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Solve the equation by completing the square.
x^2 + 10x= -81

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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So slopes of  the line and given parallel line are equal so equation of line is y-1=-2(x-0)

y+2x=1

What is  slopes ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given that line passing through point(0,1)

Line is parallel to the line y=-2x+3

So slopes of the line and given parallel line are equal .

So, equation of line is y-1=m(x-0)

M is slope

m=-2

y-1=-2(x-0)

y+2x=1

So slopes of  the line and given parallel line are equal so equation of line is y-1=-2(x-0)

y+2x=1

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Carrie has 4 more pints of paint than Bryan.

Carrie has 3 gallons of paint, which is equivalent to 12 quarts (1 gallon = 4 quarts). On the other hand, Bryan has 10 quarts of paint.

To compare the quantities in the same unit, we note that 1 quart is equal to 2 pints.

Carrie's 12 quarts of paint is equivalent to 12 × 2 = 24 pints.

Bryan's 10 quarts is equivalent to 10 × 2 = 20 pints.

To find the difference, we subtract Bryan's pint quantity from Carrie's:

24 - 20 = 4 pints.

Therefore, Carrie has 4 more pints of paint than Bryan.

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Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

Answer:

a³b < 0

Step-by-step explanation:

If a > 0 then a³ > 0

and b < 0

then

a³b → + × - → -

that is a³b < 0

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

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Step-by-step explanation:

p+4<-24

collect like terms

p<-28

\(\\ \rm\Rrightarrow p+4<-24\)

\(\\ \rm\Rrightarrow p<-24-4\)

\(\\ \rm\Rrightarrow p<-28\)

So

\(\\ \rm\Rrightarrow p\in (-\infty,-28)\)

Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Answer:

D

Step-by-step explanation:

The correct answer is D, try graphing them on desmos.

Statement C is true"Every lens has two focal points".Option C is correct.

The point where rays or waves converge after being reflected or refracted, or the place where rays or waves appear to diverge.

Every lens has two focal points. Because There are two focal points on each lens, one on each side. Lenses, in contrast to mirrors, can let light through either face depending on the direction the incident rays are coming from.

Another statement is incorrect due to following reasons,

The focal length is the distance between the lens's focal point and its center. The focal point is where two parallel rays converge after going through the lens. If the medium is the same on both sides, the focus point and, consequently, the focal lengths, will also be the same.

Every lens has two identically spaced-apart focal points on its two opposite sides. The focal length is the measurement between the lens and the point of focus. The focal length is always positive for converging lenses and always negative for divergent lenses.

Hence option C is correct.

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Answer:

T(1,0)

Step-by-step explanation:

Answer:

\(y = 75\)

Step-by-step explanation:

Given

\(y\ \alpha\ \ x\)

\(y=24; x =16\)

Required

Find y when \(x = 50\)

We have:

\(y\ \alpha\ \ x\)

Express as equation

\(y = kx\)

Solve for k

\(k = \frac{y}{x}\)

When \(y=24; x =16\)

\(k = \frac{24}{16}\)

\(k = \frac{3}{2}\)

When \(x = 50\), we have:

\(y = kx\)

\(y = \frac{3}{2} * 50\)

\(y = 75\)

The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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Answer:

The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.

The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.

Step-by-step explanation:

The place value of 7 in words in 5.3479 is seven thousandths

The given number is 5.3479

The underlined digit has been identified as 7

The place values of each of the digits in 5.3479 are:

5 = 5 units

3 = 3 tens

4 = 5 hundredths

7 = 7 thousandths

9 = 9 ten thousandths

Therefore, the place value of 7 in words in 5.3479 is seven thousandths

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The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

Step-by-step explanation:

The domain of the function is,

[-5,infinity) and the range of the function is [2,infinity)

Answer:

Step-by-step explanation:

The answer is x≥2

Answer:

p0 = 0.05

Step-by-step explanation:

Using variable concepts, it is found that:

In the rat experiment, it was concluded that the students influenced the rats behavior, hence:

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1. The functiοn \(f(x) = 3x2^x+4-1\)undergοes the fοllοwing transfοrmatiοns

A vertical translatiοn dοwnward by 1 unit (the \("-1\)" at the end)

An upward vertical stretch by a factοr οf 3 (the "3" cοefficient in frοnt)

An expοnential grοwth with base 2 (the expοnent "x" in the term \("2^x"\))

A hοrizοntal shift tο the left by 4 units (the "-4" in the expοnent οf \("2^x"\))

2. The functiοn \(f(x) = -1/2x5^x-2+6\) undergοes the fοllοwing transfοrmatiοns:

3. The functiοn \(g(x) = 1/5log(x+5)+3\) undergοes the fοllοwing transfοrmatiοns:

4. The functiοn \(g(x) = -4log(x)-2\) undergοes the fοllοwing transfοrmatiοns:

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If \(4^{-2}\) is divided by \(4^{-8}\) the answer is \(4^{6}\) = 1296

Given:

4^-2 divided by 4^-8

= \(4^{-2}\)/\(4^{-8}\)

= 1/\(4^{2}\)/1/\(4^{8}\)

= 1/\(4^{2}\) * \(4^{8}\)/1

= \(4^{8}\)/\(4^{2}\)

= \(4^{6}\) = 1296

Therefore If \(4^{-2}\) is divided by \(4^{-8}\) the answer is \(4^{6}\) = 1296.

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Answer:

The length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

Step-by-step explanation:

Given that the length of a rectangle is 3 yards more than twice the width, and the area of the rectangle is 54 yards, the following calculation must be performed to find the dimensions of the rectangle, knowing that the area of a rectangle arises from multiplying its base by its height:

2X + 3 + X = 54

3X + 3 = 54

3X = 54 - 3

X = 51/3

X = 17

(17 x 2) + 3 = 37

Therefore, the length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

Answer:

14x10 5step-by-step explanation: 105=

100,0001 4x10,000 140,000.

More

So you add 2,918+1,264=4,182

Answer:

3/10

Step-by-step explanation:

From the question :

Let amount rytis get = x

Hence, amount Linda gets = 3x

Hence, amount Adam gets = 2 times what Linda gets = 2(3x) = 6x

Hence, total amount shared :

x + 3x + 6x = 10x

Amount Linda got = 3x

Therefore, fraction Linda gets = Amount gotten by Linda / total amount = 3x / 10x = 3/10

Hence, fraction gotten by Linda = 3/10

The fraction of the amount of money does Linda gets is 3/10 and this can be determined by using the arithmetic operations.

Given :

The following steps can be used in order to determine the fraction of the amount of money does Linda get:

Step 1 - Let the total amount of money Rytis get be 'x'.

Step 2 - So according to the given data, the total money Linda has is 3x.

Step 3 - According to the given data, the total money Adam has is 2(3x).

Step 4 - So, the total amount of money shared is:

x + 3x + 6x = 10x

Step 5 - So, the fraction of the amount of money does Linda get is:

\(\rm =\dfrac{3x}{10x}\)

\(= \dfrac{3}{10}\)

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