The diagram shows a semi circle inside a rectangle of length 150m. Calculate the perimeter

Step-by-step explanation:

1. AB = BC (B is the midpoint of AC)

2. DE = EF (E is the midpoint of DF)

3. EB is common

4. ∠ABE = ∠CBE; ∠BED = ∠BEF (EB⊥AC, EB⊥DF)

5. ΔDEB ≅ ΔFEB (RHS)

6. DB = FB (corresponding ∠s of ≅ Δs)

7. ∠EFB = ∠CBF; ∠EDB = ∠ABD (alternate interior angles, AC║DF)

8. ΔABD ≅ ΔCBF (SAS)

Answer:

B. A reflection across the y axis.

Step-by-step explanation:

Only B. A reflection across the y axis will work because all the other options make it move somewhere else or flip it upside down. The trapezoid has a line of symmetry down the y-axis so reflecting it across the y-axis will make the same exact figure in the same exact spot.

Answer:

2.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using SOH CAH TOA in trigonometry identity to find the sin Y, cos Y and Tan Y

Note that the hypotenuse is the longest side = 25

The opposite will be the side facing the acute angle Y

Opposite = 7

Adjacent = 24

For Sin Y

[tex]\sin =\frac{Opposite}{Hypotenuse}[/tex]

Sin Y = 7/25

For cos Y:

[tex]\cos Y = \frac{Adjacent}{Hypotenuse}[/tex]

Cos Y = 24/25

For tan Y:

[tex]\tan Y = \frac{Opposite}{Adjacent }[/tex]

Tan Y = 7/24

Answer:

Given

Hope it helps..

Step-by-step explanation:

The options that apply are:

4/18= 6/27

3/4= 9/12

How to check:

Multiple the middle two terms

Then divide the product by one of the outer terms

If you get the other outer term, its a valid proportion

Answer:

i believe that would be -8...

Step-by-step explanation:

Answer:

the correct answer is -8

plz mark as brainliest

Step-by-step explanation:

Answer: y ≥ (3/5)*x - 3

Step-by-step explanation:

In the graph, we can see that we are above a bold line, that goes through the points (0, -3) and (5, 0)

First, let's find the equation for this line:

y = a*x + b

the value of a is the slope and is equal to:

a = (0 - (-3))/(5 -0) = 3/5

and the value of b is the point where the line intersects the y-axis, in this case, b = -3

then our line is

y = (3/5)*x - 3

As the shaded part is above the line, this equality represents the minimum value that y can take for a given x, and because the line is not a doted line, we know that the equality is valid, so we must use the ≥ symbol.

y ≥ (3/5)*x - 3

The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.

Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.

Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example,  1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term)  and common differene d = 2- 1 = 1.

Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.

Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.

Learn more about arithmetic progression here:
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Answer:

[tex]h=\frac{1}{3} \pi r^{2} v[/tex]

Step-by-step explanation:

height is equal to one third times pi times radius squared times volume

The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²).

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given volume of the cone,

V=(1/3)πR²H

Manipulate the above formula as,

[V (3/1)]/(πR²) = H

H = 3V/(πR²)

Hence "The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²)".

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Answer:

72.5%

Step-by-step explanation:

To express a value as a %:

value/whole x 100 = 29 / 40 x 100

This gives you 72.5%

Hope this helps

Answer:

33

Step-by-step explanation:

V = 3*2 * 5 1/2

V = 6 * 11/2

V = 33

Answer:

V=whl

Step-by-step explanation:

V=51/2 * 3*2

V=153

Answer: D

Step-by-step explanation:

The equation would be (x+2)^2 + (y-3)^2 = 4 if I did it right. (Sorry if it’s wrong!)

Answer = D :)

Step-by-step explanation:

Answer:

It will take 20 times for both cost to be same

Step-by-step explanation:

What we want to do here is to calculate the number of times it will take someone who’s wants to rent a boat by Billyboat will be able to rent Lisa boat.

The first thing to do here is calculate how much that is charged to rent Billyboats

That would be;

Let the number of times be n

so the amount will be

105 + 9.50n

Now, renting at 14.75 at n times would be 14.75n

Mathematically, we equate both

14.75n = 105 + 9.5n

14.75n - 9.5n = 105

5.25n = 105

n = 105/5.25

n = 20 times

Answer:

C

Step-by-step explanation:

The y-intercept is at x=0, y=3.

Answer:

[tex]y>2x-5[/tex]

Step-by-step explanation:

[tex]y +2>1/3 (6x-9)[/tex]

Expand 1/3(6x-9).

[tex]y +2>6/3x-9/3[/tex]

[tex]y +2>2x-3[/tex]

Subtract 2 on both sides.

[tex]y +2-2>2x-3-2[/tex]

[tex]y>2x-5[/tex]

The rewritten form of y +2 > 1/3 (6x – 9) where the y-term us isolated is; y > 2x -5

To isolate the y-term;

The following operations are carried out;

By finally isolating y; we have;

y > 2x -5

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Answer:

Since the slope is -2 and y-int. is 3 the slope-intercept form is y = -2x + 3 which in standard form is 2x + y = 3.

Answer:

y = -2x + 3

Step-by-step explanation:

→ We know the slope so we can automatically plug that into the y = mx + c formula so,

y = -2x + c

→ Now we substitute in the coordinates (0,3) to find the c value and therefore complete the equation

y = -2x + c

3 = ( -2 × 0 ) + c ⇔ 3 = 0 + c ⇔ c = 3

y = -2x + 3

Answer: B) The heights of girls who live on a certain street in the city of Buffalo

Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.

Answer:

(i) ∠ABH  = 14.5°

(ii) The length of AH = 4.6 m

Step-by-step explanation:

To solve the problem, we will follow the steps below;

(i)Finding  ∠ABH

first lets find <HBC

<BHC + <HBC + <BCH  = 180°  (Sum of interior angle in a polygon)

46° + <HBC  + 90 = 180°

 <HBC+ 136°  = 180°

subtract 136 from both-side of the equation

 <HBC+ 136° - 136°  = 180° -136°

 <HBC  = 44°

lets find <ABC

To do that, we need to first find <BAC

Using the sine rule

[tex]\frac{sin A}{a}[/tex] =  [tex]\frac{sin C}{c}[/tex]

A = ?

a=6.9

C=90

c=13.2

[tex]\frac{sin A}{6.9}[/tex] = [tex]\frac{sin 90}{13.2}[/tex]

sin A = 6.9 sin 90  /13.2

sinA = 0.522727

A = sin⁻¹ ( 0.522727)

A ≈ 31.5 °

<BAC  = 31.5°

<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)

31.5° +<ABC + 90° = 180°

<ABC  + 121.5°  = 180°

subtract 121.5° from both-side of the equation

<ABC  + 121.5° - 121.5°  = 180° - 121.5°

<ABC = 58.5°

<ABH = <ABC - <HBC

           =58.5° - 44°

            =14.5°

∠ABH = 14.5°

(ii) Finding the length of AH

To find length AH, we need to first find ∠AHB

<AHB + <BHC = 180°  ( angle on a straight line)

<AHB + 46° = 180°

subtract 46° from both-side of the equation

<AHB + 46°- 46° = 180° - 46°

<AHB  = 134°

Using sine rule,

[tex]\frac{sin 134}{13.2}[/tex]  = [tex]\frac{sin 14.5}{AH}[/tex]

AH = 13.2 sin 14.5 / sin 134

AH≈4.6 m

length AH = 4.6 m

Answer:

center (6,-4)

radius = √7 unit

Step-by-step explanation:

Mathematically, the equation of a circle can be written as follows;

(x-a)^2 + (y-b)^2 = r^2

Where (a,b) represents the center of the circle with r representing the radius of the circle.

Now looking at the values in the question, we can clearly see that a = 6, while b represents -4.

The radius of the circle is √7

So the circle center is (6,-4) while √7 is the circle center

Step-by-step explanation:

You hiked 5400 - 3800 = 1600 feet in 4 hours so the mean change is 1600 / 4 = 400 ft/hour.

Answer:

Finding the vertex by completing the square

1) The vertex = (4/3, -4/3)

2) The vertex = (-1/2, 36)

3) The vertex = (2/3, 26/3)

Finding the value of x by completing the square

1) x = 1 or -4

2) x = 3/2 or -7/2

3) x = 1 or -3

Step-by-step explanation:

Finding the vertex by completing the square

The vertex form of the quadratic equation y = ax² + bx + c is written as follows;

y = a(x - h) + k

Therefore, we have;

Y = 3·x² + 4 - 8·x = a(x - h)² + k

Hence, a  = 3

Which gives;

3×(x² - 2·x·h + h²) + k

Hence, we have 3×2×h = 8

h = 8/6 = 4/3

The constant term = k

We note that 3 × h² + k = 4

∴ k = 4 - 16/3 = -4/3

The vertex form is therefore;

Y = 3(x - 4/3)² - 4/3

The vertex = (4/3, -4/3)

2) Where Y = 4·x² + 4·x + 36

a = 4

4× -2·h = 4

∴ h = 4/(4 × (-2)) = 4/-8 = -1/2

Also, 4 × h² + k = 36

Which gives;

4 × (-1/2)² × k = 36

k = 36

The vertex form becomes

y = 4(x - (-1/2)) + 36

The vertex = (-1/2, 36)

3) Where Y = -3·x² + 4·x + 10, we have

a = -3

3×2×h = 4

∴ h = 4/(2×3) = 2/3

a×h² + c = k

-(3)×(2/3)² + 10 =  26/3

Which gives;

Y = -3(x - 2/3) + 26/3

The vertex = (2/3, 26/3)

To find the value of x by completing the square, we have;

1) 2·x² = -6·x + 8

2·x² + 6·x =  8

2·(x² + 3·x) = 8

x² + 3·x = 8/2 = 4

x² + 3·x + (3/2)² = 4 + (3/2)² = 25/4

(x + 3/2)² = 25/4

∴ x + 3/2 = ±5/2

x = 5/2 - 3/2 or -5/2 - 3/2

x = 1 or -4

2) 8·x² + 16·x = 42

8·(x² + 2·x) = 42

x² + 2·x = 42/8 = 21/4

x² + 2·x + 1 = 21/4 + 1 = 25/4

(x + 1)² = 25/4

x + 1 = √(25/4) = ± 5/2

x = 5/2 - 1 or -5/2 - 1

∴ x = 3/2 or -7/2

3) -x² + 2·x = -3

-x² + 2·x = -3

-1×(-x² + 2·x) = -1 ×-3 = 3

x² - 2·x = 3

x² - 2·x + 1 = 3 + 1 = 4

(x - 1)² = 4

x - 1 = √4 = ±2

∴ x = 2 - 1 or -2 - 1

x = 1 or -3

Answer:

Step-by-step explanation:

area of side triangles=2(1/2×6×4)=24 units²

area of 3 rectangles=6×7+2(5×7)==42+70=112 units²

or=(6+5+5)×7=16×7=112 units²

Total surface area=24+112=136 units²

Answer:

x = 3

Step-by-step explanation:

log(4x - 10)32 is not properly formed; it's also ambiguous.

If you mean to say that (4x - 10) is the base, then you have to do the rather awkward typing shown below:

log               32     =      5

      (4x - 10)                                         (where (4x - 10) is assumed to

                                                             be the base)

                      log                32

                             (4x - 10)      

Then (4x - 10)                                 = (4x - 10)^5

or                                            32 = (4x - 10)^5, or

                                               2^5 = (4x - 10)^5

which tellus us that 2 = 4x - 10, or     4x = 12, or x = 3

Answer: tan(70)=x/800

Step-by-step explanation:

Since we are looking at the altitude and x and 800 are given, we will need tangent. Tangent is opposite/adjacent. We can eliminate sin(70). Between our 2 tangent choices, the answer is tan(70)=x/800. Tan(70)=800/x is very close but incorrect. 800/x is adjacent/opposite. That is not a trigonometric function. We are looking for opposite/adjacent.

Answer:

The answer is option D

Step-by-step explanation:

Just got it right on edge :)

Answer:

d

Step-by-step explanation:

Answer:

D) y=-5

Step-by-step explanation:

..............

Answer:

6.4

Step-by-step explanation:

By the Pythagorean Theorem:

[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]

Hope this helps!

Answer:

To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4

Answer:

complementary, b = 90 - 37 = 53

step-by-step explanation:

Answer:

see below

Step-by-step explanation:

These angles are complementary.

b + 37 = 90

b = 53°

Answer:

H' = (4, -2)

Step-by-step explanation:

Translating point H three units up and one unit right places it at (4, 2).

Then after a reflection across the x-axis, the y value is reversed, and the point is placed at (4, -2)

Answer:

Car M:

50.4/2 = 25.2

car M uses up 1 gallon every 25.2 miles

Car P:

Just from the graph, you can see that it uses up 1 gallon every 30 miles

The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.