\\=50+125=\boxed{175}[/tex]

[tex] \boxed{ \boxed{ \mathrm{ \: \: \: \: \: \: \: \: \: 175 \: \: \: \: \: \: \: \: \: }}}[/tex]

Plugging the value of x as 5 in the given expression we get,

[tex] \hookrightarrow \: 2 {x}^{2} +x (100 - 15x)[/tex]

[tex] \hookrightarrow \: 2(5) {}^{2} + 5(100 - (15 \times 5))[/tex]

[tex] \hookrightarrow \: (2 \times 25) + 5(100 - 75)[/tex]

[tex] \hookrightarrow \: 50 + 5(25)[/tex]

[tex] \hookrightarrow \: 50 + 125[/tex]

[tex] \hookrightarrow \: 175[/tex]

Answer:

0.81

Step-by-step explanation:

Answer:

0.81818181818181....

Step-by-step explanation:

It is irrational

Answer:

Derivative of any constant is zero

you can solve it by first derivative rule

Answer:

Derivative of any constant is zero

Step-by-step explanation:

9514 1404 393

Answer:

  similar by AA

Step-by-step explanation:

Each of the smaller right triangles shares an acute angle with the original (largest) triangle, so all of the triangles are similar by the AA similarity postulate.

Answer:

3x(7-3)y2=21

Step-by-step explanation:

hope it is write

Answer:

-4%   -1/25

Step-by-step explanation:

To convert a decimal to a percentage, multiply it by 100.

-0.04 * 100 = -4

To convert a decimal to a fraction, put the decimal as a fraction over 1 and multiply until the numerator (top number) is a whole number and then simplify.

[tex]\frac{-0.04}{1}[/tex] x [tex]\frac{100}{100}[/tex] = [tex]\frac{-4}{100}[/tex]

-4/100 simplified = -1/25 (because 4 goes into 100 25 times)

In the given line segment, the coordinates of Point A and Point B is (1, 3) and (4, 6).

So, according to the given image:

Then, Point B is the point with coordinates (4, 6), while Point A is the line (1, 3).

Therefore, in the given line segment, the coordinates of Point A and Point B is (1, 3) and (4, 6).

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The correct question is given below:
Given the directed line segment AB: Point A is the line with coordinates ______ and Point B is the point with coordinates ______.​

Part (a)

We have some unknown number x which is a placeholder for a positive whole number (eg: x = 4).

What's happening to x are these two things, in this exact order

We multiply first, then add. The order is important. We're following the order of operations PEMDAS here. If we knew what x was, then we'd go forward in the PEMDAS chain; however, we don't know what x is. So we go backwards in the chain to isolate x. This will undo every operation applied to x.

So,

C = 85x+60

C-60 = 85x

85x = C-60

x = (C-60)/85

In the second step, I subtracted 60 from both sides to undo the "plus 60" operation. Then in the last step, I divided both sides by 85 to undo the multiplication.

===============================================================

Part (b)

How many ski trips can we take if we spend $315? We simply plug in C = 315 into that equation we just found at the end of part (a).

Doing so gets us...

x = (C-60)/85

x = (315-60)/85

x = 255/85

x = 3

We can take 3 ski trips if we spent a total of $315

Repeat the same steps for C = 485

x = (C-60)/85

x = (485-60)/85

x = 425/85

x = 5

We can take 5 ski trips if we spent a total of $485

Note how plugging something like x = 5 into the original equation yields:

C = 85x+60

C = 85*5+60

C = 425+60

C = 485

Showing that x = 5 leads to C = 485. This helps confirm the second answer. I'll let you check the first answer.

Answer:

Step-by-step explanation:

The vector AP is in the same directionas AB but its length is 1/3 of AB

No AB = (7-(-2)) i + (-2-4)j = 9i -6j.

It follows that AP = (1/3)(9i-6j) = 3i - 2j.

Now OP = OA +AP = (-2i + 4 j ) + (3i-2j) = i + 2j

So P(1,2).

Hello there!

Formulas

[tex] \displaystyle \large{ \sin (2 \theta) = 2 \sin \theta \cos \theta} \\ \displaystyle \large{ \cos (2 \theta) = \begin{cases} 2 { \cos}^{2} \theta - 1 \\ 1 - 2 { \sin}^{2} \theta \\ { \cos}^{2} \theta - { \sin}^{2} \theta \end{cases}}[/tex]

First, we have to find cos(theta). We know that the theta lies in Q3 which is negative for both sin and cos. To find cos, you can use the identity or Pythagoras.

Recall

[tex] \displaystyle \large \tt{ \sin \theta = \frac{opposite}{hypotenuse} } \\ \displaystyle \large \tt{ \cos \theta = \frac{adjacent}{hypotenuse} }[/tex]

Finding cos, I will use Pythagoras.

Recall Pythagorean

[tex] \displaystyle \large{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]

From sin = -1/6

[tex] \displaystyle \large{ {1}^{2} + {b}^{2} = {6}^{2} } \\ \displaystyle \large{1 + {b}^{2} = 36 } \\ \displaystyle \large{ {b}^{2} = 36 - 1 } \\ \displaystyle \large{ {b}^{2} = 35 } \\ \displaystyle \large{ {b} = \sqrt{35} }[/tex]

b is our adjacent. Hence,

[tex] \displaystyle \large{ \cos \theta = \frac{ \sqrt{35} }{6} }[/tex]

Since theta is in Q3, cos < 0 or in negative.

[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]

Finding sin(2theta)

[tex] \displaystyle \large{ \sin \theta = - \frac{ 1 }{6} }[/tex]

Hence,

[tex] \displaystyle \large{ \sin 2 \theta = 2( - \frac{ 1 }{6} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = ( - \frac{ 1 }{3} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = \frac{ \sqrt{35} }{18} }[/tex]

Recall

Finding cos(2theta)

The cos of 2theta has multiple formulas. All of them are same and also identity to each others.

I will be using the first one as it only involves cos, not sin.

[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]

Therefore,

[tex] \displaystyle \large{ \cos2 \theta = 2 { ( - \frac{ \sqrt{35} }{6} )}^{2} - 1 } \\ \displaystyle \large{ \cos2 \theta = 2 (\frac{ 35}{36}) - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - \frac{18}{18} \longrightarrow \boxed{\frac{17}{18} }}[/tex]

Answer

The last choice.

Let me know if you have any questions!

Answer:

the answer is 3-3n

Step-by-step explanation:

6-(n-1)x3

=3-3n

An equation for the nth term of the arithmetic sequence is aₙ=9-3n.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is 6,3,0,-3,...

Here, first term a=6 and common difference is 3-6=-3

Substitute a=6 and d=-3 in aₙ=a+(n-1)d, we get

aₙ=6+(n-1)(-3)

aₙ=6-3n+3

aₙ=9-3n

Therefore, an equation for the nth term of the arithmetic sequence is aₙ=9-3n.

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Answer:

[tex] = 3e + 10f - 9[/tex]

Step-by-step explanation:

[tex]4e + 2f - 9 + 8f - e[/tex]

[tex]3e + 2f - 9 + 8f[/tex]

[tex] \boxed{\green{= 3e + 10f - 9}}[/tex]