& triangle is inscribed
in a rectangle, as shown below. What is the area of the shaded
region?
5 cm
3 cm
5 cm
11 cm
A. 40 cm2
C. 47.5 cm2
B. 62.5 cm2
D. 22.75 cm2

Answer:

73.3 cm

Step-by-step explanation:

As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;

So, if we substitute a = 3, in our Formula, it will yield to

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]

Now, as we know that, for any triangle we also have a formula that is ;

Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having

[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]

[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]

[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]

Answer:

x=6

Step-by-step explanation:

(I don't know if you mean question 2 3x= 18 or 2 times 3x = 18)

2.3x = 18
3x = 18 / 2 = 9
x = 9/3 = 3

Or : x = 18/3 = 6

Answer:

Step-by-step explanation:

Solution:

Volume of the rectangular prism formula:

[tex]: \Longrightarrow \sf{V=l*w*h}[/tex]

Given:

Then, you multiply.

[tex]\sf{32*10*16=\boxed{\sf{5120}}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

2.3<x<8.7

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Length of a circle = circumference = 2πr = 24π

                                            Radius (r) = 24π/2π

                                                             = 12cm

Using an exponential function, it is found that it's annual growth rate is of 4%.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:

A(10) = 1.5A(0).

Thus:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]1.5A(0) = A(0)(1 + r)^{10}[/tex]

[tex](1 + r)^{10} = 1.5[/tex]

[tex]\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}[/tex]

1 + r = 1.04.

r = 0.04.

0.04 x 100% = 4%.

It's annual growth rate is of 4%.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

6 tomato plants

Step-by-step explanation:

[tex]18\frac{1}{6}= \frac{18\times6+1}{6}=\frac{108+1}{6}= \frac{109}{6}[/tex]

[tex]2\frac{2}{3}= \frac{2\times3+2}{3}=\frac{6+2}{3}= \frac{8}{3}[/tex]

then the number of tomato plants that Jordan will be able to put a fence around using this roll :

[tex]\frac{\frac{109}{6}}{\frac{8}{3}}= \frac{109}{6}}\times\frac{3}{8} = \frac{109}{2}}\times\frac{1}{8}= \frac{109}{16} = 6.8125[/tex]

then he can put fence only around 6 plants.

Answer: 10m +27

Step-by-step explanation: Add all the sides together to calculate Perimeter.

2(2m +10)+2m+7+2m +2m

4m + 20 + 2m +7 +2m +2m

10m +27

Answer:

$20.9

Step-by-step explanation:

First you find what 45% of the cost is:

0.45 x 38 = 17.1

Then, because this is a special/decrease in original price, you subtract:

38 - 17.1 = 20.9

$20.9

Probably between obtuse angle or triangle because sometimes they trick you

But I'm not 100 percent sure

Answer:

It is right

Step-by-step explanation:

Right triangles will always form a corner like an L shape

Answer:

-3

Step-by-step explanation:

I don't know what u r trying to find out so pls tell me what u r trying to find out.

But if u r trying to find out y here,

It is impossible to find out value of y, as we don't have the value of a or any other hints which will help in finding y.

But we can write the equation in a different way,

that is...

A - y = - 16°

Answer:

9 x 2/8 = 9/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 divided by 2/8 but make the 2/8 into a decimal and the turn back to a fraction if it ask if not then leave it how it is and if you have to round which you prolly wont have to but ask to make sure ight

Answer:

The Answer is C. 50

Step-by-step explanation:

To pack 600 granola bars, 50 boxes are needed.

The correct option is C.

To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.

Number of boxes = Total granola bars / Granola bars per box

Number of boxes = 600 / 12

Number of boxes = 50

So, 50 boxes are needed to pack 600 granola bars.

The correct answer is option C: 50.

To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ3

A=(1/2)(b1+b2)h =

=(48x+68)in² = (1/2)( b1+(9x+12))8

=b1= 3x+5

Answer:

[tex]6^{6}[/tex]

Step-by-step explanation:

When the coefficient is the same (in this case it is 6), you can subtract the exponents when it's being divided.

So in this case, the exponents are 9 and 3. The 9 is being divided by the 3, So:

[tex]6^{9-3}[/tex]

[tex]6^{6}[/tex]

Answer:

rotation

Step-by-step explanation:

reflection

Answer:

rotation then translations-- C

Step-by-step explanation:

yes. and bc taking the quiz rn

Answer:

wheres the question ?

Step-by-step explanation:

The possible number of different phone numbers will be 128000000

The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

In this exercise we have to use the knowledge of probability to find the phone number, so:

1 280 000 000 different ways.

First we have to establish some information about this exercise such as:

Thus, now calculating the possibilities of occurrence, we have:

[tex]8\times 2\times 10=160[/tex]

[tex]8\times 10^6=8000000[/tex]

[tex]160\times 8000000=1280000000[/tex]

See more about probability follow

brainly.com/question/795909

Answer:

1/18

Step-by-step explanation:

probability of getting a three= 1/6

probability of getting a three on a wheel=1/3

probability of winning= 1/6x1/3=1/18

The angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

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

(c is opposite side to angle A)

Consider the diagram attached below.

In the diagram given, we have:

AB = tree with length of 45 ft

AC = cable, with length of 'x' ft (assume)

BC = distance of the base of the cable from the base of the tree of measurement 30 ft.

AD = vertical height of the point A (the top of the tree and cable) from the ground of 'h ft' (assume),

Using the cosine rule for the triangle ABC, taking:

|AC| = x = length of the side opposite to the known angle

|AB| = 45 ft and BC = 30 ft are rest of the two sides,

Angle opposite to AC is of 86°

Thus, we get:

[tex]45^2 + 30^2 -2(30)(45)\cos(86^\circ) = x^2\\\\2925 - 188.34 \approx x^2\\\\x \approx \sqrt{2736.66} \approx 52.31 \: \rm ft[/tex]

(took positive root because of x being length, which is a non-negative quantity).

For triangle ABD, using the sine ratio from the perspective of angle A, we get:
[tex]\sin(m\angle A) = \dfrac{\text{side opposite to A}}{\text{length of hypotenuse}} \\\\\sin(86^\circ) = \dfrac{h}{45}\\\\h = \sin(86^\circ) \times 45 \approx 44.89 \: \rm ft[/tex]

Now, for the triangle ACD, using the sine ratio from the perspective of angle C (smaller than 90°), we get:

[tex]\sin(m\angle C) = \dfrac{\text{side opposite to C}}{\text{length of hypotenuse}} \\\\\sin(\theta^\circ) = \dfrac{h}{x} \approx \dfrac{44.89}{52.31} \approx 0.858\\\\\theta =\sin^{-1}(0.858) \approx 59.09, 120.90[/tex]

Taking the angle smaller than 90°, we get:

[tex]\theta \approx 59.09^\circ \approx 59^\circ[/tex]

Thus, the angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

Learn more about law of cosines here:

https://brainly.com/question/17289163

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Answer:

That wasn't the correct answer

Step-by-step explanation:

c^2=45^2+30^2 - 2(45)(30)*Cos(94

c^2=2925+188.3425

c^2=3113.3425

take the square root:

c is approx. 55.8

sin86/55.8=sinx/45

55.8sinx=45sin94

divide both sides by 55.8

sinx=0.8045

sin^-1(0.8045)=53.6

Answer is 53.6 or "L" on the scavenger hunt worksheet

Step-by-step explanation:

12(5 + 3x) + 18

60+36x+18

C)36x+78

Answer:

0.0016

Step-by-step explanation:

Hope this helps!

Answer:

[tex]\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]4 - 3 \sec ^ { 2 } \theta = 0[/tex]

Let's solve this.

Isolate sec²θ.

[tex]4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}[/tex]

Now, we now that, cos θ is the reciprocal of sec θ. Therefore,

[tex]\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}[/tex]

Bring the square root on both the sides of the equation to remove the square.

[tex]\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}[/tex]

If,

[tex]\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Also if,

[tex]\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

8/75 is the answers for the question

Answer:

n²+n+2

Step-by-step explanation:

1)Find the difference between the numbers.

Difference= +1,+2,+3,+4,+5

2)Find the second difference between the first differences.

Difference= +1 each time

2 differences=Quadratic sequence

3)Quadratic Sequence Equation= an²+bn+c

Find the values of a, b and c by using these terms:

a (bottom)

2a+b (middle)

a+b+c (top)

4)Substitute values into equation

a=1    b=1    c=2

n²+n+2

Answer:

what is there supposed to be a picture

Answer:

Down Here ↓↓↓

Step-by-step explanation:

Hello!

Standard Form of a Quadratic: [tex]ax^2 + bx +c[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

To solve a quadratic using the quadratic formula, you have to plug values in for "a", "b", and "c" into the quadratic equation. Let's go over an example question.

Question: [tex]2x^2 +4x+2[/tex]

Solution:

Determine the values of "a", "b", and "c".

Plug it into the quadratic equation to solve.

Solve:

The value of x is -1.