the sum of three consecutive odd integers is 321. what are the three consecutive odd integers?

define in words variables for the unknown values
create an equation
solve using algebra

Hence , the construction of the triangle is given below.

 AB = 10 cm           BC = 6 cm           AC = 11 cm

We have to find ∠A, ∠B, and ∠C.

To construct a triangle,

Firstly draw a line segment AB = 10 cm

From A we need a point C at a distance of 6 cm. So with A as the center, draw an arc of 6cm in length from point A.

From B we need a point C at a distance of 11 cm. So with B as the center, draw an arc of 11cm in length from point B.

Mark the point of intersection of the arcs as C.

Meet points C to A and B respectively.

By using a protractor measure the angles of A, B, and C.

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The value invested in each security will be:

stock= $38000 ,

bonds= $46000

cds= $3000

Let the money invested in stocks be 'x', bonds be 'y' and CDs be 'z'.

Total money received as fund = x+y+z = $115000 -(Eqn 1)

$15000 more is invesed in bonds as compared to CDs i.e y = z + $15000 - (Eqn2)

Stocks pay 6.8%, bonds pay 3.6% and CDs pay 4% interest

Interest earned from stocks = 6.8% of x = 0.068x

Interest earned from bonds = 3.6% of x = 0.036x

Interest earned from CDs = 4% of x = 0.04x

Total interest earned = 0.068x + 0.036y + 0.04z = $5840 - (Eqn 3)

x + y + z =$115000 ----(1)

y = z + $15000 -----(2)

0.068x + 0.036y + 0.04z = $5840 ------(3)

Putting y = z+$15000 in Eqn 1 gives us:

x + (z+$15000) + z = $115000 ==> x = $100000 - 2z ----(Eqn 4)

Similarly,

Putting y = z+$15000 in Eqn 3 gives us:

0.068x + 0.036(z+$15000) + 0.04z = $5480 ==> 0.068x + 0.076z = $4940 ----(Eqn 5)

Putting Eqn 4 in Eqn 5,

0.068($100000 - 2z) + 0.076z = $4940

Hence, 0.06z = $1860

z = $31000

Put z = $31000 in Eqn 4 and get x = $100000 - 2z = $38000

Put z = $31000 in Eqn 2 and get y = z + $15000 = $46000

Hence final answer: x = $38000 , y = $46000, z = $31000

where x is the money invested in stocks, y in bonds and z in CDs.

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A decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount, the equivalent amount expressed as cents of $5.74 is 574 cents and $0.16 is 16 cents

We know that 1 dollar is equal to 100 cents

So, x dollar = x(100) cents

For $5.74 = 5.74(100) cents

                 = 574 cents

For $0.16 = 0.16(100) cents

                 = 16 cents

Integer and non-integer numbers are represented using the decimal numeral system, also known as the base-ten positional numeral system, denary, or decanary. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.

It is indicated by a '.', for instance, 3.14

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Answer:

3.5

Step-by-step explanation:

21x+6

21/21    6/21

x=3.5

Answer:

no

Step-by-step explanation:

89382

Answer: 21x^3 + 3 + 12x^2 + x

Step-by-step explanation:

Answer:

39.3°, 140.7°

Step-by-step explanation:

supplementary angles means that together they have 180°.

so, when we have 2 angles, x and y.

x + y = 180

x = y - 101.4

using the second equation in the first

y - 101.4 + y = 180

2y - 101.4 = 180

2y = 281.4

y = 281.4/2 = 140.7°

x = y - 101.4 = 140.7 - 101.4 = 39.3°

so, the starting angle is 39.3°, and every supplementary angle is then 140.7°.

Answer:

-4

Step-by-step explanation:

keep value of x as 1 in 5x+1

g(1)=-5×1+1

=-4

The location of a center of dilation in the figure is at the point where the corresponding vertex of the pre–image and image overlaps, which is point N, the correct option is therefore;

The given pre–image = Parallelogram LMNO

The image obtained from the pre–image = Parallelogram L'M'N'O'

Required: The location of the center of dilation

Solution:

The center of dilation is the point about which the figure or image is dilated.

It is the point that does not change following the dilation.

A vertex on the pre–image that gives an image vertex at the same point, is at the center of dilation which does not change in both the pre–image and image.

Therefore, given that point N and N' coincides, which indicates that the distance the pre–image point N is dilated to get the image point, N is 0. The center of dilation is at the vertex N.

The correct option is therefore;

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Answer:

On a vertex of figure LMNO

Step-by-step explanation:

The patient consumed 935 milliliters of fluids in 24 hours.

Restrictions of fluid per day = 1000 milliliters

Consumption of fluid by patient in past 24 hours are :

    Milk = 3 ounces

IV fluid = 725 Milliliters

  Juice = 4 ounces

As we know that,

One fluid ounce = 30 milliliters

Then,     Milk = 3 × 30  = 90 milliliters

               Juice = 4 × 30 = 120 milliliters

To determine the total amount of fluids we will add the total amount of Milk, IV fluids and Juice.

