Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217

(B)

Step-by-step explanation:

The graph has zeros at x = -5 and x = 3 and passes through (4, 9). We can write the equation for the graph as

[tex]y = (x + 5)(x - 3) + c[/tex]

Since the graph passes through (4, 9), we can solve for c, which gives us c = 0. Therefore, the equation for the graph is

[tex]y = (x + 5)(x - 3) = x^2 + 2x - 15[/tex]

Answer:

Step-by-step explanation:

The answer is B) y= x^2+2x-15

Step-by-step explanation:

ii hope this will help you

please mark me as brinalist friend

Answer:

x = 1

x = -2

Step-by-step explanation:

Hello!

We can solve the quadratic by factoring the equation.

Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Given our equation: [tex]x^2 + x - 2 = 0[/tex]

Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.

Set each factor to 0 and solve for x:

The solutions for x are 1 and -2.

Answer:

40 years old.

Step-by-step explanation:

We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.

[tex]x+5=y[/tex]

We also know that the sum of their ages is 85.

[tex]x+y=85[/tex]

We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:

[tex]x+(x+5)=85[/tex]

We can combine like terms to get

[tex]2x+5=85[/tex]

Subtracting 5 from both sides results in

[tex]2x=80[/tex]

After that, we can divide both sides by 2 to get

[tex]x=40[/tex]

Thus, Elga is 40 years old.

Answer:

e = 40

a=45

Step-by-step explanation:

a + e = 85

a = e+5

e + 5 + e = 85

2e = 80

e = 40

a=45

Answer:

determine the number of miles the car drives in a year.

divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.

Step-by-step explanation:

Answer:

P>-6/5

Step-by-step explanation:

2(P+1)+3(P+2)>2

Use the distributive property to multiply 2 by P+1

2P+2+3(P+2)>2

Use the distributive property to multiply 3 by P+2

2P+2+3P+6>2

Combine 2P and 3P to get 5P

5P+2+6>2

Add 2 and 6 to get 8

5P+8>2

Subtract 8 from both sides

5P>2−8

Subtract 8 from 2 to get −6.

5P>−6

Divide both sides by 5. Since 5 is positive

P>−6/5

​  

Answer:

1. centimeter

2. kilogram

3. gram

4. milligram

5. centimeter

6. meter

7. kilometer

8. liter

9. kiloliter

10. millimeter

Step-by-step explanation:

you really cannot answer that yourself ?

you don't understand yet the difference between length or distance, area, volume, weight, ... ?

I how this helps then

1. is length, and it is rather short. so, we use a rather small unit to express it.

2. is weight. and a big one. so, we use a bigger unit.

3. is weight. but a small one.

4. is weight. and a really tiny one.

5. is length. similar dimension of size as the finger.

6. is length. and a bigger one.

7. is length. and a truly big one.

8. is volume. liquid volume at that. but rather small.

9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...

10. is length. and a very tiny one.

Hello!

3a = 7b =>

=> 3 × a = 7 × b =>

=> a/b = 7/3

Good luck! :)

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

9514 1404 393

Answer:

  372 m²

Step-by-step explanation:

A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.

The area of one of them is ...

  A = 1/2(b1 +b2)h

So, the area of the two of them together is ...

  A = (2)(1/2)(b1 +b2)h = (b1 +b2)h

  A = (13 m + 18 m)(12 m) = 372 m²

9514 1404 393

Answer:

  7.5

Step-by-step explanation:

Corresponding sides are proportional, so ...

  UV/VW = LM/MN

  x/6 = 15/12

  x = 6(15/12) = 15/2

  x = 7.5

Answer:

C.

Step-by-step explanation:

The function shifted left five units instead of right five units.

There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.

9514 1404 393

Answer:

  1,222,200

Step-by-step explanation:

A search using a computer program found ...

  5432 × 225 = 1,222,200

__

1000 mod 225 = 100

4 × 225 = 900

This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.

Answer:

the total of marbles = 7 red + 11 blue + 7 Yellow

= 25 marbles

P ( b n r) = 11/25 + 7/24

=0.732

Step-by-step explanation:

1. find the total marbles

2. find the probability of each without replacement means the demoinator will reduce

3.add the two probability

Answer:

A is that answer

A) y<2x-3

Answer:

please provide an image.

Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.

