The curve with equation y = x³ +3 has two tangents parallel to the line with equation
y = 12x-1. Find the co-ordinates of the two points.

Answer: 1/8x - 5/6

Step-by-step explanation:

Let's move the similar terms of the problem together.

So first we have:

-3/4x + 7/8x

And then we have:

-1/3 - 1/2

So to add/subtract fractions, the denominators have to be equal. We can change the -3/4 into -6/8 by just multiplying by 2/2 which is just 1. (Anything multiplied by 1 is just itself). So then we have:

-6/8x + 7/8x ---> 1/8x

Next, the second part.

Since neither denominators (3 or 2) can turn into one another by multiplying them with a number, we'll just multiply them with the opposite denominator.
So then we have:

-1/3 * (2/2) = -2/6
-1/2 * (3/3) = -3/6

-2/6 - 3/6 = -5/6

So finally we have:

1/8x - 5/6

Hence its proven that f and g are inverse of one another

What is a Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given,

f(x)= 2x-3/2

g(x)= 2x+3/2

Step 1: show that fog=x

f(g(x))

[2((2x + 3) / 2) - 3]/2

[(2x + 3) - 3] / 2

(2x + 3 - 3) / 2

2x / 2

x , which is equals to x

Now, for Step 2: gof = x

g(f(x))

g((2x - 3)/2)

[2((2x - 3)/2) + 3]/2

[(2x - 3) + 3]/2

(2x - 3 + 3)/2

2x/2

x , which is equals to x

Since, both fog(x) and gof(x) equals to x

Hence, its proven that f and g are inverse of one another

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Answer:

48

Step-by-step explanation:

1 ) Simplify...

[tex]6^2-\left(-12\right)[/tex]

[tex]=6^2+12[/tex]

[tex]6^2=36[/tex]

[tex]=36+12[/tex]

2 ) Add the numbers...

[tex]36+12 =[/tex]

[tex]48[/tex]

Hope this helps! :)

Answer:

[tex]134^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem,

[tex]m\angle z=m\angle A+m\angle B=134^{\circ}[/tex]

Using the exterior angle theorem, angle z is measured as 134°.which is the correct answer that would be an option (D).

The exterior angle theorem is a triangle theorem that asserts that the measure of the external angle created by an extended side of a triangle is equal to the sum of the measures of the triangle's remote interior angles.

The given data will be the following as:

Exterior angle to angle C of triangle ABC = z

The remote interior angle of triangle ABC are angled A = 58° and angle B = 44°.

Therefore:

The measure of angle z = measure of angle A + measure of angle B [according to the exterior angle theorem]

Substitute the values and we get

Measure of ∠z = 77 + 57

Measure of ∠z = 134°

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The equivalent multiplication sentence that shows associative property is 3x(1×6)

Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.

This means that if a,b,c are real numbers then a×(b×c)=b×(a×c)

using the associative property,1×(3×6)= 3×(1×6)

To verify the statement,let's find out

solving the parentheses first

1×(3×6)=1×18= 18

3×(1×6)= 3×6= 18

this means that 1×(3×6) and 3×(1×6) are associative

therefore 1×(3×6)=3×(1×6)

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The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66

We have the following data to solve the question with

sample size = 17

standard deviation s = 1.5

Confidence interval = 99%

mean = 6.6 days

α = 1 - 0.99

= 0.01

df = degree of freedom = n -1  

17 - 1 = 16

tα/2 = 0.01 / 2

=  t 0.005, 16

t critical value = 2.9208

99 % confidence interval =

X ± t critical * s/√n

[tex]6.6 +-2.9208 * \frac{1.5}{\sqrt{17} }[/tex]

6.6 ± 1.0626

6.6 - 1.0626, 6.6 + 1.0626

= 5.54, 7.66

The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66

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Answer:

least

- 1/4 ft

- 14 3/4 ft

- 15 1/2 ft

- 20 3/5 ft

greatest

Answer:

- 20 3/5 ft

- 15 1/2 ft

- 14 3/4 ft

- 1/4 ft

I the number is larger looking but have a negative symbol, then it is smaller.

For example, -1 is greater than -6. Also -1/4 is greater than -20 3/5.

Trust me, I am a year ahead in school, so trust me.

I hope this helped.

