How to solve using quadratic equations 4x^2+7x-20=0

Answer:

y-0 = 1/2(x-0)

y = 1/2(x)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-0 = 1/2(x-0)

y = 1/2(x)

Answer:

Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine

Step-by-step explanation:

Given the data:

Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9

New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1

To test if volume filled by old machine varies more than volume filled by new machine :

Hypothesis :

H0 : s1² = s2²

H1 : s1² > s2²

Using calculator :

Sample size, n and variance of each machine is :

Old machine :

s1² = 0.37889

n = 10

New machine :

s2² = 0.006111

n = 9

Using the Ftest :

Ftest statistic = larger sample variance / smaller sample variance

Ftest statistic = 0.37889 / 0.006111

Ftest statistic = 62.001

Decision region :

Reject H0 ; If Test statistic > Critical value

The FCritical value at 0.05

DFnumerator = 10 - 1 = 9

DFdenominator = 9 - 1 = 8

Fcritical(0.05, 9, 8) = 3.388

Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine

Step-by-step explanation:

Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]

Hence, dθ/dt = π/90.

From the Law of Cosines:

[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]

Since a = 13 and b = 19:

[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]

Simplify:

[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]

Solve for dc/dt:

[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]

Evaluate. Hence:

[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  [tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]

Answer:

b or a

Step-by-step explanation:

Answer:

1/2 base×height

1/2 .5×4

1/2.20

20 divided by 2 is 10

1/1×10

10cm2

ans

Answer:

A child who weighs 84 pounds should be given 94.5 milligrams of the drug.

Step-by-step explanation:

Givens:

1kg=2.5 milligrams of dosage

Weight of child = 84 pounds

1 pound = 0.45 kg

Solution:

Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg

Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.

Answer:

multiples of 2 2,4,6,8,10,12,14,16,18,20

multiples of 3 3,6,9,12,15,,18,21,24,27,30

Step-by-step explanation:

Lcm is 6

Answer:

117.8

Step-by-step explanation:

Surface area = πr²+πrl (whee r = radius and l = slant height)

= π×3²+π×3×9.5

= 75π/2

= 117.8

Answer:

46374

Step-by-step explanation:

The smallest 5-digit number is 20046

While the greatest is 66420

So 66420-20046=46374

Answer:

12 x^5y^12

Step-by-step explanation:

3x^2y^5 * 4x^3y^7

Multiply the constants

3*4 = 12

Multiply the x terms

x^2 * x^3

We know a^b* a^c = a^(b+c)

x^(2+3) = x^5

Multiply the y terms

y^6 * y^7 = y&(5+7) = y^12

Put them back together

12 x^5y^12

Answer:

Hello,

Step-by-step explanation:

[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]

Answer:

a = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = [tex]\frac{1}{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a = 4[tex]\sqrt{3}[/tex]

Answer:

y+4=-3(x+8)

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

.08x600=48

Answer:

Step-by-step explanation:

total patients = 600

% of patients had eye surgery = 8%

Number of patients that had eye surgery ?= x

% of pt that had eye surgery =  no. of pt that had surgery/ total number of pt

8/100= x/600

x=(8x600) /100

x= 4800/100

x= 48

Number of patients that had eye surgery were 48

Answer:

Step-by-step explanation:

4x - 13 = x +  5           Add 13 to both sides

4x = x + 18                 Subtract x

3x = 18                       Divide by 3

x = 6

Answer:

1.25 dollars per quart

Step-by-step explanation:

There are 4 quarts per gallon

3 gallons * 4 quarts/ gallon = 12 quarts

15 dollars/ 12 quarts

1.25 dollars per quart

Answer:

It's 81

Step-by-step explanation:

You can use a calculator on go.ogle :D

Answer:

Consider the following identity:

Let a = 2, b = 1/2

Use the algebraic identity given below

[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]

[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]

[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

8(-2x+1) =0

Divide each side by 8

-2x+1 = 0

Add 2x to each side

-2x+1+2x = 2x

1 = 2x

Divide by 2

1/2 = 2x/2

1/2 =x

Answer:

1/2

Step-by-step explanation:

8(-2x+1)=0

Use distributive property first

-16x+8=0

Subtract 8 on both sides

-16x=-8

Divide both sides by -16 to get x by itself

x=0.5

Which is also equal to 1/2

Therefore, x is equal to 1/2

Answer:

-7/25

Step-by-step explanation:

1/5 ÷ (-5/7)

Copy dot flip

1/5 * -7/5

-7/25

Answer:

m=3*sqrt(2) and n=3

Step-by-step explanation:

tan(45)=3/n

1=3/n, n=3. As it's a right angled triangle, 3^2+3^2=m^2, m=3*sqrt(2)

Answer:

Step-by-step explanation:

#1

A) P(FEMALE|APPLE)

apple total = 346

apple/female = 194

194/346 = .56 = 56 %

B) P(APPLE|MALE)

male total = 320

apple male = 152

152/320 = .475 = 47.5%

C) female prefer Microsoft

152:168 = 76:84 = 38:42 = 19:21

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

(a) 31

(b) 32

Step-by-step explanation:

We will do (b) first since it will help us do (a).

(b)

There are [tex]n(A)=5[/tex] elements in [tex]A[/tex]. Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is

[tex]2^{n(A)}=2^5=32[/tex]

(a)

A subset of [tex]A[/tex] is called proper if it does not equal [tex]A[/tex]. The only subset of [tex]A[/tex] that is not proper is [tex]A[/tex] itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is

[tex]32-1=31[/tex]

Answer:

G=21, F=9, M=6, L=7, E=20, D=15, B=10, R=12.5, T=16, N=13.5, W=18, H=36, Z=12

*I=5*

Step-by-step explanation:

I basically just found the scale factor/proportion from two given sides and then used that to find the remaining sides.

*I'm not sure about 'I' since the edge of the paper was cut off so I want sure if it was a 5 or a 15 on the left most problem in the third row. I assumed it was 15. If it's not, just shout it out in the comments and I'll fix it! :)*

You can fill the letters in at the bottom XD

I hope this helped! :D

Answer:

11. Yes

12. No

Step-by-step explanation:

11. The x values only have 1 y value, so it makes it a function.

12. The x value 0 has 2 y values -4 and 4, therefore it is not a function, because in functions that x value can only have one y value,

Please Mark my answer brilliant

Answer:

so your answer is (0.5,-1)

Answer:

n= (z)22E2

n=10× 99%÷ 0.07

Answer:

117.8

Step-by-step explanation:

surface area = πr²+πrl, where r = radius and l = slant height

so,

πr²+πrl

= π×3²+π×3×9.5

= 75π/2

= 117.8 (rounded to the nearest tenth)