In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Dominique needs to solve the system of equations by graphing. Which statement is true about the system?
2x-3y=12
y=-3/5x+2
A)Both equations are in slope-intercept form.
B)Neither equation is in slope-intercept form.
C)The first equation is y= 2/3x-4 when written in slope-intercept form.
D)The second equation is 3x+5y=10 when written in slope-intercept form.
Answer:
Option C) The first equation is y= 2/3x-4 when written in slope-intercept form
Step-by-step explanation:
we have
[tex]2x-3y=12[/tex] ----> First equation
The first equation is in standard form
Convert to slope intercept form
Isolate the variable y
[tex]3y=2x-12[/tex]
Divide by 3 both sides
[tex]y=\frac{2}{3}x-4[/tex]
[tex]y=-\frac{3}{5}x+2[/tex] ----> Second equation
The second equation is in slope intercept form
Convert to standard form
Multiply by 5 both sides to remove the fraction
[tex]5y=-3x+10[/tex]
[tex]3x+5y=10[/tex]
Verify each statement
case A) Both equations are in slope-intercept form.
False
Because only the second equation is in slope -intercept form
case B) Neither equation is in slope-intercept form
False
Because, the second equation is in slope -intercept form
case C) The first equation is y= 2/3x-4 when written in slope-intercept form
True (see the procedure)
case D)The second equation is 3x+5y=10 when written in slope-intercept form.
False
Because, the second equation is 3x+5y=10 when written in standard form
Suppose you buy a movie for $12.98 the sales tax is 6% find the total cost
What does the symbol "kg" represent in the metric system?
how else can the ratio 14 to 1 be written
Kayla has a tshirt store. she sold three times as many white tshirts as blue tshirts. she sold a total of 48 tshirts. How many white tshirts did kayla sell
An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:
Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 8 ft and a length of 14 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. 2(14 + 8) = 44 square feet 1 over 2.(14 + 8) = 11 square feet 2(14 × 8) = 224 square feet 1 over 2.(14 × 8) = 56 square feet
Answer:
D) 1 over 2. (14 × 8) = 56 square feet
Step-by-step explanation:
You first need to look at the w x h formula (width x height).
W= 14
H= 8
14 x 8= 112
Then, you have to divide 112 by 2. The reason why is because 112 is the area of the whole rectangle, but you only need the area to the triangle, which is half of the rectangle.
112 ÷ 2= 56 sq. ft.
Therefore, the answer is D. Hope this helped!! <3
a pair of jeans cost 75% as much as a pair of corduroy pants what is the cost of each if the total cost for the jeans and courds is $42
j= jeans
c= corduroy
jeans = 0.75C
0.75 +c = 42
1.75c = 42
c = 42/1.75 = 24
jeans cost 24*0.75 = 18
corduroys cost $24
Jeans cost $18
Answer with Step-by-step explanation:
Let j denote the cost of jeans
and c denotes the cost of corduroy
A pair of jeans cost 75% as much as a pair of corduroy pants.
i.e. j = 0.75c
The total cost for the jeans and corduroy is $42
i.e. j+c=42
⇒ 0.75c+c=42
⇒ 1.75c=42
Dividing both sides by 1.75,we get
c=24
Putting value of c in j= 0.75c gives
j=18
Hence, Cost of jeans=$18
and cost of corduroy=$24
Elevator 1 in a building moved from ground position to a final position of +17 feet. Elevator 2 in the same building moved from ground to a final position of −22 feet. Which statement best describes the final positions of these two elevators?
Answer:Elevator is +17 above ground level while -22 is below
Step-by-step explanation:
Since it is + and - i know +is positive that mean up and - is negative which mean down so -22 is below while +16 is above
What is the next term for the given arithmetic sequence 0,2,4,6
2n2-24n+72 factor completely
There are two numbers, which sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers
Jessie received the following scores on her math tests this year. (45, 65, 70, 80, 85, 100) Suppose the teacher removes the lowest and highest scores. (65, 70, 80, 85) What are the interquartile ranges of Jessie’s original scores and her new scores?
Answer:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
Step-by-step explanation:
Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)
Where Q3 is the mid-value of the second half of a dataset and
Q1 is the mid-value of the first half of a dataset.
Original score = 45, 65, 70, 80, 85, 100
Q1 of original score:
First half of original score = 45, 65, 70
Therefore Q1 = 65
Q3 of original score:
Second half of original score = 80, 85, 100
Therefore Q3 = 85
:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score
:. IQR = 85 - 65 = 20
New score = 65, 70, 80, 85
Q1 of new score:
First half of new score = 65, 70
Therefore Q1 = (65+70)/2 = 67.5
Q3 of new score:
Second half of new score = 80, 85
Therefore Q3 = (80 + 85)/2 = 82.5
:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score
:. IQR = 82.5 - 67.5 = 15
Therefore:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
X^2 + 4x - 21 Factor into two binomials
PLZ I NEED THE ANSWER ;c
The sum of 5 consecutive integers is 505
505/5 = 101
so 101 is the middle number, now add the 2 below it and the 2 above it
99 + 100 + 101 + 102 +103 = 505
A rectangular board is 1.8 meters long and 1.5 meters wide. What is the area of the board in square millimeters?
The area of the rectangular board is 2,700,000 mm².
Explanation:The subject of this question is Mathematics and it's likely suitable for a Middle School student. The question asks for the area of a rectangular board given specific length and width in meters, and requires the answer in square millimeters.
First, let's calculate the area of the rectangular board in square meters (m²) by multiplying the length and the width. So, 1.8 m * 1.5 m equals 2.7 m². Now, to convert the area from square meters to square millimeters (mm²), remember that 1 m² is equal to 1,000,000 mm². Therefore, the area of the board in square millimeters is 2.7 m² * 1,000,000 equals 2,700,000 mm².
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Define a function f : R → R by the formula
f(x) = 2x − 8.
Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =
5+1x10 is the answer 60 or 15? there are no parenthesis***
If T is the point at a distance 3pi/5 from P(1, 0) on the unit circle with its center at (0, 0), in what quadrant does T lie?
Final answer:
The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.
Explanation:
If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.
Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.
Solve −2x2 +3x − 9 = 0
To solve the equation -2x^2 + 3x - 9 = 0, we can use the quadratic formula. This equation does not have any real solutions, but it has complex solutions involving imaginary numbers.
Explanation:To solve the equation -2x^2 + 3x - 9 = 0, we can use the quadratic formula. Substituting the values a = -2, b = 3, and c = -9 into the formula, we can then simplify to find the solutions for x.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the values, we have:
x = (-3 ± sqrt(3^2 - 4(-2)(-9))) / (2(-2))
Simplifying further, we get:
x = (-3 ± sqrt(9 - 72)) / -4
x = (-3 ± sqrt(-63)) / -4
Since the square root of a negative number is not a real number, this equation does not have any real solutions. The equation has complex solutions, which involve the use of imaginary numbers.
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Solve the equation. 20x-7=5+16x
What is the sine value of pi over 6?
Answer:
The sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
Step-by-step explanation:
we have to find the value of [tex]sin\dfrac{\pi}{6}[/tex]
we know that value of [tex]sin\dfrac{\pi}{6}[/tex] is [tex]\dfrac{1}{2}[/tex]
Hence, the sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
How to find the distance between a point and a line
Final answer:
To find the distance between a point and a line, you need to find the equation of the line, find the coordinates of the point, substitute the coordinates into the equation, and calculate the perpendicular distance.
Explanation:
To find the distance between a point and a line, you need to use the formula for the distance from a point to a line. Here are the steps:
First, find the equation of the line.
Next, find the coordinates of the given point.
Substitute the coordinates of the point into the equation of the line to find the perpendicular distance from the point to the line.
The distance between the point and the line is the perpendicular distance found in step 3.
For example, let's say the equation of the line is y = 2x + 3, and the coordinates of the point are (4,5). To find the distance between the point and the line:
The equation of the line is y = 2x + 3.
The coordinates of the point are (4,5).
Substituting the coordinates (4,5) into the equation y = 2x + 3 gives 5 = 2(4) + 3, which simplifies to 5 = 11.
The perpendicular distance from the point to the line is |5 - 11|, which is equal to 6.
Therefore, the distance between the point (4,5) and the line y = 2x + 3 is 6 units.
Why is expected income a large factor in choosing a retirement plan
Expected income is crucial in choosing a retirement plan because it influences permanent income for savings, the adequacy of funds against inflation, and financial security post-retirement.
Choosing a retirement plan is a vital financial decision; expected income plays a large role because it directly affects a person's ability to save and sustains their lifestyle after they retire. The idea of permanent income, which is the average annual income an individual expects to receive for the rest of their lives, influences how much they allocate to retirement savings. It's crucial for asset accumulation and ensuring financial security.
Retirement funds sourced from plans like private company pensions or defined benefits can be fixed and may not keep up with inflation, leading to a potential loss of purchasing power over time. Therefore, understanding one's expected income helps in selecting retirement plans that can adjust and possibly increase over time to hedge against inflation. Additionally, individuals must consider the impact of future income changes on their current saving and consumption patterns.
Behavioral economics factors in human psychology and behavior, suggesting that individuals may not always make rational financial decisions due to a lack of self-control or understanding of long-term benefits, influencing retirement plan choices. Thus, expected income is a significant consideration for individuals when choosing a retirement plan, as it determines their ability to save enough to maintain their desired lifestyle in retirement.
Which of the following inequalities represents a number n that is less than or equal to 3 but greater than –2?
Which expression is equal to 7(1+3)
A.) 7+21
B.) 7+3
C.) 1+21
D.) 7+4
I would say D. 7+4 because it is the only one that makes since to me
Determine the sign of cos pi divided by seven without using a calculator.
Answer:
The [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
Step-by-step explanation:
we need to determine the sign of [tex]\cos \frac{\pi}{7}[/tex] without using calculator
Cartesian system ( shown in figure -1)
The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant-1 , Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]
and in first quadrant all trigonometric ratios has positive sign
so, [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
For which value of x should the expression be further simplified
√14x
56
11
5
Or 39
Three-fourths of the yard is covered in grass but 4/5 of the grass has died. How much of the yard has dead grass?
multiply the 2 together:
3/4 x 4/5 = 12/20 = 3/5 has dead grass
To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.
To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).
Performing the multiplication of these two fractions:
Multiply the numerators: 3 × 4 = 12.Multiply the denominators: 4 × 5 = 20.Combine the products to form the new fraction: 12/20.Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:
Divide the numerator: 12 ÷ 4 = 3.Divide the denominator: 20 ÷ 4 = 5.The simplified fraction is 3/5.Therefore, the correct answer is that 3/5 of the yard has dead grass.