Given the function f(x) = −5x2 − x + 20, find f(3).

Using the given information, the width of the river is 505.96 m

From the question, we are to determine the width of the river

Consider the given diagram,

Let F be the first position of the biker

S be the second position

and C be the position of the church

First, we will determine the distance covered from F to S

Speed = 160m/min

Time = 4 minutes

Using the formula,

Distance = Speed × Time

Distance covered = 160 × 4

Distance covered = 640 m

That is, /FS/ = 640 m

Now, consider ΔFSC

∠F = 90° - 70° = 20°

∠S = 90° + 56° = 146°

and ∠C = 180° - 20° - 146° = 14°

By the Law of Sines

[tex]\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}[/tex]

∴ [tex]\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}[/tex]

[tex]/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}[/tex]

/FC/ = 1479.33 m

Now,

By SOH CAH TOA

[tex]cos \ 70^\circ = \frac{d}{/FC/}[/tex]

NOTE: d is the width of the river

∴ d = /FC/ × cos70°

d = 1479.33 × cos70°

d = 505.96 m

Hence, the width of the river is 505.96 m

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Answer:

When the initial velocity is 6m/s and acceleration is 3m/s², the final velocity after a distance of 29m is √210m/s.

Step-by-step explanation:

Concept: In the problem it is given that u = 6m/s, a = 3m/s² and s = 29m. We need to find the v. In such kinematical problems, we have an equation v² = u² + 2as. From this relation we can find v.

v² = 6² + 2×3×29

v² = 36 + 174

v² = 210

v = √210 m/s

So, the final velocity is the under-root of 210 or √210 m/s.

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Answer:

-2

Step-by-step explanation:

15-8+-9

bodmas

15-8=7

7-9

=-2

The height of figure 1 that is similar to figure 2 is: D. 4 units.

The corresponding linear measurements of similar figures are proportional. Therefore, we would have:

4x/2x = x + 1/x

Solve for x

2 = x + 1/x

2x = x + 1

2x - x = 1

x = 1

Height of figure 1 = 4x = 4(1) = 4 units.

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The true statements about the arcs and angles in circle C are:

In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:

m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

60 + 90 + m∠DCE + 90 = 360

240 + m∠DCE = 360

m∠DCE = 360 - 240

m∠DCE = 120°.

Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:

m∠DFE =  m∠DCE

m∠DFE =  120

m∠DFE = 1/2 × 120

m∠DFE = 60°.

Therefore, ∠EFD ≅ ∠EGD.

From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.

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Answer:

A C E

took quiz

Answer:

it is a 50 50 %chance so it is random this is called probability the probability of blue is half so it is by chance I chose blue

Answer:

(-3, 0, 4, 6) (option D)

Step-by-step explanation:

The "range" of a function is all possible y-values. In this image, there are x's entered on the left side--which I know to be x values because a function, f(x) is essentially the outcome of what happens when x is entered.

So, the y-values are featured on the right. All of these values are the possible values for y, or, what we call the range.

Meaning that the range of this function is (-3, 0, 4, 6)

Answer:

BC ≈ 19.4 cm

Step-by-step explanation:

using the cosine ratio in the right triangle

cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6.3}{BC}[/tex] ( multiply both sides by BC )

BC × cos71° = 6.3 ( divide both sides by cos71° )

BC = [tex]\frac{6.3}{cos71}[/tex] ≈ 19.4 cm ( to 3 sig. figs )

Answer:

19.4°

Step-by-step explanation:

I put the image of how I did it if you don't understand let me know

Answer:

A. 345

B. 180

Step-by-step explanation:

That is the right answer

Step-by-step explanation:

hope this help you the result is In square

Answer:

Step-by-step explanation:

The answer is (C).

Ingrid would have to pay 64 per month more than clem.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given;

fico        interest monthly      score rate

720-850          5.59%             $860

700-719           5.71%              $872

675-699          6.25%             $924

620-674          7.40%              $1039

560-619           8.53%              $1157

500-559          9.29%               $1238

Clem's score is 733 which is 924 on the chart.

Ingrid's score is 688 which allows her to pay 860 per month.

924 - 860 =  64

Hence,

Ingrid would have to pay 64 per month more than clem.

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Answer: 35.675

Step-by-step explanation:

10.465−(−25.21)

The opposite of −25.21 is 25.21.

10.465+25.21

Add 10.465 and 25.21 to get 35.675.

35.675

Answer:

50 miles per hour

Step-by-step explanation:

Step 1: We subtract 600 from 1000. That gives us 400 miles for the second day.

Step 2: Now we divide that by 8, giving us 50 miles per hour. We have our answer!