Fluids consume by patient = 90 + 725 + 120

                                          = 935 milliliters

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Step-by-step explanation:

2 . (6² + 2²) ÷ 4 - 10

= 2 . (36 + 4) ÷ 4 - 10

= 2 . 40 ÷ 4 - 10

= 80 ÷ 4 - 10

= 20 - 10

= 10

Answer:

x=-4

Step-by-step explanation:

this is if by roots, the problem is asking for the zeros of the equation

Answer: y = -1/5x -3

Step-by-step explanation:

Answer:

Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct

I am simply providing an explanation in case you need it

Step-by-step explanation:

The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b

where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis

Given two points (x₁, y₁) and (x₂, y₂)  on the straight line, we can compute the slope as follows

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

Two distinct points on the line are at (0, -3) and (5,-4)

[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]

So we know the equation to be

[tex]y = - \frac{1}{5}x + b[/tex]

To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b

However, looking at the graph we see that the line crosses the y axis at

y = -3. So this is the value for the y intercept i.e. b

The equation of the line is therefore

[tex]y = - \frac{1}{5}x - 3[/tex]

The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

From the graph, we have the y-intercept to be

y-intercept = (0, y), where y > 0

This means that the graph starts above the origin

This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)

Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

In this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height

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Answer:

One litre of water has a mass of almost exactly one kilogram.kilograms = liters × density of a liquid.

Answer:

Look below

Step-by-step explanation:

The LCM of 25 and 100 is 100

The GCF of 25 and 100 are 25.

The time it would take from when you threw the ball until it lands on the ground below is equal to 2.16 seconds.

Given the following data:

Height of building =  (42.0+A) m =  (42.0+9) m = 51 m.

Initial speed of ball = (14.5+B) m/s = (14.5+8) m/s = 22.5 m/s.

Scientific data:

Acceleration due to gravity = 9.8 m/s²

Generally speaking, when this ball is thrown straight up at a certain speed, it begins to slow down as a result of the effect of downward gravitational acceleration. Consequently, the ball reaches a maximum height where it can't go higher anymore and then starts to fall down due to gravity.

In order to determine the time it would take from when you threw the ball until it lands on the ground below, we would apply the second equation of motion:

S = ut + ½gt²

½gt² + ut - S = 0

Substituting the given parameters into the formula, we have;

0.5(9.8)t + 22.5t - 51 = 0.

4.9t + 22.5t - 51 = 0.

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]t = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-22.5\; \pm \;\sqrt{22.5^2 - 4(0.5)(-51)}}{2 \times 0.5}\\\\t = \frac{-22.5\; \pm \;\sqrt{506.25 + 102}}{2}\\\\t = \frac{-22.5\; \pm \;\sqrt{608.25}}{2}[/tex]

t = 2.16 or -47.16

Since the time cannot be negative, the value of t to three significant figures is equal to 2.16 seconds.

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Complete Question:

Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from when you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.

A=9, B=8

Answer:

f(7) = 92

Step-by-step explanation:

f(7) means what is the value of f(x) when x = 7

substitute x = 7 into f(x)

f(7) = 2(7)² - 6 = 2(49) - 6 = 98 - 6 = 92

The estimate (to one decimal place) of the average rate of change f is 1.7

The interval is given as

x = 1 to x = 4

This can be represented as

(a, b) = (1, 4)

From the attached graph, we have

f(1) = 2

f(4) = 7

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(4) - f(1)]/[4 - 1]

So, we have

Rate = [7 - 2]/[4 - 1]

Evaluate

Rate = 1.7

Hence, the estimate (to one decimal place) of the average rate of change f is 1.7

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The sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.

The term sinusoidal refers to a curve, also known as a sine wave or a sinusoidal, that shows smooth, periodic oscillation. It is named after the function y=sin (x). Sinusoidal appear often in mathematics, physics, engineering, signal processing, and many other fields.

A general form of a cosine function is given as shown below,

g(x) = a cos(bx+c) + d

Where the values of the given constant is,

a = amplitude

b = The period is of 2pi/B

c = phase shift

d = vertical shift

Since for the given condition the greatest value is 48 and the smallest value is 30 (a difference of 18), therefore, the amplitude is of the function can be written as,

2a = 18

a = 9

Further, a conventional cosine function with amplitude 9 would fluctuate between -9 and 9, while this one ranges between 30 and 48, resulting in d = 39 vertical shift.

Also, The minimum and maximum values form half the period, therefore, we can write,

π/B = 2.7 - 2.1

B = π/0.6

B = 1.67π.

Furthermore, The maximum value in the normal function is at x = 0, but the greatest value in this function is at x = 2.1, thus, the phase shift is 2.1 units to the right, or c = -2.1.

Hence, the sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.

