For all functions of the form f(x) = ax^2 + bx + c, which is true when b=0

Answer:

  8 miles per hour

Step-by-step explanation:

Let s represent Sue's running speed in miles per hour. Then her total exercise time was ...

  time = distance/speed

  4 = (16/s) + (1/(s/16)) . . . . . using distance in miles and time in hours

  4 = 16/s +16/s = 32/s . . . . simplify

  s = 32/4 = 8 . . . . . . . . . . . multiply by s/4

Sue's running speed was 8 miles per hour.

Answer:

yes it is 2/3

Step-by-step explanation:

Answer:

70 weeks

Step-by-step explanation:

500g = .5kg

140 - .5w = 105

35 = .5w

70 = w

Answer:

1/3 feet.

Step-by-step explanation:

The length = area / width

= 7/9 / 2 1/3

= 7/9 / 7/3

= 7/9 * 3/7

= 3/9

= 1/3 feet,

Answer:

The length of the rectangle is [tex]\dfrac{ 1}{3} \text{ feet}[/tex] .

Step-by-step explanation:

The complete question is: The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?

Let the length of the rectangle be represented as 'L' and the width of the rectangle be represented as 'W'.

As we know that the area of the rectangle is given by;

  Area of rectangle =  Length of rectangle [tex]\times[/tex] Width of rectangle

                                   Or

                       A  =  L [tex]\times[/tex] W

Here, we know the value of A = 7/9 square feet and W = 2 1/3 feet.

SO,        [tex]\frac{7}{9} = \text{L} \times 2\frac{1}{3}[/tex]

             [tex]\frac{7}{9} = \text{L} \times \frac{7}{3}[/tex]

              [tex]\text{L} = \frac{7\times 3}{9\times 7}[/tex]

              [tex]\text{L} = \frac{ 1}{3} \text{ feet}[/tex]

Hence, the length of the rectangle is [tex]\frac{ 1}{3} \text{ feet}[/tex] .

Answer:

b = 0

Step-by-step explanation:

The standard form of a regular quadratic equation is ax² + bx + c and the standard form of the difference of squares is ax² - c. This means that b = 0 because there is no x term.

The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.

(i) For x = 6.9:

mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)

= 2.22

(ii) For x = 6.99:

mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)

= 2.020

(iii) For x = 6.999:

mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)

= 2.002002

(iv) For x = 6.9999:

mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)

= 2.000200

(v) For x = 7.1:

mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)

= 1.818182

(vi) For x = 7.01:

mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)

= 1.980198

(vii) For x = 7.001:

mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)

= 1.998002

(viii) For x = 7.0001:

mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)

= 1.999800

By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.

Using the point-slope form, we have:

y - y₁ = m(x - x₁)

Substituting the values of P(7, -2), we have:

y - (-2) = 2(x - 7)

y = 2x -16

Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

Learn more about the equation of the tangent line here:

https://brainly.com/question/31583945

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Answer:

5

Step-by-step explanation:

firstly, what are complementry angles.complementary angles are angles that su

m up to 90°

(12x-18)+(5x+23)=90

collecting like terms

12x+5x+23-18=90

17x-5-90=0

17x-95=0

17x=95

divide through by 17

x=5

The measure of the smaller angle when complementary angles are given is 42 degree.

Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.

The first angle of the triangle is (12x - 18).

The measure of the second angle of the triangle is (5x + 23).

As both angles are complementary, their sum would be equal to 90 degree.

(12x - 18) + (5x + 23) = 90

12x -  18 + 5x + 23 = 90

17x = 85

x = 5

Substitute the value of x = 5 in the given angles.

(1) 12x - 18 = 12×5 - 18

    = 42 degrees

(2) 5x + 23 = 5×5 +23

    = 48 degrees

Therefore, the smaller angle is found to be 42 degrees.  

To know more about angles with examples, here

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Answer:

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Step-by-step explanation:

The Following statement in the form  âˆ€x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Answer:

1. 8/4+ 3= 5

2. 5/(10/2)= 1

3. 5+10/2=10

4. 8/2+5x5= 29

5. 5+3/15+2= 10.15

6. 30+6x11-11= 25.11

7. 12 + (19+2) / 3 =19

Step-by-step explanation:

---------------------------------------------

Student name : Aparna Guha

Class : 8th

Division : B

School : St. John's Marhauli

Suggested subject : Maths

Work given on : 08 : 07 : 2020

Completed on : 08 : 07 : 2020

Posted on : 08 : 07 : 2020

Topic : Worksheet 1

Teacher's name : Manish Goel

School name : St. John's Marhauli

----------------------------------------------

Answer:

[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]

The slope can be founded with this formula:

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

And replacing we got:

[tex] m =\frac{-3 -9}{11-5}= -2[/tex]

And the best answer for this case would be :

