Which number is written in scientific notation? 4. 5 times 10 Superscript negative 3 14. 5 times 10 Superscript 2 0. 78 times 10 Superscript negative 6 5. 7 times 4 Superscript 8.

a = 2, b = -18, c = 40

[tex]Given:\ Polynomial\ f(x)=ax^2+bx+c\ has\ zoroes\ 4\ aud\ 5[/tex]

[tex]and\ f(-1)=60[/tex]

[tex]Tofind:\ a,\ b,\ c[/tex]

[tex]Solution:\ As\ 4\ and\ 5\ are\ zeroes\ so\ f(4)=f(5)=0[/tex]

[tex]f(4)=a(4)^2+b(4)+c=0\Rightarrow16a+4b+c=0-(1)[/tex]

[tex]f(5)=a(5)^2+b(5)+c=0\Rightarrow25a+5b+c=0[/tex]

[tex]f(-1)=a(-1)^2+b(-1)+c=60\Rightarrowa-b+c=60-(3)[/tex]

[tex]subtracting\ (1)\ from\ (2)[/tex]

[tex]25a+5b+c-(16a+4b+c)=0\Rightarrow9a+b=0\Rightarrowb=-9a[/tex]

[tex]subtracting\ (3)\ from(2):[/tex]

[tex]25a+5b+c-(a-b+c)=0-60\Rightarrow24a+6b=-60[/tex]

[tex]putting\ b=-9a[/tex]

[tex]24a+6(-9a)=-60\Rightarrow24a-54a=-60\Rightarrow-30a=-60[/tex]

[tex]a=\frac{-60}{-30}=2[/tex] [tex]\Rightarrow[/tex] [tex]a=2[/tex]

[tex]b=-9a=-9\times2=-18[/tex]

[tex]c=-a+b\neq60=-2-18+60=-20+60=40[/tex]

I hope this helps you

:)

The length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

Length of arc = ∅/360 × 2πr, where the radius of the circle is r, and the reference angle is ∅.

We are given the following:

Radius (r) = 3 units

Reference angle (∅) = 46°

Plug in the values into the length of arc formula:

Length of arc = 46/360 × 2π(3)

Length of arc = 2.41 units.

Therefore, the length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

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Let that be x

[tex]\\ \rm\rightarrowtail tan\theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \rm\rightarrowtail tan20=\dfrac{x}{10}[/tex]

[tex]\\ \rm\rightarrowtail 0.364=\dfrac{x}{10}[/tex]

[tex]\\ \rm\rightarrowtail x=10(0.364)[/tex]

[tex]\\ \rm\rightarrowtail x=3.64mi[/tex]

Answer:

[tex]\displaystyle 4\:mi.[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{10}{h} = cot\:20 \hookrightarrow 10 = hcot\:20 \hookrightarrow \frac{10}{cot\:20} = h; 3,6397023427... \\ \\ \boxed{4 \approx h}[/tex]

OR

[tex]\displaystyle \frac{h}{10} = tan\:20 \hookrightarrow 10tan\:20 = h; 3,6397023427... \\ \\ \boxed{4 \approx h}[/tex]

I am joyous to assist you at any time.

Answer: 10.62 irrational

Step-by-step explanation: You can divide 69.15 by 5.25 which equals 74.4 then divide by 7 which equals 10.62

Answer:

h = 24 cm

Step-by-step explanation:

Let [tex]x[/tex] = height of ΔCBD

Let [tex]h[/tex] = height of ΔABE

As ΔABE ~ ΔCBD then AE : CD = [tex]h[/tex] : [tex]x[/tex]

Given:

[tex]\implies 20 : 10 = h : x[/tex]

[tex]\implies \dfrac{20}{10}=\dfrac{h}{x}[/tex]

Cross multiply:

[tex]\implies 20x=10h[/tex]

Simplify:

[tex]\implies 2x=h[/tex]

As we are told that [tex]x+h=36 \ \sf cm[/tex]

[tex]\implies h=36-x[/tex]

Equate the two equations for [tex]h[/tex] and solve for [tex]x[/tex]:

[tex]\implies 2x=36-x[/tex]

[tex]\implies 3x=36[/tex]

[tex]\implies x=12[/tex]

Since [tex]h=2x[/tex] then

[tex]\implies h=2 \cdot 12[/tex]

[tex]\implies h=24 \ \sf cm[/tex]

Answer:

(n/4)-1

Step-by-step explanation:

Answer:

Monica has 1 more card than Joey

Step-by-step explanation:

its simple math

Answer: Square is a 17*17. Ok so its 121-25=96

Step-by-step explanation:

96

Answer: B. K < 13. K is 12.5, 12.5 is less than 13

1. Its not D because at the ending points of the number line; 10-20, which is less than 30.

2 It is not C because K is not on 15

3 It is not A because 12.5 is less than 13.

Hope it helps!!

