Mr McCormick's wife is building some IKEA furniture, and the table below from the instructions show the lengths of different parts. Which part letter is the longest?
LENGTH (IN.)


Part A

Part B

Part C

Part D

If Δ ABC , medians AR, BS , and CQ then the value of AP = 2/3 AR,

BP = 2/3 BS, and CP = 2/3 CQ.

The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

Given: ΔABC, medians AR, BS, and CQ

AP = 2/3 AR, BP = 2/3 BS, and  CP = 2/3 CQ.

Slope of [tex]$\overline{A R}=\frac{3 c}{3 b+3 a}=\frac{c}{b+a}$[/tex]

Slope of [tex]$\overline{B S}=\frac{6 c}{6 b-3 a}=\frac{2 c}{2 b-a}$[/tex]

Slope of [tex]$\overline{C Q}=\frac{3 c}{3 b-6 a}=\frac{c}{b-2 a}$[/tex]

AR contained in the line [tex]$y=\left(\frac{c}{b+a}\right) x[/tex], BS contained in the line [tex]$y=\left(\frac{2 c}{2 b+a}\right)(x-3 a)[/tex], CQ contained in the line [tex]$y=\left(\frac{c}{b-2 a}\right)(x-6 a)$[/tex]

To find the coordinates of P, find the intersection point of two medians, BS and CQ.

[tex]$y=\left(\frac{2 c}{2 b-a}\right)(x-3 a) \text[/tex] and [tex]$y=\left(\frac{c}{b-2 a}\right)(x-6 a)[/tex]

[tex]$\frac{2 c}{2 b-a}(x-3 a) &=\frac{c}{b-2 a}(x-6 a) \\[/tex]

simplifying the above equation, we get

[tex]2 c(x-3 a)(b-2 a) &=c(x-6 a)(2 b-a) \\[/tex]

[tex]2 c\left(b x-2 a x-3 a b+6 a^2\right) &=c\left(2 b x-a x-12 a b+6 a^2\right)[/tex]

[tex]2 b c x-4 a c x-6 a b c+12 a^2 c &=2 b c x-a c x-12 a b c+6 a^2 c \\[/tex]

[tex]-3 a c x &=-6 a b c-6 a^2 c \\[/tex]

x = 2b + 2a

To find the value of y,

[tex]$y=\frac{2 c}{2 b-a}(x-3 a)[/tex]

simplifying the above equation, we get

[tex]$=\frac{2 c}{2 b-a}(2 b+2 a-3 a)[/tex]

[tex]$=\frac{2 c(2 b-a)}{2 b-a}=2 c$$[/tex]

So the coordinates of P are (2b + 2a, 2c).

Now, show that P is on AR.

[tex]$&y=\left(\frac{c}{b+a}\right)(2 b+2 a)=\frac{2 c(b+a)}{b+a}=2 c[/tex]

Thus, the three medians intersect at the same point.

To find the lengths of AR, AP, BS, BP, CQ, and CP

Using the Distance Formula.

[tex]A R &=\sqrt{\left((3 b+3 a)-0^2\right)+(3 c-0)^2} \\[/tex]

simplifying the above equation, we get

[tex]&=\sqrt{(3(b+a))^2+(3 c)^2} \\[/tex]

[tex]&=\sqrt{9\left((b+a)^2+c^2\right)} \\[/tex]

[tex]&=3 \sqrt{(b+a)^2+c^2} \\[/tex]

[tex]A P &=\sqrt{\left((2 b+2 a)-0^2\right)+(2 c-0)^2} \\[/tex]

[tex]&=\sqrt{(2(b+a))^2+\left(2 c^2\right)} \\[/tex]

[tex]&=\sqrt{4\left((b+a)^2+c^2\right)} \\[/tex]

[tex]&=2 \sqrt{(b+a)^2+c^2}[/tex]

[tex]B S &=\sqrt{(6 b-3 a)^2+(6 c-0)^2} \\[/tex]

[tex]&=\sqrt{(3(2 b-a))^2+(3(2 c))^2} \\[/tex]

[tex]&=\sqrt{9(2 b-a)^2+9(2 c)^2} \\[/tex]

[tex]&=3 \sqrt{(2 b-a)^2+4 c^2}[/tex]

[tex]B P &=\sqrt{(6 b-(2 b+2 a))^2+(6 c-2 c)^2} \\[/tex]

[tex]&=\sqrt{(4 b-2 a)^2+(4 c)^2} \\[/tex]

