can someone please help!
find the minimum value of the function f(x)=0.2x^2-x+5.2
to the nearest hundredth.

Water is the Adjacent of this right triangle. 350 yards is the length of the Hypotenuse. We have given angle B, 40 degrees.

_________________________________________________________

According to SOH CAH TOA, we use CAH (cosineΘ = adjacent/hypotenuse).

cosine40 = x/350

[multiply both sides by 350]

350 · cosine40 = x

[put calculator in degree mode]

x ≈ 268 yards

So, the distance across the water from sailboat to the island is 268 yards.

_________________________________________________________

Let's use pythagorean theorem since we already know the adjacent and hypotenuse to find the opposite (opposite is also known as height).

a^2 + b^2 = c^2

a^2 + (268)^2 = (350)^2

a^2 + 71824 = 122500

a^2 = 122500 - 71824

a^2 = 50676

[square both sides]

[tex]\sqrt{a^2}[/tex] = [tex]\sqrt{50676}[/tex]

a = [tex]\sqrt{50676}[/tex]

a ≈ 225

So, the height, opposite, of the lighthouse is 225 yards.

_________________________________________________________

Answer:

i). 2    ii). 2

Step-by-step explanation:

i). 4p = 18 - 5(2)

4p = 18 - 10

4p = 8

p = 2

ii). 4(2) = 18 - 5q

8 = 18 - 5q

-10 = - 5q

q = 2

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

Point-slope equation for line of slope 3 that passes through (1,-2):

y+2 = 3(x-1)

Answer:

Ratio (r) = 2

n = 7

Step-by-step explanation:

The formula for the sum of the nth term of a G.P is given as:

Sn = a(1-r^n)/(1-r)

Where n = Number of terms

r = Common ratio

The sum of the 1st nth term gp is 127.

Hence:

127 = 1(1-r^n)/(1-r)

The sum of the reciprocal is 127/64

The formula is inverted , hence:

Sn = 1/a(1-r^n)/(1-r)

127/64 = r^(1-n)(1-r^n)/(1-r)

Hence:

1/64 = r^(1-n)

r^(n-1) = 64

r^(n-1) = 2⁶

Hence:

r = 2

Solving for n

n - 1 = 6

n = 6 + 1

n = 7

Therefore:

r = 2

n = 7

Answer:

The difference is

Step-by-step explanation:

Given

Large triangle

[tex]Base = 5cm; Height=9cm[/tex]

Small triangle

[tex]Base = 2cm; Height=6cm[/tex]

See attachment for logo

Required

The difference in their areas

Area is calculated as:

[tex]Area = 0.5 * base * height[/tex]

For the large triangle

[tex]Area = 0.5 * 5cm * 9cm[/tex]

[tex]Area = 22.5cm^2[/tex]

For the small triangle

[tex]Area = 0.5 * 2cm * 6cm[/tex]

[tex]Area = 6cm^2[/tex]

The difference (d) is calculated as:

[tex]d = 22.5cm^2 - 6cm^2[/tex]

[tex]d = 16.5cm^2[/tex]  

Answer:

254.34 ft^2

Step-by-step explanation:

The equation for area of a circle is π*r^2, where r is the radius of the circle. So we do 3.14*9^2 for the answer

Answer:

254.34 ft

Step-by-step explanation:

radius (9)

multiply it by itself (9x9)

so then you get 81

then the two radius squared (81) is multiplied by pi (3.14)

Split it into two rectangles:

6 x 2 x 2 = 24

3 x 2 x 2 = 12

Now add:

24 + 23 = 36 cubic feet

Answer:

Step-by-step explanation:

Y intercept is at  (0,1) so b=1

slope is go 4 down 1 right so slope is -4

Equation is

-4x+1=y

Answer:

10.55

Step-by-step explanation:

Answer:

gradient = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope (gradient) and c the y- intercept )

Given

8y + 4x = 5 ( subtract 4x from both sides )

8y = - 4x + 5 ( divide the terms by 8 )

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{8}[/tex] ← in slope- intercept form

with gradient = - [tex]\frac{1}{2}[/tex]

Given a line with gradient m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2

2 is the gradient of a line that is perpendicular to 8y+4x=5​

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane

The slope of line can also be called ad gradient of a line.

The standard form of line or slope intercept form of a line is given by

y=mx+c

where m is the slope of line and c is the y intercept.

The given equation of line is  8y+4x=5​

We need to convert the equation of line to Slope intercept form

8y=5-4x

Divide both sides by 8

y=5/8-4/8x

y=-1/2x+5/8

So m is -1/2.

Two lines are said to be perpendicular if m₁m₂ =-1

if m₁=-1/2

then we need to calculate m₂

-1/2m₂=-1

m₂=2

Hence gradient of a line that is perpendicular to 8y+4x=5​ is 2.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ2

Given:

The volume of a cylinder is 95 cubic centimetres.

To find:

The equation that can be used to find h, the height of the cylinder.

Solution:

We know that, the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

We know that the base of the cylinder is a circle and the area of the circle is [tex]\pi r^2[/tex]. So, the base area of the cylinder is [tex]B=\pi r^2[/tex].

Now, volume of the cylinder is

[tex]V=Bh[/tex]

The volume of a cylinder is 95 cubic centimetres.

[tex]95=Bh[/tex]

[tex]\dfrac{95}{B}=h[/tex]

[tex]h=\dfrac{95}{B}[/tex]

Where B is the base area of the cylinder.

Therefore, the correct option is G.

Answer:

The key features needed to determine if these two linear functions intersect would be their y-intercept and their slopes. We need this information because it would allow us to graph these two linear functions, and if we can graph them, we can see if these lines intersect. 

Step-by-step explanation:

Took the "quiz"

(Please mark Brainliest)

Answer:

15/8

Step-by-step explanation:

the mixed answer is 1 7/8

but also the answer is 15/8

Answer:

3

Step-by-step explanation:

105/7hrs

15/1hr

15/60min

0.25/per minute

0.25*12

= 3

Answer:

Step-by-step explanation:

Base area * height

Answer:

i think that the answer is BH or Base area × Hight

Answer:

the answer is .24

Step-by-step explanation:

when you multiply 0.1 x 2.4 it equals out to .24

0.1 x 2.4= .24

Answer:

1.) 1.12/10= 1 2/10= 1.2%       10*1.2%=12

2.) 8/10=0.80%                     10*0.80=8

3.)10/12=0.83%                     12*0.83=10    

%*whole

Answer:

-2/3

Step-by-step explanation:

2-4 / 2-(-1)

2-4 / 2+1

-2/3

Since both equations equal y they need to equal each other.

2x - 5 = -3x + 10

Add 3x to both sides:

5x -5 = 10

Add 5 to both sides

5x = 15

Divide both sides by 5

X = 3

Now solve for y by replacing x with 3:

Y = 2(3)-5 = 6-5 = 1

Y = -3(3)+ 10 = -9+ 10 = 1

Check: replace y with 1 and solve for x:

1 = 2x -5

Add 5 to both sides

6 = 2x

Divide both sides by 2

X = 3 ( True)

Answer:

2/3

Step-by-step explanation:

When a line is parallel to another, it means that there are never going to be any solutions(they won't ever intersect each other.) To do so, the slope of the lines have to be the same. It doesn't matter what the y-intercept is.

So the slope of the second line is going to be the same as the first line: 2/3

Answer:

that is what it would look like

Hope it helps!❤❤

Step-by-step explanation:

1. -6u= -29-7

-6u÷-6= -36÷-6

u= 6

2. 6m= -23-1

6m÷6= -24÷6

m=-4

3. 4d=37-5

4d÷4=32÷4

d=8

Answer:

4. -6u+7=-29

-6u=-29-7

-6u=-36

-6u=-36

(divide both sides by-6 )

-6u/-6=-36/-6

u=6.

5. 6m+1=-23

6m=-23-1

6m=-24

divide-24 by 6

m=-4

6. 5+4d=37

4d=37-5

4d=32

divide by 4

d=8

Answer:

56

Step-by-step explanation:

x+x+8=104

2x=96

x=48

48+8=56

Answer:

401.92

Step-by-step explanation:

The formula used the calculate the volume of a cylinder is

πr^2h

π= 3.14

H= 8

r= 4

Volume= 3.14 × 4^2 × 8

= 3.14 × 16×8

= 401.92

Hence the volume is 401.92

Answer:

64 degrees.

Step-by-step explanation:

We are given that angle QRP is 32 degrees.

We are also given that angle PRS is 84 degrees.

Add those two angles to get the measure of angle QRS.

measure of angle QRS= 116 degrees.

Same-side interior angles are supplementary

So,

116+ angle PQR= 180

subtract both sides by 116.

PQR=64

Therefore the measure of angle PQR is 64 degrees.

I hope this helps

Answer: 30%

Step-by-step explanation: