Which of the following statements would be the reason in line 4 of the proof?
A.) Definition of supplementary
B.) Two <'s supplementary to equal <'s are =
C.) Substitution

Answer:

it is 1500 and .97 on  

Step-by-step explanation:

Answer:

a = 1500 (initial Bone density)

b = 0.97 (remaining percentage every year)

x = x (years)

Step-by-step explanation:

The question already sets x as the "years" variable, and the function must be expressed:

[tex]f(x) = a*b^x[/tex]

Then we can set a as the initial bone density: 1,500 kg/mg3

and b as the remaining percentage after each year: 100% - 3% = 97%

In decimal notation: 97% is equivalent to 0.97

The x exponent of b represents the succesive density reduction each year.

For example, replacing for values for the first 5 years we obtain the following results:

(Note: results are limited and rounded to two decimals)

[tex]f(x) = 1500*0.97^1 = 1455[/tex]

[tex]f(x) = 1500*0.97^2 = 1411.35[/tex]

[tex]f(x) = 1500*0.97^3 = 1369,01[/tex]

[tex]f(x) = 1500*0.97^4 = 1327,94[/tex]

[tex]f(x) = 1500*0.97^5 = 1288,10[/tex]

Step-by-step explanation:

1 and 2 share the same line (a line equals 180°) if 1 = 100° then 180°-100°=80°

2=80°

bc and 4 also share a straight line. if bc=30° then 180°-30°=150°

4=150°

this can be checked by adding them all together. a circle is equal to 360°.

100°+80°+30°+150°=360°

San makes up the straight line that makes up 1 and 2 (as you can see I have already answered the question a million times over) and as it is a straight line it is 180° which is backed up by all of the double checked math.

Answer:

180 is correct

Step-by-step explanation:

3rd one for the answer all the other ones are wrong. It shifted down

ANSWER

[tex]y = \sqrt[3]{x + 4} - 1[/tex]

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x} [/tex]

The transformation

[tex]y = \sqrt[3]{x + k} - c[/tex]

shifts the graph of the base function k units left and c units down.

Since the graph is shifted 4 units left, k= 4

Also, the graph is shifted 1 unit down.

This implies that c=1

The new equation is

[tex]y = \sqrt[3]{x + 4} - 1[/tex]

The last option is correct.

Answer:

a=5, b=-2

Step-by-step explanation:

If you simplify the equation, you get:

3ax +6 -4x -4b - 11x - 14 = 0 =>

3ax - 15x -4b -8 = 0

group together x's and constants:

(3a-15)x -8 -4b = 0

To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2

Answer:

BF and HG

Step-by-step explanation:

this is because skew lines are lines that are not parrallel but are never going to intercet each other.

Answer:Lines BF and HG are skew.

Step-by-step explanation:

A skew lines are two lines that lie on different planes, will never intersect, and are not parallel.

Answer:

y=0.5x+3

Step-by-step explanation:

Answer:  [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Step-by-step explanation:

The equation of the line in Point-Slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope and ([tex]x_1,y_1[/tex]) is a point on the line.

You can identify that in the equation of the line [tex]y-3=4(x+2)[/tex], the slope is:

[tex]m=4[/tex]

By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:

[tex]m=-\frac{1}{4}[/tex]

 Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation  [tex]y-y_1=m(x-x_1)[/tex] to get the equation of this line:

 [tex]y-7=-\frac{1}{4}(x-(-5))[/tex]

 [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Answer:

≈ 7.07

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (- 7, - 2)

d = [tex]\sqrt{(-7-0)^2+(-2+1)^2}[/tex]

  = [tex]\sqrt{(-7)^2+(-1)^2}[/tex]

  = [tex]\sqrt{49+1}[/tex] = [tex]\sqrt{50}[/tex] ≈ 7.07

Answer:

-10√5 + 30

Step-by-step explanation:

This is a product of two monomials, so we would kind of like FOIL this.

F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT.

O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT.

I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT.

L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT.

Doing this will give 5 - 10√5 + 25. Combine like-terms to end up with -10√5 + 30 [or 30 - 10√5].

I am joyous to assist you anytime.

Answer:

[tex] \frac{5x + 2}{x} = \frac{ - 12}{x - 1} [/tex]

[tex]equivalent \: to \\ \: (5x + 2)(x - 1) = - 12x[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {5x+2} {x} = \frac {-12} {x-1}[/tex]

We multiply both sides of the equation by "x":

[tex]5x+2 = \frac {-12x} {x-1}[/tex]

We multiply both sides of the equation by "x-1":[tex](5x+2) (x-1) = - 12x[/tex]

ANswer:[tex](5x+2) (x-1) = - 12x[/tex]

Answer:

C

Step-by-step explanation:

Since you are basically interested in what the graph looks like, there is no need to go beyond a good graphing program like Desmos. The graph is provided below.

Red: y = -1/2  x + 4

Blue:2y + x = -8

Since both of them have the same slope, they never meet.

The correct answer is C: No solution

Check the picture below.

so the figure is really just 3 triangles and one square, we can simply get the area of each shape and sum them up, and that's the area of the composite

[tex]\bf \stackrel{\textit{green triangle}}{\cfrac{1}{2}(9)(3.5)}+\stackrel{\textit{brown triangle}}{\cfrac{1}{2}(2)(2)}+\stackrel{\textit{purple square}}{(2\cdot 2)}+\stackrel{\textit{pink triangle}}{\cfrac{1}{2}(5)(2)} \\\\\\ 15.75+2+4+5\implies 26.75[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

We have

the right traingle with the legs a = 3.5 and b = 2 + 2 + 5 = 9

the trapezoid with the bases b₁ = 2 + 2 + 5 = 9, b₂ = 5 and the height h = 2.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

Substitute:

[tex]A=\dfrac{(3.5)(9)}{2}=15.75[/tex]

The formula of an area of a trapezoid:

[tex]A=\dfrac{(b_1+b_2)h}{2}[/tex]

Substitute:

[tex]A=\dfrac{(9+2)(2)}{2}=11[/tex]

The area of the shape:

[tex]\bold{A=15.75+11=26.75}[/tex]

Answer:

B. -3

Step-by-step explanation:

The answer is -3

Because

Slope-intercept form: y= mx + b (m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y))

To find the slope, use the slope formula and plug in 2 points:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

(x₁ , y₁) = (5, 2)

(x₂ , y₂) = (10, 6)

[tex]m=\frac{6-2}{10-5} =\frac{4}{5}[/tex]

[tex]y=\frac{4}{5}x+b[/tex]    To find b, plug in a point into the equation (5, 2)

[tex]2=\frac{4}{5}(5)+b[/tex]

2 = 4 + b

-2 = b

[tex]y=\frac{4}{5}x -2[/tex]

Answer:

y = 4/5x -2

Step-by-step explanation:

equation of a line passing through two points is given by

y - y₁ = m (x - x₁), where m = (y₂ - y₁) / (x₂ - x₁)

y₂ = 6, y₁ = 2

x₂ = 10, x₁ =5

m = (6-2)/(10-5)

m = 4/5

y - 2 = 4/5 (x - 5)

multiply both sides by 5

5(y -2) = 4(x - 5)

5y -10 = 4x -20

5y = 4x -20 +10

5y = 4x -10

divide through by 5

y =4/5x -2

Answer: 1

Step-by-step explanation:

8 likes playing soccer

6 likes swimming

2 likes both

So in other words, because the 2 students likes swimming and playing soccer, they must be coming from the combined number of students (8+6=14) leaving only 1 who doesn't like to play either swimming/soccer.

There are 3 students who do not like either playing soccer or swimming and it can be determined by using set operation.

Given that,

In a class, there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playing soccer.

We have to determine,

How many students do not like either playing soccer or swimming?

According to the question,

Let x be the number of students who do not like either playing soccer or swimming.

Total number of students = n(U) = 15

Number of students who like playing soccer = n(A) = 8

Number of students who like swimming = n(B) = 6

Then,

The number of students like both = 2

Number of students who like swimming = Total number of students who like swimming - number of students like both

Number of students who like swimming  = 6 -2 = 4

And Number of students who like playing soccer = Total number of students who like playing soccer - number of students like both

Number of students who like swimming  = 8 -2 = 6

Therefore,

The total number of students = Number of students who like swimming + Number of students who like swimming + Number of students who do not like either playing soccer or swimming.

[tex]\rm 15 = (8-2) + (6-2) + x +2\\\\15 = 6+4+x+2\\\\15 = 12+x\\\\x = 15-12\\\\x=3[/tex]

Hence, there are 3 students who do not like either playing soccer or swimming.

To know more about Sets click the link given below.

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A triangle's angles always add up to a total 180º, and a right triangle always has an angle equal to 90º.

90º + 34º + xº = 180º

124º + xº = 180º

xº = 56º

Answer:

1923 cm²

Step-by-step explanation:

The surface area of a sphere is A = 4πr².

The first spherical beach ball has a radius of 24 cm:

A = 4π (24)²

A ≈ 7238 cm²

The second spherical beach ball has a radius 3 cm greater, or 27 cm:

A = 4π (27)²

A ≈ 9161 cm²

So the difference in area is:

9161 - 7238

1923 cm²

Answer:

1923 cm²

Step-by-step explanation:

Equation for the surface area of a sphere is 4πr².

The surface area of the bigger ball is (27²×4×π) = 2916π

The surface area of the smaller ball is (24²×4×π) = 2304π

The difference is 2916π-2304π = 612π

This is 1923 cm²

Answer:

3

Step-by-step explanation:

Graphing the best-fit quadratic curve for the data-set can be done using Ms. Excel Application.

The first basic step is to enter the data into any two adjacent columns of the excel workbook. Highlight the two columns where the values have been entered, click on the insert tab and then select the x,y scatter-plot feature. This will create an x,y scatter-plot for the data.

Next, click on the Add Chart Element feature and add a polynomial trend-line of order 2 which is basically a quadratic curve. Finally, check the display equation on chart box. This step will plot the quadratic curve as well as give the equation of the best-fit quadratic curve.

The attachment below shows the best-fit quadratic curve to the data-set and its corresponding equation.

A good approximation for the value of c from the equation is thus 3. This is simply the y-intercept of the curve. 3.21 is closer to 3.

Answer:

The length of the new image is 3 cm

Step-by-step explanation:

we know that

To find the length of the new image, multiply the length of the original image by the scale factor

Let

A'B'-----> the length of the new image

z ----> the scale factor

we have that

AB=1.5 cm

z=2

A'B'=z*AB

A'B'=2*1.5=3 cm

Answer:

x=-2.6

y=5.2

Step-by-step explanation:

The endpoint of line AB are at:

A(-4,8) and B(2,-4)

The x-coordinate of the point that divides this AB in the ratio m:n=3:10 is

[tex]x=\frac{mx_2+nx_1}{m+n}[/tex]

We substitute the given values to obtain;

[tex]x=\frac{3(2)+10(-4)}{3+10}[/tex]

We simplify to get:

[tex]x=\frac{6-40}{13}[/tex]

[tex]x=\frac{-34}{13}[/tex]

[tex]x=-2.6[/tex]

The y-coordinate of the point that divides this AB in the ratio m:n=3:10 is

[tex]y=\frac{my_2+ny_1}{m+n}[/tex]

We substitute the given values to obtain;

[tex]y=\frac{3(-4)+10(8)}{3+10}[/tex]

We simplify to get:

[tex]y=\frac{-12+80}{13}[/tex]

[tex]y=\frac{68}{13}[/tex]

[tex]y=5.2[/tex]

Answer:

x= -2.6

y= 5.2

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

30 divided by 2 to find a radius. that equals 15.

The answer to that is 15!

The answer is 12 because there are 16 cups in 1 gallon. 192/16 is 12! Hope this helps! :)

Answer:

Convert 192 cups to gallons. Enter your answers in the boxes. There are (16) cups in 1 gallon. Therefore, 192 cups is equal to (12) gallons.

Answer:

[tex]6x-4y[/tex] →  4.  [tex]2(3x-2y)[/tex]

[tex]6-4x[/tex] →    3.  [tex]2(3-2x)[/tex]

[tex]6x-4x[/tex] →  1. [tex]2x[/tex]

[tex]6x-4[/tex] →   2. [tex]2(3x-2)[/tex]

Step-by-step explanation:

You need to:

 Factor out 2 from [tex]6x-4y[/tex],  then you get the equivalent expression:

[tex]=2(3x-2y)[/tex] this matches with OPTION 4

Factor out 2 from [tex]6-4y[/tex], then you get the equivalent expression:

[tex]=2(3-2x)[/tex] this matches with OPTION 3

Make the subtraction for [tex]6x-4x[/tex],  then you get the equivalent expression:

[tex]=2x[/tex] this matches with OPTION 1

Factor out 2 from [tex]6x-4[/tex],  then you get the equivalent expression:

[tex]=2(3x-2)[/tex] this matches with OPTION 2

Answer:

6x-4y=2(3x-2y),

6-4x=2(3-2x),

6x-4x=2x,

6x-4=2(3x-2)

Step-by-step explanation:

We have been given 4 expressions

6x−4y, 6−4x, 6x−4x, 6x−4

Now we need to simplify or factor so that we can match each expression with an equivalent expression.

6x-4y=2(3x-2y)

6-4x=2(3-2x)

6x-4x=2x

6x-4=2(3x-2)

Now we can easily see that right side is unique for each of the given expression which can be easily matched with given choices.

Answer:

150°

Step-by-step explanation:

(30x+30)=2(20x-5)

x=4

AB=30×4+30=150

Answer:

150°

Step-by-step explanation:

The angle at the centre subtended by arc AB is twice the inscribed angle, that is

30x + 30 = 2(20x - 5) ← distribute

30x + 30 = 40x - 10 ( subtract 40x from both sides )

- 10x + 30 = - 10 ( subtract 30 from both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

Hence

arc AB = (30 × 4) + 30 = 120 + 30 = 150°

Answer:

D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or  [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]

Step-by-step explanation:

The given equation is:

[tex]3x^2+8x=5[/tex]

Divide through by 3;

[tex]x^2+\frac{8}{3}x=\frac{5}{3}[/tex]

Add the square of half the coefficient of x to both sides.

[tex]x^2+\frac{8}{3}x+(\frac{4}{3})^2=\frac{5}{3}++(\frac{4}{3})^2[/tex]

[tex]x^2+\frac{8}{3}x+\frac{16}{9}=\frac{5}{3}+\frac{16}{9}[/tex]

The left hand side is now a perfect square:

[tex](x+\frac{4}{3})^2=\frac{31}{9}[/tex]

Take square root

[tex]x+\frac{4}{3}=\pm \sqrt{ \frac{31}{9}}[/tex]

[tex]x=-\frac{4}{3}\pm \sqrt{ \frac{31}{9}}[/tex]

[tex]x=-\frac{4}{3}\pm \frac{\sqrt{31}}{3}[/tex]

D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or  [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]

Answer: The graph of g(x) is the graph of f(x) compresed vertically.

Step-by-step explanation:

Given the parent function [tex]f(x)^2[/tex], there are some transformations rules:

If [tex]f(x)=a(x^2)[/tex] when [tex]a>1[/tex], then it is stretched vertically.

If [tex]f(x)=a(x^2)[/tex] when [tex]0<a<1[/tex], then it is compresed vertically.

If [tex]f(x)=(ax)^2[/tex] when [tex]0<a<1[/tex], then it is stretched horizontally.

If [tex]f(x)=(ax)^2[/tex] when [tex]a>1[/tex], then it is compresed horizontally.

In this case for [tex]g(x)=\frac{2}{5}x^2[/tex], it has the form [tex]f(x)=a(x^2)[/tex] and [tex]0<a<1[/tex], then the graph of g(x) is the graph of f(x) compresed vertically.

The graphs of the functions f(x) = x^2 and g(x) = 2/5x^2 both represent parabolas, with g(x) being vertically compressed by a factor of 2/5 compared to f(x), which makes the g(x) graph appear narrower and less steep than the f(x) graph.

The functions f(x) = x2 and g(x) = 2/5x2 both represent parabolas, which are U-shaped curves on a graph. The significant difference between these two functions is their scaling, or how they stretch or compress vertically. The function f(x) = x2 has no scaling factor, which means it represents a standard square function with a one-to-one ratio. On the other hand, the function g(x) = 2/5x2 has a scaling factor of 2/5, meaning the graph of g(x) compared to f(x), will be vertically compressed by a factor of 2/5. This means the heights on the graph of g(x) are 2/5 times the corresponding heights on the graph of f(x). Therefore, the g(x) graph will appear narrower and less steep than the f(x) graph.

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The answer is C 84. Your welcome

Answer:

The measure of angle B is [tex]132\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

In an inscribed quadrilateral, opposite angles are supplementary

so

[tex]x\°+(2x+36)\°=180\°[/tex]

[tex]3x=180\°-36\°[/tex]

[tex]3x=144\°[/tex]

[tex]x=48\°[/tex]

step 2

Find the measure of angle B

[tex]B=(2x+36)\°[/tex]

[tex]B=(2(48)+36)\°=132\°[/tex]

Answer:

B)4,989,600

Step-by-step explanation:

The letters of 'MATHEMATICS'  contains 11 letters.

The following letters repeats twice, TT,MM,AA.

When we talk of distinguishable wasy, we are referring to arrangement without repetition.

Therefore the letters of "MATHEMATICS" can be arranged in [tex]\frac{11!}{2!2!2!}=4,989,600[/tex] distinguishable ways.

The correct answer is B.

Answer:

- 121

Step-by-step explanation:

The recursive formula allows us to find the next term in a sequence from the previous term, thus

f(1) = - 3f(0) + 2 = - 3 × 5 + 2 = - 15 + 2 = - 13

f(2) = - 3f(1) = - 3 × - 13 + 2 = 39 + 2 = 41

f(3) = - 3f(2) + 2 = - 3 × 41 + 2 = - 123 + 2 = - 121