Please help right away

ANSWER

a)The x-intercepts are:

(-4,0) and (2,0)

b) The axis of symmetry is x=-1

c) The vertex of this function is (-1,-9)

d)Domain: { [tex]x|x \in \: R[/tex]}

e) Range : {[tex]y |y \geqslant - 9[/tex]}

EXPLANATION

The given function is:

[tex]f(x) = {x}^{2} + 2x - 8[/tex]

We complete the square to write this function in the form:

[tex]f(x)=a{(x - h)}^{2} + k[/tex]

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 2x + {1}^{2} - {1}^{2} - 8[/tex]

[tex]f(x) = {(x + 1)}^{2} - 9[/tex]

The vertex of this function is (h,k) which is (-1,-9)

The equation of axis of symmetry is x=h

But h=-1, hence the axis of symmetry isx=-1

To find the x-intercepts, we put f(x)=0

[tex]{(x + 1)}^{2} - 9 = 0[/tex]

[tex]{(x + 1)}^{2} = 9[/tex]

[tex]x + 1= \pm \sqrt{9} [/tex]

[tex]x= - 1 \pm3[/tex]

x=-4, 2

The x-intercepts are:

(-4,0) and (2,0)

The given function is a polynomial function, the domain is all real numbers.

[tex]x|x \in \: R[/tex]

e) The function has a minimum value of y=-9.

Therefore the range is

[tex]y |y \geqslant - 9[/tex]

Using the intercepts and vertex we can now draw this graph easily.

The graph of this function is shown in the attachment.

Final answer:

To address the student's question about the quadratic function, x-intercepts are found by setting the equation to zero, the axis of symmetry is calculated using -b/(2a), and the vertex is derived from these elements. The domain is all real numbers, and the range is all y-values greater than or equal to the y-value of the vertex. Finally, the function is graphically represented by plotting key points and drawing a parabola.

Explanation:

The student has inquired about the quadratic function f(x) = x2 + 2x - 8.

The x-intercepts of a quadratic function are the values of x where f(x) = 0. To find the x-intercepts, we set the equation to zero and solve for x: x2 + 2x - 8 = 0. In this case, the x-intercepts can be found using factorization or the quadratic formula.

The axis of symmetry is a vertical line that divides the parabola into two mirror images. For a quadratic function in the form of f(x) = ax2 + bx + c, the axis of symmetry equation is x = -b/(2a). We can use this formula to find the axis of symmetry for the given function.

The vertex of the function is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. To find the vertex, we use the axis of symmetry and plug that x-value into the function to find the corresponding y-value.

The domain of any quadratic function is all real numbers, which is denoted as {x | x is a real number}.

The range of a quadratic function depends on whether the parabola opens upwards or downwards. For the given function f(x) = x2 + 2x - 8, which opens upwards, the range is {y | y is greater than or equal to the y-value of the vertex}.

To graph the function, plot the vertex, axis of symmetry, and x-intercepts on a coordinate plane, then draw a smooth curve through these points to complete the parabola.

Answer:

-4 units per unit

Step-by-step explanation:

As x increases from a = -2 to b = 2 (a change of 4 units), f(x) changes from f(-2) = 25 to f(2) = 9, a decrease of 16.  Thus, the average rate of change of f(x) on the interval [-2, 2] is:

    -16

---------- = -4 units per unit.

     4

Answer:

a is 12 inches cubed because there are four hidden blocks

b is 9 inches cubed because you can see there are 9 cubes

12w-27=-34+14w

Add 34 to each side:

12w + 7 = 14w

Subtract 12w from each side:

7 = 2w

Divide both sides by 2:

w = 7/2 ( depending on how you need to write the answer it could also be written as 3 1/2 or 3.5)

Answer:

w=7/2

Step-by-step explanation:

12w-27=-34+14w

12w-27+27=-34+14w+27

12w=14w-7

12w-14w=14w-7-14w

-2w=-7

w=7/2

If you need a decimal divide 7 by 2

hope this helps mark me brainliest

Answer: 500*20%=100-50=50

Step-by-step explanation:

500*20%=100-50=50

Answer:

2940

Step-by-step explanation:

Hello There!

To Solve This Equation, I Would Not Use Addition Till The Very End.

Remember, 42 + Something Equals 2,982.

That is The Same As Subtracting 42 From 2,982

2,940 Is Your Answer.

Answer: The parabola does not intercept the x-axis.

