what is slope in algebra 1?

Answer:

put 1/2as a value of x in the equation and then solve .then the answer will be -1

Answer:

[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]

Step-by-step explanation:

[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]

In order to calculate f(1/2) ,all we have to do

is replacing x by 1/2 in the expression of f.

Then

[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]

        [tex]=\frac{\sqrt{1+3} }{3-5}[/tex]

        [tex]=\frac{\sqrt{4} }{-2}[/tex]

        [tex]=\frac{2}{-2}[/tex]

        [tex]=-1[/tex]

Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)

To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.

Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.

Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.

Evaluating f(x) at x = 0, we get:

f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)

= (-2)(4)(5)

= -40

Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.

Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative

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Full Question:

f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?

The difference in the given functions is 2x^3 + 6x^2 -8x + 1

Given the following function a shown

f(x)= 2x^3 + 6x^2 -5x - 3

g(x)= 3x-4

Take the difference

(f-g)(x) = f(x) - g(x)

Substitute

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - (3x - 4)

Expand

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - 3x + 4

(f-g)(x) = 2x^3 + 6x^2 -8x + 1

Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1

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Answer:

y = -t

Step-by-step explanation:

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

   and parallel to a vector <a, b, c> is given by :

   x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    (answer)

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Answer:

ai) m = 17, applicable past x = 23/17; aii) m = 4; applicable past 3 dad jokes

Step-by-step explanation:

to calculate slope you use the (y2 - y1) / (x2 - x1) equation

so for the first one

(62 - 11) / (5 - 2)

51 / 3 = 17

the equation for this is y = 17x + b

plug in values to find b

11 = 34 + b

b is -23

y = 17x - 23

because distance cannot be negative we must find when x is exactly 0 to find where it is applicable

17x = 23

x = 23/17

for the second one we can subtract again

(10 - 2) / (5 - 3)

8 / 2

4 is the slope

like before we must find b and then find where y is 0

y = 4x + b

2 = 12 + b

b = -10

y = 4x - 10

4x = 10

x = 5/2

since you cannot have 1/2 a dad joke we round up from 2 1/2 to 3

Step-by-step explanation:

sin(x/2) = sqrt((1 - cos(x))/2)

cos(x/2) = sqrt((1 + cos(x))/2)

tan(x/2) = sin(x/2)/cos(x/2)

sin(x) = 15/17

so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.

via Pythagoras we get the 3rd, horizontal side :

17² = 15² + side²

289 = 225 + side²

64 = side²

side = 8

cos(x) = 8/17

sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =

= 0.514495755...

cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =

= 0.857492926...

tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =

= 3/5 = 0.6

Answer:

4 r^3

Step-by-step explanation:

sqrt ( 16 r^6 )    = sqrt ( 4^2 * (r^3)^2  )    =   4 r^3

The best buy is (d) a 9 oz box of rice $1.25

The best buy is the product that has the least unit rate.

The unit rate is calculated as:

Unit = Price/Weight

So, we have:

Box 1:

Unit rate = $0.90/6 oz = $0.150 per oz

Box 2:

Unit rate = $1.93/12 oz = $0.161 per oz

Box 3:

Unit rate = $2.42/16 oz = $0.151 per oz

Box 4:

Unit rate = $1.25/9 oz = $0.139 per oz

The least unit price is $0.139 per oz for box 4

Hence, the best buy is (d) a 9 oz box of rice $1.25

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Answer:

the answer is -7+-25=-32

first one b 315, second d

Step-by-step explanation:

18*=3*+315

7*+4*=a*

Answer:

14.30

Step-by-step explanation:

6.50/5=1.3

so one ice cream is 1.30 pounds

1.30X11=14.3

so 11 ice creams is 14.30 pounds

Answer:

90°

Step-by-step explanation:

A complement angle is the same as a right angle

Hii!

___________________________________________________________

Answer:

Step-by-step explanation:

The sum of complementary angles is always 90 degrees.

We can find the complements of these two angles by setting up an equation.

x+42=90

Subtract 42 from both sides

x=48

This problem can be solved the same way!

x+35=90

Subtract 35 from both sides

x=55

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Hope that this helped! Best wishes.

