1- Finding angle measures between intersecting lines

NOTE: Angles not necessarily drawn to scale

x = ??

Given:

x gets  larger and larger in the negative direction.

To find:

The polynomial function which gets larger and larger in the negative direction.

Solution:

In options a, c and d, degree of polynomials are even and leading coefficient is positive. So,

[tex]f(x)\to \infty\text{ as }x\to -\infty[/tex]

In option b, degree of polynomial is odd and leading coefficient is positive. So,

[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]

Therefore, the function in option b, [tex]f(x)=6x^3+4x^2-15x+32[/tex] gets larger and larger in the negative direction as x gets  larger and larger in the negative direction.

Hence, the correct option is b.

We want to see which polynomial function gets larger and larger as the variable increases in the negative direction. We will see that the correct option is d: f(x) = 8x^6 + 1

Here you need to remember two things.

As the larger the exponent is, the faster the polynomial grows.

When we evaluate a negative number in an even exponent, the outcome is always positive.

Then the polynomials that get larger and larger as x increases in the negative direction are all the polynomials with a even leading exponent, particularly, the one that increases faster is the one with the largest leading exponent, which is:

d. f(x) = 8x^6 + 1

If you want to learn more, you can read:

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Answer:

What is the starting temp?

Step-by-step explanation:

Answer:

a. the measure of angle A is 113 degrees

the measure of angle B is 67 degrees

Step-by-step explanation:

Remember, linear pairs have a sum of 180 degrees when added. So, if you add your angle measures and set it equal to 180, then you just need to solve from there.

7x-13+3x+13=180

combine like terms

(7x+3x)+(-13+13)=180

10x+0=180

10x=180

divide both sides by 10 to isolate x

x=18

now that you have x, plug it into your angle measures

m<a: 7(18)-13

126-13

113

m<b: 3(18)-13

54+13

67

Answer:

$300

Step-by-step explanation:

You want to calculate the interest on $2500 at 4% interest per year after 3 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $2500.00.

r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.

t is the time involved, 3....year(s) time periods.

So, t is 3....year time periods.

To find the simple interest, we multiply 2500 × 0.04 × 3 to get that:

The interest is: $300.00

Usually now, the interest is added onto the principal to figure some new amount after 3 year(s),

or 2500.00 + 300.00 = 2800.00

Step-by-step explanation:

a. 8,435 is divisible by 5

b. 981 is divisible by 3 and 9

Answer:

The equality is not true.

Step-by-step explanation:

[tex](4^2 +24) = |(3 - 7) - 16|[/tex]

[tex](16 +24) = |(3 - 7) - 16|[/tex]

[tex]40 = |(3 - 7) - 16|[/tex]

[tex]40 = |(- 4) - 16|[/tex]

[tex]40 = |-20|[/tex]

[tex]40 = 20[/tex]

But

[tex]40 \neq 20[/tex]

Answer:

39.25

Step-by-step explanation:

the formula is a = (3.14 × [tex]r^{2}[/tex]) / 2

the equation is a = (3.14 ×[tex]5^{2}[/tex]) / 2

5 is the radius

1. [tex]5^{2}[/tex] = 25

2. 3.14 × 25 = 78.5

3. 78.5 / 2 = 39.25

I hope this helped! :)

Answer:

12.5π or 39.25

Step-by-step explanation:

10 is diameter, we first find the radius which is 10/2 = 5 and so we know the area formula of the circle is πr^2 so 5^2 is 25 and then there's a π at the end so 25π, but it's a semicircle so 25π/2 which is 12.5π, if it's in base 10 (decimal form) then simply do 12.5 x 3.14 = 39.25

Answer:

6

Step-by-step explanation:

6-1=5

5 x 5= 25

Answer:

a) 15

b) 25

c) p = 15w + 25, where p is puppets and w is weeks

Step-by-step explanation:

a) Gepetto makes 15 puppets a week, so as the weeks increase by 1, puppets increases by 15, making the slope 15

b) Gepetto started out with 25 puppets. This means that when x = 0 (0 weeks), there will be 25 puppets already

c) The slope and y-intercept were incorporated into an equation in slope-intercept form.

Answer:

t=1.06x+10 where x=The amount of tickets bought

Step-by-step explanation:

you multiply x by 1.06 to add the extra tax onto it.

You add the 10 to add the $10 booking fee

Answer/Step-by-step explanation:

An easy way to be sure two lines are perpendicular is if the product of both slopes equals -1.

That is: [tex] (m_1)(m_2) = -1 [/tex]. Where, m1 and m2 are slopes of both lines respectively.

Let's find the slope of the both lines.

Slope of the line that slants upward from left to right using coordinates (0, 0) and (2, 2) of two points on the line:

[tex] m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} [/tex]

[tex] m_1 = 1 [/tex]

Slope of the line that slants downwards from left to right using coordinates (2, 2) and (0, 4) of two points on the line:

[tex] m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{0 - 2} = \frac{2}{-2} [/tex]

[tex] m_2 = -1 [/tex]

Find the product of both slopes

[tex] (m_1)(m_2) = (1)(-1) = -1 [/tex]

Therefore, we know the lines are perpendicular because [tex] (m_1)(m_2) = -1 [/tex].