Answer:

256x^8

Step-by-step explanation:

Hope this helped

Maybe mark brainiest?

Answer:

a

Step-by-step explanation:

The value of the hypotenuse y will be equal to y = 2.8 inches.

The volume of the prism is equal to the product of the area of its base and the height of the prism.

[tex]\rm V=Area \ of\ triangular \ base\times Height \ of \ prism[/tex]

The volume oif the prism is =4 cubic inches

Height of the prism = x inches

Base of the right angle isosceles triangle will be =x inches

The hypotenuse is given = y

Now

[tex]\rm V=\dfrac{1}{2}\times Base\times Height \times height \ of \ prism[/tex]

[tex]V=\dfrac{1}{2} \times x \times x \times x[/tex]

[tex]x^3=8[/tex]

[tex]x=2[/tex]

Now by pythagorus theorem

[tex]y^2=h^2+b^2[/tex]

[tex]y^2=x^2+x^2[/tex]

[tex]y^2=2x^2=2\times 2^2[/tex]

[tex]y=2\sqrt{2}=2.82[/tex]

Thus the value of the hypotenuse y will be equal to y = 2.8 inches.

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Answer:

2.8 INCHES

Step-by-step explanation:

Answer:

The coordinate of the image of a point is (2, +3) under the translation (x , y) → (x - 2),( y + 3). Find the coordinate of the preimage.

We are just looking for x and y and we know (2, +3) → (x - 2, y + 3)

2 = x - 2

x = 4

-3 = y + 3

y = -6

(x , y) = (4, -6)

How to find a 

Answer:

y = x - 5

Step-by-step explanation:

Line A

Equation

Answer:

The graph of g is translated down 5 units from the graph of f and stretched horizontally

Step-by-step explanation:

was correct on test :)

pls brainliest XD

.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.

Answer:

Side A is 4

Step-by-step explanation:

Answer:

A.4

Step-by-step explanation:

a = √(c² - b²)

a= √(5² -3b²)=4

Answer:

8

Step-by-step explanation:

first multiple 12 by 12 then divide by 18 then you'll get 2 times 4 and that's how you get 8.

Answer:

8

Step-by-step explanation:

A=πr^2

64π=πr^2

since answer is in terms of pi, ignore the pi.

sqrt(64)=8

Answer:

he correct answer is D. 12 adult tickets, 4 child ticket

Step-by-step explanation:

Answer:

c. 2x.

Step-by-step explanation:

16x2 - 14x

Common factor of 16 and 14 =  2'

for x2 and x it is x,

Answer: 2x.

Answer:

5x/1/2 = 1x



answer  1.12 <3


hope it helps


use brainly<3

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this

8 - 2x = 4 + x

-4 -2x = -4 + x

4 - 2x = x

next combine the like terms of the 2x so

4 - 2x = x

4 + 2x = +2x

4 = 2x

now you divide 4 by 2 so like this

4 = 2x

2   2

and your answer is x = 2 try to solve the other one if you need help ask me

=======================================================

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, flop it over, and change its sign.

In this case, we take [tex]\boxed{-3}[/tex], change its sign:

[tex]\boxed{3}[/tex]

3 can also be written as

[tex]\boxed{\frac{3}{1} }[/tex]

Now the numerator & denominator switch places:

[tex]\boxed{\frac{1}{3}}[/tex]

So that's the slope of the new line.

Now, let's write the equation in point-slope form:-

[tex]\bigstar{\underline{\boxed{\pmb{y-y_1=m(x-1)}}}[/tex]

Where

y₁  is the y-coordinate of the point (in this case, y₁ = 3)

m = slope (1/3)

x₁= the x-coordinate of the point (in this case, it's -2)

Plug in the values:-

[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x-(-2)}}[/tex]

[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x+2)} }\longleftarrow\sf{Point-Slope~Formula:)}}[/tex]

===============================================

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

30000 simple interest ,50000 total repayment.

Step-by-step explanation:

sorry iam terrible at explaining,

Step-by-step explanation:

percentage of green marbles=

(total green marbles÷ total marbles )×100

Answer:

58.58

Step-by-step explanation:

[tex] \frac{1}{2} \times 10 \times 3 \\ 5 \times 3 = 15.....(1)[/tex]

[tex] \frac{1}{2} \times 10 \times 10 \\ 5 \times 10 = 50...(2)[/tex]

Add one and two :- 15+ 50 = 65

Answer:

Step-by-step explanation:

Anything going from lower left to upper right is a positive slope.

The lines are not easily seen. My best estimate is that one point is (2,5)

Use the two points you are sure of.

(0,-1) and (1,2)

Givens

Formula

m = (y2 - y1)/(x2 - x1)

Solution

m = (2 - - 1) / (1 - 0)

m = 3/1

m = 3

2×+3y=6

-8×-3y=12

-6×=18

×=18/-6

×=-3

——————

2×+3y=6

2(3)+3y=6

6+3y=6

3y=6-6

3y=0

Y=0/3

Y=0

——————

×=3

Y=0

————

2×+3y=6

2(3)+3(0)=6

6=6

Answer:

60 cm

Step-by-step explanation:

The perimeter of a polygon means adding up all the side lengths.

In this case, we need to add up 13, 12, 8, 8, and 19

Adding all of these gets us 60

The average squared distance between the points is their variance

The average squared distance is 8/3

The given parameters are:

R={(x,y): 0<=x<=2, 0<=y<=2}

The point = (2,2).

f(x,y) = (x-2)² + (y-2)²

The squared distance is calculated as:

D² = f(x,y) = (x-2)² + (y-2)²

Where the area (A) is:

A = xy

Substitute the maximum values of x and y in A = xy

A = 2 * 2

A = 4

The minimum values of x and y are 0.

So, the limits for the integrals are 0 to 2

The integral becomes

[tex]D\² = \int \int (x-2)\² + (y-2)\² dx dy[/tex]

Expand

[tex]D\² = \int \int x\² -4x + 4 + (y-2)\² dx dy[/tex]

Evaluate the inner integral with respect to x from 0 to 2

[tex]D\² = \int \frac 13x^3 -2x^2 + 4x + x(y-2)\² |\limits^2_0 dy[/tex]

Expand

[tex]D\² = \int [\frac 13(2)^3 -2(2)^2 + 4(2) + (2)(y-2)\²] dy[/tex]

Simplify

[tex]D\² = \int \frac 83 + (2)(y-2)\² dy[/tex]

Expand

[tex]D\² = \int \frac 83 + 2y^2-8y + 8 \ dy[/tex]

Evaluate the integral with respect to y from 0 to 2

[tex]D\² = [\frac 83y + \frac 23y^3- 4y^2 + 8y ]|\limits^2_0[/tex]

Expand

[tex]D\² = \frac 83*2 + \frac 23*2^3- 4*2^2 + 8*2[/tex]

D² = 32/3

The average squared distance (AD²) is calculated as:

AD² = D²/A

So, we have:

AD² = 32/3 [tex]\div[/tex] 4

Evaluate the quotient

AD² = 32/12

Simplify

AD² = 8/3

Hence, the average squared distance is 8/3

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The average squared distance between the points of R = {(x,y): 0<=x<= h, 0<=y<=k } is 8/3.

How do determine the average squared distance?

From the given parameters R = {(x,y): 0<=x<= h, 0<=y<=k }

The squared distance from point (h, k) is calculated as

D² = f(x,y) = (x-2)² + (y-2)²

Where the area (A) will be

A = xy

Substitute the maximum values of x and y

A = 2 × 2 = 4

The minimum values of x and y are 0.

So, The integral becomes

[tex]D^{2} = \int \int(x-2)^2 +(y-2)^2 dx dy\\\\D^{2} = \int \int\limits^2_0 (x)^2 -4x + 4+(y-2)^2 dx dy\\\\D^{2} = \int1/3(x)^3-2x^{2} +4x + 4+x(y-2)^2 dy\\\\D^{2} = \int8/3+2y^{2} -8y +8 dy[/tex]

[tex]D^2 = {8/3y +2/3y^2 -4y^2+8y[/tex]

By expanding we get,

D^2 = 32/3

The average squared distance (AD²) is calculated as:

AD² = D²/A

AD² = 32/3  4

AD² = 32/12

AD² = 8/3

Hence, the average squared distance is 8/3

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