[tex]&=\sqrt{(2(2 b-a))^2+(2(2 c))^2} \\[/tex]

[tex]&=2 \sqrt{(2 b-a)^2+4 c^2} \\[/tex]

[tex]C Q &=\sqrt{(6 a-3 b)^2+(0-3 c)^2} \\[/tex]

[tex]&=\sqrt{(3(2 a-b))^2+(-3 c)^2} \\[/tex]

[tex]&=\sqrt{9\left((2 a-b)+c^2\right)} \\[/tex]

[tex]&=3 \sqrt{(2 a-b)^2+c^2} \\[/tex]

[tex]C P &=\sqrt{(6 a-(2 b+2 a))+(0-2 c)^2} \\[/tex]

[tex]&=\sqrt{(4 a-2 b)^2+(-2 c)^2} \\[/tex]

[tex]&=\sqrt{(2(2 a-b))^2+4 c^2} \\[/tex]

[tex]&=\sqrt{4(2 a-b)^2+4 c^2}[/tex]

Show that the P is two thirds of the distance from the vertices to the midpoints.

[tex]$\frac{2}{3} A R &=\frac{2}{3}\left(3 \sqrt{(b+a)^2+c^2}\right) \\[/tex]

[tex]&=2 \sqrt{(b+a)^2+c^2} \\[/tex] = A P

[tex]$\frac{2}{3} B S &=\frac{2}{3}\left(3 \sqrt{(2 b-a)^2+4 c^2}\right) \\[/tex]

[tex]$&=2 \sqrt{(2 b-a)^2+4 c^2} \\[/tex] = B P

[tex]$\frac{2}{3} C Q &=\frac{2}{3}\left(3 \sqrt{(2 a-b)^2+c^2}\right) \\[/tex]

[tex]&=2 \sqrt{(2 a-b)^2+c^2} \\[/tex] = C P

Therefore, AP = 2/3 AR, BP = 2/3 BS, and CP = 2/3 CQ.

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Answer:

Step-by-step explanation:

So we do it this way.

[2+2 x(-2)+3]^2

2x-2 =-4

Multiplication comes first

Then we do addition

(negatives last)

2+3+(-4) = 1

1^2=1

Hope this helps!^^

The resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>

In this question,

Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north.

The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second.

We need to find Amy's resultant velocity.

We write the direction vector for Amy in component form.

Due north is equivalent to 90° from the horizontal.

x-component:

x = 10 cos(90°)

x = 0

And y-component:

y = 10 sin(90°)

y = 10

The component form for Amy’s vector is <0, 10>.

Now we write the direction vector for wind in component form.

40 east of north is equivalent to 50° from the horizontal.

x-component:

x = 2.8 cos(50°)

x = 1.8

And y-component:

y = 2.8 sin(50°)

y = 2.14

The component form for the wind’s vector is <1.8, 2.14>

Add the vectors for Amy and the wind.

<0, 10> + <1.8, 2.14> = <1.8, 12.14>

Now, we determine the vector's magnitude by using Pythagoras theorem.

Let v be the velocity of Amy.

Let θ be the angle made by Amy with the horizontal

⇒ tan(θ) = |y/x|

⇒ tan(θ) = |12.14 / 1.8|

⇒ θ = 81.6°

81.6° with the horizontal is equivalent to 8.4° east of north.

Therefore, the resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>

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Answer:

(0, - 9 )

Step-by-step explanation:

the y- intercept is where the line crosses the y- axis

the line crosses the y- axis at (0, - 9 ) and is the y- intercept

Answer:

2:1

Step-by-step explanation:

There are 4 brothers, 2 sister so

4 (boys): 2(sister) => 2:1 (Simplified form)

Answer:

7) x ≥ -3

8) x < -8

Explanation:

[tex]\sf -3(2x-7) \leq 39[/tex]

distribute

[tex]\sf -6x + 21 \leq 39[/tex]

relocate variables

[tex]\sf -6x \leq 39-21[/tex]

simplify

[tex]\sf -6x \leq 18[/tex]

dividing both sides by (-), changes the inequality sign

[tex]\sf x \geq -3[/tex]

[tex]\sf 4x + 9 < x - 15[/tex]

collect like terms

[tex]\sf 4x -x < - 15-9[/tex]

simplify

[tex]\sf 3x < - 24[/tex]

divide both sides by (+)3

[tex]\sf x < -8[/tex]

Step-by-step explanation:

I'm not sure but this is the solution hehe

The value of j is j = 103 - k = 115 - f.

A collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.

