Find k and the roots if

3x^2+kx+4=0 and the sum of the roots is 3

Answer:

12 gallons of 20% salt solution

Step-by-step explanation:

Let

x -----> the number of gallons of 20% salt solution

we know that

20%=20/100=0.20

40%=40/100=0.40

25%=25/100=0.25

so

0.20(x)+0.40(4)=0.25(x+4)

Solve for x

0.20x+1.60=0.25x+1

0.25x-0.20x=1.60-1

0.05x=0.60

x=12 gallons

By solving a linear equation, we will see that we must use 12 gallons of 20% salt solution.

If we mix x gallons of 20% salt with 4 gallons of 40% salt, we will have a total mass of (x + 4 gall).

And the concentration on the left side is the known one, and we want the concentration of the mixture to e 25%, so we will have that:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

(the percentages must be written in decimal form).

Now we can solve this linear equation for x:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

4gal*0.40 = x*0.25 - x*0.20 + 4gal*0.25

4gal*0.40 -  4gal*0.25 =  x*0.25 - x*0.20

4gal*0.15 = x*0.05

(4gal*0.15)/0.05 = x = 12

So you should use 12 gallons of the 20% salt solution.

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The point which will lie in the solution set to the following system of inequalities is:

                          (2,5)

The system of inequality is given by:

       y>-3x+3--------(1)

and  y>x+2----------(2)

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.

a)

 (2,-5)

when x=2 and y= -5

then by first inequality we have:

-5>-3×2+3

i.e.

-5>-6+3

i.e.

-5>-3

which is a false identity.

This means that the point will not lie in the solution set.

b)

(-2,5)

when x= -2 and y=5

then  by first inequality we have:

5>-3×(-2)+3

i.e.

5>6+3

i.e.

5>9

which is a false identity.

Hence, option: b is incorrect.

c)

(2,5)

when x=2 and y=5

then by first inequality:

    5>-3×2+3

i.e.  5>-6+3

i.e.  5>-3

which is true

and by second identity:

      5>2+2

i.e.  5>4

which is again true.

Hence, (2,5) lie in the solution set.

d)

(-2,-5)

when x= -2 and y= -5

then by first inequality we have:

-5>-3×(-2)+3

i.e.

-5>6+3

i.e.

-5>9

which is a false identity.

Hence, the point (-2,-5) do not lie in the solution set.

Answer:

3 3/7 hours.

Step-by-step explanation:

We work in  rates / hour:

Anita  does 1/8 of the pool in 1 hour and Chao does 1/6 in an hour.

Let x be the time they would clean the pool working together,  then we have:

1/8 + 1/6 = 1/x

3/24 + 4/24 = 1/x

7/24 = 1/x

7x= 24

x = 24/7 hours.

It will take 24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds) hours to clean a typical pool Anita and Chao working together.

The typical setup for these work problems is

                         [tex]\frac{t}{a}+\frac{t}{b} =1[/tex]

Here, a and b are how long they can do it by themselves, and t is how long they work together.

                      ⇒[tex]\frac{t}{8}+\frac{t}{6} =1[/tex]

Now, we will do LCM of 8 and 6 and we get 24;

                     ⇒[tex]\frac{3t+4t}{24} =1[/tex]

                     ⇒[tex]\frac{7t}{24}=1[/tex]

Now, we will multiply 24 on both sides, and we get;

                    ⇒[tex]7t=24[/tex]

Now, we will divide by 7 on both sides, we get:

                   ⇒[tex]t=\frac{24}7}[/tex]

Hence, the answer is [tex]\frac{24}7}[/tex] hours.

x=24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds)

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.

The lowest common multiple of 3 and 8? Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Multiples of 8 are 8, 16, 24, 32, 40... So the lowest common multiple of 3 and 8 is 24.