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While installing 250 feet of PVC conduit given the details we have in the question, The amount of cement needed is 1 1/4  can of PVC cement

Given data

PVC conduit required to be installed =  250 feet

Each 100-foot section takes 1/2 can of PVC cement

Each 50-ft section takes 1/4 can of PVC cement

250 feet will be split into two which is 200 feet and 50 feet. We solve for each separately then add up

solving for 200 feet

200 feet contains how many 100-foot, this is solved as follows:

= 200 / 100

= 2

And each 100-foot takes 1/2 can of PVC cement, therefore:

2 * 1/2 = 1

solving for 50 feet

50 feet takes 1/4 can of PVC cement

= 1/4

The sum: 1 + 1/4 = 1 1/4 ( mix number )

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Step-by-step explanation:

both statements are wrong.

a right (or right-angled) triangle has a 90° angle. that is all.

an equilateral triangle has 3 equally long sides.

but that also implies that the 3 angles must be equal too.

the sum of all angles in a triangle must be 180°.

if all angles are equally large, that means

180 = 3×angle

angle = 180/3 = 60°.

that means none of the angles can be 90°, so, no right-angled triangle can be equilateral.

and no equilateral triangle can be right-angled.

Answer:Jorge and  Mike

Step-by-step explanation:

Nobody goes if Mike goes

Answer:

[tex]p(x) = -5x^3 -6x^2 + 3x + 1[/tex]

Step-by-step explanation:

Given cubic function:

[tex]p(x) = ax^3 + bx^2 + cx + d[/tex]

As point (0, 1) is on the curve, substitute x = 0 into the function, set it to 1, and solve for d:

[tex]\begin{aligned} p(0) & = 1\\ \implies a(0)^3 + b(0)^2 + c(0) + d & = 1\\ \implies d & = 1 \end{aligned}[/tex]

Differentiate the function:

[tex]\begin{aligned} p(x)& = ax^3 + bx^2 + cx + d\\\implies p'(x)&=3 \cdot ax^{3-1}+2 \cdot bx^{2-1}+1 \cdot cx^{1-1}+0 \\p'(x)&=3ax^2+2bx+c\end{aligned}[/tex]

The tangent equation at the point (0, 1) is y = 3x + 1.  

Therefore, the gradient of the tangent equation when x = 0 is 3.

To find the gradient of the function at a given point, substitute the x-value of that point into the differentiated function.  Therefore, substitute x = 0 into the differentiated function, set it to 3, and solve for c:

[tex]\begin{aligned}p'(0) & =3 \\ \implies 3a(0)^2+2b(0)+c & =3\\ \implies c & = 3\end{aligned}[/tex]

Substitute the found values of c and d into the function:

[tex]p(x) = ax^3 + bx^2 + 3x + 1[/tex]

Substitute point (-1, -3) into the function and solve for b:

[tex]\begin{aligned}p(-1) & = -3\\\implies a(-1)^3 + b(-1)^2 + 3(-1) + 1 & = -3\\-a+b-3+1&=-3\\-a+b&=-1\\b&=a-1\end{aligned}[/tex]

To find the turning points of a function, set the differentiated function to zero and solve for x.  

As there is a turning point of function p(x) when x = -1, substitute x = -1 into the differentiated function and set it to zero (remembering to substitute the found value of c = 3 into the differentiated function):

[tex]\begin{aligned} p'(-1) & =0\\\implies 3a(-1)^2+2b(-1)+3 & = 0\\3a-2b+3&=0\end{aligned}[/tex]

Substitute the found expression for b into the equation and solve for a:

[tex]\begin{aligned}3a-2b+3&=0\\\implies 3a-2(a-1)+3&=0\\3a-2a+2+3&=0\\a+5&=0\\a&=-5\end{aligned}[/tex]

Finally, substitute the found value of a into the found expression for b and solve for b:

[tex]\begin{aligned}b & = a-1\\\implies b & = -5-1\\b & = -6\end{aligned}[/tex]

Therefore:

Differentiation Rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]

Answer:

see explanation

Step-by-step explanation:

-9x = -3y

-6x = 2  1/5y

3x = 0y

9x = 2y

A statement that best describes the area of the triangle is It is one-half the area of a square of side length 4 units.

The area of a triangle can be found by the formula:
= 1/2 x base x height

The base is 4 units and the height if 4 units.

Area of the triangle is:

= 1/2 x 4 x 4

= 8 units²

The area of a square of side length 4 units. is:

= 4 x 4

= 16 units²

In conclusion, option B is correct.

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Based on the probability of rain in Nevada, the probability that it will not rain is 0.7.

The probability that if it does not rain, the school bus will be on time is 0.85.

The probability that it will rain and the school bus will still be on time is 0.6.

The probability that it will not rain in Nevada can be found by the formula:

= 1 - probability of rain in Nevada

= 1 - 0.3

= 0.7

The probability that if it does not rain, the school bus will be on time is:

= 1 - probability of the school bus being late if it does not rain

= 1 - 0.15

= 0.85

The probability that it will rain and the school bus will still be on time is:

= 1 - probability of the school bus being late if it rains

= 1 - 0.4

= 0.6

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