Step-by-step explanation:

The parabola intercepts the x-axis when [tex]y=0[/tex], then, you need to substitute [tex]y=0[/tex] into the equation:

[tex]y=4x^2 -4x+9\\0=4x^2 -4x+9[/tex]

Now, use the Quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case:

[tex]a=4\\b=-4\\c=9[/tex]

Substituting these values and evaluating, you get:

[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(4)(9)}}{2(4)}\\\\x=\frac{4\±\sqrt{-128}}{8}[/tex]

Remeber that:

[tex]\sqrt{-1}=i[/tex]

Then, rewriting:

[tex]x=\frac{4\±8i\sqrt{2}}{8}[/tex]

Simplifying:

 [tex]x=\frac{4(1\±2i\sqrt{2}}{4(2)}\\\\x=\frac{1\±2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±\frac{2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±i\sqrt{2}[/tex]

Then:

[tex]x_1=\frac{1}{2}+i\sqrt{2}[/tex]

[tex]x_2=\frac{1}{2}-i\sqrt{2}[/tex]

The roots are complex, therefore, the parabola does not intercept the x-axis.

Answer:

22.62

Step-by-step explanation:

Given:

Side of square = 16

Length of diagonal= x

If the sides of square are 16, then by using pythagora theorem we can calculte length of diagonal:

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

  =[tex]16\sqrt{2}[/tex]

  =22.62 !

Answer:

[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We are given that the measure of angle θ is 600° and we are to fin the point (x, y) corresponding to angle θ on the unit circle,

We know that the x,y coordinates in the unit circle are the cosine and sine ratios, respectively.

θ = 600

1 unit circle= 360°

It means that 600° corresponds to 600° - 360° = 240°.

So, θ =  360° + 240°

180° < 240° < 270° (this tells that the point is in the third quadrant and its coordinates are negative)

240° - 180° = 60° (using the supplementary angles to find the sin and cos)[tex]\sin 60^\circ = \frac{\sqrt{3}}{2}\\\\\cos 60^\circ= \frac{1}{2}[/tex]

Therefore, the x-coordinate is the cos of the given angle while y-coordinate is the sine of the given angle and the coordinates are:

[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]

Answer:

The graph is a parabola with vertex (0 , -2)

Equation: y = x² -2

For x = -2, y = (-2)² -2 ⇒  y = 4 - 2  ⇒  y = 2

For x = -1, y = (-1)² -2 ⇒  y = 1 - 2  ⇒  y = -1

For x = 0, y = (0)² -2 ⇒  y = 0 - 2  ⇒  y = -2

For x = 1, y = (1)² -2 ⇒  y = 1 - 2  ⇒  y = -1

For x = 2, y = (2)² -2 ⇒  y = 4 - 2  ⇒  y = 2

Answer:

15.6

Step-by-step explanation:

40% × 39 = 15.6

Hope this helps

The value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex] is approximately [tex]\(65.386^\circ\)[/tex] or [tex]\(1.141\)[/tex] radians.

To find the value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex], you can use a calculator or trigonometric tables. However, if you want to understand how to solve it step by step, here's how you can do it:

1. First, calculate the ratio [tex]\( \frac{100}{41} \)[/tex]. This gives you approximately [tex]\(2.439\)[/tex].

2. Now, you need to find the angle whose tangent is [tex]\(2.439\)[/tex]. You can do this using a calculator or by using trigonometric identities.

  Typically, this is done using an inverse tangent function, often denoted as [tex]\(\tan^{-1}\)[/tex], [tex]\(\arctan\)[/tex], or [tex]\(\text{atan}\)[/tex] depending on the notation of your calculator or programming language.

So, [tex]\(\tan^{-1}\left(\frac{100}{41}\right) \approx 65.386^\circ\)[/tex].

Therefore, the value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex] is approximately [tex]\(65.386^\circ\)[/tex].

Answer:

Good day! Use trigonometry to define the formula.

Step-by-step explanation:

The height of the tree that the sun appears just over it top is 12 meters

The situation forms a right angle triangle.

The height of the tree is the opposite side of the triangle.

His distance away from the base of the tree is the adjacent side of the right angle triangle.

Therefore,

Using trigonometric ratio,

tan 32 = opposite / adjacent

tan 32 = h / 20

cross multiply

height of the tree = 20 tan 32

height of the tree = 20 × 0.6248693519

height of the tree = 12.4973870382

height of the tree ≈ 12 meters

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Answer:

216[tex]\pi[/tex]

Step-by-step explanation:

Plug the given values into the equation:

SA = ([tex]\pi[/tex])(9)(15) + [tex](\pi)[/tex] [tex](9^{2})[/tex]

Condense the equation:

216[tex]\pi[/tex]

Answer:

216 is going o be your answer

Step-by-step explanation:

Answer: 88.5

Step-by-step explanation:

First you need to order the data set from least to greatest:

So,

77,83,83,85,87,90,90,93,94,99

Then you find the middle number, in this case it's 87 and 90.

