Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.

The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is

units, and its area is

square units.

Answers:0m/s

Step-by-step explanation: once she has completed one lap, displacement is 0, therefore her velocity is 0m/s

The average velocity of her is zero.

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.

Given

A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m.

She completes one lap in 100 seconds.

The formula is used to find average velocity is;

[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}[/tex]

Here, the runner displacement is zero.

Therefore,

[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}\\\\\rm Average \ velocity=\dfrac{0 }{100}\\\\\rm Average \ velocity=0[/tex]

Hence, the average velocity of her is zero.

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Answer:

x=8

Step-by-step explanation:

To solve this, we must use the Pythagorean theorem.

a=15, b=x, and c=17

[tex](15)^2 +b^2=(17)^2\\\\b=\sqrt{17^2-15^2} \\\\b=\sqrt{289-225} \\\\b=\sqrt{64} \\\\b=8[/tex]

a^2+b^2=c^2

In this case, 15=a and 17=c and if you substitute the variables as the numbers, you would get the equation 15^2+b^2=17^2. If you simplify that you would get 225+b^2=289. You subtract 225 from both sides and you get left with b^2=64. The square root of 64 is 8 so I’m this problem x is 8.

ANSWER~ 8

Answer:

Roy is 10 years old at present and Joan is 5 years old at present

Step-by-step explanation:

Let

x----> Roy's age

y----> Joan's age

we know that

x=2y ----> equation A

(x+3)+(y+3)=21 ----> equation B

substitute equation A in equation B

(2y+3)+(y+3)=21

solve for y

3y+6=21

3y=21-6

3y=15

y=5 years

Find the value of x

x=2y  ----> x=2(5)=10 years

therefore

Roy is 10 years old at present

Joan is 5 years old at present

Answer:

Roy is 10 and Joan is 5

Step-by-step explanation:

Answer:

the solution is (5, -6)

Step-by-step explanation:

Let the numbers be x and y.  Then x + y = -1 (meaning that either x or y is negative), and x - y = 11.

Solve the system:

x + y = -1

x - y = 11

-------------

2x    = 10, or x = 5.  If x = 5, then x - y = 11 becomes 5 - y = 11, or y = -6.

Then the solution is (5, -6).

Is the sum of 5 and -6 equal to -1?  YES.

If -6 is subtracted from +5, is the difference 11?  Yes.

Final answer:

The two numbers in the system of equations are 5 and -6. By adding the equations x + y = -1 and x - y = 11, we find x = 5, and substituting back, we find y = -6.

Explanation:

Let's define the two unknown numbers as x and y. According to the question, we have two equations. The first one, x + y = -1, tells us the sum of the two numbers is -1. The second one, x - y = 11, tells us the difference between the two numbers is 11.

To solve this system of linear equations, we can use the method of substitution or elimination. However, adding both equations is the simplest approach here:

Adding both equations, we get:

2x = 10

Now we can solve for x by dividing both sides by 2:

x = 5

Substituting the value of x into one of the original equations to find y:

5 + y = -1

Solving for y gives us:

y = -1 - 5

y = -6

So the two numbers are 5 and -6.

For this case we have that by definition, the point-slope equation is of the form:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes

We find the slope of the line according to the given points:

[tex](x1, y1) :( 7, -21)\\(x2, y2): (- 4,23)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {23 - (- 21)} {- 4-7} = \frac {44} {- 11} = - 4[/tex]

So:

[tex]m = -4\\(x_ {0}, y_ {0}) :( 7, -21)[/tex]

Substituting:

[tex]y - (- 21) = - 4 (x-7)\\y + 21 = -4x + 28[/tex]

Answer:

[tex]y + 21 = -4x + 28[/tex]

Answer:

y = - 4x + 28

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, - 21) and (x₂, y₂ ) = (- 4, 23)

m = [tex]\frac{23+21}{-4-7}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4

Using m = - 4 and (a, b ) = (7, - 21), then

y + 21 = - 4(x - 7) ← in point- slope form

Distribute right side and simplify

y + 21 = - 4x + 28 ← in slope- intercept form

there are 30 marbles in the jar originally

Answer:

Its 9 1/16

Step-by-step explanation:

I guessed and got it right. I just knew it wasn't 9 and the two 16 answers didn't make sense, lol. In the future I think just go with the one closest (but not exact) to the shown thingy, not sure tho?

