Which of the two functions below has the largest maximum y-value?
f(x) = -3x^4-14
g(x) = -x^3 + 2

Answer:

k = -11

Step-by-step explanation:

Let [tex]p(x) = x^3-6x^2+kx+10[/tex]

And x+2 is a factor of p(x)

Let x+2 = 0 => x = -2

Putting in p(x)

=> p(-2) = [tex](-2)^3-6(-2)^2+k(-2)+10[/tex]

By remainder theorem, Remainder will be zero

=> 0 = -8-6(4)-2k+10

=> 0 = -8-24+10-2k

=> 0 = -22-2k

=> -2k = 22

Dividing both sides by -2

=> k = -11

Answer:

1 - 8/9 + 4/9 = 9/9 -8/9 +4/9 = (9-8+4)/9 = 5/9

Step-by-step explanation:

Answer:

The answer is 5/9.

Step-by-step explanation:

First, you have to make all the denorminator of the fractions the same by multultiplying :

[tex]1 - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{1}{ 1} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{1 \times 9}{1 \times 9} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{9}{9} - \frac{8}{9} + \frac{4}{9} [/tex]

Next, you have to make it into 1 fraction and simplify :

[tex] \frac{9}{9} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{9 - 8 + 4}{9} [/tex]

[tex] = \frac{5}{9} [/tex]

Answer:

The speed of the car engine is 15.4m/s

Step-by-step explanation:

Given

Power = 2100; when Speed = 15

Required

Find Speed when Power = 2200

The question says power is proportional to square of speed;

Mathematically;

[tex]Power\ \alpha \ Speed^2[/tex]

Represent Power with P and Speed with S

[tex]P\ \alpha \ S^2[/tex]

Convert proportion to an equation

[tex]P\ = \ kS^2[/tex]

Where k is proportionality constant

Make k the subject of formula

[tex]\frac{P}{S^2} = k[/tex]

When P = 2100 and S = 15

[tex]\frac{2100}{15^2} = k[/tex]

When P = 2200 and S is unknown

[tex]\frac{2200}{S^2} = k[/tex]

Recall that [tex]\frac{2100}{15^2} = k[/tex]

So;

[tex]\frac{2200}{S^2} = k[/tex] becomes

[tex]\frac{2200}{S^2} = \frac{2100}{15^2}[/tex]

Cross Multiply

[tex]S^2 * 2100 = 2200 * 15^2[/tex]

[tex]S^2 * 2100 = 2200 * 225[/tex]

[tex]S^2 * 2100 = 495000[/tex]

Divide both sides by 2100

[tex]S^2 = \frac{495000}{2100}[/tex]

[tex]S^2 =235.714285714[/tex]

Take Square Roots of both sides

[tex]S = \sqrt{235.714285714}[/tex]

[tex]S =15.3529894716[/tex]

[tex]S = 15.4[/tex] (Approximated)

Answer: D. 95%

Step-by-step explanation: If the difference of the scores given is 5 above and below the mean, that represents 2 standard deviations.

In normal distribution, 2 standard deviations above and below the mean represent 95% of all the inputs.

Answer:

Domain is [-4, 4]

Range is [0, 4]

Step-by-step explanation:

Domain is the fancy name for the values of x that works for the graph (input), in this case, from -4 to 4, inclusive.

Range is the fancy name for the values of y that works for the graph (output), in this case, from 0 to 4, inclusive.

Answer:

[tex]g(x) = x^{2} + 6\cdot x + 7[/tex]

Step-by-step explanation:

The blue parabola is only a translated version of the red parabola. The standard form of a vertical parabola centered at (h,k), that is, a parabola whose axis of symmetry is parallel to y-axis, is of the form:

[tex]y - k = C\cdot (x-h)^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex with respect to origin, dimensionless.

[tex]C[/tex] - Vertex constant, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, then vertex is an absolute maximum).

Since both parabolas have absolute minima and it is told that have the same shape, the vertex constant of the blue parabola is:

[tex]C = 1[/tex]

After a quick glance, the location of the vertex of the blue parabola with respect to the origin is:

[tex]V(x,y) = (-3,-2)[/tex]

The standard form of the blue parabola is [tex]y+2 = (x+3)^{2}[/tex]. Its expanded form is obtained after expanding the algebraic expression and clearing the independent variable (y):

[tex]y + 2 = x^{2} +6\cdot x + 9[/tex]

[tex]y = x^{2} + 6\cdot x + 7[/tex]

Then, the blue parabola is represented by the following equations:

[tex]g(x) = x^{2} + 6\cdot x + 7[/tex]

Answer:

D 0.6

Step-by-step explanation:

plato/edmentum

Answer: 0.6

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The Absolute value of -3 is 3 because it's the distance away from 0. Both have the same distance away from 0.

The opposite number of the integer number negative 3 will be 3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in arithmetic. The opposite, a shift in the sign, and negation are other names for this number.

The number is given below.

⇒ - 3

The opposite of the number negative 3 will be given as,

⇒ - (-3)

⇒ 3

The opposite number of the integer number negative 3 will be 3.

More about the Algebra link is given below.

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Answer:

When they create 3.44 products and make a revenue of $76.027, they will break even.

Step-by-step explanation:

To do this, simply graph the 2 equation in a graphing calculator and analyze the graph for where the 2 graphs intersect. Discard the negative intersection because we cannot have a negative production. You should see that your intersection point is (3.441, 76.027).

Answer:

He could put the first card he removed into his pocket

Step-by-step explanation:

With regards to the above, he could put the first card he removed into his pocket so that the amount of card he has to draw the second time will be affected hence make it dependent.

Take for instance, there are 52 cards in total, if he picks the first card and did not replace it, then the probability of taking second card will be 50/51 since the total cards left in the deck is now 51.

Keeping the card out of the deck can be done to ensure that the events are dependent.

Probability is a measure of the likeliness of an event to occur and it is measured between 0 to 1 , where 0 represents unlikeliness of the event and 1 represents certainty.

It is given in the question that he would have to keep the first card out of the deck before removing the second card.

Two events are dependent if the probability of one event changes based on the result of the other.

To be clear, an action on its own (like drawing a card) is not an event. An event is a possible outcome (or set of outcomes) we could observe.

Since we assume all 52 cards have an equal chance of being drawn on the first pick (that being 152), the only way to change this probability for the second pick is to keep the first card out of the deck.

This reduces the size of the deck to 51, meaning each remaining card has a 51 chance of being picked—except for the card he drew first, which now has a 0% chance of being drawn again.

Therefore keeping the card out of the deck can be done to ensure that the events are dependent.

To know more about Probability

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Answer:

(a) [tex]4\frac{1}{5}[/tex]

(b)  [tex]7\frac{7}{24}[/tex]

Step-by-step explanation:

One way of operating with mixed numbers is to first convert them into improper fractions, and operate with them following the simple rules of fraction multiplication, and at the end convert the answer into mixed number.

(a) For this operation let's first convert [tex]5\,\frac{2}{5}[/tex] into an improper fraction:

[tex]5\frac{2}{5} =5+\frac{2}{5} =\frac{25}{5} +\frac{2}{5} =\frac{27}{5}[/tex]

Now perform the requested operation:

[tex]\frac{7}{9} \,*\,\frac{27}{5} =\frac{189}{45} =\frac{21}{5} =4\frac{1}{5}[/tex]

(b) Start by converting both mixed numbers into improper fractions and then operate as indicated:

[tex]1\frac{3}{4} =\frac{4+3}{4} =\frac{7}{4} \\4\frac{1}{6} =\frac{24+1}{6} =\frac{25}{6}[/tex]

[tex]\frac{7}{4} *\frac{25}{6} =\frac{175}{24} =7\frac{7}{24}[/tex]

Answer:

12 years old

Step-by-step explanation:

Let's call Sydney's age x and Sam's age 2x. We can write:

x + 2x = 36

3x = 36

x = 12 so the answer is 12 years old.