The final cost of the sliced turkey and provolone cheese is $31.84

The first step is to calculate the cost of the sliced turkey

The pounds of turkey is 24.8

The amount of the turkey is $1.89

The cost is = 24.8/1.89

= 13.21

The next step is to calculate the cost of the provolone cheese

The pounds of the provolone cheese 38.2

The amount of provolone cheese is $2.05

The cost is = 38.2/2.05

= 18.63

Therefore the final cost can be calculated as follows

= 13.21 + 18.63

= 31.84

Hence the final cost is $31.84

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Answer:

Slope = -2

Y-intercept = -8

Step-by-step explanation:

Hello!

Slope-Intercept Form: y = mx + b

The m variable in this equation would be -2, and it is also the slope of the equation.

The b variable in this equation is -8, which is the y-intercept of the equation.

Answer:

y intercept -8

slope -2

Step-by-step explanation:

y = -2x-8

This is written in slope intercept form

y = mx+b

The slope is m  which is -2

The y intercept is b which is -8

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]0.\underline{25}\implies \cfrac{25}{1\underline{00}}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ y=0.25x-7\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x-7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{1}\implies -4}}[/tex]

so we're really looking for the equation of a line whose slope is -4 and it passes through (-6 , 8)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-6)}) \implies y -8= -4 (x +6) \\\\\\ y-8=-4x-24\implies {\Large \begin{array}{llll} y=-4x-16 \end{array}}[/tex]

Answer:

Step-by-step explanation:

The probability of no defects with 2% rate of defects:

Probability of exactly one defect:

Probability of one or no defects:

This indicates that:

The probability that this whole shipment will be accepted is 72.39%.

If he has 2 more pennies than nickels. the number of pennies is  10.6  and the number of nickels that Levi has is  12.6.

n = number of nickels

n-2 = number of pennies

Hence,

5n +1(n -2) = 74

Collect like terms

6n = 76

Divide both side by 6n

n = 76/6

n = 12.6 ( nickels)

Pennies

n-2

= 12.6 -2

= 10.6

Therefore Levi  has 10.6 pennies and 12.6 nickels.

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Answer:

Step-by-step explanation:

Jb

Answer: C & E

Step-by-step explanation: A is a lie, function 1 is pos

B is a lie function 1 is pos

C is true

D is a lie

E is true

The perimeter of the given rectangular room is found as -

Part a: p = 11 m.

Part b: p = 46 m.

As, given in the question-

The rectangular room has-

l m long and b m wide,

perimeter p, where p = 2l+2b  ...eq 1

Part a: perimeter of a room for, 3.5 m long and 2 m wide.

Put l = 3.5  and b = 2 in  eq 1.

p = 2l+2b

p = 2(3.5) +2(2)

p = 7 + 4

p = 11 m.

Part b: perimeter of a room for, 20 m long and 3 m wide.

Put l = 20  and b = 3 in  eq 1.

p = 2(20) +2(3)

p = 40 + 6

p = 46 m.

Thus, the perimeter of the given rectangular room is found as 46m.

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Answer:

Option 1. It is positive and increasing.

Step-by-step explanation:

Answer:

the equation is 37.45-5.35v=0

Step-by-step explanation:

37.45-5.35v=0

minus 37.45 to both sides

-5.35v=-37.45

divide -5.35 from both sides

v=7

after 7 days she will finish the card

Answer: This is a 1 by 5 rectangle

perimeter = 12 units

========================================================

Work Shown:

Label the vertices A,B,C,D

A =  (1, 4)

B = (1, 5)

C = (6, 5)

D = (6, 4)

The x coordinates of points A and B are the same (x = 1). The difference in y values of these points is 5-4 = 1 unit. This is the height of the rectangle. In other words, it's the length of segment AB.

Points B and C have the same y coordinate (y = 5). The difference in x value is 6-1 = 5 which is the horizontal length of the rectangle. This is the length of segment BC.

In short, this is a 1 by 5 rectangle. It's one unit tall and five units across.

--------

Perimeter = 2*(length+width)

Perimeter = 2*(5+1)

Perimeter = 2*6

Perimeter = 12 units

Or you can add up the four sides (1,5,1 and 5) to get the same result.