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[tex]

A=3(4b^2+2b+6) \\

A=\boxed{12b^2+6b+18}

[/tex]

Answer:

a)zw  = 44.295 cos(1.924) +isin(1.924))

b) z/w= 4.921 cos(-0.936) + isin(-0.936)

Step-by-step explanation:

Given:

z=13+7i

w=3(cos(1.43)+isin(1.43)  

a. convert zw using De Moivre's theorem  

First coverting z into  polar form:

13^2 + 7^2  = 14.765

[tex]\sqrt{14.765}[/tex] =r

θ= arctan (7/13)

 = 0.49394                            (28.301 in degrees)

z= 14.765(cos(0.49394)+isin(0.49394)  )

Now finding zw

zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be multiplied

14.765 x 3=44.295

whereas the angles will be added

.494+1.43=1.924

Thus:

zw  = 44.295 cos(1.924) +isin(1.924))

b)

finding z/w

z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be divided

14.765 / 3 = 4.921

whereas the angles will be subtracted:

.494-1.43=-0.936

Thus:

z/w= 4.921 cos(-0.936) + isin(-0.936) !

Answer:

Polygons are 2 dimensional figures and have NO volume.

Maybe you are thinking of polyhedrons?

If 2 polyhedrons have the same volume, they are probably NOT congruent.

Step-by-step explanation:

Final answer:

Polygons are considered congruent if they can be superimposed with matching corresponding segments and angles. Polygons with equal area or equal content are not necessarily congruent; they may have the same size but their shapes can differ.

Explanation:

When referring to two polygons, the term "congruent" is used to describe figures where not only the corresponding angles are equal but also the lengths of corresponding sides are equal. In contrast, polygons having the same volume, which applies to three-dimensional solids or having the same area, which applies to two-dimensional figures, do not necessarily need to be congruent. According to our established theorems in geometry, two polygons are considered congruent if they can be superimposed on one another such that every corresponding segment and angle matches. In the case of polygons, this means that the lengths of sides and angles are exactly the same in both figures.

The concept of equal area differs from congruence. Polygons of equal area have the same total size in terms of square units, but their shapes can be vastly different. Therefore, polygons with equal area or equal content aren't necessarily congruent because congruence requires the polygons to have identical size and shape, with all corresponding sides and angles being equal. Equal content refers to the possibility of adding other polygons of equal area to two non-congruent polygons to achieve two resulting polygons with equal area. It's important to note that while congruent figures will always have equal content and area, figures with equal content and area may not be congruent.

To calculate the likelihood of drawing cards 5 and 6 in sequence from a shuffled deck of 8 cards, we multiply the individual probabilities of drawing each card. The result is a probability of 1/56.

The question asked is a probability question which involves finding the likelihood of drawing two specific cards in sequence from a shuffled deck. However, the detailed information provided relates to different scenarios involving card colors numbered cards, and rolling dice. It does not directly provide the information needed for calculating the specific probability of selecting cards 5 and 6 from a stack of 8 cards numbered 1-8. Nonetheless, if we base our calculation on a standard probabilistic approach without considering the provided scenarios:

The probability of selecting the card number 5 first from the stack of 8 is 1/8 since there is one card number 5 out of eight total cards. Once card number 5 has been selected, it is no longer in the stack, so there are now seven cards left. The probability of selecting card number 6 after that is 1/7. Therefore, the probability of selecting card 5 and then card 6 in the sequence is the product of the two probabilities: 1/8 * 1/7 = 1/56.

17680 cm2

Using the formula V=W*H*L. The area can be divided by two since it is a right triangle. That gives you the height and length which is 85. 9.5*85*85

Answer:

[tex]3m =\frac{57}{5}=11.4=11\ \frac{2}{5}[/tex]

Step-by-step explanation:

We know that

[tex]m = 3\ \frac{4}{5}[/tex]

Therefore

[tex]m = 3+\frac{4}{5}\\\\m=\frac{19}{5}[/tex]

Now multiply the value of m by 3.

[tex]m=\frac{19}{5}\\\\3m=3*\frac{19}{5}\\\\3m =\frac{57}{5}=11.4[/tex]

The answer is 3m = 11.4

Answer:

C.14

Step-by-step explanation:

Answer:

The answer is 195

Step-by-step explanation:

The formula is V= 1/2 of the height times the two bases

V=1/2*h*b*b

V=1/2*13*6*5

V=195 meters squared.

Hoped this helped!

Answer: 390

Step-by-step explanation:

Length x Width x Height = Volume

Answer:

I'm pretty sure it's the one you chose, which means the 2nd pic.