Answer:

first one

Step-by-step explanation:

Tracey bought 10 movies

some cost 13 and the others 16

Let x be the movies that cost 13 and y ones that cost 16

we can state that

since Tracey both ten

since the total price is 139

so the system is :

[tex]\left \{ {{13x+16y=139} \atop {x+y=10}} \right.[/tex]

Answer:

120 flags

Step-by-step explanation:

Given that:

The flag of country Perralia has to contain three differently-colored stripes of the same width, r = 3 stripes

all of which must be positioned either vertically or horizontally =  2

If the flag of Perralia must consist of the national colors, which include green, red, yellow, black, and blue. So the number  of color n = 5 colors

The objective is to determine how many different flags can be created.

Let us recall that;the arrangement of objects taking into account the different orders or arrangement is called permutation.

The same is applicable in this scenario as well.

The number of flags that can be created can be determined by considering the permutation of :

[tex]P_r = \dfrac{n!}{(n-r)!}[/tex]

[tex]P_r = \dfrac{5!}{(5-3)!}[/tex]

[tex]P_r = \dfrac{5!}{(2)!}[/tex]

[tex]P_r = \dfrac{5 \times 4 \times 3 \times 2!}{(2)!}[/tex]

[tex]P_r = {5 \times 4 \times 3[/tex]

[tex]P_r = 60[/tex]

However, Since all of the must be positioned either vertically or horizontally =  2

Then the total number pf flags that be created = 2 × 60 = 120 flags

Answer:

b

Step-by-step explanation:

Answer:

B) (x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Consecutive angles cut by a common transversal are supplementary. That means that

x + 87 =180             Subtract 87 from both sides.

x+87-87=180-87

x = 93

Answer: 14 cm

Step-by-step explanation:

let's total length = h

white = 1/4h

remain = h - 1/4h

=3/4h

blue = 1/2 of remaining

=1/2 of 3/4h

=3/8h

remain part black = 3/4h - 3/8h

=3/8h

according to the question

3/8h = 5 1/4 cm

h = 14 cm

length of the pipe is 14 cm

Answer:

The length of the pipe is 14.

Solution,

Let the total length be X cm

[tex]x - \frac{x}{4} -{ (x - \frac{x}{4} ) \times \frac{1}{2}} = 5 \frac{1}{4} \\ x - \frac{x}{4} - \frac{x}{2} + \frac{x}{8} = \frac{21}{4} \\ \frac{8x - 2x - 4x + x}{8} = \frac{21}{4} \\ \frac{3x}{8} = \frac{21}{4} \\ 3x \times 4 = 21 \times 8 \\ 12x = 168 \\ x = \frac{168}{12} \\ x = 14[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

solution,

[tex]x = \frac{far \: arc - near \: arc}{2} \\ \: \: \: \: = \frac{250 - (360 - 250)}{2} \\ \: \: \: \: \: = \frac{250 - 110}{2} \\ \: \: = \frac{140}{2} \\ \: \: = 70[/tex]

Hope this helps..

Good luck on your assignment

Answer:

x - intercept -> Jan threw the javelin to a distance of 90 meters

relative maximum or minimum -> the highest point the javelin reached was 14 meters above the ground

increasing or decreasing interval -> Jan threw the javelin a distance of 90 meters

Step-by-step explanation:

x - intercept is where y = 0. Check where y is 0. At x = 90. Meaning it's Jan threw the javelin to a distance of 90 meters

relative maximum or minimum -> there is only a maximum on the graph, look at how the points never go down and back up, but rather up then down.

increasing or decreasing interval is basically just the interval or the x values and they go to 90 so..

Answer:

1386 in³

Step-by-step explanation:

Volume of the composite cone = volume of a hemisphere + volume of a cone

=>Find the volume of cone

Volume of cone = ⅓πr²h

π = 3.142

r = 7 in

h = =√(15² - 7²) [using Pythagorean theorem to solve for height given the slant height and radius]

h = √(225 - 49)

h = √176 ≈ 13 in

Volume of cone = ⅓*3.142*7²*13

= ⅓*2001.454 ≈ 667 in³

=>Find volume of hemisphere.

