The required expressions about the geometry figure can be proven as follows;
1. The measure of ∠2 and ∠3 are congruent by the substitution property of equality
2. ∠2 and ∠3 are congruent, (∠2≅∠3) by the property of equality
What is the property of equality?The property of equality are properties that enable the solution of algebraic equations to be found and they include, addition, subtraction, multiplication, division, reflexive, substitution, transitive and symmetric properties.
1. The required paragraph to prove that ∠2 ≅ ∠3 is as follows:
Given that ∠1 and ∠2 form a linear pair, then their sum is 180°. Given that the sum of the measure of ∠1 and ∠3 is also 180°, then the sum of ∠1 and ∠2 is equal to the sum of ∠1 and ∠3. Therefore, by the addition property of equality, ∠2 ≅ ∠3.
2. The two column proof is as follows:
Statement [tex]{}[/tex] Reasons
1. ∠ABC = ∠1 + ∠2 is ⊥ 1. Given
2. ∠ABC = 90° 2. Definition of a perpendicular line
3. ∠1 + ∠2 = 90° 3. Substitution property of equality
4. ∠1 and ∠3 are complementary 4. Given
5. ∠1 +∠3 = 90° 5. Definition of complementary
6. ∠1 + ∠2 = ∠1 +∠3 6. Substitution property of equality
7. ∠2 ≅ ∠3 7. Addition property of equality
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Consider the expressions (2.4 x 10/8) and (9.2 x 10/6) Find the difference of the expressions.
Find the product of the expressions
The difference of the values is -12.9 while the product of the expression is 45.9
How to solve for the differenceWe have to solve for
2.4 x 10/8
= 2.4 x 1.25
= 3
(9.2 x 10/6)
= 9.2 x 1.667
= 15.3
The difference between the values wpuld be
3 - 15.3
= -12.3
The product of the expressions would be solved by
3 x 15.3
= 45.9
Hence we would say that the difference that is in the values that we have here is -12.9 while the product of these values is given as 45.9
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Find the difference: 11/21 - 3/7
We will operate as follows:
[tex]\frac{11}{21}-\frac{3}{7}=\frac{2}{21}[/tex]There was a big snowstorm on Friday night. By Saturday afternoon, 3 inches of the snow had melted. There were still 8 inches of snow left. Solve an equation to find how many inches of snow fell during the snowstorm.
Answer:
13 correct me if i am wrong
Step-by-step explanation:
Compute P9, 2 please help me solve this
Answer:
72
Step-by-step explanation:
Formula: P (n,r) = n! ÷ (n - r)!
n = Total number of objects in a set
r = The number of items you choose
!/Factorial = Product of all positive numbers less than or equal to the given positive number
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
P (9,2) = 9! ÷ (9-2)!
362,880 ÷ 5,040 = 72
Can you give me two examples of a absolute value parent function
SOLUTION:
Step 1:
In this question, we are given the following:
Can you give me two examples of an absolute value parent function?
Step 2:
What is the parent function for absolute value?
An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.
Examples include:
1. The absolute value parent function, written as: f(x)=| x |, is defined as:f(x)={x if x>00 if x=0−x if x<0.
[tex]f(x)\text{ =}\lvert x\rvert[/tex], is defined as:
[tex]f(x)\text{ =}\lvert x\rvert[/tex][tex]\begin{gathered} f(x)\text{ =}\lvert x\rvert \\ \text{if x > 0, then f(x) = x} \\ \text{if x < 0, then f(x) = x} \end{gathered}[/tex]2. The second example of absolute value function is:
[tex]f(x)\text{ =}\lvert\sin x\rvert[/tex]An arch is in the shape of a parabola. It has a span of 72 meters and a maximum height of 9 meters.
Answer:
Equation of the parabola:
[tex]y=-\frac{1}{144}x^2+9[/tex]The height of the arch 18 meters from the center is 6.75m
Explanation:
The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0
Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9
Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.
With all this, we can try to find the general form of a parabola. The general form is:
[tex]y=ax^2+bx+c[/tex]c is the y-intercept. We know that c = 9
We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]SInce the x-coordinate of the vertex is x = 0
[tex]0=-\frac{b}{2a}[/tex]If we solve:
[tex]b=0[/tex]So far we have:
[tex]y=ax^2+9[/tex]Finally, to find a, we can use the point (36, 0) (one of the roots)
[tex]0=a(36)^2+9[/tex]And solve:
[tex]\begin{gathered} 324a=-9 \\ . \\ a=-\frac{9}{1296}=-\frac{1}{144} \end{gathered}[/tex]Thus, the equation of the arch is:
[tex]y=-\frac{1}{144}x^2+9[/tex]Evaluating this equation for x = 18, we can find the height of the arch:
[tex]y=-\frac{1}{144}(18)^2+9=-\frac{9}{4}+9=-6.75[/tex]1. the interest on $2,00 for 2 years is 320 what is the simples interest rate
2. if the interest earned on an account after 2 years is $15, how much would it be after 10 years?
1. The simple interest rate is 80%
2. The interest earned on the account after 10 years is $75
What is simple interest?Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.
The formula for simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal or initial amountR is the interest rateT is the time taken for the interestFrom the information given, we are to determine the interest rate, R
Substitute the values into the formula, we have;
320 = 200 × R × 2/100
Now, cross multiply, we have;
320(100) = 400R
Find the product of the values
400R = 32000
Divide both sides by the coefficient of the interest rate, we get
R = 32000/400
Find the quotient
R = 80%
If the interest for 2 years is $15
Then in 10 years = $x
cross multiply
x = 150/2
Find the quotient
x = $75
Hence, the rate is 80%
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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
60 and 274.
Step-by-step explanation:
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the
measures of the indicated sides, and the scale factor.
CB and AB
D
2.4
729
2
610
E
2.6
F
C
3.6
A
72⁰
3x-0.6
2x
61 B
2
| ADEF - AABC;x=15;CB=39; AB=3; 3
2
ADEF-ACBA; x = 3; CB=3; AB=3.9; 3
2
ADEF-ACBA; x = 1; CB = 3.9; AB = 3; 3
3
ADBF - AABC;x=1.5; CB=3; AB=3.9; 2
Scale factor means ratio of the sides of the triangle then the measures of the indicated sides, and the scale factor of CB and AB exists ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
What is meant by scale factor?A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Each pair of given polygons are similar.
Similarity statement for the given polygons:
In ΔDEF and ΔABC,
∠D = ∠A (Angle)
∠E = ∠B (Angle)
Therefore, ΔDEF ΔABC (by AA similarity)
If two triangles are similar, then their sides are proportional.
[tex]$\Rightarrow \frac{D F}{A C}=\frac{D E}{A B}$[/tex]
[tex]$\Rightarrow \frac{2.4}{3.6}=\frac{2}{2 x}$[/tex]
By using cross multiplication, we get
⇒ 2.4 × 2x = 2 × 3.6
simplifying the above equation, we get
⇒ 4.8x = 7.2
⇒ x = 1.5
Therefore, the value of x = 1.5.
Substitute x = 1.5 in CB and AB,
CB = 3x – 0.6 = 3(1.5) – 0.6 = 3.9
AB = 2x = 2(1.5) = 3
Scale factor means ratio of the sides of the triangle.
⇒ DF/AC = 2.4/3.6 = 2/3
Therefore, the correct answer is option a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
The complete question is:
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.
[tex]$\overline{C B}$[/tex] and [tex]$\overline{A B}$[/tex]
a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3;
b) ΔDEF - ΔCBA; x=3 ; C B=3 ; A B=3.9 ; 2/3
c) ΔDEF - ΔCBA; x=1 ; C B=3.9 ; A B=3 ; 2/3
d) ΔDEF - ΔABC; x=1.5 ; C B=3 ; A B=3.9 ; 3/2
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Given the function h(x) = x^2 – 7x + 6, determine the average rate of change of the function over the interval 3 < x < 7.hurry please need answer.
Answer:Explanation:
The average rate of change = 3
The average rate of change for a function f(x) is an intervale a < x < b can be calculated using the following equation:
[tex]\frac{f(b)-f(a)_{}}{b-a}[/tex]Therefore, the average rate of change of the function h(x) = x^2 – 7x + 6 in the interval 3 < x < 7 is:
[tex]\frac{h(7)-h(3)}{7-3}[/tex]Where h(7) and h(3) are equal to:
[tex]\begin{gathered} h(7)=7^2-7(7)+6 \\ h(7)=49-49+6 \\ h(7)=6 \\ h(3)=3^2-7(3)+6 \\ h(3)=9-21+6 \\ h(3)=-6 \end{gathered}[/tex]So, the average rate of change is:
[tex]\frac{6-(-6)}{7-3}=\frac{6+6}{4}=\frac{12}{4}=3[/tex]Therefore, the answer is 3.
Help!
A. 5
B. 3
C. 4
D. 16
Answer: the andwer to that is C
Step-by-step explanation:
Find the value of x so that f(x) = 7.
For the given function f(x) = 7 , the value of x is 5.
solution:
We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:
(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)
Where:
(xA , yA) , (xB , yB) given
to find , (xC , yC)
(xA , yA) = (2,0) , (xB , yB) = (5,7) and yC = 7
to find xC ,
xC - xA = (yC - yA) / (yB - yA) . (xB - xA)
xC = xA + (yC - yA) / (yB - yA) . (xB - xA)
xC = 2 + (7-0)/(7-0) x (5 - 2)
xC = 2 + (5 - 2)
xC = 2 + 3
xC = 5
so the value of x in given function f(x) = 7 is 5.
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A(-3,-2) and M (2,6) find the coordinates of the other endpoint
The other endpoint of the segment is (7, 14)
How to determine the coordinate of the other endpoint?From the question, we have:
On the segment, we have the following endpoints
Endpoint 1, A = (-3,-2)
Midpoint, M = (2,6)
The midpoint of the segment is calculated using
Midpoint (x, y) = 1/2 * (x1 + x2, y1 + y2)
Where
(x1, y1) = (-3,-2)
(x, y) = (2,6)
Substitute the known values in the above equation
So, we have
(2, 6) = 1/2 * (-3 + x, -2 + y)
Multiply both sides of the equation by 2
So, we have
(4, 12) = (-3 + x, -2 + y)
By comparison, we have
-3 + x = 4
-2 + y = 12
Evaluate the like terms in the above equation
So, we have
x = 7
y = 14
When the above solution is represented as a coordinate, we have the following
(x, y) = (7, 14)
Hence, the other endpoint of the segment where the segment has the endpoint (-3,-2) and midpoint (2,6) is (7, 14)
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SOmE ONE PLEASE PLEASE I BEG HELP on number 4.
The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4
The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.
y = 3/4|x-6|-8
y = 3/4(-(x-6))-8
y= 3/4( -x + 6) -8
y = 3(-x + 6 - 32)/4
4y = -3x - 24
y = -3(x + 24)/4
For another function of y
y = 3/4|x-6|-8
y= 3/4( x - 6) -8
y = 3(x - 6 - 32)/4
4y = 3(x - 38)
y = 3(x - 38)/4
The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4
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7. Jill was 80th in a class of 200, whereas Nathan, who is in the same class, has a percentile rank of 80. Which student has the higher standing in the class?
The student that has the higher standing in the class is Jill
How to determine the student that has the higher standing in the class?The given parameters are:
Number of students = 200
Jill's position =80th
Nathan's position = Percentile rank of 80
The above means that
Nathan's position = 80 percentage of the number of students in the class
Substitute the known values in the above equation
So, we have the following equation
Nathan's position = 80 percentage of 200
Rewrite as
Nathan's position = 80 percentage * 200
Express as percentage
Nathan's position = 80% * 200
Express 80% as decimal
Nathan's position = 0.80 * 200
Evaluate the product
Nathan's position = 160
So, we have
Jill's position =80th
Nathan's position = 160th
By comparing the positions, 80th is greater than 160th
Hence, Jill has the higher standing in the class
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3. Perform the indicated operation. Show all necessary work.
(a) -1.424-2.9
(b) 1.424-(-2.9)
(c) -1.424-(-2.9) -0.576
Answer:
The result of the indicated operations are:
(a) -4.324.
(b) 4.324.
(c) 0.9
What are operations on decimals?Addition, subtraction, multiplication, and division are the basic operations on decimals.We shall first convert the decimal integers to like decimals before adding and subtracting them. Decimals having the same number of decimal places are said to be like decimals. The decimal points of the addends will be aligned, and if necessary, zeroes will be added at the end of one number to equalize the decimal places. then carry on adding (or removing) as usual. The decimal point should be positioned exactly where it is in the extra numbers in the response (or subtracted)(a) -1.424-2.9
Calculate the sum of the decimals,
The result is -4.324.
(b) 1.424-(-2.9)
Remove the bracket and change the sign in the middle and add the decimals to get the sum,
1.424 + 2.9 = 4.324.
(c) -1.424-(-2.9) -0.576
Remove the parentheses and change the sign,
-1.424 + 2.9 - 0.576
Add the negative decimal numbers and subtract them from the positive decimal number.
-2 + 2.9 = 0.9
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How many lines of symmetry does the figure at the right have?
Lines of symmetry, a line that divides a figure into two mirror parts, for example:
As we can see, the only line of symmetry that we can draw in our figure is:
Answer: One
help meeeeeeee please
The value of the average price per square foot in 2002 is $101. 5
What is a function?A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.
The variables are;
Independent variableDependent variableGiven the function;
P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190
Where;
P is the average price per square feett is the number of years since 1992For the year 2002 , the value of t would be 10
Substitute the value into the formula
P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190
expand the bracket, we have
P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90
multiply through
P(10) = 18 - 2. + 30. 5 + 55. 90
Add the values
P(10) = $101. 5
Hence, the value is $101. 5
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The lines below are perpendicular. If the slope of the green line is ž, what isthe slope of the red line?maO A A. -O B.O c. - 3O D.1Nim
-3/2 (option A)
Explanation:The line of green and red are perpendicular.
For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line.
slope of one line (green) = 2/3
slope of red line = negative reciprocal of green line
slope = 2/3
reciprocal of line = 3/2
negative reciprocal of the line = -3/2
The slope of the red line = -3/2 (option A)
There are two bags of marbles. The first contains one blue, one yellow and two reds. The seconds contains one red, one blue and two yellows. A random marble from each bag is removed. What is the probability of removing a blue and yellow? Give answer as a fraction.
Answer:
3/16
We assume that the marbles are drawn without replacement.
P(blue and yellow)
= P(b1 and y2) + P(y1 and b2)
= P(b1) P(y2) + P(y1) P(b2)
= (1/4)(1/2) + (1/4)(1/4)
= 1/8 + 1/16 = 2/16 + 1/16 = 3/16
who can solve this equation 4x-6=x+9 ??
Answer:
x = 5
Step-by-step explanation:
Hello!
According to the question, what's the value of 4x-6=x+9
4x-6=x+9
Collect like terms
x - 4x = -6 - 9
-3x = -15
Divide both sides by the coefficient of x which is -3
-3x/-3 = -15/-3
x = 5
When checking
4x-6=x+9
(4)(5)−6 = 5+9
14=14
True
1.25x + 1.49 = 100.
The value of x comes to 78.808 after solving the given expression 1.25x + 1.49 = 100.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)A single term or a collection of terms can be used to create an algebraic expression. For instance, 4x and y are the two terms in the expression 4x + y.So, 1.25x + 1.49 = 100:
Now, solve as follows:
1.25x + 1.49 = 1001.25x = 100 - 1.491.25x = 98.51x = 98.51/1.25x = 78.808Therefore, the value of x comes to 78.808 after solving the given expression.
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Given f(x) = 8(12 − x) — 5, what is the value of f(-2)?
Answer:
f(2)=8(12-x)-5
=8(12-2)-5
f(2)=8(10)-5
=75
On a map which is a scale of 1 inch to 12 feet the area of the restaurant is 60 and two squared Han says the actual area of the restaurant is 720 ft.² do you agree or disagree? Explain your reasoning.
Han is therefore mistaken in what he claims. The area is 8640 [tex]feet^{2}[/tex]
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
Let "x" represent the restaurant's actual space.
You are aware that the map's scale is 1 inch to 12 feet. As a fraction, this is written as follows:
[tex]\frac{1inch}{12feet}[/tex]
Calculate the restaurant's scale drawing area. Such is:
([tex]\frac{1inch}{12feet}[/tex]) ² = [tex]\frac{1inch^{2} }{144feet^{2} } }[/tex]
We can set up this percentage and then solve for "x" to determine the precise location of the restaurant because the restaurant's location is indicated on the map.
Such is:
[tex]\frac{144}{1}[/tex] = [tex]\frac{x}{60}[/tex]
60 (144) = x
x = 8640 [tex]feet^{2}[/tex]
Han is therefore mistaken in what he claims.
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A store sells juice in different sizes. Determine which size is the best buy and the unit price.8 oz $2.4024 oz $6.4864 oz $14.08
To determine which is the best buy, we need to first find the unit price of each
8 oz $2.40
Unit price
$2.40/8 = $0.3
1 oz = $0.3
24 oz $6.48
Unit price
$6.48/24 =$0.27
1 oz = $0.27
64 oz $14.08
Unit price
$14.08/64 =$0.22
From the above the best best buy is the one with the lowest price which is $0.22
The best buy is;
64 oz $14.08
and the unit rate is $0.22 per oz
y=x2^+9x+7 in vertex form
Answer: (-9/2,-53/4)
Step-by-step explanation:
Answer:
[tex]y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.a is the leading coefficient.To find the vertex form of a quadratic equation, complete the square.
Given quadratic equation:
[tex]y=x^2+9x+7[/tex]
Add and subtract the square of half the coefficient of the term in x to the right side of the equation:
[tex]\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2[/tex]
[tex]\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}[/tex]
[tex]\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}[/tex]
Factor the perfect square trinomial formed by the first 3 terms:
[tex]\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]
Only 1 and 9 please show work THANK YOU
Simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
As given,
Simplify the following expression to a single complex number,
1) [tex]\sqrt{-9}[/tex] = [tex]\sqrt{9}\sqrt{-1}[/tex] = 3i
where i is the complex number representing [tex]\sqrt{-1}[/tex]
2) √-16 = 4i
3) √-6 √-24
= √6 ×6 ×4
= 6 ×4
= 24
4) √-3 √-75
=√ 3×75
= √3 × 3 ×25
= 3 ×5
=15
5) [tex]\frac{2 +\sqrt{-12} }{2}[/tex]
= (2 + 2√-3) /2
= 1 + √3 i
6) [tex]\frac{4+\sqrt{-20}}{2}[/tex] = [tex]\frac{4+\sqrt{20}\sqrt{-1}}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}\sqrt{-1})}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}i)}{2}[/tex] = [tex]\frac{2(2+\sqrt{5}i)}{2}[/tex] = 2 + [tex]\sqrt{5}i[/tex]
where i is the complex number representing [tex]\sqrt{-1}[/tex]
Therefore, simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
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Estimate 5.209 + 2.667 by rounding to the nearest whole number.
Answer:
I'm pretty sure it would be 8 though forgive me if I'm wrong
What are the coordinates of a point 4/5 of the way B to A
A(3,-4)
B(13,11)
[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]
There was a jar of cookies on the table. First Ken came along. He was hungry
because he missed lunch, so he ate half the cookies in the jar. Mary came in the
kitchen next. She didn't have dessert at lunch so she ate one third of the cookies
left in the jar. Karen followed her to the cookie jar and she took three fourths of
the remaining cookies. Susan ran into the kitchen, grabbed one cookie from the
jar and ran out again. That left one cookie in the jar. How many were in the jar to
begin with?
Answer:
There were 24 cookies in the jar at the beginning.
Step-by-step explanation:
There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.