The table shows some values of x and y that satisfy the equation y = acosx + b
180

120
150
4 -3V3
-2

0
30
60
10
4 + 3V3
7
Find the value of y when x = 45

X

90
4

Answer:

8x^6 + 6x^2 - 9x + 11

Step-by-step explanation:

Well, I combined like terms.

There's only two terms you can combine here anyhow; those being 14x^2 and -8x^2.

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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The probability of P(4) is 1/8. 12.5%, 0.125.

The probability of a number less than 10 is 8/8. 1 , 100%

The probability of a prime number is 1/2. 0.5. 50%.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

Probability of spinning 4 = number of possible outcomes / number of sections

1/8 = 0.125 = 12.5%

Probability of spinning a number less than 8 = possible outcomes / total sections

8/8 = 1 = 100%

Probability of spinning a prime number = number of possible outcomes / total sections

Prime numbers between 1 and 8 = : 2, 3, 5, 7

4/8 = 0.5 = 50%

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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 amount of cholesterol that is in each is given as  c = 19, E = 275 and P = 9

We have to define the variables as:

E + C + P = 303

3C + 4P = 93,

we have to make pizza, P the subject

4P = 93 - 3C,

P = (93 - 3C) / 4

2E + C = 569,

2E = 569 - C

E = (567-C) / 2

We have to form the equation

(569-C)/2 + C + (93-3C)/4 = 303

We have to multiply the equation by 4

(569-C)2 + 4C + 93-3C = 1212

1138 - 2c + 4c + 93 - 3c = 1212

-C = 1212- 93 -1138

-c = -19

hence c = 19 mg for 1 cupcake

E = (569- 19)/2

275 for 1 egg

P =  (93-3C)/4

P = 93 - 57 / 4

= 36 / 4

= 9 for one pizza

Hence we would have c = 19, E = 275 and P = 9

19 + 275 + 9 = 303 (proves it to be correct)

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19+274 + 7 = 300 mg

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]

i responded to this already but it it is FALSE

Answer: False

Step-by-step explanation: Ratio is A:B = A/B

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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The angle x to the nearest degree is 40°

Given,

The depth of submarine that a ship's sonar detects = 440 feet

The distance from submarine to ship in oceans surface = 600 feet

We have to find the angle x.

The figure is given below:

Here, we have to use the tangents definition:

That is,

tan θ = opposite side / adjacent side

Here,

tan x = 440 / 600

We want to find x,

So,

x = tan⁻¹ (440 / 600)

x = tan⁻¹ (0.73333)

x = 40.28°

By taking nearest angle, we get x as 40°

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Answer:

Yes

Step-by-step explanation:

Every number is divisible by 10, in this case you just need to tale of the zero at the end. 570,746 is the answer.

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: 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]

Answer:

20 +2x+1=7, hope this is the answer

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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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:

-4

Step-by-step explanation:

keep value of x as 1 in 5x+1

g(1)=-5×1+1

=-4

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 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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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:

no

Step-by-step explanation:

89382

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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Answer:Jorge and  Mike

Step-by-step explanation:

Nobody goes if Mike goes

Answer:

4 y + -10 x + 7

Step-by-step explanation:

Simplify the following:

2 (2 x + 2 y) - 14 x + 7

2 (2 y + 2 x) = 4 y + 4 x:

(4 y + 4 x) - 14 x + 7

Grouping like terms, 4 y + 4 x - 14 x + 7 = 4 y + (4 x - 14 x) + 7:

4 y + (4 x - 14 x) + 7

4 x - 14 x = -10 x:

Answer: 4 y + -10 x + 7

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:

20 - i

Step-by-step explanation:

In complex number addition/subtraction, add the imaginary part and add the real part separately.

The error is while adding imaginary part, you have to combine the coefficients of the imaginary numbers. So, -3 +2 will give us -1. So, the result is -i.

16  - 3i + 4+  2i = 16 + 4  -3i + 2i

                         = 20 - i

Answer:

20 - i

Step-by-step explanation:

The error made during second step:

When adding or subtracting expression, we add or subtract like terms.

(16 - 3i) + (4 + 2i) get rid of parenthesis

16 - 3i + 4 + 2i add/subtract like terms

20 - i (the mistake is made here, instead of "i" they typed i^2)

Answer:

3.5

Step-by-step explanation:

21x+6

21/21    6/21

x=3.5

Answer:

see explanation

Step-by-step explanation:

-9x = -3y

-6x = 2  1/5y

3x = 0y

9x = 2y

Answer:

Look below

Step-by-step explanation:

The LCM of 25 and 100 is 100

The GCF of 25 and 100 are 25.