Michael drove from home to work at an average speed of 45 mph. His return trip home took 45 minutes longer because he could only drive at 35 mph. Find the distance from his home to his work.

Answer:

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

4|3x-1| + 3 > 11

4|3x-1| > 11-3

4|3x-1| > 8

|3x-1| > 2

3x-1>2 or 3x-1<-2

3x>2+1 3x<-2+1

3x>3 3x<-1

x>1 x<-1÷3

Solution: ]-♾️ , -1÷3 [ U ] 1,+♾️ [

The rate of the plane in still air is 870km/h and the rate of the wind 210km/h.

Speed has the dimensions of distance divided by time.

Let Speed of airplane be x km/h and Speed of Wind be y km/h

Speed direction of wind (x+y)

Speed in opposition of wind (x-y)

Now, using speed x time= distance

7( x-y)=4620

(x-y)=4620/7

=660------------------(1)

Similarly,

8(x+y)=8640

(x+y) =8640/8=1080-----------------------(2)

Adding (1) and (2)

2x=1740

x=870 km/h

Subtracting (1) from (2)

2y=420

=>y=210 km/h

So rate of airplane =870km/h

rate of wind=210km/h

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The volume of the bottom section of the figure is:

V = 48 cm³

Remember that for a rectangular prism of length L, width W, and height H, the volume is V.

V = L*W*H

For the bottom section the dimensions are:

Length = 6cm

Width = 4cm

Height = 4cm - 2cm = 2cm

Replacing these in the volume equation we get:

V = (6cm)*(4cm)*(2cm) = 48cm³

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Answer:

Step-by-step explanation:That’s t up to you STOP CHEATING!!

Answers: sin(2∅) = 120/169,  cos(2∅) = 119/169, tan(2∅) = 120/119

Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.

Analysis:

If cos∅ = adjacent/hypotenuse =  12/13,

Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5

sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12

sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169

cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169

tan(2∅) = sin(2∅) / cos(2∅)  = 120/169 ÷ 119/169 = 120/119

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Answer:

12,500,000

Step-by-step explanation:

2^5 = 2×2×2×2×2 = 32

5^8 = 5×5×5×5×5×5×5×5 = 390625

32×390625 = 12,500,000

Hope you understood and brainliest please

Answer:

p = 14 inches

Step-by-step explanation:

using either the sine or cosine ratios

using the sine ratio and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{p}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

p = 14

The steps are shown on the screenshots as well.

The trig ratios used were sine and tangent

Make sure your calculator is in degree mode.

The mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The question is incomplete.

The complete question is in the picture please refer to the picture.

We have given an arithmetic expression:

[tex]=\dfrac{9}{2}+3\left(4-1\right)-7+2^3[/tex]

Step 1:

[tex]=\dfrac{9}{2}+3(3)-7+2^3[/tex]

Step 2:

[tex]=\dfrac{9}{2}+3(3)-7+8[/tex]

Step 3 should be:

[tex]=\dfrac{9}{2}(3)-7+8[/tex]

The mistake made in the step 3

Thus, the mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,

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Let S be the given sum, so

[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]

[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]

Multiply both sides by 1/4.

[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]

Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :

[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

Solve for S :

[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]

[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]

Therefore, the number of sides is 11.

The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.

In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.

The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:

It is to be noted that referenced plots are not indicated hence, the general answer.

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The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.

What is a Stem-and-Leap Plot?

In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.

The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:

Minimum

First Quartile

Median (Second Quartile)

Third Quartile; and

Maximum.

It is to be noted that referenced plots are not indicated hence, the general answer.

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Answer:

V ≈ 662.68

Step-by-step explanation:

15 div by 2 = 7.5 (Radius)

7.5 x 1.5 = 11.25 (height)

Pi x 7.5^2 x 11.25/3
= 662.68

Answer:

-5 degrees is colder than -3 degrees farienheight.

Step-by-step explanation:

Let's take this and eliminate every answer-

"The lowest temperature is -3 degrees."

-5 is lower than -3.

"The highest temperature is -5 degrees."

-5 degrees is the lowest temperature, not the highest!

"-5 is warmer than 3 degrees."

-5 is the LOWEST TEMPERATURE.

This leaves us with "-5 is colder than -3 degrees," which is correct because -5 is the smallest temperature and therefore, it is the coldest.

Answer: 330 pupils

Step-by-step explanation:

the number of pupils are in the lower school

= (1- 1/5 - ¼) × 600

= (20/20 - 4/20 - 5/20)×600

= (11/20) ×600

= 330 pupils

Answer: 818.4

Step-by-step explanation:

Using the area of a sector formula, we get the area of the entire sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)[/tex].

Using the formula [tex]A=\frac{1}{2} ab \sin C[/tex], we get the area of the triangle is [tex]\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ})[/tex].

So, the area of the shaded sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)-\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ}) \approx \boxed{818.4}[/tex]

A fraction is a way to describe a part of a whole. The fraction that can replace the question mark is 1/2.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The fraction that can replace the question mark is,

9 × ? = (3/2) + (3/2) + (3/2)

9 × ? = 3(3/2)

9 × ? = 9/2

9 × ? = 9/2

? = 9/(2×9)

? = 1/2

Hence, the fraction that can replace the question mark is 1/2.

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Answer: $409.55

Step-by-step explanation:

100% - 16% = 84%

84% of 487.56 = 409.5504.

Round to nearest hundredth.

$409.55

In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."

According to the question,

Given

Length of AE=5.2

Length of  AC=11.7

Length of  CD=10.5

As shown in figure

In trapezoid ABCD,

AB is parallel to CD, AC is the transversal.

AC and BD intersect at point E.

In ΔABE and ΔCDE,

∠BAE ≅∠ECD

∠ABE ≅∠EDC

By AA theorem,

ΔABE ~ ΔCDE

Therefore,

[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]

  AE + EC = AC

⇒ 5.2 + EC = 11.7

⇒ EC = 11.7 - 5.2

⇒ EC = 6.5units

Substitute the value in the given proportion we get,

   [tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]

⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]

⇒[tex]AB = 8.4[/tex] units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.

Bobblehead:

Ticket:

It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.

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Answer:

si quroma mande' cromo jajaja

Step-by-step explanation:

Answer:

f(10) means to input x = 10 into the function.

From inspection of the given function:

[tex]\sf f(10)=\dfrac{10}{2}=5[/tex]

the "10" is the numerator of the fraction.

Therefore, swap the "10" for "x" to give the function in terms of x:

[tex]\sf f(x)=\dfrac{x}{2}[/tex]

For a function

x is the input or domain

y is the output or range

Here

So

x=10

y=10/2

Hence the function is

The answer is no solution.

Answer:

Step-by-step explanation:

this year you earned $75500. Last year you earned $72400. What the rate of change on your earnings since last y?

Answer:

J

Step-by-step explanation:

To find perimeter we add. 10+6 is 16. The third side has to be much bigger than this. So, J is the answer and J is 19 which wouldnt make sense as the length of the third side.

#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

Answer:

6 23/25

Step-by-step explanation:

[tex]0.92\\\\\frac{0.92\cdot \:100}{100}\\\\=\frac{92}{100}\\\\= \frac{4\cdot \:23}{4\cdot \:25}\\\\=\frac{23}{25}\\\\= 6+\frac{23}{25}\\\\=6\frac{23}{25}[/tex]

Answer:

The twins are 21 years old right now.

(x+4) + (x+4) = 50

Step-by-step explanation:

Let x = the current age of one of the twins.

They are twins, that means they are the same age. So the other twin is also x years old.

In four years, the age will be x+4.

Both of them together will be:

(x+4) + (x+4)

The question says that total (of their ages in 4 years) will be 50.

(x+4) + (x+4) = 50

Combine like terms.

2x + 8 = 50

Subtract 8.

2x = 42

Divide by 2.

x = 21

The twins are currently 21.

To check: in four years they will be 25; then the sum of their ages will be 50. Check! Hope this helps!