According to the rational root theorem, which of the following are possible
roots of the polynomial function below?
F(x) = 8x2-3x2 + 5x + 15

Answer: C

Step-by-step explanation:

(-1,4) is the vertex. reflect (-2,3) and (-3,0) onto the other side of the y-axis. you may use desmos to plug in the functions and the answer will be C, since it goes through the points given and reflected.

Final answer:

The function represented by the given set of points is f(x) = -x^2 - 2x + 3.

Explanation:

To determine the function represented by the given set of points, we can use the general form of a quadratic equation, y = ax^2 + bx + c. Substituting the points (-3,0), (-2,3), and (-1,4) into the equation, we can set up a system of equations and solve for the values of a, b, and c. The resulting function is f(x) = -x^2 - 2x + 3, which corresponds to option C.

Answer:

8x+ 6 is the translated mathematical expression.

Step-by-step explanation:

We are given the following English expression which are to translate into a mathematical expression:

'The sum of 6 and the product of 8 and x” into a mathematical expression'

Translating it in small chunks:

1. the sum of 6 ---> +6

2. product of 8 and x ---> 8x

Therefore, combining these we get the mathematical expression 8x + 6

For this case we must rewrite the given expression mathematically.

The sum of 6 and something else is written as:

[tex]6+[/tex]

The product of 8 and x is written as:

[tex]8x[/tex]

Finally, the expression is given by:

[tex]6 + 8x[/tex]

Answer:

The expression is given by:

[tex]6 + 8x[/tex]

The ladder resting against the house forms a triangle similar to the one in the image below

To answer this question you must use Pythagorean theorem

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

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = x

b = 4

c = 20

^^^Plug these numbers into the theorem

[tex]x^{2} +4^{2} =20^{2}[/tex]

solve for x

[tex]x^{2}[/tex] + 16 = 400

[tex]x^{2}[/tex] = 384

x = 8√6

or

x ≈ 19.5959....

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Acute isosceles triangle

Step-by-step explanation:

because an acute angle is more than 45 but less then 90.

that's all i know sorry!

Answer:

{0,-8}

Step-by-step explanation:

Factor!

3x(x+8)=0

3x=0  or x+8=0

x=0    or x=-8

Answer:

x=0    x =-8

Step-by-step explanation:

3x^2+24x=0

Factour out a 3x

3x(x+8) =0

Using the zero product property

3x =0   x+8 =0

x=0     x+8-8 =0-8

x=0    x =-8

Answer:

C

Step-by-step explanation:

first you subtract 1 from 4 to get 3 and then you add 3 to -2 to get 1 so the coordinates are (3, 1)

The coordinate of B' is,

B' = (3, 1)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;'

Rectangle ABCD has vertex coordinates A(1, -2), B(4, -2), C(4,-4), and

D(1, -4).

Since, It is translated 1 unit to the left and 3 units up.

Now, The rule for translated 1 unit to the left and 3 units up is,

(x, y) = (x - 1, y + 3)

So, The coordinate of B' is,

B' = (4 - 1, - 2 + 3)

B' = (3, 1)

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Answer:

Roberto wins:1/4

roberto loses:3/4

Step-by-step explanation:

Answer:

Roberto wins:1/4

roberto loses:3/4

Step-by-step explanation:

Answer:

(x²/4) + (y²/16) ≤ 1

Step-by-step explanation:

The general form of the ellipse in the graph is

x²/4 + y²/16 = 1

we want to find the inequality which represents the shaded area this will determine whether which of the following 2 choices are correct

Choice 1: x²/4 + y²/16 ≥ 1

Choice 2: x²/4 + y²/16 ≤ 1

we note that point (0,0) lies inside the shaded area. Which means if we substitute (0,0), it should create an equality that is valid.

try choice 1: 0²/4 + 0²/16  = 0 ≥ 1 (not valid because obviously zero is smaller than 1)  

try choice 1: 0²/4 + 0²/16  = 0 ≤ 1 (this is valid, hence choice 2  is the answer)

Answer:

43.98 cm

Step-by-step explanation:

Circumference is π x diameter

Diameter is 2 x radius

276.32/π = 87.955 (3dp)

87.955/2 = 43.978 (3dp)

43.98cm = radius

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(y2-y1) ^ 2 + (x2-x1) ^ 2}[/tex]

We find the distance AB:

[tex]A: (3,4)\\B: (- 5, -2)[/tex]

[tex]AB = \sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\AB = \sqrt {(- 5-3) ^ 2 + (- 2-4) ^ 2}\\AB = \sqrt {(- 8) ^ 2 + (- 6) ^ 2}\\AB = \sqrt {64 + 36}\\AB = \sqrt {100}\\AB = 10[/tex]

We have the BC distance:

[tex]B: (- 5, -2)\\C: (5, -2)[/tex]

[tex]BC = \sqrt {(5 - (- 5)) ^ 2 + (- 2 - (- 2)) ^ 2}\\BC = \sqrt {(5 + 5) ^ 2 + (- 2 + 2) ^ 2}\\BC = \sqrt {(10) ^ 2 + (0) ^ 2}\\BC = \sqrt {100}\\BC = 10[/tex]

We find the CA distance:

[tex]C: (5, -2)\\A: (3,4)[/tex]

[tex]CA = \sqrt {(3-5) ^ 2 + (4 - (- 2)) ^ 2}CA = \sqrt {(- 2) ^ 2 + (4 + 2) ^ 2}\\CA = \sqrt {4 + 36}\\CA = \sqrt {40}\\CA = \sqrt {4 * 10}\\CA = 2 \sqrt {10}[/tex]

Thus, the perimeter is given by:

[tex]10 + 10 + 2 \sqrt {10} = 20 + 2 \sqrt {10}[/tex]

ANswer:

[tex]20 + 2 \sqrt {10}[/tex]

Answer:

16 inches

Step-by-step explanation:

We are given that the diagonal of a parallelogram is 10 inches long and makes angles of 25° and 43° with the sides.

So the angles of the parallelogram are:

α = 25° + 43° = 68°

β = 180° - 68° = 112°

Using the sine law assuming x to be the longest side of the parallelogram:

[tex]\frac{x}{sin43} =\frac{10}{sin 25}[/tex]

[tex] x = 1 6 . 1 4 [/tex]

Therefore, the longest side is 16 inches.

Answer:

(- 1, 0), (9, 0)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (4, 75), so

y = a(x - 4)² + 75

To find a substitute (0, 27) into the equation

27 = a(- 4)² + 75 , that is

27 = 16a + 75 ( subtract 75 from both sides )

16a = - 48 ( divide both sides by 16 )

a = - 3, thus

y = - 3(x - 4)² + 75 ← equation in vertex form

To obtain the x- intercepts let y = 0

- 3(x - 4)² + 75 = 0 ( subtract 75 from both sides )

- 3(x - 4)² = - 75 ( divide both sides by - 3 )

(x - 4)² = 25 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{25}[/tex] = ± 5

Add 4 to both sides

x = 4 ± 5, hence

x = 4 - 5 = - 1 or x = 4 + 5 = 9

Substitute these values into the equation for corresponding values of y

x = - 1 : y = - 3(- 5)² + 75 = - 75 + 75 = 0 → (- 1, 0)

x = 9 : y = - 3(5)² + 75 = = 75 + 75 = 0 → (9, 0)

The x- intercepts are (- 1, 0), (9, 0)

Answer:

The x intercepts are (-1, 0) and (9, 0).

Step-by-step explanation:

We can write the equation in vertex form:

y = a(x - b)^2 + c

Here b = 4 and c = 75 so we have

y = a(x - 4)^2 + 75 where a is a constant to be found.

The y-intercept is (0,27) so

27 = a(0 - 4)^2 + 75

16a = 27 - 75

a = -48/16 = -3

So to find the x-intercepts we solve the equation:

-3(x - 4)^2 + 75 = 0

(x - 4)^2 = -75 / -3 = 25

x - 4 = +/- √25

x =   5+ 4 = 9 , -5 + 4 = -1.

bearing in mind that parallel lines have the same exact slope, hmmm what is the slope of y = -10x + 3 anyway?