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Answer:

4/25

Step-by-step explanation:

4/5 ÷ 5 = 4/5 × 1/5 = 4/25

The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:

P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.

The probability = 1/2.

The probability of an event defines the chance of the occurrence of that event. It is given by the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.

If we suppose an event to be A, the total number of possible outcomes favorable to A be n, and the total number of outcomes in the experiment be S, then the probability of event A can be given as:

P(A) = n/S.

In the question, we are asked to find the formula that defines the probability that a point on the grid will be in the blue area, where the grid contains 20 squares, 10 of them being shaded blue.

We take the event that the chosen point is in the blue area as A.

The total number of outcomes favorable to this event A can be given by n, which will be equal to the number of blue squares = 10

The total number of outcomes in the experiment can be given by S, which will be equal to the number of squares = 20.

Now, the formula for the probability of event A can be written as

P(A) = n/S = 10/20 = 1/2.

The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:

P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.

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The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have (−5, 3) be a point on the terminal side of θ.

Perpendicular = -5

Base = 3

From Pythagoras' theorem:

Hypotenuse² =  (3)² + (-5)²

Hypotenuse = √34

cosθ = 3/√34

cscθ = -√34/5

tanθ = -5/3

Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

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Answer:

Step-by-step explanation:

Answer:

11 + x = 28

Step-by-step explanation:

The number of books they bought must add to 28.

The final answer of the Inventory is $3540.

The term inventory refers to the raw materials used in production as well as the goods produced that are available for sale.

FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold

Ending inventory comprises of goods bought in May, September and November

cost of the ending inventory :

(4 x $130) + (12 x $135) + (10 x$140) = $3540

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Answer:

314 in²  (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex.  The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

To find the area of a regular polygon, we first need to calculate the apothem.   The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]

Area of a Regular Polygon

[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]

[tex]\implies \sf A=314.3672216...[/tex]

[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]

Answer:

A. 24

Step-by-step explanation:

Least common multiple of 8 and 12 = 24

8× 1 = 8 12×1 = 12

8×2 = 16 12×2=24

8×3 = 24

L.C.M (8,12) = 24

The greatest multiple that occurs in both the multiples of 8 and 12, is 24.

Hence, the least common multiple here is 24.

Answer:

1/(7^5)=1/16807

Step-by-step explanation:

Assuming 7-key mean zero up to 7,

# of possible codes = 17^5 = 16807

=====

Probability of first try correct = 1/7^5

Answer: Point G.

Step-by-step explanation:

Count the number of spaces between points A and B. Then divide that number by 2 and count that many spaces from one point.

14/2=7

I hope this helps!! Pls mark brainliest :)

Answer:

12.5%

Step-by-step explanation:

To find what percent of 120 15 is, we must find what 15/120 is.

15/120 = 0.125. To convert to a percent, we move the decimal two places to the right. So, the answer is 12.5%.

Brainliest, please :)

Answer:

12.5%

Step-by-step explanation:

Answer:

$800

Step-by-step explanation:

per hour $40×10hours=$400

$400÷$50=8 times initial fee

8×$50=$400 total initial fee

$400hours fee+$400 initial fee=$800 total payment

Answer:

a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.

b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.

c. When the time is greater than 360 minutes, the temperature of the turkey decreases.

Answer:

right angle

acute

acute

obtuse

obtuse

Step-by-step explanation:

Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.

< DBF = <DBE + <EBF

< DBF = 25 + 65 = 90 (right angle)

<EBD = 25 (given) (acute)

<DBC = 50 (given) (acute)

<ABE = <ABF + <FBE

<ABE = 40 + 65

<ABE = 105 (obtuse)

<CBF = <CBD + <DBE + <EBF

<CBF = 50 + 25 + 65

<CBF = 140 (obtuse)

Answer:

y = 4x - 5

Step-by-step explanation:

y = mx + b

By putting above values in equation (i)

-1 = 4 (1) + b

-1 = 4 + b

-5 = b

b = -5

y = 4x - 5