Because there is two middle numbers in the data set, you need to find the average between those numbers.

The average between 87 and 90 is 88.5.

Hope this helps :)

The median of the Data set B: {87, 90, 77, 83, 99, 94, 93, 90, 85, 83} is 88.5.

Median is the mid-value of the given data set when the set of the data is properly arranged.

The value of the data set is {87, 90, 77, 83, 99, 94, 93, 90, 85, 83}, now rearranging the set we will get,

77, 83, 83, 85, 87, 90, 90, 93, 94, 99

As we can see that the number of data points in the set is 10, therefore, the value of the median is the arithmetic average of the 5th and the 6th term,

[tex]\text{The average of the 5^{th} and the 6^{th} value}=\dfrac{87 + 90}{2} = 88.5[/tex]The average of the 5th and 6th = (87+90)/2 = 88.5

hence, the median of the Data set B: {87, 90, 77, 83, 99, 94, 93, 90, 85, 83} is 88.5.

Learn more about Median:

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Answer:

[tex]0.46\pi\ radians[/tex]

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ units[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(5)=31.4\ units[/tex]

step 2

Find  the measure in radians for the central angle of a circle whose radius is 5 and intercepted arc length is 7.2 units

Remember that

The circumference of [tex]31.4\ units[/tex] subtends a central angle of [tex]2\pi \ radians[/tex]

so

using proportion

Let

x-----> the central angle in radians

[tex]\frac{2\pi}{31.4}=\frac{x}{7.2} \\ \\x=2\pi (7.2)/31.4\\ \\x=0.46\pi\ radians[/tex]

Answer:

D)y-intercept of f(x) is greater than the y-intercept of g(x)

Step-by-step explanation:

Y-intercept is the point y-coordinate value on graph where graph line intersects the y-axis and the value of x coordinate on x-axis is zero at that point.

From the given graph of f(x), it can be seen that

y-intercept of f(x) is 2

For the given function g(x)

finding y-intercept

when x=0

y=-3

because g(x) = 3 for 1<x≤3

As 2>-3

hence y-intercept of f(x)>g(x) !

ANSWER

D. 4 minutes 40 seconds

EXPLANATION

The given data set showing the number of seconds of each song the playlist is:

283,204,198,229,173,230,168,236,215,204

Let the length of the 11th song be x.

Because he wants the mean to be 3 minutes 40 seconds, which is equal to 220 seconds, we write and solve the following equation for x.

[tex] \frac{283 + 204 + 198 + 229 + 173 + 230 + 168 + 236 + 215 + 204 + x}{11} = 220[/tex]

[tex] \frac{2140 + x}{11} = 220[/tex]

[tex]2140 + x = 2420[/tex]

[tex]x = 2420 - 2140[/tex]

[tex]x = 280[/tex]

We convert 280 seconds to minutes.

[tex] \frac{280}{60} = 4 \frac{2}{3} = 4mins : 40 sec[/tex]

The correct choice is D

Answer:

The measure of angle FGH is m∠FGH=48°

Step-by-step explanation:

step 1

Find the measure of arc FG in terms of x

we know that

The inscribed angle measures half that of the arc comprising

m∠FHG=(1/2)[arc FG]

substitute the given values

(28x−3°)=(1/2)[arc FG]

arc FG=(56x−6°)

step 2

Find the value of x

we know that

arc FG+arc FH+arc GH=360° -----> by complete circle

substitute the values

(56x−6°)+(31x+3°)+ (33x+3°)=360°

120x=360°

x=3°

step 3

Find the measure of angle m∠FGH

we know that

The inscribed angle measures half that of the arc comprising

m∠FGH=(1/2)[arc FH]

substitute the given values

m∠FGH=(1/2)[31x+3°]

m∠FGH=(1/2)[31(3)+3°]

m∠FGH=48°

See the attached picture:

Expand

5x + 5x - 15y + 12 (4x - 6y)

Expand

5x + 5x - 15y + 48x - 72y

Collect like terms

(5x + 5x + 48x) + (-15y - 72y)

Simplify

= 58x - 87y

Answer:

Perfect positive association

Step-by-step explanation:

Definition: A perfect positive association means that a relationship appears to exist between two variables, and that relationship is positive 100% of the time. Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase. (+1 indicates a perfect positive linear relationship)

Definition: A perfect negative association means that a relationship appears to exist between two variables, and that relationship is negative 100% of the time. Two variables have negative association when the values of one variable tend to decrease as the values of the other variable increase. (-1 indicates a perfect negative linear relationship)

Values between 0.3 and 0.7 (-0.3 and -0.7) indicate a moderate positive (negative) linear relationship.

From the graph we can see that this relationship shows perfect positive association (both variables increase and we can plot the straight line which will include all points)

Answer:

perfect positive

Step-by-step explanation:

ANSWER

D.

[tex]f(x) = - {x}^{4} + {x}^{3} + 3 {x}^{2} [/tex]

EXPLANATION

The given graph rises on the left and falls on the right.

This implies that the degree of the function is even.

Since the graph opens downward, the coefficient of the leading term must be negative.

The graph graph of the function also has 3 intercepts with one of them having an even multiplicity.

This means that the degree must be 4.

Therefore the last choice is correct.

Answer:

D

Step-by-step explanation:

13 because each diagonal in a rectangle are the same

Answer:

the answer is 126!

Step-by-step explanation:

i worked it out myself, and got it correct! have a great day :)

There are 126 ways can a committee of 4 be chosen from a group of 9 people, the correct option is B.

The solution is obtained through a combination where we choose "r of n", where r is the amount of things we choose and n the total number of things that can be chosen.

The combinations form uses factorial numbers. This is the formula:

[tex]\rm ^nC_r=\dfrac{n!}{(n-r)!r!}[/tex]

Where the value of n is 9 and r is 4.

The number of ways can a committee of 4 be chosen from a group of 9 people is;

[tex]\rm ^nC_r=\dfrac{n!}{(n-r)!r!}\\\\\rm ^9C_4=\dfrac{9!}{(9-4)!4!}\\\\ ^9C_4=\dfrac{9!}{5!4!}\\\\ ^9C_4=\dfrac{9\times 8 \times 7 \times 6 \times 5!}{5!\times 4\times 3\times 2\times 1}\\\\ ^9C_4=\dfrac{3024}{24}\\\\ ^9C_4=126[/tex]

Hence, there are 126 ways can a committee of 4 be chosen from a group of 9 people, the correct option is B.

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For this case we must find the sum of the given series. For this we must expand the series for each value of k.

[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]

Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.

[tex]-1-3-5-7 =\\-16[/tex]

The value of the series is -16

ANswer:

-16

For this case we have that by definition, the Pythagorean theorem states that:

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

Where:

a, b: Are the legs

c: It is the hypotenuse

According to the figure we have to:

[tex]a = 20\\b = 21[/tex]

Substituting in the formula we have:

[tex]c = \sqrt {(20) ^ 2 + (21) ^ 2}\\c = \sqrt {400 + 441}\\c = \sqrt {841}\\c = 29[/tex]

Answer:

Option D

Answer:

841

Step-by-step explanation:

hope this helps

Answer:

y = 23

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other, thus

∠1 = 90° and ∠1 = 4y - 2, so equating gives

4y - 2 = 90 ( add 2 to both sides )

4y = 92 ( divide both sides by 4 )

y = 23

Step-by-step explanation:

Area of a parallelogram is the base times the height.

A = bh

A = (13 cm) (3 cm)

A = 39 cm²

Answer:

The area is 39 square cm.

Step-by-step explanation:

The area of a parallelogram is given as :

[tex]A=base\times height[/tex]

Given is:

base = 13 cm

height = 3 cm

So, area of the parallelogram becomes:

[tex]A=13\times3[/tex]

[tex]A=39[/tex] square cm.

Therefore, the area of the parallelogram is 39 square centimeters.

Answer:

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Step-by-step explanation:

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Linear relationship always produces a straight line and are without exponential.

Lets check all the given options:

1. the total area, in square meters, y, of a square garden if the side length is x meters.

The area of a square is [tex](side)^{2}[/tex]

Here, side is 'x' and area 'y' will be [tex]x^{2}[/tex].

This is not linear.

2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

The equation forms:

[tex]y=6+0.2x[/tex]

When x = 1

[tex]y=6.2[/tex]

When x = 2

[tex]y=6+0.2(2)[/tex]

=> [tex]y=6.4[/tex]

When x = 3

[tex]y=6+0.2(3)[/tex]

=> [tex]y=6.6[/tex]

This is a linear relation.

3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

The equation forms:

[tex]y=15+8x[/tex]

When x = 1

[tex]y=15+8=23[/tex]

When x = 2

[tex]y=15+8(2)[/tex]

=> [tex]y=31[/tex]

When x = 3

[tex]y=15+8(3)[/tex]

=> [tex]y=39[/tex]

This is also linear.

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

The equation forms:

[tex]y=62x[/tex]

When x = 1

[tex]y=62[/tex]

When x = 2

[tex]y=62(2)[/tex]

=> [tex]y=124[/tex]

When y = 3

[tex]y=62(3)[/tex]

=> [tex]y=186[/tex]

This is also linear in nature.