Answer:

I think It is the first one, that is a cone flipped and there is a hole in it.

6(7-4)+10

First distribute 6 into the parentheses

42-24+10= 28

So your answer is A. 28

Final answer:

To evaluate 6(x - 4) + 10 when x = 7, after substituting and simplifying, the result is 28 (option A).

Explanation:

Step-by-Step Solution

To evaluate the expression 6(x - 4) + 10 when x = 7, follow these steps:

Therefore, the expression 6(x - 4) + 10 when x = 7 equals to option A. 28.

Answer:

False

Step-by-step explanation:

The number of degrees of freedom associated with the t-test, when the data are gathered from a paired samples experiment with 12 pairs, is;

12 - 1 = 11

The paired samples t-test is equivalent to a one sample t-test for the mean. The degrees of freedom are obtained by subtracting one from the number of pairs;

Answer:

D. [tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We can use a process of elimination in order to easily solve this.

The shape of [tex]g(x)=-|x|[/tex] will be two diagonal lines that meet at (0,0)

[tex]g(x)=-x^2[/tex] Will be an upside down parabola

[tex]g(x)=-x[/tex] Will be a line with a slope of -1.

This means that the answer must be D

Answer:

The correct option is D.

Step-by-step explanation:

From the given graph it is clear that the y-intercept of the function is -1. It means the graph passes through (0,-1).

Check each function, whether the function passes through the point (0,-1) or not. Substitute x=0 it each function to find the y-intercept.

In option A,

[tex]g(x)=|x|[/tex]

[tex]g(0)=|0|=0[/tex]

The y-intercept of the function is at (0,0).

In option B,

[tex]g(x)=x^2[/tex]

[tex]g(0)=0^2=0[/tex]

The y-intercept of the function is at (0,0).

In option C,

[tex]g(x)=x[/tex]

[tex]g(0)=0[/tex]

The y-intercept of the function is at (0,0).

In option D,

[tex]g(x)=-2^x[/tex]

[tex]g(0)=-1[/tex]

The y-intercept of the function is at (0,-1).

The graph of [tex]g(x)=-2^x[/tex] passes through the point (0,-1).

Therefore the correct option is D.

let's firstly convert the mixed fractions to improper fractions and then sum them up.

[tex]\bf \stackrel{mixed}{2\frac{2}{8}}\implies \cfrac{2\cdot 8+2}{8}\implies \stackrel{improper}{\cfrac{18}{8}}~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{18}{8}+\cfrac{9}{4}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)18+(2)9}{8}}\implies \cfrac{18+18}{8}\implies \cfrac{36}{8}\implies \cfrac{9}{2}\implies 4\frac{1}{2}[/tex]

The answer is:

The dimensions of the paper for Gift C, are: 25" x 12"

and its area is:

[tex]GiftCArea=300inch^{2}[/tex]

To solve the problem, we need to calculate the total area of the remaining paper, and then, subtract it from the paper used for the gift A and B.

We know that:

[tex]GiftA=TotalPaperArea*\frac{2}{5}\\\\GiftB=TotalPaperArea*\frac{1}{3}[/tex]

Now, the paper for Gift C will be:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

From the statement we know that the dimenstions of the remaining paper are 25" x 45", so calculating the area we have:

[tex]TotalArea=25inch*45inch=1125inch^{2}[/tex]

Now, calculating the area of the paper for Gift A and B, we have:

[tex]GiftA=1125inch^{2}*\frac{2}{5}=450inch^{2}\\\\GiftB=1125inch^{2}*\frac{1}{3}=375inch^{2}[/tex]

Then, calculating the paper for Gift C, we have:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

[tex]GiftCArea=1125inch^{2}-(450inch^{2}+375inch^{2}+)[/tex]

[tex]GiftCArea=1125inch^{2}-825inch^{2}=300inch^{2}[/tex]

[tex]GiftCArea=300inch^{2}[/tex]

Therefore, calculating the dimensions of the paper for Gift C, knowing the height of the paper (25inches), we have::

[tex]GiftCArea=Height*Width\\\\Width=\frac{GiftCArea}{25inches}=\frac{300inches^{2} }{25inches}=12inches[/tex]

Hence, the dimensions of the paper for Gift C, are: 25" x 12".