[tex]m=-2[/tex]

Step-by-step explanation:

For this case we have the following two points given:

[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]

The slope can be founded with this formula:

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

And replacing we got:

[tex] m =\frac{-3 -9}{11-5}= -2[/tex]

And the best answer for this case would be :

[tex]m=-2[/tex]

Answer:

4.521 ( A )

Step-by-step explanation:

The determine the F-STAT employ the use of one way anova in excel to solve the problem. the way to solve  this using one way anova by excel  is

Attached is the image of the excel solution

Answer:

42°

Step-by-step explanation:

AD is a line

AEC and DEC are both 90°

AEB and CEB make up 90°

AEB+CEB=AEC substitute

AEB+48=90 Next use Subtraction property of equality

AEB=42

Hope this helps, if so please give me brainliest, it helps a lot. :)

Have a good day!

Answer:

∠AEB=42

Step-by-step explanation:

∠AEB and ∠BEC are inside of ∠AEC.

∠AEC is a right angle, Since ∠AEC and ∠CED are on a straight line, they must add to 180 degrees. ∠CED is a right angle (the little square in the corner tell us this), so ∠AEC must also be a right angle. This is because a right angle is 90 degrees (∠CED+∠AEC=180 --> 90+∠AEC=180 --> ∠AEC=90)

Therefore, the 2 angles (AEB and BEC) inside of ∠AEC must add to 90 degrees.

∠AEB+ ∠BEC= 90

We know that ∠BEC=48

∠AEB+48=90

We want to find out what ∠AEB is. We must get ∠AEB by itself. 48 is being added, and the inverse of addition is subtraction. Subtract 48 from both sides.

∠AEB+48-48=90-48

∠AEB=90-48

∠AEB=42

Answer:

n = 5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 30 = n/ 5 sqrt(3)

5 sqrt(3) tan 30 = n

5 sqrt(3) * 1/ sqrt(3) = n

5 = n

Answer:

answer B

Step-by-step explanation:

hello,

[tex]f(x)=x+1\\g(x)=5x \ \ so\\(fog)(-1)=f(g(-1))=f(-5)=-5+1=-4[/tex]

so the winner is the answer B

hope this helps

Answer:

D)  

(ƒ ∘ g)(–1) = –4

Step-by-step explanation:

Answer:

The probability that exactly 30% of these 10 telephone users do not have landlines in their homes is 0.2668.

Step-by-step explanation:

We are given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes).

A random sample of 10 of these customers is selected.

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 10 customers

            r = number of success = 30% of 10 = 3

            p = probability of success which in our question is the probability

                  that telephone users do not have landlines in their homes,

                   i.e. p = 30%

Let X = Number of telephone users who do not have landlines in their homes

So, X ~ Binom(n = 10, p = 0.30)

Now, the probability that exactly 30% of these 10 telephone users do not have landlines in their homes is given by = P(X = 3)

           P(X = 3) =  [tex]\binom{10}{3}\times 0.30^{3} \times (1-0.30)^{10-3}[/tex]

                         =  [tex]120 \times 0.30^{3} \times 0.70^{7}[/tex]

                         =  0.2668

Answer:

15%

Step-by-step explanation:

The tank's capacity is 200,000 gallons.

170,000 gallons were used.

200,000 - 170,000 = 30,000

30,000 gallons of fuel are still there.

percent = part/total * 100%

percent = 30,000/200,000 * 100% = 15%

Answer:

Step-by-step explanation:

There are two distinct statements but put together, it is:

- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.

For Susan Collins, she advocates gun control too.

So the symbolic or algebraic representation is:

(SC = DF): (MC ~ AE), (PM ~ WA)

OR

(GC = GC): (MC ~ AE), (PM ~ WA)

Where ":" represents "such that" or "given that"

" ~ " represents "support or promotion of"

It can now be read thus;

Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.

The correct answer is C. 65

Explanation:

The serving size of the soft drink is 8oz, besides this, the amount of sugar for this serving size according to the label is 26 grames. Now, to calculate the amount of sugar in 20oz, one of the simplest methods is to use a rule of three, because three values are known, and one is missing. The process is shown below:

1. Write the known values and use x to represent the unknown values

8 oz  =  26 grames of sugar      

20 oz  =  x

2. Use cross multiplication (this means multiply 8 x 6) and divide it into the remaining value

[tex]x = \frac{26 x 20}{ 8}[/tex]   or  x = 26 x 20 / 8

3. Solve the equation

[tex]x =\frac{520}{8}[/tex]      or x = 520 / 8

[tex]x = 65[/tex]

Answer:65

Step-by-step explanation:

Answer:

Step-by-step explanation:

axis: x= 2

vertex: (2,3)

Answer:

a) 82

b) 97

Step-by-step explanation:

a) 354 - (95+95)

