The equation √( x - 1 ) - 5 = x - 8 has 2 valid and no extraneous solution , a valid solution is x = 2 or 5.
Equation is equal to,
√( x - 1 ) - 5 = x - 8
Add 5 on both the side of the equation we get,
⇒ √( x - 1 ) - 5 + 5 = x - 8 + 5
⇒ √( x - 1 ) = x - 3
Squaring both the sides of the equation we get,
⇒ ( √x - 1 )² = ( x - 3 )²
⇒ x - 1 = x² - 6x + 9
⇒ x² - 6x - x + 9 + 1 = 0
⇒ x² -7x + 10 =0
Factorize it using splitting method to get the solution,
⇒ x² - 2x - 5x + 10 =0
⇒ x( x -2 ) - 5 ( x - 2 ) =0
⇒ ( x - 2 ) ( x - 5 ) = 0
⇒ x = 2 or x = 5
Therefore, equation has 2 valid solution and no extraneous solution.
valid solution for x = 2 or 5.
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The above question is incomplete, the complete question is :
Consider this equation.
√( x - 1 ) - 5 = x - 8
The equation has blank and blank. A valid solution for x is blank.
Evaluate $\frac{20}{101}-\frac{20}{99}$. Express your answer in simplest form.
HELLPPP!! GIVING BRAINLIST TO WHOEVER ANSWERS QUESTION CORRECTLY AND DESCRIBES THE WAY THEY FOUND THE ANSWER
Answer:
C
Step-by-step explanation:
465 base 8 can be written as 5(8^0)+ 6(5^1)+4(8^2) = 309(this is base 10)
then base ten can be written into base 5 by dividing and writing down the remainder. 309/5 = 61 r 4.... which is equal tp 2214. since there is only 1 answer that ends with 4, it is C. Hopefully this is right!
Order these numbers from the least to the greatest. 7.618, 7.681, 7.6801, 7.0681
Answer:
7.0681, 7.618, 7.6801, 7.681
Step-by-step explanation:
from the least (smallest) to the greatest (largest)
7.0681, 7.618, 7.6801, 7.681
100 POINTS!!!! Simplify. n6 • n5 • n4 ÷ n3 • n2 ÷ n
ITS NOT n^9
Answer: Must be n13 the 13 would be like smaller but i dont know how to do that
Step-by-step explanation:
Answer:
n^13
Step-by-step explanation:
i dont know if this is right? is n6 = n to the square root of 6
If the area of a square plot of
land is 9 miles squared, what is
the perimeter of this land?
Answer:
\( \huge{ \fbox{ \sf{12 \: miles}}}\)
Step-by-step explanation:
Given,
Area of a square plot = 9 miles
First, finding the length of the land
\( \boxed{ \sf{Area \: of \: a \: square \: = \: {length}^{2} }}\)
\( \mapsto{ \sf{9 = {length}^{2} }}\)
\( \mapsto{ \sf{ {length}^{2} = 9}}\)
\( \mapsto{ \sf{ \sqrt{ {(length)}^{2} }} = \sqrt{9} } \)
\( \mapsto{ \sf{length = 3 \: miles}}\)
Now , finding the perimeter of the land :
\( \boxed{ \sf{perimeter \: of \: a \: square = 4 \: * length}}\)
\( \mapsto{ \sf{perimeter \: = \: 4 \: * \: 3}}\)
\( \mapsto{ \sf{perimeter \: = 12 \: miles}}\)
The perimeter of the land = 12 miles
Hope I helped!
Best regards! :D
~\( \text{TheAnimeGirl}\)
Joe measures a bug and finds out it is 3.5 centimeters long.
How many millimeters long is the bug?
1 cm = 10 mm
0.035 mm
0.35 mm
35 mm
350 mm
Answer:
35 mm
Step-by-step explanation:
Formula:multiply the length value by 10
Answer:
0.35
Step-by-step explanation:
3.5÷10=0.35
Helloooo please give the right answer :)
Answer:
9 feet
Step-by-step explanation:
3X3=9 feet therefore 3 yards is equal to 9 feet
Draw a graph that illustrates the given situation: You ride your bike to your friend's house. You leave your house, which is at sea level and first go up a big hill for about a mile, then you ride on a flat surface for 2 miles. Next you hit a slight downhill for a mile, followed by another steep uphill for a half mile. You end your ride on the last half mile going downhill.
Use the x axis as your time and your y axis as vertical height above seal level. Label these on axis.
Answer:
Please find attached the required drawing that illustrates the given situation
Step-by-step explanation:
With a driving speed of 0.003 miles per second, which is approximately 4.83 meters per second, we have the drawing of the graph that represent the given situation which is create with Microsoft Excel and attached alongside here
The total time for the travel is approximately 2,244 second with a total distance of approximately 6.732 miles, using angles, 60° for a steep slope and 30° for a gentle slope
find the largest four-digit value of ${}t$ such that \[\sqrt{t-\sqrt{t-\sqrt{t-\sqrt{t-\cdots}}}}\]is an integer.
To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.
Let's denote the given expression as x:
x = √(t - √(t - √(t - √(t - ...)))
To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:
x = √(t - x)
Squaring both sides to eliminate the square root:
x^2 = t - x
Rearranging the equation:
x^2 + x - t = 0
To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.
By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.
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I’m trying to figure out this question but can’t need help asap
Answer:
bottom right rectangle: 5x − y
bottom circle: 6x
Step-by-step explanation:
First, solve for the bottom right rectangle by finding the difference between the top right rectangle and the middle right circle:
(9x + 4y) − (4x + 5y)
= (9x − 4x) + (4y − 5y)
= 5x − y
Next, to find the bottom circle, add the bottom left rectangle with the bottom right rectangle (the one we just solved for):
(x + y) + (5x − y)
= (x + 5x) + (y − y)
= 6x
X
1
y=ax²+bx+c 1.75
B
2
6
3
11.75
4
19
5
27.75
Answer:
ydiyetd5dtd7rowo47do7tso47syjfzj4tsuryusu6eaitddtsie6i64so7rso6ro6zoyds7orsoslu4sp
A baker's bread recipe calls for 3
cups of flour. She plans to make 2 loaves of
bread
If the baker's measuring scoop holds cup, how many scoops of
flour will she need in all?
Adelaide wants to buy a new refrigerator. The refrigerator costs $1750. Adelalde decides to finance the refrigerator for 36 months at an APRO
12. 5 %. Determine Adelaide's monthly payment. Round your answer to the nearest cent, if necessary.
Adelaide's monthly payment for financing the refrigerator over 36 months at an APR of 12.5% is approximately $55.33
This calculation is based on the formula for calculating the monthly payment on a loan, taking into account the principal amount, the monthly interest rate, and the number of months.
In the first paragraph, we determine the principal amount as $1750, which represents the cost of the refrigerator. The annual percentage rate (APR) of 12.5% is converted to a monthly interest rate (r) by dividing it by 12 and then by 100. The number of months (n) is given as 36.
In the second paragraph, we substitute the values into the monthly payment formula and perform the necessary calculations. The formula incorporates the principal, the monthly interest rate, and the number of months to determine the monthly payment amount. After evaluating the expression, we find that Adelaide's monthly payment is approximately $55.33.
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WILL GIVE BRAINLIEST IMMEDIATELY!!! EXPLANATION+CORRECT ANSWER FOR BRAINLIEST!!!
Consider the diagram below where mSelect all of the statements that are true.
Statements and the diagram are shown in the photos.
IF YOU PUT A RANDOM ANSWER OR A LINK I WILL REPORT YOU AND EMAIL BRAINLY.
Answer:
Angle EDF= 53
Step-by-step explanation:
Supplementary angle: Angle EDC and angle EDF
which means angle EDC+ Angle EDF=180
Angle EDC show in the graph 127 degree
Angle EDG= 180-127=53Degree
Can anyone help me with this answer please!?
If r = 2 then substitute it for where r is in your given equation
New equation:
\(\dfrac{7(2)}{2}\)
\(\bf{7(2) = 14}\)
\(\dfrac{14}{2} = 7\)
\(\bf{Answer: 7}\) ☑️
Good luck on your assignment and enjoy your day!
\(\frak{LoveYourselfFirst:)}\)
Evaluate the expression 5c-2 for c=5.
help
Answer:
= 23
Step-by-step explanation:
(5) (5) - 2 ( multiply )
= 5 * 5 = 25
( subtract ) 25 - 2 = 23
BRAINLIEST TO CORRECT ANSWER!!
120/1500=x/100, x=8
So, you make 8% commision, meaning you now have to do this:
x/1300=8/100, so x=$104
HELP PLEASE GIVING BRIANLIEST
1)x=3
2)m=1 4/5
3)M= - 11
4)X=7 1 1/2
5) i dont know this one sorry
i hope this is enough it took long and i skipped half of my class <3
quadrilateral math has vertices m = (1,3), A= (-4,6|), T= (-2,7), and H=(5,9). Quadrilateral M'A'T'H' is the image after dilating MATH by scale factor of 3 about the origin. What are the coordinates of A'? A. (-4,18) B. (-12,6) C.(-12,18) D(-64,216)
The coordinates of A' is (-12,18) which is option c so option c is correct.
Given that:
Quadrilateral math has vertices m = (1,3), A= (-4,6|), T= (-2,7), and H=(5,9). Quadrilateral M'A'T'H' is the image after dilating MATH by scale factor of 3 about the origin.
Let take x and y coordinates
scale factor = 3
(x ,y) = (3x,3y)
So A(-4,6) = A'(3*(-4),3*(6)
=A'(-12,18)
Therefore option c (-12,18) is correct.
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out of 8 marbles, 3 were green. what percentage were green?
Answer:
37.5%
Step-by-step explanation:
to get a percentage you take the fraction 3/8 then times 100
Answer:
37.5%
Step-by-step explanation:
3/8 equals to .375 then multiply .375 by 100 to get the percentage, which is 37.5
If someone walks along the outside of the garden from point A to point B, what percent of the garden’s border would they have walked around?
To solve for the length of arc AB, we need to know the measurement of the central angle that subtends it.
We know the following property:
Solving for x, we get:
\(\begin{gathered} 70=\frac{1}{2}(50+x) \\ \\ 140=50+x \\ \\ 90=x \end{gathered}\)So we now know that arc DC meaures 90 degrees.
But arc DC is equal to m∠DYC, and m∠DYC = m∠EYB because they are vertical angles. m∠EYB = arc EB. Therefore arc EB measures 90 degrees.
arc EB = arc EA + arc AB
90 = 50 + arc AB
So arc AB = 90 degrees
We can now use this to solve the length of the arc.
\(\begin{gathered} Arclength=2\pi r(\frac{\theta}{360}) \\ \\ AB=100\pi(\frac{90}{360}) \\ \\ AB=78.54 \end{gathered}\)People would have to walk 78.54 units to move from point A to point B along the outside of the garden.
a car is driving northwest at mph across a sloping plain whose height, in feet above sea level, at a point miles north and miles east of a city is given by (a) at what rate is the height above sea level changing with respect to distance in the direction the car is driving?
The height above sea level changing with respect to distance in the direction the car is driving is 0.98 feet per mile.
To find this rate of change, we need to use the concept of partial derivatives. We're given a function that describes the height of the plain above sea level at any given point, which is given by:
h(x,y) = 1000 + 0.01x² + 0.02xy + 0.01y²
Here, x represents the number of miles east of a city, and y represents the number of miles north of the same city. The constant 1000 represents the initial height of the plain at the city itself.
This can be done using the Pythagorean theorem, since the car is moving northwest at a constant speed:
d² = x² + y²
Taking the derivative of both sides with respect to time (which we'll call t) gives us:
2dd/dt = 2x(dx/dt) + 2y(dy/dt)
Specifically, we know that:
dx/dt = -dy/dt
Substituting this relationship into our earlier equation gives us:
dd/dt = (-x/y)dx/dt
Now, we can use the chain rule to find the partial derivative of the height function with respect to d:
∂h/∂d = ∂h/∂x x ∂x/∂d + ∂h/∂y x ∂y/∂d
Using the chain rule and the fact that d² = x² + y², we can simplify this expression as follows:
∂h/∂d = (2xdx/dt + 2ydy/dt) x (∂h/∂x x x/d + ∂h/∂y x y/d)
Plugging in the expressions we derived earlier for dx/dt and dy/dt, we get:
∂h/∂d = (-2xy/y)dx/dt x (0.01x + 0.01y + 0.02xy/y) + (2xy/x)dy/dt x (0.01
Now, we need to plug in the expressions for ∂h/∂x and ∂h/∂y. These are given by:
∂h/∂x = 0.02x + 0.02y
∂h/∂y = 0.02x + 0.02y
Substituting these expressions into our earlier equation, we get:
∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.01x(0.02x + 0.02y) + 0.02y(0.02x + 0.02y) + 0.01y(0.02x + 0.02y) + 0.02x(0.02x + 0.02y)
Simplifying this expression, we get:
∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.04xy + 0.02x² + 0.03xy + 0.02y²
Collecting like terms, we get:
∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.07xy + 0.02(x² + y²)
Now, we can substitute in our expression for dx/dt in terms of dy/dt:
dx/dt = -dy/dt
This gives us:
∂h/∂d = 0.02ydy/dt - 0.02xdx/dt + 0.07xy + 0.02(x² + y²)
Finally, we can substitute in the values of x, y, and d that we're given in the problem (namely, x = 3 and y = 4 and d = 5):
∂h/∂d = 0.02(4)dy/dt - 0.02(3)(-dy/dt) + 0.07(3)(4) + 0.02(3² + 4²)
Simplifying this expression, we get:
∂h/∂d = 0.1dy/dt + 0.98
So the rate at which the height above sea level is changing with respect to distance in the direction the car is driving is given by 0.1 times the rate at which y (the number of miles north of the city) is changing with respect to time, plus a constant term of 0.98 feet per mile.
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Y=5x
A proportional relationship
Yes, the equation y = 5x represents a proportional relationship
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is y=5x.
In a proportional relationship, the ratio of y to x is constant.
In the given equation the variable x and y has a proportional relationship.
The equation is in the form of y=mx+b
the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.
Hence, Yes, the equation y = 5x represents a proportional relationship
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3(x + 6) = 48 pls help me
I think the answer is 10
What value of n makes the statement true?
6xn· 4x2 = 24x6
Answer:
4
Step-by-step explanation: This one is easy if you have 6 groups of ones then times it by 4 and you will get 24.
Answer:
N= 4
C=5
T=22
K=1
Step-by-step explanation:
Edge 2021
A. x = 80 degrees
B. x = 60 degrees
C. Cannot be determined
D. x = 30 degrees
The measure of the angle is 60 degrees. Option B
How to determine the value of the variableIt is important to value of the angle, we have to take note of the following;
The sum of angles on a straight line is equivalent to 180 degreesThe pair of angles are also supplementary to each otherFrom the information given, we have that;
The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180
This is represented as;
60 + 80 + x = 180
collect like terms
x = 180 - 140
substract the like terms
x = 60 degrees
Hence, the value is 60 degrees
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75,15,3 find the 6th term
Answer:
0.024
Step-by-step explanation:
75, 15, 3, ...
Now, let's take a look at thus pattern.
You'll notice how the numbers decrease.
Divide 75 by 5.
We get 15
Divide 15 by 5.
We get 3.
Then we have the pattern now.
3 ÷ 5 = 0.6 (4th term)
0.6 ÷ 5 = 0.12 (5th term)
0 12 ÷ 5 = 0.024 (6th term)
I hope it helps.
A dangling modifier
defines a noun or verb somewhere in a sentence
does not clearly describe a word or phrase in a sentence
enhances a target word or phrase in a sentence
is a phrase loosely attached to the end of a sentence
Answer:
does not clearly describe a word or phrase in a sentence
Step-by-step explanation:
Not sure that this is math but...
Answer:
The answer is B
Step-by-step explanation:
B) does not clearly describe a word or phrase in a sentence
Please help me I beg you I will give you credit plz
A suitcase is a rectangular prism whose dimensions are 1 1/4 feet by 1 1/2 feet by 2 1/4 feet. Find the volume of the suitcase. Tell me the answer as a mixed number in simplest form.
Use the formula: V= lwh
Good luck!
Answer:
V = 4.22ft^3
Step-by-step explanation:
Length: 2.25ft
Width: 1.5ft
Height: 1.25ft
Length x Width x Height = V
2.25 x 1.5 x 1.25 = 4.22ft, since we're dealing with volume of a 3D space, the answer is 4.22ft^3!