Kristy wanted to divide her paint evenly into two-3 1/2-gallon containers. She had 5 1/4 gallons of paint. How much paint did she pour into each container? (HELP NEEDED)

The complete factorization of the given polynomial is (x² + 1)(x + 2).

To factorize the polynomial [tex]x^3 + 2x^2 + x + 2[/tex], we first look for any common factors. In this case, we don't have any common factors, so we move on to factoring by grouping.

Unfortunately, this cubic polynomial does not factorize nicely into simpler terms using rational numbers. It would involve using heavy algebra and complex numbers to factor. Usually, for a cubic polynomial of this nature, a numerical method will be employed to find its roots.

We can group the terms as [tex]x^3 + 2x^2 + x + 2[/tex]). Taking out the common factors from each group, we get:

[tex]x^2[/tex](x + 2) + 1(x + 2).

Now, notice that we have a common binomial term (x + 2), so we can factor that out as well:

([tex]x^2[/tex] + 1)(x + 2).

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Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

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

r - radius

We have C = 21.99 ft. Substitute and solve for r:

[tex]21.99=2\pi r[/tex]             divide both sides by 2π

[tex]r=\dfrac{21.99}{2\pi}[/tex]

Use [tex]\pi\approx3.14[/tex]

[tex]r\approx\dfrac{21.99}{2(3.14)}=\dfrac{21.99}{6.28}\approx3.5[/tex]

The radius of a circle with a circumference of 21.99 feet is 3.50 ft

where

r = radius

Therefore,

circumference = 21.99 ft

circumference = 2πr

circumference = 2 × 3.14 × r

21.99 = 6.28r

divide both sides by 6.28

r = 21.99 / 6.28

r = 3.50159235669

r = 3.50 ft

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Answer: second option

Step-by-step explanation:

The standard form of a quadratic equation is:

[tex]ax^2+bx+c=0[/tex]

Then, to write the quadratic equation given in the problem in standard form, you must substract 1 from both sides of the equation. Then you have:

[tex]2x^2+5x-1=0[/tex]

Given the quadratic equation above, to find the value of [tex]b^2-4ac[/tex]  you must substitute:

a=2; b=5 and c=-1 into [tex]b^2-4ac[/tex]

Thenrefore, you obtain the following result:

[tex]5^2-4(2)(-1)=33[/tex]

Answer:

[tex]33[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]1=2x^2+5x[/tex]

We want to rewrite this equation in the form;

[tex]ax^2+bx+c=0[/tex]

We add [tex]-1[/tex] to both sides of the equation to obtain;

[tex]0=2x^2+5x-1[/tex]

This is the same as

[tex]2x^2+5x-1=0[/tex]

This implies that;

[tex]a=2,b=5,c=-1[/tex]

We substitute these values into the expression [tex]b^2-4ac[/tex]

[tex]\Rightarrow 5^{2}-4(2)(-1)[/tex]

[tex]=25+8[/tex]

[tex]=33[/tex]

Answer:

d) [tex]\cos(\theta)=-\frac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

If   [tex]\sin(\theta)=\frac{2}{3}[/tex] and [tex]\tan(\theta)\:<\:0[/tex], then

[tex]\theta[/tex] is in quadrant 2.

Recall that;

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

We substitute the given sine ratio to obtain;

[tex](\frac{2}{3})^2+\cos^2(\theta)=1[/tex]

[tex]\frac{4}{9}+\cos^2(\theta)=1[/tex]

[tex]\cos^2(\theta)=1-\frac{4}{9}[/tex]

[tex]\cos^2(\theta)=\frac{5}{9}[/tex]

[tex]\cos(\theta)=\pm \sqrt{\frac{5}{9}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{5}}{3}[/tex]

We are in the second quadrant, therefore

[tex]\cos(\theta)=-\frac{\sqrt{5}}{3}[/tex]

Answer:

Step-by-step explanation:

We want to scale by a factor of 1/10 so |a| = 1/10. This means that the graph is compressed vertically.

We do not reflect across the x axis so a = 1/10.

The new parabola is: y = 1/10 x^2

The new equation of the parabola will be  [tex]y=\frac{x^{2} }{10}[/tex].

The given parabola is:

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

A parabola is a plane curve that is mirror-symmetrical and is approximately U-shaped.

When the parabola y=x² is scaled vertically by a factor of 1/10.

The new equation of parabola will be = [tex]y=\frac{x^{2} }{10}[/tex].

This means the graph of a new parabola will look similar to the previous parabola(symmetric about the origin) but outputs(function values) will be different.

Hence, the new equation of the parabola will be  [tex]y=\frac{x^{2} }{10}[/tex].

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Answer:

[tex]\frac{2y+3}{7y-1}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{10y^2+15y}{35y^2-5y}[/tex]

Factor both the numerator and the denominator.

[tex]=\frac{5y(2y+3)}{5y(7y-1)}[/tex]

Cancel out the common factors.

[tex]=\frac{2y+3}{7y-1}[/tex]

Answer:

The correct answer is,

(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)

Step-by-step explanation:

It is given an expression,

(10y² + 15y)/(35y² - 5y)

To simplify the given expression

Taking 5y as common from both numerator and denominator,

(10y² + 15y )/( 35y² - 5y) = 5y( 2y + 3)/5y( 7y - 1)

 = (2y + 3 )/( 7y - 1)

Therefore the simplified form of given expression is given by,

(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)

Answer:

138.3ft^3

Step-by-step explanation:

Volume for cylinders : V = pi*r^2*h

Volume for cones : V = pi*r^2*(h/3)

Since we know the radius (r) is 2 and the height is 10 and 3 for the cylinder and cone respectively, all we do is plug in.

Volume for cylinder is about 125.7ft^3

Volume for cone is about 12.6ft^3

Then just add them together for a total of 138.3ft^3

The two angles shown ( 134 and X) make a straight line.

A straight line equals 180 degrees.

To find X subtract 134 from 180.

X = 180 - 134

x = 46

Answer:

A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.

Step-by-step explanation:

The relative frequencies given are at most 0.02 apart.  This means they are reasonably close.

The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.

However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.

Since the relative frequencies are reasonably close, the number cube is likely to be fair.

Answer:

Option A and C are true.

Step-by-step explanation:

Given : Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.

Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome

Outcome :                     1            2            3             4

Relative Frequency :   0.23     0.24      0.26       0.27

To find : Which statements about Dina's experiment are true?

Solution :

Option A - The relative frequencies in the table are reasonably close.

This statement is true, as we see that the relative frequency are all between 0.23 to 0.27 that are reasonably close.

Option B - The theoretical probability of rolling an even number is 0.51.

This statement is not true, as the theoretical probability of rolling even numbers is

2 even numbers from 4, so probability is

[tex]P=\frac{2}{4}=\frac{1}{2}=0.5[/tex]

Option C - The relative probability of rolling an even number is 0.51.

This statement is true, as the relative frequency of an even number is 0.24+0.27=0.51

Option D - The number cube is not likely to be fair.

The statement is not true, as the relative frequency are reasonably close which  implies that the number cube is likely to be fair and sum of the relative frequency is 1.

Therefore, Option A and C are correct.

Answer: Angles 1 and 5

Step-by-step explanation: Corresponding angles are angles that have the same measures.

Since angle 1 and 5 have the same measure on these lines, that means that the answer must be angle 1 and 5.

The initial value is when Y equals when x is 0.

Replace x with 0 in the equation and solve for y.

Y = -4x -3

y = -4(0) - 3

y = 0-3

y = -3

Answer:

-3

Step-by-step explanation:

The initial value of an equation is when x=0

y = −4x − 3

Let x =0

y = -4(0) -3

y = 0-3

y=-3

The initial value is -3

Answer:

2.05 meters

Step-by-step explanation:

Superimpose a triangle when drawing out the situation.  The distance the ladder reaches up the tree is the side of the triangle opposite of the angle.  The distance the ladder is from the tree is side adjacent to the triangle.  We can use tangent to solve this.

Tan X = (opposite side)/(adjacent side)

Tan 64 = a/1

Tan 64 = a         (anything over 1 is just itself)

2.050303842 = a   (use tan on your calculator)

Answer:5.5

Step-by-step explanation:

A. P. E. X.

The length of the line segment EF will be 55 units. Then the correct option is B.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

In the diagram, the line segment EF is the given as the half of the sum of the line segment BC and the line segment AD.

EF = (BC + AD) / 2

From the diagram, the length of the line segment AD is 7.6 units and the length of the line segment BC is 3.4 units.

Put these values in equation. Then the length of the line segment EF will be

EF = (3.4+ 7.6) / 2

EF = 11 / 2

EF = 5.5 units

Thus, the length of the line segment EF will be 55 units.

Then the correct option is B.

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Answer:

HOPEFULLY THIS HELPS YOU

Arithmetic sequence: an = a1 + (n-1)d

In this case: an = 7 +(n-1)(-4)

Answer:

[tex]\large\boxed{g)\ 6xy^2=(3x)(2y^2)}\\\boxed{h)\ 25a^3b^2=(5a^2b^2)(5a)}\\\boxed{i)\ 6x+6y+6p=6(x+y+p)}[/tex]

Step-by-step explanation:

[tex]g)\ 6xy^2=3\cdot2\cdot x\cdot y\cdot y=(3\cdot x)(2\cdot y\cdot y)=(3x)(2y^2)\\\\h)\ 25a^3b^2=5\cdot5\cdot a\cdot a\cdot a\cdot b\cdot b=(5\cdot a\cdot a\cdot b\cdot b)(5\cdot a)=(5a^2b^2)(5a)\\\\i)\ 6x+6y+6p=6\cdot x+6\cdot y+6\cdot p=6(x+y+p)[/tex]

Other way for g) and h):

[tex]g)\ \dfrac{6xy^2}{3x}=\dfrac{6}{3}\cdot\dfrac{xy^2}{x}=2y^2\\\\6xy^2=(3x)(2y^2)\\\\h)\ \dfrac{25a^3b^2}{5a^2b^2}=\dfrac{25}{5}\cdot\dfrac{a^3}{a^2}\cdot\dfrac{b^2}{b^2}=5a\\\\25a^3b^2=(5a^2b^2)(5a)[/tex]

To factor by identifying a common factor in each term, divide out the greatest common factor of the terms.

To factor by identifying a common factor in each term, we look for a number or variable that can be divided out of each term. Let's go through the expressions one by one:

g) 6xy2 = (3x) ?

We can see that both terms have a common factor of 3x. Dividing each term by 3x gives us 2y2.

h) 25a3b2 = (5a2b2) ?

Again, both terms have a common factor, which is 5a2b2. Dividing each term by 5a2b2 gives us 5a.

i) 6x + 6y + 6p

Here, all three terms have a common factor of 6. Dividing each term by 6 gives us x + y + p.

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Answer:

60ft/s

Step-by-step explanation:

To find the rate

rate = f(3) - f(0)

         -------------

         3-0

rate = 200-380

         ---------------

         3-0

rate = -180/3   = -60 ft/s

The negative tells us it is falling

The fall falls 60ft/s

Answer:

The correct answer is 60 feet / second.

Step-by-step explanation:

We are given the height of a ball which is falling from a height of 280 feet for 3 seconds.

We are to find the ball's rate of fall during the first 3 seconds.

For that, we will take the difference between the heights and divide it by the time.

Ball's rate = [tex] \frac { 3 8 0 - 2 0 0 } { 3 } [/tex] = 60 feet / second

Answer:

B and D

Step-by-step explanation:

The surface area is the area of each face of the cube. The volume is the amount that will fill the cube. These are two separate processes which cannot give you the same measurement by calculating one part of the surface area. B is false.

Doubling the sides of the cube will not double the surface area. It will quadruple it. D is false too.

Answer:

A

Step-by-step explanation:

Each hour is 30 degrees. 11 to 6 is 7 hours so 30 * 7 = 210 degrees, which is greater than a semicircle, which is 180 degrees.

Answer:

A. The hands are at 11 and 6; arc measured clockwise

Step-by-step explanation:

A semicircle measures 180º and when you measure the distance from 11 to 6 the difference in the hands of the clock by each hour is given by the equation:

[tex]\frac{360}{12}[/tex]= 30

So there are 7 numbers between the 11 and the 6 if you measure it clockwise, that means that the angle formed by the two hands of the clock measured clockwise is:

7*30= 210

Wich is greater than 180º, which is why that is the correct answer.

Step-by-step explanation:

An hour and a half is 90 minutes.

Knowing this, set up a proportion.

20 over 15 is equal to x over 90.

x is equal to: 120 miles

Answer:

if you want to find a percent first you have to find the fraction. for an example for other, if 75 people out of 300 people are working you would divide 75 by 300. that would give you .25. then you multipluy by a hundred. that would give you 25 percent

Step-by-step explanation:

Answer:

15+c-d

Step-by-step explanation:

4(3+1/4c-1/2d) or in decimals 4(3+0.25c-0.5d)

distribute the 4 (in other words use the distributive property)

4 · 3 = 12

4 · 0.25 = 1

4 · 0.5 = 2

12 + 1 + 2 = 15

15 + c-d is your answer

hope I helped <3

Answer:

85°

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral add up to 180°.in the figure provided, angle d is opposite the angle whose value is 95° while angle c is opposite the angle marked 110°.  there fore its value can be calculated as follows:

angle d= 180-95

angle d=85°

Answer:

Step-by-step explanation:

the relative frequency of elementary

school students who prefer watching

football to the total number of

elementary school students, as a

percentage rounded to the nearest

whole number

.[tex]\frac{(26)}{137} \\=0.1897\\=19%[/tex]

the relative frequency of middle

school students who prefer watching

basketball to the total number of

students, as a percentage rounded

to the nearest whole number

=[tex]\frac{50}{502} =0.0996\\\\=9.96%\\=10%[/tex]

the difference of the number of

students who like watching baseball

and the number of students who like

watching soccer

=102-59=43

the difference of the number of high

school students who like watching

soccer and the number of high

school students who like watching

tennis ..

