The law of cosines is a² + b² - 2abcosC = c². Find the value of 2abcosC.
A. 20
B. 40
C. 37
D. -40​

Part (a)

Decreasing means that as x increases, y decreases.

So the intervals are [tex](-8, -4), (0, 5), (9, \infty)[/tex]

Part (b)

A local minimum is where the function changes from decreasing to increasing.

So, the local minima are at [tex]x=-4, 5[/tex]

Part (c)

The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative

Part (d)

The degree is given by the number of roots (including multiplicity).

From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.

Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)

However, since the graph has the same end behavior in both directions, the degree must be even.

So, the possible answers are any even number that is at least 6

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct option is A.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

A histogram is a statistical information presentation that employs rectangles to illustrate the frequency of data items in equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most frequent kind of histogram.

The best graph that can represent the given situation is Histogram. Hence, the correct option is A.

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5%3×4+14-15 answers thes questions

She did 21 question correctly.

Let number of correct answers : x

Let number of wrong answer : y

Given, Total question wrote : 30

So,  

      x + y = 30          (i) - equation

Got 8 point on each correct answer, total point : 8*x

Got -2 point on each wrong answer, total point : (-2)*y

Total point she score was : 150          (given)

so, our next equation is

                                      8*x - 2*y = 150       (ii) - equation

                                      y = 30 - x            [from (i) - equation]

put in (ii) - equation, we get

                                    8*x - 2*(30 - x) = 150

                                    8*x - 60 + 2*x = 150

                                    10*x = 210

                                       x = 21

Therefor, only 21 answers are correct.

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Given the parameterization

[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]

take the normal vector to be

[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]

(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)

Compute the magnitude of the normal vector.

[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]

so that the area element reduces to

[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]

Evaluate the integrand at [tex]\vec r[/tex] to get

[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]

The surface integral reduces to

[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]

Answer:

  16x² +48x +36

Step-by-step explanation:

A perfect square trinomial is of the form ...

  (a +b)² = a² +2ab +b²

We want to match this form.

__

Comparing the known terms, we see ...

  16x² = a²   ⇒   a = 4x

  36 = b²   ⇒   b = 6

The missing term is the linear term:

  2ab = 2(4x)(6) = 48x

  ? = 48

Answer:

6.25 litres

Step-by-step explanation:

ratio 1:4

25/4 = 6.25

4 * 6.25 = 25

1 * 6.25 = 6.25

= 6.25 litres of concentrate

Answer:

6.25 litres of juice concentrate

Answer:

4 (2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5

Step-by-step explanation:

If she arrives by boat;

The distance she needs to row = Lake diameter

Distance = Lake diameter = 2 x Radius

Boat distance = 2 x 2 miles = 4 miles

So;

When moving on foot

The distance that needs to be moved D = Half of the circle circle

∴ D = π × Radius

The distance that needs to be moved D = π × 2 miles = 2π Miles

Arc length = Radius × θ

String length = radius x 2 x sin (θ / 2)

0 ≤ θ ≤ π, 0 ≤ sin (θ / 2) ≤ 1

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Answer:

91 degrees

Step-by-step explanation:

Sum of angles in a quadrilateral: 360 degrees

87, 89, 91, 93 are four consecutive odd numbers that add up to 360

third angle is 91 degrees

The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

An investment is a payment made to acquire the securities of other firms with the intention of making a profit.

We are assuming the interest will be compounded annually

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

P = $7000

r = 3% = 0.03

t = 10 years

n = 1

[tex]\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}[/tex]

After calculating:

A = $9407.41

I = A - P = 9407.41 - 7000 = $2,407.41

Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

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Answer :

Points at (1, 3) and (3, 3) and (2, 1)

Explanation:

The original graph (dashed) is an absolute value function meaning f(x) = |x|

Given: y = 2f(x - 2) + 1

f(x - 2) means you plug in x - 2 for x in f(x) function

the new graph equation is: y = 2|x - 2| + 1

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Visual:

Answer:

D

Step-by-step explanation:

The correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11

The correct question is as given below:-

Need help ASAP. Choose the expression that represents a cubic expression.

a. 2x + 11

b . −3x² − 2x + 11

c . 4x³ − 3x² − 2x + 11

d . 5x⁴ + 4x³ − 3x² − 2x + 11

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The polynomial having a degree of three is called the cubic polynomial which means that the maximum power of the polynomial will be three and the solutions will also be three.

Here in the option, we can see that the maximum power of the polynomial is three and it will have a maximum of three solutions.

The third-degree expression will be:-

E = 4x³ − 3x² − 2x + 11

Therefore the correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11

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Since we have given that

Measure of revolution = 360°

Now, the measure of [tex]\frac{3}{4}[/tex] of revolution.

So, it becomes,

[tex]\frac{3}{4}[/tex]×360

= 3 × 90

= 270

Hence, the measure of 3/4 of revolution is 270°.

Hope this helped and have a good day

Answer:

[tex]x = \frac{y - 1150}{5} [/tex]

Step-by-step explanation:

[tex]y - 1150 = 5x \\ \frac{y - 1150}{5} = x \\ x = \frac{y - 1150}{5} [/tex]

Explanation:

Equation: x + 1 = 9

Solving Steps:

x + 1 = 9                 (subtract both sides by 1)

x + 1 - 1 = 9 - 1        (simplify the following)

x = 8

Then check for solution:

x + 1 = 9

                         [insert x = 8]

8 + 1 = 9

9  =  9

As both sides are equal, the statement is true.