The value of the expression given as (7/4x - 5) - (2y - 3.5) - (-1/4x + 5) is 2x - 2y - 6.5

In this question, the representation of the expression is given as

(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)

Start by removing the brackets in the expression

So, we have

7/4x - 5 - 2y + 3.5 + 1/4x - 5

Evaluate the fractions in the expression

The expression becomes

1.75x - 5 - 2y + 3.5 + 0.25x - 5

Collect the like terms

1.75x + 0.25x - 2y - 5  + 3.5  - 5

Evaluate the like terms

2x - 2y - 6.5

Hence, the solution is 2x - 2y - 6.5

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Answer:

7.

[tex] \frac{1}{4} [/tex]

8.

[tex]2[/tex]

9.

[tex] - \frac {5}{4} [/tex]

10.

[tex]3[/tex]

Step-by-step explanation:

rate of change is slop

Answer:

1.7

Step-by-step explanation:

[tex]\frac{17 \text{ in}}{10 \text{ hr}}=1.7[/tex] in/hr

The answer is option A) A factor of f(x) is (x – 1).

What is the remaining theorem?

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.

f(x) = 4x3 - 4x2 - 16x + 16 [Given]

One aspect is (x - 2)

The remaining theorem is used to:

Where q(x) is the quotient polynomial and r(x) is the remainder polynomial, f(x) = (x-2)q(x) + r(x).

As (x-2) is a factor of f, r(x) equals 0. (x)

f(x) = (x-2)·q(x) (x)

q(x) = f(x)/ (x-2) (x-2)

[4x3 - 4x2 - 16x + 16]/ (x - 2) (x - 2)

= [4x2 (x - 1) - 16 (x - 1)]

/ (x - 2) (x - 2)

By even more simplifying

= [(x - 1) (4x2 - 16)]

/ (x - 2) (x - 2)

excluding 4 as common

= [(x - 1) 4 (x2 - 4)]

/ (x - 2) (x - 2)

With the use of the algebraic formula a2 - b2 = (a + b) (a - b)

= [(x - 1) 4 (x + 2) (x - 2)]

/ (x - 2) (x - 2)

= [4 (x - 1) (x - 2) (x + 2)]

/ (x - 2) (x - 2)

The roots are therefore 2, -2, and 1.
there the ans is A) A factor of f(x) is (x – 1).

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Answer:

$1598

Step-by-step explanation:

1st week

4*15=60

32*9=288

59*3=177

60+177+288=525

2nd week

5*15=75

59*7=413

32*4=128

75+413+128=616

3rd week

8*15=120

3*59=177

5*32=160

120+177+160=457

525+616+457=$1598

Answer: The prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3 or 23 × 33.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

D

Step-by-step explanation:

[tex]m\angle EBD=33^{\circ} \implies m\angle EBC=33^{\circ} \\ \\ \therefore m\angle DBC=m\angle EBD+m\angle EBC=66^{\circ} \\ \\ m\angle DBC=66^{\circ} \implies m\angle ABD=66^{\circ} \\ \\ \therefore m\angle ABC=m\angle ABD+m\angle DBC=132^{\circ}[/tex]

The median race time for this event is 38 minutes.

Given:

Race times for a recent 5k run are normally distributed with a mean time of 38 minutes and standard deviation of 3.5 minutes.

a.

X is normally distributed in (38,3.5).

so here the mean and the median are equal to each other.

Mean = 38

Median = mean

Median = 38 minutes.

Therefore the median race time for this event is 38 minutes.

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Answer: A

Step-by-step explanation: A

A

The subject of the equation is x and it can be written as x = t/6.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

The given equation is

6x = t

Divide both sides by 6

6x/ 6 = t/ 6

x = t/ 6

So, the subject of the equation is x - t/6.

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The probability that three cards have the same number, using the hypergeometric distribution, is of:

0.0448 = 4.48%.

The probability mass function for the hypergeometric distribution is defined as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the function are listed below:

In the context of this problem, the values of these parameters are given as follows:

N = 28, k = 4, n = 5, x = 3.

Hence for one color, the probability that three cards have the same number is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,28,5,4) = \frac{C_{4,3}C_{24,2}}{C_{28,5}} = 0.0112[/tex]

There are four colors, hence the probability is:

p = 4 x 0.0112 = 0.0448 = 4.48%.

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Answer:

8 hours

3 hours

Step-by-step explanation:

24/3=8

24/8=3