=36-11=25

Answer:

arc EAC = 280 degrees

Step-by-step explanation:

Given: the measure of arc AB is 55  and the measure of arc CD is 25

Vertical angles are equal so <AOB = <DOE = 55

In a circle, the degree measure of an arc is equal to the measure of the central angle.

so if <DOE = 55 then arc DE = 55

As you know, the arc angle to a full angle in a circle = 360

so

arc EAC = 360 - arc CD - arc DE

arc EAC = 360 - 55 - 25

arc EAC = 280

Answer:

arc EAC = 280 degrees

The measure of EAC = 280°

A circle is a round-shaped figure with all points lie in the same plane, the distance between all the points on the circle and the center of the circle is equal.

The line that passes through the center of the circle and has end point on the circumference is called the diameter, the radius is half the measure of the diameter.

The circumference is the perimeter of the circle, it is the distance that is covered by a man to take one round around the circle.

The area is defined as the space required by a two dimensional object in space.

The chord AD and BE is the diameter of the circle,

They intersect each other, the sector formed by the circle is of equal measure.

The measure of arc AB is 55 and,

The measure of arc CD is 25

The sector ED = AB = 55 degree.

The measure of EAC = 360 - measure of ED and DC

The measure of EAC = 360 - 55 - 25

The measure of EAC = 280°

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Answer:

x equals six start fraction one over two end fraction

Step-by-step explanation:

Segments which are parallel have the same slope. Find the slope of of YZ. Then using that value, find the slope WX and solve for the value of x.

Slope of YZ is:

[tex]m = \frac{y_2-y_1}{x_2-x_1}=\frac{2-6}{2-5}=\frac{-4}{-3}=\frac{4}{3}[/tex]

Since they are parallel, then WX has a slope of 4/3 too.

Slope of WX is:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\\frac{4}{3}=\frac{-2--4}{x-5}\\\\\frac{4}{3}=\frac{2}{x-5}\\\\\frac{4}{3} (x-5) = 2\\\\4x -20=6\\\\4x = 26\\\\x = 6\frac{1}{2}[/tex]

Answer:

9

Step-by-step explanation:

9.05= 9.0=9

0 isn't greater than five, so you leave it as 9

Answer: tithe area of figure b is 315.

Step-by-step explanation:

You would need 8 vans because:

48/6 = 8

16/2=8

Plus, if you add the number of students and teachers together it equals 64. Then divide it by the number of people who can fit into the van, which is 8.

64/8=8 vans

there will be needed 10 buses so other people can fit in

Answer:

[tex]\large\boxed{(x-9)^2+(y+5)^2=4}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (9, -5) and the radius r = 2. Substitute:

[tex](x-9)^2+(y-(-5))^2=2^2\\\\(x-9)^2+(y+5)^2=4[/tex]

ANSWER

[tex]x = 6[/tex]

EXPLANATION

The given equation is

[tex] \sqrt{3x + 7} = x - 1[/tex]

We square both sides of the equation to obtain,

[tex](\sqrt{3x + 7} ) ^{2} =( x - 1)^{2} [/tex]

This implies that,

[tex]3x + 7 = {x}^{2} - 2x + 1[/tex]

Rewrite in standard quadratic equation form.

[tex] {x}^{2} - 2x - 3x+ 1 - 7 = 0[/tex]

[tex]{x}^{2} -5x - 6= 0[/tex]

Factor

[tex](x - 6)(x + 1) = 0[/tex]

This implies that,

[tex]x = 6 \: x = - 1[/tex]

We check for extraneous solution by substituting each x-value into the original equation.

When x=-1,

[tex]\sqrt{3( - 1)+ 7} = - 1- 1[/tex]

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

2=-2....False

Hence x=-1 is an extraneous solution.

When x=6,

[tex]\sqrt{3( 6)+ 7} = 6- 1[/tex]

[tex]\sqrt{25} = 5[/tex]

5=5 is True.

Hence x=6 is the only solution.