Answer: x<1 or x>5
Step-by-step explanation:
|-x+3|>2
-x+3>2
-x+3-3>2-3
-x>-1
x<1
-x+3<-2
-x+3-3<-2-3
-x<-5
x>5
x<1 or x>5
Write a coordinate proof to prove the Centroid Theorem.
Given: Δ A B C , medians AR, BS , and CQ
Prove: The medians intersect at point P and P is two thirds of the distance from each vertex to the midpoint of the opposite side.
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.
What is meant by Centroid Theorem?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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203X12 estimate to check for reasonableness
2436 ≈ 2400 is the estimate products of 203X12 .
What is estimate products?
Round the numbers to some nearby figures that you can mentally multiply to estimate the product of multiplication. Rounding all variables to the biggest digit (place value) they have is one way to estimate values.Example -Estimation is frequently accomplished through sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.203X12
= 2436
We can take compatible numbers
200 × 12
2400
So, 2436 ≈ 2400
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pls helpppp its nearly due and i need a solution AND a answer x
Answer:
Step-by-step explanation:
If ab is 4 times bc;
then ab= 4bc
ac= 5bc=75
bc= 75/5 = 15 cm
ab= (4*bc)
= 4 * 15 = 60
What are the coordinates of the vertices of the image after a 90-degree counter-
clockwise rotation about the origin?
3+
(2, 3)
2+
4
(-3,-1)
1 0
1
2.
1
3
(2, -1)
+X
4
triangle
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)
please answer correctly and ignore the bottom ill do that part just the top for you guys and gals please!
Answer:
7) x ≥ -3
8) x < -8
Explanation:
[tex]\sf If \ u^n < a, \ then -\sqrt[n]{a} < u < \sqrt[n]{a}[/tex][tex]\sf If \ u^n > a, \ then \ u < -\sqrt[n]{a} \ \ or \ \ u > \sqrt[n]{a}[/tex]7.[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]
8.[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]
You make $7.25/hr and your boss
promises at least 3 hours but no
more than 18 hours per week.
Payroll (FICA) taxes of 7.65% are
withheld from your paycheck.
Be sure to deduct your tax
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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Which statement is logically equivalent to the following conditional statement?
"If it is a rectangle, then it does not have exactly three sides."?
O If it has exactly three sides, then it is not a rectangle.
O If it is not a rectangle, then it has exactly three sides.
O If it does not have exactly three sides, then it is a rectangle.
O If it is not a rectangle, then it does not have exactly three sides.
The equivalent statement is:
" If it has exactly three sides, then it is not a rectangle."
Which statement is logically equivalent to the conditional statement?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
Describe the effect of a dilation on the length of a line segment.
The scale factor determines whether line segment dilation is longer or shorter.
What is dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.The effect of dilation on the length of a line segment:
A line segment dilation is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than one (k > 1), the image will be larger than the pre-image, making the image's segments (sides) longer than the pre-corresponding image's sides (an enlargement).Therefore, a line segment dilation is longer or shorter in the ratio given by the scale factor.
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4 1-2 ft long and 45 in long which one is shorter
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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[2+2*(-2)+3]^2
what are the steps to solve?
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!^^
what is the slope of a line parallel to line 9x+3y=2
please help :
A fair coin is tossed 29 times. what is the probability that at most 27 heads occur?
Answer:
0.99999994412
Step-by-step explanation:
You want the probability at most 27 heads occur in 29 tosses of a fair coin.
ProbabilityThe 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>
Andy has 4 brothers and 2 sisters. What is
the ratio of boys to girls in his family? Please help me find the answer:)
Answer:
2:1
Step-by-step explanation:
There are 4 brothers, 2 sister so
4 (boys): 2(sister) => 2:1 (Simplified form)
Someone please help.
In a trivia game, each correct answer is worth 10 points in the first round, 15 points in the second round, and 25 points in the third round. You score 370 points by answering 24 questions correctly. You score 55 more points in the third round than you do in the first round, How many questions do you answer correctly in each round?
The questions answered in each round was 12 in the first round, 5 in the second round and 7 in the third round.
What is an equation?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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ANSWER QUICKLY
only if its correct tho, or else i report xx <3
Answer:
D. -0.48
Step-by-step explanation:
A. -0.56
B. -0.056
C. -0.5 (-0.50)
D. -0.48
-0.48 is the largest number because it is the closest number to 0
Answer:
-0.056
Step-by-step explanation:
All work is shown in the screenshot that I have attached to this answer! :)
Solve each equation. Check each solution. 5x/4 - 3/x= 1/4
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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If f + j = 115 and j+k= 103 what is the value of j
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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Solve for x: 1/3(2x − 8) = 4.
A. 2
B. 6
C. 10
D. 10/3
Answer:
C.10
Step-by-step explanation:
x=10
You can enter it into the calculator to check it.
Hope this helped! ;)
Porfabor ayuda con esto de matemáticas
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
one straight section of road rises from an elevation of 1070m to 1132m. the run is approximately 1.3km . what is the percent grade of the road?
The percent grade of the road will be 4.7692%.
How to calculate the percentage?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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PLS PLS HELP ME THIS
Answer:
Yes
Step-by-step explanation:
Points D and E are on plane F.
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Similar solids have exactly the same shape, but not necessarily the same size.
Answer:
I pretty sure that is false. similar solids are the same shape but can be different sizes.
find the volume of the object.
please HURRY
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
A is between points B and C. AB = 2x - 3, BC = 7x - 10, and AC = 32.
What is the value of x?
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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A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C? Write and solve an equation to find the answer.
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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PLEASE HELP ME!!! THIS IS TOO HARD!!! Emily runs 2,000 feet away from her house, and she ran back. How many miles did she run in total.
Answer: 4000
Step-by-step explanation: 2000 there and 2000 back. 2000+2000=4000
Hope this helps!
383,72728,3536,627,2772,636,773,739,629,452,103,648,193,373,382,556,34,7685,834,55,948,3597,527,548,65,86,589,2468,963,469,1457,73,56,986,688,45,. find the mean of the given data
Answer: Average x = 2991.75
Step-by-step explanation: The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
Average = Sum / Count
= 107703 / 36
= 2991.75
A transformation that shifts the graph up/down or left/right is called which one of the following?
Answer:A translation
Step-by-step explanation:
A translation
Step-by-step explanation:A shift of the graph up, down, left, or right, without changing the shape, size, or dimensions of the graph, is called a translation. Examples: If f (x) = x2 + 2x, the equation if the graph is shifted is 4 units up.
Write an equation of a parabola with the given focus and directrix.
focus: (0,3) ; directrix: y=-1
Answer:
ur6eywg6wwggeueuewgv
the population of halifax is about. time as big as the population of balnamore
The population of Halifax is about 1000 times as greater as the population of Balnamore.
What are comparing numbers?The process of defining similarities between two numbers and determining which number is greater, smaller, or equal to the other number is known as comparing numbers.
Here we will compare the numbers by using counting.
We know that a number with more digits is typically greater than one with fewer.
i) The population of Birmingham is about 10 times as big as the population of Halifax because the population of Birmingham is 9,00,000 is greater than Halifax's 90,000 by 10.
ii) The population of London is about 1000 times as big as the population of Longton. Because the population of London has three more zero digits than the population of Longton.
iii)The population of Halifax is about 1000 times as big as the population of Balnamore. Because the population of Halifax has three more zero digits than the population of Balnamore.
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