Step-by-step explanation:

Order the dataset from least to greatest:

-38 → -13 → -9 → -2 → 14 → 28

Then find the values that lies in the middle:

-38 → -13 → -9 → -2 → 14 → 28

Since there are 2 values, find the average of those 2 values:

[tex]\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5[/tex]

The median value = -5.5.

The median value of data set B is -5.5, which is less than the median value of  3.1 in dataset A.

Answer:

[tex]f(x) = \frac{5}{x}[/tex]

[tex]g(x) = x - 4[/tex]

Step-by-step explanation:

Composite function:

[tex]h(x) = f(g(x)) = (f \circ g)(x)[/tex]

h(x) = 5/x-4

We have x on the denominator and not the numerator, so the outer function is given by:

[tex]f(x) = \frac{5}{x}[/tex]

The denominator is x - 4, so this is the inner function, so:

[tex]g(x) = x - 4[/tex]

Answer:

7

Step-by-step explanation:

Substitute 2 for x.

[tex] {2}^{2} + 3 = 7[/tex]

Answer:

(0.8165 ; 0.8819)

Lower boundary = 0.8165

Upper boundary = 0.8819

Step-by-step explanation:

Given :

Sample proportion. Phat = x/ n = 276/ 325 = 0.8492

Confidence interval :

Phat ± margin of error

Margin of Error = Zα/2* [√Phat(1 - Phat) / n]

Phat ± Zα/2* [√Phat(1 - Phat) / n]

The 90% Z critical value is = 1.645

0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)

0.8492 ± 1.645*[√0.8492(0.1508) / 325]

0.8492 ± 1.645*√0.0003940288

0.8492 ± 0.0326535

Lower boundary = 0.8492 - 0.0326535 = 0.8165

Upper boundary = 0.8492 + 0.0326535 = 0.8819

Confidence interval = (0.8165 ; 0.8819)

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

[tex]x(t) = (v_0\cos{\alpha})t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]

In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that [tex]v_0 = 2048, \alpha = 30[/tex].

So

[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]

(a) After how many seconds will the bullet hit the ground?

It hits the ground when [tex]y(t) = 0[/tex]. So

[tex]1024t - 16t^2 = 0[/tex]

[tex]16t^2 - 1024t = 0[/tex]

[tex]16t(t - 64) = 0[/tex]

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

[tex]x(64) = 1773.62(64) = 113511.7[/tex]

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

[tex]y^{\prime}(t) = 1024 - 32t[/tex]

[tex]1024 - 32t = 0[/tex]

[tex]32t = 1024[/tex]

[tex]t = \frac{1024}{32} = 32[/tex]

At this instant, the height is:

[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]

The maximum height attained by the bullet is of 16,384 feet.

Answer:

is that the full question?

Answer:

Solution:-

Given,

ab =perpendicular (p)= 6cm

ac =hypotenuse (h)= 12cm

cd =base (b)= ?

using , Pythagoras theorem we have ,

b²=√h²-p²

or,cd²=√ac²-ab²

= √12²-6²

= √144-36

=√108

=√10.8²

=10.8cm

the length of cd is 10.8 cm

hope it is helpful to you

Answer:

42÷2

Step-by-step explanation:

Answer:

Answer is 3bu2(DeEZ)=1

Step-by-step explanation:

The scatter plot showing data gathered and line of best fit is attached below :

Answer:

69

Step-by-step explanation:

Given the regression model :

y = 1.73x + 0.0924

Where,

y = number of pink flowers

x = Red flowers

Slope = 1.73

Intercept = 0.0924

The number of pink flower that are predicted to bloom on a shrub of 40 red flowers :

Put x = 40 and calculate the value of y

y = 1.73(40) + 0.0924

y = 69.2 + 0.0924

y = 69.2924

Number of pink flowers = 69

Answer:

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

Step-by-step explanation:

Given the data :

35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

The next to highest frequency group has a frequency of 4 and the highest frequency of 6

Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16

Answer:

hey there hope this answer helps you out

Step-by-step explanation:

we have two functions f(x) and g(x) such that

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} + 6x[/tex]

solving for f ° g, we'll substitute the x in f(x) by the value of g(x)

[tex]fog = \frac{1}{g(x)} [/tex]

[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]

taking x common in denominator

[tex]fog = \frac{1}{x(x + 6)} [/tex]

for a function to exist it should not have 0 in its denominator

checking the values of x for which the denominator of f ° g becomes 0 :-

so the function doesn't exist at values x = 0, -6

Step-by-step explanation:

The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)