The rational exponent form of the given expression is b³. The correct option is the second option b³
Evaluating an expressionFrom the question, we are to determine the rational exponent form of the given expression
The given expression is
[tex]\sqrt{b^{6} }[/tex]
From one of the laws of indices, we have that
[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
Thus,
[tex]\sqrt{b^{6} } = b^{\frac{6}{2} }[/tex]
= [tex]b^{3}[/tex]
∴√b⁶ = b³
Hence, the rational exponent form of the given expression is b³. The correct option is the second option b³
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Mr. Sanchez’s class sold fruit pies for $1.73 each and Mr. Kelly’s class sold bottles of fruit juice for $1.44 each. Together, the classes sold 83 items and earned $130.83 for their school. Write and solve a system of equations that models this problem. Show all your work.
Answer:
p = 39 f = 44
Step-by-step explanation:
p = $ 1.73
f = $ 1.44
equation
p + f = 83
1.73 p + 1.44 (83 - p) = $ 130.83
p = 39 (amount of times fruit pies were sold).
Therefore,
p = 39
f = 44
In studies that use more than one data collector, how is the consistency of the data evaluated?.
The way that the consistency of data is evaluated if more than one data collector is used is; Inter - rater reliability
How to find consistency in data research?When researching data about anything, it is pertinent to note that sometimes, we have to use more than one data collector just to get a more thorough result which only one person may not be able to generate.
Now, the way that consistency of data is evaluated when more than one data collector is used is via Inter-rater reliability. This is because Inter-rater reliability is the extent to which two or more raters or observers agree.
The benefit of Inter-rater reliability is that It addresses the issue of consistency of the implementation of a rating system. Inter-rater reliability can be evaluated by using a number of different statistics.
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pleasee help with these functions
By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)
How to evaluate a composed function
Let be f and g functions, there is a composition of f with respect to g when the input of the former is substituted by the output of the latter. It is to notice that composition is a binary operation between functions.
If we know that f(x) = - (1/2) · x² + 5 · x, g(x) = x² + 2 and x = -2, then the composed function evaluated is:
f(g (x)) = - (1/2) · (x² + 2)² + 5 · (x² + 2)
f(g (- 2)) = - (1/2) · 6² + 5 · 6
f(g (- 2)) = 12
By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)
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im in summer school and i need to pass this please help me
g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
Which statement compares the graph of the two functions?
First, a vertical shift of N units is written as:
g(x) = f(x) + N
if N > 0 the shift is upwards.If N < 0 the shift is downwards.A horizontal shift of N units is written as:
g(x) = f(x + N).
if N < 0, the shift is to the right.If N > 0, the shift is to the left.In this case, we have:
g(x) = f(x + 8) + 4
So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
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PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)
2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).
3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.
4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.
The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph.
It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.
From the data given, we can write the slope and y-intercept form:
y = mx + b
here, m = 10 and b = 300
y = 10x + 300
The number of fat grams in an item has that number of fat calories.
As we have the regression line:
y = 10x + 300
Put x = 1 in the regression line:
y = 10(1) + 300
y = 310 calories
For x = 14
y = 10(14) + 300 = 440
But the actual value from the graph is 330.
Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
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The interior angle of the regular pentagon below measures 108°, and the
pentagon has rotational symmetry. What is the following measure of
an interior angle after a 90° rotation around the point of symmetry?
Given line AC is tangent to circle O.
If m(arc BY)= 44, enter the m∠YAC.
(The figure is not drawn to scale.)
The measure of <YAC from the figure is. 68 degrees
Circle theoremThe given figure is made up of line and angles.
Since the line AC is tangential to the circle, hence <BAC = 90 degrees and;
<BAY + <YAC = 90degrees
Determine the measure of <BAY
<BAY = 1/2(arcBY)
<BAY = 1/2(44)
<BAY = 22degrees
From the expression above;
<YAC = 90 - 22
<YAC = 68 degrees
Hence the measure of <YAC from the figure is. 68 degrees
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Which of the following best describes the folding method needed to create a
perpendicular line segment?
A. Fold tracing paper at a point on the line segment and twist it, creating an acute angle.
B. Fold tracing paper at a point on the line segment and extend the line segment indefinitely.
C. Fold tracing paper at a point not on the line segment so that the line segment lies upon itself.
D. Fold tracing paper so that the line segment's endpoints line up with each other.
Fold tracing paper so that the line segment's endpoints line up with each other , Option D is the correct answer.
What is a Perpendicular ?A perpendicular is a line drawn at 90 degree to a given line or line segment .
Fold tracing paper so that the line segment's endpoints line up with each other.
After drawing a line segment ,
when the end point will be on each other and a crease will be made by pressing the paper , The crease formed will be perpendicular to the line segment.
Therefore, Option D is the correct answer.
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Answer:
The correct answer is C.
Step-by-step explanation:
Fold tracing paper so that the line segment's endpoints line up with each other.
Wendy and two friends went out to eat and decided they would split the bill. The total bill was 35.40. They also decided to leave a 20% tip. What is the price that each person paid?
Answer:
14.16
Step-by-step explanation:
we first calculate the total amount of money paid, which is 35.40 plus 20%, we use this calculation:
35.40×1.20 = 42.48
now, this amount is split to 3 people, so:
42.48/3 = 14.16
and that is our answer
Venn diagrams in maths
Answer:
Step-by-step explanation:
Solve 1 2 1 2x = x2 − 7x 10 4x by rewriting the equation as a proportion. which proportion is equivalent to the original equation?
The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Rational expressionsGiven the following expression
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
In order to find the equivalent proportion, we will find the LCM of the right side expression to have:
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
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Answer: For the next part
✔ x = 1 and x = 8
✔ x = 0
Use the discriminant to describe the roots of each equation. Then select the best description.
3x^2 - 2 + 7x =0
Answer options:
•double root
•imaginary root
•real and irrational root
•real and rational root
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
How to determine the characteristics of the roots of a quadratic equation by discriminant
Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
d < 0 - conjugated complex roots.d = 0 - equal real roots (real and rational root).d > 0 - different real roots (real and irrational root).If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
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If f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction, what is the value of (StartFraction f Over g EndFraction) (5)?
Eleven-halves
StartFraction 27 Over 10 EndFraction
160
270
The value of (StartFraction f Over g EndFraction) (5) will be 270
Fraction is a number that is stated as a quotient in mathematics, when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
Given f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction
We have to find the value of (StartFraction f Over g EndFraction) (5)
Given that the functions f and g are defined by f(x) = 7 + 4x and g(x) = 1/2x
First find the value of (f/g)(x):
(f/g)(x) = (7+4x)/(1/2x)
=(7+4x)(2x)
=7(2x)+4x(2x)
(f/g)(x) = 14x + 8x^2
Put x=5 in the above function,
(f/g)(5) = 14(5) + 8(5)^2
= 70+8(25)
= 70+200
(f/g)(5) = 270
Hence value of (StartFraction f Over g EndFraction) (5) will be 270
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Answer: D.270
Step-by-step explanation:
just got it right on unit test on edge
umm.. i fr don’t know how to do this … help pls
Answer:
2 solutions: ( -4,0 )
( -6,0 )
2 Non solution: ( 2,0 )
( 4,0 )
Answers:
Refer to the graph below
Two solution points are (-5,-4) and (-4,-3)
Non solution points are (0,3) and (1,4)
=========================================================
Explanation:
The boundary line for [tex]y \ge 3x+3[/tex] is [tex]y = 3x+3[/tex]
This linear equation has a y intercept of (0,3) and another point on the line is (1,6). Plot these two points and draw a straight line through them. This line is a solid boundary line because of the "or equal to" as part of the inequality sign. This means points on the boundary adjacent to the shaded region area part of the solution set.
Because of the "greater than" portion, we'll shade above the solid boundary line. This only works because y is isolated.
Keep in mind that we're also told that [tex]y < -2[/tex] which means we'll also shade the region below the boundary line [tex]y = -2[/tex]. This is a dashed line through -2 on the y axis. A dashed line does not include points on the boundary as part of the solution.
---------------
To summarize: We shade above y = 3x+3 (solid) but below y = -2 (dashed).
Refer to the diagram below to see what's going on.
The entire southwest region is shaded.
That blue shaded region represents all (x,y) points that make the system true.
For example, the point (-5,-4) is in the blue region.
Notice how plugging the coordinates into the first inequality gets us...
[tex]y \ge 3x+3\\\\-4 \ge 3(-5)+3\\\\-4 \ge -15+3\\\\-4 \ge -12\\\\[/tex]
which is a true statement. If you plugged y = -4 into [tex]y < -2[/tex], you would also get another true statement.
Both inequalities are true for (x,y) = (-5,-4) which confirms it to be a solution point.
You should also find that a point like (-4,-3) is another solution in the blue region following similar steps. There are infinitely many solution points to pick from. Feel free to choose others.
Non-solution points are such that they aren't in the shaded region. We could also pick points on the dashed boundary line as non-solutions.
Side note: you can pick points on the solid boundary as solution points, but those points must be adjacent to the shaded region. The point (0,3) is NOT a solution even though it's on the solid boundary line.
15. What is 5¹/4 ÷ 2²/7 ?
A. 2 ¹⁹/64
B. 12
C. 2
D. 12 ¹⁹/64
Please help it's urgent... I'll mark brainlist if you answer and get it right
Answer:
A 2 19/64
Step-by-step explanation:
change the proper fractions into mixed fractions then remember to reciprocate the number at your right hand then calculate good day.
PLEASE ANSWER ASAP ACTUALLY ANSWER PLEASE AS SOON AS YOU CAN PLEASE I NEED IT
Graph the quadratic equation. Zoom and pan your graph to establish an appropriate viewing window.
X^2 + 2x - 24 = 0
Step-by-step explanation:
x=4,-6
im pretty sure this is correct
is y+15=30,y=20 true or false?
Answer:
Y + 15 = 30
Y = 30 - 15
Y = 15
15 is not equal to 20
False
All the edges of the object in the diagram are equal in length. The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges. What is the shape of the cross-section resulting from the cut?
The shape of the cross-section resulting from the cut is rhombus.
What is a rhombus?A rhombus simply means a shape that has opposite sides to be parallel and the sides are equal.
Given:
object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.
Edges of the object in the diagram are equal in length and that the object is cut by a vertical plane containing A and B.
Hence, the shape of the cross-section resulting from the cut is a rhombus.
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L 1.9.3 Test (CST): Foundations of Geometry
Question 19 of 25
Which of the diagrams below represents the statement "If it is a tree, then it
has leaves"?
has leaves
tree
Figure A
O A. Figure A
OB. Figure B
tree
has leaves
Figure B
Figure A is a diagram which represents the statement "If it is a tree, then it has leaves."
How to analyze and interpret the diagram?In figure A, we can observe that the subset representing "trees" lie inside another subset which represents "has leaves." Thus, we can logically deduce that the statement "All trees have leaves" and "if it is a tree, it has leaves" is represented by figure A.
On the other hand, we can observe that the subset representing "has leaves" lie inside another subset which represents "trees," which contradicts the given statement "If it is a tree, then it has leaves."
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Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x + 3?
Answer:
There are no "following values" in the problem.
Step-by-step explanation:
ƒ(x) = -2x + 3
For any value of X, enter that number in the equation and calculate f(x) [y].
For example, if x is 2:
ƒ(x) = -2x + 3
ƒ(2) = -2(2) + 3
y = -2(2) + 3
y = -4+3
y = -1
The ordered pair for when x=2 would be (2,-1)
There is a swimming pool which has a length of 15 m and a width of 12 m. There is a 2 m wide path around the pool. If the cost of the path is $5 per , what is the cost of the path? Use words, numbers, and/or symbols to justify your answer.
The cost of the path around the swimming pool with length 15m and width 12m is $1,190
Area of a rectangleLength = 15mWidth = 12mPathway with 2m wide:
Length = 15m + 2m = 17mWidth = 12m + 2m = 14mArea of the path = length × width
= 17m × 14m
= 238 square meters
Cost of the path = $5 per square meterTotal cost of the path = 238 square meters × $5
= $1,190
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PLS HELPPPP I NEED AN ANSWER ASAP WILL GIVE BRAINIEST
What are the alternate exterior angle pairs in the picture below?
∠1 and ∠2, ∠7 and ∠8
∠1 and ∠8, ∠2 and ∠7
∠1 and ∠7, ∠2 and ∠8
Answer:
∠1 and ∠2, ∠7 and ∠8
Answer:
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
just took the quiz
PLEASE ANSWER ASAP!!!!!!
The function f(x)=−6sin(7/3x+1/6)−5 models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit.
Over what range of temperatures does the average rate of change in temperature fall?
Enter a value in each box to correctly complete the statement.
The range in the average rate of change in temperature of the substance is from a low
temperature of ____ F to a high of ________ F
The range in the average rate of change in temperature of the substance is from a low temperature of 1 F to a high of -11 F.
What is a formula for Fahrenheit?The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) ;
°F = (9/5 × °C) + 32.
Given function:
f(x)= -6 sin(7/3 x+ 1/6) -5
The function will be maximum at the 7/3 x +1/6= 3π/2
So, the maximum temperature will be
= -6 sin (3π/2) -5
= 6 -5
= 1 F
The function will be minimum at the 7/3 x +1/6= π/2
Therefore, the maximum temperature will be
= -6 sin (π/2) - 5
= -6 -5
= -11 F
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Please help!
Find m<1
1
60°
63°
Answer:
i think 150 degrees
Step-by-step explanation:
the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°
what expression is equivalent to 1/3y
1. 1/3(y+12)-12
2. 1/6y+1/3(y+3)
3. 1/6y+1/6(y+12)-2
4. 1/3y+1/3(6-y)
The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Hence, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Therefore, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?
The true statement is Peter walks at a rate of 13 over 4 miles per hour.
What is the true statement?Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases. When the hour Peter walks increases, the distance he walks also increases.
Here are the options:
Peter walks at a rate of StartFraction 4 over 13 EndFraction miles per hour.
Peter walks at a rate of 4 miles per hour.
Peter walks at a rate of StartFraction 13 over 4 EndFraction miles per hour.
Peter walks at a rate of 13 miles per hour.
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what is the value of k? ____ units
Answer:
2
Step-by-step explanation:
Corresponding sides are proportional in these similar triangles.
__
short side/long side = k/4 = 4/8
k = 4(4/8) . . . . multiply by 4
k = 2
_____
Additional comment
The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...
l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN
l = 2√5
m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN
m = 4√5
The similarity statements are ...
ΔLMN ~ ΔLNO ~ ΔNMO
4x=5-2y
y-2x=7
to solve using subsitution, what can be subsituted in place of y in the first equation?
Answer:
y = 7+2x
Step-by-step explanation:
4x = 5 - 2y __(1)
y - 2x = 7 __(2)
From eq (2) ,
y = 7 + 2x
Hence, we can substitute (7+2x) in place of y in the first equation.
in a dilation, what is preserved and what is altered?
Answer:
A dilation preserves angle measures.
A dilation alters the length of line segments by the same proportion.
Step-by-step explanation:
A dilatation is a transformation that alters a figure's size while maintaining its shape and orientation. Each linear measure of the figure, such as a side length, is multiplied by the scale factor of a dilatation. A dilation is a transformation where all line segments' lengths are altered uniformly. While a dilatation can alter a figure's size, it cannot alter a figure's form. Dilations are not isometries as the figure's size changes.
What is the area of Vivian’s garage door?
The area of Vivian’s garage door is 62.5 square feet
Area of composite shape.The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;
Area = Area of rectangle + area of trapezoid
Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet
Hence the area of Vivian’s garage door is 62.5 square feet
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