Which statements are true of the given function?
Check all that apply.

A) f[-1/2] = -2
B) f(0) = 3/2
C) f(1) = -1
D) f(2) = 1
E) f(4) = 7/2

(B and E are the answers)

Answer: The solution to the system of equations is x = -5 and y = 0.

Step-by-step explanation:

To solve this system of equations by substitution, you can start by solving one of the equations for one of the variables. For example, you can solve the first equation for x:

x + 2y = -5

x = -5 - 2y

Then, you can substitute this expression for x into the second equation to solve for y:

-(-5 - 2y) - 2y = 5

5 + 2y - 2y = 5

5 = 5

Now that you have solved for y, you can substitute this value back into one of the original equations to solve for x. If you substitute y = 0 back into the first equation, you get:

x + 2(0) = -5

x = -5

So, the solution to the system of equations is x = -5 and y = 0.

The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is 91/216.

Scenario 1: draw two black on the first draw

P(B,B) = (4/9)(3/8) = 12/72 = 1/6

The probability of ending up with two black by scenario 1 is 1/6.

Scenario 2: draw one black and one white; put back the white, and draw a black

P(B,W) = (4/9)(5/8) = 20/72 = 5/18

P(W,B) = (5/9)(4/8) = 20/72 = 5/18

P(one black and one white on first draw) = 5/18+5/18 = 5/9

When you put the white back, there are now 5 white and 3 black; the probability of drawing a black on the second draw is 3/8.

The probability of ending up with two black by scenario 2 is (5/9)(3/8) = 15/72. = 5/24

Scenario 3: draw two white; put both back and draw again, getting two black

P(W,W) = (5/9)(4/8) = 20/72 = 5/18

Since you put back both whites, the bag now contains the same balls it did at the beginning. The probability of drawing two black on the second draw is then 12/72 = 1/6, as before.

The probability of ending up with two black by scenario 3 is (5/18)(1/6) = 5/108.

Thus, The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is the sum of the probabilities for the three scenarios: 1/6+5/24+5/108 = 36/216+45/216+10/216 = 91/216.

To know more about probability visit: brainly.com/question/30034780

#SPJ4

The height of the zip line is 203 feet.

Trigonometric functions are required when the value of an unknown side or internal angle of a right triangle are to be determined. Some of the basic functions are: sine, cosine, tangent etc.

Tangent of an angle is the ration of the opposite side to the angle and the adjacent side.

Tan θ = opposite/ adjacent

To determine the height of the zip line required in the question, we have;

let the height be represented by h,

Tan θ = opposite/ adjacent

Tan 10 = h/ 1150

h = Tan 10 * 1150

  = 0.1763*1150

  = 202.745

h = 202.8 feet

The height of the zip line is 203 feet.

Learn more about trigonometric functions at https://brainly.com/question/25618616

#SPJ1

The volume of the right triangular prisms are 1000cm³ and  14, 400mm³ respectively

The formula for determining the volume of a right triangular prism is expressed as;

V = 1/2 bhl

Where;

Now, substitute the values, we have;

Volume, V = 1/2 × 25 × 20 × 4

Multiply the values

Volume, V = 2000/2

Divide through

Volume = 1000cm³

For the second prism;

Volume = 1/2 × 16 × 50 ×36

Volume = 14, 400mm³

Hence, the values are 1000cm³ and  14, 400mm³

Learn more about volume here:

https://brainly.com/question/1972490

#SPJ1

The expression in the form of q(x) + r(x) / b(x) is

(x + 2) + (-13x + 4) / (x² + 2x + 1).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x³ - 8x + 6) ÷ (x² + 2x + 1)

Using the long division.

x² + 2x + 1 ) x³ - 8x + 6 ( x + 2

                   x³ + 2x² + x

              (-)     (-)        (-)

                      2x² - 9x + 6

                      2x² + 4x + 2

                     (-)    (-)      (-)

                               -13x + 4

Quotient = x + 2

Remainder = -13x + 4

Thus,

Quotient + Remainder / Divisor

= (x + 2) + (-13x + 4) / (x² + 2x + 1).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

The ratios of the long leg to hypotenuse are the same for all right triangles since they are similar:

z/7 = 5/z

When z2 equals 35, multiply by 7z.

z = √35

z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The value of the variable, S when  C = 6, n = 8, T = 1 and k = 18 is 1. 036

To make a variable the subject of formula, we have to make it stand alone on one end of the equality sign.