[tex]\large\underline{ \cal{SOLUTION:}}[/tex]

[tex] \large \bold{x + 1 = 9}[/tex]

[tex] \large \bold{x = 9 - 1}[/tex]

[tex] \large \bold{x = \red{8}}[/tex]

[tex] \: [/tex]

[tex]\large\underline{ \cal{CHECKING:}}[/tex]

[tex] \large{ \bold{ \underline{ \red{8} }+ 1 = 9}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

The rate of change of radius at radius 6cm is 0.79 cm/sec.

The rate of change of a function is simply the derivative of the function with respect to the changing parameter in the function i.e. variable in the function.

So for calculating the rate of change of radius, we calculate the rate of volume change as volume is the function of radius.

As we know volume of the cylinder is given by V=πr²h

where r is the radius and h is the height of the cyclinder.

Given that rate of change of volume = 563 cm/sec

⇒ dV/dt =563 cm/sec

⇒ d(πr²h)/dt =563

taking πh outside the derivative as π and h is constant term

⇒ πh dr²/dt =563

⇒ πh (dr²/dr)(dr/dt)= 563 (applying chain rule dy/dx = (dy/du)(du/dx))

⇒ πh(2r)(dr/dt) =563

⇒dr/dt= 563/(2πhr)

given height of the cylinder h= 19cm

rate of change of radius at radius r =6cm= dr/dt= 563/(2πhr)= 563/(2*π*19*6)= 0.79 cm/sec

Therefore rate of change of radius at radius 6cm is 0.79 cm/sec.

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The given line equation is y=-1/2x+2

We have given the graph of the line

We have to determine the equation of the line,

We have to points(0,2) and (4,0)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m=0-2/4-0

m=-2/4

m=-1/2

[tex](y-y_1)=m(x-x_1)[/tex]

[tex]y-0=-1/2(x-4)\\y=-1/2x+2[/tex]

Therefore the second option is correct

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Answer:

y = 5x + 11

Step-by-step explanation:

We are given that a line passes through (-2, 1) and also it contains a slope of 5

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y axis

As we are already given the slope, we can immediately substitute it into the formula

Replace m with 5 in y=mx+b:

y = 5x +  b

Now we need to find b

As the equation passes through the point (-2, 1), we can use its values to help solve for b.

Substitute -2 as x and 1 as y:

1 = 5(-2) + b

Multiply

1 = -10 + b

Add 10 to both sides

11 = b

Substitute 11 as b in the equation

y = 5x + 11

Topic: finding the equation of the line

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The graph of the function is y = arcsec(x).

Answer:

2-4i/5

Step-by-step explanation:

[tex]\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5[/tex]

Answer:

[tex]\frac{2i}{i-2}=\frac{2-4i}{5}[/tex]

Step-by-step explanation:

The length of the base is 40 meters

We have:

Area= 160 square meters

Height = 4 meters

The area is calculated using:

Area = Base * Height

So, we have:

160 = Base * 4

Divide both sides by 4

Base = 40

Hence, the length of the base is 40 meters

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Answer:

As the x-values go to positive infinity, the function's

values go to negative infinity.

Step-by-step explanation:

upon viewing the graph you will notice that the function in blue will appear to go down (negative) as you follow the x to the right, in the positive direction.

Making your answer to be as the x goes to positive inf (right) the values of the function go to negative inf (down).

Answer:

he should check

3x and x

1/4 and 0.5

-m and 8m

-xy2 and 2xy2

Step-by-step explanation:

Answer:

The answer is A B C D H

Step-by-step explanation:

Using the normal approximation to the binomial, it is found that the probabilities are given as follows:

a) 0.0055 = 0.55%.

b) 0.2296 = 22.96%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 150, p = 0.889.

Hence the mean and the standard deviation of the approximation are:

Item a:

Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:

X = 124.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{124.5 - 133.35}{3.8473}[/tex]

Z = -2.3

Z = -2.3 has a p-value of 0.0107.

X = 123.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{123.5 - 133.35}{3.8473}[/tex]

Z = -2.56

Z = -2.56 has a p-value of 0.0052.

Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.

Item b:

The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:

X = 130.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130.5 - 133.35}{3.8473}[/tex]

Z = -0.74

Z = -0.74 has a p-value of 0.2296.

X = 112.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{112.5 - 133.35}{3.8473}[/tex]

Z = -5.42

Z = -5.42 has a p-value of 0.

Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.

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Answer:

[tex]\huge\boxed{\sf 14\ ft}[/tex]

Step-by-step explanation:

Yard sticks = 4

12-inch rulers = 2

All are placed end to end.

We know that,

1 yard = 3 feet

4 yards = 3 × 4 feet

4 yards = 12 feet

We know that:

1 inch = 0.083 feet

24 inch = 0.083 × 24 feet

24 inch = 2 feet

= 4 yardsticks + 2 12-inch rules

= 12 ft + 2 ft

= 14 ft

[tex]\rule[225]{225}{2}[/tex]

Answer:

as ABC = 3* DEF

AB = 5

DE = 15 = 5*3

AC = 3

DF = 9 = 3*3

BC = 4

EF = 12 = 4 * 3

Answer:

50

Step-by-step explanation:

Fractions are division problems. :) You have to complete that first to solve the equation (PEMDAS).

48/6 = 8

42 + 8 = 50

Answer:

45.5%

Step-by-step explanation:

The increase in population was 45.5%