Have a nice day!

[tex]\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(75^o)}{17}=\cfrac{sin(D)}{10}\implies \cfrac{10sin(75^o)}{17}=sin(D) \\\\\\ sin^{-1}\left[ \cfrac{10sin(75^o)}{17} \right]=D\implies 34.6\approx D[/tex]

since all interior angles in a triangle must be 180°, that means that C = 180 - 75 - 34.6 = 70.4.  Let's find AD, which is the other sides pair length.

[tex]\bf \cfrac{sin(75^o)}{17}=\cfrac{sin(70.4^o)}{AD}\implies ADsin(75^o)=17sin(70.4^o) \\\\\\ AD=\cfrac{17sin(70.4^o)}{sin(75^o)}\implies AD\approx 16.58[/tex]

now, check the picture below, let's find the altitude of the parallelogram.

[tex]\bf sin(34.6^o)=\cfrac{\stackrel{opposite}{h}}{\stackrel{hypotenuse}{16.58}}\implies 16.58sin(34.6^o)=h\implies 9.4\approx h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=9.4 \end{cases}\implies A=(17)(9.4)\implies A=159.8[/tex]

Answer: 0.5

Step-by-step explanation:

1-5 is half

and 6-10 is half

The probability that the number she chooses is greater than 5 is 5/10 or 1/2.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Elena randomly chooses a number from 1 to 10.

We have to find the probability that the chosen number is greater than 5.

Total amount of numbers from 1 to 10 = 10

The numbers greater than 5 from 1 to 10 are 6, 7, 8, 9 and 10.

Amount of numbers greater than 5 = 5

Probability = Number of desired outcomes / Total number of outcomes

                  = 5 / 10

                  = 1/2

Hence the required probability is 1/2.

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Answer:

D. (2, 6)

Step-by-step explanation:

Look at the picture.

Check:

(2, 6) → x = 2, y = 6

Put the coordinates of the point to the inequalities:

y < x² + 6

6 < 2² + 6

6 < 4 + 6

6 < 10    TRUE

y > x² - 4

6 > 2² - 4

6 > 4 - 4

6 > 0   TRUE

Final answer:

The correct solution to the system of inequalities is point D (2,6), as it satisfies both inequalities y < x^2 +6 and y > x^2 -4 when x=2 and y=6 are substituted into them.

Explanation:

The student is asked to select the point that is a solution to the system of inequalities.

The two inequalities given are:

< x^2 +6

y > x^2 -4

To solve this, we need to check which point(s) satisfy both inequalities. Let's evaluate the options given:

A. (0,8): Substituting x=0 into both inequalities gives 8 < 6 (false) and 8 > -4 (true), so point A does not satisfy both inequalities.

B. (-2,-4): Substituting x=-2 into both inequalities gives -4 < 10 (true) and -4 > 0 (false), so point B does not satisfy both inequalities.

C. (4,2): Substituting x=4 into both inequalities gives 2 < 22 (true) and 2 > 12 (false), so point C does not satisfy both inequalities.

D. (2,6): Substituting x=2 into both inequalities gives 6 < 10 (true) and 6 > 0 (true), so point D satisfies both inequalities and is the correct solution.

Therefore, the solution to the system of inequalities is point D (2,6).

Log base 3 of 4 + log base 3 of 11= log base 3 of 4•11; Answers is 11

Answer:

$4,723.21​

Step-by-step explanation:

Formula for COMPOUND INTEREST:

A = P ( 1 + r/n) ^ nt

Where A = principal money + interest earned,

P = Principal Money

r = interest rate in decmial

n = no. of times i.rate is compounded

nt = time

Since the qns asked to be compounded /monthly', you have the following formula:

A = 3250 ( 1 + 7.5%/12) ^ 60

7.5% is a yearly rate so divide it by 12 (as in 12 months)

60 = 5 years x 12 months

so use a calculator and you'll get $4723.206, round off and it's $4723.21

To find out how much Connie's investment in a savings account with a 7.5% annual interest rate compounded monthly will be worth in five years, use the compound interest formula. After calculations, her investment will be worth $4,723.21 in five years.

The student asks about the future value of an investment made in a savings account with compound interest. To calculate the amount Connie's investment will be worth in five years, we can use the compound interest formula, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($3,250), r is the annual interest rate (7.5% or 0.075 as a decimal), n is the number of times the interest is compounded per year (12, since it's monthly), and t is the number of years (5).

Using these values, we calculate the future value (A) as follows:

Convert the percent interest to a decimal: 7.5% = 0.075.

Divide the annual rate by the number of compounding periods: 0.075/12.

Add 1 to the interest rate per period: 1 + (0.075/12).

Calculate (1 + (0.075/12)) raised to the power of the total number of compounding periods: (1 + (0.075/12))^(12*5).

Multiply the principal by this amount: $3,250 × (1 + (0.075/12))^(12*5).

Connie's investment will grow to $$4,723.21 after five years, using compound interest.

Answer:

I would say C Sets 2 and 3 contain outliers.

Step-by-step explanation:

Set 2 has an outlier of 90, and set 3 contains an outlier of 40. 40 is not as much of an outlier as 90, so I'm not absolutely sure.

Answer:

-Sets 2 and 3 contain outliers.

Step-by-step explanation:

Mean is the average value of the set. Mean deviation is the difference of the values of the set when compared to the mean.

In set 1 the values are between 50 and 60. This means that the mean will also be between 50 and 60.

In set 2 there is one outlier that is 38. So, the range of the values are between 38 and 90. More values are between 30 and 40 so the mean will be in this range. So (90 - the mean in the range between 30 and 40) will be a large number.

The same goes for set 3.

2(x-50)

2(x+3)

7(2-x)

Find the greatest common factors and then put them outside the parentheses

The answer is A) 1 centiliter

The expression that gives us the number of miles that Mr. Roberts drove on Tuesday is (42÷2) +5.

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

42 / 2  = 21

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

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Question

On Monday, Mr. Roberts drove 42 miles. On Tuesday, he drove 5 miles more than half the distance he drove on Monday. Which expression shows how you could find the distance, in miles, Mr. Roberts drove on Tuesday?( 42 ? 5 ) × 2 42 ? ( 5 × 2 ) ( 42 ÷ 2 ) ? 5 ( 42 ÷ 2 ) + 5

Answer:

P(gummy bear) = [tex]\frac{4}{11}[/tex]

Explanation:

Probability of a certain outcome can be calculated as follows:

[tex]P(certain-outcome)=\frac{number-of-occurrences-of-this-outcome}{total-number-of-possible-outcomes}[/tex]

In the given problem we have:

20 gummy bears and 35 orange slices

We want to find P(gummy bear)

This means that:

number of occurrences of desired outcome = number of gummy bears = 20

Total number of possible outcomes = gummy bears + orange slices

Total number of possible outcomes = 20 + 35 = 55

Substitute with the givens in the above formula, we get:

[tex]P(gummy-bears)=\frac{20}{55}=\frac{4}{11}[/tex]

Hope this helps :)

Final answer:

The probability of selecting a gummy bear from a bag containing 20 gummy bears and 35 orange slices is approximately 36.36%.

Explanation:

The student's question is about finding the probability of selecting a gummy bear from a bag of sweets. Given that there are 20 gummy bears and 35 orange slices in the bag, to find the probability of selecting a gummy bear, we use the formula P(gummy bear) = (number of gummy bears) / (total number of sweets). Therefore, P(gummy bear) = 20 / (20 + 35) = 20 / 55. Simplifying this, we get approximately 0.3636, which can also be expressed as a percentage, 36.36%.

The answer is 150 degrees.

The sum of angle in a triangle is 180 degrees.. The measure of <1 from thediagram is 150 degrees

The sum of angle in a triangle is 180 degrees. From the given disgaram, the sum of the angles of the right triangle is 180 degrees.

Using the expression to find the measure of the acute angle

90 + 60+x = 180

150 + x = 180

x = 180 - 150

x = 30

Determne the value of <1

<1 + 30 = 180

<1 = 180 - 30

<1 = 150degrees

Hence the measure of <1 from thediagram is 150 degrees

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Answer:

B. g(x) = |x + 3|

Step-by-step explanation: