The area of the base of a cylinder is found by dividing the volume of the cylinder by its height. If the volume of the cylinder is represented by 5x2 + 15x + 2 and the height is 5x, which expression represents the area of the base?

Answer:

1.5 < x < 4

Step-by-step explanation:

Let x be the pH of lemon juice

As it is said that the pH is less than it will be denoted by

x<4

Similarly it is also given that lemon juice's pH is greater than 1.5

x>1.5

So,

both inequalities will be combined.

1.5 < x < 4

It is read as x is greater than 1.5 and less than 4 ..

So option 2 is correct ..

Final answer:

The correct compound inequality to represent the normal pH range of lemon juice is 1.5 < x < 4, where x is the pH value. It indicates that the pH of lemon juice is greater than 1.5 but less than 4.

Explanation:

The pH scale measures how acidic or basic a substance is. To model the normal range of pH values for lemon juice, which is said to have a pH of less than 4 and greater than 1.5, we must use a compound inequality. A compound inequality that accurately represents this scenario is 1.5 < x < 4, where x stands for the pH value of lemon juice. It is important to use the less than symbol (<) and not the less than or equal to symbol (≤) because a pH of exactly 1.5 or 4 is not included in the "normal" range as stated.

Answer:

The volume of the rectangular swimming pool is [tex]384.75\ m^{3}[/tex]  or  [tex]384\frac{3}{4}\ m^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular swimming pool is equal to

[tex]V=LWH[/tex]

we have

[tex]L=19\ m[/tex]

[tex]W=13\frac{1}{2}\ m=\frac{13*2+1}{2}=\frac{27}{2}\ m[/tex]

[tex]H=1\frac{1}{2}\ m=\frac{1*2+1}{2}=\frac{3}{2}\ m[/tex]

substitute

[tex]V=(19)(\frac{27}{2})(\frac{3}{2})[/tex]

[tex]V=\frac{1,539}{4}=384.75\ m^{3}[/tex]

Convert to mixed number

[tex]384.75=384\frac{3}{4}\ m^{3}[/tex]

Answer:

The answer is B.

Step-by-step explanation:

Simply you change 6 3/4 into decimal form which is 6.75 then you divide it by the amount which is 3/4= .75

divide 6.75 by .75 equals 9

i hope this helps

Answer:

DE and BC

Step-by-step explanation:

Because the pieces of the two sides of the triangle would be proportional the line in the middle that has specified points will be parallel to the bottom line that was specified points. and because neither f or g were specified to be proportional they are irrelevant.

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HAVE A GREAT DAY

Answer:

the vertex is:

(2, -1)

Step-by-step explanation:

First solve the equation for the variable y

[tex]x^2-16y-4x-12=0[/tex]

Add 16y on both sides of the equation

[tex]16y=x^2-16y+16y-4x-12[/tex]

[tex]16y=x^2-4x-12[/tex]

Notice that now the equation has the general form of a parabola

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

In this case

[tex]a=1\\b=-4\\c=-12[/tex]

Add [tex](\frac{b}{2}) ^ 2[/tex] and subtract [tex](\frac{b}{2}) ^ 2[/tex] on the right side of the equation

[tex](\frac{b}{2}) ^ 2=(\frac{-4}{2}) ^ 2[/tex]

[tex](\frac{b}{2}) ^ 2=(-2) ^ 2[/tex]

[tex](\frac{b}{2}) ^ 2=4[/tex]

[tex]16y=(x^2-4x+4)-4-12[/tex]

Factor the expression that is inside the parentheses

[tex]16y=(x-2)^2-16[/tex]

Divide both sides of the equality between 16

[tex]\frac{16}{16}y=\frac{1}{16}(x-2)^2-\frac{16}{16}[/tex]

[tex]y=\frac{1}{16}(x-2)^2-1[/tex]

For an equation of the form

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

the vertex is: (h, k)

In this case

[tex]h=2\\k =-1[/tex]

the vertex is:

(2, -1)

Answer:

  A.  Algebraic, common difference = −10

Step-by-step explanation:

The difference between the first two terms is -10, as it is between the next two terms. The ratio of the first two terms is -1; of the next pair: -15/-5 = 3. There is a common difference, but not a common ratio.

The sequence is algebraic with a common difference of -10.

