Consider the quadratic equation 4x2 - 11x - 3 = 0. Which of the following shows
this equation rewritten and ready to solve using factoring by grouping?
A) 4x2 - 9x - 2x - 3 = 0
B) 4x2 - 6x - 5x - 3 = 0
C) 4x2 - 12x + x - 3 = 0
D) 4x2 + 12x - x-3 = 0

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]

We can rewrite this as:

[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.

Answer:

  1/10

Step-by-step explanation:

There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...

  5/50 = 1/10

Answer:

x= -3     x = 1/2     x=-2

Step-by-step explanation:

f(x)=(x+3) (2x-1)(x+2)

Set equal to zero

0 =(x+3) (2x-1)(x+2)

Using the zero product property

x+3 =0   2x-1 =0    x+2 =0

x= -3    2x =1       x = -2

x= -3     x = 1/2     x=-2

Answer:

6x - 13y

Step-by-step explanation:

5(2x - 2y) - (4x + 3y)

10x - 10y - 4x - 3y

10x - 4x - 10y - 3y

6x - 13y

Answer:

x = 35, y = 15°

Step-by-step explanation:

6. Since ΔRST ≅ ΔXYZ, RT = XZ because of CPCTC which means:

x + 21 = 2x - 14

-x = -35

x = 35

7. Again, since ΔRST ≅ ΔXYZ, ∠R ≅ ∠X because of CPCTC which means:

4y - 10 = 3y + 5

y = 15°

Answer: The correct answer is 19 sit ups.

Step-by-step explanation: Given that the regression equation to find a  a relationship between hours of TV watched per day (x) and number of situps a person can do (y) was done.

The result was

y = ax+b

Correlation coefficient = 0.865

To predict the number of situps a person who watches 3 hours of TV

y = -1.23(3)+22.738

= 19.048

Approximately 19 situps.

Answer:

56.5

I think this is right

Answer:

C. 329

Step-by-step explanation:

So 28 is 70% of 40

so we know that 70% percent of students have phones

70% of 470

329

Thats how I solved it have a great day :)

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

    [tex]P(3) = 0.154[/tex]

b

    [tex]P(4) = 0.026[/tex]

c

   [tex]P( X \ge 3 ) = 0.18[/tex]

d

   option C is correct

Step-by-step explanation:

From the question we are told that

      The probability of success is  p =  0.4

      The sample size is n=  4

 This adults believe follow a binomial distribution is because there are only two outcome one is an adult  believes in  reincarnation and the second an adult does not believe in reincarnation

  The probability of  failure is mathematically evaluated as

              [tex]q = 1 - p[/tex]

substituting values

             [tex]q = 1 - 0.4[/tex]

             [tex]q = 0.6[/tex]

Considering a  

The  probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as

       [tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]

substituting values

     [tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination 3 . i have calculated this using a calculator and the value is  

           [tex]\left 4} \atop {}} \right.C_3 = 4[/tex]

So

         [tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]

          [tex]P(3) = 0.154[/tex]

Considering b

The probability that all of the selected adults believe in reincarnation is mathematically represented as

        [tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]

substituting values

         [tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination  . i have calculated this using a calculator and the value is  [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]

so

          [tex]P(4) = 1* (0.4)^4 * 1[/tex]

=>       [tex]P(4) = 0.026[/tex]

Considering c

the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as

     [tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]

substituting values

    [tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]

     [tex]P( X \ge 3 ) = 0.18[/tex]

From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is  [tex]p(4) = 0.026 < 0.05[/tex]

But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]

Hence 3 is not a  significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.

Answer:

6.986.

Step-by-step explanation:

6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000

We do the multiplications first    ( according to PEMDAS):-

= 6 + 9 * 0.1 + 8 * 0.01 + 6 * 0.001

= 6 + 0.9 + 0.08 + 0006

= 6.9 + 0.086

= 6 986.

The value of the equation in the decimal form is A = 6.986

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000

On simplifying the equation , we get

The value of 6 x 1 = 6

The value of 9 x 1/10 = 0.9

The value of 9 x 1/100 = 0.08

The value of 6 x 1/1000 = 0.006

So , substituting the values in the equation A , we get

A = 6 + 0.9 + 0.08 + 0.006

On simplifying the equation , we get

A = 6.986

Therefore , the value of A is 6.986

Hence , the value of the equation is 6.986

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Answer:

a.  k = -0.01014 s⁻¹

b.  [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

c.  [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

d.  y(t) = 130.485°F

Step-by-step explanation:

A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.

(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)

We are to determine :

a.  Determine the cooling constant k. k = s−1

By applying the new law of cooling

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]

[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]

Taking the integral.

[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]

㏑ (T -60) = kt + C

T - 60 = [tex]e^{kt+C}[/tex]

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

After 20 seconds, the temperature of the bar submersion is 120°F

T(20) = 120

From equation (1) ,replace t = 20s and T = 120

[tex]120 = 60 + C_1 e^{20 \ k}[/tex]

[tex]120 - 60 = C_1 e^{20 \ k}[/tex]

[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]

After 1 min i.e 60 sec , the temperature  = 100

T(60) = 100

From equation (1) ; replace t = 60 s and T = 100

[tex]100 = 60 + c_1 e^{60 \ t}[/tex]

[tex]100 - 60 =c_1 e^{60 \ t}[/tex]

[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]

Dividing equation (2) by (3) , we have:

[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]

[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]

[tex]-40 \ k = In (\dfrac{3}{2})[/tex]

- 40 k = 0.4054651

[tex]k = - \dfrac{0.4054651}{ 40}[/tex]

k = -0.01014 s⁻¹

b. What is the differential equation satisfied by the temperature y(t)?

Recall that :

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]

Since y is the temperature of the body , then :

[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

(c) What is the formula for y(t)?

From equation (1) ;

where;

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

Let y be measured in degrees Fahrenheit

[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]

From equation (2)

[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]

[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]

[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]

[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]

[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

(d) Determine the temperature of the bar at the moment it is submerged.

At the moment it is submerged t = 0

[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]

y(t) = 60 + 70.485

y(t) = 130.485°F

You would type in

32^(6/5)

Or you could type in

32^(1.2)

since 6/5 = 1.2

Either way, the final result is 64

Answer:

60% discount given in total, so only 40% is paid.

Step-by-step explanation:

22

Step-by-step explanation:

For simplicity, let

x = teary smiley

y = tongue smiley

z = plain smiley

So now our system of equations is

[tex]x + x + x = 12\:\:\:\:\:\:(1)[/tex]

[tex]y + z + x = 18\:\:\:\:\:\:\:(2)[/tex]

[tex]z + z + y = 22\:\:\:\:\:\:\:(3)[/tex]

[tex]z + y + 2x= ??\:\:\:\:\:\:(4)[/tex]

From Eqn(1), we plainly see that

[tex]3x = 12 \Rightarrow x = 4[/tex]

Now subtract Eqn(2) from Eqn(3) to get

[tex](2z + y) - (y + z + x) = 22 - 18[/tex]

[tex]\Rightarrow z - x = 4[/tex]

But we know that [tex]x = 4[/tex], which then gives us [tex]z = 8.[/tex]

Using the values of [tex]x[/tex] and [tex]z[/tex] in Eqn(2), we find that [tex]y = 6.[/tex] Now that we the values of all the variables, use them in Eqn(3) and we'll get

[tex](8) + (6) + 2(4) = 22[/tex]

Hey there! I'm happy to help!

A quadrilateral is any polygon (enclosed shape) with four sides. Let's see what each of these shapes are.

So, the only shape on your list that is a quadrilateral is 6. right trapezoid.

Have a wonderful day! :D

Answer:

1284 m^2

Step-by-step explanation:

Front face and back face:

2 * [28 m * 5 m + (22 m - 5 m) * 6 m] = 484 m^2

Left face and right face:

2 * 22 m * 8 m = 352 m^2

Bottom face and top face:

2 * 28 m * 8 m = 448 m^2

total surface area = 484 m^2 + 352 m^2 + 448 m^2 = 1284 m^2

Answer:

A.) x=90°

Step-by-step explanation:

Note:

The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.

We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:

[tex]180=135+y[/tex]

y is the unknown angle. Solve for y:

[tex]180-135=y\\\\y=45[/tex]

y is 45°. Since this and the other angle are congruent, add:

[tex]45+45=90[/tex]

Note:

Triangles angles will always add up to a total of 180°.

To find the missing angle x°, use:

[tex]180=a+b+c[/tex]

These are the angles in a triangle. Substitute any known values and solve:

[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]

The missing angle x° is 90°.

:Done

Answer:

The answer is "253"

Step-by-step explanation:

In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:

Given:

[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]

[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]

integrate the above value:

[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]

When the value of n=1 then t=0

[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]

so the value of  n is:

[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]

when we put the value t= 15 then,

[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]

Answer:

8 km

Step-by-step explanation:

            1 km

4 cm x -------- = 8 km

           0.5 cm

The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The distance between two cities on a map = 4 centimeters.

Also,  the scale

0.5 cm = 1 km

To find actual distance between cities, use ratio properly,

0.5 cm = 1 km

1 cm = 2 km

4 cm = 8 km

The distance between the actual cities is 8 km.

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Answer:

There is not sufficient evidence to support a claim of linear correlation between the two variables.

Step-by-step explanation:

(a)

The scatter plot for the provided data is attached below.

(b)

The hypothesis to test significance of linear correlation between the two variables is:

H₀: There is no linear correlation between the two variables, i.e. ρ = 0.

Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.

(c)

Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.

The correlation coefficient between the number of internet users and the award winners is,

r = 0.786.

The test statistic value is:

[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]

  [tex]=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54[/tex]

Thus, the test statistic is 2.54.

(d)

The degrees of freedom is,

df = n - 2  

  = 6 - 2

  = 4

Compute the p-value as follows:

[tex]p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064[/tex]

*Use a t-table.

p-value = 0.064 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.

Answer: the distance is  3.49 units

Step-by-step explanation:

There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.

When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:

x = R*cos(θ)

y = R*sin(θ)

Then we have:

(7,217pi/180 )

R = 7

θ = (217/180)*pi

x = 7*cos( (217/180)*pi) = -5.59

y = 7*sin( (217/180)*pi) = -4.21

So this point is (-5.59, -4.21) in rectangular coordinates.

And the other point is  (5,-23pi/36 )

R = 5

θ = -(23/36)*pi

x = 5*cos(  -(23/36)*pi ) = -2.11

y = 5*sin(  -(23/36)*pi ) = -4.53

So this point is (-2.11, - 4.53)

Then the point distance between those points is:

D = I (-2.11, -4.53) - (-5.59, -4.21) I

D = I (-2.11 + 5.59, -4.53 + 4.21) I

D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) =  3.49

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]

[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]

[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]

then substitute,

[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]

After Further Simplication,

[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]

[tex]let \: y = \cos(x) [/tex]

[tex]8 {y}^{2} - y - 3 = 0[/tex]

use quadratic formulae

[tex]y = 0.375 \: or \: - 0.25[/tex]

therefore

[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]

[tex] x = 70degrees \: or \: 104.5degrees[/tex]

Answer:

Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.

5.7735 meters. The top of the ladder is 2.8868 meters off the ground.

Now, if you meant the ladder is 60° from the ground, that’s a different story.

Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.

A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.

All lengths in this answer are rounded to the nearest tenth of a millimeter.

Step-by-step explanation:

Answer:

I noticed that to babysit my cousin was the chore that doled out the most, and I wonder why pet my dog is even a chore. Do they not love their pets?

Answer:

√69 or 8.3 feets

Step-by-step explanation:

Hypotenuse=13

Therefore

13²=x²+10²

x²=169-100

x²=69

x=√69 feets

The distance from the base of the house is  8.3 feet.

The pythagoras theorem is used to obtain the sides of a right angled triangle.

Given that;

The hypotenues of the triangle is 13-foot

The length of the opposite side is 10 feet

Thus;

13^2 = 10^2 + a^2

a^2 = 13^2  -  10^2

a = √13^2  -  10^2

a = 8.3 feet

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Answer:

99

Step-by-step explanation:

(-10)(9)(-1) + 9 =

90 + 9 = 99

Answer:

Step-by-step explanation:

x^2+20=4 first isolate the variable by subtracting 20 on both sides.

x^2=-16 again isolate the variable but this time you square root both sides.

[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify

x= ±4