Solve the equation by using the quadratic formula.
3 x squared minus 1 = 7 x

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Answer:

  y +6 = 2(x -6)

Step-by-step explanation:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -(-6))/(7 -6) = 2/1 = 2

The point-slope equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Using the slope we found and the first point, the equation is ...

  y +6 = 2(x -6)

Answers:

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Work Shown:

26)

1/2 = probability of an odd number, since half of the numbers are odd

1/2 = probability of tails

(1/2)*(1/2) = 1/4 is the probability of both events happening at the same time

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27)

13/52 = probability of pulling out one club

12/51 = probability of pulling out a second club, assuming the first one is not put back

(13/52)*(12/51) = 156/2652 = 1/17 = 0.0588 is the probability of pulling two clubs in a row (without replacement).

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28)

11/27 = probability first person has blonde hair

10/26 = probability second person has blonde hair (cannot reselect the first person again)

(11/27)*(10/26) = 110/702 = 55/351 = 0.157 is the probability of selecting two people with blonde hair

Given:

v = 150d

v represents company's production for the coming year

d represents the number of days

150 is the daily production

The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.

I hope this helps!

Answer:

v = 150d

v represents company's production for the coming year

d represents the number of days

150 is the daily production

Answer:

3/7

Step-by-step explanation:

Expected Value:

3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7

Expected value when we take one spin = 3/7

It is the sum of values multiplied by their respective probabilities.

We have 2 red, 2 purple, 2 yellow, and 1 blue sector.

Total number of Sectors = 7

∴Probability of landing on red sector = 2/7

∴Probability of landing on purple sector = 2/7

∴Probability of landing on yellow sector = 2/7

∴Probability of landing on blue sector = 1/7

Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.

X 3 1 0 -1

P(X) 1/7 2/7 2/7 2/7

Expected Value = ∑X.P(X)

=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)

= 3/7

Learn more about Expected Values on

https://brainly.com/question/15858152

#SPJ2

Answer:

O The rectangle did not change shape or size.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Isometric transformation is a transformation that preserves the shape and size of the figure. Types of isometric transformations are reflection, translation and rotation.

The rectangle represents an  isometric transformation because the rectangle did not change shape or size.

Answer:

X=90°

Y=58°

Z=32°

Step-by-step explanation:

X=180°-90°=90°

Y=180°-90°-32°=58°

Z=180°-58°-90°=32°

Answer:

x = 90°, y = 58°, z = 32°

Step-by-step explanation:

The angles in a square = 90° , then

x = 90° ( adjacent angle )

The sum of the 3 angles in a triangle = 180° , then

x + y + 32° = 180° , that is

90° + y + 32° = 180°

y + 122° = 180° ( subtract 122° from both sides )

y = 58°

y + 90° + z = 180° ( straight angle )

58° + 90° + z = 180°

148° + z = 180° ( subtract 148° from both sides )

z = 32°

Answer:

1

Step-by-step explanation:

Formulas used:

     [tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]

[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]

Answer:

[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]

Answer:

38

Step-by-step explanation:

So, we know the formula is:

D=rt or D=r*t

We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.

Here are the two sets we can look at:

t=2, d=76

t=3, d=114

Lets plug these in and solve:

76=r*2

Divide both sides by 2 to get r alone:

38=r

Now lets check if this is true by pluggin in 38 for r in the second set, and seeing if it works:

D=r*t

114=38*3

=

114=114

So 38 is our answer.

Hope this helps!

Answer:

C, D, F

Step-by-step explanation:

Shape A is not a polygon; it has a line that doesn't connect anywhere. Even if it is a polygon, it would be concave. Shape B is a concave polygon, shape E is also a concave polygon, shape G and H are also concave polygons. Only shapes C, D, and F are convex polygons. Concave polygons are shapes that cave in, and convex polygons are caves that don't cave in.

Answer:

b. Independent variable

Step-by-step explanation:

Understanding the definition of variables is necessary to grasp the notion of independent and dependent variables. The attributes or sorts of features of specific occurrences or things are specified as variables.

Independent variables are variables that are modified or altered by researchers and the consequences of these modifications are evaluated and compared. 

The term dependent variable relates to a sort of variable that assesses how the independent variable(s) impact the test results.

From the given information:

Education level is the predictor since we understand that nurses' education levels are closely correlated with their cultural competence scores. By applying the concept of the logistic regression model and using education level as an independent variable(predictor), we can simply predict their cultural competency. Thus, cultural competency is measured by using the independent variable.

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Answer:

  B.  1/2

Step-by-step explanation:

Maybe you want  the solution to ...

  [tex]9^x-1=2[/tex]

You can use logarithms, or your knowledge of powers of 3 to solve this.

  [tex]9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}[/tex]

Using logarithms, the solution looks like ...

  [tex]x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}[/tex]

Answer:

a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Step-by-step explanation:

Given the data in the question;

We know that the weight of a body varies inversely as the square of its distance from the center of the earth.

⇒F(x) = c / x²

given that; F(x) = five-ton = 5 tons

we know that the radius of earth is approximately 4000 miles

so we substitute

5 = c / (4000)²

c = 5 × ( 4000 )²

c = 8 × 10⁷

∴ Increment of work is;

Δw =  [ ( 8 × 10⁷ ) / x² ] Δx

a) For 100 miles above Earth;

W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]

= 487.8 mile-tons  

Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) For 300 miles above Earth.

W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]

= 1395.3 mile-tons

Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Answer:

73% The two-way table shows information about the preferred drinks of some people. b a How many males drank only coffee? b What is the probability that any person is male and only drinks coffee? 73% The two-way table shows information about the preferred drinks of some people

Answer:

A

Step-by-step explanation:

Because the angles must add to 180 we can see the misssing angle is 69

This means that answer is either A or C

Using SOH we can solve for side CD

sin(21)=x/18

18sin(21)=x

x=6.45

If CD= 6.45 this means that the answer is A

Answer:

The plane travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \rm mph[/tex] and [tex]\text{$3$ hours}[/tex] at an average speed of [tex]130\; \rm mph[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the number of hours that the plane travelled at an average speed of [tex]120\; \rm mph[/tex].

Given that the trip is [tex]5\; \text{hours}[/tex] long in total, the plane would have travelled at an average speed of [tex]130\; \rm mph[/tex] for [tex](5 - x)\; \text{hours}[/tex].

The plane would have travelled [tex]120\, x[/tex] miles after [tex]x\; \text{hours}[/tex] at an average speed of [tex]120\; \rm mph[/tex]. Likewise, the plane would have travelled [tex]130\, (5 - x)\; \text{miles}[/tex] after [tex](5 - x)\; \text{hours}[/tex] at an average of [tex]130\; \text{mph}[/tex].

The plane has travelled [tex]630\; \text{miles}[/tex] in total. In other words:

[tex]120\, x + 130\, (5 - x) = 630[/tex].

Solve this equation for [tex]x[/tex]: [tex]x = 2[/tex].

In other words, the plane has travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \text{mph}[/tex]. It would have travelled for [tex](5 - x)\; \text{hours} = (5 - 2)\; \text{hours} = 3 \; \text{hours}[/tex] for the other part of the trip (at an average speed of [tex]130\; \text{mph}[/tex].)

Answer:

[tex]Volume \ of \ other\ cylinder = 176 \ cm^3[/tex]

Step-by-step explanation:

Let the volume of cylinder Vₐ = 44cm³

Let radius of cylinder " a " be = rₐ

Let height of  cylinder " b" be = hₐ

     [tex]Volume_a = \pi r_a^2 h_a\\\\44 = \pi r_a^2 h_a[/tex]

Given cylinder " b ", Radius is twice cylinder " a " , that is [tex]r_b = 2 r_a[/tex]

Also Height of cylinder " b " is same as cylinder " a " , that is [tex]h_b = h_a[/tex]

       [tex]Volume_b = \pi r_b^2 h_b[/tex]

                     [tex]= \pi (2r_a)^2 h_a\\\\=4 \times \pi r_a^2 h_a\\\\= 4 \times 44\\\\= 176 \ cm^3[/tex]

Answer:

[tex]BD=13[/tex]

Step-by-step explanation:

Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.

Hence:

[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]

Solve for x. Cross-multiply:

[tex]12(x+5)=27(x)[/tex]

Distribute:

[tex]12x+60=27x[/tex]

Subtract 12x from both sides:

[tex]15x=60[/tex]

Divide both sides by 15. Thus:

[tex]x=4[/tex]

BD is the sum of BC and CD:

[tex]BD=BC+CD[/tex]

Substitute:

[tex]BD=x+(x+5)[/tex]

Substitute and evaluate:

[tex]BD=(4)+(4+5)=13[/tex]

Therefore, BD is 13.

Answer:

Step-by-step explanation:

We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is

[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to

[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.

Answer: 1872cm³

Step-by-step explanation:

First and foremost, we've to calculate the volume of the carton which will be:

= Length × Width × Height

= 13cm × 9cm × 24cm

= 2808cm³

The volume that'll be left after ⅓ of the volume is drank will be:

= 2808 - (⅓ × 2808)

= 2808cm³ - 936cm³

= 1872cm³

Answer:

let's use a sample set.

8+8, 8+4, 8+5, 8+6, 8+7

4+8, 4+4, 4+5, 4+6, 4+7

5+8, 5+4, 5+5, 5+6, 5+7

6+8, 6+4, 6+5, 6+6, 6+7

7+8, 7+4, 7+5, 7+6, 7+7

There is 25 sums.

Answer:

Yes, 2.4

Step-by-step explanation:

Y is directly dependant on x, and the constant we multiply x by to get y is 2.4.

Answer:

Yes, 2,4

Step-by-step explanation:

This explains direct proportion because it shows that y equals the 2.4x which is the direct proportion

Hopes this helps

Answer:

Step-by-step explanation:

Bisection implies dividing a given segment into equal haves by construction. So that in the given question, angle ABC would be divided into equal parts.

After drawing segment AB to given length, use a compass to construct the required angle ABC. Then use the ends of the arc for the angle to bisect the angle.

The construction to this question is herewith attached to this answer for more clarifications.

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Answer:

  15

Step-by-step explanation:

Put the value where the variable is and do the arithmetic.

  f(-3) = (-3)² -2(-3) = 9 +6

  f(-3) = 15

15

Step-by-step explanation:

f(-3)=(-3)^2 - 2(-3)

= 9 + 6 = 15

Answer:

Step-by-step explanation:

[tex]f(x)=x^2+2x-4\\g(x)=3x+1\\\\g\circ f(x)=g(f(x)=3(x^2+2x-4)+1=3x^2+6x-11[/tex]

Answer:

g(f(x)) = 3x^2 + 6x - 11.

Step-by-step explanation:

Replace the x in g(x) by f(x):

g(f(x)) = 3(x^2 + 2x - 4) + 1

= 3x^2 + 6x - 12 + 1

= 3x^2 + 6x - 11.

Answer:

Volume of the prism=60m3

Step-by-step explanation:

Volume of any prism=height*width*length

Volume of the prism=3m*5m*4m=60m3

Volume of the prism=60m3

Answer:

9.05 horse power

Step-by-step explanation:

Given:

Force = 270 Newton

Speed = 25 m/s

Power = Force * velocity

Power = 270 Newton * 25 m/s

Power = 6750 watt

Recall:

1 horse power = 746 watts

Hence, required horsepower is :

6750 watt / 746 watt

9.048 hp

9.05 horse power

Answer:

2329

Step-by-step explanation:

2000 - 125 - 127 + 1719 - 356 - 782 = 2329

Answer:

9:20 am

Step-by-step explanation:

So, lets go over two things.

Minutes and hours.

Minutes changes the second number.

You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.

Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.

In this case. we are moving the minutes place up by 5:

15+5=20

So the minutes place is 20, and does not change the hours place since it is below 60.

Next we have a increase in hours by 2:

8+1=9

So the hours place is 9, and does not reset or change the pm/am since its below 12.

Answer:

9:20am

Hope thias helps!

Answer:

9:20 am

Step-by-step explanation:

Add 1 hour

8:15 to 9:15

Add 5 minutes

9:15 to 9:20

Answer:

a) Capacities : station 1 = 3.5 , station 2 = 3.5

  Both stations have the same capacity

b) 3.5 ( it does not differ from a )

c) The value will double i.e. 3.5 * 2 = 7

Step-by-step explanation:

a) compute the capacity of each station and show if the line is balanced

for station 1

Units :            1 ,2 ,3, 4 ,5, 6

probabilities :   1/6 ( same value for all units )

for station 2

units :             3, 4

probabilities :  1/2   1/2

Capacity of station 1= ( 1/6 * 1 ) + ( 1/6 *2 ) + ( 1/6 *3) + (1/6 *4) + (1/6*5) + (1/6*6 )

                                =  3.5  

Capacity of station 2 = ( 1/2 * 3 ) + ( 1/2 * 4 )

                                  = 3.5

∴ both stations have the same capacity

B) Expected throughput of the line

= Min( capacity of station 1 , capacity of station 2 )

= 3.5  ( It does not differ from a )

C) When an additional identical machine is added to both stations the expected throughput of the line will be doubled

i.e. expected throughput = ( 3.5 ) * 2 = 7

[tex]\longrightarrow{\blue{ 0 }}[/tex] 

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex]7 - ( \frac{5}{6} \times 7) - \frac{7}{6} [/tex]

[tex] = 7 - \frac{35}{6} - \frac{7}{6} [/tex]

Since the denominators are unequal, we find the L.C.M (lowest common multiple) for the denominators.

The L. C. M is 6.

Now, multiply the L.C.M. with both numerator & denominator.

[tex] = \frac{7 \times 6}{1 \times 6} - \frac{35}{6} - \frac{7}{6} [/tex]

Now that the denominators are equal, we can add/subtract them.

[tex] = \frac{42- 35 - 7}{6} [/tex]

[tex] = \frac{42 - 42}{6} [/tex]

[tex] = \frac{ 0}{6} [/tex]

[tex] = 0[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]