Answer:

Correct answer is A.  Algebraic, common difference = −10

Answer:

140 coins total

Step-by-step explanation:

Straightforward, this reads "7 is 5% of how many?".  Algebraically, the word "is" means an equals sign, and the word "of" means you multiply.  Of course, the 5% needs to be in decimal form.  Taking the sentence above, algebraically it is:  7 = .05x.  Divide by .05 on both sides to get x = 140

The multiplicative inverse of a number is the reciprocal of the number.

For a whole number this would be making it a fraction with 1 as the numerator.

The  multiplicative inverse of 5 is 1/5

Multiplicative inverse means that the numerator and denominator switch places. Remember that all non fraction numbers can be turned into a fraction by making the denominator 1 like so...

[tex]\frac{5}{1}[/tex]

Now you can take the multiplicative inverse of 5/1 to get...

[tex]\frac{1}{5}[/tex]

^^^That is equal to 0.2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]x = 16.6\ cm[/tex]

Step-by-step explanation:

To answer this question use the secant line theorem.

If two secant segments are drawn towards a circle from an outer point, then the product of the length of the secant segment y and the length of its outer secant segment is equal to the product of the length of the other secant segment and its external secant segment.

This is:

[tex](12+6)*6 = (5+x)*5[/tex]

Now we solve the equation for the variable x

[tex]18*6 = 5*5+x*5[/tex]

[tex]108 = 25+5x[/tex]

[tex]5x = 108-25[/tex]

[tex]5x = 83[/tex]

[tex]x = \frac{83}{5}[/tex]

[tex]x = 16.6\ cm[/tex]

Answer:

16.6

Step-by-step explanation:

got it right online

Answer: Radical conjugate.

Step-by-step explanation:

By definition  [tex]a+\sqrt{b}[/tex] and [tex]a-\sqrt{b}[/tex] are called "Conjugate radicals".

Therefore, by this definition, you can know the following:

1) [tex]a+\sqrt{b}[/tex] is the conjugate of [tex]a-\sqrt{b}[/tex]

2) [tex]a-\sqrt{b}[/tex] is the conjugate of [tex]a+\sqrt{b}[/tex].

Then, since you know that [tex]3+\sqrt{11}[/tex] is a root of a polynomial function, therefore you can conclude that the name given to the other root [tex]3-\sqrt{11}[/tex] of the same function is the following:

"Radical conjugate".

Answer: x = 19.42, y = 18.47, z = 18°

Step-by-step explanation:

This is assumed to be a 90° triangle so you can use Soh Cah Toa to answer the questions. You must use a calculator for the last step.

[tex]cos\theta=\dfrac{adjacent}{hypotenuse}\implies cos72^o=\dfrac{6}{x}\implies x=\dfrac{6}{cos72^o}\implies x=19.42\\\\\\tan\theta=\dfrac{opposite}{adjacent}\implies tan72^o=\dfrac{y}{6}\implies y=6\ tan72^o}\implies y=18.47\\\\[/tex]

Use Triangle Sum Theorem to find the angle measure of z:

90° + 72° + z = 180°

   162°     + z = 180°

                  z = 18°

Answer:

If there's no limits on the shape of the triangle, the length of the third side shall be between (excluding the endpoints)

Step-by-step explanation:

Let the length of the third side be [tex]x[/tex] kilometers. The length of each side shall be positive. In other words, [tex]x > 0[/tex].

Consider the triangle inequality theorem. The sum of any two ends shall be greater than the third end. For this triangle, the lengths of the three sides are:

By the triangle inequality theorem,

[tex]\left\{\begin{aligned}& 20 + 35 > x\\ & 20 + x > 35\\ & 35 + x > 25\end{aligned}\right.[/tex].

Rewrite and simplify each inequality:

[tex]\left\{\begin{aligned}& x < 55\\ & x > 15\\ & x > -15\end{aligned}\right.[/tex]

[tex]x[/tex] shall satisfy all three inequalities. As a result, the range of [tex]x[/tex] shall be the intersection of the solution sets of all three inequalities.

Refer to the sketch attached. On the sketch, the intersection is the region where the three colored lines are above each other. That's represents the interval

[tex]15 < x < 55[/tex].

In other words, the length of the third side is supposed to be between 15 kilometers and 55 kilometers.

Answer:

the answer is 15<x<55

Step-by-step explanation:

Answer:

We'll be making 35 liters of 19% glucose.

How much of a 15% solution and a 35% solution do we mix in order to get 35 liters of a 19% glucose solution?

X = liters of 15% and Y = liters of 35%

(.15 X + .35 Y) / 35 = .19

The number of Y liters will equal (35 -X) so the equation becomes

(.15 X + .35 *(35-X) ) / 35 = .19

(.15X + 12.25 -.35X) / 35 = .19

(-.20 X / 35) + (12.25 / 35) = .19

(-.20 X / 35) + .35 = .19

(-.20 X / 35) = -.16

-.20X = -5.6

X = 28 liters of 15% and

Y = 7 liters of 35% glucose

Answer is "c" 28 liters

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf f(x)=\cfrac{20}{4+3e^{-0.2x}}\implies f(3)=\cfrac{20}{4+3e^{-0.2(\stackrel{\downarrow }{3})}}\implies f(3)=\cfrac{20}{4+3e^{-0.6}} \\\\\\ f(3)=\cfrac{20}{4+3\frac{1}{e^{0.6}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{e^{\frac{3}{5}}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{\sqrt[5]{e^3}}} \\\\\\ f(3)=\cfrac{20}{4+\frac{3}{\sqrt[5]{e^3}}}\implies f(3)\approx\cfrac{20}{4+5.6464}\implies f(3)\approx 3.5421[/tex]

you could also just use plug in 0.6 as the exponent for "e", Euler's constant, in your calculator, and that works the same.

Answer:

Choice C

Step-by-step explanation:

5 Thousand  + 15 hundred = 6500

Answer:

it c

Step-by-step explanation:

Answer:

Iris can make 2 hats in an hour.

Step-by-step explanation:

3 hats in one and a half hours is 1 hat per half hour. 2 hats would take two half hours, which is one whole hour.

She can make 2 hats.

Since she can make 3 hats in 1.5 hours, divide 1.5 by 3 to find the unit amount of hats she can make.

1.5/3=.5

.5 of an hour is 30 mins.

Now, multiply 30 mins by 2 to find the amount of time it would take to make 2 hats.

30*2=60 or 1 hour.

She can make 2 hats in an hour.

Hope this helps!

Answer:

Step-by-step explanation:

The values at two points that differ by 1 year differ by $125, so the slope is $125 per year.

The graph shows the total cost of membership, which includes the initiation fee (y-intercept) and yearly membership dues (increase per year). The slope represents the increase per year: the yearly membership dues.

The slope of a line is determined by the change in the y-axis divided by the change in the x-axis. In this case without specific graphical data, it is conjectured that the slope may represent the yearly membership cost increase or decrease over time. A positive slope shows an increase, while a negative slope shows a decrease.

The question seems to be asking about the slope of a line related to the cost of a membership at a nature preserve. However, the provided reference information does not connect directly to this question, but outlines concepts of slope in economics and business scenarios rather than the nature preserve context. In general, the slope of a line is calculated by the change in the y-axis divided by the change in the x-axis. In this context, without a graph, one can conjecture that the slope may represent the yearly membership cost increase or decrease over time. A positive slope indicates an increase, whereas a negative slope indicates a decrease.

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Answer: Option a

They are equal and parallel

Step-by-step explanation:

If a and b have the same direction then necessarily a and b are parallel.

We know that they also have the same magnitude.

Two vectors are equal if they have the same magnitude and direction.

Then we can say that a and b are equal and we can also say that they are parallel.

Therefore the correct option is the option a

The x-coordinate of the solution to the system of linear equations is 0.

To find the x-coordinate of the solution to the given system of linear equations, we need to analyze the data points provided for both Equation 1 and Equation 2.

Similarly, examining the data points for Equation 2, we notice that as x increases by 4, y increases by 1. This implies a constant rate of change and suggests that Equation 2 also follows a linear pattern. We can express Equation 2 in the slope-intercept form:

y = (1/4)x + b.

To find the x-coordinate of the solution to the system, we need to set the two equations equal to each other and solve for x.

Equating the two equations, we have:

-x + b = (1/4)x + b

By simplifying the equation, we can eliminate the b term:

-x = (1/4)x

Next, we can multiply both sides of the equation by 4 to eliminate the fraction:

-4x = x

Bringing all the x terms to one side, we get:

-4x - x = 0

Combining like terms, we have:

-5x = 0

Finally, we divide both sides of the equation by -5 to solve for x:

x = 0

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Answer:

Option B [tex]HI=5\sqrt{2}\ units[/tex]

Step-by-step explanation:

Applying the Pythagoras Theorem

[tex]HI^{2}=(y2-y1)^{2}+(x2-x1)^{2}[/tex]

substitute the given values

[tex]HI^{2}=(2+3)^{2}+(3+2)^{2}[/tex]

[tex]HI^{2}=(5)^{2}+(5)^{2}[/tex]

[tex]HI^{2}=50[/tex]

[tex]HI=5\sqrt{2}\ units[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Your answer is 17%

Step-by-step explanation:

Divide the total number of seniors by the total number of students and turn it into a percentage.

5/30= 0.16666= 17%

Answer:

14%

Step-by-step explanation:

Answer:

b.  quantitative, continuous

Step-by-step explanation:

Since here Dog = 0.07

Cat = 0.1

Snake = 0.12, and so on.

It is a numeric form So, it is quantitative data. And we can't count them(it include numbers between two natural number) so it is Continuous Variable.

The variable which is in numeric form is called Quantitative Variable. Example: Weight, Marks, etc.

And, the variable which we can't count is known as Qualitative Variable. Example: Smoking, Non- Smoking, etc.

Further Quantitative Variable can be divided into two parts:

The variable which we can count is known as the Discrete variable. It includes the natural numbers only. Example: Number of apples, Number of senior citizens in a particular area, etc.

The variable which we can't count is known as Continuous Variable. Example: Height, Weight, etc.

Answer:

24 m

Step-by-step explanation:

The last un-labeled side of the figure is 6 - 4 = 2 m

Simply add all the sides (including the one not labeled) to get the perimeter

4+6+6+2+2+4 = 24 m

Answer:

24m

Step-by-step explanation:

6 + 6 + 2 + 2 + 4 + 4 =24

Answer:

The area of the kite is [tex]56\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the kite is equal to

[tex]A=\frac{1}{2}(D1*D2)[/tex]

where

D1 and D2 are the diagonals of the kite

we have

[tex]D1=4+4=8\ cm[/tex]

[tex]D2=10+4=14\ cm[/tex]

Find the area

[tex]A=\frac{1}{2}(8*14)=56\ cm^{2}[/tex]

Answer:

r=0.8

Step-by-step explanation:

We know that a geometric series has the following look: (see picture attached).

Comparing both series, we can clearly see that r=0.8

The value of r in a geometric series can be positive, negative, or zero.

The value of r in a geometric series can be positive, negative, or zero. When r is positive, it means the population is increasing in size. When r is negative, it means the population is decreasing in size. And when r is zero, it means the population size is unchanging, which is known as zero population growth.

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The company inventory consists of 51 bags of Colombian and 33 bags of Brazilian beans. Each bag holds 80 pounds of beans, so in total the company has 4080 pounds of Colombian and 2640 pounds of Brazilian beans.

The company wants to use up its entire inventory, a total of 6720 pounds of beans.

Let [tex]r[/tex] and [tex]m[/tex] denote the amount (in pounds) of the robust and mild blends, respectively, that the company should end up producing.

To use the entire inventory, we must have

[tex]r+m=6720[/tex]

Each pound of the robust blend uses 12 ounces (3/4 = 0.75 pound) of Colombian beans, and each pound of the mild blend uses 6 ounces (3/8 = 0.375 pound) of Colombian beans, so that

[tex]0.75r+0.375m=4080[/tex]

while each pound of the robust blend uses 4 ounces (1/4 = 0.25 pound) of Brazilian beans, and each pound of the mild blend uses 10 ounces (5/8 = 0.625 pound) of Brazilian beans, so that

[tex]0.25r+0.625m=2640[/tex]

Multiply both equations by 8 to get rid of the rational coefficients:

[tex]\begin{cases}6r+3m=32640\\2r+5m=21120\end{cases}[/tex]

Subtract 3(second equation) from (first equation) to eliminate [tex]r[/tex]:

[tex](6r+3m)-3(2r+5m)=32640-3\cdot21120[/tex]

[tex]-12m=-30720\implies\boxed{m=2560}[/tex]

Then

[tex]r+2560=6720\implies\boxed{r=4160}[/tex]

So the company needs to produce 4160 pounds of the robust blend and 2560 pounds of the mild blend.

Answer:

x=10

Step-by-step explanation:

$52-$22=$30

$30/3=$10=x

The price of each shirt is x=10

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.

Given

x to represent the shirt's price

$52-$22=$30

$30/3=$10=x

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Answer: There are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

Step-by-step explanation:

Since we have given that

Percentage of anti freeze in first brand = 35%

Percentage of anti freeze in second brand = 85%

Percentage of anti freeze in mixture = 75%

Total number of gallons of mixture = 150 gallons

We will use " Mixture and Allegation":

 First brand         Second brand

      35%                      85%

                      75%

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

85%-75%         :            75%-35%

    10                :               40

     1                 :                 4

So, Number of gallons of anti freeze in first brand is given by

[tex]\dfrac{1}{5}\times 150\\\\=30\ gallons[/tex]

Number of gallons of anti freeze in second brand is given by

[tex]\dfrac{4}{5}\times 150\\\\=40\times 3\\\\=120\ gallons[/tex]

Hence, there are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

The answer is:

The interval notation will be:  (-∞,-1.59) and (-4.41,∞+)

To solve the expression, we need to perform the following steps:

- Find the roots or zeroes of the expression:

Using the quadratic equation, we have:

[tex]\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]

We are given the quadratic expression:

[tex]x^{2} +6x+7[/tex]

Where,

[tex]a=1\\b=6\\c=7[/tex]

Then, substituting and calculating we have:

[tex]\frac{-6+-\sqrt{6^{2}-4*1*7 } }{2*1}=\frac{-6+-\sqrt{36-28 } }{2}\\\\\frac{-6+-\sqrt{36-28}}{2}=\frac{-6+-\sqrt{8}}{2}\\\\x_{1}=\frac{-6+\sqrt{8}}{2}=\frac{-6+2.82}{2}=-1.59\\\\x_{2}=\frac{-6-\sqrt{8}}{2}=\frac{-6-2.82}{2}=-4.41[/tex]

- Inequality interpretation:

Now that we already know the roots of the quadratic expression, and we can see that the parabola open upwards (positive quadratic coefficient), we can conclude that the function is less than 0 between the numbers -4.41. and -1.59

The interval notation will be:and  (-∞,-1.59) and (-4.41,∞+)

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

The other guy is absolutely right, however

we can change his 4.41 to 3 + or - sqrt2

Step-by-step explanation:

So C

Answer: Option A

[tex]tan(60\°) = \sqrt{3}[/tex]

Step-by-step explanation:

We know the sides and z. So since it is a straight triangle we use the Pythagorean theorem to pull the length of the x side.

[tex]z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=\sqrt{z^2 - y^2}\\\\x=\sqrt{2^2 - 1^2}\\\\x=\sqrt{4 - 1}\\\\x=\sqrt{3}[/tex]

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case:

[tex]adjacent = y=1\\\\opposite=x =\sqrt{3}\\\\\theta=60\°[/tex]

Then:

[tex]tan(60\°) = \frac{\sqrt{3}}{1}[/tex]

[tex]tan(60\°) = \sqrt{3}[/tex]

The answer is:

The correct option is:

A. [tex]\sqrt{3}[/tex]

Since we already know the hypothenuse and the opposite side of the triangle (y), we can calculate the value of "x" using the Pythagorean Theorem.

We have that:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}[/tex]

We know that:

[tex]Hypothenuse=z=2\\Adjacent=x=1[/tex]

So, substituting and calculating we have:

[tex]2^{2}=1^{2}+Opposite^{2}[/tex]

[tex]4-1=Opposite^{2}[/tex]

[tex]Opposite^{2}=3\\Opposite=\sqrt{3}[/tex]

Then,using the following trigonometric relation:

[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}\\\\Tan(60\°)=Tan(\frac{Opposite}{Adjacent})=Tan(\frac{\sqrt{3} }{1})^=\sqrt{3[/tex]

We have that the correct option is:

A. [tex]\sqrt{3}[/tex]

Have a nice day!