Consider the two equations,

f + j = 115                                                                    ----------------------(1)

j + k = 103                                                                   ----------------------(2)

Consider equation (2),

j + k = 103

Subtracting k from each side of the equation.

j + k - k = 103 - k

j = 103 - k

Consider equation (1),

f + j = 115

Subtraction f from each side of the equation,

f + j - f = 115 - f

j = 115 - f

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Answer: Total volume= 71.21 in^3

Step-by-step explanation:

The volume of the sphere= (4/3)*π*(2^3) = 33.51 in^3

The volume of the cylinder= π*(2^2)*3 = 37.7 in^3

Total volume= 71.21 in^3

This question is incomplete

Identify the property illustrated by the equation.5+(-5)=0  Additive Inverse

What is an additive Inverse ?

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Answer:

Yes

Step-by-step explanation:

Points D and E are on plane F.

The solution of the equation 5x/4 - 3/x= 1/4 for x is (1+√241)/10 or (1 -√241)/10.

According to the given question.

We have an equation 5x/4 - 3/x= 1/4.

As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation 5x/4 - 3/x= 1/4 for x is given by

5x/4 - 3/x= 1/4

⇒ ( 5x^2 -12) /4x  = 1/4

⇒ 5x^2 - 12   = (1/4)4x                 (multiplying both the sides by 4x)

⇒ 5x^2 - 12 = x

⇒ 5x^2 - x -12 = 0

⇒ x = [tex]\frac{1\pm\sqrt{1+240} }{10}[/tex]

⇒ x = (1+√241)/10 or (1 -√241)/10

Hence, the solution of the equation 5x/4 - 3/x= 1/4 for x is (1+√241)/10 or (1 -√241)/10.

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The time taken by the water to reach 49 degree Celsius is 4 minutes.

According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.

Initial temperature of water is 21 degree Celsius.

Let us assume, water reaches at 49° C after 'm' minutes.

As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7m)°C

⇒ 21 + 7m = 49

⇒m = 4 minutes.

Hence, the time taken to reach 49° C is 4 minutes.

What is temperature?

Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.

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The value of the x in a linear equation is 7.8.

According to the statement

We have to find that the value of x.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

A is between points B and C. AB = 2x - 3, BC = 7x - 10, and AC = 32.

It means

BC = BA + AC

Then we have to substitute the values in it

Then

BC = BA + AC

7x - 10 =  2x - 3 + 32

7x - 2x = -3 +32+10

5x = 39

here the values of the x is a

x = 39/5.

x = 7.8

So, The value of the x in a linear equation is 7.8.

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Answer:

c = (y+8)/d

Step-by-step explanation:

Answer:

C.10

Step-by-step explanation:

x=10

You can enter it into the calculator to check it.

Hope this helped! ;)

The percent grade of the road will be 4.7692%.

It should be noted that the difference will be:

= (1132 - 1070)/1.3 ÷ 1000

= 62/(1.3 × 1000)

= 62/1300

= 31/650

= 0.047692

Therefore, the percent grade of the road will be 4.7692%.

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Payroll (FICA) taxes of the question is 0.2295

According to the given data,

Payroll (FICA) taxes is  7.65%

boss promises at least 3 hours but no more than 18 hours per week.

then we get, 3 × 0.0765

                     = 0.2295

therefore, payroll taxes from your paycheck and to deduct  tax

0.2295

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All About the FICA Tax

If you earn a wage or a salary, you’re likely subject to Federal Insurance Contributions Act taxes. Not to be confused with the federal income tax, FICA taxes fund the Social Security and Medicare programs. Also known as payroll taxes, FICA taxes are automatically deducted from your paycheck. Your company sends the money, along with its match (an additional 7.65% of your pay), to the government. In this article we’ll discuss what FICA taxes are, how they’re applied and who’s responsible for paying them.

Planning your finances goes beyond just taxes. Find a local financial advisor today.

FICA Taxes: The Basics

Every payday, a portion of your check is withheld by your employer. That money goes to the government in the form of payroll taxes. There are several different types of payroll taxes, including unemployment taxes, income taxes and FICA taxes. Two types of taxes fall under the category of FICA taxes: Medicare taxes and Social Security taxes.

Paying FICA taxes is mandatory for most employees and employers under the Federal Insurance Contributions Act. The funds are used to pay for both Social Security and Medicare.

If you own a business, you’re responsible for paying Social Security and Medicare taxes, too. For self-employed workers, they’re referred to as SECA taxes (or self-employment taxes) based on regulations included in the Self-Employed Contributions Act.

