The plot below shows the volume of 11 river water samples collected by an ecologist. All measurements are rounded to the nearest 1/8 gallon.

Answer:

2x² - 4x - 16

Step-by-step explanation:

(2x + 4)(x - 4)

each term in the second factor is multiplied by ech term in the first factor

2x(x - 4) + 4(x - 4) ← distribute parenthesis

= 2x² - 8x + 4x - 16 ← collect like terms

= 2x² - 4x - 16

Answer:

1. Function 1

2. Function 3

3. Function 2, Function 3, and Function 4

Step-by-step explanation:

I did this for someone else and it took me a long time to explain, so here's the answers since this is timed.

The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer: 3x+4-5x

Step-by-step explanation:

3x+4=5x

3x+4-5x=0

Answer:

B. 'x' should be 1.53 inches

Step-by-step explanation:

Given equation for the volume of the box:

\(V=(8-2x)(11-2x)(x)\)

To find the value of x that will maximize the volume, differentiate the volume, set the first derivative to zero and solve for x.

Expand the equation:

\(V=x(8-2x)(11-2x)\)

\(\implies V=x(88-16x-22x+4x^2)\)

\(\implies V=4x^3-38x^2+88x\)

Differentiate:

\(\implies \dfrac{dV}{dx}=12x^2-76x+88\)

Set to zero and solve for x:

\(\implies \dfrac{dV}{dx}=0\)

\(\implies 12x^2-76x+88=0\)

Divide by 4:

\(\implies 3x^2-19x+22=0\)

Use the quadratic formula to solve the quadratic equation.

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when}\:ax^2+bx+c=0\)

\(\implies x=\dfrac{-(-19)\pm \sqrt{(-19)^2-4(3)(22)}}{2(3)}\)

\(\implies x=\dfrac{19\pm \sqrt{97}}{6}\)

To find which value of x maximizes the volume, find the second derivative:

\(\implies \dfrac{d^2V}{dx^2}=24x-76\)

Then input the values of x into the second derivative:

\(x=\dfrac{19+\sqrt{97}}{6} \implies \dfrac{d^2V}{dx^2}=4\sqrt{97} > 0\implies \textsf{minimum}\)

\(x=\dfrac{19-\sqrt{97}}{6} \implies \dfrac{d^2V}{dx^2}=-4\sqrt{97} < 0\implies \textsf{maximum}\)

Therefore, the value of x that will maximize the volume is:

\(x=\dfrac{19-\sqrt{97}}{6}=1.53\:\sf inches \:(nearest\:hundredth)\)

Alternatively, you can input the given options of x into the formula and compare results, but this is the correct way to find/prove it.

Answer:

a)  "Like terms" are terms whose variables (and their exponents such as the 2 in x²) are the same

8y, -3y and y are all likes terms because the variables are all y

b)

\((-2x+8y-11)+(-3y-y+5)\\\\=-2x+8y-11-3y-y+5\\\\=-2x+(8y-3y-y)+(5-11)\\\\=-2x+4y-6\\\\=2(-x+2y-3)\\\\=-2(x-2y+3)\)

Answer:

Step-by-step explanation:

at most 1.

8(3x - 6) = 6(x + 8)

24x - 48 = 4x + 48                   Subtract 4x

24x - 4x - 48 = 4x -4x + 48      Combine

20x - 48 = 48                           Add 48 to both sides.

20x = 96                                 divide by 20

x = 96/20

x = 4.8

No other answer is possible.    

The sum of the given vectors is 14i+11j.

Given that are vectors u = <3, 3> and v = <11, 8> we need to find u + v,

So,

Considering the vectors, a and b in two-dimensional,

\(\overrightarrow{a} = x_1i+y_1j\\\overrightarrow{b} = x_2i+y_2j\\\)

The following step is used to find out the vector sum of a and b;

i-component of the vector a is added with the i-component of the vector b,

j-component of the vector a is added with the j-component of the vector b,

Therefore, the sum is =

\(\overrightarrow{a}+\overrightarrow{b} = (x_1+x_2)i +(y_1+y_2)j\)

Here,

\(\overrightarrow{u} = 3i+3j\\\\\overrightarrow{v} = 11i+8j\)

The sum =

\(\overrightarrow{u}+ \overrightarrow{v} =(3i+3j)+(11i+8j)\\\\= (3+11)i + (3+8)j\\\\= 14i+11j\)

Hence the sum of the given vectors is 14i+11j.

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Answer:sales tax rate would be 0.1

using the formula

Sales tax rate = Sales tax percent / 100

The value of the segment BA for the similar triangles is equal to 12.6.

The triangles ABC and ADE are similar, this implies that the length EA of the smaller triangle is similar to the length CA of the larger triangle

and the length DA of the smaller triangle is similar to the length BA of the larger triangle

so;

DA/BA = EA/CA

DA/(7 + DA) = 3.2/7.2

7.2DA = 3.2(7 + DA) {cross multiplication}

7.2DA = 22.4 + 3.2DA

7.2DA - 3.2DA = 22.4

4DA = 22.4

DA = 22.4/4 {divide through by 4}

DA = 5.6

BA = 7 + DA = 12.6

Therefore, the value of the segment BA for the similar triangles is equal to 12.6.

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The amount of wheat exported in Canada is 2.6 x 10 tons per year.

Standard form is used to transform large numbers into smaller number. In order to write a number in standard form, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example: the number 1 x 10² is equivalent to 100

2.21 x 10^7 ÷ 8.5 x 10^5 = 0.26 x 10^2 = 2.6 x 10

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Answer:

4/6

6/9

just multiply both sides by 2 and then u have an equivalent fraction

Step-by-step explanation:

have a good day and i hope i helped!

Answer:

Bro the answer is LITERALLY 1

Step-by-step explanation:

Answer:

The answer is one

Step-by-step explanation:

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:

x=5

Step-by-step explanation:

First, open up the parentheses to get 4x-2x+6=-4+5x-5. Now, move all numbers without variables to the right and those with variables to the left to get 4x-2x-5x=-4-5-6. Simplify both sides to have -3x=-15. Now divide both sides by -3 to get x=5

Step-by-step explanation:

|3y + 9| = 14

3y + 9 = ±√14

3y + 9 = ±3.742

3y = ±3.742 - 9

3y = - 5.258 or -12.742

y = -1.75267 or - 4.2474

9514 1404 393

Answer:

  2 miles 2 yards

Step-by-step explanation:

There are 1760 yards in a mile, so you are effectively performing the division ...

  (9185 380/1760) ÷ 4590

where the number in parentheses is a mixed number of miles.

You do this division the same way you do any mixed-number division. There are different possible methods you can use. One of them is to convert the mixed number to an improper fraction, then divide.

  9185 380/1760 = 9185 19/88 = (88·9185 +19)/88 = 808299/88

Then this is divided in the usual way:

  \(\dfrac{808299}{88}\div4590=\dfrac{808299}{88\cdot4590}=\dfrac{808299}{403920}=2\dfrac{459}{403920}=2\dfrac{1}{880}\)

Finding the quotient and remainder is straightforward. Reducing the fraction involves finding common factors in the numerator and denominator. As it turns out, 459 is a factor of 403920, so the fraction reduces as shown.

Now, we need to convert 1/880 miles back to yards.

  ((1/880) mi) × (1760 yd/mi) = 2 yd

So, the quotient you seek is ...

  2 miles 2 yards

Answer:

(1, -8)

Step-by-step explanation:

In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.

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The x is staying the same because it is not moving. The y, however, is changing sides.

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Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.

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I hope this helps!

-No one

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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If the parallelograms are similar, the dimensions must be proportional.

If the smaller one has dimensios 59.5, 59.5, 34 and 34, so the larger can be:

178.5, 178.5, 102 and 102 (ratio 1:3)

Letter b

Answer:

10(x^2)(y^2)

i hope this work for you

The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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Answer:

P>_5(10)^t

P<_1,000

Step-by-step explanation:

Answer:

(C)Out of 5,000 randomly chosen children, 250 children carry the virus.

Step-by-step explanation:

\(\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%\)

The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.

Option C is the correct option.

Answer:

\(\frac{9}{14}\) = 0.642857143

Step-by-step explanation:

\(\frac{1}{7}+\frac{1}{2}\)

Least common multiple of 7 and 2 is 14. Convert \(\frac{1}{7} and \frac{1}{2}\) to fractions with denominator 14.

\(\frac{2}{14} + \frac{7}{14}\)

Since \(\frac{2}{14} + \frac{7}{14}\) have the same denominator, add them by adding their numerators.

\(\frac{2+7}{14}\)

Add 2 and 7 to get 9.

\(\frac{9}{14}\)