Volume of hemisphere = ½*volume of sphere = ½*4/3πr³ = ⅔πr³

π = 3.142

r = 7 in

Volume = ⅔*3.142*7³ ≈ 719 in³

Volume of composite figure = 667+719 = 1386 in³

Answer: 3.5

Step-by-step explanation:

Answer:

In January

she used 3/5 of what she used in February.

In February she used 2/3 litres of oil.

So it is 3/5 of 2/3 to find what amount she used in January.

3/5 × 2/3 = 6/15

If we simplify 6/15 we find 2/5 as our answer.

So our answer is 2/5 litres.

Answer:

L/2

Step-by-step explanation:

If the width is half of its length, that means it is 1/2*L, as L is the length. This can be simplified into L/2, which is our answer.

Answer:L/2

Step-by-step explanation: The length is represented as L. So half the lenght is 1/2L which can also be represented as L/2. So the width is represented as L/2

Hi,

it'took 70 minutes to empty the pool.  

After 20 it's stay 45 000 litres.   So in 50 minutes, 45 000 litres are gone.  

So  :    45 000 / 50 =  4500/5 = 9*5 *100 /5 = 900

900 litres is off  every minute.

So the  pool contained  :  900 *70 =  63 000 litres  in the beginning.

Answer:

Step-by-step explanation:

surface area of two trapezoids=2[(12+8)/2×3]=2[30]=60 cm²

surface area of side rectangles=10×8+10×12=10(8+12)=200 cm²

surface area of top=10×5=50 cm²

surface area of bottom=10×3=30 cm²

Total surface area=60+200+50+30=340 cm²

Answer:

Step-by-step explanation:

to find the surface area , you need to find the area of each side(face)

top: 5*10=50

the bottom of the shape: 3*10=30

the front face:10*8=80

the sides are trapezoid shapes with:different dimensions:

side :8,12 and eight of 3 ( the shape has 3 faces the same)

area=((12+8)/2)*3= 30 (30*3 faces or sides)

add the numbers: 50+30+80+(30*3)=250 cm^2

I hope it is right and good luck

Answer:

F. cylinder

Step-by-step explanation:

A cylinder has a circle for its base, which has no vertices and is not a polygon. This, therefore, disqualifies a cylinder as a polyhedron.

Las funciones trigonométricas se utilizan fundamentalmente en la solución de triángulos

rectángulos, recordando que todo triángulo rectángulo tiene un ángulo de 90° y sus ángulos

interiores suman 180°. La notación que se acostumbra es la siguiente.

Answer:

  60 square units

Step-by-step explanation:

We can bound the trapezoid with a rectangle having opposite corners at (4, 6) and (16, 16). This rectangle will have an area of (16 -4)(16 -6) = 120 square units.

From this bounding rectangle we can subtract the areas of the corner triangles. Their x-y extents (CW from upper left) are ...

  (10×6), (2×6), (6×4), (6×4)

Their areas are half the product of these base×height dimensions, so the triangles have a total area of ...

  (1/2)(60 +12 +24 +24) = 60

Then the area of the trapezoid is the difference of the area of the bounding rectangle and the area of the corner triangles:

  trapezoid area = 120 -60 = 60 . . . . square units

Answer:

(0,5)

Step-by-step explanation:

To find the y-intercept, substitute in 0 for x and solve for y.

y=x^2 + 3x + 5

y=(0)^2 + 3(0) +5

y=0+0+5

y=5

Since there is no x coordinate for a y-intercept, the answer is (0,5)

Answer:

A. (0, -5) is the right answer on edge 2021

Answer:

Step-by-step explanation:

The claim being tested is that p not equals ≠ 0.877

A) This is the alternative hypothesis and it is a two tailed test. It means that it can be in either direction.

B)Given that z = 2.94, the p value would be determined from the normal distribution table. Since the curve is symmetrical and it is a two tailed test, the p for the left tail and the right tail would be considered. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the test z score in the right tail is 1 - 0.998 = 0.002

We would double this area to include the area in the left tail of z = - 2.94 Thus

p = 0.002 × 2 = 0.004

C) Since alpha, 0.01 > than the p value, 0.004, then we would reject the null hypothesis, H0