Answer:

Inequality would be the answer

Answer:

One number, let's call it x, is 6 more than twice the other number, let's say this number is y.

x= 2y+6

x+y=21

We're left with a system of equations.

If we substitute the first equation in the second we find the value of y.

(2y+6)+y=21

3y+6=21

3y=15

y=5

Now that we have found the value of y, we can take that value and substitute it in the second equation (since it's easier) to find the value of x.

x+ (5)=21

x=16

Now to check if our answers are correct, we plug in both values into any equation and see if they equate.

x+y=21

(16)+(5)=21

21=21

Our solution is correct!

Answer: y = (x-1)(x-1)

Step-by-step explanation:

There is pretty much no vertical shift so that immediately rules out B and C.

We can solve y = (x-1)(x-1) and get x = 1

The graph shows x = 1 as a zero, so we know this graph is correct.

Answer:

the answer is (3,4) is the solution to line A but not to line b

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

An equation is an expression that shows the relationship between two or more numbers and variables.

Let k represent the constant of proportionality

3) T = kN

28 = 250k

k = 0.112

i) T = 0.112N

ii) T = 0.112(300) = 33.6

iii) 98 = 0.0112N

N = 875

4) D = kA

270 = 5k

k = 54

i) D = 54A

ii) D = 54(4.5) = 243

iii) 324 = 54A

A = 6

5) T = kA

150 = 2.4k

k = 62.5

i) T = 62.5A

ii) T = 62.5(1.8) = 112.5

iii) 3(60) = 62.5A

A = 2.88

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

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Finding the regression equation, her average speed on the 9th day should be expected to be of 6.92 minutes per mile.

To find the equation, we need to insert the points (x,y) in the calculator.

Researching the problem on the internet, the values of x and y are given as follows:

Hence, using a calculator, the equation for the average minutes per mile after t days is given by:

V(t) = -0.15143t + 8.28

Hence, for the 9th day, t = 9, hence the estimate is:

V(9) = -0.15143(9) + 8.28 = 6.92 minutes per mile.

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[tex]4x - 2x = 7 + 3 \\ \\ 2x = 10 \\ \\ x = \frac{10}{2} \\ \\ x = 5.[/tex]

[tex]2x - 7x = - 14 - 6 \\ \\ - 5x = - 20 \\ \\ x = \frac{20}{5} \\ \\ x = 4.[/tex]

Answer:

380.1

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

A=[tex]\pi[/tex]*11*11

A~ 380.13 m^2

nearest tenth: 380.1

Answer:

$29

Step-by-step explanation:

Substitute x with 8.

3(8) + 5 = 24+5 = 29

Answer: $29

Step-by-step explanation:

x = # toys

if the number of toys is 8

substitute 8 into x

y = 3(8) + 5

y = 24 + 5

y = 29

Proved Below

[tex]\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{(x-y)^2}[/tex]

[tex]\Longrightarrow x-y =x-y[/tex]

Let's check

x-y=√(x+y)²-4xy

Solve RHS

Hence proved

Answer:

D

Step-by-step explanation:

x² + y² = 64, because when x is 0, y = ± 8, when y is 0, x = ± 8, that is the radius r

The equation of a circle with center at the origin and radius 8 is,

⇒ x² + y² = 64

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

This circle is centered at the origin, and the length of its radius is 8.

Since, The equation of a circle with center at the origin and radius r is,

⇒ x² + y² = r.

Hence, for this circle, the equation would be;

⇒ x² + y² = 8²,

or simplified,

⇒ x² + y² = 64

Thus, The equation of a circle with center at the origin and radius 8 is,

⇒ x² + y² = 64

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Answer:

10%   or   1 /10  

Step-by-step explanation:

'Fish' is on the spinner in one slot out of 10 slots

   one out of 10    = 1/10 = 10%

Answer:

10%

Step-by-step explanation:

There are 10 possible areas to land on fish is only shown once meaning there is a 1/10 chance which is = to 10%

Answer:

y=-x-7

Step-by-step explanation:

Slope-intercept form is y=mx+b

We have the equation 4x+4y=-28 and must put it into the form above. To do this first subtract 4x from both sides.

4x-4x+4y=-28-4x

This equals 4y=-4x-28. Now, divide 4 from both sides.

4y/4=-4x/4-28/4

y=-x-7

Hope this helps!

If not, I am sorry.

Answer:

5 blue marbles

10 Red marbles

3 Green marbles

Step-by-step explanation:

5 times 2 = 10

then 5-2 =3

Add 5+10+3

=18 Marbles in total

cranberry juice = 350 ml

blueberry juice = 2 liters = 2000 ml

Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40

The simplest ratio is 7 : 40    or    7/40