What are the zeroes of the polynomial function f(x)=x^3+2x^2-x-2

Answer:

Snakes have 35000 cm³ space in their habitat.

Step-by-step explanation:

First Terrarium has the dimensions of (length×width×height) =(40×25×20)=Volume of Terrarium(V1)

V1 = 20000 cm³

Similarly volume V2 of the second terrarium = (25×30×20) cm³

V2=15000 cm³

Therefore total space for the snakes V1+V2 =20000+15000 cm³

                                                                         =35000 cm³

Answer:

Subtracting

Step-by-step explanation:

We know that the slope of a line is given by the rise over run. where rise is vertical difference between two points and run is the horizontal distance between the points.

[tex]\text{if }(x_1,y_1) \text{ and }(x_2,y_2)\text{ are two points on a line, then the}\\\text{slope of the line is given by}\\\\\text{Slope, }m=\frac{y_2-y_1}{x_2-x_1}\\\\\text{since slope}=\frac{\text{Rise}}{\text{Run}}, \text{ so Rise}=y_2-y_1\\\\\text{so we can find the rise by subtracting the Y-coordinate of the left point }\\\text{from the y-coordinate of the right point}.[/tex]

Answer:

0.609 / week  ( to nearest  thousandth)

or you can state it as 60.9% of a book per week

Step-by-step explanation:

That would be 14/23 =  0.609 / week

Answer:Han's mixture tastes stronger

Step-by-step explanation: Han's mixture tastes stronger, because...

Han's uses 6 2/3 cups of water for every 1 cup of orange juice concentrate.

Clare uses 71/2 cups of water for every 1 cup of orange juice concentrate.

Answer:

Han's juice has 15% concentration which is larger and hence, his juice will be stronger.

Step-by-step explanation:

It is required to find that which juice is stronger. So, we need to find the juice with maximum fraction or percentage of juice out of both the cases.

In first case, Clare mixes [tex]2\dfrac{1}{2}=\dfrac{5}{2}[/tex] cups of water with [tex]\dfrac {1}{3}[/tex] cup of orange juice. So, the concentration of the juice will be,

[tex]\dfrac{1/3}{5/2}=\dfrac{2}{15}=13.33\%[/tex]

In the second case, Han mixes [tex]1\dfrac{2}{3}[/tex]  cups of water with [tex]\dfrac{1}{4}[/tex] cup of orange juice.

So, the concentration of the juice will be,

[tex]\dfrac{1/4}{5/3}=\dfrac{3}{20}=15\%[/tex]

Therefore, out of the two cases, Han's juice has 15% concentration which is larger and hence, his juice will be stronger.

For more details, refer the link:

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Answer:

Area of rectangle = 30 units

Step-by-step explanation:

vertices are (2,2),(-3,2),(2,8), and (-3,8)

Let find the distance between (2,2)  and (2,8). because they have same x values. that would be our width

distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]

D = [tex]\sqrt{(2-2)^2 + (8-2)^2}=\sqrt(6^2) = 6[/tex]

Width = 6

Now we find distance between (2,2) and (-3,2) because they have same y values, that would be our length

distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]

D = [tex]\sqrt{(-3-2)^2 + (2-2)^2}=\sqrt(-5^2) = \sqrt(25)= 5[/tex]

length = 5

Area of rectangle = length * width = 5*6 = 30

QUESTION 1  

If a function is continuous at [tex]x=a[/tex], then [tex]\lim_{x \to a}f(x)=f(a)[/tex]  

Let us find the limit first,  

[tex]\lim_{x \to 4} \frac{x-4}{x+5}[/tex]  

As [tex]x \rightarrow 4[/tex], [tex]x-4 \rightarrow 0[/tex],[tex]x+5 \rightarrow 9[/tex] and [tex]f(x) \rightarrow \frac{0}{9}=0[/tex]  

[tex]\therefore \lim_{x \to 4} \frac{x-4}{x+5}=0[/tex]  

Let us now find the functional value at [tex]x=4[/tex]  

[tex]f(4)=\frac{4-4}{4+5} =\frac{0}{9}=0[/tex]  

Since  

[tex]\lim_{x \to 4} f(x)=\frac{x-4}{x+5}=f(4)[/tex], the function is continuous at [tex]a=4[/tex].  

QUESTION 2  

The correct answer is table 2. See attachment.

In this table the values of x approaches zero from both sides.

This can help us determine if the one sided limits are approaching the same value.

As we are getting closer and closer to zero from both sides, the function is approaching 2.

The values are also very close to zero unlike those in table 4.

The correct answer is B

QUESTION 3

We want to evaluate;

[tex]\lim_{x \to 1} \frac{x^3+5x^2+3x-9}{x-1}[/tex]

using the properties of limits.

A direct evaluation gives [tex]\frac{1^3+5(1)^2+3(1)-9}{1-1}=\frac{0}{0}[/tex].

This indeterminate form suggests that, we simplify the function first.

We factor to obtain,

[tex]\lim_{x \to 1} \frac{(x-1)(x+3)^2}{x-1}[/tex]

We cancel common factors to get,

[tex]\lim_{x \to 1} (x+3)^2[/tex]

[tex]=(1+3)^2=16[/tex]

The correct answer is D

QUESTION 4

We can see from the table that as x approaches [tex]-2[/tex] from both sides, the function approaches [tex]-4[/tex]

Hence the limit is [tex]-4[/tex].

See attachment

The correct answer is option A

Answer: 3x + 6 -4x = 1

Simplify to -x + 6 = 1 because 3x - 4x = -1x

Answer:

Halogens - 6 valence electrons

Step-by-step explanation:

Valence electrons are the number of electrons present in the outermost shell of the atom.

Noble gases have 8 valence electrons which is the maximum and are stable. They are inert by nature since they don't have to combine with any other element to attain stability.

Halogens have 7 valence electrons. They are high electronegative and have great attraction for electrons so that they can attain stability by forming the octet.

The valence electrons in transition metals varies as a group of columns are named transition metals.

Alkali earth metals has two valence electrons.

Hence the incorrect statement here is

Halogens - 6 valence electrons

Note how 80 is four times 20. So, 4*4=16. Sam can prepare 80 wall paints in 16 weeks.

Answer:

You use  F = m x a to solve for acceleration. You can change this formula around to solve for acceleration by dividing both sides by the mass, so: a = F ÷ m. To find the acceleration, simply divide the force by the mass of the object being accelerated.

HOPE IT HELPS

F= Force

A = Acceleration

M = Mass

Answer:

a=v/t

Step-by-step explanation:

to find acceleration divide change in velocity and change in time!

Hope this helps!!

Have a great day!

Answer:

Carol drank 0.5625 gallon of water in one day.

Step-by-step explanation:

Carter drink 15.75 gallons of water in 4 weeks. Each week consists of 7 days, then there are [tex]4\cdot 7=28[/tex] days in for weeks.

If  he drank the same amount of water each day, then he drank in one day

[tex]15.75:28=0.5625[/tex] gallon of water.

Answer:

D is the answer

Answer:

The correct option is 4. The lengths of side SR and side S'R' are in the ratio 1:3.

Step-by-step explanation:

The vertices of polygon are P(0,-3), Q(3,-2), R(3,1), S(0,2), T(-2,0).

The vertices of image are P'(0,-9), Q'(9,-6), R'(9,3), S'(0,6), T'(-6,0).

It is given that polygon P'Q'R'S'T' is the image of polygon PQRST after dilation with a scale factor of 3. It means both polygons are similar.

The corresponding angles of similar figure and same and the corresponding sides are proportional. It means the sides of image are three times of the corresponding sides of pre-image.

SR and S'R' are corresponding sides.

[tex]S'R'=3\times SR[/tex]

[tex]\frac{S'R'}{3}=SR[/tex]

[tex]\frac{1}{3}=\frac{SR}{S'R'}[/tex]

[tex]1:3=SR:S'R'[/tex]

The lengths of side SR and side S'R' are in the ratio 1:3.

Therefore the correct option is 4.

Answer:

4-x

Step-by-step explanation:

u can tell cause it doesn't have the exponent on the top and all that jazz

Answer:

One number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

Let x be the smaller number and y be the bigger number.

x = x

y = 5x

6x + 3y = 3

6x + (3 * 5x) = 3

6x + 15x = 3

(÷3)

2x + 5x = 1

7x = 1

x = [tex]\frac{1}{7}[/tex]

6x + 3y = 3

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

[tex]\frac{6}{7}[/tex] + 3y = 3

3y = 3 - [tex]\frac{6}{7}[/tex]

3y = [tex]\frac{15}{7}[/tex]

Divide both sides by 3 to get 1y:

y = [tex]\frac{5}{7}[/tex]

So one number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]

Answer: 28 and 18

Step-by-step explanation:

I used the guess and test strategy to find that:  

28 - 10 = 18

28 + 18 = 46

i think it will be 5 minutes

Answer:

1.6 = x

Step-by-step explanation:

For right angles,   tan x = opposite/adjacent

tan 37 = x / 2.1

Multiply 2.1 on each side.

2.1 tan 37 = x

1.58246 =x

Rounding to the nearest tenth

Answer:

Independent Variable - Type of Phone

Dependent Variable -Type of Service

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{s}{2}-3t=-1&\text{multiply both sides by 4}\\3t-2s=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2s-12t=-4\\3t-2s=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad -9t=-1\qquad\text{divide both sides by (-9)}\\.\qqud\qquad\boxed{t=\dfrac{1}{9}}\\\\\text{Put the value of t to the second equation}\\\\3\left(\dfrac{1}{9}\right)-2s=3\\\\\dfrac{1}{3}-2s=3\qquad\text{subtract}\ \dfrac{1}{3}\ \text{from both sides}[/tex]

[tex]-2s=2\dfrac{2}{3}\qquad\text{divide both sides by (-2)}\\\\s=\dfrac{8}{3}\cdot\left(-\dfrac{1}{2}\right)\\\\\boxed{s=-\dfrac{4}{3}}\\\\Answer:\ \boxed{\left(-\dfrac{4}{3},\ \dfrac{1}{9}\right)}[/tex]

By simplifying and rearranging the given system of equations, we find that the ordered pair (s, t) that satisfies the system is (2, 1 + 2/3).

The system of equations given in the question is:
s/2 - 3t = -1
3t - 2s = 3.

We can begin solving this system by first multiplying the first equation by 2 to eliminate the fraction, giving us:
s - 6t = -2.

Next, we rearrange the second equation to be in terms of 's':
2s = 3t + 3.

We then substitute this into the first equation and solve for 't':
(3t + 3) - 6t = -2,
simplifying to:
-3t + 3 = -2,
leading us to t = 1 + 2/3.

Substituting 't' into the second equation to find 's', we get:
2s = 3(1 + 2/3) + 3, which simplifies to s = 2. Therefore the ordered pair (s,t) that satisfies the system of equations is (2, 1 + 2/3).

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Basically here all you want to do it substitute the values x=1 and x=2 for the given function. Use your slope formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}  }[/tex].

Do same for x=3 and x=4

You next divide plug in values in to this expression:

[tex]\frac{Slope  of  B}{Slope  of  A}[/tex]

Answer:

The answer is 25

Step-by-step explanation:

Therefore, there are 25 red flowers in Sakura’s garden1.

We know that for every 55 red flowers, there are 1010 yellow flowers.

The total number of flowers in the garden is 7575 (which includes both red and yellow flowers).

Let’s use the variable (x) to represent the number of red flowers in the garden. We can set up the following ratio:

[tex][ \frac{{\text{{Red flowers}}}}{{\text{{Total flowers}}}} = \frac{{55}}{{55 + 1010}} ][/tex]

Solving for (x):

[tex][ \frac{{\text{{Red flowers}}}}{{7575}} = \frac{{55}}{{55 + 1010}} ][/tex]

Cross-multiplying:

[tex][ 55 \cdot 7575 = 55x + 1010x ][/tex]

Simplifying:

[tex][ 7575 = 55x + 1010x ][/tex]

Combining like terms:

[tex][ 7575 = 1065x ][/tex]

Solving for (x):

[tex][ x = \frac{{7575}}{{1065}} = 25 ][/tex]

Answer:

40/81

Step-by-step explanation:

9/25 ÷ 729/1000

We can use copy dot flip

9/25 * 1000/729

I will rewrite to make the math easier

9/729 * 1000/25

9 goes into 729   81 times

1/81 * 1000/25

25 goes into 1000   40 times

1/81 * 40/1

40/81

Because the tree is the halfway point, the building would be twice as tall:

The building is 38 x 2 = 76 feet tall.

Answer:

76 feet

Step-by-step explanation:

based on the looooooong txt, the building n tree form two similar right-angled triangles w the rope as the hypothesis.

tree is halfway between stake and bldg so stake-to-bldg = 2 x stake-to-tree

as the triangles are similar, their sides are in the same ratio

bldg height = 2 x tree height

= 2 x 38

= 76 feet tall

Answer:

3.82 pounds.

Step-by-step explanation:

We have been given that at the grocery store, Vanessa bought 1.02 pounds of ground beef, 1.6 pounds of tomatoes, and 1.2 pounds of chicken.

To find the total weight of three items, let us add 1.02, 1.6 and 1.2.

[tex]\text{The total weight of three items}=1.02+1.6+1.2[/tex]

[tex]\text{The total weight of three items}=3.82[/tex]

Therefore, three items weigh 3.82 pounds altogether.

Final answer:

Vanessa bought a total of 2.82 pounds of food, calculated by adding the weight of the ground beef, tomatoes, and chicken she purchased.

Explanation:

To calculate the total weight of the ground beef, tomatoes, and chicken Vanessa bought, simply add up their weights:

Ground beef: 1.02 pounds

Tomatoes: 1.6 pounds

Chicken: 1.2 pounds

To find the sum, you can add these values together:

1.02 + 1.6 + 1.2 = 2.82 pounds

So, Vanessa bought a total of 2.82 pounds of food.

Answer:

Yes

Step-by-step explanation:

2√3 − 2√3 is equal to 0. So what we are trying to find out is if 0 is a rational number. 0 IS a ratinol number as it can be expressed as a fraction of integers.

Q2 Answer: Experimental = 60%, difference = 10%

Step-by-step explanation:

The prime numbers between 1 and 8 are: 2, 3, 5, and 7.

Theoretical: [tex]\dfrac{4(prime)}{8(total)} = 50\%[/tex]

Experimental: [tex]\dfrac{12(prime)}{20(total)} = 60\%[/tex]

    Experimental - Theoretical

=       60%            -      50%

=                     10%

Problem 1

To find the sample mean, we simply add up all the 40 items and then divide by 40

I will add up the values row by row, and then add up the subtotals to get the grand total

row1: 39+31+38+40+29 = 177

row2: 32+33+39+35+32 = 171

row3: 32+27+30+31+27 = 147

row4: 30+29+34+36+25 = 154

row5: 30+32+38+35+40 = 175

row6: 29+32+31+26+26 = 144

row7: 32+26+30+40+32 = 160

row8: 39+37+25+29+34 = 164

Add up the subtotals: 177+171+147+154+175+144+160+164 = 1292

Divide this over 40: 1292/40 = 32.2

So the sample mean is therefore 32.2

-----------------------

To find the proportion of defective items, we count the number of times a value less than 26 shows up. That happens exactly two times. The first in row 4 (at the end of this row) is where a 25 shows up. Another copy of 25 shows up in row 8 (bottom row). There are no other values that are less than 26.

Divide this count (2) over the total sample size (40) and we get 2/40 = 1/20 = 0.05

-----------------------

In summary, 32.2 will go in the first box while 0.05 will go in the second box.

========================================

Problem 2

There are 4 values we want (2,3,5,7) out of 8 total (1,2,3,4,5,6,7,8) so 4/8 = 0.50 = 50% is the theoretical probability

This is the list of values given to us (I broke it up to help make the numbers more readable)

3, 4, 5, 2, 7

1, 3, 7, 2, 6

2, 1, 7, 3, 6

1, 8, 3, 5, 6

Of that list, the primes {3, 5, 2, 7, 3, 7, 2, 2, 7, 3, 3, 5} show up. There are 12 primes in this list out of 20. So the experimental probability is 12/20 = 3/5 = 0.60 = 60%

Therefore, the answer that goes in the "experimental probability" box is 60. The answer that goes in the second box is not 50%. I think your teacher is aiming for "10" to go in the second box because 60% is 10 percentage points higher than 50% (which was the theoretical probability found earlier)

-----------------------

In summary, 60 will go in the first box while 10 will go in the second box.

The formula for the perimeter of a rectangle is P = 2L + 2W

you are given P (perimeter) and l (length.

Replace the letters withe the given information and solve for width:

76 = 2(31) +2W

Simplify:

76 = 62 + 2w

Subtract 62 from both sides:

14 = 2w

Divide both sides by 2:

W = 14/2

W = 7 cm

The width is 7 cm.