Which of the following correctly measures the length (in cm) of the green box shown in the image below?

0.920 cm
0.92cm
0.9cm

Applying the trigonometry ratios, we have:

a. CD = 63.6

b. CD = 33.8

c. CD = 16.1

d. CD = 15.9

The trigonometry ratios are used to find a length or angle in any right triangle. They are:

a. ∅ = 32°

hyp = 75

adj = CD

Apply CAH:

cos 32 = CD/75

CD = cos 32 × 75

CD = 63.6

b. ∅ = 56°

opp = 28

hyp = CD

Apply SOH:

sin 56 = 28/CD

CD = 28/sin 56

CD = 33.8

c.  ∅ = 43°

opp = 15

adj = CD

Apply TOA:

tan 43 = 15/CD

CD = 15/tan 43

CD = 16.1

d.  ∅ = 27°

hyp = 35

opp = CD

Apply SOH:

sin 27 = CD/35

CD = sin 27 × 35

CD = 15.9

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Answer:

Step-by-step explanation:

x - 30 = 14 - 3x

    4x = 44

      x = 11

Let's call the unknown number x

Now let's decrease it by 30, that is x-30

Now let's write out "14 decreased by three times the number", that is 14 - 3x

The problem says these are the same, that is x - 30 = 14 - 3x

We now want to isolate, or solve for, x

Move the x to one side of the equation by adding 3x to both sides

3x + x -30 = 14 - 3x + 3x

4x -30 = 14

Now move the 30 to the right hand side by adding 30 to both sides

4x - 30 + 30 = 14 + 30

4x = 44

Now all we have to do to get x is divide both sides by 4

4x/4 = 44/4

x = 11

Answer:

⠀

Step-by-step explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

⠀

⠀

We know that,

⠀

So, According to the question :

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]

⠀

Therefore,

Answer:

33.3 is your answer

Step-by-step explanation:

The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Two cones A₁ and A₂ are similar.

The radius of A₁ = 2 cm

radius of A₂ = 3 cm

The surface area of A₁ = ? cm²

surface area of A₂ = 75 cm²

Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.

Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,

(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)

We can use this relationship to solve for the surface area of A₁:

(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)

Substituting the given values, we get:

(surface area of A₁) = (2/3)² × 75

(surface area of A₁) = 4/9 × 75

(surface area of A₁) ≈ 33.3 cm²

Therefore, (surface area of A₁) ≈ 33.3 cm²

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Answer:

C. 200 hours

Step-by-step explanation:

According to the given Question ,

It means that the aeroplane covers 400 miles in 60 minutes.

and it is asked for 30 minutes , so

We know that 30 minutes is equal to 0.5 hours

By the formula ,

Distance = Speed × Time

putting the values given , we get

= 400×0.5

Distance = 200 miles

Answer: 50 students

Step-by-step explanation:

You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →

1.2x = 60 → x = 50 students :)

Answer: 50 students

Step-by-step explanation:

x + .2x = 60

1.2x = 60

x = 60/1.2

x = 50

Answer:

-243

Step-by-step explanation:

{3׳ykx-7 incluye

Answer:

when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18

Step-by-step explanation:

When it has the same numbers for its numerator and denominator it will be 100%

Answer:

-12

Step-by-step explanation:

h(x) = ½x - 14 where x = 4:

h(4) = ½(4) - 14

= 2 - 14

= -12

Answer:

105

Step-by-step explanation:

nth term=a+(n-1)d (a=first term,d=difference)

a=6,d=9-6=3

34th term=6+(34-1)3

=6+(33×3)

=6+99=105

Answer:

Can you please give us figure of following ?

Answer:

its the last one 212°

212°

212°

212°

212°

212°

Step-by-step explanation:

212°

Answer:

c

Step-by-step explanation:

c

Answer:

r:
The function is

The remainder when f(x) is divided by x−2 is 23.

To find:The value of k.

Solution:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).

It is given that, the remainder when f(x) is divided by x−2 is 23. By using remainder theorem, we get

Put x=2, to find the value of f(2).Therefore, the value of k is 8.

Step-by-step explanation:

Answer:

Part A: [tex]x^2-30x+224\geq 0[/tex]

Part B: Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Since there are 2 question-

Let,

How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:

Let,

The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.