Update:

Im silly. Solve it like this:

AE*EB=CEtimesED

so 9 which is 4.5*2 would be 4.5*4.5

thats 20.25

20.25/4(the radius)

is 5.06.

That plus 4 is the diameter, lol.

so it rounds to 9 1/16

For water 1 gram = 1 ml.

This means 45 grams are equal to 45 ml's.

Neither one is greater than the other one as they are equal.

The problem doesn't state what is being measured, so the answer could be different depending on the density of the product being measured.

ANSWER

Yes, k=-3 and y=-3x

EXPLANATION

Let's assume y varies directly as x.

Then, we can write the equation:

y=kx

From the table, when x=1, y=3

Substitute these values to obtain;

3=-k

This implies

k=-3

The equation now becomes:

y=-3x

We check for a second point to see if it satisfy the equation.

When x=5,y=-15

-15=-3(5)

-15=-15

Hence the relation represent a direct variation.

Answer:

with?

Step-by-step explanation:

To find the answer, we should multiply 132 by 6.

132*6=792

792+1=793

Tammy’s answer is correct.

Answer:

C. Center (3,-2) and radius 3

Step-by-step explanation:

The given circle has equation:

[tex]x^2+y^2-6x+4y+4=0[/tex]

We rearrange to get:

[tex]x^2-6x+y^2+4y=-4[/tex]

We add the square of half the coefficients of the linear terms to both sides of the equation:

[tex]x^2-6x+(-3)^2+y^2+4y+(2)^2=-4+(-3)^2+(2)^2[/tex]

We factor the  perfect squares and simplify to get;

[tex](x-3)^2+(y+2)^2=9[/tex]

We can rewrite as;

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

Comparing this to  the standard equation of the circle;

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

We have (3,-2) and the center and r=3 as the radius.

Answer:

The answer is C.

Step-by-step explanation:

1/2 x 4/1 = ?

We begin by multiplying the numerators:

1 x 4 = 4

And then we multiply the denominators:

2 x 1 = 2

The answer has a numerator of 4 and a denominator of 2. In other words:

1 x 4/2 x 1 =4/2

This fraction can be reduced to lowest terms:

4 ÷ 2/2 ÷ 2 =2/1 = 2

Answer:

It can be A. (not B or C)

Step-by-step explanation:

It is A because x-6=0 can be simplified to x=6. Then, 2x + 6, you can divide the whole equation resulting in x+3=0, simplify this and you get x=-3. YES

It is not B because, while x+3=0 results in a zero of -3, 6x-1 can be simplified to be divided by 6. When we do this we get x-1/6=0, which is not equivalent to 6. NO

It is not C because, while x-6=0 results in a zero of 6, -3x can be simplified with the zero product property to get -3x=0 then dividing -3 by 0 giving you 0 which is not equivalent to one. NO

Answer:

Step-by-step explanation:

B.

There is a 100% chance that the event will occur.

There is a 100% chance that the event will occur is the correct answer.

Think that you have 6 blue balls in a bags what is the odd of you getting a blue ball when you take one out of the bag?

6/6 easy right.

What does 6/6 equal to?

1 that means if something has a probability of 1 it will always happen

if something has a probability of 0 it is impossible

Answer:

Option B. $10.00

Step-by-step explanation:

Market value of a mutual fund = $40,000,000

Total outstanding shares = 4,000,000  

To find out per share value we use this formula  

[tex]\frac{\text{Market value of the shares}}{\text{total number of shares}}[/tex]

[tex]\frac{40,000,000}{4,000,000}[/tex]  = $10/share

The value of per share is $10.00

Final answer:

The absolute deviation of 15 in the data set {20, 20, 30, 15, 40} is the absolute value of (15 minus the mean 25), which is 10. So, the correct answer is B. 10.

Explanation:

To calculate the absolute deviation of a number in a data set, you subtract the number from the mean of the data set and take the absolute value of the result. The mean of the data set {20, 20, 30, 15, 40} is (20 + 20 + 30 + 15 + 40) / 5, which equals 125 / 5 or 25. The absolute deviation for the number 15 would be the absolute value of (15 - 25), which is the absolute value of -10 or simply 10. Therefore, the correct answer is B. 10.

Answer:

Step-by-step explanation:

2) Boyle's law says volume varies inversely with pressure:

V = k / P

3) V = 4 when P = 3:

4 = k / 3

k = 12

4) [tex]\left[\begin{array}{cc}P&V\\1&12\\2&6\\3&4\end{array}\right][/tex]

5) Since P = d/33 + 1:

V = 12 / (d/33 + 1)

6) [tex]\left[\begin{array}{cc}d&V\\0&12\\33&6\\66&4\\99&3\end{array}\right][/tex]

Answer:

With Veronica's hair

Median: 13

Mean: 17.9

Mode: 13,5

Without

Mean :13.8

median: 13

mode: 13,5

Step-by-step explanation:

Answer: multiply all of them by two and then put the fx2 behind the equal signs in punuations =(fx2)

Step-by-step explanation:

Answer:

16 ft²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 8 and h = 4, thus

A = 0.5 × 8 × 4 = 16 ft²

Answer:

1.875

Step-by-step explanation:

1+ 0.5 = 1.5

1.5+0.25 = 1.75

1.75+0.125 = 1.875

Answer:

1.875

Step-by-step explanation:

Answer:

The area of the circular cross section of the pipe is [tex]100\pi\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the circle (cross section of the pipe) is equal to

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

we have

[tex]r=20/2=10\ cm[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (10)^{2}[/tex]

[tex]A=100\pi\ cm^{2}[/tex]

Answer is C. This is because in quadrant 2, [tex]\sin\theta>0[/tex] so [tex]\csc\theta>0[/tex] is also true.

Answer with explanation:

Let , Theta =A

[tex]\tan A=\frac{-12}{5}\\\\ \csc A=\frac{-13}{12}[/tex]

In First Quadrant all Trigonometric Function are Positive.

→In Quadrant,II , Sine and Cosecant , Function are Positive only.

→Cosecant theta is negative.So, Terminal point can't be in Second Quadrant.

Option C:

Answer:

The answer would be c

Step-by-step explanation:

The accurate statement about the value of acceleration is 3 meters per second squared.

Given data:

Acceleration is a fundamental concept in physics that describes the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.

It can be expressed as:

a = Δv / Δt

where Δv represents the change in velocity and Δt represents the change in time.

So, the denominator of the acceleration expression has the square of time.

Hence, the statement 3 meters per second squared determines the acceleration.

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The complete question is attached below:

Which of the following is an accurate statement of an acceleration value, translated from symbols into words?

A) 3 meters per second

B) 3 meters per second squared

C) 3 square meters per second

D) 3 meters in 3 seconds

Answer:

∠ABD = 20°

Step-by-step explanation:

Since BD is the angle bisector of ∠ABC then

∠ABD = ∠DBC ← substitute values

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Hence

∠ABD = 3x - 1 = (3 × 7) - 1 = 21 - 1 = 20°

In both cases,

[tex]AB^2=AD^2[/tex]

(as a consequence of the interesecting secant-tangent theorem)

So we have

10.

[tex](4x+7)^2=(6x-3)^2[/tex]

[tex]16x^2+56x+49=36x^2-36x+9[/tex]

[tex]20x^2-92x-40=0[/tex]

[tex]5x^2-23x-10=0[/tex]

[tex](5x+2)(x-5)=0\implies\boxed{x=5}[/tex]

(omit the negative solution because that would make at least one of AB or AD have negative length)

11.

[tex](4x^2-18x-10)^2=(x^2+x+4)^2[/tex]

[tex]16x^4-144x^3+244x^2+360x+100=x^4+2x^3+9x^2+8x+16[/tex]

[tex]15x^4-146x^3+235x^2+352x+84=0[/tex]

[tex](x-7)(3x+2)(5x^2-17x-6)=0\implies\boxed{x=-\dfrac23\text{ or }x=7}[/tex]

(again, omit the solutions that would give a negative length for either AB or AD)

The value of x for first figure is x = 5 and for second x = 7 and -2/3.

The property of tangent is that "if two tangents from the same exterior point are tangent to a circle, then they are congruent".

1. The value of x using the above tangent property.

BA = AD

4x + 7 = 6x -3

4x - 6x = -3 -7

-2x = -10

x = -10/-2

x = 5

2. The value of x using the above tangent property.

BA = AD

[tex]\rm 4x^2-18x-10=x^2+x+4\\\\4x^2-18x-10-x^2-x-4=0\\\\3x^2-19x-14=0\\\\x =\dfrac{-(-19)\pm\sqrt{(-19)^2-4\times 3\times -14} }{2\times 3}\\\\x =\dfrac{19\pm\sqrt{361+168} }{6}\\\\x =\dfrac{19\pm\sqrt{529} }{6}\\\\x =\dfrac{19+23 }{6}, \ x =\dfrac{19-\ 23}{6}\\\\x =\dfrac{42}{6} , \ x =\dfrac{-4}{6}\\\\x=7, \ x=\dfrac{-2}{3}[/tex]

Hence, the value of x for first figure is x = 5 and for second x = 7 and -2/3.

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Answer:

6188 different combinations of people

Step-by-step explanation:

This is a combination problem since it does not matter the order of people that answer the phones.  The combination looks like this:

₁₇C₅ = [tex]\frac{17!}{5!(17-5)!}[/tex]

This expands to

[tex]\frac{17*16*15*14*13*12!}{5*4*3*2*1(12!)}[/tex]

The 12! cancels out in the top and bottom so the remaining multiplication leaves you with

₁₇C₅ = [tex]\frac{742560}{120}[/tex]

which divides to 6188

The number of groups of 5 people that can be selected from a total of 17 to answer 5 different phone lines is 6188. This is a combinatorics problem calculated using the combinations formula.

The question is asking us to determine how many groups of 5 people out of 17 people can answer the 5 different phone lines in an office. This problem is a combination problem in mathematics, particularly in combinatorics. Combinations refer to the selection of items without regard for the order in which they are arranged.

Here, we are selecting groups of 5 people out of 17 to answer the phone lines. The formula for combinations is C(n, r) = n! / r!(n-r)!, where n is the total number of items, r is the items to be selected, and '!' denotes the factorial.

Substituting our values into the formula, we get C(17, 5) = 17! / 5!(17-5)!. When we calculate this, the answer we obtain is 6188. Therefore, there are 6188 ways to form groups of 5 out of 17 people to answer the phone lines.

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Answer:

Step-by-step explanation:

The study doesn't prove any causation.  The only conclusion is that people with lower cholesterol levels are more likely to eat blueberries.

Answer:

There may be a correlation between eating blueberries and a lower cholesterol level.

Step-by-step explanation:

An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.

The statement that describes the best conclusion to draw from the study is :

I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.

If im not wrong, i believe the answer is C.

Answer:

  B)  6.9 cm

Step-by-step explanation:

The remaining angle is the smallest, 180° -48° -97° = 35°. The shortest side is opposite this angle. The Law of Sines tells you its length is ...

  short side = (longest side)·(sin(smallest angle)/sin(largest angle))

  = (12 cm)sin(35°)/sin(97°) ≈ 6.9 cm

The shortest side is about 6.9 cm.