Answer:
2
Step-by-step explanation:
Its an extraneous solution, not a normal solution. It shouldn't be -4, it should be 2.
The extraneous solution obtained by Kaylee is y = 4.
To solve the equation, let's follow Kaylee's approach and square both sides:
[tex](1 - y)^2 = (2y^2 - 7)[/tex]
Expanding the left side:
[tex]1 - 2y + y^2 = 2y^2 - 7[/tex]
Rearranging the equation and combining like terms:
[tex]y^2 - 2y^2 + 2y - 1 - 7 = 0\\\\-y^2 + 2y - 8 = 0[/tex]
Now, to solve this quadratic equation, we can factor it:
-(y - 4)(y + 2) = 0
Setting each factor equal to zero:
y - 4 = 0 or y + 2 = 0
Solving for y in each equation:
y = 4 or y = -2
However, we need to check if these solutions are extraneous by substituting them back into the original equation:
For y = 4:
[tex]1 - 4 = \sqrt{2(4^2) - 7}\\\\-3 = \sqrt{32 - 7}\\\\-3 = \sqrt{25}[/tex]
-3 ≠ 5
For y = -2:
[tex]1 - (-2) = \sqrt{2(-2^2) - 7}\\\\3 = \sqrt{8 - 7}\\\\3 = 1[/tex]
From the above analysis, we see that when y = 4, it leads to an extraneous solution, as it does not satisfy the original equation.
Therefore, the extraneous solution obtained by Kaylee is y = 4.
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A student made a mistake when measuring the volume of a big container. He found the volume to be 75 liters.However, the real value for the volume is 60 liters. What is the percent error?
Answer: 20%
Step-by-step explanation:
Explanation is in progress of writing:
First, I will divide 60 by 75 and multiply by 100, to find what percent of 75 is 60:
= [tex]\frac{60}{75}[/tex] · 100
= 0.8 · 100
= 80%
The percentage error of the student's measurement is 25%.
Given the following data;
Experimental value = 75 liters Real value = 60 litersPercentage error can be defined as a measure of the extent to which an experimental value differs from the theoretical value.
Mathematically, percentage error is given by this expression;
[tex]Perecent \; error = \frac{Real \; value - Experimental \; value}{Real \; value} * 100[/tex]
Substituting the values into formula, we have;
[tex]Perecent \; error = \frac{60 - 75}{60} * 100[/tex]
[tex]Perecent \; error = \frac{-15}{60} * 100[/tex]
Note: The negative sign is neglected in percentage error.
[tex]Perecent \; error = \frac{1}{4} * 100[/tex]
Percent error = 25%
Therefore, the percent error is 25%.
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Answer plz!
Which choices are equivalent to the expression below? Check all that apply.
The right options are:
Option A
Option B
Option C
Please see the attached picture.
hope it helps
Good luck on your assignment..
CAN SOMEONE PLEASE EXPLAIN THIS, I DONT NEED THE ANSWER ONLY EXPLANATION!!!!! HELP FASTTTTT THE ANSWER IS HEAT WAS ADDED
Answer:
C
Step-by-step explanation:
The substance in the second beaker must have lost heat for it to solidify
Answer:
Step-by-step explanation:
The thermometer’s temp could have made the liquid to chemically react?
A fair spinner A is spun 7 times. What is the probability of getting “Green” at least 5 times if there are 8 colors separated equally?
Answer:
[tex]6\frac{2}{3}[/tex]
Step-by-step explanation:
OK, so basically I'm pretty sure that you add all of them together and put it as a fraction over 3 so basically [tex]\frac{20}{3}[/tex] then simplify it into [tex]6\frac{2}{3}[/tex]
4 + 5 /3 squared - 2 squared
Answer:
[tex]\frac{25}{9}[/tex]
Step-by-step explanation:
[tex]4+\frac{5}{3} ^2-2^2=\frac{5}{3}^2=\frac{25}{9}[/tex]
50 points!!!!!!
Match the vocabulary word with the correct definition.
1. one-to-one correspondence
2. included side
3. corresponding angles
4. congruent figures
5. corresponding sides
6. included angle
Sides paired with one another in a
one-to-one correspondence between
figures.
If a one-to-one correspondence
between the parts of two figures is such
that the corresponding parts are equal,
then the figures are congruent.
The side of a triangle that is formed
by the common side of two angles.
A situation for which each member
of a set, such as angles of a triangle, can
be paired with one and only one
member of another set. The angle formed by two sides of a
triangle
Angles paired with one another in a
one-to-one correspondence between
geometric figures.
Answer:
5. corresponding sides -> Sides paired with one another in a one-to-one correspondence between figures.
4. congruent figures -> If a one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent.
2. included side -> The side of a triangle that is formed by the common side of two angles.
1. one-to-one correspondence -> A situation for which each member of a set, such as angles of a triangle, can be paired with one and only one member of another set.
6. included angle -> The angle formed by two sides of a triangle
3. corresponding angles -> Angles paired with one another in a one-to-one correspondence between geometric figures.
Please look at the image below. I NEED TO ANSWER THIS NOW!!
Answer:
Tbh i dont knw mahn .... i m poor and i need points to ask questions thats y m here
Step-by-step explanation:
15. Select the graph which correctly displays the function f(x) = |x + 2|– 3.
Answer:
Step-by-step explanation:
f(0)=2-3=-1 so the point (0,-1) must be on the graph
f(-5)=|-5+2|-3=3-3=0 so the point (-5,0) must be on the graph
Then, the correct answer is the second graph
The graph that correctly displays the function f(x) = |x + 2|– 3 is the second graph.
How do we graph a function?We graph a function by calculating some values of f(x), plotting the points calculated as (x, f(x)), recognizing the trend, and completing the graph.
How do we solve the given question?To solve the given question, we will plot a graph of the function
f(x) = |x + 2|– 3 and then compare the graphs with it.
Our function f(x) = |x + 2|– 3 can be written as the combination of two functions g(x) = |x+2| and h(x) = -3
Since g(x) is a modulus function, it will be V-shaped. To recognize its start point and the trend, first we calculate x, when g(x) = 0
or, |x+2| = 0
or, x + 2 = 0
or, x = -2.
We find two more points, g(-1) and g(-3) to find if the V is upright or inverted.
g(-1) = |-1+2| = 1
g(-3) = |-3+2| = 1
Since g(-1) and g(-3) are greater than g(-2), g(x) = |x+2| is an upright V-shaped function starting from the point (-2,0)
h(x) = -3, is a straight line parallel to the x-axis, passing through the point -3 on the y-axis.
∴ f(x) = g(x) + h(x) = |x+2|-3 will move the graph of g(x) 3 points down.
The graph of f(x) will then be a V-Shaped upright curve, with the start point (-2, -3) and going up.
Our graph has been attached. The graph matching our graph is the 2nd one, so that is the right option.
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help on this translation, please :)
Answer:
1) False, the point would get flipped diagonally, to -4, 4.
2) True, the point would get flipped diagonally, to -2, 6
3) False, the point would get flipped diagonally, to -3, 1
4) True, the point would get flipped diagonally, to 5, 2
5) True, the point would get flipped diagonally, to 7, 5
6) False, the point would get flipped diagonally, to -9, 3
7) True, the point would get flipped diagonally, to -5, 4
8) True, the point would get flipped diagonally, to 2, 1
Answer:
1. true
2. false
3. true
4. false
5. false
6. true
7. false
8. false
Step-by-step explanation:
DONT TRUST ME ON THESE ANSWERS CAUSE IM NOT 100% SURE :0
Which of the following equations is equivalent to the slope formula
Answer: D
Step-by-step explanation: Notice that if you multiply both sides of the equation of y2 = m (x2 - x1) + y1 by X2 - X1.
This gives you m(X2 - X1) = Y2 - Y1.
Then add Y1 to both sides to get m(X2 - X1) + Y1 = Y2.
This slope would be equivalent to the usual slope formula.
Which of the following is equivalent to 10000 lb?
Answer:
5 Tons
Step-by-step explanation:
Or 7,858.35 Pound sterling In Money Standards
PLZ HELP I NEED HELP THANK YOU
Answer:
3rd one
Step-by-step explanation:
The big prism is 10x10x15 = 1500, and all the values are bigger except for the third and fourth. However, since we are cutting something out it should be less than 1500, the only is the 3rd answer.
Answer:
1468 in^3
Step-by-step explanation:
you can just solve for the volume of the big container and then solve for the volume of the small container and subtract the volume of the small container from the big one.
big container: 10 x 10 x 15 = 1500
small container: 2 x 4 x 4 = 32
1500 - 32 = 1468
Differentiate the function.
y = (4x − 1)^2 (4 -x^5)^4
dy/dx=
Answer:
[tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (4x - 1)²(4 - x⁵)⁴
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(4x - 1)^2](4 - x^5)^4 + (4x - 1)^2\frac{d}{dx}[(4 - x^5)^4][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(4x - 1)^{2 - 1} \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^{4 - 1} \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(4x - 1) \cdot 4x^{1 - 1}](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot 4](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 8(4x - 1)(4 - x^5)^4 - 20x^4(4x - 1)^2(4 - x^5)^3[/tex]Factor: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 2(4 - x^5) - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute -5x⁴: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 20x^5 + 5x^4 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3(-22x^5 + 5x^4 + 8)[/tex]Factor: [tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
3. What is the solution to the equation 3x = 15? Express the
solution as a logarithm, make an estimate, and then evaluate.
Round to the nearest thousandth.
Answer:
x=2.4650
Step-by-step explanation:
I assume that you mean [tex]3^x=15[/tex]
so let s use the ln() function
[tex]ln(3^x)= xln(3)=ln(15)[/tex]
so x = ln(15)/ln(3)
x = 2.4650
Which inequality is true?
A. 6 - pi > 3
B. pi + 3 < 6
C. 8 pi > 24
D. 12/pi > 4
Answer:
C.
Step-by-step explanation:
Round pi to 3.14 to get a rough estimate.
6 - 3.14 > 3 FALSE
3.14 + 3 < 6 FALSE
8 * 3.14 > 24 TRUE
12 ÷ 3.14 > 4 FALSE
I need help ty i only need the answer
Answer:
50°
Step-by-step explanation:
90° add 40° makes 130°. 180° minus 130° makes 50°
Answer:
50
Step-by-step explanation:
90+50+40= 180 which is the total of a right triangle
What is the volume of the cylinder below?
Answer:
No picture
Step-by-step explanation:
The picture isnt attached :( but the equation for the volume of a cylinder is: Hx [tex]\pi r^{2}[/tex]
H= height R: Radius
So for example if the height was 10 and the radius was 2 you would do the following:
Hx[tex]\pi r^{2}[/tex]
= 10x 3.14x[tex]2^{2}[/tex]
= 10x 3.14x 4
= 10x 12.56
= 125.6cm^3 :)
[tex]\pi r^{2}[/tex] is the equation on finding the are of the circle (bottom circle or top circle) we then multiply is by its height because its like the circle being stacked up together until it reaches the height. :) Hope this helps
:))))))))))))))))))))
Answer:
C
Step-by-step explanation:
[tex]48 \geqslant 6 - 7a \\ 48 - 6 \geqslant - 7a \\ 42 \geqslant - 7a \\ a \geqslant \frac{ 42}{ -7} \\ a \geqslant - 6[/tex]
Hope this helps..
Answer:
C. [tex] a \ge -6 [/tex]
Step-by-step explanation:
[tex] 48 \ge 6 - 7a [/tex]
Add 7a to both sides.
[tex] 7a + 48 \ge 6 [/tex]
Subtract 48 from both sides.
[tex] 7a \ge -42 [/tex]
Divide both sides by 7.
[tex] a \ge -6 [/tex]
Answer: [tex] a \ge -6 [/tex]
Which statement describes a characteristic of deposition?
Several factors affect how sediment settles.
Sediment is removed from a new surface location.
Moving water affects where sediment travels.
Rocks are broken into smaller particles.
Plz help
The correct statements are:
A) Several factors affect how sediment settles.
C) Moving water affects where sediment travels.
E) Sediments are carried by a transport medium.
QUESTION:I think the question is incomplete. The whole question has 1 more option and is states that check all statements that apply. The whole question was:
Which statements describe characteristics of deposition? Check all that apply.
A) Several factors affect how sediment settles.
B) Sediment is added to a new surface location.
C) Moving water affects where sediment travels.
D) Rocks are broken into smaller particles.
E) Sediments are carried by a transport medium.
If this was not your question, then you can still relate to this, as the answer would be same.
EXPLANATION:Sediments are a mixture of different elements that are usually carried by water, air or even ice. This mixture may contain organic and inorganic particles. Several factors effect the flow and settlement of sediments, but as discussed above, they always need an transport medium to travel, and moving water serves as one.
Moving water affects where sediment travels.
Deposition is the process of accumulation of loose mineral material and organic residues on the land surface and at the bottom of water bodies.
It occurs at the foot of the slopes, in valleys and in other negative landforms of various sizes: from sinkholes to large troughs and depressions of tectonic origin, where the accumulating deposits form thick strata that gradually turn into sedimentary rocks.
At the bottom of oceans, seas, lakes and other bodies of water, deposition is the most important exogenous process.
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PLEASE HELP ME !!!!!!!!
Answer:
54
Step-by-step explanation:
90-36=54
Answer:
Angle X is 90-36 = 54 degrees
HELP NOW
3600 dollars is placed in an account with an annual interest of 9% How much will be in the account after 25 years to the nearest cent !!
Answer:
A = $ 31,043.09
A = P + I where
P (principal) = $ 3,600.00
I (interest) = $ 27,443.09
Step-by-step explanation:
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
A
Step-by-step explanation:
15:60
Simplify the ratio.
15/15:60/15
1:4
Answer:
1:4
Step-by-step explanation:
The answer is 1:4 because 15:60 simplified is 1:4
Please answer the attachment below and say which number goes in the first or second, etc.
Answer:
use calculator
Step-by-step explanation:
1/500=0.002
3 2/25=308%
2.6=2 6/10
0.25%=0.0025
Answer:
They are actually in the correct order left to right !
Step-by-step explanation:
1/500 is 0.002 because 0.002 is pronounced "two thousandths" and 0.001 is pronounced "one thousandth", but it's written as 0.001 OR the fraction 1/1000! Using this you can infer that "two thousandths" is twice as large as 1/1000.
1/25 is 0.04, so 2/25 is 0.08 add the 3 and get 3.08. When displayed percentages in decimal form 100% = 1, so 300% = 3, therefore 308% = 3.08.
In the number 2.6 the decimal .6 is in the TENTHS place and so you can formally say this as "two and six tenths", which how the fraction 2 6/10 is also said!
As stated above when displaying percentages in decimal form:
100% = 1,
25% = 0.25,
1% = 0.01,
0.25% = 0.0025!
A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 3 cm and segment BE = 3.5 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth.
Answer: 3.66 cm
Step-by-step explanation: Given a rectangular casing BCDE with segment DE = 3 cm and segment BE = 3.5 cm.
The area A of a rectangle is length multiply by width.
Where length L = 3.5 cm and
width W = 3 cm
Area A = 3.5 × 3 = 10.5 cm^2
The pipe that will fit the fiber optic line is in cylindrical shape. Where area of a cylinder = πr^2.
But area A = 10.5. Substitute the values for the area of the cylinder
10.5 = πr^2
10.5 = 3.143 × r^2
Make r^2 the subject of formula
r^2 = 10.5/3.143
r = sqrt ( 3.34225 )
r = 1.828
Diameter = 2 × radius
Diameter = 2 × 1.829
Diameter = 3.656 cm
Therefore, the smallest diameter of pipe that will fit the fiber optic line is 3.66 cm approximately.
Answer:
4.24 cm
Step-by-step explanation:
pythagorean theorem
a^2+b^2=C^2
3^2+3^2=18
square root of 18 =4.24
hope this helped :)
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
O y=-4x + 5
O y = 4x-5
O 2y = 8x - 10
0 -2y = -8x - 10
Answer:
y = -4x+5
Step-by-step explanation:
I graphed the given equation on the graph below and graphed the choices with it. Only one choice had one solution with the given equation. This equation is y = -4x+5
Answer:
O y=-4x + 5
Step-by-step explanation:
I graphed "4x - y = 5" and the other options using a graphing tool. After graphing, we can see:
"4x - y = 5" and " -2y = -8x - 10" has no solution. The lines are parallel.
"y = 4x-5" and "2y = 8x - 10" overlap over "4x - y = 5". They have an infinite number of solutions.
"y=-4x + 5" and "4x - y = 5" cross at point (1.25, 0). This means that they have one solution.
"y=-4x + 5" should be the correct answer.
A computer technician charges a flat rate for home visits plus $ 55 per hour. The technician bills $190 for a 2-hour home visit to install a new hard drive. The equation y − 190 = 55(x − 2) gives the total amount y the technician charges for x hours of work.
What is the equation in slope-intercept form?
y = 55x + 190
y = 55x + 80
y = 190x + 55
y = 2x + 55
Answer: y = 55x + 80
Step-by-step explanation:
Answer:
1. y = 55x + 80
2. the flat rate
3. The technician worked 4.5 hours
Step-by-step explanation:
Hope this helps!
someone pls help me
Answer:
x 5 2 -1 -7 -10 1 -19
y 10 4 8 6 20 24 32
Step-by-step explanation:
Hope this helps!
This is for the x section 5 2 -1 -7 -10 1 -19
This is for the y section 10 4 8 6 20 24 32
Correct me if i'm wrong
what is the y-intercept of f(x)= -x^2÷1 +4
Answer:
(0, 4)
Step-by-step explanation:
Just set x = 0 and find y = f(x):
f(0) = [-(0)^2]÷1 +4 = 0÷1 + 4 = 4
The y-intercept is (0, 4)
Kassy is traveling to Peru for her summer vacation. She looks at a map of the path of her flight. Her plane leaves from Texas, located at(5, 16) on the map’s coordinate grid, makes a stop at the halfway point, Panama, and then heads to its destination, Peru, located at(7, 8) on the map’s coordinate grid. Find the location of Panama on Kassy’s map. Enter as a coordinate with no spaces.
Answer:
(6,12)
Step-by-step explanation:
Use the mid point formula to find the answer. Add the first x value to the second and divide by two for your x midpoint, then add the first y value to the second y value and divide by two for your y midpoint.
A cafeteria has a special: one hamburger and one order of fries is $5.49, and one hamburger and two orders of fries is $6.99. Determine the price of the hamburger.
Answer:
$3.99
Step-by-step explanation:
if one fry and one Burger is $5.49, and two fries and one Burger is $6.99, the difference between those two numbers is a $1.50 so, $5.49 - $1.50 equals $3.99 also known as the amount of money for one Burger.