Answer:
[tex]\boxed{\boxed{\sf x=1}}[/tex]
Step-by-step explanation:
[tex]\sf 25x^2=-25+50x[/tex]
Simplify both sides of the equation:-
[tex]\sf 25x^2-50x=-25[/tex]
Subtract 50x-25 from both sides:-
[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]
[tex]\sf 25x^2-50x+25=0[/tex]
Factor left side of equation:-
[tex]\sf 25(x-1)(x-1)=0[/tex]
Set factors equal to 0:-
[tex]\sf x-1=0\: or\: x-1=0[/tex]
[tex]\sf x=1[/tex]
___________________
Hope this helps!
Have a great day!
1. Let
U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},
and let
V = span {(1, 0, -1), (3, 1, 2)}.
Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.
The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).
The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.
First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.
Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).
Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.
Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).
Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:
a + 3b = 0
b = 0
-a = 0
Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.
Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).
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I need the answer for 9 and 10
William is going to invest $400 and leave it in an account for 8 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for William to end up with $460?
Answer:
1.75%
Step-by-step explanation:
help me pls i need it fastest for my math project !!!!!! please help
Part A
g(x) = 9.25x
g(8) = 9.25*8
g(8) = 74
He would make $74 before taxes if he worked 8 hours.
------------------------------------------------------
Part B
g(x) = 9.25x
g(14) = 9.25*14
g(14) = 129.50
He would make $129.50 before taxes if he worked 14 hours.
------------------------------------------------------
Part C
g(x) = 9.25x
g(27.5) = 9.25*27.5
g(27.5) = 254.375
g(27.5) = 254.38
He would make $254.38 before taxes if he worked 27.5 hours.
Answer:
Solution below.
Step-by-step explanation:
SolutionThis question is basically asking you to substitute corresponding x values to find g(x).
Given the function from the question:
g(x) = 9.25x where x is the work hours and g(x) is the wages.
Given x = 8,
g(8) = 9.25 * 8 = $74.00
Given x = 14,
g(14) = 9.25 * 14 = $129.50
Given x = 27.5,
g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)
Find the equation of the line with slope m=1/5 that contains the point (-10,-15)
Answer:
the equation with the slope m=1/5 that passes through point (-10,-15) is: y = -1/5x+15
Rewrite 6 - 6 - 6 - 6 in exponential notation.
Rewriting 6-6-6-6 in exponential notation is -1.2×10¹
What is exponential notation?Exponential notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form.
When writing in exponential notation, it must be in standard l i.e writing in this format 3.577× 10⁴ not 35.77× 10³.
Though both of the expression are literally correct but 3.577× 10⁴ is the acceptable way of writing a scientific notation.
similarly 6-6-6-6 will give -12
writing -12 in exponential notation is -1.2×10¹
Therefore the exponential notation of 6-6-6-6 is -1.2×10¹.
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profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, what were profits last year.
The profits last year were $2041.66
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900
x=4900/2.4
x=2041.66
Hence, The profits last year were $2041.66
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Which of the following points best represents the location of -1;
15.
ос
OD
Ов
ОА
+
-2
в с
0
on the number line?
D
2 +
2
Tell whether the angles are complementary or supplementary. Then find the value of x.
The angles add up to 180° so the angles are supplementary.
The value of x is 31.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure,
Two angles:
3x + 25 and 2x
These two angles form a straight angle.
Now,
3x + 25 + 2x = 180
5x = 180 - 25
5x = 155
x = 31
When the sum of two angles is 90°, then the angles are known as complementary angles.
When the sum of two angles is 180°, then the angles are known as supplementary angles.
Now,
3x + 25
= 3 x 31 + 25
= 93 + 25
= 118
2x
=2 x 31
= 62
Now,
118 + 62 = 180
Thus,
The angles are supplementary.
The value of x is 31.
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All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:
11, 11, 7, 7, 4, 4
Step-by-step explanation:
Hope this helps!! :D
what is the area of this figure? 20 pts and brainliest!!!! neeed help asap!!!!!! due today!!!!
18 yd2
54 yd 2
72 yd2
90 yd2
Answer:
72yd^2
Step-by-step explanation:
Answer:
87
Step-by-step explanation:
14*3 + 9*5
He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150150150 new words per month when he lived in Brazil. In total, he learned 192019201920 new words.
How long did Wolfrich live in Portugal, and how long did he live in Brazil?
Answer:
He take 5 months in Brazil and 9 months in Portugal.
Step-by-step explanation:
Let us assume the number of months in Portugal be P
And, the number of months in Brazil be B
So, the following equations are made
P + B = 14 ..............(1)
130P + 150B = 1920 .........(2)
We can easily write as
P = 14 - B
Now put the value of P in the second equation
So,
130(14 - B) + 150B = 1920
20B = 100
B = 100 ÷ 20 = 5
P = 14 - 5 = 9
Hence, He take 5 months in Brazil and 9 months in Portugal.
What is the area of the shaded region?
Answer:
[tex] 21.5 \: {cm}^{2} [/tex]
Step-by-step explanation:
Area of the shaded region =Area of square with side 10 cm - Area of circle with radius 5 cm
[tex] = {10}^{2} - 3.14 {(5)}^{2} \\ = 100 - 3.14 \times 25 \\ = 100 - 78.5 \\ = 21.5 \: {cm}^{2} [/tex]
PLEASE HELP ME PLEASE!
Answer:
Sample
Population
Step-by-step explanation:
Explain regent? its a term I've never heard of
draw the graph of y=_3x_4
Answer:
I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo
Step-by-step explanation:
Which inequality represents the phrase "a number b is at least -16"?
Answer:
[tex]b \leqslant - 16[/tex]
Only x = -3 is less than -2.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following statement -
"A number b is at least -16"
Given is the following statement -
"a number b is at least -16".
We can write the given inequality as -
b ≥ - 16
Therefore, we can write the given statement as -
b ≥ - 16
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what number comes 4 number before 6
Answer:
ummmmmmmmmmmmmmmmmmmm i forgot srry sugar
Step-by-step explanation:
Answer:
1 comes 4 numbers before 6
Step-by-step explanation:
1,2,3,4,5,6
/ / / /
help ME PLEASE ASAP DUE NOW
Step-by-step explanation:
{x : x < 100}
means all numbers smaller than 100. but that includes all negative numbers. so, NO.
{y|y > -0.1}
while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001
so, NO
{x|x in N}
N is the set of all natural numbers. that is the set of all positive integers.
so, YES
{y : 0 < y < 1}
that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.
so, YES
{x|x in Z}
Z is the set of all integer numbers (including the negative ones). so, NO
{y : 3 <= y < 22}
ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.
so, YES.
Need the full equation, will give Brainly :)
Answer:
5x+3
Hope this helps!
Which decimal is closest in value to the fraction below?
NO
O A. 0.4
. B. 0.1111
O C. 0.222
Answer:
C.Step-by-step explanation:
2/9 = 0.222....
Basically, the two's repeat forever - that's why C would be the correct answer
Hope that helps! :)
-Aphrodite
8
TIME REMAININ
41:44
Which points are either in Quadrant ll or Quadrant IV of the coordinate plane? Check all that apply
(7.-10)
(0,2)
(8,9
(90).
Answer:
A
Step-by-step explanation:
sheeeeesh
Answer:(7.-10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
NEED HELP!!!!!!!!! ASAP!!!!!!!
Answer:
¹31.5
Step-by-step explanation:
Area of trapezium= 1/2 ×h×(b1+b2)
A=1/2×3×(12+21)
A=31.5
Question 5 (1 point)
The perimeter of a rectangular patio is 80 feet. The length is 4 feet greater than the
width. What is the width, in feet, of the patio?
Answer:
18 feet
Step-by-step explanation:
Perimeter=2(l+b)
80=2(w+w+4)
80=2(2w+4)
80=4w+8
80-8=4w
72/4=w
W=18 feet
What is the coefficient of the second term in this expression?
6b+7b2+3+10c
please help thanks :D
Answer:
7
Step-by-step explanation:
A coefficient is the front number. A term is separated by the operators such as +, -, etc.
Gain and his three friends want to share 1/3 of a cake equally. Gavin says that each friend will get 1/9 of the cake. Use the drop-down menus to explain wether or not Gavin is correct.
Gavin is incorrect. To find how much cake each person gets, divide 1/3 by 4 or multiply 1/3 by one-fourth. Therefore, each of the friends gets one-twelfth of the cake.
Good Luck!
Cluseposited $3,500 into a savings account 2 years ago. The simple interest rate is 4% how much
money did Liu earn in interest? What would the account earn in 10 years
The account and In interest
Pls help!!!
Answer:
Simple! She earned $280
Step-by-step explanation:
3500 x 2 x 4 = 28000/100 = 280
In 10yrs operating on the same frequency of rate, she's gonna earn;
3500 x 10 x 4 = 140000/100 = $1,400.
Therefore, $1400 dollars is what she's gonna earn in 10 years time.
Find the area of this circle 7cm and 3 for pi
Answer:
far t more far t
Step-by-step explanation:
[someone help] The speed of the object 7 seconds after it is dropped is ___m/sec
9514 1404 393
Answer:
68.6 m/s
Step-by-step explanation:
The speed at a given time is the derivative of the height at that time.
dh/dt = -9.8t
At t=7, the speed is ...
-9.8(7) = -68.6 . . . . . meters per second (downward)
The speed is 68.6 meters per second.
_____
Additional comment
Height is considered to be positive in the up direction, so velocity and acceleration are also positive in the up direction. The derivative of height will be the velocity. Its negative sign in this case indicates the object is moving in the downward direction. The speed is the magnitude (absolute value) of the velocity.
The number of paid days off (e.g., vacation, sick leave) taken by 9 employees at a small local business is compared to the national average. You are hired by the new business owner to help her determine whether her employees take less days off than the national average, which is determined to be 13 days. The data for the 9 local employees during the last fiscal year are: 10, 11, 8, 14, 13, 12, 12, 11, 13. What is the effect size for these data and how should it be interpreted
Answer:
-0.80, is a large effect
Step-by-step explanation:
From the given information:
The mean of the sample = [tex]\dfrac{10+ 11+ 8+ 14+ 13+ 12+12+11+13}{9}[/tex]
= 11.556
Using Excel Formula:
The standard deviation = 11.8105
We are told that the population mean = 13
Thus, the effect size can be determined by using the formula:
[tex]Effect \ size = \dfrac{sample\ mean \ ( \bar x) - population \ mean \ \mu }{standard deviation (\sigma)}[/tex]
[tex]Effect \ size = \dfrac{11.5556 -13 }{1.8105}[/tex]
Effect size = -0.80
Thus, -0.80, is a large effect
Please help will mark Brainly
Answer:
x=4 and y=2
Step-by-step explanation:
You should use graph, point of intersection(for example point M(4,2) ) is solution
And we can conclude that x=4 and y=2