Answer:
To find point [tex]\( P \)[/tex] on line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're seeking a point dividing [tex]\( GK \)[/tex] into segments at a \( 3:2 \) ratio.
Explanation:
To find the point [tex]\( P \)[/tex] on the line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're essentially looking for a point [tex]\( P \)[/tex] that divides the line segment [tex]\( GK \)[/tex] into two segments, where the ratio of the length of the segment from [tex]\( G \) to \( P \)[/tex] to the length of the segment from [tex]\( P \) to \( K \) is \( 3:2 \).[/tex]
Here's how to approach it:
1. Calculate the distances [tex]\( GP \) and \( PK \)[/tex] using the distance formula (or Pythagorean theorem if it's a 2D coordinate plane).
2. Let [tex]\( x \)[/tex] be the distance from [tex]\( G \) to \( P \)[/tex] and [tex]\( y \)[/tex] be the distance from [tex]\( P \)[/tex] to [tex]\( K \).[/tex]
3. Set up the equation [tex]\( 3x = 2y \),[/tex] representing the ratio of the lengths.
4. Solve for [tex]\( x \) and \( y \)[/tex] to find the coordinates of point [tex]\( P \).[/tex]
This process ensures that the point [tex]\( P \)[/tex] divides the line segment [tex]\( GK \)[/tex] into two segments according to the given ratio.
What is the value of y?
Enter your answer in the box.
An equation with an exponent is called an exponential equation. true or false?
Solve each inequality and give the solution in interval notation:
Sarah has a job at a salon and she earns $50 per day plus tips. Her average tip is 15% of the total amount her customers spend on services. Sarah's daily income is represented by the variable y and the amount her customers spend is represented by the variable x. Which equation represents Sarah's daily income?
11+22+33+...+1010 is divided by 5. what is the remainder? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4
a 12-ft-by-15-ft swimming pool has a 3-ft-wide no-slip surface around it. what is the outer perimeter of the no-slip surface?
Answer:
A
Step-by-step explanation:
78 ft
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24 minutes. Working together, how long will it take for them to paint the wall?
Answer: 8
Step-by-step explanation:
24 loaves of bread cost $48. How much do 10 loaves cost
3 -2 is equivalent to _____.
A -6
B -9
C 1/9
D 1/6
Thanks!
You are making balloon arrangements for a birthday party. there are 16 white balloons and 24 red balloons. each arrangement must be identical. what is the greatest number of arrangements you can make using every balloon?
This is basically a GCF problem. To find the
GCF, we list the factors of each number.
24 = 1×24, 2×12,
4×6, 8×3 ...
16 = 1×16, 2×8,
4×4, ...
The greatest common factor is 8 because it is the greatest
factor we can find.
So 8 arrangements
Match each step to its justification to solve 2x+5=19
The steps :
given subtraction property of equality subtract division property of equality divide Further ExplanationOne variable linear equation is an equation that has a variable and the exponent number is one. Can be stated in the form:
[tex]\large{\boxed{\bold{ax=b}}}[/tex]
or
ax + b = c, where a, b, and c are constants, x is a variable
Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one
Can be stated in the form:
[tex]\large{\boxed{\bold{ax+by=c}}}[/tex]
ax + by = c
x, y = variable
There are 2 general steps to solving a linear equation of one variable:
1. add or subtract both segments with the same number so that it is expected that in one segment there are only variable modifiers or constant numbers 2. Change the equation into a simple form so that the coefficient of the variable is 1This can be done by dividing or multiplying by equal numbers
An equation will remain equivalent if both segments are multiplied or divided by the same number
In the equation
2x + 5 = 19
The right steps to complete it according to the images included are:
1. 2x + 5 = 9 ⇒ given 2. both segments are subtracted by the number 52x + 5 -5 = 9-5 ⇒subtraction property of equality
3. 2x = 14 ⇒subtract 4. both segments are divided by 2 so that the coefficient x = 1[tex]{\displaystyle {\frac {2x} {2}}=~\frac{14}{2}[/tex]
⇒division property of equality
5. x = 7 ⇒ divideLearn more
the slope-intercept form of the linear equation
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a graph of a linear equation
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Keywords: variable, linear equation
P and q are on a number line. If p has a coordinate -5 and pq =7 , what could the coordinate of p be
Given quadrilateral jklm with diagonals that bisect the vertices, what kind of quadrilateral is jklm? rhombus parallelogram trapezoid generic quadrilateral (no more specific classification can be determined)
There are between 50 and 60 eggs in a basket. When Mohammed counts by 3's, there are 2 eggs left over. When he counts by 5's there are 4 left over. How many eggs are there in the basket?
The correct answer is:
59
Explanation:
The numbers between 50 and 60 that are divisible by 3 are
51, 54, 57, 60
The numbers between 50 and 60 that are divisible by 5 are
50, 55, 60
We know that when he counts by 3s, he has 2 left over; this means the number he counts to is 2 fewer than the number of eggs. This means, counting by 3s, we could have
51+2, 54+2, 57+2, or 60+2 = 53, 56, 59, 62
62 is not an option, since we know we have between 50 and 60 eggs; this gives us 53, 56 or 59.
We also know that when he counts by 5s, he has 4 left over; this means the number he counts to is 4 fewer than the number of eggs. This means, counting by 5s, we could have
50+4, 55+4, 60+4, or 54, 59, 64
64 is not an option, since we know we have between 50 and 60 eggs; this gives us 54 or 59.
The only number in both lists is 59, so this must be the answer.
Joe earns $10 per hour babysitting and $5 per hour dog walking. He also earns tips for each job. Last week Joe spent 6 more hours walking dogs than babysitting. He received $5 in tips for babysitting and $10 in tips for dog-walking. Joe earns the same total amount for each job. Write an equation to represent the situation. Use the variable H to represent the number of hours Joe spent babysitting.
Answer:
54
Step-by-step explanation:
t−12/2=3/t2−3
solve for T
–3
–1
1
3
18 tens 20 ones = Hundreds
Mick has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 10 minutes, what is the probability his first two pieces will be a jelly treat and a mint stick?
Give your answer in a percent.
To find the probability, calculate the probabilities of selecting a jelly treat and a mint stick. Then multiply these probabilities together to find the overall probability.
Explanation:To find the probability that Mick's first two pieces will be a jelly treat and a mint stick, we need to calculate the probability of selecting a jelly treat and a mint stick from the bag.
First, we need to find the total number of pieces in the bag: 2 mint sticks + 11 jelly treats + 7 fruit tart chews = 20 pieces.
The probability of selecting a jelly treat as the first piece is: 11 jelly treats / 20 total pieces = 0.55 or 55%.
After Mick has eaten one piece, there are now 19 pieces left in the bag.
The probability of selecting a mint stick as the second piece is: 2 mint sticks / 19 remaining pieces = 0.105 or 10.5%.
Therefore, the probability that Mick's first two pieces will be a jelly treat and a mint stick is 55% * 10.5% = 0.055 or 5.5%.
Harry buys a sofa set that costs $2000.00. He pays for it by installments at an interest rate of 5% per year. What is the total amount he has to pay at the end of the one year?
Harry is required to pay an additional $100 as interest for one year on the $2000 sofa, bringing the total payment to $2100 at the end of the year.
Harry buys a sofa set at a cost of $2000 with an installment plan that includes an interest rate of 5% per annum. To calculate the total amount Harry needs to pay at the end of one year, you need to calculate the interest and then add it to the principal amount.
The interest for one year is calculated as follows:
Interest = Principal imes Rate imes Time.
Interest = $2000 imes 5% imes 1 year.
Interest = $2000 imes 0.05 imes 1.
Interest = $100.
Now, we add the interest to the principal amount to find the total amount Harry has to pay by the end of the year:
Total Amount = Principal + Interest.
Total Amount = $2000 + $100.
Total Amount = $2100.
Therefore, Harry will have to pay a total of $2100 at the end of one year.
If, while training for a marathon, you ran 76 miles in 2 2/3 months, how many miles did you run each month? (Assume you ran the same amount each month)
The set of whole numbers is closed under division
True or false
Answer:
true
Step-by-step explanation:
The elevation of Death Valley-282 feet. The Mississippi River in Illinois has an elevation of 279 feet. Which is closer to sea level?
The Mississippi River is closer to sea level.
What is the length?It is the measure of distance between the two points called length.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The elevation of Death Valley is 282 feet.
The Mississippi River in Illinois has an elevation of 279 feet.
If the length of the elevation of Death Valley 282 is greater than the length of the Mississippi River 279.
The Mississippi River is closer to sea level.
More about the distance link is given below.
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#SPJ2
Is the following definition of perpendicular reversible? If yes, write it as a true biconditional. Two lines that intersect at right angles are perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles, then they are perpendicular.
C. Yes; if two lines are perpendicular, then they intersect at right angles.
D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Math Quiz Question! Measuring segments and Angles
In the diagram, m < ACB = 65
m < BCD =
How do I solve this ?
In the expression 4^9 the number 9 is called the
True or false: it is possible to determine a vector if only one of its components is known.
50 POINTS! PLEASE HELP!
Which of the binomials below is a factor of this trinomial? x2 - 3x - 4
A. x2 + 4
B. x + 4
C. x - 4
D. x + 8
Answer:
c) x - 4
Step-by-step explanation:
To do a factorization of this kind of trinomial there is a technique very easy to do it.
First, you need to see the numbers that are along with the x and the independent number.
In this case -3 and -4 (I will call them b and c)
Next, you need to think in two numbers that can acomplish the following:
x * y = c
x + y = b
So, first, think, which are two numbers that you can multiply between them to give as a result -4?.
In this case it would be -4 and 1 (-4*1 = -4)
These numbers if you do a sum you'll get -3:
-4 + 1 = -3
So the factorization becomes this:
(x - 4) (x - 1)
So, one of the factors is x - 4. Option c
What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?
A. x = −6
B. x = −4
C. y = −6
D. y = −4
we know that
The given line is parallel to the x-axis
so
the equation of the line that is parallel to the given line and passes through the point [tex](-4,-6 )[/tex] will be equal to the y-coordinate of the point
The y-coordinate of the point is [tex]-6[/tex]
therefore
the equation is
[tex]y=-6[/tex]
the answer is the option C
[tex]y=-6[/tex]
Use the data from the following chart to answer the question below.
it was 1.0 that was water this is what i have g/cm3
According to the chart, one milliliter of water would have a density of _____.
100 g/cm 3
10 g/cm 3
1 g/cm 3
cannot be determined
Answer:
1 g/cm 3
Step-by-step explanation: