Mathematics High School

how do I get from step 3 to step four? please explain.
sin x = opposite over hypotenuse
sin 45° = 50 over x
0.707106781 ≈ 50 over x
(0.707106781)x ≈ 50
x ≈ 70.71

Answers

Answer 1
step three to step four, you would need to find the square root of 0.707106781 and 50
Hope this helped :*

Related Questions

Select all of the following expressions that are equal to 2.5.
5 ÷ 2
-2(-1.25)
(-0.5)^2
-1 + (-1.5)

Answers

the first one, the second one, the fourth one

answer is
a) 5/2 = 2.5
b) -2(-1.25)

Solve the system of equations. 2.5y + 3x = 27 5x – 2.5y = 5 What equation is the result of adding the two equations? –8x = 328x = 325y + 8x = 328x – 5y = 32 What is the solution to the system? (–4, 6)(–2.75, 8.6)(2.75, 3.5)(4, 6)

Answers

a) The result of adding the two equations is
.. (2.5y +3x) +(5x -2.5y) = (27) +(5)
.. 8x = 32 . . . . . . . . . . . . . . . . . . . . . . . your 2nd selection

b) The solution to the system is (4, 6), your 4th selection.
.. This is the only choice with x=4, the solution to part (a).

Answer:

8x=32

(4,6)

Step-by-step explanation:

How do you write
2/4
as a percentage?

Answers

you would right 2 fourths in a percentage is 50%
2/4 is 50% your welcome 

Marie earns $96 in interest each year on an investment what is the rate of simple interest if her principal was $800

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$96\\ P=\textit{original amount deposited}\to& \$800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &\stackrel{each~year}{1} \end{cases} \\\\\\ 96=800(r)(1)\implies \cfrac{96}{800}=r \\\\\\ 0.12=r\implies r\%=100\cdot 0.12\implies r=\stackrel{\%}{12}[/tex]

The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).

To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.

The formula for simple interest is:

Interest = Principal * rate * time

Assuming the interest earned is for one year, we have:

$96 = $800 * rate * 1 year

To find the rate, we divide both sides by $800:

rate = $96 / $800

rate = 0.12

Converting into a percentage, the simple interest rate is 12% per year.

what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π

Answers

All the similar circles have π in common.

Thus, option (c) is correct.

When two circles are similar, it means they have the same shape but possibly different sizes.

However, the ratio of their corresponding lengths, including the circumference, remains constant.

Second, the ratio of the diameter will be constant but not congruent.

Third, the value of π is the universal constant whose value is 22/7 or 3.14.....

which is the same for every similar circle.

Thus, π has a common value.

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this is a physics question that requires a lot of math. Hoping on of you genius could help me.

Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .

How much distance is between you and the deer. I solved this =23m

What is the maximum speed you could have and still not hit the deer?

The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.

Answers

I don't know why you need the quadratic formula.  

If it takes 0.5 seconds before stepping on the breaks while going 16 m/s, then you travel 8 meters before anything happens. That means you are 44-8 = 36 meters away from the deer now. 
 v^2 = v_initial^2 + 2(acceleration)(distance)
 0 = (16 m/s)^2 + 2(-10m/s^2)(distance)
 256 m^2/s^2 / (2(10 m/s^2) = distance = 12.8 meters (13 meters after significant figures are taken into account). 
 The maximum speed would be: 
 0 = v_initial^2 + 2(-10m/s^2)(36m)
 v_initial^2 = 720m^2/s^2
 v_initial = 27 mph

Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .

1. k(x) = 2x + 3x + 2                   k(x) = g(x) ∘ h(x)

2. k(x) = 2x - 3x - 2                   k(x) = g(x) + h(x)

3. k(x) = (3x)2-x + 2-x + 1           k(x) = h(x) ÷ g(x)

4. k(x) = 23x + 2                            k(x) = g(x) - h(x)

5. k(x) = 2x(3x + 2)                     k(x) = g(x) × h(x)

6. k(x) = 3(2x) + 2                  k(x) = h(x) ∘ g(x)

Answers

the correct functions are
h(x) = 3x + 2  
g(x) = 2^x

I proceed to calculate the different values ​​of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )
 
case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.)  k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2 

case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2 

To simplify the other user's answer (which is correct):

1 = B

2 = D

3 = C

4 = A

5 = E

6 = F

Alternatively, your right boxes should look like:

4

1

3

2

5

6

What is the point called where the perpendicular bisectors of the sides of a triangle intersect

Answers

Answer: Circumcenter

This is the center of the circle that goes through the three vertices of the triangle. This circle is known as the circumcircle. It is the smallest circle possible in which the circle encompasses the triangle and none of the triangle spills outside the circle. 

A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)

Answers

This is a step function because it increases in "steps".  The wage stays constant for a 4 year period, then jumps by $2 instead of a steady increase.
Final answer:

To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.

Explanation:

To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.

The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.

So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.

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A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the building will the ladder touch if the ladder is 10 ft long and the base of the ladder is 6 ft from the base of the building?

Answers

The given question describes a right triangle with the hypotenuse as 10 ft and one of the legs as 6 ft.

We can make use of Pythagoras theorem to evaluate the length of the other side.

We know that by Pythagoras theorem, the square root of the sum of the squares of the legs of a right triangle gives the hypotenuse. Let the length of the required leg be x, then

[tex] x^2+6^2=10^2\\ \\ \Rightarrow x^2=100-36=64\\ \\ \Rightarrow x=\sqrt{64}=8. [/tex]

Therefore, the ladder reached 8 ft high on the building.

Which equation has the graph that is a parabola with a vertex at 5,3

Answers

We can solve this using vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
In our case h=5 and k=3, these are coordinates of our vertex point. 
There is no way to find a without knowing any other coefficients.
When you start solving some equations to get the parameters you always end up with identity (example 25=25). This means that your equation has an infinite number of solutions. In other words, any a will give you a parabola with vertex at the specified point.
The final answer would:
[tex]y=a(x-5)^2+3[/tex]
Where a is any real number.

How do you solve this inequality: 7 ≤ x+11

Answers

solve the inequality like an equation
7 ≤ x + 11
subtract 11 from both sides
-4 ≤ x

From there on, any number greater than or equal to -4 will be a solution to the inequality 

Hope this helps
How do you solve this inequality: 7 ≤ x+11

[tex] 7 \leq x+11 \\ \\ 7 -11\leq x \\ \\ -4 \leq x\qquad\to\qquad x\in \left[-4; +\infty) [/tex]

Can someone please help me with 4?? I’m really struggling.

Answers

4) given is that
m<DAC=y
m<BAC=3x

ABCD is a square so m<DAB = 90° because each angle in a square is a right angle so 3x+y=90° (1) ;
AC is a diagonal in the square so m<DAC=m<BAC so 3x=y (2);

Find x by substituting y to 3x from (2) into (1)
3x+3x=90
6x=90
x=90/6=15°

Answer x=15°


Write an expression to represent: four more than the product of three and a number xxx.

Answers

The number is x

product of 3 and the x = 3x

four more = 3x + 4


Answer:

x-4

Step-by-step explanation:

Trapezoid RSTV∼trapezoid WXYZ .

What is the scale factor of a dilation from RSTV to WXYZ ?

a. 14/25

b. 4/5

c. 7/8

d. 7/10

Answers

Answer:

Correct option is D

Scale factor of dilation is [tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Given the two similar figures

Trapezoid RSTV∼trapezoid WXYZ

We have to scale factor of dilation from RSTV to WXYZ.

As the two trapezoid are similar therefore their ratio of corresponding sides gives the scale factor of dilation.

Hence, [tex]\text{scale factor of dilation is=}\frac{WX}{RS}=\frac{WZ}{RV}[/tex]

i.e  [tex]\frac{28}{40}=\frac{35}{50}=\frac{7}{10}[/tex]

Hence, scale factor of dilation is [tex]\frac{7}{10}[/tex]

in the diagram, the areas of ADC and DCB are in a ratio of 3:4. what are the coordinates of point C

Answers

the complete question in the attached figure

we know that 

dAB=dAC+dCB

dAC=√((8-1)²+(-2+9)²)=√98

Area triangle ADC=dAC*CD/2

Area triangle DCB=dCB*CD/2

 Area triangle ADC/Area triangle DCB=3/4

[dAC*CD/2]/[dCB*CD/2]=3/4

dAC=(3/4)*dCB-----------------------> equation (1)

dAB=dAC+dCB=√98

dAC=√98-dCB------------------------ > equation (2)

 (1)=(2)

(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98

dCB=(4/7)√98

dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98

dAC=(3/7) )√98

find the slope point A (1.-9) and point B (8,-2)

m=(-2+9)/(8-1)=7/7=1-------------- > 45°

 dAC=(3/7)√98

the component  x of dAC  is 

dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3

the component  y of dAC  is 

dACy=dACx=3

 the coordinates of the point C are

 point A(1.-9)

Cx=Ax+dACx----------> 1+3=4

Cy=Ay+dACy----------> -9+3=-6

 the coordinates  C(4,-6)

 the answer is C(4,-6)











Answer:

C(4,-6) is correct on plato

Step-by-step explanation:

Classify the number as natural, whole, integer, rational, and/or irrational. Select all terms that are correct. 7√

Answers

i took the test the answer is Irrational i hope this helps :) 
I think It would be irrational. I hope this helps you and others to come out :)

Find the 200th term, given the first term and the common difference. A1=34 and d=15

Answers

Try this solution:
1. it is arithmetic progression, where a₁=34 and d=15. Formula for  aₓ is aₓ=a₁+d(x-1);
2. a₂₀₀=34+15*(200-1)=3019.

answer: 3019.
P.S. if it is possible check the arithmetic part.

13) Suppose a coffee cup has a diameter of 8 cm and a height of 9 cm. What is the volume of the cup? (to nearest whole number)

Answers

A coffee cup is in e shape of cylinder
Radius is 4 cm (half of diameter)
Height = 9 cm
Volume of cylinder = pi x r^2 x h
The answer is 452.16 or can be rounded to 452 cubic cm

Answer:

[tex]452\ cm^{3}[/tex]

Step-by-step explanation:

we know that

the volume of a cylinder (coffe cup) is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=8/2=4\ cm[/tex] -----> the radius is half the diameter

[tex]h=9\ cm[/tex]

substitute

[tex]V=\pi (4^{2})(9)=452.4\ cm^{3}[/tex]

Round to the nearest whole number

[tex]452.4\ cm^{3}=452\ cm^{3}[/tex]


Fiecare dintre cei 25 de elevi ai clasei a |||-a a realizat un jurnal al luni . Stiind ca pentru fiecare zi s-a folosit o pagina si ca luna are 31 de zile,afla cate pagini au jurnalele tuturor elevilor.

Answers

the question in English
Each of the 25 students in the class has  made a journal on Monday. Knowing that every day a page was used and that the month is 31 days, find out how many pages the logs of all students.

Let
x--------------> total students
y--------------> total days in a month
z--------------> total page used per one student in 1 day
T--------------> total page used per total students in 1 month

we know that
x=25 students
y=31 pages
z=1 page

T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pages

the answer is 775 pages


the answer in Romanian

lăsa
x--------------> numărul total de elevi
y--------------> total zile într-o lună
z--------------> pagina totală utilizată pentru un student în 1 zi
T--------------> pagina totală utilizată pentru toți elevii în 1 lună
noi stim aia
x=25 elevi
y=31pagini
z=1 pagină

T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pagini

răspunsul este de 775 de pagini

the elevation in denver colorado is 13 times greater than that of waikapu, hawaii. the sum of their elevations is 5600 feet. find the elevation of each city

Answers

h1 = waikapu height
h2 = denver height

A) 13 h1 = h2
B) h1 + h2 = 5,600

B) h1 + 13h1 = 5,600
B) 14h1 = 5,600
h1 = Waikapu height = 400 feet

h2 = 5,600 - h1
h2 = 5,600 -400
h2 = Denver height = 5,200


Anybody have the proper answer to this

Answers

Radius = 11 / 2 = 5.5

A = π * 5.5 * 5.5

A = 30.25 π 

3025 / 100 π mm^2

The radius of the circle is half its diameter.
.. r = d/2
.. r = (11 mm)/2 = (11/2) mm

The area is given by
.. A = π*r^2
.. = π(11/2 mm)^2

.. A = (121/4)π mm^2

helppppppppppppppppppppppppppppppppppppp

Answers

The expression x²-14x+31=63 is a quadratic equation. To solve it, you must order it:


 x²-14x+31-63=0

 x²-14x-32=0


 Then, you must apply the quadratic formula, which is shown below:


 x=(-b±√(b^2-4ac))/2a


 So you have the values of a,b and c:

:

 a=1

 b=-14

 c=-32


 When you substitute those values in the quadratic formula, you obtain:


 x=(-(-14)±√((-14)^2-4(1)(-32))/2(1)

 x1=-2

 x2=16

 So, the correct option is the third one: x=-2 or x=16

Can someone help me?

Answers

There are 1+3 = 4 people from brazil (focus on row2)
There are 4+3+2 = 9 people who scored exactly 85 points (look at column 2)

So there are 4+9 = 13 people who are from brazil or scored exactly 85 points. Subtract out those who fit both criteria. So we'll subtract off 3 people
13-3 = 10

There are 10 people who fit the criteria out of 19 total. The 19 is from adding up all the values in the table.

Divide the two values to get 10/19

Answer: 10/19

Factor ab + bc + b2 + ac.

Answers

ab + bc + b² + ac = 
(b² + bc)+(ab + ac) = 
b(b+ c)+a(b + с) = 
(b + c)(b + a)
(ab + b^2) + (bc + ac). 

{So we can get the terms with the same variables together} 

Factoring out the GCF from each term: 

b(a + b) + c(a + b). 

Then, factoring out a + b yields: 

(a + b)(b + c). 

I hope this helps!

X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X

Answers

According to ratio theorem;
x = 2/5(Q) + 3/5(P)
   = 2/5(12.5,7.5) + 3/5(2,1)
   = 2( 2.5, 1.5) + 3( 0.4, 0.2)
   = (5,3) + (1.2,0.6)
   = (6.2, 3.6)
The Coordinates of X will be;
  =(6.2, 3.6)

Answer: (6.2, 3.6)

Step-by-step explanation:

We know that  if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and  [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-

[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]

Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).

Then, coordinate of X is given by :-

[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]

Hence, the coordinate of X = (6.2, 3.6)

Jermaine did this work to solve an equation. Did he make an error?

Answers

The solution for the below equation is required:

4x + 6 - x = 2x + 3

The work done by the Jermaine is presented below :

4x + 6 - x = 2x + 3

5x + 6 = 2x + 3

Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.

So, the correct option is

Jermaine did make an error. He should have combined 4x and -1x to make 3x

3x + 6 = 2x + 3

Hope it helps..!!

Answer:

Step-by-step explanation:

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th

What is the answer to this problem?

Answers

Hey there!

To start, an isosceles triangle is any triangle with two sides of the same length. 

In this case, you are given two measurements: 20 and 30.

This means that the third side of the triangle can either be 20 or 30, since two of the sides must equal one another.

Because the question is asking for the greatest possible perimeter of the triangle, it would only make sense that the third side would have to be 30 units in length to make the greatest possible perimeter since it is the possible length that is greatest in value (20 < 30).

Therefore, knowing that the sides of the triangle are now 20, 30, and 30, add the lengths up to find the perimeter:
20+30+30
=80

Therefore, the largest possible value of the perimeter would be 80 units.

Hope this helps and I hope you have a marvelous day! :)

helpppppppppppppppppp

Answers

The answer is -1

[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]

the trig unit circle
[tex]tan \frac{3π}{4} [/tex] = [tex] - tan \frac{π}{4} [/tex]
= -1

Remember,
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
= 1 ÷ -1
= -1
By definition, Cot(α)=Adjacent leg/Opposite leg

 Then, when you substitute the values, you obtain:

 Cot(3π/4)=-(√2/2)/(√2/2)

 When you simplify the expression, you have the following result:

 Cot(3π/4)=-1

 What is the exact value of Cot(3π/4)?

 The answer is: The exact value of Cot(3π/4) is -1

Solve the system of equations using the linear combination method. {5m+3n=41 {3m−6n=9 Enter your answers in the boxes. m = n =

Answers

These are linear equations that can be solved simultaneously;
5m+3n=41
3m-6n=9   (multiplying the first equation by 3 and the second by 5)

15m+9n=123
15m-30n= 45 (subtracting the two equations)
         39n = 78
             n = 2, 
and for m, 3m = 9+6(2)
                        = 21
                     m = 7
Therefore, n=2 and m=7

Answer:

n=2 m=7

Step-by-step explanation:

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