Answer:

21- 2.50 = 18.50

he can only buy 3, 5 10 15. he can buy 9.

Answer: 4310

Step-by-step explanation: Because it is a positive exponent instead of negative, you would move the decimal to the right 3 places

y = a(x - h)² + k   is the vertex form of an equation of a parabola with vertex (h,k)

We get the coordinates of the vertex of parabola from that form: (h, k)

We also know if the parabola goes up or down: a>0 or a<0

We can tell how many roots has the equation:

(a>0 and q>0) or (a<0 and q<0) ⇒ no roots

a≠0 and q=0  ⇒  one root:  x₀=p

(a>0 and q<0) or (a<0 and q>0) ⇒ two roots

We can also determine the roots (if they exist):

a(x - h)² + k = 0

a(x - h)² = - k

(x - h)² = - k/a

x - h = √[-k/a]     ∨   x - h = - √[-k/a]  

x = √[-k/a] + h     ∨   x = - √[-k/a] + h

Usually you use this form to find the equation of parabola when you have got given the vertex and some other point from that parabola.

Answer and explanation:

To determine number if DVDs that can be bought for $20, we simply check price per DVD then calculate how many $20 can buy

Number of DVDs that can be rented for no more than $20

=$20 divided by cost of each DVD $3.50

=20/3.50

=5.714

=5 DVDs

We round down because 0.714 DVD does not qualify as one DVD

Answer:

0

Step-by-step explanation:

-7 + 7 should be equal to 0. Maybe you wrote the numbers or the sign wrong..?

Answer:

=0

Step-by-step explanation:

ese es la respuesta mijo

Answer:

20

Step-by-step explanation:

start by using system of equations

x = cola

y = root beer

x + y = 30

x = 2y

now either use substitution or elimination. for me, substitution is easier.

the second equation already has one variable isolated ( x ) so, plug that into the first equation.

2y + y = 30

y = 10

now plug your answer into the original equation.

x + 10 = 30

x = 20

hope this helps :)

Answer:

adding the $35 with the $55 be up to 90 . I think that the answer to it hope is helpful

Answer:

A. 10 times

Step-by-step explanation:

Answer:

A. Ten times.

Step-by-step explanation:

If it was one place to the right, it would have been one-tenth, so that's gone. If it was moved twice in place of either direction, it would be hundredths, so those are also eliminated. So, It's 10 times.

Answer:

integer and rational

Step-by-step explanation:

Answer:

Step-by-step explanation:

i believe it would be A...

Answer:

Step-by-step explanation:

Let the unknown number be x

[tex]75 \% \times x = 240 \\ \frac{75x}{100} = 240[/tex]

Cross Multiply

[tex]75x \times 1 = 100 \times 240 \\ 75x = 24000[/tex]

Divide both sides of the equation by 75

[tex] \frac{75x}{75} = \frac{24000}{75} [/tex]

Simplify

[tex]x = 320[/tex]

Answer:

320

Step-by-step explanation:

you would do [tex]\frac{75}{100}[/tex]*x=240

then you would multiply both sides by 100 and then divide both sides by 75 which woud give you x=240*[tex]\frac{100}{75}[/tex]

which would give you [tex]\frac{24000}{75}[/tex]=x

which then simplifies down to 320

1. (1.) -24, (2.) 6, (3.) -3

2. Positive

3. Difference = Subtraction

Product = Multiplication

Quotient = Division

Answer:

No solution

Step-by-step explanation:

Parallel lines

Answer:

no solution

Step-by-step explanation:

easy way to remember parallel lines don’t touch.....no solution ever

Answer:

Step-by-step explanation:

Given the rate at which the car elevation decreases expressed by the function

E(x) = -150x+13,500 where x is in minutes.

To evaluate E(5), we will substitute the variable x = 5 into the function as shown;

E(5) = -150(5)+13,500.

E(5) = -750+13,500.

E(5) = 13500-750

E(5) = 12750

This means that after 5minutes, the car elevation has decreased by 12,750feet

Answer:

graph 1  

Step-by-step explanation:

Graph using table of values

x           y

2       -2/3

1         -4/3

0          -2

they are all on that graph

The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

According to the question

Represents a line with a slope of -2/3  

i.e ,

m = -2/3  

y-intercept equal to that of the line

y = [tex]\frac{2}{3}x-2[/tex]

i.e ,

at y-intercept , x = 0

y = -2

Now, Putting value in standard form of line

y = mx + c

-2 = 0 + c  

c = -2

now , substituting the values of m and c in standard form of line

y = mx + c  

y =  [tex]\frac{-2}{3}x-2[/tex] --------- (equation of graph )

Now ,

x             y

0            -2

3/2         1

3             0

Only option 4 have these points

Hence, The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

To know more about slope and intercepts here:

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Answer:  y = 3/2x + 1

Step-by-step explanation:  For a perpendicular line, take the reciprocal of  "m"  and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b   Substitute for b in y = (3/2)x + 1