A wage base limit applies to employees who pay Social Security taxes. This means that gross income above a certain threshold is exempt from this tax. The wage limit changes almost every year based on inflation. In 2021, it was $142,800. For 2022, the limit rose to $147,000. This income ceiling is also the maximum amount of money that’s considered when calculating the size of Social Security benefits.

Medicare taxes, on the other hand, don’t have a wage limit. But there’s an Additional Medicare Tax that high-income individuals must pay. That has been the case since January 1, 2013.

The Additional Medicare Tax rate is 0.90% and it applies to employees’ (and self-employed workers’) wages, salaries and tips. So any part of your income that exceeds a certain amount gets taxed for Medicare at a total rate of 2.35% (1.45% + 0.90%). That income ceiling for 2021 and 2022 is $200,000 for single filers, qualifying widows and anyone with the head of household filing status; $250,000 for married couples filing joint tax returns and $125,000 for couples filing separate tax returns. You can calculate how much you owe using Form 8959.

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Answer:

(-3, 2), (1, -3) and (1, 2)

Step-by-step explanation:

When a point (x, y) is rotated 90° counterclockwise rotation new coordinates become (-y, x)

Thus the negative of the original y coordinate becomes the new x coordinate and the original x coordinate becomes the y coordinate

( 2,  3)  ----->  (-3, 2)

(-3, -1)   ----->  (1, -3)

( 2, -1)   ----->  ( 1, 2)

45 inch is shorter in length.

Feet is a unit of measuring length as per the US standard system of measurement and centimeters is the unit of length measurement as per the metric system. Feet is abbreviated as 'ft'.

Inches is another measurement of length . It is a unit used for measuring length, approximately equal to 2.54 centimetres, sometimes shown by the symbol ″

1 feet = 12 inches which means feet is a bigger unit than inch.

So 4 feet 1/2 inch = 54 inches

54 inches is greater than 45 inches,

45 inches is shorter.

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The equivalent statement is:

" If it has exactly three sides, then it is not a rectangle."

The given conditional statement is:

"If it is a rectangle, then it does not have exactly three sides"

A logically equivalent statement is any statement that has the same truth values than the above one.

For a conditional:

If P, then Q,

An equivalent statement is:

if Not Q, then Not P.

So a equivalent statement to the given one is:

"If it has exactly three sides, then it is not a rectangle."

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Answer: A: If it has exactly three sides, then it is not a rectangle.

Step-by-step explanation: Hope that helped

Answer: A; $9; B; D

Step-by-step explanation:

1. 480➗6 = 80%

2. 36➗4= $9

3. 0.85 x 20= 17

4. 28➗2 = 14

14 x 6= 84

Answer:

x = 42

Step-by-step explanation:

9*5 = x+3/5*5

45 - 3= x+3 - 3

42 = x

UR WELCOME

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

[tex]5x + 3x = 8 +48[/tex]

  ⬇️

8x = 8 + 48

          ⬇️

  8x = 56

Divide both sides of the equation by the coefficient of the variable;

[tex]x = \frac{56}{8}[/tex]

Cross out common factors;

[tex]x=7[/tex]

The questions answered in each round was 12 in the first round, 5 in the second round and 7 in the third round.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the questions in the first round, y represent that of the second round and z represent that of the third round.

You score 370 points by answering 24 questions correctly:

x + y + z = 24   (1)

Also:

10x + 15y + 25z = 370     (2)

And:

25z = 10x + 55    (3)

From the three equations:

x = 12, y = 5, z = 7

The questions answered in each round was 12 in the first round, 5 in the second round and 7 in the third round.

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2436 ≈  2400 is the estimate products of 203X12 .

What is estimate products?

203X12

= 2436

We can take compatible numbers

200 × 12

2400

So, 2436 ≈  2400

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Answer: 4000

Step-by-step explanation: 2000 there and 2000 back. 2000+2000=4000

Hope this helps!

Answer: The value of x is 20.

Algebraic function :

Given function is,  

We have to find the value of x when

The value of x is 20.

Step-by-step explanation: hope this helps

Answer:

  0.99999994412

Step-by-step explanation:

You want the probability at most 27 heads occur in 29 tosses of a fair coin.

The probability is found using a suitable calculator to find ...

  P(X ≤ 27) ≈ 0.99999994412

for 29 trials with a probability of success of 1/2 on each trial using the binomial distribution.

__

Additional comment

We checked this value by also finding the probability of 28 or 29 heads in 29 trials, then subtracting the sum of those from 1.

<95141404393>