[tex]\bf y=\stackrel{\downarrow }{-10}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies (\stackrel{x}{5},\stackrel{y}{-6})~\hfill \begin{array}{llll} y-(-6)=-10(x-5) \\\\\\ y+6=-10(x-5) \end{array}[/tex]

Answer:

Step-by-step explanation:

X=3

1. simplify both sides of the equation by combining like terms

2. add 5 to both sides

3.divide both sides by -2

For this case we have the following equation:

[tex]-4x-5 + 2x = -11[/tex]

To solve, we add similar terms to the left side of the equation:

[tex]-2x-5 = -11[/tex]

We add 5 to both sides of the equation:

[tex]-2x = -11 + 5\\-2x = -6[/tex]

We divide between -2 on both sides of the equation:

[tex]x = \frac {-6} {- 2}\\x = 3[/tex]

Thus, the solution of the equation is 3.

Answer:

[tex]x=3[/tex]

Answer:

m= -2/3 or -0.6

Step-by-step explanation:

6m-1= -5+1

6m= -4/-6

m= - 2/3 or -0.6  

Answer:

m = -2/3

Step-by-step explanation:

-5 = 6m-1

Rewrite

6m - 1 = -5

Add 1 to both sides

6m = -4

Divide both sides by 6

m = -4/6

Simplifying

m = -2/3

Answer:

m∠7 = 142°

Step-by-step explanation:

Note that a straight line's degree measurement = 180°

Note that the angle directly next to (to the left of) m∠7 has a measurement of 38°. Subtract 38 from 180:

180 - 38 = 142

m∠7 = 142°

~

Answer:

m∠7 = 142°

straight line's degree measurement = 180°

Then get the adjacent angle of 38. Subtract 38 from 180:

180 - 38 = 142

m∠7 = 142°

Hope this helped

Step-by-step explanation:

Volume of a pyramid is:

V = ⅓ AH

where A is the area of the base and H is the height of the pyramid.

The base is a triangle.  Area of a triangle is:

A = ½ bh

where b is the base length and h is the height.

A = ½ (4)(1.5)

A = 3

V = ⅓ (3)(9)

V = 9

The volume is 9 in³.

The volume of the triangular pyramid with a triangular base is 9 cubic inches.

The volume of the triangular pyramid with a height h and base area B is

Volume = 1/3 × B × h cubic units

The area of a triangle is 1/2 × b × h sq. units

where b - base and h - height the triangle.

It is given that a triangular pyramid has a triangular base with

base length b = 4 inches

height of the triangle h = 1.5 inches and

height of the pyramid = 9 inches

So, the volume of the pyramid = 1/3 × B × h

Where base area B = 1/2 × b × h

⇒ B = 1/2 × 4 × 1.5

       = 3.0 sq. inches

And the volume = 1/3 × 3.0 × 9

                             = 9 cubic inches.

Therefore, the volume of the given triangular pyramid is 9 cubic inches.

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The equations representating the number of boxes Alonzo, Cory, and Bennett loaded are b = 0.7m, b = 1.4m, and b = 0.35m respectively. This is calculated based on the fact that Alonzo loaded 14 boxes in 20 minutes, and Cory and Bennett loaded twice and a quarter as much as Alonzo respectively.

On the basis given, Alonzo loaded 14 boxes in 20 minutes. So, the number of boxes loaded per minute, m , can be calculated as b = 14 boxes ÷ 20 minutes = 0.7 m.

Cory loaded twice as many boxes as Alonzo, so his equation is b = 2 * 0.7m = 1.4m.

Bennett loaded one fourth as many boxes as Cory, which means Bennett's equation can be determined as b = 1/4 * 1.4m = 0.35m.

Based on this, the true statements are:

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The number of boxes loaded by each player can be represented by different equations. Alonzo and Bennett loaded boxes at the same rate.

Explanation:

The proportional relationship between the number of boxes, b, that each player loaded onto the truck and the number of minutes, m, spent loading boxes can be represented by the equations:

Alonzo: b = 0.71m

Bennett: b = 0.25c (where c is the number of boxes Cory loaded)

Cory: b = 2a (where a is the number of boxes Alonzo loaded)

Based on the given rates, Alonzo and Bennett loaded boxes at the same rate.

Answer:

$873

Step-by-step explanation:

Each roll results in a loss of $3.

There are 291 rolls in all.

Multiply 291 with 3: 291 x 3 = 873

The total loss is $873 for the 291 rolls.

~

Answer:

$873

Step-by-step explanation:

3$ per roll.

291 rolls in total.

291 x 3 = 873

Answer:

9 and 2/5 gallons

Step-by-step explanation:

34 x 9 gallons = 306 miles

14 / 34 = 4/10 of the gallons

4/10 simplified = 2/5

Answer: 9 2/5

Answer:

9 and 2/5 gallons

Step-by-step explanation:

320 miles on 34 gallons in simplest form is 9 and 2/5 gallons.

Give the other person brainliest

Answer:

44506

Step-by-step explanation:

458687+5800=51487

51487-6981=44506

Answer:

[tex]\large\boxed{-\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=0\ \text{and}\ x=4.\\(look\ at\ the\ picture)\\\\f(0)=5,\ f(4)=0\\\\\text{Substitute:}\\\\\dfrac{f(4)-f(0)}{4-0}=\dfrac{0-5}{4}=-\dfrac{5}{4}[/tex]

To find the average rate of change of the function from x = 0 to x = 4, subtract the y-coordinate at x = 0 from the y-coordinate at x = 4, then divide by 4. The exact answer depends on the specific values provided by the graph of the function.

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a). For the given problem, we are asked to find the average rate of change from x = 0 to x = 4. However, the specific values of f(0) and f(4) on the graph are not provided. Generally, to find the average rate of change in this case, you will need to subtract the y-coordinate at x = 0 (f(0)) from the y-coordinate at x =   4 (f(4)), then divide by the difference in x-values (4 - 0). Without the exact values from the graph, a specific numerical answer can't be provided.

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Answer:

Step-by-step explanation:

Answer: 3,-4,5

Step-by-step explanation:

Answer:

The scores for period 1 had the highest median.

Step-by-step explanation:

The median is the middle score.

Thus if the class had the highest median, it would mean that more scores are higher, that there are more high scores, than the other classes.

There is no image, but I can help you by telling you what an acute angle is:

An acute angle is any angle that has a measure LESS then 90 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

A measure of an acute angle is equal to 86°.

An acute angle can be defined as an angle that is formed by a right-angle triangle. Also, the measure of the angle of an acute angle is generally less than ninety (90) degrees.

In geometry, any angle that is lesser than ninety (90) degrees is generally referred to an acute angle such as:

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Answer:

66 cm

Step-by-step explanation:

Let's define the circumference first.

It is the boundary of any curved geometric figure specially circle.

We are given the diameter of the circle in the diagram

The diameter is:

d = 21 cm

to find the circumference, we have to find the radius of the circle first.

As radius is half of diameter

d = r/2

= 21/2

= 10.5 cm

The formula for circumference is:

[tex]C = 2\pi r\\Putting\ the\ values\\C = 2 * \frac{22}{7}*10.5\\ C = \frac{462}{7}\\ C= 66\ cm[/tex]

The circumference is 66 cm ..

Answer:

The circumference of the circle is 66 cm

Answer:

Step-by-step explanation:

We can find the vertex either by completing the square or taking advantage of the simple formula x = -b / (2a), which provides the x-coordinate of the vertex.

Here a = 2, b = -20 and c = 100.  Then the x-coordinate of the vertex is at

x = -(-20) / (2*2), or x = 5.

Next, evaluate y = 2x^2 - 20x + 100 to find the y-coordinate of the vertex.  It is y(5) = 2(5^2) - 20(5) + 100, or y(5) = 50 - 100 + 100, or 50.  y = 50.

The vertex is at (5, 50).  This states that the stock reaches its minimum value, $50 per share), after 5 months.  From that time on, the stock appreciates (increases) in value.