Using the section formula, point F lie on 3/5 in the number line.
In the given question,
On a number line, point D is at -3, and point E is at 6.
The point F lies on segment DE .
The ratio of DF to FE is 2 : 3.
We have to find where point F lie on the number line.
Since point D lies is at -3 at x axis so the point should be ( -3,0).
Point E lies is at 6 at x axis so the point should be ( 6,0).
F lies on segment DE. So let the point of F is (X, Y)
The ratio is 2:3.
Now firstly finding the value of X using section formula
X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]
where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3
Now putting the value
X = {2×6+(-3)3}/(2+3)
Simplifying
X = (12-9)/5
X = 3/5
Now firstly finding the value of Y using section formula
Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]
where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3
Now putting the value
Y = (2×0+3×0}/(2+3)
Y = 0/5
Y = 0
Hence, point F lie on 3/5 in the number line.
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the slope intercept form of the equation of the line through the given point with the given slope
through (-1, -4) slope = 5
Answer:
y=5x+1
Step-by-step explanation:
we already know the slope so we can put it in the slope intercept form
y=5x
And now we can put the coordinate points in there to find the y intercept
-4=5(-1)
-4=-5
We need to add 1 to make this equation true so the y intercept is 1
The equation will be
y=5x+1
Hopes this helps please mark brainliest
Answer:
y=5x+1
Steps are in the picture
1 million divided by 2
500,000
OR
five hundred thousand
A cylinder used for storing spools of thread has a radius of 2 units and a slant height of √29. What is the height of the cylinder?
PLS HELP ASAP!!(show work if can)
Height of cylinder is 5 units
Define Cylinder
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.The volume of the slanted cylinder is V = Base area of cylinder × Height of cylinder⇒ V = (π × radius²) × h
We have given,
Slant height of cylinder = √29
Radius is = 2 units
Now, we to have to calculate the height for that we have the formula
h = √l² - r²
where, l = slant height
r = radius of the circular base
h = height of the cylinder
Now, for the sake of simplicity
h = √l² - r²
h² = l² - r²
Now, plug in the values
h² = (√29)² - 2²
h² = 29 - 4
h² = 25
h = 5
Hence, the height of cylinder is 5 units
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Does the point (-2, 7) lie on the graph of y=-2x+1?
yes
no
The point (-2,7) is not lie on the graph of y = -2x +1 .
Given,
In the question:
To check the :
Does the point (-2, 7) lie on the graph of y=-2x+1?
Now, According to the question:
The equation is :
y = -2x + 1
Substitute the values of x = -2 and y = 7 into y = -2x +1
7 = -2(-2) + 1
LHS = 7
RHS = -2(-2) + 1 = 5
Write in the form :
7 = 5
Verify the relationship
False
Determine whether the point is on the line:
(-2, 7) not on the graph.
Hence, The point (-2,7) is not lie on the graph of y = -2x +1 .
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Isosceles Trapezoids in Summary
Check ALL of the statements that are ALWAYS true about ISOSCELES TRAPEZOIDS.
(Select all that apply.)
1. SIDES: One pair of opposite sides are parallel.
2. SIDES: One pair of opposite sides are congruent.
3. SIDES: A pair of adjacent sides are congruent.
4. ANGLES: Sum of the angles is 360°.
5. ANGLES: One set of opposite angles are congruent.
6. ANGLES: Consecutive angles are congruent.
7. ANGLES: All four angles are right angles.
8. ANGLES: Consecutive angles are supplementary.
9. DIAGONALS: One of the diagonals bisects the other.
10. DIAGONALS: Diagonals are congruent.
11. DIAGONALS: Diagonals intersect perpendicularly.
12. DIAGONALS: Diagonals bisect a pair of vertex angles of the shape.
The statements that are always true about Isosceles Trapezoids:
One pair of opposite sides are parallel.
One pair of opposite sides are congruent.
The sum of the angles is 360°.
Diagonals are congruent.
Diagonals intersect perpendicularly.
What is an isosceles trapezoids?
A convex quadrilateral having one pair of opposite sides divided by a line of symmetry is known as an isosceles trapezoid. It is a particular instance of a trapezoid. Alternately, it can be described as a trapezoid whose base angles and both legs are identical in size.
The true statements are:
One pair of opposite sides are parallel.
One pair of opposite sides are congruent.
The sum of the angles is 360°.
Diagonals are congruent.
Diagonals intersect perpendicularly.
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Can someone do this please I need help
Answer:
all are 0
thats why you should do y+4=4-7=×-7=×+4=0
Answer:
for #2 do b
Step-by-step explanation:
Angles RTG and GTU are adjacent angles. If m∠RTG=5.8° and m∠GTU=113.6°, what is m∠RTU in degrees?
If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.
∠RTU = ∠RTG + ∠GTU
∠RTU = 5.8° + 113.6°
∠RTU = 119.4°
The measure of the angle ∠RTU will be 119.4°.
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Describe the characteristics of each set of numbers
that make up the set of integers.
Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions.
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.There are numerous types of numbers, including integers, whole numbers, rationals , real numbers, and natural numbers. Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions. It has the following qualities:
Numbers below zero are considered negative numbers.
In the set of integers, zero is included.
There are overlaps between the number categories.
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In a recipe, for every tablepoon of ugar there are four teapoon of alt. If a batch ue four tablepoon of ugar, how many teapoon of alt doe it ue?
tablepoon of ugar
teapoon of alt 1 4 4
There will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.
Given, In a recipe, for every tablespoons of sugar there are four teaspoons of salt.
If a batch use four tablespoons of sugar then we have to find the number of tablespoons of salt needed.
as, 1 sugar = 4 salt
4 sugar = 4×4 salt
4 sugar = 16 salt
So, the number of tablespoons of salt needed is 16 for the use of 4 tablespoons of sugar.
Hence, there will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.
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I need help with number 7.
With the help of the given trendline equation, the length of the flight will be 3,613.34 miles.
What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the length of the flight will be:
The trendline equation is: T = 458 + 0.15DT is the cost which is given as $1000 and D is the distance.Now, calculate for D as follows:
T = 458 + 0.15D1000 = 458 + 0.15D1000 - 458 = 0.15D0.15D = 542D = 542/0.15D = 3,613.33We can write as D = 3,613.34
Therefore, with the help of the given trendline equation, the length of the flight will be 3,613.34 miles.
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Which value is the best approximation for the range in ages for the oldest 25% of viewers?
4
6
15
20
The best estimation for the range of the oldest 25% is 20, so the correct option is the last one.
Which value approximates the range for the oldest 25%?The graph is separated in four parts, each part represents a 25% of the population.
The oldest 25% would be the last segment (the line in the right of the graph).
The range is defined as the difference between the largest value and the smallest value.
The segment starts at:
a = 35
And ends at:
b = 55
Then the range is something like:
55 - 35 = 20
The correct option is the last one.
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Find the value of x.
79
118°
109
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Find the value of x ?y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
answer is B
x = 108 and y = 109
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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.
Find the value of x ?Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
Therefore the value of x and y is x = 108 and y = 109
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Andrew has 8 cassettes. Mary has x cassettes and Jim has twice as many as Andrew. Together they have four times as Mary has. Form an equation and find how many cassettes Mary has.
Answer:
mary=x
andrew=8
jim=2*8=16
together=4*mary
total=8+16=24
24/4=x
x=6
Step-by-step explanation:
TR is the angle bisector angle ATS. The m angle RTS = (17x-5) and m angle ATS= (28x + 8). find X
Applying the definition of angle bisector, the value of x is: x = 3.
What is an Angle Bisector?An angle bisector can be defined as a ray or line that divides an angle into two parts that are congruent or equal to each other in measure.
Since TR is the angle bisector that bisects angle ATS, it implies that angle ATS is divided into equal parts.
Given the following:
Measure of angle RTS = (17x - 5)°
Measure of angle ATS = (28x + 8)°
Therefore:
Measure of angle ATS = 2(measure of angle RTS) [definition of angle bisector]
Substitute
28x + 8 = 2(17x - 5)°
28x + 8 = 34x - 10
Combine like terms
28x - 34x = -8 - 10
-6x = -18
Divide both sides by -6
-6x/-6 = -18/-6
x = 3
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2.3 Find measure of angle by finding x first
Solve for x.
I need help I have forgotten how to solve for x..
Answer:
x=5
Whole angle/9x=45
Step-by-step explanation:
sum of all three angles in a triangle is 180 degrees so we can add all of these angles together and set it equal to 180 like this
9x+65+70=180
Simplify
9x+135=180
Subtract both sides of 135
9x+135=180
-135. -135
9x=45
since 9x equals 45 that is how much the angle is
Divide both sides by 9 to find x
9x=45
/9. /9
x=5
Hopes this helps please mark brainliest
Simplify: 5-(x-4)
A.-x + 9
B.-x- 7
C.x+4
D.-x-4
⇒ [tex]=5-(x)-(-4)\\=5-x+4\\=-x+5+4\\=-x+9[/tex]
⇒Note the negative sign has to multiply every term in the brackets!
Option A is the answer
Helppppp super confused !
The expression that is equivalent is 6(y + 1) and 6y + 6.
The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.
Now, let's check if the expression are equivalent by simplifying it.
3(x + 3) and 3x + 6
3x + 9 and 3x + 6
Therefore, the expressions are not equivalent.
6(y + 1) and 6y + 6
6y + 6 and 6y + 6
They are equivalent expression.
x(x + 4) and x² + 4
x² + 4x and x² + 4
They are not equivalent expression.
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The price of a gallon of gasoline is $2.25. The price when Ryan's mother started driving was 1/5 of the current price. What was the price of gasoline when Ryan's mother started driving?
The price of gasoline when Ryan's mother started driving is $0. 45
What is a fraction?A fraction can be defined as the part of a whole set, data or element.
The different types of fractions include;
Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractionsExample of mixed fractions; 2 1/ 3
Example of simple fractions; 1/ 2
Example of proper fractions; 2/5
From the information given, we have;
Price of a gallon of gasoline is $2. 25
1/ 5 of $2.25
This is represented as;
1/ 5 × $2.25
Multiply the values
$0. 45
Hence, the value is $0. 45
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Need help im so confused
please and thank you
Answer: It is b
Step-by-step explanation:
Answer: 126.5
Step-by-step explanation:
This is Pythagoras theorem so a² + b² = c²
c² is always the diagonal bit
The soccer field is rectangle and draw the route of the players on and you get the triangle
a = 120
b = 40
c² = a² + b² (square root after)
120² + 40² = 16000
Then square root that to get 126.5
I hoped this helped so please thank and rate :)
Bacteria colonies can increase by 73% every 2 days. If you start with 55 bacteria microorganisms, how large would the colony be after 10 days?
Answer:
In order to complete the equation we need to use this method :
Future Amount = I(1+r)^t
I=Initial Amount
R=Growth rate
T=Time periods
Now that we know that....
Letsss seee:
You started with 55 so
Future Amount = 55(1+r)^t
The growth rate is 73% so we have to convert to decimal so
Future Amount=55(1+.73)^t
Time period is 73% every 2 days and you want to see how large the colony would be after 10 days so you do 10/2:
Future Amount=55(1+.73)^5
Future Amount therefore equals 852.301407 BUT You have to round to the nearest whole number Sooo
The Answer is 852.Step-by-step explanation:
Hope this helpss you Tony!
Answer:
How large would the colony be after 10 days?
852 is the answer.
Step-by-step explanation:
Jorge has 20 fish for his dog sled team that he wants to divide into smaller pieces. How many pieces of fish would there be if Jorge divided each fish into tenths?
2,000
200
2
0.2
Answer:
200
Step-by-step explanation:
20*10=200
a client who weighs 70 kg is receiving a solution of 0.9% sodium chloride (normal saline) 500 ml with dopamine 800 mg at 5 ml/hour. how many mcg/kg/minute is the client receiving? (enter the numeric value only. if rounding is required, round to the nearest tenth.)
1.904 mcg/kg/min is what the client receives.
The number of mcg/kg/minute = flow rate × concentration ÷ mass of client
Flow rate = 12 ml/ hour = 12 /60 = 1/5 = 0.2 ml/min
Formula:
Concentration = mass of dopamine/volume
mass of dopamine = 800mg
volume = 500ml
Concentration = 800/ 500
= 1.6 mg/ml
= 1.6 × 1000 mcg/mg
= 1600 mcg/mg
Here the mass of the client = 70kg
Now calculating mcg/kg/minute = flow rate× concentration÷ mass of client
= 0.08 ml/min × 1600mcg/ml ÷70 kg
= 320/70
= 1.904 mcg/kg/min
Therefore mcg/kg/min is 1.904.
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a party rental company has chairs and tables for rent. the total cost to rent chairs and tables is . the total cost to rent chairs and tables is . what is the cost to rent each chair and each table?
If the total cost to rent 2 chairs and 12 tables is $107 and the total cost to rent 5 chairs and 3 tables is $38, then the costs to rent each chair and table are $2.5 and $8.5 respectively. We can solve this question using elimination and substitution methods.
How do you prove that?Elimination and substitution methods are involved in solving this problem. We're going to use the variables x for the cost of a chair and y for the cost of a table. The total cost to to rent 2 chairs and 12 tables is $107, so the equation can be written as 2x + 12y = 107. The total cost to rent 5 chairs and 3 tables is $38, so the equation can be written as 5x + 3y = 38.
To find the value for x, we need to eliminate the variable y first. Start by multiplying each term in the second equation by 4.
5x · 4 + 3y · 4 = 38 · 4
20x + 12y = 152
Then, subtract the terms in the second equation from their counterparts in the first equation.
2x + 12y = 107
20x + 12y = 152 -
-18x + 0 = -45
Finally, with a little bit of algebraic manipulation, we've got x = 2.5, hence $2.5 is the cost in to rent a chair.
-18x = -45
x = -45/-18
x = 2.5
What about the cost to rent a table? Well, we can substitute 2.5 for x in either of the equations to get the value for y. For instance, we can pick the equation 2x + 12y = 107 and substitute x with 2.5 to isolate the variable y, like this:
2(2.5) + 12y = 107
5 + 12y = 107
12y = 107 - 5 = 102
y = 8.5
The value for y turns out to be 8.5. So the cost to rent a table is $8.5.
Your question is incomplete, but it was most probably "A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 12 tables is $107. The total cost to rent 5 chairs and 3 tables is $38. What is the cost to rent each chair and each table?"
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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?
The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30
The solution to the inequality is n ≤ 5 The largest possible lengths of the sides is 13 cmInequality to represent the perimeter of a trianglePerimeter of the triangle = not more than 30 cmSide a = (2n + 3)cmSide b = (2n + 2) cmSide c = n cmSide a + side b + side c ≤ perimeter of the triangle
(2n + 3) + (2n + 2) + n ≤ 30
open parenthesis2n + 3 + 2n + 2 + n ≤ 30
5n + 5 ≤ 30
substract 5 from both sides
5n ≤ 30 - 5
5n ≤ 25
divide both sides by 5n ≤ 25/5
n ≤ 5 cm
The largest possible lengths of the sides is:
Side a = (2n + 3)cm
= 2(5) + 3
= 10 + 3
= 13 cm
Side b = (2n + 2) cm
= 2(5) + 2
= 10 + 2
= 12 cm
Side c = n cm
= 5 cm
So therefore, the largest possible length of the triangle is 13 cm
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Are the following rectangles similar? Show your work pls (yk how teachers are)
No the two rectangles are not similar as the ratios of the sides are not equal.
Two rectangles are said to be similar if the ratio of the sides of the rectangles are equal.
Now let us consider the given rectangles:
In rectangle ABCD:
AB = 18
AD = 36
In rectangle WXYZ :
WX = 25
XY = 45
Now the ratio of the sides of the rectangle are:
AB/AD = 18 / 36 = 1 / 2
WX/XY = 25 / 45 = 5 / 9
Thus we can see that AB : AD ≠ WX : XY
Hence the rectangles are not similar.
If the ratios of the adjacent sides of two rectangles are equal, then they are similar. A rectangle is a quadrilateral in the Euclidean plane because it has four right angles.
Other definitions include a parallelogram with a right angle or a quadrilateral that is equiangular, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
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Show how you would solve the problem.
a^2 (squared) + b^2(squared) = c squared
Using the Pythagorean Theorem and the given values, we can solve for c.
a^2 + b^2 = c^2
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
√400 = √c^2
c = 20
PLEASE HELP ANSWER JUST ONE OF THEM AT LEAST!
Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.
(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.
$
(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.
(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.
$
Answer:
(a) $2.40
(b) Chips: 4/7
Drink: 3/7
(c) $9.60
Step-by-step explanation:
Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.
(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.
chips : water = 4 : 3
chips/water = 4/3
c/1.8 = 4/3
3c = 1.8 × 4
c = 0.6 × 4
c = 2.4
$2.40
(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.
4 + 3 = 7
Chips: 4/7
Drink: 3/7
(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.
Last week it was 100%.
This week it is 37.5% less.
100% - 37.5% = 62.5%
This week, it is 62.5% of last week.
Let x = last week's amount.
62.5% of (last week's amount) = $6
62.5% × x = 6
0.625x = 6
Divide both sides by 0.625
x = 6/0.625
x = 9.6
$9.60
K =
√2abc
1 + a²-b(squared)+c² - 5b
If a = 4, b = -2 and c = -1
evaluate K
K=
I need a quick answer please !!!
——————————————————
The diagram (below) shows a game in which you use the pieces at the top to form solid rows at the bottom. Using only translations and rotations, describe the transformations of the pieces at
the top that will form two solid rows at the bottom.
meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow
Solve the inequality for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
7x+1/2 >4
The value of x in the Inequality (7x + 1)/2> 4 is x > 1.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, the inequality is given as:
(7x + 1)/2> 4
Cross multiply
7x + 1 > 2 × 4
7x + 1 > 8
Collect like terms
7x > 8 - 1
7x > 7
Divide
x > 7/7
x > 1
Therefore, x > 1.
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