Be Part B:

Hint:

J=Jessica

30-J=Martha

(J-6)*((30-J)-6)<=80

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

Solve:

Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has

Let,

"x" be the number of cookies when Jessica started

"30-x" be the number of cookies when Martha started

Given us that:

Each of them ate 6 cookies from their bag

Therefore,  

Cookie left in each bag are:

(x-6) which is - Jessica

30 - x - 6 = (24 - x) - Martha

Solution - (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

Thus,

[tex](x-6)(24-x\leq 80[/tex]

[tex]24x-x^2-144+6x\leq 80[/tex]

[tex]-x^2+30x-144-80\leq 0[/tex]

[tex]-x^2+30x-244\leq 0[/tex]

[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]

[tex]x^2-30x+224\leq 0[/tex]

Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]

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

Solve:

Part B: Solve the quadratic equation:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]

[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]

[tex]14\le \:x\le \:16[/tex]

The solution is x=16 cookies

Thus, (30-x)=30-16=14 cookies

Now we know that;

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

So,

The number of cookies left in each bag  is equal to

Jessica:

16-6=10 cookies

Martha:

14-6=8 cookies

10 > 8

As a result, Jessica has at least 2 cookies more than Martha.

Fill in blank for:

The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.

Jessica has at least __2__ cookies more than Martha.​

~Lenvy~

Answer:

6xba^2 + 6yba^7 + 48ab

Step-by-step explanation:

To do this, you have to multiply 6ab by each of the inside terms,

So you can write it out like this

6ab (xa + ya^6 + 8)

6ab(xa) + 6ab(ya^6) + 6ab(8)

Then you can simplify:

6xba^2 + 6yba^7 + 48ab

(When you multiply the same variable by itself, you turn it into an exponent)

For example x * x = x^2

Or x^4 * x^3 = x^7

Answer:

each notebook would cost $4

Step-by-step explanation:

21-13=8.    8/2=4

x + 10 = - 6x - 18

7x = - 28

x = - 4

and y = - 4 + 10 = - 6

Answer:

c=5

Step-by-step explanation:

4(c-3)=8 Distribute

4c-12=8 Add 12 to both sides

4c=20 Divide by 4 on both sides

c=5

Answer:

Step-by-step explanation:

METHOD 1:

4(c - 3) = 8    |divide both sides by 4

4(c - 3)/4 = 8/4

c - 3 = 2     |add 3 to both sides

c - 3 + 3 = 2 + 3

c = 5

METHOD 2:

4(c - 3) = 8     |use the distributive property: a(b - c) = ab - ac

4 · c - 4 · 3 = 8

4c - 12 = 8      |add 12 to both sides

4c - 12 + 12 = 8 + 12

4c = 20     |divide both sides by 4

4c/4 = 20/4

c = 5

Answer:

1. 301.6 [tex]in^{3}[/tex]

2. 576 [tex]in^{3}[/tex]

3. 274.41 [tex]in^{3}[/tex]

Step-by-step explanation:

We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and [tex]\frac{12}{3} =4[/tex]. That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.

Then, you can find the volume of the box, because you know its dimentions are 12x12x4.

Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)

Answer:

[tex]2m[/tex]

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]

They give us the area as [tex]6m^2[/tex], so let's include it in the equation.

[tex]6 = \frac{1}{2}bh[/tex]

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that [tex]h = b-4[/tex]

So replace [tex]h[/tex] in the equation with [tex]b-4[/tex].

You will now get:

[tex]6 = \frac{1}{2}b(b-4)[/tex]

Now we can work towards solving. Let's get simplifying.

[tex]12 = b(b-4)\\12 = b^2 - 4b\\[/tex]

bring everything to one side so we can make a quadratic and factor:

[tex]0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2[/tex]

We get that [tex]b=6[/tex].

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that [tex]h = b - 4[/tex], so to find h, we just sub in our b value into that.

[tex]h = (6) - 4 = 2[/tex]

We find that [tex]h=2[/tex]

Answer:

Can u post a picture so I can see what your talking about!?

The vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

[tex]y=a(x-h)^2+k[/tex]

Here, (h, k) is the vertex point.

Substitute the values for h and k in the above vertex form.

[tex]f(x) = a(x -5)^2+ 3[/tex]

Use another point and substitute in values for x and f(x). Solve for a.

[tex]5 = a(6 - 5)^2 +3\\5-3=a(1)\\a=2[/tex]

Rewrite the function, using the values for h, k, and a. The function is

[tex]f(x) = 2(x -5)^2+ 3[/tex]

Hence, the vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

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Answer: 1st slot: 2 | 2nd slot: 5 | 3rd slot: 3 | correct on edge 2023!

Answer:

1/10

Step-by-step explanation:

There are ten options and Salad is one of them; therefore, the answer would be 1/10.

Answer:

LCM of 3 and 2 is 6

so, firstly we had to make the denominator same:-

[tex] \frac{2(2a + 1) + 3(3a - 1)} {6} [/tex]

[tex] \frac{4a + 2 + 9a - 3}{6} [/tex]

[tex] \frac{13a - 1}{6} [/tex]

Step-by-step explanation:

hope this helps you!!!

XxITSCHOCOLOVERxX

The simplified equation of [tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex] is [tex]\frac{13a-1}{6}[/tex]

[tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex]

[tex]\frac{2a+1}{3}+\frac{3a-1}{2} = \frac{2(2a+1)+3(3a-1)}{6}[/tex]

open the bracket in the numerator

Therefore,

[tex]\frac{2(2a+1)+3(3a-1)}{6}=\frac{4a+2 + 9a-3}{6}[/tex]

combine like terms in the numerator

[tex]\frac{4a+2 + 9a-3}{6}=\frac{4a+9a+2-3}{6}[/tex]

Hence,

[tex]\frac{4a+9a+2-3}{6}=\frac{13a-1}{6}[/tex]

Therefore, the final equation is as follows

[tex]\frac{2a+1}{3}+\frac{3a-1}{2}=\frac{13a-1}{6}[/tex]

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Answer:

4/12 and 3/8

Step-by-step explanation:

Answer:

392 square inches

Step-by-step explanation:
To solve this we need to look at this quadrilateral as two shapes that share a side - a triangle and a rectangle.

You can see in the attatchment how I have drawn a dotted line indicating where they share a side.

From here we find the area of each shape seperately and add those areas together!

Rectangle:
Looking at the rectangle portion we can see that the width is 16 in and the length is 19 inches.  Don't be fooled by the long 30 inch side.  Remember, we are only looking at the portion that makes up the rectangle.

A = l*w = 16*19 = 304 inches squared

Triangle:
To find the area of the triangle, we use the formula A = (b*h)/2 where b = the length of the base and h = the height.

We can see in this attatched drawing that the height of the triangle is the same length as the width of the rectangle which is 16 inches.  

To find the base, you can do one of two things.  

1) use the pythagorian theorem (A^2 + B^2 = C^2) to solve for the missing side of the right triangle, where A is 16 inches, B is unknown and C is 19.4 inches.

2) *easier* using the information given, we can see that the longest side of this shape is 30 inches and is made up of the length of the rectangle (19 inches) and the base of the triangle (which is unkown - we can call it x)

Given that we know the total length and the length of the portion that belongs to the rectangle, we can say x = 30-19 = 11.  Therefore the base of the rectangle is 11 inches.

From here we use b*h/2
11*16/2 = 88 = area of the triangle in square inches.

Now for the easy part - add up the areas for the total!
Area (rectangle) + Area (triangle) = Area (total)
304 + 88 = 392 square inches

Answer:

Slope formula;

y2(second y coordinate) - y1(first y coordinate)

____________________________________

x2(second x coordinate) - x1(first x coordinate)

Plug in values:

  2 - 1                 1

_______ = ________, your slope is -1/14.

-17 - (-3)            -14

Answer:

6

Step-by-step explanation:

-3x=-27+9

-3x=-18

x=-18/-3

x=6

Answer:

[tex]\displaystyle 6 = x[/tex]

Step-by-step explanation:

[tex]\displaystyle -3x - 9 = -27 \hookrightarrow \frac{-3x}{-3} = \frac{-18}{-3} \\ \\ x = 6[/tex]

I am joyous to assist you at any time.