Yuki wants to make a reduced-size copy
of a drawing. The original drawing is
14 inches long. Yuki's copier can only
reduce by 75%. Find the length of a copy
after Yuki reduces it 4 times at 75% each
time. Round your answer to the nearest
hundredth of an inch.

Answer:

60466176

Step-by-step explanation:

Volume is a three-dimensional scalar quantity. The volume of the composite figure is 14 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the composite figure is,

Volume = (1/3 ×1.5 × 2 × 2) + (2 × 1.5 × 4)

             = 2 ft³ + 12 ft³

             = 14 ft³

Hence, the volume of the composite figure is 14 ft³.

Learn more about Volume:

https://brainly.com/question/13338592

#SPJ1

We use Tan in this case:

Tan=(opposite/adjacent)

Tan(36)=23/x

x=23/Tan(36)

x=31.64 length

Hope it helps!

Answer:

x ≈ 31.64

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

The given trigonometric ratios all use the angle of 36°.

From inspection of the given diagram:

Therefore, we should use the tan trig ratio.

[tex]\implies \sf \tan(36^{\circ})=\dfrac{23}{x}[/tex]

[tex]\implies \sf x=\dfrac{23}{\tan(36^{\circ})}[/tex]

Substituting the given value for tan 36°:

[tex]\implies \sf x \approx \dfrac{23}{0.727}[/tex]

[tex]\implies \sf x\approx31.64[/tex]

The answers are given below:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

1. (cos x. cos y)(tan x + tan y) = sin (x+ y)

  (cos x. cos y)(tan x + tan y)

= cos x. cos y (sinx/ cos x + sin y/ cos y)

= sin x cos y + sin y cos x

= sin (x+ y)    [ sin ( x +y)]= sin x cos y + sin y cos x

= RHS

3. [tex]-\sin ^2\left(x\right)-\cos \left(2x\right)=0[/tex]

Using identity

[tex]-\cos ^2\left(x\right)=0[/tex]

cos ² x=0

Applying [tex]x^{n} =0[/tex] then x=0

So, cos x =0

General solution will be [tex]x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

Learn more about trigonometry here:

https://brainly.com/question/12537661

#SPJ1

32/40 = 24/dg

32dg = 40 x 24

32dg = 960

dg = 960/32

dg = 30

Answer: DG = 30

Answer:

Step-by-step explanation:

these are 2 similar triangles, so we can solve with an equation

FC : CE = DG : ED

24 : 32 = x : 40

x = 24 * 40 : 32

x = 960 : 32

x = 30

DG = 30 units

------------------------------

24 : 32 = 30 : 40

0.75 = 0.75

The answer is good

Answer:

  (a)  Horizontal line test

Step-by-step explanation:

A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.

The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.

If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.

A function will have an inverse function if it passes the Horizontal Line Test.

__

Additional comment

The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.

The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.

Answer:

B

Step-by-step explanation:

We see the graph of y=x², so eliminate A.

Since the second graph opens downwards, the coefficient of x² must be negative, so eliminate C.

Also, the axis of symmetry is x = 0, so eliminate D.

This leaves us with B

Answer:

sorry i dont know the answer .

Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

7[tex]\sqrt{2}[/tex]

The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.

If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.

Special Right Triangles

Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.

Formulas

All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).

In these triangles, both of the legs are congruent.

Solving for c

Since we are given b, we can just plug the b-value into the formula that solves for c.

The answer cannot be simplified further, so this is the final answer.

Answer:

Second option

Step-by-step explanation:

It is a right triangle isosceles

a = b = 7

c = hypotenuse

[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]

Hope this helps

Answer:

cos65 = sin25 = p

tan205 = tan25 = p/√(1-√p)

Step-by-step explanation:

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec)

some Trigonometric identities used in the question:

in the question it is given,

sin25 = p

using above mentioned identity:-

cos 65 = cos(90-25) = sin25 = p

hence value of cos65 is p.

for, tan205 we have to first find the cos25

so to find cos25 we use above mentioned identity,

cos²25 + sin²25 = 1

cos²25 + √p      = 1

cos²25               = 1-√p

cos25               = √(1-√p)  

now to find out tan205 use third identity mentioned above,

tan205 = tan(π+25) = tan25

tan25 = sin25/cos25

tan25 = p/√(1-√p)  

learn more about trigonometry at

https://brainly.com/question/26719838

#SPJ10

Answer:

a) 19 cm

Step-by-step explanation:

Area of a parallelogram: b • h

Given values:

Substitute these values into the formula:

⇒ A = b • h

⇒ 228 = b • 12 [multiply]

⇒ 228 = 12b [divide both sides by 12]

⇒ 228 ÷ 12 = 12b ÷ 12

⇒ 19 = b

Therefore, the base of the parallelogram is 19 cm.

Answer:

C

Step-by-step explanation:

if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C

It's whichever graph is an absolute function and is shifted to the right by 2 and is shifted down by 1.

Since I don't have a picture of the graph this is the best I can do to help.

Answer:

see attached

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Given function:

[tex]r(x) = |x - 2| - 1[/tex]

The parent function of the given function is:  [tex]f(x) = |x|[/tex]

Translated 2 units to the right:  [tex]f(x-2)=|x-2|[/tex]

Translated 1 unit down:  [tex]f(x-2)-1=|x-2|-1[/tex]

Graph of Modulus function

Line y = x where x ≥ 0

Line y = -x where x ≤ 0

Vertex at (0, 0)

Therefore, the graph of the given function is the graph of the modulus function translated 2 units to the right and 1 unit down.  So, its vertex is at (2, -1).

Learn more here:

https://brainly.com/question/27815602

The closest benchmark for 99% is 100%.

We know that benchmarks in mathematics are the norm or point of comparison that something can be measured, compared, or evaluated against. Benchmark values are values that can be used to estimate and contrast other values or quantities. Typically, benchmark figures are multiples of 10 or 100. 0 percent, 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent are the most popular benchmark percentages.

Here we have to find the closest benchmark for 99%. Clearly, from the definition 100% is the required answer.

We can conclude that the closest benchmark for 99% is 100%.

Know more about the benchmarks here -

https://brainly.com/question/1201714

#SPJ10

9x + 3 = 30
9x = 27
x = 3

Then 3x + 1 = 3 * 3 + 1 = 10

[tex]9x + 3 = 30 \\ \\ 9x = 30 - 3 \\ \\ 9x = 27 \\ \\ x = \frac{27}{9} \\ \\ x = 3.[/tex]

putting x = 3 in 3x + 1

[tex]3x + 1 \\ \\ 3 \times 3 + 1 \\ \\ 9 + 1 \\ \\ 10.[/tex]

The value of 3x + 1 is 10.

Answer:

The equation of the graph is   y = -lx - 4l - 1.

Step-by-step explanation:

As the values of y are same before and after (4, -1)

the slope of the graph is change on point (4, -1)

the equation of first line is

y - (-1) = 1 (x -4)

the equation of the second line is:

y - (-1) = -1 (x - 4)

As value of y should remain same in both equations

therefore: y - (-1) = - lx - 4l

y = - lx - 4l -1

The equation of the graph is   y = -lx - 4l - 1.

Learn more about to write equation from graph here - https://brainly.com/question/8498923

#SPJ10

The value of the expression, g/2 + 3 when x = 8 is: 7.

Given the expression, g/2+3, to find it's value when g = 8, plug in the value of g into the expression and solve.

g/2 + 3

8/2 + 3

Divide

4 + 3

= 7

The value of the expression is: 7.

Learn more about evaluating an expression on:

https://brainly.com/question/4009675

#SPJ1

Answer:

lets make this like a table

x   y

3=21

4=28

5=35

so since y is bigger lets divide that by x

21/3=7

so the rate of change is 7

Hope This Helps!!!

The quadratic is continuous over its entire domain, which is to say we can evaluate the limit by direct substitution:

[tex]\displaystyle \lim_{x\to-3} (x^2 - 2x + 4) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = \boxed{19}[/tex]

You are mistaking (-3)² for -3². They are not the same number.

(-3)² = (-1 × 3)² = (-1)² × 3² = 1 × 9 = 9

-3² = -1 × 3² = -1 × 9 = -9

Answer:

[tex]2*2^1^/^4[/tex]

(≈2.378)

Step-by-step explanation:

we know that:

[tex]a^x*a^y=a^x^+^y[/tex]

[this is the same as multiplying any exponents]

3/4 + 1/2 = 1 + 1/4

if [[tex]a^x*a^y=a^x^+^y[/tex]], then [[tex]a^x^+^y=a^x*a^y[/tex]] must also be true

so,

[tex]2^1^+^1^/^4=2^1*2^1^/^4\\[/tex]

= [tex]2*2^1^/^4[/tex]

([tex]2^1^/^4 = 1.189207115[/tex])

1.189207115 · 2 = 2.37841423001

(rounded to 2.378)

Answer:

[tex]2*2^1^/^4[/tex]

(2.37841)

Explanation:

3/4 + 1/2 = 1 + 1/4

= [tex]2*2^1^/^4[/tex]

([tex]2^1^/^4 = 1.189207115[/tex])

(2)(1.189207115) = 2.37841423001

Answer:

c = 5√5

Step-by-step explanation:

When we have a right triangle, there is a property about its measurements that is always true, and its called the "Pythagorean Theorem"

First, let's understand the basic terms we use to describe the sides of a triangle:

we can call one leg "a", the other leg "b" and the slanted side "c"

("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)

the pythagorean theorem:

a² + b² = c²

here, our "a" is 5, our "b" is 10 {and we don't know what c is}

let's try plugging these values into our formula:

a² + b² = c²

5² + 10² = c²

25 + 100 = c²      

125 = c²

now, we know what c² is--but we want to know c,

so we must take the square root of both sides

√125 = √c²

√125 = c

now, while √125 is our answer, we can simplify further!

this is because 125 can be made up of 5 · 25

so, [tex]\sqrt{125} = \sqrt{5*25}[/tex]

and

[tex]\sqrt{5*25}=\sqrt{5}*\sqrt{25}[/tex]

we can take out the square root of 25 (5):

[tex]=\sqrt{5}*5[/tex]

we write this as such: [tex]5\sqrt{5}[/tex]

so, in simplest radical form, c = 5√5

(√125)

hope this helps!! have a lovely day :)

Answer:

x=3

Step-by-step explanation:

6x-3x=16-7

3x=16-7

3x=9

x=3

The total amount of money Ethan made in a week including commission is $812.5

Amount of commission earned = 25% of $1250

= 25/100 × $1,250

= 0.25 × 1250

= $312.5

Total earnings = Base salary + Amount of commission earned

= $500 + $312.5

= $812.5

Learn more about income:

https://brainly.com/question/13793671

#SPJ1

Answer:

5, 8, 11, ...

Step-by-step explanation:

f(n)=3n+2

the first three terms will be f(1), f(2), and f(3).

f(1)=3(1)+2=5

f(2)=3(2)+2=8

f(3)=3(3)+2=11

Hope this helps!

If not, I am sorry.

Answer:

i think the answer is C. 1/2

When we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

The given function is [tex]y=2-\sqrt{x}[/tex].

We need to find which is the graph of the given function from the options.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Take, x=0, 1, 4, 9, 16, 25, 36,....

Now, when x=0, y=2.

When x=1, y=1.

When x=4, y=0.

When x=9, y=-1

So, when we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

To learn more about graphs visit:

https://brainly.com/question/16608196.

#SPJ1

Answer:

fraction:4/10 or 2/5

decimal: 0.4

percent: 40%

Step-by-step explanation:

The rectangle is divided into 10 parts, this is a total number that goes on the bottom of a fraction. 4 parts are shaded, that number goes on the top of the fraction.

4/10 is shown in the image. But 4/10 can be reduced. You should always simplify a fraction when it is possible.

4/10 = 2/5

As for the decimal, 4/10 spoken, "four tenths" tells you the decimal 0.4 (we all say "point four", but this is properly called "four-tenths" also) You can divide, because a fraction bar is a division symbol:

4÷10 OR 2÷5 and you will get the decimal 0.4

To change the decimal to a percent, multiply by 100.

0.4 × 100 is 40

0.4 is 40%

fraction:: 4/10 or 2/5 (simplified)

decimal: 0.04

percentage: 4%