The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction
Emanuel did a mistake in her first step by taking negative sign twice.
What is multiplicative rule with different sign ?Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.
Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.
For instance:
8 x 4 = 32(-8) x (-4) = 3210 x 9 = 90(-10) x (-9) = 90According to question,
= [tex]\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)[/tex]
Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.
Correct steps are:
Step 1:
[tex]\frac{(3)(4)(-1)}{(5)(9)(2)}[/tex]
Step 2:
[tex]\frac{-12}{90}[/tex]
Step 3:
[tex]-\frac{2}{15}[/tex]
Therefore, the step 1 was miscalculated by Emanuel.
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The complete question is -
Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)
Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction
Step 3 StartFraction 12 over 90 EndFraction
Step 4 StartFraction 2 over 15 EndFraction
In which step did his first error occur?
Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
-Write the piecewise function for 0 to 2 miles.
f(x) = ?
The piecewise function is
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
How to determine the piecewise function?From the question, we have:
Fares = $2.00 ⇒ up to (and including) 1/2 miles
Fares = $0.70 increment ⇒ greater than 1/2 miles
Let x represent the number of miles, and f(x) the fares.
So, we have:
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
The above represents the piecewise function
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1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20
The sum of 225 consecutive positive integers only has digits 1 or 0. What is the smallest possible value of the sum?
Answer:
1 +10=11 (since 0 is neither negative or positive the first and second positive integerswith 1 or 0
Solve the following system of equations:
3x-5y=-11
7x+2y=-12.
Express your answer as an ordered pair. (x, y)
Answer: (-2, 1)
Step-by-step explanation:
We will graph the given equations. The point of intersection is the solution to the system of equations. See attached.
They intersect at the point (-2, 1) giving us an answer of x = -2 and y = 1, but this question asks for the answer as an ordered pair so we leave it as is.
Solve for xxx in the diagram below.
Answer:
x = 34
Step-by-step explanation:
The three angles form a straight line and are thus supplementary angles. The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:
180 = 2x + 112
68 = 2x
x = 34
Solve for X. Please solve this.
Answer:
32
Step-by-step explanation:
Opposite angles are congruent, so Angle BAC is 58 degrees.
Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.
Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.
Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.
Solve the polynomial congruence x^2-3x+2 is congruent to 0 mod 5. Solve for x=? or x=?,when k is any integer
The solutions of x² - 3x + 2 ≡ mod 5 does not exist.
How to solve Polynomial Congruence?
We are given the Polynomial;
x² - 3x + 2 ≡ mod 5
Finding the roots of the equation gives;
x² - 2x - x + 2 = 0(mod 5)
x(x - 2) - 1(x - 2) = 0(mod 5)
Thus, RHS = 0(mod 5) = 0
The roots of the equation are;
x = 1 and x = 2
Thus, the solutions of x² - 3x + 2 ≡ mod 5 does not exist.
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these box plots show the basketball scores for two teams.
The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.
What is a box plot ?A box plot is used to study the distribution and level of a set of scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
A box plot is symmetric when the median is at the center of the box and negatively skewed if the median is closer to the upper quartile.
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Helllllllppppppppppp what Is 20 divided by 8
Answer:
2.5
Step-by-step explanation:
IVE BEEN WATCHING YOUR ACCOUNT STOP STEALING POINTS OR YOUR ACCOUNT WILL BE TERMINATED.
Can someone pls pls PLS, help me out? ASAP!! (Geometry)
“Complete the proof”
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)
4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)
5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)
f(x) is a function. O A. True 0 False 6 12 9 f(x) 3 4 7
Answer:Answer: true
Step-by-step explanation: f(x) is a function because each x value (left oval) has one y value (right oval)!
Total area=
Help asap please thank u so much
The total area of the figure shown is 320 square units.
How to get the total surface area?
We can see that we have 4 triangular faces and one square face.
The area of a square of side length S is:
A = S²
Here we can see that the side length of the square is 10 units, then the area of the base is:
a = (10)² = 100
For a triangle of base B and height H, the area is:
[tex]A = B*H/2[/tex]
Here we can see that the base measures 10 units and the height 11 units, so the area of each triangular face is:
A' = (10)*(11)/2 = 55
Then the total area is:
area = 100 + 4*55 = 320
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What are the solutions of sin(2theta)+sin(theta)=cos(theta) on the interval [0, 360]
The solutions are: θ = 90º, 270º, 30º, and 150º
Given,
sin2θ = cosθ
sin2 θ = 2sinθ cosθ
2sinθ cosθ = cosθ
2sinθ cosθ - cosθ = 0
factor
cosθ(2sinθ-1) = 0
cosθ = 0 or 2sinθ - 1 = 0
cosθ = 0 when θ=90º or θ=270º (look on the unit circle)
2sinθ - 1 = 0
2sinθ = 1
sinθ = 1/2
look at the unit circle and see that sinθ=1/2 when θ=30º
sin is positive in Quadrant2 as well as Quadrant 1
180º-30º=150º
θ=150º
answers: θ=90º, 270º, 30º, and 150º
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The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) f(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. f(x) is an odd degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a positive leading coefficient.
Last option. The correct statement about the graph is g(x) is an odd degree polynomial with a positive leading coefficient.
How to solve the questionWe have the function as
[tex]f(x) = x^2 - 2x + 1[/tex]
The polynomial that we have here is of an even degree. The highest degree we have here is 2. The coefficient that has the highest degree is 1.
Hence all of the options that have f(x) are incorrect.
The answer to the question is option 4.
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When y = -8, x = 8, what is x when y = -6?
Answer:
x = 6
Step-by-step explanation:
y = -8
x = 8
-x = -8 = y
-x = y
now, when y is -6
-x = y = -6
-x = -6
x = 6
Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)
A) Does y vary directly with x?
B) What is the constant of variation?
Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
Variationy = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
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11. Write four solutions for each of the following equation: (i)7x + 2y = 9 (ii) 2x = -5y
The solutions of the equations are (0,4.5), (1, 1), (2, -2.5) & (3, -6) and (0,0), (1, -0.4), (2, -0.8) & (3, -1.2)
How to determine the solutions?Equation 1
7x + 2y = 9
Make y the subject
2y = 9- 7x
Divide by 2
y = 4.5 - 3.5x
Let x = 0, 1, 2 and 3
y = 4.5 - 3.5 * 0 = 4.5
y = 4.5 - 3.5 * 1 = 1
y = 4.5 - 3.5 * 2 = -2.5
y = 4.5 - 3.5 * 3 = -6
Hence, the solutions of the equation are (0,4.5), (1, 1), (2, -2.5) and (3, -6)
Equation 2
2x = -5y
Make y the subject
y = -0.4x
Let x = 0, 1, 2 and 3
y = -0.4 * 0 = 0
y = -0.4 * 1 = -0.4
y = -0.4 * 2 = -0.8
y = -0.4 * 3 = -1.2
Hence, the solutions of the equation are (0,0), (1, -0.4), (2, -0.8) and (3, -1.2)
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The area of the triangle shown is represented by A=s(s−12)(s−9)(s−7)−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle? Round your answer to the nearest hundredth. (25 points to answer!! please))
The height h of the triangle is 5.42 ft
How to find height of a triangle?The height of the triangle can be found using the formula below:
Area = 1 / 2 bh
where
b = baseh = heightTherefore,
A = √s(s - a)(s - b)(s - c)
Hence,
s = 14 + 7 + 11 / 2 = 32 / 2 = 16
A = √16(16 - 11)(16 - 7)(16 - 14)
A = √1440
A = 37.947331922
A = 37.95 ft²
37.95 = 1 / 2 × 14 × h
h = 37.95 / 7
h = 5.42104741743
h = 5.42 ft
Therefore, the height h of the triangle is 5.42 ft
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Does anyone know how to do this
Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.
What is the area of a rectangle?The area of a rectangle of length l and width w is given as follows:
A = lw.
In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:
A = 80.w = l + 2.Then:
l(l + 2) = 80
l² + 2l - 80 = 0
(l + 10)(l - 8) = 0.
We need the positive measure, hence:
l - 8= 0 -> l = 8 units.
w = l + 2 = 10 units.
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Question is in the pic.
Answer is C as all other choices are even numbers therefore make the equation non-integer.
Answer:
C)7
Step-by-step explanation:
Due to the fact that all other options are even numbers so it Wii make the equation non-integer.
Explain how to solve 4^(x + 3) = 7 (x+3 being an exponent) using the change of base formula. Include the solution for x in your answer—round your answer to the nearest thousandth.
Using natural logarithms properties, we will see that:
x = -1.596
How to solve the equation?
Here we can use the property:
[tex]ln(a^b) = b*ln(a)[/tex]
Now we have the equation:
[tex]4^{x + 3 }= 7[/tex]
If we apply the natural logarithm in both sides, we get:
[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]
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Analyzing the Discrim
Which values of c will cause the quadratic equation-x²+3x+c=0 to have no real number solutions? Check all that
apply.
0-5
0 0 0
9
Intro
ant of a Quadratic Equation
Done
The values of x that will give the quadratic equation no real number solutions are -5 and 9
What are real roots of a quadratic equation?Real roots of a quadratic equation are values of x, whose numbers can be represented on a number line.
Analysis:
We have -[tex]x^{2}[/tex] +3x +c = 0
[tex]b^{2}[/tex] - 4ac is called the discriminant of a quadratic equation.
if [tex]b^{2}[/tex] - 4ac < 0, then the quadratic equation has no real root.
where a = -1, b = 3 c = c
[tex](3)^{2}[/tex] -4(-1)c < 0
9 + 4c < 0
4c < -9
c < -9/2
Which means values lower than -9/2 would give the solution no real root.
From, the options, only -5 would give no real solution, since it is lower than -9/2.
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Identify the factors of 6ab − 8a 21b − 28. (2a 4)(3b − 7) (2a − 4)(3b 7) (2a 7)(3b − 4) (2a − 7)(3b 4)
Answer: ) (2a+7)(3b- 4)
Step-by-step explanation:
Nancy left a bin outside in her garden to collect rainwater. she notices that 1 over 2 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin. show your work. explain your answer in words.
[tex]\frac{3}{4}[/tex] gallons of water fill the bin.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Given: Nancy left a bin outside in her garden to collect rainwater.
She notices that 1 over 2 gallons of water fills 2 over 3 of the bin.
To Find: Write and solve an expression to find the amount of water that will fill the entire bin.
Let's say the amount of Water to fill the bin = W gallon
Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{2W}{3}[/tex]Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{1}{2}[/tex] gallonEquate both:
[tex]\frac{2W}{3} =\frac{1}{2}[/tex] is the expression to find the amount of water that will fill the entire bin.
[tex]\frac{2W}{3} =\frac{1}{2} \\2W=\frac{3}{2} \\W=\frac{3}{4}[/tex]
Therefore, [tex]\frac{3}{4}[/tex] gallons of water fill the bin.
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Joe and Sue were trying to calculate the square inches of paper needed to create a cone for the cotton candy. The radius
was 2 in and the height was 6 inches and there was a 1/2 in of overlap for the glue.
Calculations
Joe
2π√10+ √10
Sue
12π + 3
choose the correct statements below.
select one or more:
Sue was correct.
Joe was correct.
Sue used the correct height and radius and calculated the overlap by adding the area for the strip of glue.
Neither were correct.
Joe used the height and radius to calculate the slant height.
The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
How to find the square inches of paper needed.The square inches of paper needed A = surface area of cone + area of overlap
Surface area of cone
The surface area of the cone is given by A = πr[r + √(h² + r²)] where
r = radius of cone = 2 in and h = height of cone = 6 in.So, A = πr[r + √(h² + r²)]
A = π × 2 × [2 + √(6² + 2²)]
A = π × 2 × [2 + √(36 + 4)]
A = π × 2 × [2 + √40]
A = π × 2 × [2 + 2√10]
A = 2π[2 + 2√10]
A = 4π + 4π√10
The area of overlap
The area of overlap A' = wL where
w = width of overlap = 1/2 in and L = slant height of cone = √(h² + r²)So, A' = wL
A' = w[√(h² + r²)]
A' = 1/2[√(6² + 2²)]
A' = 1/2[√(36 + 4)]
A' = 1/2[√40]
A' = 1/2 × 2√10
A' = √10
So, the number of square inches of paper needed is A" = A + A'
= 4π + 8π√10 + √10
Since the number of square inches of paper needed is 4π + 4π√10 + √10
So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
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Which of the following statements about angles is NOT correct?
Complementary angles are two angles whose sum is 90 degrees.
The measure of an obtuse angle is always greater than the measure of an acute angle.
The measure of an acute angle and the measure of an obtuse angle added together will always
be supplementary.
Two right angles that share a leg are supplementary.
ANSWER: The third statement appears to be incorrect.
Which statement is true of the graph on the
right?
The average salary doubled between year 1
and 2.
The average salary tripled between year 1
and 3.
The average salary increased by the same
amount each year.
DONE
1. The TRUE statement about the graph, which is represented here by the data table, is D. The average salary increased by some irregular amount each year.
2. The average salary per year between 2001 and 2006 is $3,600?
What is an average?An average number is the mean of a total value.
The average is computed as the total value of observations divided by the number of observations.
Data for the graph and Calculations:Year Salary
2001 $1,500
2002 2,600
2003 3,200
2004 4,100
2005 5,000
2006 5,200
Total $21,600
Average = $3,600 ($21,600/6)
Thus, the graph or the data table shows that D. The average salary increased by some irregular amount each year.
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Question Completion:1. Option D: The average salary increased by some regular amount each year.
2, What is the average salary per year between 2001 and 2006?
Answer: C-The average salary increased by the same amount each year.
NEXT ANSWER-B
Step-by-step explanation:
The lengths of three sides of a triangle are 2x + 1/5 feet , 4x + 1/2 feet , and x+ 1 5 . what is the perimeter of the triangle? the drondown menuto complete the answer
Answer:
7x + 9/10 ft
Step-by-step explanation:
To find the perimeter of a triangle, add the lengths of the three sides
P = 2x + 1/5 + 4x + 1/2 + x+ 1/ 5
Combine like terms
P = 7x + 2/5 +1/2
Get a common denominator
P = 7x + 2/5(2/2) + 1/2 * (5/5)
= 7x + 4/10 + 5/10
= 7x + 9/10
please put it in expanded form and solve it
Answer:
1/xyz^3
Step-by-step explanation:
exponents are subtracted when divided
x^0 is 1
negative exponents are positive in the denominator
(4x^0y^-2z^-3) / (4xy-1)
(4xy^-2z^-3) / (4xy^-1)
x-1y^-1z^-3
1/xyz^3