What are the coordinates of the point on the directed line segment from (-10, 2) to
(-3, -5) that partitions the segment into a ratio of 4 to 3?
Answer:
(-6, -2)
Step-by-step explanation:
For points A(-10, 2) and B(-3, -5), you want the point P that makes AP/PB = 4/3.
SetupUsing (x, y) for the coordinates of P, we have ...
AP/PB = 4/3
((x, y) -(-10, 2))/((-3, -5) -(x, y)) = 4/3
SolutionThis simplifies to ...
(x+10, y-2)/(-3-x, -5-y) = 4/3
Cross multiplying gives ...
3(x +10, y -2) = 4(-3 -x, -5 -y)
(3x+30, 3y-6) = (-12-4x, -20-4y)
Treating these equations separately, we have ...
3x +30 = -12 -4x ⇒ 7x = -42 ⇒ x = -6
3y -6 = -20 -4y ⇒ 7y = -14 ⇒ y = -2
The point that partitions the segment is (-6, -2).
__
Additional comment
The point that partitions AB in the ratio m/n is ...
P = (mB +nA)/(m+n)
P = (4(-3, -5) +3(-10, 2))/(4+3) = (-12-30, -20+6)/7 = (-42, -14)/7 = (-6, -2)
Above, we started from the basic requirement, rather than using the formula that results from that requirement.
a coin is flipped, and a number cube is rolled. what is the probability of getting heads on the coin and a number less than 3 on the number cube
The required probability for the given case is obtained as 1/6.
What is probability?Probability is the measurement of the chance for a random event.
It is the ratio of the favorable outcome to the total possible outcome.
It always lies in the interval [0, 1].
The sample space for the given case can be written as follow,
The total number of sample space elements are,
Possible outcomes for coin × Possible outcomes for cube
= 2 × 6 = 12
Now, the number of favorable outcomes for the given event is as below,
Number of head × Number of numbers less than 3
= 1 × 2 = 2
Now, the probability is given as,
P(Head on coin and less than 3 on cube) = 2/12 = 1/6
Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is given as 1/6.
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Factors 3x^4-5x^3+6x^2-15x completely over the set of integers
The Factors of 3x^4-5x^3+6x^2-15x completely over the set of integers will give 5(1-3x).
How can this be calculated?In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller
The expression can be broken down after the other as
[2x4 = 8] + [5x3=15] + [6x2=12]
= [8-15+12-15x]
=5-15x
then we can factorize as
5(1-3x)
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Michael pays $34.65 for eleven 18-count boxes of granola bars. How much does 1 box of granola bars cost?
One box of granola bars costs $
Answer:−cnotu+53.65
Step-by-step explanation: I don't really know how I got it. But it was quite easy.
Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.
Answer:
Step-by-step explanation:
Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.
you have the base and the height in the drawing, the area of the rectangle is found by multiplying the base by the height, 6 x 4 = 24 cm²The base of this rectangle is 4 cm.The height of this rectangle is 6 cmThe Area of this rectangle is 24cm²Answer:
24 cm²
Step-by-step explanation:
Solution Given:
The base of this rectangle is 4 cm. The height of this rectangle is 6 cm
height =6 cm
base = 4cm
Since
Area of Rectangle= base*height
=6*4
=24 cm²
Therefore, the area of this rectangle is 24 cm².
1-9 Enrichment Worksheet
Geometry Crossword Puzzle
12
NAME
16
13
19
3
18
10
ACROSS
3. Points on the same line
are -
4. A point on a line and all
points of the line to one
side of it.
9. An angle whose measure
is greater than 90.
10. Two endpoints and all
points between them.
16. A flat figure with no
thickness that extends
indefinitely in all
directions.
1
17. Segments of equal length
segments.
are -
18. Two noncollinear rays
with a common endpoint.
19. If m ZA+ m ZB = 180,
then ZA and ZB are -
angles.
17
2
15
9
4
8
14
18
DATE
DOWN
1. The set of all points collinear to two points
is a.
Glencoe Division, Macmillan/McGraw-Hill
7
2. The point where the x- and y-axis meet.
5. An angle whose measure is less than 90.
6. If m ZA+ m ZD = 90, then ZA and ZB are
angles.
7. Lines that meet at a 90° angle are
8. Two angles with a common side but no
common interior points are
10. An "angle" formed by opposite rays is a
_________ angle.
11. The middle point of a line.segment.
12. Points that lie in the same plane are -
13. The four parts of a coordinate plane.
14. Two nonadjacent angles formed by two
intersecting lines are - angles.
15. In angle ABC, point B is the
Answer:
Look at the image I attached to this answer for the answers.
This is a crossword puzzle on geometry terms and concepts, including lines, angles, and planes.
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tia equally shares 8 cookies among herself and 4 friends which fraction shows how many cookies each person gets?
answers:
8/4
8/5
5/8
4/8
Answer: The answer is 8/5
Answer:
Each person gets 8/5 part of cookie
help pls i don’t know the last two!
Drag each label to the correct location on the image.
Identify which equations have one solution, infinitely many solutions, or no solution.
3u+40+2u6u- 30-u
2.3y +3.2-y= 2.1 + 1.3y + 1.1
No Solution
One Solution
2.2z+ 3z = 4.5-3.2
x+²+x= x
²x + ² + x = ² x 20 +4r = 32 - 2r
²/²
Infinitely Many Solutions
No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r. One solution: 2x + 4 = 3x + 1/2
What is the linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
If the value of the variable is zero, then the no solution.
If the value of the variable is one, then the one solution.
If the value of the variable is infinity, then the infinite many solutions.
No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r.
One solution: 2x + 4 = 3x + 1/2
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algebra: please check the picture, there is 2 question
answer for 50 point
The {-4, 0, 1} represents members of the domain of the graphed function.
What is the domain of the function?
A function is a mathematical object that accepts input, appears to apply a rule to it, and returns the result.
A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result.
The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs.
The range refers to the outputs which are actually used.
We have,
collection of the ordered pairs represents a function:
{(4, 19), (-2, 77), (0, 10), (1/2, 9/5), (1, 10), (-3, 0), (100, 100)
a) Domain of the function is:
{ -2, -3, 0, 1/2, 1, 4, 100}.
b) Range of the function is:
{ 0, 9/5, 10, 19, 77, 100}.
Hence, the Domain of the function is { -2, -3, 0, 1/2, 1, 4, 100} and the Range of the function is {0, 9/5, 10, 19, 77, 100}.
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The vertices of ABC are A(3,-4), B(-4,-2), and C(1,1). For the translation below, give the vertices of A’B’C
T(-5, -2 (ДАВС)
The vertices of A'B'C' are A, B, and C
(Simplify your answers. Type ordered pairs.)
The translated vertices from the given vertices are:
A(3, -4) → A'(-2, -6)
B(-4, -2) → B'(-9, -4)
C(1, 1) → C'(-4, -1)
What is the translation rule?The translation rule for the coordinates of a graph is given by
(x, y) → (x + a, y + b)
Here the coordinates (x, y) are translated by (a, b) units.
Calculation:The given vertices of a ΔABC are:
A(3, -4), B(-4, -2), and C(1, 1)
If the vertices are translated by T(-5, -2) units, then the new vertices after translation are calculated by using the rule (x, y) → (x + a, y + b). Here (a, b) is (-5, -2).
Thus,
A(3, -4) → (3 - 5, -4 - 2) ⇒ A'(-2, -6)
B(-4, -2) → (-4 - 5, -2 - 2) ⇒ B'(-9, -4)
C(1, 1) → (1 - 5, 1 - 2) ⇒ C'(-4, -1)
Therefore, the translated version of the ΔABC is ΔA'B'C' and its vertices are A'(-2, -6), B'(-9, -4), and C'(-4, -1).
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Factor 24cd − 36c2d.
12c2d(2 − 6)
12cd(2 − 36c2d)
6cd(4 − 36c2d)
4cd(6 − 9c)
Answer:
4cdb ( 6 − 9c )
Step-by-step explanation:
24cd = 4cd × 6
36c²d = 4cd × 9c
24cd − 36c²d = 4cd ( 6 − 9c )
24 divided by 4•2 - 2
Answer:
the answer is 10
Step-by-step explanation:
The value of the numerical expression 24 / (4 × 2 - 2) will be 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 24 / (4 × 2 - 2)
Simplify the expression, then we have
⇒ 24 / (4 × 2 - 2)
⇒ 24 / (8 - 2)
⇒ 24 / 6
⇒ 4
The value of the numerical expression 24 / (4 × 2 - 2) will be 4.
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The area of the triangle is 22.4 cm². Calculate the length, b, of the longest side of the triangle.
The length, b, which is the longest side of the triangle, can be found to be 13.172 cm.
How to find the length ?To find the area of 22.4 cm², the formula used was:
Area = 1/2 x a x b x Sin(C)
Using this formula, we can find the value of side a to be :
22.4 = 1/2 x 3.7 x a x Sin(97°)
a = 12. 199 cm
We can then use the Cosine rule to find the value of b, which is the longest side:
b² = a² + c² - 2 x a x c x Cos(B)
b = √ ( a² + c² - 2 x a x c x Cos(B))
b = 13. 172 cm
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What tastes juicier?
Mixture A: 2 cups of concentrate and 3 cups of water
Mixture B: 6 cups of concentrate and 8 cups of water
Group of answer choices
Mixture B
Mixture A
They taste the same
Answer:
Mixture B
Step-by-step explanation:
A) the concentrate per cup is 2/3
B) the concentrate per cup is 6/8 = 3/4
The concentration of B is higher, so it will taste juicier.
which fraction is equivalent to -4/8
Answer:
-2/4
Step-by-step explanation:
A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of: Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation. 1) 50 mph 2) 70 mph 3) x mph 4) (x+10)mph 5) (x-5)mph
If a train traveled 300 miles. The time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.
How to find the time?Distance = Rate × Time
Time =Distance/Rate
1. 50 mph
Time = 300/50
Time = 6 hours
2. 70 mph
Time = 300/70
Time = 4.29 hours
3. x mph
Time = 300/x
Time = 300/x hours
4. (x+10)mph
300/(x+10) hours
5. (x-5)mph
300/(x-5) hours
Therefore the time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.
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4 adults took their 5 children to a movie. The price for the 9 people was $160. The 5 children recieved a 20% discount on their tickets. The cost for a child ticket is how much less than the cost of an adult ticket?
The cost for a child ticket was $4 less than the cost of an adult ticket.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the cost of adult tickets be x.
The 5 children received a 20% discount on their tickets.
So;
x-20% of x
= (x-20/100) × x
= x-0.2x
= 0.8x
Here, 4x+5×0.8x=160
⇒ 4x+4x=160
⇒ 8x=160
⇒ x=20
So, the cost of children is 20-20% of 20
= 20-0.2×20
= 20-4
= 16
Therefore, the cost for a child ticket was $4 less than the cost of an adult ticket.
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The diagram shows the lengths of corresponding sides of similar triangles A'B'C' and ABC. Which expression gives the perimeter of A'B'C'?
The expression that gives the perimeter of the A'B'C is 2 (a + b + c).
Option B is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The side length of triangle A'B'C' is twice the length of the corresponding side length of triangle ABC.
The perimeter of a triangle.
= Sum of all the three sides
Now,
The perimeter of the triangle ABC.
= a + b + c
Thus,
The perimeter of the triangle A'B'C'.
= 2 (a + b + c)
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Create a problem that could be solved by multiplying (−3) × (−6).
A problem that could be solved by multiplying (−3) × (−6) is "the product of -3 and -6"
How to determine the productFrom the question, we have the following parameters that can be used in our computation:
(-3) x (-6)
In the above expression, we can see that
-3 and -6 are multiplied
This means that the problem is a product expression
And a problem that can represent (-3) x (-6) is "the product of -3 and -6"
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(x+1)=(7x-5) how do i solve this
Step-by-step explanation:
You start with x+1=7x-5
Basically you want all the x's on one side and all the constants on the other
(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side
(x+6)-x=7x-x, to get rid of the x on the left side
We are now left with 6x=6
No we simplify, 6x/6=6/6
Now we have x=1, which is the answer
I hope this made sense.
x= 1.
Step-by-step explanation:1. Write the expression.[tex](x+1)=(7x-5)\\ \\x+1=7x-5[/tex]
2. Subtract "1" from both sides of the equation.[tex]x+1-1=7x-5-1\\ \\x=7x-6[/tex]
3. Subtract "7x" from both sides of the equation.[tex]x-7x=7x-6-7x\\ \\-6x=-6[/tex]
4. Divide both sides by "-6".[tex]\frac{-6x}{-6} =\frac{-6}{-6} \\ \\x=1[/tex]
5. Verify.[tex](1)+1=7(1)-5\\ \\2=7-5\\ \\2=2[/tex]
That's correct!
6. Conclude.x= 1.
The sum of two consecutive mile markers on the interstate is 365. Find the numbers on the markers.
Answer:
x is the first mile marker
then, x+%2B+1 the second mile marker
given:
x%2Bx+%2B+1=655
2x+=655-1
2x+=654
x+=654%2F2
x+=327->the first mile marker
and
x+%2B+1=328 the second mile marker
26
Select the correct answer.
The height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t. Find the eceleration at time t.
O A.
100-cos t
OB.
-sin t
O C.
-cos t
O D. 100-sin t
Reset
Next
-sint is the acceleration at time t.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Given, the height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t.
We need to find the acceleration at time t.
s(t) = 100 + cos t.
To find the acceleration we have to differentiate the above equation.
d/dt=d/dt(100+cost)
=d/dt(100)+d/dt(cost)
=0+(-sint)
s'(t) = -sint.
Hence, the acceleration at time t is -sint.
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A family of bears is going to a movie. The following data points represent the ticket and candy price (in dollars) for each bear. Sort the data from least to greatest. Find the interquartile range (IQR) of the data set.
The interquartile range (IQR) is a measure of dispersion, which is a measure of how spread out a data set is. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
Q1 = ( n +1 ) / 4th observation
= ( 9 + 1) / 4
= 2.5 th obseravation
That is the average of 2nd and 3rd observations.
Q1 = 2
Q3 = 3 ( n + 1) / 4 th observation
= 3 ( 9 + 1) / 4
= 7.5 th observation
That is the average of the 7th and 8th observation
Q3 = 5.5
Interquartile range = Q3 - Q1 = 5.5 - 2 = 3.5
In this data set, the first quartile is the average of the second and third observations (2), and the third quartile is the average of the seventh and eighth observations (5.5). Subtracting the first quartile from the third quartile gives us an IQR of 3.5. This means that the values in the data set are spread out over a range of 3.5 dollars.
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Jordan is working two summer jobs, making $6 per hour walking dogs and making $15 per hour clearing tables. In a given week, he can work a maximum of 11 total hours and must earn at least $120. If xx represents the number of hours walking dogs and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
xx=5 and yy=6
Step-by-step explanation:
Hope it helps you
Joseph is 3 times as old as his son now, if 10 years ago the sum of their ages was 44 ,how old was Joseph when his son was born ?
Answer:
Step-by-step explanation:
j = 3s
(j-10 + s-10) =44
3s-20 + s =44
4s = 64
s = 16
j=3*16
j=48
currently Joseph is 48, the son is 16, so
16 years ago, when the son was born, Joseph was 32
Answer:
Joseph was 34 years old when his son was born.
Caleb is a fashion designer. He designed a jacket with 2 types of fabric. Now Caleb has to make samples. He buys 68 yards of nylon and 94 yards of wool. The nylon is $3 a yard, and a yard of wool is 3 times more expensive. How much did Caleb spend?
To find out how much the wool costs, we need to multiply the price of a yard of nylon by 3, since the wool is 3 times more expensive. So a yard of wool costs $3 * 3 = $<<3*3=9>>9.
To find out how many yards of wool Caleb bought, we need to divide the total number of yards by the number of fabrics, since he bought the same amount of each fabric. So Caleb bought 68 / 2 = <<68/2=34>>34 yards of wool.
To find out how much Caleb spent on wool, we need to multiply the number of yards of wool by the price of a yard of wool. So Caleb spent 34 * $9 = $<<34*9=306>>306 on wool.
To find out how much Caleb spent on nylon, we need to multiply the number of yards of nylon by the price of a yard of nylon. So Caleb spent 68 * $3 = $<<68*3=204>>204 on nylon.
To find out how much Caleb spent in total, we need to add the amount he spent on wool and the amount he spent on nylon. So Caleb spent $306 + $204 = $<<306+204=510>>510 in total. Answer: \boxed{510}.
Find the y-intercept from the line of best fit y = 6 + 2x.
Answer:
y - intercept = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6 + 2x , that is
y = 2x + 6 ← is in slope- intercept form
with y- intercept c = 6
Solve the equation for x.
−0.28x − 8.4 = 8.26
x = 59.5
x = −59.5
x = 50.5
x = −50.5
The value of x after solving −0.28x − 8.4 = 8.26 is x = −59.5 .
What is linear equation in one variable ?
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
To solve linear equation in one variable:
Step 1: Simplify each side, if needed.
Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.
Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.
Given :
-0.28x - 8.4 = 8.26
Adding 8.4 both the sides , we get
-0.28x + (-8.4 + 8.4) = 8.26 + 8.4
-0.28x = 16.66
x = - (16.66/0.28)
x = -59.5
Hence , the value of x after solving −0.28x − 8.4 = 8.26 is x = −59.5 .
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A person starts walking from home and walks:
2 miles East
3 miles Southeast
6 miles South
7 miles Southwest
3 miles East
This person has walked a total of
miles
Find the total displacement vector for this walk:
If this person walked straight home, they'd have to walk
miles
This person has walked a total of 21 miles and the total displacement vector for this walk is 13.153 in northeast direction by the concept of distance and displacement.
What is distance and displacement?Unaffected by direction, distance describes an object's entire movement. Displacement, in contrast, refers to a shift in an object's position. Because of this, the primary distinction between distance and displacement is that one is a scalar and the other is a vector.
According to question let us determine the total distance 2 miles+3 miles+6 miles+7 miles+3 miles =21 miles
So, this person has walked a total of 21 miles
Now let us find displacement vector as follows:
Divide into parts: Each leg on the Southeast and Southwest diagonals is the hypotenuse, therefore multiply by (2) /2.
x-axis is given as 2+3*(√ (2) /2) +0 -7(√ (2) /2) +3 =1.464
Similarly, y-axis is given as 0- 3(√ (2) /2)- 6- 7(√ (2) /2) +0=-13.071
The coordinates of the given ques are as follows: <1.464, -13.071>
By Pythagoras theorem, the hypotenuse of the given coordinates is 13.153 in northeast which is our required displacement.
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Chau sells beaded necklaces.Each large necklace sells for $6.30 and each small necklace sells for $4.80.How much will he earn from selling 4 large necklaces and 5 small necklaces?