From the information given, we have the equation as;

C = n/Tk(1 + S²)

Now, let's cross multiply to make 'S' the subject of formula, we get;

C× Tk(1 + S²) = n

Divide both sides by the coefficient of S

1 + S² = n/CTk

collect '1' to the other side;

S² = n/CTk + 1

Take the square root of both sides

S = [tex]\sqrt{\frac{n}{CTk} + 1 }[/tex]

Now, substitute the values

S = [tex]\sqrt{\frac{8}{6* 1 * 18} + 1 }[/tex]

Multiply the values

S = [tex]\sqrt{1. 074}[/tex]

S = 1. 036

Thus, the value is 1. 036

Learn about subject of formula here:

https://brainly.com/question/10643782

#SPJ1

Answer:

a)  8.4

b)  8.5

c)  The mean and median will be one less (7.4 and 7.5).

Step-by-step explanation:

Given number of boxes in each stack:

To find the mean of the number of boxes in a stack, divide the total number of boxes by the number of stacks:

[tex]\implies \sf Mean=\dfrac{5+7+9+ 11+13+ 10+9+ 8+ 7+5}{10}=\dfrac{84}{10}=8.4[/tex]

The median is the middle value when all data values are placed in order of size.

To find the median of the number of boxes in a stack, first place the numbers in order of size:

As there is an even number of boxes (10), the median is the mean of the two middle values:

[tex]\implies \sf Median=\dfrac{8+9}{2}=\dfrac{17}{2}=8.5[/tex]

If one box is removed from each stack, the total number of boxes is 10 less than before.  Therefore:

[tex]\implies \sf Mean=\dfrac{84-10}{10}=\dfrac{74}{10}=7.4[/tex]

The number of boxes in each stack will be (in order of size):

Therefore, the median is 7.5.

So, if one box is removed from each stack:

The equation of the line through the point (7,8) and (-12, -11) is y = x + 1. Thus, option c is correct.

Linear equations are characterised by variables with a power of one. Where ax+b = 0 is one example with one variable, where a and b are real numbers and x is the variable.

Linear algebra covers a wide range of topics. Applications, abstract, and numerical methods are all part of its range. Numerous other disciplines, including fractal geometry, differential equations, difference equations, relativity, archaeology, and demography, depend on linear algebra.

Using the slope formula, we can find the equation of the line [passing through the point (7,8) and (-12, -11) i.e.

y₂ - y₁ = m(x₂ - x₁)

Putting the values

-11 - 8 = m(-12 - 7)

-19 = m(-19)

m = -19/-19

m = 1

Now, we have slope so find the line

y - 8 = 1(x - 7)

y = x - 7 + 8

y = x + 1

y - (-11)= 1(x - (-12))

y + 11= x  12

y = x + 1

Thus, The equation of the line through the point (7,8) and (-12, -11) is y = x + 1.

Learn more about linear equation

https://brainly.com/question/11897796

#SPJ1

Answer:

4 balls for $2.50

Step-by-step explanation:

If 4 balls=$2.50

Then,$2.50+2.50= $6.25

$6.25 for 8 balls

Answer:

The answer is 3w - g - 4

Step-by-step explanation:

(8w - 4g + 1) - (5w + 3g - 5)

8w - 4g + 1 - 5w + 3g - 5

Rearrange terms

8w - 5w - 4g + 3g + 1 - 5

Combine like terms

(8w - 5w) = 3w   ( -4g + 3g) = -g  (1 - 5) = - 4

Answer:

3w - g - 4

The relations in this problem are classified as functions or not as follows:

1. Not a function.

2. Function.

3. Not a function.

4. Function.

5. Function.

A relation represents a function if each value of the input is mapped to only one value of the output.

Hence, a graph will represent a function if, and only if, it contains no vertically aligned points, that is, if there isn't a vertical line that will cross the graph of the relation in more than one point.

Then the graphs that are not functions in this problem are given as follows:

More can be learned about relations and functions at https://brainly.com/question/29701528

#SPJ1

The kinetic energy of the toy motorized airplane is 8 Joule.

Kinetic energy is the work or energy an object has due to it's motion. The standard unit of kinetic energy is Joule which is kg m²/s².

The formula for calculating Kinetic energy is,

KE = [tex]\frac{1}{2}[/tex] mv²

where m is the mass of the object and v is the velocity of the object.

Here, mass = 4 kg and velocity = 2 meter/second

KE = [tex]\frac{1}{2}[/tex] × 4 × 2²

     = 8 Joule

Hence the kinetic energy of the airplane is 8 Joule.

Learn more about Kinetic Energy here :

https://brainly.com/question/26472013

#SPJ1

The sample space for the experiment of spinning a four-part spinner is the set of all possible outcomes of the experiment.

In this case, the sample space would be: s = {q, r, s, t}

This means that the possible outcomes of the experiment are q, r, s, and t. Each of these outcomes is equally likely to occur when the spinner is spun.

Option s = {q, r, r, t} is incorrect because it includes two occurrences of the outcome r, which is not possible in this experiment.

Option s = {r, a, t} is incorrect because it includes the outcome a, which is not part of the sample space.

Option s = {s, q, q} is incorrect because it includes two occurrences of the outcome q, which is not possible in this experiment.

To learn more about the sample space, visit:

brainly.com/question/24273864

#SPJ4

Answer :

2827.43 cm²

Step-by-step explanation:

1/5/2023

7:20PM

Answer:

2827.4 cm²

Step-by-step explanation:

A = 4πr²

A = 4π(15)² = 2827.4 cm²

Since Ten students compared the amount (in dollars) they spent on books each week with the box plot showing the results, the median amount they spent each week is $50. The difference of the first and third quartiles of the data set is $45.

In Mathematics, a box plot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the box-and-whisker plot (box plot) shown above, the five-number summary for the given data set include the following:

For the difference, we have:

Difference = Third quartile - First quartile

Difference = 65 - 20

Difference = 45.

Read more on box plot here: brainly.com/question/14277132

#SPJ1

Answer:

Step-by-step explanation:

0.00940718736

The required solution to the given expression is 4x² + 5x - 4y - 3.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

y + 2x - 3 + 4x² + 3x - 5y

We have to determine the solution to the given expression.

As per the question, we have

y + 2x - 3 + 4x² + 3x - 5y

Rearrange the variables in the above expression,

4x² + 2x + 3x + y - 5y - 3

Combine likewise terms in the expression,

4x² + 5x - 4y - 3

Thus, the required solution is 4x² + 5x - 4y - 3.

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

The question seems to be incomplete the correct question would be:

Find the solution to the below expression.

y + 2x - 3 + 4x² + 3x - 5y

The congruent angles are - ∠GHF ~ ∠KHJ, ∠GFH ~ ∠KJH and ∠FGH ~ ∠JKH.

The proportion that relates corresponding sides are -

HG/HK = GF/JK = HF/HJ

What is congruency?

Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent.

It is given that ΔFGH is congruent to ΔJKH.

If two triangles are similar.

Then it is known that -

HG/HK = GF/JK = HF/HJ

And all the corresponding angles are equal.

Angles that are congruent to each other is -

Angle GHF ~ KHJ as they are vertically opposite angles.

Angle GFH ~ KJH as they are corresponding angles.

Angle FGH ~ JKH as they are corresponding angles.

The sides which are corresponding and equal are -

HG/HK = GF/JK = HF/HJ

So, GF = JK

GH = HK

FH = HJ

Therefore, all the corresponding angles and sides are listed.

To learn more about congruency from the given link

https://brainly.com/question/1675117

#SPJ1

Total comparisons required to order an array of 5 elements using the selection sort =29

Selection sort finds the smallest element and swaps it into the first position. The, from the remaining N-1 elements after the first one (which we know is the smallest), it finds the next smallest and swaps it into the 2nd position. And so on.

To find the smallest element from a group of N elements takes N-1 comparisons. Basically, compare item 1 to 2, remember the smallest. Compare item 3 to smallest and remember which ever is smaller, and so on. You end up doing 1 comparison for every element from 2 through N.

We have to find the smallest element N-1 times*, but each time we have a smaller list to look through.

So let’s turn to an array of 5 elements. To find the smallest element will take4 comparisons. Next time through we do 3 comparisons and so on:

Total comparisons = 4+3+2+1 = 10

For N elements it takes 1+2+3+…+N-1 = (N-1)N/2 comparisons.

You don’t have to run through an Nth time because after sorting N-1 items, the Nth item must be in the correct position already. Or, if you like, the Nth loop does N-N=0 comparisons so we can ignore it.

only counting comparisons of elements in the array. A loop is going to have to do a comparison of the loop variable to the length of the array every time it repeats. Usually those comparisons are disregarded because, unless the elements of the array are integers, the item comparisons take considerably more time than the index comparisons, and any way, it won’t increase the asymptotic complexity, only the constant of proportionality. If you want to count the index comparisons, you have one for every item comparison (because the inner loop does one item comparison per loop iteration) + 1 for each end of the inner loop (a loop that runs X times does X+1 comparisons) and then another N-1 for the outer loop + 1 for the loop end. For N = 5 there will be 10 + 4 + 4 + 1 = 19 index comparisons and 10 + 19 = 29 total comparisons.

total comparisons required to order an array of 5 elements using the selection sort =29

of course, if you write this in a language like java that does array bounds checking, you’ll add two more comparisons for each array access. And the compare function is probably a function call, so you’re increasing stack depth which potentially adds comparisons to make sure that doesn’t overflow… you know what? I think I’ll just stop there.

To know more about Selection sort visit brainly.com/question/13161882

#SPJ4

Answer: 3. 5.4

Step-by-step explanation:

we can convert all of these numbers to decimal form. 3 = 3.00,1.05=1.05, 5.4 = 5.40, and 4.2= 4.20. As we can see here, 1.05 is clearly the smallest, 3.00 is the second smallest, and 5 is larger than 4 s o its 5.4

Answer:

See the explanation below.

Step-by-step explanation:

17) 40=x+45

x = -5

18) 70 = -2 + 8x

72 = 8x

x = 9

19) 19x - 3 = 17x + 11

2x = 14

x = 7

20) -2 + 14x = 12x + 14

2x = 16

x = 8

21) 11x - 3 + 18x + 9 = 180

29x + 6 = 180

29x = 174

x = 6

22) 6x - 4 + 14x + 4 = 180

20x = 180

x = 9

23) 68 + x + x + 128 = 180

196 + 2x = 180

2x = -16

x = -8

24) x + 87 + x + 107 = 180

2x + 194 = 180

2x = -14

x = -7

25) 70 + 12x - 10 = 180

60 + 12x = 180

12x = 120

x = 10

Answer:

[tex]\textsf{19.} \quad \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]

[tex]\textsf{20.} \quad \textsf{Center}: \;\;(-4, 1)[/tex]

[tex]\textsf{21.} \quad \textsf{Major axis}:\;\;4\sqrt{3}[/tex]

[tex]\textsf{22.} \quad \textsf{Minor axis}:\;\;4\sqrt{2}[/tex]

[tex]\textsf{23.} \quad \textsf{Sum of the focal radii}:\;\;4 \sqrt{3}[/tex]

[tex]\textsf{24.} \quad \textsf{Foci}:\;\;(-6, 1)\;\; \textsf{and}\;\;(-2,1)[/tex]

[tex]\begin{aligned}\textsf{25.} \quad &\textsf{Vertices}:\;\;(-4-2\sqrt{3}, 1) \;\; \textsf{and}\;\; (-4+2\sqrt{3}, 1)\\ &\textsf{Co-vertices}:\;\;(-4, 1-2\sqrt{2}) \;\; \textsf{and}\;\; (-4, 1+2\sqrt{2})\end{aligned}[/tex]

[tex]\textsf{26.} \quad \textsf{Eccentricity}\;\;\dfrac{\sqrt{3}}{3}[/tex]

27.  See attachment.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\end{minipage}}[/tex]

Given equation:

[tex]2(x+4)^2+3(y-1)^2=24[/tex]

To write the equation of the ellipse in standard form, divide both sides by 24 so that the right side of the equation is equal to one:

[tex]\implies \dfrac{2(x+4)^2}{24}+\dfrac{3(y-1)^2}{24}=\dfrac{24}{24}[/tex]

[tex]\implies \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]

Therefore:

The center of the ellipse is (h, k).

Therefore, the coordinates of the center are (-4, 1).

As a > b, the ellipse is horizontal, so 2a is the major axis and 2b is the minor axis.  Therefore:

The focal radius is the distance from a point on the ellipse to a focus.

The sum of the focal radii is equal to the length of the major axis.

Therefore, the sum of the focal radii is 4√3.

As a > b, the coordinates of the foci are (h±c, k).

As c² = a² - b², first find the value of c:

[tex]\implies c^2=12-8[/tex]

[tex]\implies c=\sqrt{4}=2[/tex]

Therefore, the coordinates of the foci are:

As a > b, the coordinates of the vertices are (h±a, k):

and the coordinates of the co-vertices are (h, k±b):

The eccentricity of the ellipse is:

[tex]\implies e=\dfrac{c}{a}=\dfrac{2}{2\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]

The time when the altitude of the balloon is 370.4 feet is 6 minutes.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope the steeper is its graph or the rate of change is large.

We know The slope of the line is (y₂ - y₁)/(x₂ - x₁).

Therefore, The slope of the line passing through the points

​(0​,428​) and ​(10​,​332) is,

Slope(m) = (332 - 428)/(10 - 0).

Slope(m) = - 9.6, So the balloon is descending at a rate of - 9.6 feet per minute.

Now, To obtain the y-intercept.

428 = - 9.6(0) + b.

b = 428.

Therefore, The equation of the required line is,

y = - 9.6x + 428, where y is the altitude and x is the number of minutes.

So, The time in minutes when the altitude of the balloon is 370.4 feet is,

370.4 = - 9.6x + 428.

- 9.6x = - 57.6.

x = 57.6/9.6.

x = 6 minutes.

learn more about lines and slopes here :

https://brainly.com/question/16180119

#SPJ1

Answer: 1.25

2 1/2 (1/2)

2 1/2 (servings) x 1/2 (cups of milk)

Answer:

A. The total change in the value on the gift card will be -149$

B. Yes, Arleen has enough to buy a Wheelbarrow for 50$

Step-by-step explanation:

A.

To calculate the total change in value of the gift card we need to sum all expenses.

4 days of rental + cost of the rake = total change in value

(4 * -35$) - 9$ = -149$

B.

If the value of the gift card was 200$, then we have to subtract the expenses from the gift card value and check whether we have enough to buy a Wheelbarrow.

200$ - 149$ = 51$ > 50$

The object falls from 115200 ft above the ground.

What is the quadratic equation?

A quadratic equation is any algebraic equation of the highest degree. The standard form of the quadratic equation in a variable is ax² + bx + c = 0, where a and b are coefficients, are constant, and is a non-zero numbers.

The acceleration of the object is given by the equation a = 32 - (v^2)/8 ft/s^2. Since the object is initially at rest, we can assume that v = 0 at the start of its fall.

To find the height from which the object fell, we need to use the equations of motion for uniformly accelerated motion. The equation for the distance traveled by an object under constant acceleration is:

d = 1/2 at^2 + vt + d0

where d is the distance traveled, a is the acceleration, t is the time, and d0 is the initial distance (which is zero in this case, since the object is initially at rest).

We know that the object is falling for one minute, and we can convert that to seconds by multiplying by 60. The acceleration is given by a = 32 - (v^2)/8, we know that v = 0, so a = 32 - (0^2)/8 = 32 ft/s^2.

Plugging in the values, we get:

d = 1/2 (32 ft/s^2) (60 s)^2

d = 32 x (3600)

d = 115,200 ft

This is the distance that the object fell. To find the height from which it fell, we simply have to take the distance and negate it.

So the height from which the object fell is:

-115,200 ft

Hence, the object falls from 115200 ft above the ground.

To learn more about the quadratic equation visit,

https://brainly.com/question/1214333

#SPJ1