354 - 190

164

164 ÷ 2 = 82

(82+82+95+95=254)

b) 8439 cm^2 = 87x

8439 cm^2 ÷ 87 = 87x ÷ 87

97 = x

Answer:

Ima need the answer too

Step-by-step explanation:

Answer:

the genre

Step-by-step explanation:

Answer:

The  polar form  is  sinθ  = 2 r³cos⁴θ

Step-by-step explanation:

Explanation:-

Given function y = 2 x⁴

Parametric Form  x = r cosθ ....(i)

                     and y = r sinθ ....(ii)

            squaring  x² = r² cos ²θ

                            y² = r² sin²θ

         adding   x² +  y² = r² cos ²θ+r² s in²θ

                                    =  r²( cos ²θ+s in²θ)

                                   =  r²( 1)

                     x² +  y² =    r²

Given function y = 2 x⁴

Now convert into polar form

                        r sinθ  = 2 (r cos θ )⁴

                         r sinθ  = 2 (r )⁴cos θ )⁴

                           sinθ  = 2 r ³cos⁴θ

Answer: None of the above.

Step-by-step explanation:

Forecast error is the difference which occurs between the actual observation and a given one over a period of time.

Forecast errors can sometimes be negative, this is due or caused by the difference which arises from the actual and given figures. Forecasting errors help to improve forecasting feedbacks which helps drive better results.

Answer:

16

Step-by-step explanation:

Area of circle Formula: A = πr²

d = 2r

Simply plug in what you know:

201.0624 = 3.1416r²

64 = r²

r = 8

d = 2(8)

d = 16

Answer: L = 20.25

Step-by-step explanation:

[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]

Given: T = 5, π = 22/7

[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]

Answer:

Step-by-step explanation:

Let the angle be x

To find the indicated angle we use sine

sin ∅ = opposite / hypotenuse

From the question

7 is the hypotenuse

4 is the opposite

sin x = 4/7

x = sin-¹ 4/7

x = 34.85

x = 35° to the nearest degree

Hope this helps you

Answer:

S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}

Step-by-step explanation:

The sample space is the set of all possible outcomes in the experiment of rolling a six-sided die and then drawing a playing card and checking its color.

There are 6 possible outcomes for the die roll and two for the color of the card, which yields a total of 12 possible outcomes. The sample space is:

S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}

Answer:

7x^2-4x+3y^2      ( the ^ means the exponent EX: 5^2 is 5 squared. )

Step-by-step explanation:

Remove the parenthesis (a) = a

12x^2-11y^2-13x- (5x^2-14y^2-9x)

-(5x^2 - 14y^2 - 9x)

Distribute parenthesis

-(5x^2) - (14y^2) - (-9x)

Apply minus - plus rules

-5x^2 + 14y^2 + 9x

= 12x^2 - 11y^2 - 13x - 5x^2 + 14y^2 + 9x

Simplify

12x^2-11y^2-13x-5x^2+14y^2+9x

Group like terms

12x^2-5x^2-13x+9x-11y^2+14y^2

Add similar elements

7x^2-13x+9x-11y^2+14y^2

Add similar elements ( - 13x + 9x = -4x )

7x^2-4x-11y^2+14y^2

Add similar elements 11y^2 + 14y^2 = 3y^2

7x^2-4x+3y^2

Answer:

[tex]y(t) = 3x+8e^{-3x} -1[/tex]

Step-by-step explanation:

Recall that the following laplace transforms

[tex]L(y') = sY(s)-y(0)[/tex]

[tex]L(t) = \frac{1}{s^2}[/tex]

The laplace transform is linear, so, applying the laplace transform to the equation we get

[tex]L(y'+3y) = sY(s)-7+3Y(s) = L(9t) = \frac{9}{s^2}[/tex]

By some algebraic manipulations, we get

[tex] Y(s)(s+3) = \frac{9+7s^2}{s^2}[/tex]

which is equivalent to

[tex] Y(s) = \frac{9+7s^2}{s^2(s+3)} = \frac{9}{s^2(s+3)}+\frac{7}{s+3}[/tex]

By using the partial fraction decomposition, we get

[tex] \frac{9}{s^2(s+3)} = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3}[/tex]

then

[tex]Y(s) = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3} + \frac{7}{s+3} = \frac{8}{s+3} + \frac{3}{s^2}-\frac{1}{s}[/tex]

Using that

[tex] L(e^{-ax}) = \frac{1}{s+a}[/tex]

[tex]L(1) = \frac{1}{s}[/tex]

by taking the inverse on both sides we get

[tex] y(t) = L^{-1}(\frac{8}{s+3})+L^{-1}(\frac{3}{s^2})+L^{-1}(-\frac{1}{s}) = 8e^{-3x} + 3x-1[/tex]